Finite Group Databasebeta

← #17963160

Subgroups — #17963160

Order 4352.

1486 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763755C211yesmaximal, characteristic
2C2×#11763753C211yesmaximal, characteristic
3C2×#11763753C211yesmaximal, characteristic
4C2×C4×C4⋊#595C211yesmaximal, characteristic
5#14543969C214yesmaximal
6#14543964C214yesmaximal
7#14543962C211yesmaximal, characteristic
8#14543962C211yesmaximal, characteristic
9C4×C4⋊C4×D17C211yesmaximal, characteristic
10C22×C4⋊#595C2211yescharacteristic
11C22×C4⋊#595C2211yescharacteristic
12C22×C4⋊#595C2214yes—
13C22×C4⋊#595C2211yescharacteristic
14C22×C4⋊#595C2211yescharacteristic
15C22×C4×#595C2212yes—
16#11763755—24no—
17#11763753—24no—
18#11763753—24no—
19C4×C4⋊#595—24no—
20C2×(C2×#595)⋊C4C2212yes—
21C2×(C2×#595)⋊C4C2212yes—
22C2×(C2×#595)⋊C4C2214yes—
23C2×(C2×#595)⋊C4C2212yes—
24C2×(C2×#595)⋊C4C2214yes—
25C2×(C2×#595)⋊C4C2214yes—
26C2×C4⋊C4×D17C2212yes—
27C2×C42×D17C2211yescharacteristic
28C2×C42×D17C2211yescharacteristic
29C2×C42×D17C2211yescharacteristic
30C4⋊C4×Dic17C412yescomplemented
31C4×#63225C411yescharacteristic, complemented
32C4×#63225C411yescharacteristic, complemented
33C4×C4⋊Dic17C411yescharacteristic, complemented
34#11762660C412yescomplemented
35#95×D17C2212yes—
36C4×C4⋊C4×C17C411yescharacteristic, complemented
37C23×#595C2312yes—
38C23×#595C2312yes—
39C23×#595C2312yes—
40C23×#595C2312yes—
41C22×C4×D17C2312yes—
42C22×C4×D17C2311yescharacteristic
43C22×C4×D17C2311yescharacteristic
44C22×C4×D17C2312yes—
45C22×C4×D17C2311yescharacteristic
46C2×C4⋊#595—22no—
47C2×C4⋊#595—22no—
48C2×C4⋊#595—22no—
49C2×C4⋊#595—22no—
50C2×C4⋊#595—28no—
51C2×C4⋊#595—22no—
52C2×C4⋊#595—22no—
53C2×C4⋊#595—22no—
54C2×C4⋊#595—22no—
55C2×C4⋊#595—28no—
56C2×C4⋊#595—22no—
57C2×C4⋊#595—22no—
58C2×C4⋊#595—44no—
59C2×C4⋊#595D414yes—
60C2×C4⋊#595Q814yes—
61C2×C4×#595—24no—
62C2×C4×#595—44no—
63C2×C4⋊C4×C17C2×C412yes—
64C2×C42×C17C2×C411yescharacteristic
65C2×C42×C17C2×C411yescharacteristic
66C2×C42×C17C2×C411yescharacteristic
67C2×C4⋊Dic17C2×C412yes—
68C2×#63225C2×C412yes—
69C2×#63225C2×C412yes—
70C2×C4×Dic17C2×C412yes—
71C2×C4×Dic17C2×C412yes—
72C2×C4×Dic17C2×C411yescharacteristic
73C2×C4×Dic17C2×C411yescharacteristic
74C2×C4×Dic17C2×C411yescharacteristic
75C2×C4×Dic17C2×C411yescharacteristic
76C2×C4×Dic17C2×C411yescharacteristic
77C4⋊C4×D17—24no—
78C4⋊C4×D17—24no—
79C42×D17—22no—
80C42×D17—22no—
81C42×D17—22no—
82C42×D17—22no—
83C42×D17D414yes—
84C42×D17Q814yes—
85(C2×#595)⋊C4—28no—
86(C2×#595)⋊C4—24no—
87(C2×#595)⋊C4—24no—
88(C2×#595)⋊C4—24no—
89(C2×#595)⋊C4—28no—
90(C2×#595)⋊C4—44no—
91C17×#95C2×C412yes—
92#10587502C2×C412yes—
93#10587502C2×C412yes—
94#10587502C2×C412yes—
95C23×D17C2411yescharacteristic
96C22×#595—22no—
97C22×#595—22no—
98C22×#595—22no—
99C22×#595—22no—
100C22×#595—24no—
101C22×#595—24no—
102C22×#595—24no—
103C22×#595—24no—
104C22×#595—22no—
105C22×#595—22no—
106C22×#595—22no—
107C22×#595—22no—
108C22×#595—22no—
109C22×#595—22no—
110C22×#595—24no—
111C22×#595—24no—
112C22×#595—24no—
113C22×#595—24no—
114C22×#595C2×D414yes—
115C22×#595C2×Q814yes—
116C22×C4×C17C22×C412yes—
117C22×C4×C17C22×C411yescharacteristic
118C22×C4×C17C22×C411yescharacteristic
119C22×C4×C17C22×C412yes—
120C22×C4×C17C22×C411yescharacteristic
121C22×Dic17C22×C412yes—
122C22×Dic17C22×C411yescharacteristic
123C22×Dic17C22×C411yescharacteristic
124C22×Dic17C22×C412yes—
125C22×Dic17C22×C411yescharacteristic
126C2×C4×D17—22no—
127C2×C4×D17—22no—
128C2×C4×D17—22no—
129C2×C4×D17—22no—
130C2×C4×D17—22no—
131C2×C4×D17—22no—
132C2×C4×D17—22no—
133C2×C4×D17—22no—
134C2×C4×D17—22no—
135C2×C4×D17—22no—
136C2×C4×D17—22no—
137C2×C4×D17—22no—
138C2×C4×D17—22no—
139C2×C4×D17—22no—
140C2×C4×D17C2×D412yes—
141C2×C4×D17C2×D412yes—
142C2×C4×D17C2×D412yes—
143C2×C4×D17C2×D412yes—
144C2×C4×D17C2×Q812yes—
145C2×C4×D17C2×Q812yes—
146C2×C4×D17C2×Q812yes—
147C2×C4×D17C2×Q812yes—
148C2×C4×D17#4114yes—
149C2×C4×D17#4114yes—
150C2×C4×D17#4112yes—
151C2×C4×D17#4112yes—
152C4⋊#595—28no—
153C4⋊#595—28no—
154C4⋊#595—416no—
155C4⋊#595—44no—
156C4⋊#595—44no—
157C4×#595—48no—
158C4⋊C4×C17—24no—
159C42×C17—22no—
160C42×C17—22no—
161C42×C17C4⋊C414yescomplemented
162C4⋊Dic17—24no—
163#63225—24no—
164#63225—24no—
165C4×Dic17—22no—
166C4×Dic17—22no—
167C4×Dic17—24no—
168C4×Dic17—24no—
169C4×Dic17C4⋊C414yescomplemented
170C4×Dic17C4⋊C414yescomplemented
171C4×Dic17C4⋊C414yescomplemented
172#13909—171nomaximal, Sylow
173C23×C17C23×C411yescharacteristic
174C22×D17C22×D411yescharacteristic
175C22×D17C22×D411yescharacteristic
176C22×D17C22×Q811yescharacteristic
177C22×D17C22×Q811yescharacteristic
178C22×D17C2×#4111yescharacteristic
179C22×D17C2×#4111yescharacteristic
180C22×D17C2×#4112yes—
181C22×D17C2×#4112yes—
182C22×D17H(5,𝔽2)12yes—
183C22×D172−1+412yes—
184C2×#595—24no—
185C2×#595—24no—
186C2×#595—28no—
187C2×#595—28no—
188C2×#595—42no—
189C2×#595—42no—
190C2×#595—42no—
191C2×#595—42no—
192C2×#595—44no—
193C2×#595—44no—
194C2×#595—42no—
195C2×#595—42no—
196C2×#595—42no—
197C2×#595—42no—
198C2×#595—42no—
199C2×#595—42no—
200C2×#595—44no—
201C2×#595—44no—
202C2×#595—44no—
203C2×#595—44no—
204C2×C4×C17—22no—
205C2×C4×C17—22no—
206C2×C4×C17—22no—
207C2×C4×C17—22no—
208C2×C4×C17—22no—
209C2×C4×C17—22no—
210C2×C4×C17—22no—
211C2×C4×C17C2×C4⋊C412yes—
212C2×C4×C17C2×C4⋊C412yes—
213C2×C4×C17C2×C4⋊C412yes—
214C2×C4×C17#11714yes—
215C2×C4×C17C4×D412yes—
216C2×C4×C17C4×Q812yes—
217C2×Dic17—22no—
218C2×Dic17—22no—
219C2×Dic17—22no—
220C2×Dic17—22no—
221C2×Dic17—22no—
222C2×Dic17—22no—
223C2×Dic17—22no—
224C2×Dic17C2×C4⋊C412yes—
225C2×Dic17C2×C4⋊C412yes—
226C2×Dic17C2×C4⋊C412yes—
227C2×Dic17#11714yes—
228C2×Dic17C4×D412yes—
229C2×Dic17C4×Q812yes—
230C4×D17—22no—
231C4×D17—22no—
232C4×D17—24no—
233C4×D17—22no—
234C4×D17—22no—
235C4×D17—24no—
236C4×D17—24no—
237C4×D17—24no—
238C4×D17—24no—
239C4×D17—24no—
240C4×D17—42no—
241C4×D17—42no—
242C4×D17—42no—
243C4×D17—42no—
244C4×D17#12114yes—
245C4×D17C22⋊Q814yes—
246C4×D17#12514yes—
247C4×D17C4⋊Q814yes—
248C2×#384—171no—
249C2×#382—171no—
250C2×#382—171no—
251C2×C4×C4⋊C4—171no—
252C2×C4×C4⋊C4—171no—
253#1441—174no—
254#1436—174no—
255C4⋊#95—171no—
256C4⋊#95—171no—
257C22×C17C22×C4⋊C411yescharacteristic
258C22×C17C2×#11712yes—
259C22×C17C2×C4×D411yescharacteristic
260C22×C17C2×C4×Q811yescharacteristic
261C22×C17#52012yes—
262C2×D17C2×#12111yescharacteristic
263C2×D17C2×C22⋊Q811yescharacteristic
264C2×D17C2×#12511yescharacteristic
265C2×D17C2×C4⋊Q811yescharacteristic
266C2×D17#53211yescharacteristic
267C2×D17#53211yescharacteristic
268C2×D17#53312yes—
269C2×D17#53511yescharacteristic
270C2×D17#53611yescharacteristic
271C2×D17#54412yes—
272C2×D17#54612yes—
273C2×D17#54812yes—
274C2×D17#55212yes—
275C2×D17#55312yes—
276C2×D17#55412yes—
277C2×D17#55612yes—
278C2×D17#55712yes—
279C2×D17#55912yes—
280#595—44no—
281#595—44no—
282#595—82no—
283#595—82no—
284C4×C17—22no—
285C4×C17—24no—
286C4×C17—22no—
287C4×C17—42no—
288C4×C17#38914yes—
289Dic17—22no—
290Dic17—24no—
291Dic17—22no—
292Dic17—42no—
293Dic17#38914yes—
294C22×C4⋊C4—171no—
295C22×C4⋊C4—171no—
296C22×C4⋊C4—172no—
297C22×C4⋊C4—171no—
298C22×C4⋊C4—171no—
299C22×C4⋊C4—174no—
300C22×C42—171no—
301C22×C42—171no—
302C22×C42—171no—
303C22×C42—172no—
304#384—344no—
305#382—344no—
306#382—344no—
307C4×C4⋊C4—172no—
308C4×C4⋊C4—171no—
309C4×C4⋊C4—171no—
310C4×C4⋊C4—171no—
311C4×C4⋊C4—172no—
312C4×C4⋊C4—344no—
313C4×C4⋊C4#59511yescharacteristic, complemented
314C2×#95—172no—
315C2×#95—174no—
316C2×#95—172no—
317C2×#95—174no—
318C2×#95—172no—
319C2×#95—172no—
320C2×#95—174no—
321C2×C17#228511yescharacteristic
322C2×C17C2×#38911yescharacteristic
323C2×C17#231711yescharacteristic
324C2×C17#235212yes—
325C2×C17#235512yes—
326D17#254411yescharacteristic
327D17#254511yescharacteristic
328D17#255012yes—
329D17#256511yescharacteristic
330D17#256611yescharacteristic
331D17#257012yes—
332C23×C4—171no—
333C23×C4—172no—
334C23×C4—171no—
335C23×C4—171no—
336C23×C4—172no—
337C23×C4—172no—
338C23×C4—172no—
339C23×C4—172no—
340C23×C4—172no—
341C2×C4⋊C4—174no—
342C2×C4⋊C4—174no—
343C2×C4⋊C4—172no—
344C2×C4⋊C4—172no—
345C2×C4⋊C4—172no—
346C2×C4⋊C4—344no—
347C2×C4⋊C4—344no—
348C2×C4⋊C4—342no—
349C2×C4⋊C4—342no—
350C2×C4⋊C4—342no—
351C2×C4⋊C4—342no—
352C2×C4⋊C4—342no—
353C2×C4⋊C4—342no—
354C2×C4⋊C4—348no—
355C2×C4⋊C4—342no—
356C2×C4⋊C4—342no—
357C2×C4⋊C4—342no—
358C2×C4⋊C4—342no—
359C2×C4⋊C4—348no—
360C2×C4⋊C4—684no—
361C2×C4⋊C4C2×#59512yes—
362C2×C42—171no—
363C2×C42—171no—
364C2×C42—171no—
365C2×C42—174no—
366C2×C42—174no—
367C2×C42—172no—
368C2×C42—172no—
369C2×C42—171no—
370C2×C42—171no—
371C2×C42—342no—
372C2×C42—342no—
373C2×C42—342no—
374C2×C42—342no—
375C2×C42—344no—
376C2×C42—684no—
377C2×C42C2×#59511yescharacteristic
378C2×C42C2×#59511yescharacteristic
379C2×C42C2×#59511yescharacteristic
380#95—172no—
381#95—172no—
382#95—172no—
383#95—344no—
384#95—344no—
385#95—344no—
386#95—348no—
387#95—348no—
388#95—684no—
389#95C2×#59512yes—
390C17#1390911yescharacteristic, complemented, Sylow
391C24—171no—
392C22×C4—171no—
393C22×C4—172no—
394C22×C4—172no—
395C22×C4—172no—
396C22×C4—172no—
397C22×C4—172no—
398C22×C4—172no—
399C22×C4—171no—
400C22×C4—172no—
401C22×C4—171no—
402C22×C4—172no—
403C22×C4—172no—
404C22×C4—172no—
405C22×C4—172no—
406C22×C4—174no—
407C22×C4—174no—
408C22×C4—174no—
409C22×C4—174no—
410C22×C4—172no—
411C22×C4—342no—
412C22×C4—342no—
413C22×C4—342no—
414C22×C4—342no—
415C22×C4—342no—
416C22×C4—342no—
417C22×C4—342no—
418C22×C4—342no—
419C22×C4—342no—
420C22×C4—342no—
421C22×C4—342no—
422C22×C4—342no—
423C22×C4—342no—
424C22×C4—342no—
425C22×C4—342no—
426C22×C4—342no—
427C22×C4—344no—
428C22×C4—344no—
429C22×C4—344no—
430C22×C4—342no—
431C22×C4—342no—
432C22×C4—344no—
433C22×C4—342no—
434C22×C4—342no—
435C22×C4—342no—
436C22×C4—344no—
437C22×C4—344no—
438C22×C4—342no—
439C22×C4—344no—
440C22×C4—342no—
441C22×C4—342no—
442C22×C4—344no—
443C22×C4C22×#59512yes—
444C22×C4C22×#59511yescharacteristic
445C22×C4C22×#59511yescharacteristic
446C22×C4C22×#59512yes—
447C22×C4C22×#59511yescharacteristic
448C4⋊C4—24no—
449C4⋊C4—344no—
450C4⋊C4—344no—
451C4⋊C4—348no—
452C4⋊C4—348no—
453C4⋊C4—344no—
454C4⋊C4—684no—
455C4⋊C4—684no—
456C4⋊C4—6816no—
457C42—22no—
458C42—22no—
459C42—174no—
460C42—174no—
461C42—174no—
462C42—344no—
463C42—344no—
464C42—342no—
465C42—342no—
466C42—688no—
467C42C4⋊#59514yescomplemented
468C23—171no—
469C23—171no—
470C23—172no—
471C23—172no—
472C23—171no—
473C23—171no—
474C23—171no—
475C23—171no—
476C23—172no—
477C23—172no—
478C23C23×#59511yescharacteristic
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—172no—
487C2×C4—172no—
488C2×C4—172no—
489C2×C4—174no—
490C2×C4—174no—
491C2×C4—174no—
492C2×C4—174no—
493C2×C4—172no—
494C2×C4—172no—
495C2×C4—174no—
496C2×C4—342no—
497C2×C4—344no—
498C2×C4—342no—
499C2×C4—342no—
500C2×C4—344no—
501C2×C4—342no—
502C2×C4—344no—
503C2×C4—344no—
504C2×C4—344no—
505C2×C4—344no—
506C2×C4—342no—
507C2×C4—342no—
508C2×C4—342no—
509C2×C4—342no—
510C2×C4—344no—
511C2×C4—344no—
512C2×C4—348no—
513C2×C4—348no—
514C2×C4—342no—
515C2×C4—342no—
516C2×C4—342no—
517C2×C4—682no—
518C2×C4—682no—
519C2×C4—682no—
520C2×C4—682no—
521C2×C4—682no—
522C2×C4—682no—
523C2×C4—682no—
524C2×C4—682no—
525C2×C4—684no—
526C2×C4—684no—
527C2×C4—682no—
528C2×C4—682no—
529C2×C4—684no—
530C2×C4—682no—
531C2×C4—682no—
532C2×C4—682no—
533C2×C4—682no—
534C2×C4—684no—
535C2×C4—684no—
536C2×C4—684no—
537C2×C4C2×C4⋊#59512yes—
538C2×C4C2×C4⋊#59512yes—
539C2×C4C2×C4⋊#59512yes—
540C2×C4#1058767714yes—
541C2×C4D4×#59512yes—
542C2×C4Q8×#59512yes—
543C22—171no—
544C22—171no—
545C22—172no—
546C22—171no—
547C22—171no—
548C22—171no—
549C22—171no—
550C22—171no—
551C22—171no—
552C22—172no—
553C22—172no—
554C22—172no—
555C22—172no—
556C22—172no—
557C22—172no—
558C22—172no—
559C22—172no—
560C22—172no—
561C22C22×C4⋊#59511yescharacteristic
562C22C2×#1058767712yes—
563C22C2×D4×#59511yescharacteristic
564C22C2×Q8×#59511yescharacteristic
565C22#1176387812yes—
566C4—22no—
567C4—22no—
568C4—24no—
569C4—42no—
570C4—174no—
571C4—342no—
572C4—342no—
573C4—344no—
574C4—684no—
575C4—684no—
576C4—682no—
577C4—1362no—
578C4—1362no—
579C4#1176376014yes—
580C2—171no—
581C2—171no—
582C2—171no—
583C2—171no—
584C2—172no—
585C2—172no—
586C2#1454523311yescharacteristic
587C2C2×#1176376011yescharacteristic
588C2#1454526511yescharacteristic
589C2#1454530012yes—
590C2#1454530312yes—
subgroupG/H
center, FrattiniC23C23×#595
commutator, socleC23×C17C23×C4
FittingC4×C4⋊C4×C17C4
prime radical, cosocleC23×D17C24
hypercenterC4×C4⋊C4#595
hypocenterC17#13909
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
30. C4⋊C4×Dic17C4semidirect
31. C4×#63225C4semidirect
32. C4×#63225C4semidirect
33. C4×C4⋊Dic17C4semidirect
34. #11762660C4semidirect
36. C4×C4⋊C4×C17C4semidirect
161. C42×C17C4⋊C4semidirect
169. C4×Dic17C4⋊C4semidirect
170. C4×Dic17C4⋊C4semidirect
171. C4×Dic17C4⋊C4semidirect
313. C4×C4⋊C4#595semidirect
390. C17#13909semidirect
467. C42C4⋊#595semidirect

Maximal subgroups

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

subgroupindex
C2×#117637552
C2×#117637532
C2×C4×C4⋊#5952
#145439692
#145439642
#145439622
C4×C4⋊C4×D172
#1390917