Finite Group Databasebeta

← #17979938

Subgroups — #17979938

Order 4352.

1996 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545616C214yesmaximal, complemented
2#14545609C214yesmaximal, complemented
3#14545594C214yesmaximal, complemented
4#14545593C212yesmaximal, complemented
5#41×#3624C212yesmaximal, complemented
6#14545578C212yesmaximal, complemented
7#14545527C212yesmaximal, complemented
8#14545514C214yesmaximal, complemented
9#14545468C212yesmaximal, complemented
10#14545448C211yesmaximal, characteristic, complemented
11C4×#10587678C212yesmaximal, complemented
12C2×C4×#63243C211yesmaximal, characteristic, complemented
13#14542079C211yesmaximal, characteristic
14C2×#10587678C2214yes—
15C22×#63243C2212yes—
16#11763861C2218yescomplemented
17#11763860C2214yescomplemented
18Q8×#3624C2214yescomplemented
19#11763844C2214yescomplemented
20#11763842C2218yes—
21#11763840C2218yes—
22#11763840C2218yescomplemented
23#11763838C2218yes—
24D4×#3624C2218yes—
25D4×#3624C2214yescomplemented
26#11763833C2218yescomplemented
27#11763828C2212yes—
28#11763827C2212yes—
29#11763826C2212yes—
30#11763826C2214yescomplemented
31#11763825C2211yescharacteristic
32#11763825C2211yescharacteristic
33#11763825C2214yescomplemented
34#11763816C2214yes—
35#11763810C2212yes—
36#11763783C2214yes—
37#11763777C2212yes—
38#11763774C2214yes—
39#11763773C2218yescomplemented
40C4×#63243C2211yescharacteristic
41C4×#63243C2212yes—
42C4×#63243C2212yes—
43C4×#63243C2211yescharacteristic
44C4×#63243C2212yes—
45C4×#63247C2214yescomplemented
46C2×#10587542C2212yes—
47C4×#63242C2212yes—
48C2×C4×#3624C2212yes—
49C2×C4×#3624C2214yescomplemented
50#11763366C411yescharacteristic
51#11763364C411yescharacteristic
52#11763364C2211yescharacteristic
53#11763357C411yescharacteristic
54#11763357C2211yescharacteristic
55#11763341C412yes—
56#11763341C412yes—
57#11763340C412yes—
58#11763340C2212yes—
59#11763338C412yes—
60#11763338C2212yes—
61#11763319C412yes—
62#11763319C2212yes—
63#11763316C412yes—
64#41×Dic17C2212yes—
65C4×#63254C2212yes—
66C4×#63254C2212yes—
67C2×C42×D17C2211yescharacteristic
68C17×#532C411yescharacteristic
69C2×#41×C17C2×C412yes—
70C2×#63254C2×C412yes—
71C2×#63254C2312yes—
72C22×C4×D17C2×C411yescharacteristic
73C22×C4×D17C2×C411yescharacteristic
74C22×C4×D17C2311yescharacteristic
75C2×#63247C2318yes—
76C22×#3624C2314yes—
77C22×#3624C2318yes—
78#10587678—216no—
79C2×#63243—28no—
80C2×#63243C2312yes—
81C2×#63243C2314yes—
82C2×#63243C2312yes—
83C2×#63242C2314yes—
84C17×C4⋊Q8C2×C411yescharacteristic
85C17×#127C2×C411yescharacteristic
86C17×#124C2×C412yes—
87C17×#121C2×C412yes—
88C17×#121C2×C412yes—
89C4×D4×C17C2×C412yes—
90C4×D4×C17C2×C412yes—
91C2×C42×C17C2×C411yescharacteristic
92#10587632C2×C412yes—
93#10587632C2×C412yes—
94Q8×Dic17C2×C412yes—
95Q8×Dic17C2312yes—
96#10587624C2×C412yes—
97#10587624C2×C412yes—
98#10587624C2×C412yes—
99#10587624C2×C412yes—
100#10587623C2×C414yes—
101#10587622C2×C412yes—
102#10587622C2×C412yes—
103#10587621C2×C414yes—
104D4×Dic17C2×C412yes—
105D4×Dic17C2×C414yes—
106D4×Dic17C2×C412yes—
107D4×Dic17C2312yes—
108D4×Dic17C2314yes—
109D4×Dic17C2312yes—
110C4×C22⋊D17C2×C414yes—
111C4×C22⋊D17C2×C414yes—
112#10587612C2×C412yes—
113#10587612C2×C414yes—
114#10587610C2×C412yes—
115#10587610C2×C412yes—
116C2×C4×Dic17C2×C411yescharacteristic
117C2×C4×Dic17C2311yescharacteristic
118C2×C4×Dic17C2314yes—
119C2×C4×Dic17C2311yescharacteristic
120#10587583C2×C412yes—
121#10587583C2×C412yes—
122#10587578C2×C412yes—
123#10587578C2312yes—
124#10587576C2×C412yes—
125#10587576C2×C412yes—
126#10587573C2×C412yes—
127#10587573C2312yes—
128#10587569C2×C414yes—
129#10587569C2×C414yes—
130#10587567C2×C414yes—
131#10587567C2314yes—
132#10587565C2×C414yes—
133#10587565C2×C414yes—
134#10587563C2×C414yes—
135#10587563C2314yes—
136C42×D17C2×C411yescharacteristic
137C42×D17C2×C411yescharacteristic
138C42×D17C2×C411yescharacteristic
139C42×D17C2×C411yescharacteristic
140C42×D17C2311yescharacteristic
141C42×D17C2311yescharacteristic
142C42×D17C2311yescharacteristic
143C42×D17C2311yescharacteristic
144#10587556C2×C412yes—
145#10587555C2×C411yescharacteristic
146#10587555C2×C411yescharacteristic
147C4×Dic34C2×C412yes—
148C4×Dic34C2×C412yes—
149C22⋊#3624C2312yes—
150C22⋊#3624C2312yes—
151C22⋊#3624C2318yes—
152C22⋊#3624C2318yes—
153#10587544C2314yes—
154#10587544C2318yes—
155#10587543C2314yes—
156#10587542C2312yes—
157#10587542C2312yes—
158#10587542C2314yes—
159#10587542C2318yes—
160C4⋊#3624C2312yes—
161C4⋊#3624C2312yes—
162C4⋊#3624C2318yes—
163C4×#3624C2312yes—
164C4×#3624C2312yes—
165C4×#3624C2314yes—
166C4×#3624C2312yes—
167C4×#3624C2318yes—
168C4×#3624C2312yes—
169C4×#3624C2314yes—
170C23×D17C22×C411yescharacteristic
171#41×C17—28no—
172C2×Q8×C17C22×C412yes—
173C2×D4×C17C22×C412yes—
174C2×D4×C17C22×C412yes—
175C2×D4×C17C22×C414yes—
176C2×D4×C17C22×C412yes—
177C22×C4×C17C22×C411yescharacteristic
178C22×C4×C17C22×C414yes—
179C22×C4×C17C22×C411yescharacteristic
180C22×C4×C17C22×C411yescharacteristic
181C2×C22⋊D17C22×C414yes—
182C2×C22⋊D17C22×C414yes—
183C22×Dic17C22×C411yescharacteristic
184C22×Dic17C22×C411yescharacteristic
185C22×Dic17C22×C414yes—
186C22×Dic17C2411yescharacteristic
187C22×Dic17C2414yes—
188#63254—28no—
189#63254—44no—
190C2×C4×D17—24no—
191C2×C4×D17—24no—
192C2×C4×D17—42no—
193C2×C4×D17C22×C411yescharacteristic
194C2×C4×D17C22×C411yescharacteristic
195C2×C4×D17C22×C411yescharacteristic
196C2×C4×D17C22×C411yescharacteristic
197C2×C4×D17C22×C411yescharacteristic
198C2×C4×D17C22×C411yescharacteristic
199C2×C4×D17C22×C411yescharacteristic
200C2×C4×D17C22×C411yescharacteristic
201C2×C4×D17C22×C411yescharacteristic
202C2×C4×D17C22×C411yescharacteristic
203C2×C4×D17C2411yescharacteristic
204C2×C4×D17C2411yescharacteristic
205C2×Dic34C22×C412yes—
206C2×Dic34C22×C412yes—
207#63247—216no—
208C2×#3624—28no—
209C2×#3624—216no—
210C2×#3624C2414yes—
211C2×#3624C2414yes—
212C2×#3624C2414yes—
213C2×#3624C2414yes—
214#63243—24no—
215#63243—28no—
216#63243#4118yescomplemented
217#63242—28no—
218C4⋊C4×C17C22×C412yes—
219C4⋊C4×C17C22×C412yes—
220C22⋊C4×C17C22×C414yes—
221C22⋊C4×C17C22×C414yes—
222C42×C17C22×C411yescharacteristic
223C42×C17C22×C411yescharacteristic
224C42×C17C22×C411yescharacteristic
225C42×C17C22×C411yescharacteristic
226C22⋊Dic17C22×C414yes—
227C22⋊Dic17C22×C414yes—
228C22⋊Dic17C22×C414yes—
229C22⋊Dic17C22×C414yes—
230C22⋊Dic17C22×C414yes—
231#63227C22×C414yes—
232#63227C22×C414yes—
233C4⋊Dic17C22×C412yes—
234C4⋊Dic17C22×C412yes—
235C4⋊Dic17C22×C412yes—
236C4⋊Dic17C22×C412yes—
237C4⋊Dic17C22×C414yes—
238C4⋊Dic17C22×C414yes—
239#63225C22×C414yes—
240#63225C22×C414yes—
241#63225C22×C414yes—
242#63225C22×C414yes—
243C4×Dic17C22×C414yes—
244C4×Dic17C22×C411yescharacteristic
245C4×Dic17C22×C411yescharacteristic
246C4×Dic17C22×C411yescharacteristic
247C4×Dic17C22×C411yescharacteristic
248C4×Dic17C22×C411yescharacteristic
249C4×Dic17C22×C411yescharacteristic
250C4×Dic17C22×C411yescharacteristic
251C4×Dic17C22×C411yescharacteristic
252C4×Dic17C22×C414yes—
253C4×Dic17C2411yescharacteristic
254C4×Dic17C2411yescharacteristic
255C4×Dic17C2411yescharacteristic
256C4×Dic17C2414yes—
257C4×Dic17C2411yescharacteristic
258#60210—171nomaximal, Sylow
259C23×C17C23×C414yes—
260C23×C17C23×C411yescharacteristic
261C22×D17—22no—
262C22×D17—22no—
263C22×D17—41no—
264C22×D17C23×C411yescharacteristic
265C22×D17C23×C411yescharacteristic
266Q8×C17—24no—
267D4×C17—28no—
268D4×C17—24no—
269D4×C17—24no—
270D4×C17—42no—
271C2×C4×C17—22no—
272C2×C4×C17—28no—
273C2×C4×C17—41no—
274C2×C4×C17#13114yescomplemented
275C2×C4×C17C23×C411yescharacteristic
276C2×C4×C17C23×C411yescharacteristic
277C2×C4×C17C23×C411yescharacteristic
278C2×C4×C17C23×C414yes—
279C2×C4×C17C23×C411yescharacteristic
280C2×C4×C17C23×C411yescharacteristic
281C2×C4×C17C23×C411yescharacteristic
282C22⋊D17—28no—
283C22⋊D17—44no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—28no—
287C2×Dic17—22no—
288C2×Dic17—28no—
289C2×Dic17C23×C411yescharacteristic
290C2×Dic17C23×C411yescharacteristic
291C2×Dic17C23×C411yescharacteristic
292C2×Dic17C23×C411yescharacteristic
293C2×Dic17C23×C414yes—
294C2×Dic17C23×C414yes—
295C2×Dic17C23×C411yescharacteristic
296C2×Dic17C2511yescharacteristic
297C4×D17—22no—
298C4×D17—22no—
299C4×D17—22no—
300C4×D17—22no—
301C4×D17—22no—
302C4×D17—22no—
303C4×D17—22no—
304C4×D17—22no—
305C4×D17—22no—
306C4×D17—41no—
307C4×D17—41no—
308C4×D17C2×#4114yes—
309Dic34—24no—
310Dic34—42no—
311#3624—24no—
312#3624—24no—
313#3624—24no—
314#3624C2×#4118yes—
315#3444—171no—
316#2969—174no—
317#2968—174no—
318#2965—172no—
319#2965—174no—
320C8×#41—172no—
321#2962—172no—
322#2935—172no—
323#2933—174no—
324#2922—172no—
325C2×#431—171no—
326C4×#131—172no—
327C2×C4×M16—171no—
328C22×C17—21no—
329C22×C17—21no—
330C22×C17—24no—
331C22×C17—24no—
332C22×C17—24no—
333C22×C17C2×#13112yes—
334C22×C17C24×C411yescharacteristic
335C2×D17—21no—
336C2×D17—21no—
337C2×D17—21no—
338C2×D17—21no—
339C2×D17—21no—
340C2×D17—44no—
341C2×D17C4×#4112yes—
342C4×C17—21no—
343C4×C17—24no—
344C4×C17—21no—
345C4×C17—21no—
346C4×C17C4×#4112yes—
347C4×C17C2×#13112yes—
348C4×C17C2×#13112yes—
349Dic17—24no—
350Dic17—21no—
351Dic17—21no—
352Dic17—21no—
353Dic17—24no—
354Dic17—21no—
355Dic17#56812yes—
356Dic17C22×#4112yes—
357C2×#131—174no—
358C22×M16—172no—
359#533—171no—
360#533—171no—
361#533—171no—
362#532—171no—
363#532—171no—
364#532#59511yescharacteristic
365#529—172no—
366#529—172no—
367#529—172no—
368#529—172no—
369#529—172no—
370#529—172no—
371#525—172no—
372#525—172no—
373#525—172no—
374C4×#41—172no—
375C4×#41—172no—
376C4×#41—172no—
377C22×C42—171no—
378#446—174no—
379#446—178no—
380C8×Q8—174no—
381#436—178no—
382#436—174no—
383#435—178no—
384#435—178no—
385#435—178no—
386C8×D4—178no—
387C8×D4—174no—
388#433—178no—
389#431—171no—
390#431—171no—
391#431—172no—
392#431—172no—
393#431—172no—
394#431—174no—
395#431—174no—
396#424—174no—
397C2×C4⋊C8—172no—
398#408—174no—
399C2×C22⋊C8—172no—
400#405—178no—
401#405—174no—
402C4×M16—171no—
403C4×M16—171no—
404C4×M16—172no—
405C4×M16—172no—
406C4×M16—172no—
407C4×M16—174no—
408C2×#97—172no—
409C2×C4×C8—172no—
410C2×C4×C8—174no—
411C2×C4×C8—172no—
412C2×C17—22no—
413C2×C17—44no—
414C2×C17C2×C4×#4111yescharacteristic
415C2×C17C22×#13111yescharacteristic
416C2×C17C2×#56811yescharacteristic
417D17—22no—
418D17—41no—
419C2×#41—172no—
420C2×#41—172no—
421C2×#41C2×#59512yes—
422C23×C4—171no—
423C23×C4—171no—
424C23×C4—171no—
425#131—3416no—
426C2×M16—172no—
427C2×M16—172no—
428C2×M16—174no—
429C2×M16—178no—
430C2×M16—348no—
431C22×C8—174no—
432C22×C8—174no—
433C22×C8—178no—
434C4⋊Q8—171no—
435C4⋊Q8—171no—
436C4⋊Q8C2×#59511yescharacteristic
437#127C2×#59511yescharacteristic
438#126—174no—
439#126—174no—
440#125—172no—
441#125—172no—
442#125—172no—
443#124—172no—
444#124—172no—
445#124C2×#59512yes—
446#123—174no—
447#123—174no—
448#123—174no—
449C22⋊Q8—172no—
450C22⋊Q8—172no—
451C22⋊Q8—172no—
452C22⋊Q8—172no—
453C22⋊Q8—172no—
454C22⋊Q8—172no—
455#121—172no—
456#121—172no—
457#121—172no—
458#121—172no—
459#121C2×#59512yes—
460#121C2×#59512yes—
461#120—174no—
462C4×Q8—172no—
463C4×Q8—172no—
464C4×Q8—172no—
465C4×Q8—172no—
466C4×Q8—172no—
467C4×Q8—172no—
468C4×D4—174no—
469C4×D4—174no—
470C4×D4—172no—
471C4×D4—172no—
472C4×D4—172no—
473C4×D4—172no—
474C4×D4—174no—
475C4×D4—174no—
476C4×D4—174no—
477C4×D4—174no—
478C4×D4C2×#59512yes—
479C4×D4C2×#59512yes—
480#117—172no—
481#117—174no—
482#117—172no—
483#117—172no—
484#117—174no—
485#117—174no—
486C2×C42—174no—
487C2×C42—171no—
488C2×C42—171no—
489C2×C42—171no—
490C2×C42—171no—
491C2×C42—171no—
492C2×C42—171no—
493C2×C42—171no—
494C2×C42—171no—
495C2×C42—171no—
496C2×C42—171no—
497C2×C42—171no—
498C2×C42C2×#59511yescharacteristic
499C4⋊C8—172no—
500C4⋊C8—172no—
501C4⋊C8—178no—
502C4⋊C8—174no—
503C4⋊C8—178no—
504C22⋊C8—174no—
505C22⋊C8—172no—
506C22⋊C8—172no—
507C22⋊C8—178no—
508C22⋊C8—178no—
509#97—172no—
510#97—172no—
511#97—174no—
512#97—178no—
513C4×C8—172no—
514C4×C8—172no—
515C4×C8—172no—
516C4×C8—172no—
517C4×C8—174no—
518C4×C8—174no—
519C4×C8—178no—
520C17#6021011yescharacteristic, complemented, Sylow
521C24—171no—
522#41—28no—
523#41—348no—
524#41—684no—
525C2×Q8—172no—
526C2×Q8—172no—
527C2×Q8C22×#59512yes—
528C2×D4—174no—
529C2×D4—174no—
530C2×D4C22×#59514yes—
531C2×D4C22×#59512yes—
532C2×D4C22×#59512yes—
533C2×D4C22×#59512yes—
534C22×C4—171no—
535C22×C4—171no—
536C22×C4—171no—
537C22×C4—174no—
538C22×C4—171no—
539C22×C4—174no—
540C22×C4—171no—
541C22×C4—171no—
542C22×C4—171no—
543C22×C4—171no—
544C22×C4—171no—
545C22×C4—171no—
546C22×C4—171no—
547C22×C4—171no—
548C22×C4—171no—
549C22×C4—171no—
550C22×C4—171no—
551C22×C4—344no—
552C22×C4—344no—
553C22×C4—682no—
554C22×C4C22×#59511yescharacteristic
555C22×C4C22×#59514yes—
556C22×C4C22×#59511yescharacteristic
557C22×C4C22×#59511yescharacteristic
558M16—178no—
559M16—348no—
560M16—3416no—
561M16—344no—
562C2×C8—174no—
563C2×C8—174no—
564C2×C8—174no—
565C2×C8—174no—
566C2×C8—348no—
567C2×C8—3416no—
568C2×C8—348no—
569C4⋊C4—172no—
570C4⋊C4—172no—
571C4⋊C4—172no—
572C4⋊C4—172no—
573C4⋊C4—174no—
574C4⋊C4—174no—
575C4⋊C4—174no—
576C4⋊C4—174no—
577C4⋊C4—174no—
578C4⋊C4—174no—
579C4⋊C4C22×#59512yes—
580C4⋊C4C22×#59512yes—
581C22⋊C4—174no—
582C22⋊C4—174no—
583C22⋊C4—174no—
584C22⋊C4—174no—
585C22⋊C4—174no—
586C22⋊C4—174no—
587C22⋊C4—174no—
588C22⋊C4C22×#59514yes—
589C22⋊C4C22×#59514yes—
590C42—171no—
591C42—171no—
592C42—174no—
593C42—171no—
594C42—171no—
595C42—171no—
596C42—171no—
597C42—171no—
598C42—171no—
599C42—171no—
600C42—171no—
601C42—174no—
602C42—171no—
603C42—171no—
604C42—174no—
605C42C22×#59511yescharacteristic
606C42C22×#59511yescharacteristic
607C42C22×#59511yescharacteristic
608C42C22×#59511yescharacteristic
609C23—171no—
610C23—171no—
611C23—342no—
612C23—342no—
613C23—681no—
614C23C23×#59514yes—
615C23C23×#59511yescharacteristic
616Q8—24no—
617Q8—344no—
618Q8—682no—
619D4—28no—
620D4—24no—
621D4—24no—
622D4—42no—
623D4—348no—
624D4—684no—
625C2×C4—22no—
626C2×C4—28no—
627C2×C4—41no—
628C2×C4—171no—
629C2×C4—171no—
630C2×C4—174no—
631C2×C4—171no—
632C2×C4—171no—
633C2×C4—171no—
634C2×C4—171no—
635C2×C4—174no—
636C2×C4—174no—
637C2×C4—342no—
638C2×C4—342no—
639C2×C4—342no—
640C2×C4—342no—
641C2×C4—342no—
642C2×C4—348no—
643C2×C4—342no—
644C2×C4—348no—
645C2×C4—342no—
646C2×C4—342no—
647C2×C4—342no—
648C2×C4—342no—
649C2×C4—342no—
650C2×C4—342no—
651C2×C4—681no—
652C2×C4—681no—
653C2×C4#1058767814yescomplemented
654C2×C4C23×#59511yescharacteristic
655C2×C4C23×#59511yescharacteristic
656C2×C4C23×#59511yescharacteristic
657C2×C4C23×#59514yes—
658C2×C4C23×#59511yescharacteristic
659C2×C4C23×#59511yescharacteristic
660C2×C4C23×#59511yescharacteristic
661C8—178no—
662C8—344no—
663C8—344no—
664C8—344no—
665C22—21no—
666C22—21no—
667C22—24no—
668C22—24no—
669C22—24no—
670C22—172no—
671C22—341no—
672C22—341no—
673C22—341no—
674C22—341no—
675C22—341no—
676C22—684no—
677C22C2×#1058767812yes—
678C22C24×#59511yescharacteristic
679C4—21no—
680C4—24no—
681C4—21no—
682C4—21no—
683C4—172no—
684C4—172no—
685C4—341no—
686C4—344no—
687C4—341no—
688C4—341no—
689C4—341no—
690C4—344no—
691C4#41×#59512yes—
692C4C2×#1058767812yes—
693C4C2×#1058767812yes—
694C2—22no—
695C2—44no—
696C2—342no—
697C2—681no—
698C2C2×#41×#59511yescharacteristic
699C2C22×#1058767811yescharacteristic
700C2D17⋊#56811yescharacteristic
subgroupG/H
centerC2×C4C23×#595
commutator, socleC22×C17C24×C4
FrattiniC22C24×#595
FittingC17×#532C4
prime radical#14542079C2
cosocleC2×Dic17C25
hypercenter#532#595
hypocenterC17#60210
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14545616C2semidirect
2. #14545609C2semidirect
3. #14545594C2semidirect
4. #14545593C2semidirect
5. #41×#3624C2semidirect
6. #14545578C2semidirect
7. #14545527C2semidirect
8. #14545514C2semidirect
9. #14545468C2semidirect
10. #14545448C2semidirect
11. C4×#10587678C2semidirect
12. C2×C4×#63243C2semidirect
16. #11763861C22semidirect
17. #11763860C22semidirect
18. Q8×#3624C22semidirect
19. #11763844C22semidirect
22. #11763840C22semidirect
25. D4×#3624C22semidirect
26. #11763833C22semidirect
30. #11763826C22semidirect
33. #11763825C22semidirect
39. #11763773C22semidirect
45. C4×#63247C22semidirect
49. C2×C4×#3624C22semidirect
216. #63243#41semidirect
274. C2×C4×C17#131semidirect
520. C17#60210semidirect
653. C2×C4#10587678semidirect

Maximal subgroups

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

subgroupindex
#145456162
#145456092
#145455942
#145455932
#41×#36242
#145455782
#145455272
#145455142
#145454682
#145454482
C4×#105876782
C2×C4×#632432
#145420792
#6021017