Finite Group Databasebeta

← #17242108

Subgroups — #17242108

Order 4352.

1512 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537121C211yesmaximal, characteristic, complemented
2#14537092C211yesmaximal, characteristic, complemented
3#14536733C211yesmaximal, characteristic, complemented
4#14536727C211yesmaximal, characteristic
5#14536549C211yesmaximal, characteristic, complemented
6#14536534C211yesmaximal, characteristic, complemented
7#14536527C211yesmaximal, characteristic, complemented
8#14536482C211yesmaximal, characteristic
9#14536436C211yesmaximal, characteristic
10#14536339C211yesmaximal, characteristic, complemented
11#14536200C211yesmaximal, characteristic, complemented
12#14536198C211yesmaximal, characteristic, complemented
13#14536095C211yesmaximal, characteristic, complemented
14#14535913C211yesmaximal, characteristic, complemented
15#14535767C211yesmaximal, characteristic, complemented
16#14535665C211yesmaximal, characteristic, complemented
17#14535566C211yesmaximal, characteristic, complemented
18#14535284C211yesmaximal, characteristic
19#14534957C211yesmaximal, characteristic, complemented
20#14534956C211yesmaximal, characteristic, complemented
21#14534492C211yesmaximal, characteristic, complemented
22#14534445C211yesmaximal, characteristic, complemented
23#14534433C211yesmaximal, characteristic, complemented
24#14534433C211yesmaximal, characteristic, complemented
25#14534019C211yesmaximal, characteristic, complemented
26#14534008C211yesmaximal, characteristic, complemented
27#14532475C211yesmaximal, characteristic, complemented
28#14532460C211yesmaximal, characteristic, complemented
29#14531427C211yesmaximal, characteristic
30#14531229C211yesmaximal, characteristic
31C17×#2318C211yesmaximal, characteristic
32C2×#10587555C2211yescharacteristic
33C2×#10587576C2211yescharacteristic
34C2×#10587610C2211yescharacteristic
35C2×#10587564C2211yescharacteristic
36C2×#10587612C2211yescharacteristic
37C22×C4×Dic17C2211yescharacteristic
38#11762751C2211yescharacteristic
39#11762751C2211yescharacteristic
40#11762751C2211yescharacteristic
41#11762751C2211yescharacteristic
42#11762751C2211yescharacteristic
43#11762751C2211yescharacteristic
44#11762751C2211yescharacteristic
45#11762751C2211yescharacteristic
46#11762751C2211yescharacteristic
47#11762751C2211yescharacteristic
48#11762751C2211yescharacteristic
49#11762748C2211yescharacteristic
50#11762748C2211yescharacteristic
51#11762748C2211yescharacteristic
52#11762745C2211yescharacteristic
53#11762745C2211yescharacteristic
54#11762743C2211yescharacteristic
55#11762742C2211yescharacteristic
56#11762742C2211yescharacteristic
57#11762741C2211yescharacteristic
58#11762741C2211yescharacteristic
59#11762741C2211yescharacteristic
60#11762741C2211yescharacteristic
61#11762741C2211yescharacteristic
62#11762732C2211yescharacteristic
63#11762732C2211yescharacteristic
64#11762732C2211yescharacteristic
65#11762732C2211yescharacteristic
66#11762732C2211yescharacteristic
67#11762732C2211yescharacteristic
68#11762730C2211yescharacteristic
69#11762730C2211yescharacteristic
70#11762730C2211yescharacteristic
71#11762730C2211yescharacteristic
72#11762730C2211yescharacteristic
73#11762730C2211yescharacteristic
74#11762730C2211yescharacteristic
75#11762729C2211yescharacteristic
76#11762729C2211yescharacteristic
77#11762729C2211yescharacteristic
78#11762721C2211yescharacteristic
79#11762721C2211yescharacteristic
80#11762721C2211yescharacteristic
81#11762721C2211yescharacteristic
82#11762721C2211yescharacteristic
83#11762721C2211yescharacteristic
84#11762721C2211yescharacteristic
85#11762721C2211yescharacteristic
86#11762715C2211yescharacteristic
87#11762715C2211yescharacteristic
88#11762713C2211yescharacteristic
89#11762713C2211yescharacteristic
90#11762713C2211yescharacteristic
91#11762713C2211yescharacteristic
92#11762713C2211yescharacteristic
93#11762713C2211yescharacteristic
94#11762713C2211yescharacteristic
95#11762713C2211yescharacteristic
96#11762713C2211yescharacteristic
97#11762713C2211yescharacteristic
98#11762713C2211yescharacteristic
99#11762712C2211yescharacteristic
100#11762712C2211yescharacteristic
101#11762708C2211yescharacteristic
102#11762708C2211yescharacteristic
103#11762708C2211yescharacteristic
104#11762708C2211yescharacteristic
105#11762708C2211yescharacteristic
106#11762707C2211yescharacteristic
107#11762707C2211yescharacteristic
108#11762706C2211yescharacteristic
109#11762706C2211yescharacteristic
110#11762706C2211yescharacteristic
111#11762705C2211yescharacteristic
112#11762702C2211yescharacteristic
113#11762702C2211yescharacteristic
114#11762702C2211yescharacteristic
115#11762702C2211yescharacteristic
116#11762702C2211yescharacteristic
117#11762702C2211yescharacteristic
118#11762696C2211yescharacteristic
119#11762696C2211yescharacteristic
120#11762696C2211yescharacteristic
121#11762696C2211yescharacteristic
122#11762696C2211yescharacteristic
123#11762696C2211yescharacteristic
124#11762696C2211yescharacteristic
125#11762696C2211yescharacteristic
126#11762696C2211yescharacteristic
127#11762695C2211yescharacteristic
128#11762695C2211yescharacteristic
129#11762693C2211yescharacteristic
130#11762693C2211yescharacteristic
131#11762692C2211yescharacteristic
132#11762692C2211yescharacteristic
133#11762692C2211yescharacteristic
134#11762692C2211yescharacteristic
135#11762692C2211yescharacteristic
136#11762692C2211yescharacteristic
137#11762692C2211yescharacteristic
138#11762692C2211yescharacteristic
139#11762692C2211yescharacteristic
140#11762689C2211yescharacteristic
141#11762689C2211yescharacteristic
142#11762684C2211yescharacteristic
143#11762684C2211yescharacteristic
144#11762684C2211yescharacteristic
145#11762684C2211yescharacteristic
146#11762684C2211yescharacteristic
147#11762682C2211yescharacteristic
148#11762682C2211yescharacteristic
149#11762682C2211yescharacteristic
150#11762682C2211yescharacteristic
151#11762681C2211yescharacteristic
152#11762681C2211yescharacteristic
153#11762681C2211yescharacteristic
154#11762678C2211yescharacteristic
155#11762675C2211yescharacteristic
156#11762674C2211yescharacteristic
157#11762674C2211yescharacteristic
158#11762672C2211yescharacteristic
159#11762672C2211yescharacteristic
160#11762669C2211yescharacteristic
161#11762669C2211yescharacteristic
162#11762669C2211yescharacteristic
163#11762669C2211yescharacteristic
164#11762669C2211yescharacteristic
165#11762667C2211yescharacteristic
166C4×C4⋊Dic17C2211yescharacteristic
167C4×C4⋊Dic17C2211yescharacteristic
168C4×C22⋊Dic17C2211yescharacteristic
169C4×C22⋊Dic17C2211yescharacteristic
170#11762655C2211yescharacteristic
171#11762655C2211yescharacteristic
172C2×C4×D4×C17C2211yescharacteristic
173C17×#388C2211yescharacteristic
174C17×#388C2211yescharacteristic
175C17×#387C2211yescharacteristic
176C17×#387C2211yescharacteristic
177C17×#386C2211yescharacteristic
178C17×#386C2211yescharacteristic
179C17×#385C2211yescharacteristic
180C17×#385C2211yescharacteristic
181C17×#383C2211yescharacteristic
182C17×#382C2211yescharacteristic
183C17×#381C2211yescharacteristic
184C17×#380C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic
186C2×C17×#95C2211yescharacteristic
187C22×D4×C17C2311yescharacteristic
188C23×C4×C17C2311yescharacteristic
189C23×C4×C17C2311yescharacteristic
190C23×C4×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C23×Dic17C2311yescharacteristic
193C23×Dic17C2311yescharacteristic
194C22×Dic34C2311yescharacteristic
195C22×Dic34C2311yescharacteristic
196C22×Dic34C2311yescharacteristic
197C22×Dic34C2311yescharacteristic
198C22×Dic34C2311yescharacteristic
199C4×D4×C17Q818yescomplemented
200C2×C4⋊C4×C17C2311yescharacteristic
201C2×C4⋊C4×C17C2311yescharacteristic
202C2×C4⋊C4×C17C2311yescharacteristic
203C2×C4⋊C4×C17C2311yescharacteristic
204C2×C4⋊C4×C17C2311yescharacteristic
205C2×C22⋊C4×C17C2311yescharacteristic
206C2×C22⋊C4×C17C2311yescharacteristic
207C2×C22⋊C4×C17C2311yescharacteristic
208C2×C22⋊C4×C17C2311yescharacteristic
209C2×C22⋊C4×C17C2311yescharacteristic
210C2×C22⋊C4×C17C2311yescharacteristic
211C2×C22⋊C4×C17C2311yescharacteristic
212C2×C22⋊C4×C17C2311yescharacteristic
213C2×C42×C17C2311yescharacteristic
214C2×C42×C17C2311yescharacteristic
215C2×C42×C17C2311yescharacteristic
216C2×C22⋊Dic17C2311yescharacteristic
217C2×C22⋊Dic17C2311yescharacteristic
218C2×C22⋊Dic17C2311yescharacteristic
219C2×C22⋊Dic17C2311yescharacteristic
220C2×C22⋊Dic17C2311yescharacteristic
221C2×C22⋊Dic17C2311yescharacteristic
222C2×C22⋊Dic17C2311yescharacteristic
223C2×C22⋊Dic17C2311yescharacteristic
224C2×C22⋊Dic17C2311yescharacteristic
225C2×C22⋊Dic17C2311yescharacteristic
226C2×C22⋊Dic17C2311yescharacteristic
227C2×C22⋊Dic17C2311yescharacteristic
228C2×C22⋊Dic17C2311yescharacteristic
229C2×C22⋊Dic17C2311yescharacteristic
230#10587612—42no—
231C2×C4⋊Dic17C2311yescharacteristic
232C2×C4⋊Dic17C2311yescharacteristic
233C2×C4⋊Dic17C2311yescharacteristic
234C2×C4⋊Dic17C2311yescharacteristic
235C2×C4⋊Dic17C2311yescharacteristic
236C2×C4⋊Dic17C2311yescharacteristic
237C2×C4⋊Dic17C2311yescharacteristic
238C2×C4⋊Dic17C2311yescharacteristic
239C2×C4⋊Dic17C2311yescharacteristic
240C2×C4⋊Dic17C2311yescharacteristic
241C2×C4⋊Dic17C2311yescharacteristic
242C2×C4⋊Dic17C2311yescharacteristic
243C2×C4⋊Dic17C2311yescharacteristic
244C2×C4⋊Dic17C2311yescharacteristic
245C2×C4⋊Dic17C2311yescharacteristic
246C2×C4⋊Dic17C2311yescharacteristic
247C2×C4⋊Dic17C2311yescharacteristic
248C2×C4⋊Dic17C2311yescharacteristic
249C2×C4⋊Dic17C2311yescharacteristic
250C2×C4⋊Dic17C2311yescharacteristic
251C2×C4⋊Dic17C2311yescharacteristic
252#10587610—42no—
253C2×#63225C2311yescharacteristic
254C2×#63225C2311yescharacteristic
255C2×#63225C2311yescharacteristic
256C2×#63225C2311yescharacteristic
257C2×#63225C2311yescharacteristic
258C2×#63225C2311yescharacteristic
259C2×#63225C2311yescharacteristic
260C2×#63225C2311yescharacteristic
261C2×#63225C2311yescharacteristic
262C2×#63225C2311yescharacteristic
263C2×#63225C2311yescharacteristic
264C2×#63225C2311yescharacteristic
265C2×#63225C2311yescharacteristic
266C2×#63225C2311yescharacteristic
267C2×#63225C2311yescharacteristic
268C2×#63225C2311yescharacteristic
269C2×#63225C2311yescharacteristic
270C2×#63225C2311yescharacteristic
271C2×C4×Dic17—42no—
272C2×C4×Dic17C2311yescharacteristic
273C2×C4×Dic17C2311yescharacteristic
274C2×C4×Dic17C2311yescharacteristic
275C2×C4×Dic17C2311yescharacteristic
276C2×C4×Dic17C2311yescharacteristic
277C2×C4×Dic17C2311yescharacteristic
278C2×C4×Dic17C2311yescharacteristic
279C2×C4×Dic17C2311yescharacteristic
280C2×C4×Dic17C2311yescharacteristic
281C2×C4×Dic17C2311yescharacteristic
282#10587576—42no—
283#10587564—42no—
284#10587555—42no—
285C17×#95C2311yescharacteristic
286C17×#95C2311yescharacteristic
287C17×#95C2311yescharacteristic
288C17×#95C2311yescharacteristic
289C17×#95C2311yescharacteristic
290C17×#95C2311yescharacteristic
291C17×#95C2311yescharacteristic
292C17×#95C2311yescharacteristic
293C17×#95C2311yescharacteristic
294C17×#95C2311yescharacteristic
295C17×#95C2311yescharacteristic
296C17×#95C2311yescharacteristic
297C17×#95C2311yescharacteristic
298C17×#95C2311yescharacteristic
299#10587502C2311yescharacteristic
300#10587502C2311yescharacteristic
301#10587502C2311yescharacteristic
302#10587502C2311yescharacteristic
303#10587502C2311yescharacteristic
304#10587502C2311yescharacteristic
305#10587502C2311yescharacteristic
306#10587502C2311yescharacteristic
307#10587502C2311yescharacteristic
308#10587502C2311yescharacteristic
309#10587502C2311yescharacteristic
310#10587502C2311yescharacteristic
311#10587502C2311yescharacteristic
312#10587502C2311yescharacteristic
313#10587502C2311yescharacteristic
314#10587502C2311yescharacteristic
315#10587502C2311yescharacteristic
316#10587502C2311yescharacteristic
317#10587502C2311yescharacteristic
318#10587502C2311yescharacteristic
319#10587502C2311yescharacteristic
320#10587502C2311yescharacteristic
321#10587502C2311yescharacteristic
322#10587502C2311yescharacteristic
323#10587502C2311yescharacteristic
324#10587502C2311yescharacteristic
325#10587502C2311yescharacteristic
326#10587502C2311yescharacteristic
327#10587502C2311yescharacteristic
328#10587502C2311yescharacteristic
329#10587502C2311yescharacteristic
330#10587502C2311yescharacteristic
331#10587502C2311yescharacteristic
332#10587502C2311yescharacteristic
333#10587502C2311yescharacteristic
334#10587502C2311yescharacteristic
335#10587502C2311yescharacteristic
336#10587502C2311yescharacteristic
337#10587502C2311yescharacteristic
338#10587502C2311yescharacteristic
339#10587502C2311yescharacteristic
340#10587502C2311yescharacteristic
341#10587502C2311yescharacteristic
342#10587502C2311yescharacteristic
343#10587502C2311yescharacteristic
344#10587502C2311yescharacteristic
345#10587502C2311yescharacteristic
346#10587502C2311yescharacteristic
347#10587502C2311yescharacteristic
348#10587502C2311yescharacteristic
349C24×C17C2411yescharacteristic
350C24×C17C2411yescharacteristic
351C2×D4×C17—41no—
352C2×D4×C17—41no—
353C2×D4×C17C2×Q814yes—
354C22×C4×C17—41no—
355C22×C4×C17—41no—
356C22×C4×C17—41no—
357C22×C4×C17—41no—
358C22×C4×C17—41no—
359C22×C4×C17—41no—
360C22×C4×C17—41no—
361C22×C4×C17—41no—
362C22×C4×C17—41no—
363C22×C4×C17—41no—
364C22×C4×C17C2×Q814yes—
365C22×C4×C17C2×Q814yes—
366C22×C4×C17C2411yescharacteristic
367C22×C4×C17C2411yescharacteristic
368C22×C4×C17C2411yescharacteristic
369C22×C4×C17C2411yescharacteristic
370C22×C4×C17C2411yescharacteristic
371C22×C4×C17C2411yescharacteristic
372C22×C4×C17C2411yescharacteristic
373C22×C4×C17C2411yescharacteristic
374C22×C4×C17C2411yescharacteristic
375C22×C4×C17C2411yescharacteristic
376C22×C4×C17C2411yescharacteristic
377C22×C4×C17C2411yescharacteristic
378C22×C4×C17C2411yescharacteristic
379C22×Dic17—22no—
380C22×Dic17—41no—
381C22×Dic17—41no—
382C22×Dic17—41no—
383C22×Dic17—41no—
384C22×Dic17—41no—
385C22×Dic17C2411yescharacteristic
386C22×Dic17C2411yescharacteristic
387C22×Dic17C2411yescharacteristic
388C22×Dic17C2411yescharacteristic
389C22×Dic17C2411yescharacteristic
390C22×Dic17C2411yescharacteristic
391C22×Dic17C2411yescharacteristic
392C22×Dic17C2411yescharacteristic
393C22×Dic17C2411yescharacteristic
394C22×Dic17C2411yescharacteristic
395C22×Dic17C2411yescharacteristic
396C22×Dic17C2411yescharacteristic
397C22×Dic17C2411yescharacteristic
398C22×Dic17C2411yescharacteristic
399C22×Dic17C2411yescharacteristic
400C22×Dic17C2411yescharacteristic
401C2×Dic34—22no—
402C2×Dic34—41no—
403C2×Dic34—41no—
404C2×Dic34—41no—
405C2×Dic34—41no—
406C2×Dic34—41no—
407C2×Dic34—41no—
408C2×Dic34—41no—
409C2×Dic34—41no—
410C2×Dic34—41no—
411C2×Dic34—41no—
412C2×Dic34—41no—
413C2×Dic34—41no—
414C2×Dic34—41no—
415C2×Dic34—41no—
416C4⋊C4×C17—41no—
417C4⋊C4×C17—41no—
418C4⋊C4×C17—41no—
419C4⋊C4×C17—41no—
420C4⋊C4×C17C2×Q814yes—
421C22⋊C4×C17—41no—
422C22⋊C4×C17—41no—
423C22⋊C4×C17—41no—
424C22⋊C4×C17—41no—
425C22⋊C4×C17—41no—
426C22⋊C4×C17—41no—
427C22⋊C4×C17C2×Q814yes—
428C22⋊C4×C17C2×Q814yes—
429C42×C17—41no—
430C42×C17—41no—
431C42×C17C2×Q814yes—
432C22⋊Dic17—22no—
433C22⋊Dic17—41no—
434C22⋊Dic17—41no—
435C22⋊Dic17—41no—
436C22⋊Dic17—41no—
437C22⋊Dic17—41no—
438C22⋊Dic17—41no—
439C22⋊Dic17—41no—
440C22⋊Dic17—41no—
441C22⋊Dic17—41no—
442C22⋊Dic17—41no—
443C22⋊Dic17—41no—
444C22⋊Dic17—41no—
445C22⋊Dic17—41no—
446C4⋊Dic17—22no—
447C4⋊Dic17—22no—
448C4⋊Dic17—22no—
449C4⋊Dic17—41no—
450C4⋊Dic17—41no—
451C4⋊Dic17—41no—
452C4⋊Dic17—41no—
453C4⋊Dic17—41no—
454C4⋊Dic17—41no—
455C4⋊Dic17—41no—
456C4⋊Dic17—41no—
457C4⋊Dic17—41no—
458C4⋊Dic17—41no—
459C4⋊Dic17—41no—
460C4⋊Dic17—41no—
461C4⋊Dic17—41no—
462C4⋊Dic17—41no—
463C4⋊Dic17—41no—
464C4⋊Dic17—41no—
465C4⋊Dic17—41no—
466C4⋊Dic17—41no—
467#63225—22no—
468#63225—41no—
469#63225—41no—
470#63225—41no—
471#63225—41no—
472#63225—41no—
473#63225—41no—
474#63225—41no—
475#63225—41no—
476#63225—41no—
477#63225—41no—
478#63225—41no—
479#63225—41no—
480#63225—41no—
481#63225—41no—
482#63225—41no—
483#63225—41no—
484#63225—41no—
485C4×Dic17—22no—
486C4×Dic17—22no—
487C4×Dic17—41no—
488C4×Dic17—41no—
489C4×Dic17—41no—
490C4×Dic17—41no—
491C4×Dic17—41no—
492C4×Dic17—41no—
493C4×Dic17—41no—
494C4×Dic17—41no—
495#36755—171nomaximal, Sylow
496C23×C17—21no—
497C23×C17—21no—
498C23×C17—21no—
499C23×C17—21no—
500C23×C17—21no—
501C23×C17—21no—
502C23×C17—21no—
503C23×C17—21no—
504C23×C17—21no—
505C23×C17—21no—
506C23×C17—21no—
507C23×C17—21no—
508C23×C17C22×Q812yes—
509C23×C17C22×Q812yes—
510C23×C17C2511yescharacteristic
511D4×C17—44no—
512C2×C4×C17—21no—
513C2×C4×C17—21no—
514C2×C4×C17—21no—
515C2×C4×C17—21no—
516C2×C4×C17—21no—
517C2×C4×C17—21no—
518C2×C4×C17—21no—
519C2×C4×C17—21no—
520C2×C4×C17—21no—
521C2×C4×C17—21no—
522C2×C4×C17—21no—
523C2×C4×C17—21no—
524C2×C4×C17—21no—
525C2×C4×C17—21no—
526C2×C4×C17—21no—
527C2×C4×C17—21no—
528C2×C4×C17—21no—
529C2×C4×C17—21no—
530C2×C4×C17—21no—
531C2×C4×C17—21no—
532C2×C4×C17—21no—
533C2×C4×C17—21no—
534C2×C4×C17—21no—
535C2×C4×C17—21no—
536C2×C4×C17—21no—
537C2×C4×C17—21no—
538C2×C4×C17—21no—
539C2×C4×C17—21no—
540C2×C4×C17—21no—
541C2×C4×C17—21no—
542C2×C4×C17—21no—
543C2×C4×C17—21no—
544C2×C4×C17—21no—
545C2×C4×C17—21no—
546C2×C4×C17—44no—
547C2×C4×C17—44no—
548C2×C4×C17—82no—
549C2×C4×C17—82no—
550C2×C4×C17C22×Q812yes—
551C2×C4×C17C22×Q812yes—
552C2×C4×C17C22×Q812yes—
553C2×C4×C17C22×Q812yes—
554C2×C4×C17C22×Q812yes—
555C2×Dic17—21no—
556C2×Dic17—21no—
557C2×Dic17—21no—
558C2×Dic17—21no—
559C2×Dic17—21no—
560C2×Dic17—21no—
561C2×Dic17—21no—
562C2×Dic17—21no—
563C2×Dic17—21no—
564C2×Dic17—21no—
565C2×Dic17—21no—
566C2×Dic17—21no—
567C2×Dic17—21no—
568C2×Dic17—21no—
569C2×Dic17—21no—
570C2×Dic17—21no—
571C2×Dic17—21no—
572C2×Dic17—21no—
573C2×Dic17—21no—
574C2×Dic17—21no—
575C2×Dic17—21no—
576C2×Dic17—21no—
577C2×Dic17—21no—
578C2×Dic17—21no—
579C2×Dic17—21no—
580C2×Dic17—21no—
581C2×Dic17—21no—
582C2×Dic17—21no—
583C2×Dic17—21no—
584C2×Dic17—21no—
585C2×Dic17—21no—
586C2×Dic17—21no—
587C2×Dic17—21no—
588C2×Dic17—21no—
589C2×Dic17—21no—
590C2×Dic17—21no—
591C2×Dic17—21no—
592C2×Dic17—21no—
593C2×Dic17—21no—
594C2×Dic17—21no—
595C2×Dic17—21no—
596C2×Dic17—21no—
597C2×Dic17—21no—
598C2×Dic17—21no—
599C2×Dic17—21no—
600C2×Dic17—21no—
601C2×Dic17—21no—
602C2×Dic17—44no—
603C2×Dic17—44no—
604C2×Dic17H(5,𝔽2)12yes—
605Dic34—82no—
606Dic34—82no—
607Dic34—82no—
608Dic34—82no—
609Dic34—82no—
610#2855—171no—
611#2851—171no—
612#2805—171no—
613#2804—171no—
614#2790—171no—
615#2788—171no—
616#2788—171no—
617#2784—171no—
618#2780—171no—
619#2774—171no—
620#2763—171no—
621#2763—171no—
622#2755—171no—
623#2742—171no—
624#2729—171no—
625#2720—171no—
626#2713—171no—
627#2692—171no—
628#2665—171no—
629#2665—171no—
630#2612—171no—
631#2607—171no—
632#2605—171no—
633#2605—171no—
634#2570—171no—
635#2569—171no—
636#2439—171no—
637#2438—171no—
638#2319—171no—
639#2318D1711yescharacteristic
640#2290—171no—
641C22×C17—22no—
642C22×C17—22no—
643C22×C17—22no—
644C22×C17—22no—
645C22×C17—22no—
646C22×C17—22no—
647C22×C17—41no—
648C22×C17—41no—
649C22×C17—41no—
650C22×C17—41no—
651C22×C17—41no—
652C22×C17—41no—
653C22×C17—41no—
654C22×C17—41no—
655C22×C17C23×Q811yescharacteristic
656C22×C17C2×H(5,𝔽2)11yescharacteristic
657C22×C17#58511yescharacteristic
658C22×C17#58511yescharacteristic
659C22×C17#58511yescharacteristic
660C22×C17#58511yescharacteristic
661C22×C17#58511yescharacteristic
662C4×C17—22no—
663C4×C17—22no—
664C4×C17—22no—
665C4×C17—22no—
666C4×C17—22no—
667C4×C17—41no—
668C4×C17—41no—
669C4×C17—41no—
670C4×C17—41no—
671C4×C17—41no—
672C4×C17—41no—
673C4×C17—41no—
674C4×C17—41no—
675Dic17—22no—
676Dic17—41no—
677Dic17—41no—
678Dic17—41no—
679Dic17—41no—
680Dic17—41no—
681Dic17—41no—
682Dic17—41no—
683Dic17—41no—
684Dic17—41no—
685Dic17—41no—
686Dic17—41no—
687Dic17—41no—
688Dic17—41no—
689Dic17—41no—
690Dic17—41no—
691C2×C4⋊Q8—171no—
692C2×#125—171no—
693C2×C22⋊Q8—171no—
694C2×C22⋊Q8—171no—
695C2×C4×D4C2×D1711yescharacteristic
696C2×#117—171no—
697C22×C42—171no—
698#400—171no—
699#400—171no—
700#400—171no—
701#400—171no—
702#400—171no—
703#400—171no—
704#400—171no—
705#400—171no—
706#400—171no—
707#400—171no—
708#400—171no—
709#400—171no—
710#400—171no—
711#400—171no—
712#399—171no—
713#399—171no—
714#398—171no—
715#398—171no—
716#398—171no—
717#398—171no—
718#398—171no—
719#398—171no—
720#398—171no—
721#398—171no—
722#396—171no—
723#396—171no—
724#396—171no—
725#396—171no—
726#396—171no—
727#396—171no—
728#395—171no—
729#395—171no—
730#395—171no—
731#395—171no—
732#395—171no—
733#395—171no—
734#395—171no—
735#395—171no—
736#395—171no—
737#395—171no—
738#393—171no—
739#393—171no—
740#393—171no—
741#393—171no—
742#393—171no—
743#393—171no—
744#393—171no—
745#393—171no—
746#391—171no—
747#391—171no—
748#391—171no—
749#391—171no—
750#391—171no—
751#391—171no—
752#391—171no—
753#391—171no—
754#391—171no—
755#391—171no—
756#391—171no—
757#391—171no—
758#391—171no—
759#390—171no—
760#390—171no—
761#389—171no—
762#389—171no—
763#389—171no—
764#389—171no—
765#389—171no—
766#389—171no—
767#389—171no—
768#389—171no—
769#389—171no—
770#389—171no—
771#389—171no—
772#388—171no—
773#388—171no—
774#388—171no—
775#388—171no—
776#388—171no—
777#388—171no—
778#388C2×D1711yescharacteristic
779#388C2×D1711yescharacteristic
780#387—171no—
781#387—171no—
782#387—171no—
783#387—171no—
784#387—171no—
785#387—171no—
786#387—171no—
787#387—171no—
788#387—171no—
789#387—171no—
790#387—171no—
791#387—171no—
792#387—171no—
793#387—171no—
794#387—171no—
795#387—171no—
796#387—171no—
797#387—171no—
798#387—171no—
799#387—171no—
800#387—171no—
801#387—171no—
802#387C2×D1711yescharacteristic
803#387C2×D1711yescharacteristic
804#386—171no—
805#386—171no—
806#386C2×D1711yescharacteristic
807#386C2×D1711yescharacteristic
808#385—171no—
809#385—171no—
810#385—171no—
811#385—171no—
812#385—171no—
813#385—171no—
814#385—171no—
815#385—171no—
816#385—171no—
817#385—171no—
818#385—171no—
819#385—171no—
820#385C2×D1711yescharacteristic
821#385C2×D1711yescharacteristic
822#384—171no—
823#383C2×D1711yescharacteristic
824#382—171no—
825#382—171no—
826#382—171no—
827#382C2×D1711yescharacteristic
828#381—171no—
829#381—171no—
830#381C2×D1711yescharacteristic
831#380—171no—
832#380—171no—
833#380—171no—
834#380—171no—
835#380—171no—
836#380—171no—
837#380C2×D1711yescharacteristic
838C4×C4⋊C4—171no—
839C4×C4⋊C4—171no—
840C4×C22⋊C4—171no—
841C4×C22⋊C4—171no—
842C4×C22⋊C4C2×D1711yescharacteristic
843#376—171no—
844#376—171no—
845C2×#95C2×D1711yescharacteristic
846C2×C17—42no—
847C2×C17—42no—
848C2×C17#345811yescharacteristic
849C2×C17#350111yescharacteristic
850C2×C17#350411yescharacteristic
851C2×C17#353311yescharacteristic
852C2×C17#354011yescharacteristic
853C2×C17#356611yescharacteristic
854C2×C17#356811yescharacteristic
855C22×Q8—171no—
856C22×Q8—171no—
857C22×Q8—171no—
858C22×Q8—171no—
859C22×Q8—171no—
860C22×D4C22×D1711yescharacteristic
861C23×C4—171no—
862C23×C4—171no—
863C23×C4C22×D1711yescharacteristic
864C23×C4C22×D1711yescharacteristic
865C23×C4C22×D1711yescharacteristic
866C23×C4C22×D1711yescharacteristic
867C4⋊Q8—682no—
868#125—682no—
869C22⋊Q8—682no—
870C22⋊Q8—682no—
871C4×D4Dic3418yescomplemented
872#117—682no—
873C2×C4⋊C4—171no—
874C2×C4⋊C4—171no—
875C2×C4⋊C4—171no—
876C2×C4⋊C4—171no—
877C2×C4⋊C4—171no—
878C2×C4⋊C4—171no—
879C2×C4⋊C4—171no—
880C2×C4⋊C4—171no—
881C2×C4⋊C4—171no—
882C2×C4⋊C4—171no—
883C2×C4⋊C4—171no—
884C2×C4⋊C4—171no—
885C2×C4⋊C4—171no—
886C2×C4⋊C4—171no—
887C2×C4⋊C4—171no—
888C2×C4⋊C4—171no—
889C2×C4⋊C4—171no—
890C2×C4⋊C4—171no—
891C2×C4⋊C4—171no—
892C2×C4⋊C4—171no—
893C2×C4⋊C4—171no—
894C2×C4⋊C4—171no—
895C2×C4⋊C4—171no—
896C2×C4⋊C4—171no—
897C2×C4⋊C4—171no—
898C2×C4⋊C4—171no—
899C2×C4⋊C4—171no—
900C2×C4⋊C4—171no—
901C2×C4⋊C4—171no—
902C2×C4⋊C4—171no—
903C2×C4⋊C4—171no—
904C2×C4⋊C4—171no—
905C2×C4⋊C4—171no—
906C2×C4⋊C4—171no—
907C2×C4⋊C4—171no—
908C2×C4⋊C4—171no—
909C2×C4⋊C4—171no—
910C2×C4⋊C4—171no—
911C2×C4⋊C4—171no—
912C2×C4⋊C4C22×D1711yescharacteristic
913C2×C4⋊C4C22×D1711yescharacteristic
914C2×C4⋊C4C22×D1711yescharacteristic
915C2×C4⋊C4C22×D1711yescharacteristic
916C2×C4⋊C4C22×D1711yescharacteristic
917C2×C22⋊C4—171no—
918C2×C22⋊C4—171no—
919C2×C22⋊C4—171no—
920C2×C22⋊C4—171no—
921C2×C22⋊C4—171no—
922C2×C22⋊C4—171no—
923C2×C22⋊C4—171no—
924C2×C22⋊C4—171no—
925C2×C22⋊C4—171no—
926C2×C22⋊C4—171no—
927C2×C22⋊C4—171no—
928C2×C22⋊C4—171no—
929C2×C22⋊C4—171no—
930C2×C22⋊C4—171no—
931C2×C22⋊C4C22×D1711yescharacteristic
932C2×C22⋊C4C22×D1711yescharacteristic
933C2×C22⋊C4C22×D1711yescharacteristic
934C2×C22⋊C4C22×D1711yescharacteristic
935C2×C22⋊C4C22×D1711yescharacteristic
936C2×C22⋊C4C22×D1711yescharacteristic
937C2×C22⋊C4C22×D1711yescharacteristic
938C2×C22⋊C4C22×D1711yescharacteristic
939C2×C42—171no—
940C2×C42—171no—
941C2×C42—171no—
942C2×C42—171no—
943C2×C42—171no—
944C2×C42—171no—
945C2×C42—171no—
946C2×C42—171no—
947C2×C42—171no—
948C2×C42—171no—
949C2×C42—682no—
950C2×C42C22×D1711yescharacteristic
951C2×C42C22×D1711yescharacteristic
952C2×C42C22×D1711yescharacteristic
953#95—171no—
954#95—171no—
955#95—171no—
956#95—171no—
957#95—171no—
958#95—171no—
959#95—171no—
960#95—171no—
961#95—171no—
962#95—171no—
963#95—171no—
964#95—171no—
965#95—171no—
966#95—171no—
967#95—171no—
968#95—171no—
969#95—171no—
970#95—171no—
971#95—171no—
972#95—171no—
973#95—171no—
974#95—171no—
975#95—171no—
976#95—171no—
977#95—171no—
978#95—171no—
979#95—171no—
980#95—171no—
981#95—171no—
982#95—171no—
983#95—171no—
984#95—171no—
985#95—171no—
986#95—171no—
987#95—171no—
988#95—171no—
989#95—171no—
990#95—171no—
991#95—171no—
992#95—171no—
993#95—171no—
994#95—171no—
995#95—171no—
996#95—171no—
997#95—171no—
998#95—171no—
999#95—171no—
1000#95—171no—
1001#95—171no—
1002#95—171no—
1003#95C22×D1711yescharacteristic
1004#95C22×D1711yescharacteristic
1005#95C22×D1711yescharacteristic
1006#95C22×D1711yescharacteristic
1007#95C22×D1711yescharacteristic
1008#95C22×D1711yescharacteristic
1009#95C22×D1711yescharacteristic
1010#95C22×D1711yescharacteristic
1011#95C22×D1711yescharacteristic
1012#95C22×D1711yescharacteristic
1013#95C22×D1711yescharacteristic
1014#95C22×D1711yescharacteristic
1015#95C22×D1711yescharacteristic
1016#95C22×D1711yescharacteristic
1017C17#3675511yescharacteristic, complemented, Sylow
1018C24C23×D1711yescharacteristic
1019C24C23×D1711yescharacteristic
1020C2×Q8—342no—
1021C2×Q8—681no—
1022C2×Q8—681no—
1023C2×Q8—681no—
1024C2×Q8—681no—
1025C2×Q8—681no—
1026C2×Q8—681no—
1027C2×Q8—681no—
1028C2×Q8—681no—
1029C2×Q8—681no—
1030C2×Q8—681no—
1031C2×Q8—681no—
1032C2×Q8—681no—
1033C2×Q8—681no—
1034C2×Q8—681no—
1035C2×D4—41no—
1036C2×D4—41no—
1037C2×D4C2×Dic3414yes—
1038C22×C4—41no—
1039C22×C4—41no—
1040C22×C4—41no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—41no—
1048C22×C4—171no—
1049C22×C4—171no—
1050C22×C4—171no—
1051C22×C4—171no—
1052C22×C4—171no—
1053C22×C4—171no—
1054C22×C4—171no—
1055C22×C4—171no—
1056C22×C4—171no—
1057C22×C4—171no—
1058C22×C4—171no—
1059C22×C4—171no—
1060C22×C4—171no—
1061C22×C4—171no—
1062C22×C4—171no—
1063C22×C4—171no—
1064C22×C4—342no—
1065C22×C4—681no—
1066C22×C4—681no—
1067C22×C4—681no—
1068C22×C4—681no—
1069C22×C4—681no—
1070C22×C4C2×Dic3414yes—
1071C22×C4C2×Dic3414yes—
1072C22×C4C23×D1711yescharacteristic
1073C22×C4C23×D1711yescharacteristic
1074C22×C4C23×D1711yescharacteristic
1075C22×C4C23×D1711yescharacteristic
1076C22×C4C23×D1711yescharacteristic
1077C22×C4C23×D1711yescharacteristic
1078C22×C4C23×D1711yescharacteristic
1079C22×C4C23×D1711yescharacteristic
1080C22×C4C23×D1711yescharacteristic
1081C22×C4C23×D1711yescharacteristic
1082C22×C4C23×D1711yescharacteristic
1083C22×C4C23×D1711yescharacteristic
1084C22×C4C23×D1711yescharacteristic
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—342no—
1090C4⋊C4—342no—
1091C4⋊C4—342no—
1092C4⋊C4—342no—
1093C4⋊C4—681no—
1094C4⋊C4—681no—
1095C4⋊C4—681no—
1096C4⋊C4—681no—
1097C4⋊C4—681no—
1098C4⋊C4—681no—
1099C4⋊C4—681no—
1100C4⋊C4—681no—
1101C4⋊C4—681no—
1102C4⋊C4—681no—
1103C4⋊C4—681no—
1104C4⋊C4—681no—
1105C4⋊C4—681no—
1106C4⋊C4—681no—
1107C4⋊C4—681no—
1108C4⋊C4—681no—
1109C4⋊C4—681no—
1110C4⋊C4—681no—
1111C4⋊C4—681no—
1112C4⋊C4—681no—
1113C4⋊C4—681no—
1114C4⋊C4—681no—
1115C4⋊C4—681no—
1116C4⋊C4—681no—
1117C4⋊C4—681no—
1118C4⋊C4—681no—
1119C4⋊C4—681no—
1120C4⋊C4—681no—
1121C4⋊C4—681no—
1122C4⋊C4—681no—
1123C4⋊C4—681no—
1124C4⋊C4—681no—
1125C4⋊C4—681no—
1126C4⋊C4—681no—
1127C4⋊C4—681no—
1128C4⋊C4C2×Dic3414yes—
1129C22⋊C4—41no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—41no—
1134C22⋊C4—41no—
1135C22⋊C4—342no—
1136C22⋊C4—681no—
1137C22⋊C4—681no—
1138C22⋊C4—681no—
1139C22⋊C4—681no—
1140C22⋊C4—681no—
1141C22⋊C4—681no—
1142C22⋊C4—681no—
1143C22⋊C4—681no—
1144C22⋊C4—681no—
1145C22⋊C4—681no—
1146C22⋊C4—681no—
1147C22⋊C4—681no—
1148C22⋊C4—681no—
1149C22⋊C4C2×Dic3414yes—
1150C22⋊C4C2×Dic3414yes—
1151C42—41no—
1152C42—41no—
1153C42—342no—
1154C42—342no—
1155C42—681no—
1156C42—681no—
1157C42—681no—
1158C42—681no—
1159C42—681no—
1160C42—681no—
1161C42—681no—
1162C42—681no—
1163C42C2×Dic3414yes—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23C22×Dic3412yes—
1177C23C22×Dic3412yes—
1178C23C24×D1711yescharacteristic
1179Q8—1362no—
1180Q8—1362no—
1181Q8—1362no—
1182Q8—1362no—
1183Q8—1362no—
1184D4—44no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—44no—
1220C2×C4—44no—
1221C2×C4—82no—
1222C2×C4—82no—
1223C2×C4—172no—
1224C2×C4—341no—
1225C2×C4—341no—
1226C2×C4—341no—
1227C2×C4—341no—
1228C2×C4—341no—
1229C2×C4—341no—
1230C2×C4—341no—
1231C2×C4—341no—
1232C2×C4—341no—
1233C2×C4—341no—
1234C2×C4—341no—
1235C2×C4—341no—
1236C2×C4—341no—
1237C2×C4—341no—
1238C2×C4—341no—
1239C2×C4—341no—
1240C2×C4—341no—
1241C2×C4—341no—
1242C2×C4—341no—
1243C2×C4—341no—
1244C2×C4—341no—
1245C2×C4—341no—
1246C2×C4—341no—
1247C2×C4—341no—
1248C2×C4—341no—
1249C2×C4—341no—
1250C2×C4—341no—
1251C2×C4—341no—
1252C2×C4—341no—
1253C2×C4—341no—
1254C2×C4—341no—
1255C2×C4—341no—
1256C2×C4—341no—
1257C2×C4—341no—
1258C2×C4—341no—
1259C2×C4—341no—
1260C2×C4—341no—
1261C2×C4—341no—
1262C2×C4—341no—
1263C2×C4—341no—
1264C2×C4—341no—
1265C2×C4—341no—
1266C2×C4—341no—
1267C2×C4—341no—
1268C2×C4—341no—
1269C2×C4—341no—
1270C2×C4—341no—
1271C2×C4—684no—
1272C2×C4—684no—
1273C2×C4C22×Dic3412yes—
1274C2×C4C22×Dic3412yes—
1275C2×C4C22×Dic3412yes—
1276C2×C4C22×Dic3412yes—
1277C2×C4C22×Dic3412yes—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22C23×Dic3411yescharacteristic
1293C22H(5,𝔽2)×D1711yescharacteristic
1294C22#1176364411yescharacteristic
1295C22#1176364411yescharacteristic
1296C22#1176364511yescharacteristic
1297C22#1176364511yescharacteristic
1298C22#1176364611yescharacteristic
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—342no—
1313C4—681no—
1314C4—681no—
1315C4—681no—
1316C4—681no—
1317C4—681no—
1318C4—681no—
1319C4—681no—
1320C4—681no—
1321C4—681no—
1322C4—681no—
1323C4—681no—
1324C4—681no—
1325C4—681no—
1326C4—681no—
1327C4—681no—
1328C2—42no—
1329C2—42no—
1330C2#1454218911yescharacteristic
1331C2#1454258211yescharacteristic
1332C2#1454260611yescharacteristic
1333C2#1454295911yescharacteristic
1334C2#1454305511yescharacteristic
1335C2#1454344011yescharacteristic
1336C2#1454347711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2318C2
prime radicalC22×D4×C17C23
hypercenter#2318D17
hypocenterC17#36755
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2318

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14537121C2semidirect
2. #14537092C2semidirect
3. #14536733C2semidirect
5. #14536549C2semidirect
6. #14536534C2semidirect
7. #14536527C2semidirect
10. #14536339C2semidirect
11. #14536200C2semidirect
12. #14536198C2semidirect
13. #14536095C2semidirect
14. #14535913C2semidirect
15. #14535767C2semidirect
16. #14535665C2semidirect
17. #14535566C2semidirect
19. #14534957C2semidirect
20. #14534956C2semidirect
21. #14534492C2semidirect
22. #14534445C2semidirect
23. #14534433C2semidirect
24. #14534433C2semidirect
25. #14534019C2semidirect
26. #14534008C2semidirect
27. #14532475C2semidirect
28. #14532460C2semidirect
199. C4×D4×C17Q8semidirect
871. C4×D4Dic34semidirect
1017. C17#36755semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145371212
#145370922
#145367332
#145367272
#145365492
#145365342
#145365272
#145364822
#145364362
#145363392
#145362002
#145361982
#145360952
#145359132
#145357672
#145356652
#145355662
#145352842
#145349572
#145349562
#145344922
#145344452
#145344332
#145340192
#145340082
#145324752
#145324602
#145314272
#145312292
C17×#23182
#3675517