Finite Group Databasebeta

← #17248875

Subgroups — #17248875

Order 4352.

1526 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14537122C211yesmaximal, characteristic, complemented
2#14537104C211yesmaximal, characteristic
3#14536666C211yesmaximal, characteristic, complemented
4#14536662C211yesmaximal, characteristic, complemented
5#14536343C211yesmaximal, characteristic, complemented
6#14536254C211yesmaximal, characteristic, complemented
7#14536246C211yesmaximal, characteristic, complemented
8#14536238C211yesmaximal, characteristic, complemented
9#14536182C211yesmaximal, characteristic, complemented
10#14536154C211yesmaximal, characteristic, complemented
11#14536129C211yesmaximal, characteristic, complemented
12#14536092C211yesmaximal, characteristic, complemented
13#14536069C211yesmaximal, characteristic, complemented
14#14535988C211yesmaximal, characteristic, complemented
15#14535947C211yesmaximal, characteristic, complemented
16#14535910C211yesmaximal, characteristic, complemented
17#14535860C211yesmaximal, characteristic, complemented
18#14534602C211yesmaximal, characteristic, complemented
19#14534569C211yesmaximal, characteristic
20#14533959C211yesmaximal, characteristic
21#14533794C211yesmaximal, characteristic, complemented
22#14533266C211yesmaximal, characteristic, complemented
23#14533176C211yesmaximal, characteristic, complemented
24#14533170C211yesmaximal, characteristic, complemented
25#14533113C211yesmaximal, characteristic
26#14533109C211yesmaximal, characteristic
27#14533085C211yesmaximal, characteristic
28#14531513C211yesmaximal, characteristic, complemented
29#14531414C211yesmaximal, characteristic
30D17×#387C211yesmaximal, characteristic, complemented
31C17×#2773C211yesmaximal, characteristic, complemented
32C2×#10587569C2211yescharacteristic
33C2×#10587569C2211yescharacteristic
34C2×#10587583C2211yescharacteristic
35C2×#10587583C2211yescharacteristic
36C2×#10587582C2211yescharacteristic
37C2×#10587567C2211yescharacteristic
38C2×C4⋊C4×D17C2211yescharacteristic
39C2×C4⋊C4×D17C2211yescharacteristic
40C2×C42×D17C2211yescharacteristic
41C17⋊#401C2211yescharacteristic
42C17⋊#401C2211yescharacteristic
43#11762751C2211yescharacteristic
44#11762751C2211yescharacteristic
45#11762751C2211yescharacteristic
46#11762751C2211yescharacteristic
47#11762751C2211yescharacteristic
48#11762751C2211yescharacteristic
49#11762751C2211yescharacteristic
50#11762751C2211yescharacteristic
51#11762750C2211yescharacteristic
52#11762750C2211yescharacteristic
53#11762750C2211yescharacteristic
54#11762749C2211yescharacteristic
55#11762749C2211yescharacteristic
56#11762748C2211yescharacteristic
57#11762748C2211yescharacteristic
58#11762748C2211yescharacteristic
59#11762747C2211yescharacteristic
60#11762747C2211yescharacteristic
61#11762745C2211yescharacteristic
62#11762742C2211yescharacteristic
63#11762742C2211yescharacteristic
64#11762742C2211yescharacteristic
65#11762742C2211yescharacteristic
66#11762742C2211yescharacteristic
67#11762741C2211yescharacteristic
68#11762740C2211yescharacteristic
69#11762739C2211yescharacteristic
70#11762739C2211yescharacteristic
71#11762737C2211yescharacteristic
72#11762737C2211yescharacteristic
73#11762734C2211yescharacteristic
74#11762734C2211yescharacteristic
75#11762730C2211yescharacteristic
76#11762730C2211yescharacteristic
77#11762729C2211yescharacteristic
78#11762729C2211yescharacteristic
79#11762729C2211yescharacteristic
80#11762721C2211yescharacteristic
81#11762721C2211yescharacteristic
82#11762721C2211yescharacteristic
83#11762715C2211yescharacteristic
84#11762715C2211yescharacteristic
85#11762715C2211yescharacteristic
86#11762714C2211yescharacteristic
87#11762714C2211yescharacteristic
88#11762713C2211yescharacteristic
89#11762713C2211yescharacteristic
90#11762713C2211yescharacteristic
91#11762713C2211yescharacteristic
92#11762713C2211yescharacteristic
93#11762707C2211yescharacteristic
94#11762706C2211yescharacteristic
95#11762706C2211yescharacteristic
96#11762706C2211yescharacteristic
97#11762705C2211yescharacteristic
98#11762705C2211yescharacteristic
99#11762703C2211yescharacteristic
100#11762703C2211yescharacteristic
101#11762702C2211yescharacteristic
102#11762702C2211yescharacteristic
103#11762702C2211yescharacteristic
104#11762697C2211yescharacteristic
105#11762697C2211yescharacteristic
106#11762696C2211yescharacteristic
107#11762696C2211yescharacteristic
108#11762696C2211yescharacteristic
109#11762696C2211yescharacteristic
110#11762695C2211yescharacteristic
111#11762695C2211yescharacteristic
112#11762695C2211yescharacteristic
113#11762695C2211yescharacteristic
114#11762695C2211yescharacteristic
115#11762695C2211yescharacteristic
116#11762695C2211yescharacteristic
117#11762695C2211yescharacteristic
118#11762695C2211yescharacteristic
119#11762694C2211yescharacteristic
120#11762694C2211yescharacteristic
121#11762694C2211yescharacteristic
122#11762694C2211yescharacteristic
123#11762694C2211yescharacteristic
124#11762693C2211yescharacteristic
125#11762693C2211yescharacteristic
126#11762693C2211yescharacteristic
127#11762693C2211yescharacteristic
128#11762692C2211yescharacteristic
129#11762692C2211yescharacteristic
130#11762691C2211yescharacteristic
131#11762691C2211yescharacteristic
132#11762690C2211yescharacteristic
133#11762685C2211yescharacteristic
134#11762685C2211yescharacteristic
135#11762685C2211yescharacteristic
136#11762685C2211yescharacteristic
137#11762684C2211yescharacteristic
138#11762684C2211yescharacteristic
139#11762683C2211yescharacteristic
140#11762683C2211yescharacteristic
141#11762680C2211yescharacteristic
142#11762680C2211yescharacteristic
143#11762680C2211yescharacteristic
144#11762680C2211yescharacteristic
145#11762676C2211yescharacteristic
146#11762676C2211yescharacteristic
147#11762676C2211yescharacteristic
148#11762675C2211yescharacteristic
149#11762674C2211yescharacteristic
150#11762674C2211yescharacteristic
151#11762674C2211yescharacteristic
152#11762671C2211yescharacteristic
153#11762671C2211yescharacteristic
154#11762671C2211yescharacteristic
155#11762671C2211yescharacteristic
156#11762671C2211yescharacteristic
157#11762671C2211yescharacteristic
158#11762670C2211yescharacteristic
159#11762668C2211yescharacteristic
160#11762667C2211yescharacteristic
161#11762667C2211yescharacteristic
162#11762667C2211yescharacteristic
163#11762666C2211yescharacteristic
164#11762666C2211yescharacteristic
165C4×#63227C2211yescharacteristic
166C4×#63227C2211yescharacteristic
167#11762656C2211yescharacteristic
168#95×D17C2211yescharacteristic
169#95×D17C2211yescharacteristic
170#95×D17C2211yescharacteristic
171#95×D17C2211yescharacteristic
172C17×#400C2211yescharacteristic
173C17×#399C2211yescharacteristic
174C17×#399C2211yescharacteristic
175C17×#398C2211yescharacteristic
176C17×#397C2211yescharacteristic
177C17×#397C2211yescharacteristic
178C17×#389C2211yescharacteristic
179C17×#389C2211yescharacteristic
180C17×#388C2211yescharacteristic
181C17×#388C2211yescharacteristic
182C17×#388C2211yescharacteristic
183C17×#387C2211yescharacteristic
184C17×#387C2211yescharacteristic
185C17×#387C2211yescharacteristic
186C17×#382C2211yescharacteristic
187C22×C22⋊D17C2311yescharacteristic
188C23×Dic17C2311yescharacteristic
189C22×C4×D17C2311yescharacteristic
190C22×C4×D17C2311yescharacteristic
191C22×C4×D17C2311yescharacteristic
192C22×C4×D17C2311yescharacteristic
193C22×C4×D17C2311yescharacteristic
194C22×C4×D17C2311yescharacteristic
195C22×C4×D17C2311yescharacteristic
196C22×Dic34C2311yescharacteristic
197C22×Dic34C2311yescharacteristic
198C22×Dic34C2311yescharacteristic
199C2×C4⋊C4×C17C2311yescharacteristic
200C2×C4⋊C4×C17C2311yescharacteristic
201C2×C4⋊C4×C17C2311yescharacteristic
202C2×C4⋊C4×C17C2311yescharacteristic
203C2×C4⋊C4×C17C2311yescharacteristic
204C2×C4⋊C4×C17C2311yescharacteristic
205C2×C4⋊C4×C17C2311yescharacteristic
206C2×C4⋊C4×C17C2311yescharacteristic
207C2×C4⋊C4×C17C2311yescharacteristic
208C2×C4⋊C4×C17C2311yescharacteristic
209C2×C4⋊C4×C17C2311yescharacteristic
210C2×C22⋊C4×C17C2311yescharacteristic
211C2×C22⋊C4×C17C2311yescharacteristic
212C2×C22⋊C4×C17C2311yescharacteristic
213C2×C22⋊C4×C17C2311yescharacteristic
214C2×C22⋊C4×C17C2311yescharacteristic
215C2×C22⋊C4×C17C2311yescharacteristic
216C2×C22⋊C4×C17C2311yescharacteristic
217C2×C42×C17C2311yescharacteristic
218C2×C42×C17C2311yescharacteristic
219C2×C42×C17C2311yescharacteristic
220C2×C22⋊Dic17C2311yescharacteristic
221C2×C22⋊Dic17C2311yescharacteristic
222C2×C22⋊Dic17C2311yescharacteristic
223C2×C22⋊Dic17C2311yescharacteristic
224C2×C22⋊Dic17C2311yescharacteristic
225C2×C22⋊Dic17C2311yescharacteristic
226C2×#63227C2311yescharacteristic
227C2×#63227C2311yescharacteristic
228C2×#63227C2311yescharacteristic
229C2×#63227C2311yescharacteristic
230C2×#63227C2311yescharacteristic
231C2×#63227C2311yescharacteristic
232C2×#63227C2311yescharacteristic
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×#63225C2311yescharacteristic
246C2×#63225C2311yescharacteristic
247C2×#63225C2311yescharacteristic
248C2×#63225C2311yescharacteristic
249C2×#63225C2311yescharacteristic
250C2×#63225C2311yescharacteristic
251C2×#63225C2311yescharacteristic
252C2×#63225C2311yescharacteristic
253C2×#63225C2311yescharacteristic
254C2×#63225C2311yescharacteristic
255C2×#63225C2311yescharacteristic
256C2×#63225C2311yescharacteristic
257C2×#63225C2311yescharacteristic
258C2×#63225C2311yescharacteristic
259C2×#63225C2311yescharacteristic
260C2×#63225C2311yescharacteristic
261C2×#63225C2311yescharacteristic
262C2×C4×Dic17C2311yescharacteristic
263C2×C4×Dic17C2311yescharacteristic
264C2×C4×Dic17C2311yescharacteristic
265C2×C4×Dic17C2311yescharacteristic
266C2×C4×Dic17C2311yescharacteristic
267C2×C4×Dic17C2311yescharacteristic
268C2×C4×Dic17C2311yescharacteristic
269C2×C4×Dic17C2311yescharacteristic
270#10587583—24no—
271#10587583—42no—
272#10587582—42no—
273C4⋊C4×D17—24no—
274C4⋊C4×D17—42no—
275#10587569—42no—
276#10587569—42no—
277#10587567—24no—
278C42×D17—42no—
279C17×#95C2311yescharacteristic
280C17×#95C2311yescharacteristic
281C17×#95C2311yescharacteristic
282C17×#95C2311yescharacteristic
283C17×#95C2311yescharacteristic
284C17×#95C2311yescharacteristic
285C17×#95C2311yescharacteristic
286C17×#95C2311yescharacteristic
287C17×#95C2311yescharacteristic
288C17×#95C2311yescharacteristic
289C17×#95C2311yescharacteristic
290C17×#95C2311yescharacteristic
291C17×#95C2311yescharacteristic
292C17×#95C2311yescharacteristic
293#10587502C2311yescharacteristic
294#10587502C2311yescharacteristic
295#10587502C2311yescharacteristic
296#10587502C2311yescharacteristic
297#10587502C2311yescharacteristic
298#10587502C2311yescharacteristic
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
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351C24×C17C2411yescharacteristic
352C23×D17C2411yescharacteristic
353C22×C4×C17C2411yescharacteristic
354C22×C4×C17C2411yescharacteristic
355C22×C4×C17C2411yescharacteristic
356C22×C4×C17C2411yescharacteristic
357C22×C4×C17C2411yescharacteristic
358C22×C4×C17C2411yescharacteristic
359C22×C4×C17C2411yescharacteristic
360C22×C4×C17C2411yescharacteristic
361C22×C4×C17C2411yescharacteristic
362C22×C4×C17C2411yescharacteristic
363C22×C4×C17C2411yescharacteristic
364C22×C4×C17C2411yescharacteristic
365C22×C4×C17C2411yescharacteristic
366C22×C4×C17C2411yescharacteristic
367C2×C22⋊D17—22no—
368C2×C22⋊D17—22no—
369C2×C22⋊D17—22no—
370C22×Dic17—22no—
371C22×Dic17—41no—
372C22×Dic17—41no—
373C22×Dic17C2411yescharacteristic
374C22×Dic17C2411yescharacteristic
375C22×Dic17C2411yescharacteristic
376C22×Dic17C2411yescharacteristic
377C22×Dic17C2411yescharacteristic
378C22×Dic17C2411yescharacteristic
379C22×Dic17C2411yescharacteristic
380C22×Dic17C2411yescharacteristic
381C22×Dic17C2411yescharacteristic
382C22×Dic17C2411yescharacteristic
383C22×Dic17C2411yescharacteristic
384C22×Dic17C2411yescharacteristic
385C22×Dic17C2411yescharacteristic
386C22×Dic17C2411yescharacteristic
387C22×Dic17C2411yescharacteristic
388C2×C4×D17—22no—
389C2×C4×D17—22no—
390C2×C4×D17—22no—
391C2×C4×D17—22no—
392C2×C4×D17—22no—
393C2×C4×D17—22no—
394C2×C4×D17—22no—
395C2×C4×D17—22no—
396C2×C4×D17—22no—
397C2×C4×D17—22no—
398C2×C4×D17—22no—
399C2×C4×D17—41no—
400C2×C4×D17—41no—
401C2×C4×D17—41no—
402C2×C4×D17—41no—
403C2×C4×D17—41no—
404C2×C4×D17—41no—
405C2×C4×D17—41no—
406C2×C4×D17—41no—
407C2×C4×D17—41no—
408C2×C4×D17#4114yes—
409C2×Dic34—22no—
410C2×Dic34—22no—
411C2×Dic34—41no—
412C2×Dic34—41no—
413C2×Dic34—41no—
414C2×Dic34—41no—
415C2×Dic34—41no—
416C2×Dic34—41no—
417C2×Dic34—41no—
418C4⋊C4×C17—22no—
419C4⋊C4×C17—22no—
420C4⋊C4×C17—22no—
421C4⋊C4×C17—22no—
422C4⋊C4×C17—41no—
423C4⋊C4×C17—41no—
424C4⋊C4×C17—41no—
425C4⋊C4×C17—41no—
426C4⋊C4×C17—41no—
427C4⋊C4×C17—41no—
428C4⋊C4×C17—41no—
429C22⋊C4×C17—22no—
430C22⋊C4×C17—22no—
431C22⋊C4×C17—41no—
432C22⋊C4×C17—41no—
433C22⋊C4×C17—41no—
434C22⋊C4×C17—41no—
435C22⋊C4×C17—41no—
436C42×C17—41no—
437C42×C17—41no—
438C42×C17—41no—
439C22⋊Dic17—41no—
440C22⋊Dic17—41no—
441C22⋊Dic17—41no—
442C22⋊Dic17—41no—
443C22⋊Dic17—41no—
444C22⋊Dic17—41no—
445#63227—22no—
446#63227—22no—
447#63227—22no—
448#63227—22no—
449#63227—22no—
450#63227—22no—
451#63227—22no—
452C4⋊Dic17—22no—
453C4⋊Dic17—22no—
454C4⋊Dic17—22no—
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—
464#63225—22no—
465#63225—22no—
466#63225—22no—
467#63225—41no—
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—
481C4×Dic17—22no—
482C4×Dic17—41no—
483C4×Dic17—41no—
484C4×Dic17—41no—
485C4×Dic17—41no—
486C4×Dic17—41no—
487C4×Dic17—41no—
488C4×Dic17—41no—
489#36999—171nomaximal, Sylow
490C23×C17—21no—
491C23×C17—21no—
492C23×C17—21no—
493C23×C17—21no—
494C23×C17—21no—
495C23×C17—21no—
496C23×C17—21no—
497C23×C17C2511yescharacteristic
498C22×D17—21no—
499C22×D17—21no—
500C22×D17—21no—
501C22×D17—21no—
502C22×D17C2×#4112yes—
503C22×D17H(5,𝔽2)12yes—
504C22×D172−1+412yes—
505C2×C4×C17—21no—
506C2×C4×C17—21no—
507C2×C4×C17—21no—
508C2×C4×C17—21no—
509C2×C4×C17—21no—
510C2×C4×C17—21no—
511C2×C4×C17—21no—
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×C17C2×#4112yes—
546C2×C4×C172−1+412yes—
547C22⋊D17—44no—
548C2×Dic17—21no—
549C2×Dic17—21no—
550C2×Dic17—21no—
551C2×Dic17—21no—
552C2×Dic17—21no—
553C2×Dic17—21no—
554C2×Dic17—21no—
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—82no—
593C2×Dic17C2×#4112yes—
594C4×D17—44no—
595C4×D17—44no—
596C4×D17—44no—
597C4×D17—44no—
598C4×D17—44no—
599C4×D17—82no—
600C4×D17—82no—
601Dic34—82no—
602Dic34—82no—
603Dic34—82no—
604#2855—171no—
605#2853—171no—
606#2799—171no—
607#2798—171no—
608#2774—171no—
609#2773D1711yescharacteristic, complemented
610#2767—171no—
611#2767—171no—
612#2766—171no—
613#2762—171no—
614#2759—171no—
615#2758—171no—
616#2755—171no—
617#2754—171no—
618#2747—171no—
619#2745—171no—
620#2742—171no—
621#2738—171no—
622#2627—171no—
623#2623—171no—
624#2564—171no—
625#2549—171no—
626#2503—171no—
627#2493—171no—
628#2493—171no—
629#2488—171no—
630#2488—171no—
631#2486—171no—
632#2329—171no—
633#2318—171no—
634C2×#387—171no—
635C22×C17—41no—
636C22×C17—41no—
637C22×C17—41no—
638C22×C17—41no—
639C22×C17—41no—
640C22×C17—41no—
641C22×C17—41no—
642C22×C17C22×#4111yescharacteristic
643C22×C17C2×H(5,𝔽2)11yescharacteristic
644C22×C17C2×2−1+411yescharacteristic
645C22×C17C2×2−1+411yescharacteristic
646C22×C17#58511yescharacteristic
647C22×C17#58511yescharacteristic
648C22×C17#58511yescharacteristic
649C2×D17—22no—
650C2×D17—22no—
651C2×D17—22no—
652C2×D17—22no—
653C2×D17—22no—
654C2×D17—22no—
655C2×D17#54214yes—
656C4×C17—22no—
657C4×C17—22no—
658C4×C17—41no—
659C4×C17—41no—
660C4×C17—41no—
661C4×C17—41no—
662C4×C17—41no—
663C4×C17—41no—
664C4×C17—41no—
665C4×C17—41no—
666C4×C17—41no—
667C4×C17—41no—
668C4×C17—41no—
669C4×C17—41no—
670Dic17—22no—
671Dic17—41no—
672Dic17—41no—
673Dic17—41no—
674Dic17—41no—
675Dic17—41no—
676Dic17—41no—
677Dic17—41no—
678Dic17—41no—
679Dic17—41no—
680Dic17—41no—
681Dic17—41no—
682Dic17—41no—
683Dic17—41no—
684Dic17—41no—
685C2×#123—171no—
686C2×#123—171no—
687C2×C22⋊Q8—171no—
688C2×C22⋊Q8—171no—
689C2×C22⋊Q8—171no—
690C2×C4×D4—171no—
691C22×C4⋊C4—171no—
692C22×C4⋊C4—171no—
693C22×C42—171no—
694#401—171no—
695#401—171no—
696#400—171no—
697#400—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#400—171no—
713#400—171no—
714#400C2×D1711yescharacteristic
715#399—171no—
716#399C2×D1711yescharacteristic
717#399C2×D1711yescharacteristic
718#398—171no—
719#398—171no—
720#398—171no—
721#398—171no—
722#398—171no—
723#398—171no—
724#398—171no—
725#398—171no—
726#398—171no—
727#398C2×D1711yescharacteristic
728#397—171no—
729#397—171no—
730#397—171no—
731#397—171no—
732#397C2×D1711yescharacteristic
733#397C2×D1711yescharacteristic
734#395—171no—
735#395—171no—
736#395—171no—
737#395—171no—
738#395—171no—
739#393—171no—
740#393—171no—
741#393—171no—
742#391—171no—
743#391—171no—
744#391—171no—
745#391—171no—
746#391—171no—
747#391—171no—
748#391—171no—
749#391—171no—
750#391—171no—
751#391—171no—
752#389—171no—
753#389—171no—
754#389—171no—
755#389—171no—
756#389—171no—
757#389—171no—
758#389C2×D1711yescharacteristic
759#389C2×D1711yescharacteristic
760#388—171no—
761#388—171no—
762#388—171no—
763#388—171no—
764#388—171no—
765#388—171no—
766#388—171no—
767#388C2×D1711yescharacteristic
768#388C2×D1711yescharacteristic
769#388C2×D1711yescharacteristic
770#387—171no—
771#387—171no—
772#387—171no—
773#387—171no—
774#387—171no—
775#387—171no—
776#387—171no—
777#387—171no—
778#387—171no—
779#387—171no—
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#387C2×D1711yescharacteristic
798#387C2×D1711yescharacteristic
799#387C2×D1711yescharacteristic
800#386—171no—
801#386—171no—
802#386—171no—
803#386—171no—
804#385—171no—
805#385—171no—
806#385—171no—
807#385—171no—
808#385—171no—
809#385—171no—
810#385—171no—
811#385—171no—
812#383—171no—
813#383—171no—
814#383—171no—
815#382—171no—
816#382—171no—
817#382—171no—
818#382—171no—
819#382C2×D1711yescharacteristic
820#381—171no—
821#381—171no—
822#381—171no—
823#381—171no—
824#381—171no—
825#381—171no—
826#381—171no—
827#380—171no—
828#380—171no—
829#380—171no—
830#380—171no—
831#380—171no—
832#380—171no—
833C4×C22⋊C4—171no—
834C4×C22⋊C4—171no—
835C4×C22⋊C4—171no—
836C2×#95—171no—
837C2×#95—171no—
838C2×#95—171no—
839C2×#95—171no—
840C2×C17—81no—
841C2×C17C2×#54211yescharacteristic
842C2×C17#349111yescharacteristic
843C2×C17#350711yescharacteristic
844C2×C17#353311yescharacteristic
845C2×C17#353511yescharacteristic
846C2×C17#356311yescharacteristic
847C2×C17#356411yescharacteristic
848D17—24no—
849C22×Q8—171no—
850C22×Q8—171no—
851C22×Q8—171no—
852C22×D4—171no—
853C23×C4—171no—
854C23×C4—171no—
855C23×C4—171no—
856C23×C4—171no—
857C23×C4—171no—
858C23×C4—171no—
859C23×C4—171no—
860C23×C4—171no—
861#123—682no—
862#123—682no—
863C22⋊Q8—344no—
864C22⋊Q8—682no—
865C22⋊Q8—682no—
866C4×D4—344no—
867C2×C4⋊C4—171no—
868C2×C4⋊C4—171no—
869C2×C4⋊C4—171no—
870C2×C4⋊C4—171no—
871C2×C4⋊C4—171no—
872C2×C4⋊C4—171no—
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—344no—
897C2×C4⋊C4—682no—
898C2×C4⋊C4C22×D1711yescharacteristic
899C2×C4⋊C4C22×D1711yescharacteristic
900C2×C4⋊C4C22×D1711yescharacteristic
901C2×C4⋊C4C22×D1711yescharacteristic
902C2×C4⋊C4C22×D1711yescharacteristic
903C2×C4⋊C4C22×D1711yescharacteristic
904C2×C4⋊C4C22×D1711yescharacteristic
905C2×C4⋊C4C22×D1711yescharacteristic
906C2×C4⋊C4C22×D1711yescharacteristic
907C2×C4⋊C4C22×D1711yescharacteristic
908C2×C4⋊C4C22×D1711yescharacteristic
909C2×C22⋊C4—171no—
910C2×C22⋊C4—171no—
911C2×C22⋊C4—171no—
912C2×C22⋊C4—171no—
913C2×C22⋊C4—171no—
914C2×C22⋊C4—171no—
915C2×C22⋊C4—171no—
916C2×C22⋊C4—171no—
917C2×C22⋊C4—171no—
918C2×C22⋊C4—171no—
919C2×C22⋊C4—171no—
920C2×C22⋊C4—171no—
921C2×C22⋊C4—171no—
922C2×C22⋊C4C22×D1711yescharacteristic
923C2×C22⋊C4C22×D1711yescharacteristic
924C2×C22⋊C4C22×D1711yescharacteristic
925C2×C22⋊C4C22×D1711yescharacteristic
926C2×C22⋊C4C22×D1711yescharacteristic
927C2×C22⋊C4C22×D1711yescharacteristic
928C2×C22⋊C4C22×D1711yescharacteristic
929C2×C42—171no—
930C2×C42—171no—
931C2×C42—171no—
932C2×C42—171no—
933C2×C42—171no—
934C2×C42—171no—
935C2×C42—171no—
936C2×C42—171no—
937C2×C42—682no—
938C2×C42C22×D1711yescharacteristic
939C2×C42C22×D1711yescharacteristic
940C2×C42C22×D1711yescharacteristic
941#95—171no—
942#95—171no—
943#95—171no—
944#95—171no—
945#95—171no—
946#95—171no—
947#95—171no—
948#95—171no—
949#95—171no—
950#95—171no—
951#95—171no—
952#95—171no—
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#95C22×D1711yescharacteristic
1000#95C22×D1711yescharacteristic
1001#95C22×D1711yescharacteristic
1002#95C22×D1711yescharacteristic
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
1013C17#3699911yescharacteristic, complemented, Sylow
1014C24—171no—
1015C24C23×D1711yescharacteristic
1016C2×Q8—342no—
1017C2×Q8—342no—
1018C2×Q8—681no—
1019C2×Q8—681no—
1020C2×Q8—681no—
1021C2×Q8—681no—
1022C2×Q8—681no—
1023C2×Q8—681no—
1024C2×Q8—681no—
1025C2×D4—342no—
1026C2×D4—342no—
1027C2×D4—342no—
1028C22×C4—171no—
1029C22×C4—174no—
1030C22×C4—171no—
1031C22×C4—171no—
1032C22×C4—171no—
1033C22×C4—171no—
1034C22×C4—171no—
1035C22×C4—171no—
1036C22×C4—171no—
1037C22×C4—171no—
1038C22×C4—171no—
1039C22×C4—171no—
1040C22×C4—171no—
1041C22×C4—171no—
1042C22×C4—171no—
1043C22×C4—171no—
1044C22×C4—342no—
1045C22×C4—342no—
1046C22×C4—342no—
1047C22×C4—342no—
1048C22×C4—342no—
1049C22×C4—342no—
1050C22×C4—342no—
1051C22×C4—342no—
1052C22×C4—342no—
1053C22×C4—342no—
1054C22×C4—342no—
1055C22×C4—342no—
1056C22×C4—681no—
1057C22×C4—681no—
1058C22×C4—681no—
1059C22×C4—681no—
1060C22×C4—681no—
1061C22×C4—681no—
1062C22×C4—681no—
1063C22×C4—681no—
1064C22×C4—681no—
1065C22×C4—681no—
1066C22×C4—681no—
1067C22×C4C23×D1711yescharacteristic
1068C22×C4C23×D1711yescharacteristic
1069C22×C4C23×D1711yescharacteristic
1070C22×C4C23×D1711yescharacteristic
1071C22×C4C23×D1711yescharacteristic
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
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—22no—
1084C4⋊C4—22no—
1085C4⋊C4—41no—
1086C4⋊C4—41no—
1087C4⋊C4—41no—
1088C4⋊C4—41no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—41no—
1092C4⋊C4—342no—
1093C4⋊C4—342no—
1094C4⋊C4—342no—
1095C4⋊C4—342no—
1096C4⋊C4—342no—
1097C4⋊C4—342no—
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—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—41no—
1124C22⋊C4—41no—
1125C22⋊C4—41no—
1126C22⋊C4—41no—
1127C22⋊C4—41no—
1128C22⋊C4—342no—
1129C22⋊C4—342no—
1130C22⋊C4—342no—
1131C22⋊C4—342no—
1132C22⋊C4—342no—
1133C22⋊C4—342no—
1134C22⋊C4—342no—
1135C22⋊C4—681no—
1136C22⋊C4—681no—
1137C22⋊C4—681no—
1138C22⋊C4—681no—
1139C22⋊C4—681no—
1140C22⋊C4—681no—
1141C42—41no—
1142C42—41no—
1143C42—41no—
1144C42—342no—
1145C42—681no—
1146C42—681no—
1147C42—681no—
1148C42—681no—
1149C42—681no—
1150C42—681no—
1151C42—681no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—172no—
1160C23—172no—
1161C23—172no—
1162C23—341no—
1163C23—341no—
1164C23—341no—
1165C23—341no—
1166C23C24×D1711yescharacteristic
1167Q8—1362no—
1168Q8—1362no—
1169Q8—1362no—
1170D4—684no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
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—172no—
1212C2×C4—341no—
1213C2×C4—341no—
1214C2×C4—341no—
1215C2×C4—341no—
1216C2×C4—341no—
1217C2×C4—341no—
1218C2×C4—341no—
1219C2×C4—341no—
1220C2×C4—341no—
1221C2×C4—341no—
1222C2×C4—341no—
1223C2×C4—341no—
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—684no—
1257C2×C4—684no—
1258C2×C4—684no—
1259C2×C4—684no—
1260C2×C4—684no—
1261C2×C4—1362no—
1262C2×C4—1362no—
1263C2×C4—1362no—
1264C2×C4#41×D1712yes—
1265C2×C4#1058769712yes—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—174no—
1274C22—342no—
1275C22—342no—
1276C22—342no—
1277C22—342no—
1278C22—342no—
1279C22—342no—
1280C22C2×#41×D1711yescharacteristic
1281C22H(5,𝔽2)×D1711yescharacteristic
1282C222−1+4×D1711yescharacteristic
1283C22C2×#1058769711yescharacteristic
1284C22#1176364411yescharacteristic
1285C22#1176364511yescharacteristic
1286C22#1176364611yescharacteristic
1287C4—22no—
1288C4—22no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—342no—
1302C4—681no—
1303C4—681no—
1304C4—681no—
1305C4—681no—
1306C4—681no—
1307C4—681no—
1308C4—681no—
1309C4—681no—
1310C4—681no—
1311C4—681no—
1312C4—681no—
1313C4—681no—
1314C4—681no—
1315C4—681no—
1316C2—81no—
1317C2—344no—
1318C2D17×#54211yescharacteristic
1319C2#1454247911yescharacteristic
1320C2#1454264111yescharacteristic
1321C2#1454294411yescharacteristic
1322C2#1454299011yescharacteristic
1323C2#1454339111yescharacteristic
1324C2#1454339911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2773C2
prime radicalC22×C22⋊D17C23
hypercenter#2773D17
hypocenterC17#36999
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2773

Complements

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

NH ≅ G/Ntype
1. #14537122C2semidirect
3. #14536666C2semidirect
4. #14536662C2semidirect
5. #14536343C2semidirect
6. #14536254C2semidirect
7. #14536246C2semidirect
8. #14536238C2semidirect
9. #14536182C2semidirect
10. #14536154C2semidirect
11. #14536129C2semidirect
12. #14536092C2semidirect
13. #14536069C2semidirect
14. #14535988C2semidirect
15. #14535947C2semidirect
16. #14535910C2semidirect
17. #14535860C2semidirect
18. #14534602C2semidirect
21. #14533794C2semidirect
22. #14533266C2semidirect
23. #14533176C2semidirect
24. #14533170C2semidirect
28. #14531513C2semidirect
30. D17×#387C2semidirect
31. C17×#2773C2semidirect
609. #2773D17semidirect
1013. C17#36999semidirect

Maximal subgroups

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

subgroupindex
#145371222
#145371042
#145366662
#145366622
#145363432
#145362542
#145362462
#145362382
#145361822
#145361542
#145361292
#145360922
#145360692
#145359882
#145359472
#145359102
#145358602
#145346022
#145345692
#145339592
#145337942
#145332662
#145331762
#145331702
#145331132
#145331092
#145330852
#145315132
#145314142
D17×#3872
C17×#27732
#3699917