Finite Group Databasebeta

← #17973663

Subgroups — #17973663

Order 4352.

814 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14544955C211yesmaximal, characteristic, complemented
2#14544954C211yesmaximal, characteristic, complemented
3#14544883C211yesmaximal, characteristic, complemented
4#14544881C211yesmaximal, characteristic, complemented
5#14544839C211yesmaximal, characteristic, complemented
6#14544838C211yesmaximal, characteristic, complemented
7#14544838C211yesmaximal, characteristic, complemented
8#14544837C211yesmaximal, characteristic, complemented
9#14544729C211yesmaximal, characteristic
10#14544729C211yesmaximal, characteristic
11#14544639C211yesmaximal, characteristic
12#14544518C211yesmaximal, characteristic
13#14544518C211yesmaximal, characteristic
14#14544445C211yesmaximal, characteristic
15#14531318C211yesmaximal, characteristic
16C22×#63242C2211yescharacteristic
17C22×#63242C2211yescharacteristic
18C2×#10587544C2211yescharacteristic
19C2×#10587544C2211yescharacteristic
20C2×C4⋊#3624C2211yescharacteristic
21C2×C4⋊#3624C2211yescharacteristic
22C2×C4⋊#3624C2211yescharacteristic
23C2×C4⋊#3624C2211yescharacteristic
24C2×#10587543C2211yescharacteristic
25C2×#10587543C2211yescharacteristic
26C2×C4×#3624C2211yescharacteristic
27C2×C4×#3624C2211yescharacteristic
28C2×C4×#3624C2211yescharacteristic
29C2×C4×#3624C2211yescharacteristic
30#11763675C2211yescharacteristic
31#11763675C2211yescharacteristic
32#11763675C2211yescharacteristic
33#11763675C2211yescharacteristic
34#11763675C2211yescharacteristic
35#11763675C2211yescharacteristic
36#11763675C2211yescharacteristic
37#11763675C2211yescharacteristic
38#11763675C2211yescharacteristic
39#11763675C2211yescharacteristic
40#11763675C2211yescharacteristic
41#11763675C2211yescharacteristic
42#11763675C2211yescharacteristic
43#11763675C2211yescharacteristic
44C2×#10587582C411yescharacteristic
45C2×#10587573C2211yescharacteristic
46C2×C42×D17C2211yescharacteristic
47#11762713C411yescharacteristic
48#11762706C411yescharacteristic
49#11762693C411yescharacteristic
50#11762683C411yescharacteristic
51#11762680C411yescharacteristic
52#11762668C411yescharacteristic
53C4⋊C4×Dic17C2211yescharacteristic
54#11762660C2211yescharacteristic
55#11762660C2211yescharacteristic
56#11762656C2211yescharacteristic
57#11762656C2211yescharacteristic
58C17×#387C411yescharacteristic
59C22×C4×D17C2×C411yescharacteristic
60C22×C4×D17C2×C411yescharacteristic
61C22×C4×D17C2311yescharacteristic
62C22×Dic34C2×C411yescharacteristic
63C22×#3624C2311yescharacteristic
64C22×#3624C2311yescharacteristic
65C22×#3624C2311yescharacteristic
66C22×#3624C2311yescharacteristic
67C22×#3624C2311yescharacteristic
68C22×#3624C2311yescharacteristic
69C22×#3624C2311yescharacteristic
70C22×#3624C2311yescharacteristic
71C2×#63242—22no—
72C2×#63242—41no—
73C2×#63242—41no—
74C2×#63242—41no—
75C2×#63242—41no—
76C2×#63242Q814yescomplemented
77C2×C4⋊C4×C17C2×C411yescharacteristic
78C2×C4⋊C4×C17C2×C411yescharacteristic
79C2×C42×C17C2×C411yescharacteristic
80C2×#63227C2×C411yescharacteristic
81C2×#63227C2×C411yescharacteristic
82C2×#63227C2×C411yescharacteristic
83C2×#63227C2×C411yescharacteristic
84C2×C4⋊Dic17C2×C411yescharacteristic
85C2×#63225C2×C411yescharacteristic
86C2×#63225C2×C411yescharacteristic
87C2×#63225C2×C411yescharacteristic
88C2×#63225C2×C411yescharacteristic
89C2×#63225C2×C411yescharacteristic
90C2×#63225C2×C411yescharacteristic
91C2×C4×Dic17C2×C411yescharacteristic
92C2×C4×Dic17C2311yescharacteristic
93C2×C4×Dic17C2311yescharacteristic
94C2×C4×Dic17C2311yescharacteristic
95C2×C4×Dic17C2311yescharacteristic
96C2×C4×Dic17C2311yescharacteristic
97C2×C4×Dic17C2311yescharacteristic
98#10587582C818yescomplemented
99#10587573—41no—
100#10587573—41no—
101C42×D17—41no—
102C42×D17—41no—
103#10587544—41no—
104#10587544—41no—
105#10587543—22no—
106#10587543—22no—
107C4⋊#3624—41no—
108C4⋊#3624—41no—
109C4⋊#3624—41no—
110C4⋊#3624—41no—
111C4×#3624—41no—
112C4×#3624—41no—
113C4×#3624—41no—
114C4×#3624—41no—
115C17×#95C2×C411yescharacteristic
116C17×#95C2×C411yescharacteristic
117C17×#95C2×C411yescharacteristic
118C17×#95C2×C411yescharacteristic
119#10587502C2×C411yescharacteristic
120#10587502C2×C411yescharacteristic
121#10587502C2×C411yescharacteristic
122#10587502C2×C411yescharacteristic
123#10587502C2×C411yescharacteristic
124#10587502C2×C411yescharacteristic
125C23×D17C22×C411yescharacteristic
126C22×C4×C17C22×C411yescharacteristic
127C22×C4×C17C22×C411yescharacteristic
128C22×C4×C17C22×C411yescharacteristic
129C22×C4×C17C22×C411yescharacteristic
130C22×C4×C17C22×C411yescharacteristic
131C22×C4×C17C22×C411yescharacteristic
132C22×C4×C17C22×C411yescharacteristic
133C22×Dic17C22×C411yescharacteristic
134C22×Dic17C22×C411yescharacteristic
135C22×Dic17C22×C411yescharacteristic
136C22×Dic17C22×C411yescharacteristic
137C22×Dic17C22×C411yescharacteristic
138C22×Dic17C22×C411yescharacteristic
139C22×Dic17C2411yescharacteristic
140C2×C4×D17—21no—
141C2×C4×D17—21no—
142C2×C4×D17—21no—
143C2×C4×D17—21no—
144C2×C4×D17—22no—
145C2×C4×D17—41no—
146C2×C4×D17—41no—
147C2×C4×D17—41no—
148C2×C4×D17—41no—
149C2×C4×D17C2×C814yes—
150C2×C4×D17C2×Q812yes—
151C2×C4×D17#4112yes—
152C2×Dic34—41no—
153C2×Dic34—41no—
154C2×Dic34C2×C814yescomplemented
155C2×#3624—21no—
156C2×#3624—21no—
157C2×#3624—21no—
158C2×#3624—21no—
159C2×#3624—21no—
160C2×#3624—21no—
161C2×#3624—21no—
162C2×#3624—21no—
163C2×#3624—21no—
164C2×#3624—21no—
165C2×#3624—21no—
166C2×#3624—21no—
167C2×#3624—21no—
168C2×#3624—21no—
169C2×#3624—21no—
170C2×#3624—21no—
171C2×#3624—21no—
172C2×#3624—21no—
173C2×#3624—21no—
174C2×#3624—21no—
175C2×#3624—21no—
176C2×#3624—21no—
177C2×#3624C2×Q812yes—
178C2×#3624C2×Q812yes—
179#63242—44no—
180#63242—44no—
181C4⋊C4×C17—41no—
182C4⋊C4×C17C2×C814yescomplemented
183C42×C17—41no—
184#63227—22no—
185#63227—22no—
186#63227C2×C814yes—
187#63227C2×C814yes—
188C4⋊Dic17—41no—
189#63225—41no—
190#63225—41no—
191#63225—41no—
192#63225—41no—
193#63225C2×C814yescomplemented
194#63225C2×C814yescomplemented
195C4×Dic17—21no—
196C4×Dic17—21no—
197C4×Dic17—21no—
198C4×Dic17—21no—
199C4×Dic17—21no—
200C4×Dic17—21no—
201C4×Dic17—21no—
202C4×Dic17—21no—
203C4×Dic17—21no—
204C4×Dic17—21no—
205C4×Dic17—21no—
206C4×Dic17—21no—
207C4×Dic17—41no—
208#22287—171nomaximal, Sylow
209C23×C17C23×C411yescharacteristic
210C22×D17—21no—
211C22×D17—21no—
212C22×D17—21no—
213C22×D17—21no—
214C22×D17C4×Q812yes—
215C22×D17C22×C812yes—
216C22×D17#13112yes—
217C2×C4×C17—21no—
218C2×C4×C17—21no—
219C2×C4×C17—21no—
220C2×C4×C17—21no—
221C2×C4×C17—21no—
222C2×C4×C17—21no—
223C2×C4×C17—21no—
224C2×C4×C17—21no—
225C2×C4×C17—21no—
226C2×C4×C17—21no—
227C2×C4×C17—21no—
228C2×C4×C17—21no—
229C2×C4×C17—21no—
230C2×C4×C17—21no—
231C2×C4×C17—21no—
232C2×C4×C17—21no—
233C2×C4×C17—21no—
234C2×C4×C17C4×Q812yes—
235C2×C4×C17C22×C812yes—
236C2×C4×C17C22×C812yes—
237C2×C4×C17C22×C812yes—
238C2×Dic17—21no—
239C2×Dic17—21no—
240C2×Dic17—21no—
241C2×Dic17—21no—
242C2×Dic17—21no—
243C2×Dic17—21no—
244C2×Dic17—21no—
245C2×Dic17—21no—
246C2×Dic17—21no—
247C2×Dic17—21no—
248C2×Dic17—21no—
249C2×Dic17—21no—
250C2×Dic17—21no—
251C2×Dic17—21no—
252C2×Dic17—21no—
253C2×Dic17C22×C812yes—
254C2×Dic17C22×C812yes—
255C2×Dic17C22×C812yes—
256C2×Dic17C22×Q811yescharacteristic
257C2×Dic17C2×#4111yescharacteristic
258C2×Dic17H(5,𝔽2)11yescharacteristic
259C2×Dic17H(5,𝔽2)11yescharacteristic
260C2×Dic17H(5,𝔽2)11yescharacteristic
261C2×Dic172−1+411yescharacteristic
262C4×D17—22no—
263C4×D17—22no—
264C4×D17—22no—
265C4×D17—22no—
266C4×D17—44no—
267C4×D17—44no—
268Dic34—44no—
269#3624—22no—
270#3624—22no—
271#3624—41no—
272#3624—41no—
273#3624—41no—
274#3624—41no—
275#3624—41no—
276#3624—41no—
277C4×C22⋊Q8—171no—
278#1984—171no—
279#1984—171no—
280#1939—171no—
281#1939—171no—
282#1916—171no—
283#1916—171no—
284#1916—171no—
285#1916—171no—
286#1850—171no—
287#1850—171no—
288#1797—171no—
289C8×C22⋊C4—171no—
290C8×C22⋊C4—171no—
291C2×#336—171no—
292C22×C17C2×C4×Q811yescharacteristic
293C22×C17#51811yescharacteristic
294C22×C17#52011yescharacteristic
295C22×C17C23×C811yescharacteristic
296C22×C17C2×#13111yescharacteristic
297C22×C17#56811yescharacteristic
298C22×C17#56811yescharacteristic
299C2×D17—22no—
300C2×D17—22no—
301C2×D17—22no—
302C2×D17—22no—
303C2×D17—22no—
304C2×D17—22no—
305C2×D17C8×Q814yes—
306C4×C17—22no—
307C4×C17—22no—
308C4×C17—22no—
309C4×C17—22no—
310C4×C17—41no—
311C4×C17—41no—
312C4×C17—41no—
313Dic17—22no—
314Dic17—22no—
315Dic17—22no—
316Dic17—41no—
317Dic17—41no—
318Dic17—41no—
319Dic17#53811yescharacteristic
320Dic17#53911yescharacteristic
321Dic17#54311yescharacteristic
322Dic17#54411yescharacteristic
323C23×C8—171no—
324C23×C8—171no—
325C2×C22⋊Q8—171no—
326C2×C4×Q8—171no—
327C22×C42—171no—
328C2×C4⋊C8—171no—
329C2×C4⋊C8—171no—
330C2×C4⋊C8—171no—
331C2×C4⋊C8—171no—
332C2×C4⋊C8—171no—
333C2×C4⋊C8—171no—
334C2×C22⋊C8—171no—
335C2×C22⋊C8—171no—
336C2×C4×C8—171no—
337C2×C4×C8—171no—
338C2×C4×C8—171no—
339C2×C4×C8—171no—
340#391—171no—
341#389—171no—
342#387—171no—
343#387#59511yescharacteristic
344#385—171no—
345#385—171no—
346#380—171no—
347C4×C4⋊C4—171no—
348C4×C4⋊C4—171no—
349C4×C4⋊C4—171no—
350C4×C22⋊C4—171no—
351C4×C22⋊C4—171no—
352#336—171no—
353#336—171no—
354#336—171no—
355#336—171no—
356#336—171no—
357#336—171no—
358#336—171no—
359#336—171no—
360#336—171no—
361#336—171no—
362#336—171no—
363#336—171no—
364#336—171no—
365#336—171no—
366C2×C17#232911yescharacteristic
367C2×C17C2×C8×Q811yescharacteristic
368C2×C17#296111yescharacteristic
369C2×C17#297211yescharacteristic
370C2×C17#297611yescharacteristic
371C2×C17#298811yescharacteristic
372C2×C17#299211yescharacteristic
373D17—24no—
374C22×Q8—171no—
375C23×C4—171no—
376C23×C4—171no—
377C23×C4—171no—
378C22×C8—171no—
379C22×C8—171no—
380C22×C8—174no—
381C22×C8—171no—
382C22×C8—171no—
383C22×C8—171no—
384C22×C8—171no—
385C22×C8—171no—
386C22×C8—171no—
387C22×C8—342no—
388C22×C8—681no—
389C22×C8—681no—
390C22×C8—681no—
391C22×C8—681no—
392C22⋊Q8—178no—
393C4×Q8—681no—
394C4×Q8—681no—
395C2×C4⋊C4—171no—
396C2×C4⋊C4—171no—
397C2×C4⋊C4—171no—
398C2×C4⋊C4—171no—
399C2×C4⋊C4—171no—
400C2×C4⋊C4—171no—
401C2×C4⋊C4—171no—
402C2×C4⋊C4C2×#59511yescharacteristic
403C2×C4⋊C4C2×#59511yescharacteristic
404C2×C22⋊C4—171no—
405C2×C22⋊C4—171no—
406C2×C22⋊C4—171no—
407C2×C22⋊C4—171no—
408C2×C42—171no—
409C2×C42—171no—
410C2×C42—171no—
411C2×C42—171no—
412C2×C42—171no—
413C2×C42—171no—
414C2×C42—171no—
415C2×C42—681no—
416C2×C42—681no—
417C2×C42C2×#59511yescharacteristic
418C4⋊C8—681no—
419C4⋊C8—681no—
420C4⋊C8—681no—
421C4⋊C8—681no—
422C4⋊C8—681no—
423C4⋊C8—681no—
424C22⋊C8—342no—
425C22⋊C8—342no—
426C4×C8—681no—
427C4×C8—681no—
428C4×C8—681no—
429C4×C8—681no—
430#95—171no—
431#95—171no—
432#95—171no—
433#95—171no—
434#95—171no—
435#95—171no—
436#95C2×#59511yescharacteristic
437#95C2×#59511yescharacteristic
438#95C2×#59511yescharacteristic
439#95C2×#59511yescharacteristic
440C17#2228711yescharacteristic, complemented, Sylow
441C24—171no—
442C2×Q8—174no—
443C2×Q8—681no—
444C2×Q8—681no—
445C22×C4—171no—
446C22×C4—171no—
447C22×C4—171no—
448C22×C4—171no—
449C22×C4—172no—
450C22×C4—172no—
451C22×C4—174no—
452C22×C4—171no—
453C22×C4—171no—
454C22×C4—171no—
455C22×C4—341no—
456C22×C4—341no—
457C22×C4—341no—
458C22×C4—341no—
459C22×C4—342no—
460C22×C4—681no—
461C22×C4—681no—
462C22×C4—681no—
463C22×C4—681no—
464C22×C4C22×#59511yescharacteristic
465C22×C4C22×#59511yescharacteristic
466C22×C4C22×#59511yescharacteristic
467C22×C4C22×#59511yescharacteristic
468C22×C4C22×#59511yescharacteristic
469C22×C4C22×#59511yescharacteristic
470C22×C4C22×#59511yescharacteristic
471C2×C8—172no—
472C2×C8—172no—
473C2×C8—341no—
474C2×C8—341no—
475C2×C8—341no—
476C2×C8—341no—
477C2×C8—341no—
478C2×C8—341no—
479C2×C8—341no—
480C2×C8—341no—
481C2×C8—341no—
482C2×C8—341no—
483C2×C8—341no—
484C2×C8—341no—
485C2×C8—341no—
486C2×C8—341no—
487C2×C8—341no—
488C2×C8—341no—
489C2×C8—341no—
490C2×C8—341no—
491C2×C8—341no—
492C2×C8—341no—
493C2×C8—341no—
494C2×C8—341no—
495C2×C8—684no—
496C2×C8—684no—
497C4⋊C4—41no—
498C4⋊C4—174no—
499C4⋊C4—174no—
500C4⋊C4—681no—
501C4⋊C4—681no—
502C4⋊C4—681no—
503C4⋊C4—681no—
504C4⋊C4—681no—
505C4⋊C4#6324214yescomplemented
506C22⋊C4—174no—
507C22⋊C4—174no—
508C22⋊C4—342no—
509C22⋊C4—342no—
510C42—41no—
511C42—341no—
512C42—341no—
513C42—341no—
514C42—341no—
515C42—341no—
516C42—341no—
517C42—341no—
518C42—341no—
519C42—341no—
520C42—341no—
521C42—341no—
522C42—341no—
523C42—681no—
524C23—172no—
525C23—172no—
526C23—172no—
527C23—341no—
528C23—341no—
529C23—341no—
530C23—341no—
531C23C23×#59511yescharacteristic
532Q8—684no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—171no—
551C2×C4—171no—
552C2×C4—171no—
553C2×C4—171no—
554C2×C4—171no—
555C2×C4—171no—
556C2×C4—172no—
557C2×C4—172no—
558C2×C4—172no—
559C2×C4—342no—
560C2×C4—342no—
561C2×C4—342no—
562C2×C4—342no—
563C2×C4—341no—
564C2×C4—341no—
565C2×C4—341no—
566C2×C4—341no—
567C2×C4—341no—
568C2×C4—341no—
569C2×C4—341no—
570C2×C4—341no—
571C2×C4—341no—
572C2×C4—341no—
573C2×C4—341no—
574C2×C4—341no—
575C2×C4—341no—
576C2×C4—341no—
577C2×C4—341no—
578C2×C4—684no—
579C2×C4—684no—
580C2×C4C2×#6324212yes—
581C2×C4C2×#6324212yes—
582C2×C4C2×#6324212yes—
583C2×C4Q8×#59512yes—
584C8—342no—
585C8—342no—
586C8—681no—
587C8—681no—
588C8—681no—
589C8—681no—
590C8—681no—
591C8—681no—
592C22—174no—
593C22—342no—
594C22—342no—
595C22—342no—
596C22—342no—
597C22—342no—
598C22—342no—
599C22C2×Q8×#59511yescharacteristic
600C22#1176387611yescharacteristic
601C22#1176387811yescharacteristic
602C22C22×#6324211yescharacteristic
603C22D17⋊#13111yescharacteristic
604C22#1176388811yescharacteristic
605C22#1176388811yescharacteristic
606C4—22no—
607C4—22no—
608C4—22no—
609C4—22no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—171no—
614C4—171no—
615C4—171no—
616C4—171no—
617C4—342no—
618C4—342no—
619C4—342no—
620C4—681no—
621C4—681no—
622C4—681no—
623C2—344no—
624C2#1454527711yescharacteristic
625C2Q8×#6324211yescharacteristic
626C2#1454557611yescharacteristic
627C2#1454563211yescharacteristic
628C2#1454565211yescharacteristic
629C2#1454570111yescharacteristic
630C2#1454572211yescharacteristic
subgroupG/H
center, FrattiniC23C23×#595
commutatorC22×C17C23×C8
FittingC17×#387C4
socleC23×C17C23×C4
prime radicalC23×D17C22×C4
cosocleC22×Dic17C24
hypercenter#387#595
hypocenterC17#22287
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #14544955C2semidirect
2. #14544954C2semidirect
3. #14544883C2semidirect
4. #14544881C2semidirect
5. #14544839C2semidirect
6. #14544838C2semidirect
7. #14544838C2semidirect
8. #14544837C2semidirect
76. C2×#63242Q8semidirect
98. #10587582C8semidirect
154. C2×Dic34C2×C8semidirect
182. C4⋊C4×C17C2×C8semidirect
193. #63225C2×C8semidirect
194. #63225C2×C8semidirect
440. C17#22287semidirect
505. C4⋊C4#63242semidirect

Maximal subgroups

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

subgroupindex
#145449552
#145449542
#145448832
#145448812
#145448392
#145448382
#145448372
#145447292
#145446392
#145445182
#145444452
#145313182
#2228717