Finite Group Databasebeta

← #14775694

Subgroups — #14775694

Order 2816.

834 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622460C211yesmaximal, characteristic
2#13071710C211yesmaximal, characteristic, complemented
3#13071527C211yesmaximal, characteristic
4#13069581C211yesmaximal, characteristic, complemented
5#13069386C211yesmaximal, characteristic, complemented
6#13069359C211yesmaximal, characteristic, complemented
7#13069354C211yesmaximal, characteristic, complemented
8#13069195C211yesmaximal, characteristic, complemented
9#13069188C211yesmaximal, characteristic, complemented
10#13068880C211yesmaximal, characteristic
11#13068866C211yesmaximal, characteristic
12#13068442C211yesmaximal, characteristic
13#13068442C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C11×#1770C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33#10622602—21no—
34#10622602—21no—
35#10622591—21no—
36#10622585—21no—
37#10622549C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622460C418yescomplemented
46#10622280—21no—
47D11×#95—21no—
48#10622265—21no—
49#10622262—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C4×D44—22no—
93C4×D44—22no—
94C4×D44—22no—
95C4×D44—41no—
96C4×D44—41no—
97C4×D44C2×C414yes—
98#66923—22no—
99#66923C2×C414yescomplemented
100C11×C4⋊C8C2×C414yescomplemented
101C11×#97—41no—
102C11×#97—41no—
103C4×C8×C11—22no—
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115#66885—22no—
116#66885C2×C414yes—
117#66885C2×C414yes—
118#66885Q814yes—
119#66882—41no—
120#66882C2×C414yescomplemented
121#66881—41no—
122#66881C2×C414yescomplemented
123#22972—111nomaximal, Sylow
124C23×D11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44C22×C412yes—
143C2×D44C2×Q812yes—
144C2×D44#4112yes—
145C2×C4×D11—24no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—81no—
151C2×C4×D11—81no—
152C2×C4×D11—81no—
153C2×C4×D11—81no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C2×C8×C11C2×Q812yes—
166C11×C4⋊C4—41no—
167C11×C4⋊C4—41no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11C22×C412yes—
173C42×C11#4112yes—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—42no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22×C412yes—
188C4⋊Dic11C22×C412yes—
189C4⋊Dic11C22×C412yes—
190C4⋊Dic11C2×Q812yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—24no—
193Dic11⋊C4—42no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196Dic11⋊C4—81no—
197C4×Dic11—42no—
198C4×Dic11—81no—
199C4×Dic11—81no—
200C2×#478—111no—
201#2370—111no—
202#2349—111no—
203#1991—111no—
204#1949—111no—
205#1944—111no—
206#1943—111no—
207#1919—111no—
208#1918—111no—
209#1864—111no—
210#1862—111no—
211#1770D1111yescharacteristic, complemented
212#1762—111no—
213#1762—111no—
214C4×#102—111no—
215C23×C11C22×D411yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—41no—
220C22×D11—41no—
221C22×D11—41no—
222C22×D11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11C4×D412yes—
240C2×C4×C11C4×D412yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×Q811yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268D44—22no—
269D44—22no—
270D44—22no—
271D44C4×Q814yes—
272C4×D11—84no—
273C4×D11—84no—
274C4×D11—84no—
275C8×C11—22no—
276C8×C11—22no—
277C8×C11—22no—
278C8×C11—41no—
279C2×#125—111no—
280C2×C4×D4—111no—
281C2×C4×D4—111no—
282C2×C4×D4—111no—
283#478—118no—
284C2×#107—111no—
285C2×#107—111no—
286C2×#106—111no—
287C2×#106—111no—
288C2×C4⋊C8C2×D1111yescharacteristic
289C2×#102—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#97C2×D1111yescharacteristic
294C2×#97C2×D1111yescharacteristic
295C2×C4×C8C2×D1111yescharacteristic
296#389—111no—
297#389—111no—
298#389—111no—
299#389—111no—
300#389—221no—
301#387—221no—
302#387—221no—
303#385—221no—
304#385—221no—
305#382—111no—
306#380—221no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—221no—
311C4×C4⋊C4C2×D1111yescharacteristic
312C2×#95—221no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#336C2×D1111yescharacteristic
322#336C2×D1111yescharacteristic
323C22×C11C2×C4×D411yescharacteristic
324C22×C11#54611yescharacteristic
325C22×C11D4×Q811yescharacteristic
326C22×C11#57511yescharacteristic
327C22×C11#57511yescharacteristic
328C22×C11#57611yescharacteristic
329C22×C11#57711yescharacteristic
330C2×D11—24no—
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11C2×C4×Q811yescharacteristic
344C4×C11#52011yescharacteristic
345C4×C11#55211yescharacteristic
346C4×C11#55411yescharacteristic
347Dic11—42no—
348Dic11—42no—
349Dic11—42no—
350Dic11—42no—
351Dic11—81no—
352Dic11—81no—
353Dic11—81no—
354C22×D4—111no—
355C23×C4—221no—
356C23×C4—221no—
357C23×C4—221no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#125—114no—
363#125—222no—
364C4×D4—114no—
365C4×D4—222no—
366C4×D4—222no—
367C4×D4—222no—
368C4×D4—441no—
369C4×D4—441no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4D4411yescharacteristic
384C2×C4⋊C4D4411yescharacteristic
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C42—221no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394#107—114no—
395#107—441no—
396#106—114no—
397#106—441no—
398C4⋊C8C4×D1114yescomplemented
399#102—114no—
400#102—114no—
401#102—114no—
402#102—222no—
403#97—41no—
404#97—41no—
405C4×C8—22no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95D4411yescharacteristic
416#95D4411yescharacteristic
417C2×C11#236011yescharacteristic
418C2×C11#294311yescharacteristic
419C2×C11#294611yescharacteristic
420C2×C11#332211yescharacteristic
421C2×C11#332311yescharacteristic
422C2×C11#338811yescharacteristic
423C2×C11#338911yescharacteristic
424D11—44no—
425C24—221no—
426C2×D4—112no—
427C2×D4—112no—
428C2×D4—112no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—224no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4—881no—
445C22×C4—881no—
446C22×C4—881no—
447C22×C4—881no—
448C22×C4C2×D4411yescharacteristic
449C22×C4C2×D4411yescharacteristic
450C22×C4C2×D4411yescharacteristic
451C22×C4C2×D4411yescharacteristic
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×D4411yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8C2×C4×D1112yes—
465C2×C8C2×C4×D1112yes—
466C2×C8Q8×D1112yes—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—112no—
470C4⋊C4—112no—
471C4⋊C4—112no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—442no—
486C4⋊C4—881no—
487C4⋊C4—881no—
488C4⋊C4—881no—
489C22⋊C4—224no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—442no—
497C42—881no—
498C42—881no—
499C42C2×C4×D1112yes—
500C42#433912yes—
501C11#2297211yescharacteristic, complemented, Sylow
502C23—222no—
503C23—222no—
504C23—222no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23C22×D4411yescharacteristic
510D4—114no—
511D4—222no—
512D4—222no—
513D4—222no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—884no—
552C2×C4—884no—
553C2×C4—884no—
554C2×C4C4×D4412yes—
555C2×C4C4×D4412yes—
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C2×#433911yescharacteristic
558C2×C4#6703711yescharacteristic
559C2×C4C2×Q8×D1111yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#6704311yescharacteristic
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C22—224no—
567C22—442no—
568C22—442no—
569C22—442no—
570C22—442no—
571C22—442no—
572C22—442no—
573C22C2×C4×D4411yescharacteristic
574C22#1062308511yescharacteristic
575C22Q8×D4411yescharacteristic
576C22#1062327911yescharacteristic
577C22#1062327911yescharacteristic
578C22#1062328211yescharacteristic
579C22#1062328311yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—442no—
587C4—442no—
588C4—442no—
589C4—442no—
590C4—881no—
591C4—881no—
592C4—881no—
593C4#1062304211yescharacteristic
594C4#1062306011yescharacteristic
595C4#1062307711yescharacteristic
596C4C4×Q8×D1111yescharacteristic
597C2—444no—
598C2#1307162311yescharacteristic
599C2#1307741811yescharacteristic
600C2#1307745011yescharacteristic
601C2#1308081911yescharacteristic
602C2#1308083411yescharacteristic
603C2#1308156311yescharacteristic
604C2#1308157611yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1770C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1770D11
hypocenterC11#22972
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1770

Complements

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

NH ≅ G/Ntype
2. #13071710C2semidirect
4. #13069581C2semidirect
5. #13069386C2semidirect
6. #13069359C2semidirect
7. #13069354C2semidirect
8. #13069195C2semidirect
9. #13069188C2semidirect
15. C11×#1770C2semidirect
45. #10622460C4semidirect
99. #66923C2×C4semidirect
100. C11×C4⋊C8C2×C4semidirect
120. #66882C2×C4semidirect
122. #66881C2×C4semidirect
211. #1770D11semidirect
398. C4⋊C8C4×D11semidirect
501. C11#22972semidirect

Maximal subgroups

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

subgroupindex
C2×#106224602
#130717102
#130715272
#130695812
#130693862
#130693592
#130693542
#130691952
#130691882
#130688802
#130688662
#130684422
C4×#668852
C11×#17702
#2297211