Finite Group Databasebeta

← #17194635

Subgroups — #17194635

Order 4352.

3246 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763319C211yesmaximal, characteristic
2C2×#11763288C211yesmaximal, characteristic, complemented
3C2×#117×D17C211yesmaximal, characteristic, complemented
4#14531779C212yesmaximal, complemented
5#14531775C212yesmaximal, complemented
6#14531767C212yesmaximal, complemented
7#14531765C212yesmaximal, complemented
8#14531732C212yesmaximal, complemented
9#14531712C212yesmaximal, complemented
10#14531711C212yesmaximal, complemented
11#14531682C212yesmaximal, complemented
12#14531479C211yesmaximal, characteristic, complemented
13#14531466C211yesmaximal, characteristic, complemented
14#14531462C211yesmaximal, characteristic, complemented
15#14531406C211yesmaximal, characteristic, complemented
16#14531374C211yesmaximal, characteristic, complemented
17C4×#10587583C211yesmaximal, characteristic, complemented
18#14531314C211yesmaximal, characteristic, complemented
19#14531300C211yesmaximal, characteristic, complemented
20C4×#10587624C211yesmaximal, characteristic, complemented
21D17×#380C211yesmaximal, characteristic, complemented
22#14531138C211yesmaximal, characteristic, complemented
23C17×#2324C211yesmaximal, characteristic, complemented
24C22×#63254C2211yescharacteristic
25C23×C4×D17C2211yescharacteristic
26#11763319C4116yescomplemented
27C2×#10587569C2212yes—
28C2×#10587583C2211yescharacteristic
29C2×#10587610C2211yescharacteristic
30C2×#10587624C2211yescharacteristic
31C2×#10587623C2212yes—
32#11763288—28no—
33C2×C4×Dic34C2211yescharacteristic, complemented
34C2×#10587573C2211yescharacteristic, complemented
35C2×D4×Dic17C2212yes—
36C2×D4×Dic17C2211yescharacteristic, complemented
37C2×C4×C22⋊D17C2212yes—
38C2×C4×C22⋊D17C2212yes—
39C2×#10587567C2212yes—
40C2×#10587567C2212yes—
41C2×#10587567C2212yes—
42C2×#10587612C2211yescharacteristic
43C2×#10587578C2211yescharacteristic
44C2×#10587578C2211yescharacteristic
45C2×#10587578C2211yescharacteristic
46C2×#10587558C2211yescharacteristic
47C2×#10587558C2211yescharacteristic
48C2×#10587563C2211yescharacteristic
49C2×#10587563C2211yescharacteristic
50C2×#10587563C2212yescomplemented
51#117×D17—28no—
52C22×#63225C2212yescomplemented
53C2×C4⋊C4×D17C2211yescharacteristic
54C2×C4⋊C4×D17C2211yescharacteristic
55C2×C4⋊C4×D17C2211yescharacteristic
56C2×C4⋊C4×D17C2211yescharacteristic
57C2×C22⋊C4×D17C2211yescharacteristic
58C2×C22⋊C4×D17C2211yescharacteristic
59C2×C22⋊C4×D17C2212yes—
60C2×C42×D17C2211yescharacteristic
61C2×C42×D17C2211yescharacteristic
62#11762715C2211yescharacteristic, complemented
63#11762714C2211yescharacteristic, complemented
64#11762712C2212yes—
65#11762712C2211yescharacteristic, complemented
66#11762708C2211yescharacteristic, complemented
67#11762707C2211yescharacteristic, complemented
68#11762706C2212yescomplemented
69#11762705C2211yescharacteristic, complemented
70#11762704C2212yescomplemented
71#11762703C2212yes—
72#11762703C2212yes—
73#11762703C2212yescomplemented
74#11762702C2212yescomplemented
75#11762697C2212yes—
76#11762697C2212yes—
77#11762697C2212yescomplemented
78#11762696C2212yescomplemented
79#11762694C2212yescomplemented
80#11762692C2212yescomplemented
81#11762690C2212yescomplemented
82#11762689C2212yes—
83#11762685C2212yes—
84#11762685C2212yes—
85#11762685C2212yes—
86#11762685C2212yes—
87#11762684C2212yescomplemented
88#11762683C2212yes—
89#11762683C2212yes—
90#11762680C2212yes—
91#11762680C2212yes—
92#11762678C2212yescomplemented
93#11762673C2212yescomplemented
94#11762669C2211yescharacteristic
95#11762668C2212yes—
96#11762667C2212yes—
97#11762667C2212yescomplemented
98#11762667C2212yescomplemented
99#11762666C2211yescharacteristic
100#11762666C2211yescharacteristic
101C4⋊C4×Dic17C2211yescharacteristic, complemented
102C4⋊C4×Dic17C2211yescharacteristic, complemented
103C4⋊C4×Dic17C2212yescomplemented
104C4×#63225C2212yescomplemented
105C4×C4⋊Dic17C2211yescharacteristic, complemented
106C4×C4⋊Dic17C2212yescomplemented
107#11762660C2212yescomplemented
108C22⋊C4×Dic17C2212yescomplemented
109C4×#63227C2212yes—
110C4×#63227C2212yes—
111C4×C22⋊Dic17C2212yescomplemented
112#11762656C2212yes—
113#11762656C2212yes—
114#95×D17C2212yes—
115C2×C17×#121C2211yescharacteristic
116C2×C4×D4×C17C2211yescharacteristic, complemented
117C2×C17×#117C2211yescharacteristic
118C17×#390C2212yes—
119C17×#390C2211yescharacteristic, complemented
120C17×#389C2211yescharacteristic, complemented
121C17×#388C2212yescomplemented
122C17×#386C2212yes—
123C17×#385C2212yescomplemented
124C17×#380C2211yescharacteristic
125C4×C4⋊C4×C17C2211yescharacteristic, complemented
126C24×D17C2311yescharacteristic
127C22×D4×C17C2311yescharacteristic
128C22×D4×C17C2312yes—
129C23×C4×C17C2311yescharacteristic
130C23×C4×C17C2312yes—
131C22×C22⋊D17C2312yes—
132C22×C22⋊D17C2312yes—
133C23×Dic17C2312yes—
134C23×Dic17C2311yescharacteristic
135C23×Dic17C2312yes—
136C2×#63254—24no—
137C2×#63254—24no—
138C2×#63254C2×C418yescomplemented
139C22×C4×D17—24no—
140C22×C4×D17—24no—
141C22×C4×D17C2×C418yescomplemented
142C22×C4×D17C2311yescharacteristic
143C22×C4×D17C2311yescharacteristic
144C22×C4×D17C2311yescharacteristic
145C22×C4×D17C2311yescharacteristic
146C22×C4×D17C2311yescharacteristic
147C22×C4×D17C2311yescharacteristic
148C22×C4×D17C2311yescharacteristic
149C22×C4×D17C2312yes—
150C22×C4×D17C2312yes—
151C22×C4×D17C2311yescharacteristic
152C22×Dic34C2311yescharacteristic
153C17×#121C2×C418yescomplemented
154C4×D4×C17—24no—
155C17×#117—24no—
156C2×C4⋊C4×C17C2311yescharacteristic
157C2×C4⋊C4×C17C2311yescharacteristic
158C2×C4⋊C4×C17C2311yescharacteristic
159C2×C4⋊C4×C17C2311yescharacteristic
160C2×C4⋊C4×C17C2312yes—
161C2×C4⋊C4×C17C2311yescharacteristic
162C2×C22⋊C4×C17C2311yescharacteristic
163C2×C22⋊C4×C17C2312yes—
164C2×C22⋊C4×C17C2311yescharacteristic
165C2×C22⋊C4×C17C2312yes—
166C2×C22⋊C4×C17C2312yes—
167C2×C22⋊C4×C17C2312yes—
168C2×C22⋊C4×C17C2312yes—
169C2×C42×C17C2311yescharacteristic
170C2×C42×C17C2312yes—
171C2×C42×C17C2311yescharacteristic
172C2×C22⋊Dic17C2311yescharacteristic
173C2×C22⋊Dic17C2312yes—
174C2×C22⋊Dic17C2311yescharacteristic
175C2×C22⋊Dic17C2312yes—
176C2×C22⋊Dic17C2312yes—
177C2×C22⋊Dic17C2312yes—
178C2×C22⋊Dic17C2312yes—
179C2×C22⋊Dic17C2312yes—
180#10587624C2×C418yescomplemented
181#10587623C2×C4116yescomplemented
182D4×Dic17—24no—
183D4×Dic17C2×C4116yescomplemented
184C4×C22⋊D17—28no—
185C4×C22⋊D17—44no—
186C2×#63227C2311yescharacteristic
187C2×#63227C2311yescharacteristic
188C2×#63227C2312yes—
189C2×#63227C2312yes—
190C2×#63227C2312yes—
191C2×#63227C2312yes—
192C2×#63227C2311yescharacteristic
193C2×#63227C2311yescharacteristic
194#10587612—24no—
195C2×C4⋊Dic17C2311yescharacteristic
196C2×C4⋊Dic17C2311yescharacteristic
197C2×C4⋊Dic17C2311yescharacteristic
198C2×C4⋊Dic17C2311yescharacteristic
199C2×C4⋊Dic17C2312yes—
200C2×C4⋊Dic17C2312yes—
201C2×C4⋊Dic17C2311yescharacteristic
202#10587610C2×C418yescomplemented
203C2×#63225—28no—
204C2×#63225C2312yes—
205C2×#63225C2312yes—
206C2×#63225C2312yes—
207C2×#63225C2311yescharacteristic
208C2×#63225C2311yescharacteristic
209C2×#63225C2312yes—
210C2×#63225C2312yes—
211C2×#63225C2312yes—
212C2×#63225C2312yes—
213C2×#63225C2311yescharacteristic
214C2×#63225C2311yescharacteristic
215C2×C4×Dic17C2312yes—
216C2×C4×Dic17C2311yescharacteristic
217C2×C4×Dic17C2311yescharacteristic
218C2×C4×Dic17C2312yes—
219C2×C4×Dic17C2311yescharacteristic
220C2×C4×Dic17C2311yescharacteristic
221C2×C4×Dic17C2311yescharacteristic
222C2×C4×Dic17C2312yes—
223C2×C4×Dic17C2312yes—
224C2×C4×Dic17C2312yes—
225C2×C4×Dic17C2312yes—
226C2×C4×Dic17C2311yescharacteristic
227#10587583C2×C418yescomplemented
228#10587578—24no—
229#10587578—24no—
230#10587578C2×C418yescomplemented
231C4⋊C4×D17—24no—
232C4⋊C4×D17—24no—
233C4⋊C4×D17—24no—
234C4⋊C4×D17—24no—
235#10587573—24no—
236#10587569C2×C4116yescomplemented
237#10587567—28no—
238#10587567—44no—
239#10587567C2×C4116yescomplemented
240C22⋊C4×D17—24no—
241C22⋊C4×D17—24no—
242C22⋊C4×D17—44no—
243#10587563—24no—
244#10587563—24no—
245#10587563—28no—
246#10587558—24no—
247#10587558D418yescomplemented
248C42×D17—24no—
249C42×D17—24no—
250C4×Dic34—24no—
251C17×#95C2312yes—
252C17×#95C2312yes—
253C17×#95C2312yes—
254#10587502C2312yes—
255#10587502C2312yes—
256#10587502C2312yes—
257#10587502C2312yes—
258#10587502C2312yes—
259#10587502C2312yes—
260#10587502C2312yes—
261#10587502C2312yes—
262#10587502C2312yes—
263#10587502C2312yes—
264#10587502C2312yes—
265#10587502C2312yes—
266#10587502C2312yes—
267C24×C17C2412yes—
268C24×C17C2411yescharacteristic
269C23×D17—22no—
270C23×D17—22no—
271C23×D17—22no—
272C23×D17—22no—
273C23×D17—41no—
274C23×D17—41no—
275C23×D17C22×C414yes—
276C23×D17C2411yescharacteristic
277C23×D17C2411yescharacteristic
278C2×D4×C17—22no—
279C2×D4×C17—22no—
280C2×D4×C17—42no—
281C2×D4×C17—42no—
282C2×D4×C17C22×C414yes—
283C2×D4×C17C22×C418yes—
284C22×C4×C17—22no—
285C22×C4×C17—22no—
286C22×C4×C17—24no—
287C22×C4×C17—42no—
288C22×C4×C17—42no—
289C22×C4×C17C22×C414yes—
290C22×C4×C17C2412yes—
291C22×C4×C17C2411yescharacteristic
292C22×C4×C17C2412yes—
293C22×C4×C17C2411yescharacteristic
294C22×C4×C17C2411yescharacteristic
295C22×C4×C17C2412yes—
296C22×C4×C17C2411yescharacteristic
297C22×C4×C17C2411yescharacteristic
298C22×C4×C17C2411yescharacteristic
299C2×C22⋊D17—24no—
300C2×C22⋊D17—24no—
301C2×C22⋊D17—24no—
302C2×C22⋊D17—24no—
303C2×C22⋊D17C22×C418yes—
304C2×C22⋊D17C22×C418yes—
305C22×Dic17—22no—
306C22×Dic17—24no—
307C22×Dic17—22no—
308C22×Dic17—24no—
309C22×Dic17—24no—
310C22×Dic17—42no—
311C22×Dic17—42no—
312C22×Dic17C22×C414yes—
313C22×Dic17C22×C418yes—
314C22×Dic17C2412yes—
315C22×Dic17C2411yescharacteristic
316C22×Dic17C2412yes—
317C22×Dic17C2411yescharacteristic
318C22×Dic17C2412yes—
319C22×Dic17C2411yescharacteristic
320C22×Dic17C2412yes—
321C22×Dic17C2411yescharacteristic
322C22×Dic17C2411yescharacteristic
323C22×Dic17C2411yescharacteristic
324#63254—232no—
325C2×C4×D17—22no—
326C2×C4×D17—22no—
327C2×C4×D17—22no—
328C2×C4×D17—22no—
329C2×C4×D17—22no—
330C2×C4×D17—22no—
331C2×C4×D17—232no—
332C2×C4×D17—22no—
333C2×C4×D17—22no—
334C2×C4×D17—22no—
335C2×C4×D17—22no—
336C2×C4×D17—22no—
337C2×C4×D17—22no—
338C2×C4×D17—22no—
339C2×C4×D17—22no—
340C2×C4×D17—24no—
341C2×C4×D17—24no—
342C2×C4×D17—41no—
343C2×C4×D17—41no—
344C2×C4×D17—41no—
345C2×C4×D17—41no—
346C2×C4×D17—42no—
347C2×C4×D17—42no—
348C2×C4×D17—42no—
349C2×C4×D17—42no—
350C2×C4×D17C22×C414yes—
351C2×C4×D17C22×C414yes—
352C2×C4×D17C22×C414yes—
353C2×C4×D17C22×C414yes—
354C2×C4×D17C2×D414yes—
355C2×C4×D17#4114yes—
356C2×Dic34—22no—
357C2×Dic34—22no—
358C2×Dic34C22×C414yes—
359C4⋊C4×C17—22no—
360C4⋊C4×C17—22no—
361C4⋊C4×C17—22no—
362C4⋊C4×C17—22no—
363C4⋊C4×C17—42no—
364C4⋊C4×C17C22×C414yes—
365C22⋊C4×C17—22no—
366C22⋊C4×C17—22no—
367C22⋊C4×C17—24no—
368C22⋊C4×C17—42no—
369C22⋊C4×C17—42no—
370C22⋊C4×C17—42no—
371C22⋊C4×C17C22×C418yes—
372C42×C17—22no—
373C42×C17—42no—
374C42×C17C2×D414yes—
375C22⋊Dic17—22no—
376C22⋊Dic17—22no—
377C22⋊Dic17—24no—
378C22⋊Dic17—42no—
379C22⋊Dic17—42no—
380C22⋊Dic17—42no—
381C22⋊Dic17C22×C418yes—
382C22⋊Dic17C22×C418yes—
383#63227—22no—
384#63227—22no—
385#63227—24no—
386#63227—24no—
387#63227C22×C418yes—
388#63227C22×C418yes—
389#63227C2×D414yes—
390#63227C2×D414yes—
391C4⋊Dic17—22no—
392C4⋊Dic17—22no—
393C4⋊Dic17—22no—
394C4⋊Dic17—22no—
395C4⋊Dic17—42no—
396C4⋊Dic17C22×C418yes—
397C4⋊Dic17C22×C414yes—
398#63225—24no—
399#63225—22no—
400#63225—22no—
401#63225—24no—
402#63225—24no—
403#63225—24no—
404#63225—42no—
405#63225—42no—
406#63225C22×C418yes—
407#63225C2×D414yes—
408#63225C2×D414yes—
409C4×Dic17—24no—
410C4×Dic17—22no—
411C4×Dic17—22no—
412C4×Dic17—22no—
413C4×Dic17—22no—
414C4×Dic17—22no—
415C4×Dic17—24no—
416C4×Dic17—42no—
417C4×Dic17—42no—
418C4×Dic17—42no—
419C4×Dic17C22×C418yes—
420C4×Dic17C2×D414yes—
421#34202—171nomaximal, Sylow
422C23×C17—21no—
423C23×C17—22no—
424C23×C17—22no—
425C23×C17—21no—
426C23×C17—21no—
427C23×C17—22no—
428C23×C17—22no—
429C23×C17—21no—
430C23×C17—22no—
431C23×C17—22no—
432C23×C17—21no—
433C23×C17—21no—
434C23×C17C23×C412yes—
435C23×C17C23×C414yes—
436C23×C17C2511yescharacteristic
437C22×D17—21no—
438C22×D17—21no—
439C22×D17—21no—
440C22×D17—21no—
441C22×D17—21no—
442C22×D17—21no—
443C22×D17—21no—
444C22×D17—21no—
445C22×D17—28no—
446C22×D17—28no—
447C22×D17—44no—
448C22×D17—44no—
449C22×D17—44no—
450C22×D17—44no—
451C22×D17—44no—
452C22×D17C23×C412yes—
453C22×D17C23×C412yes—
454C22×D17C22×D412yes—
455C22×D17C2×#4112yes—
456C22×D17H(5,𝔽2)12yes—
457C22×D172−1+412yes—
458D4×C17—28no—
459D4×C17—48no—
460C2×C4×C17—21no—
461C2×C4×C17—21no—
462C2×C4×C17—21no—
463C2×C4×C17—21no—
464C2×C4×C17—21no—
465C2×C4×C17—22no—
466C2×C4×C17—22no—
467C2×C4×C17—21no—
468C2×C4×C17—28no—
469C2×C4×C17—21no—
470C2×C4×C17—21no—
471C2×C4×C17—22no—
472C2×C4×C17—22no—
473C2×C4×C17—21no—
474C2×C4×C17—22no—
475C2×C4×C17—22no—
476C2×C4×C17—21no—
477C2×C4×C17—22no—
478C2×C4×C17—21no—
479C2×C4×C17—21no—
480C2×C4×C17—22no—
481C2×C4×C17—84no—
482C2×C4×C17C23×C412yes—
483C2×C4×C17C23×C414yes—
484C2×C4×C17C23×C412yes—
485C2×C4×C17C22×D412yes—
486C2×C4×C17C22×D412yes—
487C2×C4×C17C22×D412yes—
488C2×C4×C17C2×#4112yes—
489C22⋊D17—216no—
490C22⋊D17—216no—
491C2×Dic17—22no—
492C2×Dic17—21no—
493C2×Dic17—22no—
494C2×Dic17—21no—
495C2×Dic17—21no—
496C2×Dic17—22no—
497C2×Dic17—21no—
498C2×Dic17—22no—
499C2×Dic17—21no—
500C2×Dic17—21no—
501C2×Dic17—28no—
502C2×Dic17—216no—
503C2×Dic17—22no—
504C2×Dic17—21no—
505C2×Dic17—21no—
506C2×Dic17—22no—
507C2×Dic17—21no—
508C2×Dic17—22no—
509C2×Dic17—22no—
510C2×Dic17—21no—
511C2×Dic17—21no—
512C2×Dic17—22no—
513C2×Dic17—22no—
514C2×Dic17—21no—
515C2×Dic17—84no—
516C2×Dic17C23×C412yes—
517C2×Dic17C23×C414yes—
518C2×Dic17C23×C414yes—
519C2×Dic17C23×C412yes—
520C2×Dic17C22×D412yes—
521C2×Dic17C22×D412yes—
522C2×Dic17C22×D412yes—
523C2×Dic17C2×#4112yes—
524C4×D17—28no—
525C4×D17—28no—
526C4×D17—28no—
527C4×D17—44no—
528C4×D17—44no—
529C4×D17—44no—
530C4×D17—44no—
531C4×D17—84no—
532C4×D17—84no—
533C4×D17C4×D4116yescomplemented
534Dic34—28no—
535C2×#525—171no—
536C2×#520—171no—
537C22×#117—171no—
538#2359—172no—
539#2359—172no—
540#2358—172no—
541#2358—172no—
542#2354—172no—
543#2352—172no—
544#2352—172no—
545D4×C4⋊C4—172no—
546#2324—171no—
547#2324D1711yescharacteristic, complemented
548#2323—171no—
549#2323—171no—
550#2317—171no—
551#2311—171no—
552C4×C22⋊Q8—171no—
553C4×C22⋊Q8—171no—
554C4×#121—171no—
555C4×#121—171no—
556C2×#380—171no—
557#2274—171no—
558C22×C17—24no—
559C22×C17—22no—
560C22×C17—24no—
561C22×C17—22no—
562C22×C17—22no—
563C22×C17—24no—
564C22×C17—42no—
565C22×C17—41no—
566C22×C17—41no—
567C22×C17—42no—
568C22×C17—41no—
569C22×C17—42no—
570C22×C17—41no—
571C22×C17—42no—
572C22×C17C24×C411yescharacteristic
573C22×C17C23×D411yescharacteristic
574C22×C17C22×#4111yescharacteristic
575C22×C17C2×H(5,𝔽2)11yescharacteristic
576C22×C17C2×2−1+411yescharacteristic
577C22×C17#58511yescharacteristic
578C22×C17#58511yescharacteristic
579C2×D17—22no—
580C2×D17—22no—
581C2×D17—22no—
582C2×D17—22no—
583C2×D17—22no—
584C2×D17—22no—
585C2×D17—22no—
586C2×D17—22no—
587C2×D17—22no—
588C2×D17—22no—
589C2×D17—22no—
590C2×D17—22no—
591C2×D17—416no—
592C2×D17C2×C4×D414yes—
593C2×D17#52014yescomplemented
594C4×C17—22no—
595C4×C17—24no—
596C4×C17—22no—
597C4×C17—22no—
598C4×C17—41no—
599C4×C17—42no—
600C4×C17—41no—
601C4×C17—42no—
602C4×C17C2×C4×D414yes—
603Dic17—24no—
604Dic17—22no—
605Dic17—24no—
606Dic17—22no—
607Dic17—22no—
608Dic17—41no—
609Dic17—42no—
610Dic17—41no—
611Dic17—42no—
612Dic17C2×C4×D414yes—
613C22×#41—171no—
614C24×C4—171no—
615#525—1716no—
616C2×#123—172no—
617C2×C22⋊Q8—171no—
618C2×C22⋊Q8—171no—
619C2×#121—171no—
620C2×#121C2×D1711yescharacteristic
621C2×#120—172no—
622#520—348no—
623C2×C4×Q8—171no—
624C2×C4×Q8—171no—
625C2×C4×D4—172no—
626C2×C4×D4—171no—
627C2×C4×D4—172no—
628C2×C4×D4—172no—
629C2×C4×D4—172no—
630C2×C4×D4—172no—
631C2×C4×D4—172no—
632C2×C4×D4C2×D1711yescharacteristic, complemented
633C2×#117—171no—
634C2×#117—171no—
635C2×#117—171no—
636C2×#117—171no—
637C2×#117—171no—
638C2×#117—172no—
639C2×#117—171no—
640C2×#117—171no—
641C2×#117—171no—
642C2×#117—348no—
643C2×#117C2×D1711yescharacteristic
644C22×C4⋊C4—172no—
645C22×C4⋊C4—171no—
646C22×C4⋊C4—171no—
647C22×C4⋊C4—171no—
648C22×C4⋊C4—171no—
649C22×C22⋊C4—171no—
650C22×C22⋊C4—171no—
651C22×C22⋊C4—172no—
652C22×C42—171no—
653C22×C42—171no—
654#391—171no—
655#391—171no—
656#390—171no—
657#390—172no—
658#390C2×D1712yes—
659#390C2×D1711yescharacteristic, complemented
660#389—171no—
661#389—171no—
662#389—172no—
663#389—171no—
664#389—172no—
665#389C2×D1711yescharacteristic, complemented
666#388—172no—
667#388—172no—
668#388—172no—
669#388—172no—
670#388—172no—
671#388—172no—
672#388—172no—
673#388C2×D1712yescomplemented
674#387—172no—
675#387—172no—
676#387—172no—
677#387—172no—
678#386—172no—
679#386—172no—
680#386—172no—
681#386—172no—
682#386—172no—
683#386C2×D1712yes—
684#385—172no—
685#385—172no—
686#385—172no—
687#385—172no—
688#385—172no—
689#385C2×D1712yescomplemented
690#384—172no—
691#382—172no—
692#380—171no—
693#380—171no—
694#380—171no—
695#380—172no—
696#380—172no—
697#380—172no—
698#380—172no—
699#380C2×D1711yescharacteristic
700C4×C4⋊C4—171no—
701C4×C4⋊C4—171no—
702C4×C4⋊C4—172no—
703C4×C4⋊C4—171no—
704C4×C4⋊C4—172no—
705C4×C4⋊C4—172no—
706C4×C4⋊C4—172no—
707C4×C4⋊C4C2×D1711yescharacteristic, complemented
708C4×C22⋊C4—172no—
709C4×C22⋊C4—172no—
710C4×C22⋊C4—172no—
711C4×C22⋊C4—172no—
712C4×C22⋊C4—172no—
713C4×C22⋊C4—172no—
714C2×#95—172no—
715C2×C17—42no—
716C2×C17—44no—
717C2×C17C22×C4×D411yescharacteristic
718C2×C17C2×#52011yescharacteristic
719C2×C17#342811yescharacteristic
720C2×C17#348811yescharacteristic
721C2×C17#348911yescharacteristic
722C2×C17#349411yescharacteristic
723C2×C17#349511yescharacteristic
724D17—24no—
725D17—24no—
726C25—171no—
727C2×#41—178no—
728C2×#41—344no—
729C2×#41—344no—
730C22×Q8—171no—
731C22×D4—172no—
732C22×D4—172no—
733C22×D4C22×D1711yescharacteristic
734C22×D4C22×D1712yes—
735C23×C4—171no—
736C23×C4—172no—
737C23×C4—171no—
738C23×C4—178no—
739C23×C4—171no—
740C23×C4—171no—
741C23×C4—171no—
742C23×C4—172no—
743C23×C4—171no—
744C23×C4—171no—
745C23×C4—171no—
746C23×C4—171no—
747C23×C4—172no—
748C23×C4—172no—
749C23×C4—344no—
750C23×C4—344no—
751C23×C4C22×D1711yescharacteristic
752C23×C4C22×D1712yes—
753#123—1716no—
754C22⋊Q8—178no—
755C22⋊Q8—178no—
756#121—178no—
757#121C4×D1718yescomplemented
758#120—1716no—
759C4×Q8—344no—
760C4×Q8—344no—
761C4×D4—24no—
762C4×D4—1716no—
763C4×D4—1716no—
764C4×D4—344no—
765C4×D4—348no—
766C4×D4—348no—
767C4×D4—684no—
768C4×D4—684no—
769#117—24no—
770#117—178no—
771#117—178no—
772#117—344no—
773#117—344no—
774#117—344no—
775#117—344no—
776#117—348no—
777#117—344no—
778#117—344no—
779C2×C4⋊C4—171no—
780C2×C4⋊C4—171no—
781C2×C4⋊C4—171no—
782C2×C4⋊C4—172no—
783C2×C4⋊C4—172no—
784C2×C4⋊C4—172no—
785C2×C4⋊C4—171no—
786C2×C4⋊C4—171no—
787C2×C4⋊C4—171no—
788C2×C4⋊C4—171no—
789C2×C4⋊C4—171no—
790C2×C4⋊C4—172no—
791C2×C4⋊C4—172no—
792C2×C4⋊C4—172no—
793C2×C4⋊C4—171no—
794C2×C4⋊C4—172no—
795C2×C4⋊C4—172no—
796C2×C4⋊C4—172no—
797C2×C4⋊C4—344no—
798C2×C4⋊C4—344no—
799C2×C4⋊C4—344no—
800C2×C4⋊C4—344no—
801C2×C4⋊C4—348no—
802C2×C4⋊C4C22×D1711yescharacteristic
803C2×C4⋊C4C22×D1711yescharacteristic
804C2×C4⋊C4C22×D1711yescharacteristic
805C2×C4⋊C4C22×D1711yescharacteristic
806C2×C4⋊C4C22×D1712yes—
807C2×C4⋊C4C22×D1711yescharacteristic
808C2×C22⋊C4—172no—
809C2×C22⋊C4—172no—
810C2×C22⋊C4—171no—
811C2×C22⋊C4—171no—
812C2×C22⋊C4—172no—
813C2×C22⋊C4—172no—
814C2×C22⋊C4—171no—
815C2×C22⋊C4—171no—
816C2×C22⋊C4—172no—
817C2×C22⋊C4—171no—
818C2×C22⋊C4—171no—
819C2×C22⋊C4—172no—
820C2×C22⋊C4—172no—
821C2×C22⋊C4—172no—
822C2×C22⋊C4—172no—
823C2×C22⋊C4—172no—
824C2×C22⋊C4—344no—
825C2×C22⋊C4—344no—
826C2×C22⋊C4—684no—
827C2×C22⋊C4C22×D1711yescharacteristic
828C2×C22⋊C4C22×D1711yescharacteristic
829C2×C22⋊C4C22×D1712yes—
830C2×C22⋊C4C22×D1712yes—
831C2×C22⋊C4C22×D1712yes—
832C2×C22⋊C4C22×D1712yes—
833C2×C22⋊C4C22×D1712yes—
834C2×C42—171no—
835C2×C42—172no—
836C2×C42—171no—
837C2×C42—171no—
838C2×C42—171no—
839C2×C42—171no—
840C2×C42—171no—
841C2×C42—172no—
842C2×C42—172no—
843C2×C42—172no—
844C2×C42—172no—
845C2×C42—172no—
846C2×C42—344no—
847C2×C42—344no—
848C2×C42C22×D1711yescharacteristic
849C2×C42C22×D1712yes—
850C2×C42C22×D1711yescharacteristic
851#95—172no—
852#95—172no—
853#95—172no—
854#95—172no—
855#95—172no—
856#95—172no—
857#95—172no—
858#95—172no—
859#95—172no—
860#95—172no—
861#95—172no—
862#95—172no—
863#95—172no—
864#95C22×D1712yes—
865#95C22×D1712yes—
866#95C22×D1712yes—
867C17#3420211yescharacteristic, complemented, Sylow
868C24—171no—
869C24—171no—
870C24—174no—
871C24—342no—
872C24—342no—
873C24—342no—
874C24—342no—
875C24—681no—
876C24—681no—
877C24C23×D1711yescharacteristic
878C24C23×D1712yes—
879#41—3432no—
880C2×Q8—174no—
881C2×Q8—342no—
882C2×Q8—342no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—178no—
888C2×D4—178no—
889C2×D4—344no—
890C2×D4—344no—
891C2×D4—344no—
892C2×D4—344no—
893C2×D4C2×C4×D1714yes—
894C2×D4C2×C4×D1718yes—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—24no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—171no—
901C22×C4—174no—
902C22×C4—174no—
903C22×C4—174no—
904C22×C4—174no—
905C22×C4—178no—
906C22×C4—171no—
907C22×C4—172no—
908C22×C4—172no—
909C22×C4—171no—
910C22×C4—171no—
911C22×C4—174no—
912C22×C4—174no—
913C22×C4—174no—
914C22×C4—171no—
915C22×C4—172no—
916C22×C4—172no—
917C22×C4—171no—
918C22×C4—342no—
919C22×C4—342no—
920C22×C4—3432no—
921C22×C4—342no—
922C22×C4—342no—
923C22×C4—342no—
924C22×C4—342no—
925C22×C4—342no—
926C22×C4—342no—
927C22×C4—342no—
928C22×C4—342no—
929C22×C4—344no—
930C22×C4—344no—
931C22×C4—344no—
932C22×C4—342no—
933C22×C4—342no—
934C22×C4—344no—
935C22×C4—344no—
936C22×C4—342no—
937C22×C4—342no—
938C22×C4—342no—
939C22×C4—342no—
940C22×C4—681no—
941C22×C4—681no—
942C22×C4—681no—
943C22×C4—681no—
944C22×C4—682no—
945C22×C4—682no—
946C22×C4—682no—
947C22×C4—682no—
948C22×C4—682no—
949C22×C4—682no—
950C22×C4C2×C4×D1714yes—
951C22×C4C23×D1711yescharacteristic
952C22×C4C23×D1712yes—
953C22×C4C23×D1712yes—
954C22×C4C23×D1711yescharacteristic
955C22×C4C23×D1712yes—
956C22×C4C23×D1711yescharacteristic
957C22×C4C23×D1711yescharacteristic
958C22×C4C23×D1711yescharacteristic
959C22×C4C23×D1711yescharacteristic
960C4⋊C4—22no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—42no—
965C4⋊C4—174no—
966C4⋊C4—178no—
967C4⋊C4—178no—
968C4⋊C4—174no—
969C4⋊C4—174no—
970C4⋊C4—344no—
971C4⋊C4—342no—
972C4⋊C4—342no—
973C4⋊C4—342no—
974C4⋊C4—342no—
975C4⋊C4—344no—
976C4⋊C4—344no—
977C4⋊C4—344no—
978C4⋊C4—342no—
979C4⋊C4—342no—
980C4⋊C4—682no—
981C4⋊C4—682no—
982C4⋊C4—682no—
983C4⋊C4C2×C4×D1714yes—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—24no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—178no—
991C22⋊C4—178no—
992C22⋊C4—178no—
993C22⋊C4—178no—
994C22⋊C4—174no—
995C22⋊C4—174no—
996C22⋊C4—342no—
997C22⋊C4—342no—
998C22⋊C4—344no—
999C22⋊C4—344no—
1000C22⋊C4—342no—
1001C22⋊C4—342no—
1002C22⋊C4—344no—
1003C22⋊C4—682no—
1004C22⋊C4—682no—
1005C22⋊C4—682no—
1006C22⋊C4C2×C4×D1718yes—
1007C42—22no—
1008C42—42no—
1009C42—178no—
1010C42—174no—
1011C42—342no—
1012C42—342no—
1013C42—344no—
1014C42—342no—
1015C42—342no—
1016C42—342no—
1017C42—344no—
1018C42—682no—
1019C42—682no—
1020C42—682no—
1021C42D4×D1714yes—
1022C23—21no—
1023C23—22no—
1024C23—21no—
1025C23—22no—
1026C23—21no—
1027C23—22no—
1028C23—22no—
1029C23—21no—
1030C23—22no—
1031C23—22no—
1032C23—21no—
1033C23—21no—
1034C23—172no—
1035C23—172no—
1036C23—172no—
1037C23—172no—
1038C23—172no—
1039C23—172no—
1040C23—348no—
1041C23—348no—
1042C23—341no—
1043C23—341no—
1044C23—341no—
1045C23—341no—
1046C23—341no—
1047C23—341no—
1048C23—341no—
1049C23—341no—
1050C23—684no—
1051C23—684no—
1052C23—684no—
1053C23—684no—
1054C23—684no—
1055C23C22×C4×D1712yes—
1056C23C22×C4×D1714yes—
1057C23C24×D1711yescharacteristic
1058Q8—348no—
1059D4—28no—
1060D4—48no—
1061D4—3416no—
1062D4—3416no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—28no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—84no—
1085C2×C4—172no—
1086C2×C4—172no—
1087C2×C4—172no—
1088C2×C4—1716no—
1089C2×C4—174no—
1090C2×C4—172no—
1091C2×C4—174no—
1092C2×C4—172no—
1093C2×C4—172no—
1094C2×C4—348no—
1095C2×C4—348no—
1096C2×C4—348no—
1097C2×C4—3416no—
1098C2×C4—341no—
1099C2×C4—342no—
1100C2×C4—341no—
1101C2×C4—342no—
1102C2×C4—342no—
1103C2×C4—341no—
1104C2×C4—341no—
1105C2×C4—342no—
1106C2×C4—341no—
1107C2×C4—341no—
1108C2×C4—348no—
1109C2×C4—341no—
1110C2×C4—341no—
1111C2×C4—342no—
1112C2×C4—342no—
1113C2×C4—342no—
1114C2×C4—342no—
1115C2×C4—341no—
1116C2×C4—341no—
1117C2×C4—342no—
1118C2×C4—341no—
1119C2×C4—341no—
1120C2×C4—342no—
1121C2×C4—684no—
1122C2×C4—684no—
1123C2×C4—684no—
1124C2×C4—684no—
1125C2×C4—1364no—
1126C2×C4—1364no—
1127C2×C4—1364no—
1128C2×C4C22×C4×D1714yes—
1129C2×C4C22×C4×D1712yes—
1130C2×C4C22×C4×D1712yes—
1131C2×C4C2×D4×D1712yes—
1132C2×C4C2×D4×D1712yes—
1133C2×C4C2×D4×D1712yes—
1134C2×C4#41×D1712yes—
1135C22—22no—
1136C22—24no—
1137C22—24no—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—42no—
1142C22—41no—
1143C22—41no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—42no—
1149C22—174no—
1150C22—174no—
1151C22—342no—
1152C22—342no—
1153C22—342no—
1154C22—342no—
1155C22—342no—
1156C22—342no—
1157C22—342no—
1158C22—342no—
1159C22—342no—
1160C22—342no—
1161C22—342no—
1162C22—342no—
1163C22—6816no—
1164C22C23×C4×D1711yescharacteristic
1165C22C22×D4×D1711yescharacteristic
1166C22C2×#41×D1711yescharacteristic
1167C22H(5,𝔽2)×D1711yescharacteristic
1168C222−1+4×D1711yescharacteristic
1169C22#1176364411yescharacteristic
1170C22#1176364411yescharacteristic
1171C4—22no—
1172C4—22no—
1173C4—22no—
1174C4—24no—
1175C4—42no—
1176C4—41no—
1177C4—41no—
1178C4—42no—
1179C4—174no—
1180C4—342no—
1181C4—342no—
1182C4—342no—
1183C4—344no—
1184C4—344no—
1185C4—681no—
1186C4—682no—
1187C4—681no—
1188C4—682no—
1189C4C4×D4×D1714yes—
1190C2—42no—
1191C2—44no—
1192C2—344no—
1193C2—344no—
1194C2C2×C4×D4×D1711yescharacteristic
1195C2D17×#52011yescharacteristic
1196C2#1454198211yescharacteristic
1197C2#1454245111yescharacteristic
1198C2#1454245911yescharacteristic
1199C2#1454251111yescharacteristic
1200C2#1454253411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2324C2
socle, cosocleC23×C17C25
prime radicalC2×#11763319C2
hypercenter#2324D17
hypocenterC17#34202
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×#11763288C2semidirect
3. C2×#117×D17C2semidirect
4. #14531779C2semidirect
5. #14531775C2semidirect
6. #14531767C2semidirect
7. #14531765C2semidirect
8. #14531732C2semidirect
9. #14531712C2semidirect
10. #14531711C2semidirect
11. #14531682C2semidirect
12. #14531479C2semidirect
13. #14531466C2semidirect
14. #14531462C2semidirect
15. #14531406C2semidirect
16. #14531374C2semidirect
17. C4×#10587583C2semidirect
18. #14531314C2semidirect
19. #14531300C2semidirect
20. C4×#10587624C2semidirect
21. D17×#380C2semidirect
22. #14531138C2semidirect
23. C17×#2324C2semidirect
26. #11763319C4semidirect
33. C2×C4×Dic34C22semidirect
34. C2×#10587573C22semidirect
36. C2×D4×Dic17C22semidirect
50. C2×#10587563C22semidirect
52. C22×#63225C22semidirect
62. #11762715C22semidirect
63. #11762714C22semidirect
65. #11762712C22semidirect
66. #11762708C22semidirect
67. #11762707C22semidirect
68. #11762706C22semidirect
69. #11762705C22semidirect
70. #11762704C22semidirect
73. #11762703C22semidirect
74. #11762702C22semidirect
77. #11762697C22semidirect
78. #11762696C22semidirect
79. #11762694C22semidirect
80. #11762692C22semidirect
81. #11762690C22semidirect
87. #11762684C22semidirect
92. #11762678C22semidirect
93. #11762673C22semidirect
97. #11762667C22semidirect
98. #11762667C22semidirect
101. C4⋊C4×Dic17C22semidirect
102. C4⋊C4×Dic17C22semidirect
103. C4⋊C4×Dic17C22semidirect
104. C4×#63225C22semidirect
105. C4×C4⋊Dic17C22semidirect
106. C4×C4⋊Dic17C22semidirect
107. #11762660C22semidirect
108. C22⋊C4×Dic17C22semidirect
111. C4×C22⋊Dic17C22semidirect
116. C2×C4×D4×C17C22semidirect
119. C17×#390C22semidirect
120. C17×#389C22semidirect
121. C17×#388C22semidirect
123. C17×#385C22semidirect
125. C4×C4⋊C4×C17C22semidirect
138. C2×#63254C2×C4semidirect
141. C22×C4×D17C2×C4semidirect
153. C17×#121C2×C4semidirect
180. #10587624C2×C4semidirect
181. #10587623C2×C4semidirect
183. D4×Dic17C2×C4semidirect
202. #10587610C2×C4semidirect
227. #10587583C2×C4semidirect
230. #10587578C2×C4semidirect
236. #10587569C2×C4semidirect
239. #10587567C2×C4semidirect
247. #10587558D4semidirect
533. C4×D17C4×D4semidirect
547. #2324D17semidirect
593. C2×D17#520semidirect
632. C2×C4×D4C2×D17semidirect
659. #390C2×D17semidirect
665. #389C2×D17semidirect
673. #388C2×D17semidirect
689. #385C2×D17semidirect
707. C4×C4⋊C4C2×D17semidirect
757. #121C4×D17semidirect
867. C17#34202semidirect

Maximal subgroups

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

subgroupindex
C2×#117633192
C2×#117632882
C2×#117×D172
#145317792
#145317752
#145317672
#145317652
#145317322
#145317122
#145317112
#145316822
#145314792
#145314662
#145314622
#145314062
#145313742
C4×#105875832
#145313142
#145313002
C4×#105876242
D17×#3802
#145311382
C17×#23242
#3420217