Finite Group Databasebeta

← #14826381

Subgroups — #14826381

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071710C211yesmaximal, characteristic, complemented
2#13070004C211yesmaximal, characteristic
3#13069954C211yesmaximal, characteristic, complemented
4#13069951C211yesmaximal, characteristic, complemented
5#13069762C211yesmaximal, characteristic
6#13069574C211yesmaximal, characteristic, complemented
7#13069356C211yesmaximal, characteristic, complemented
8#13069240C211yesmaximal, characteristic
9#13069233C211yesmaximal, characteristic
10#13069191C211yesmaximal, characteristic, complemented
11#13069184C211yesmaximal, characteristic, complemented
12#13069182C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic
14#13068441C211yesmaximal, characteristic
15C11×#2454C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66923C2211yescharacteristic
19C11×#399—21no—
20C11×#396—21no—
21C11×#390C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#385—21no—
26C11×#380—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622591—21no—
33#10622585—21no—
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622265—21no—
46#10622262—21no—
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C11×#125—22no—
62C11×#125—41no—
63C4×D4×C11—22no—
64C4×D4×C11—41no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66923—22no—
98#66923—22no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103#66896—22no—
104#66896—22no—
105#66896—41no—
106#66896Q814yes—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112#66872—22no—
113#66872—22no—
114#66871—22no—
115#66871—41no—
116C4⋊(C11⋊C8)—41no—
117#66867—41no—
118#27027—111nomaximal, Sylow
119C24×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11C2×Q812yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11—81no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—41no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—42no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4—81no—
154C11×C4⋊C4#4112yes—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—81no—
158C11×C22⋊C4—81no—
159C11×C22⋊C4—81no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11C2×Q812yes—
172C4⋊Dic11#4112yes—
173C4⋊Dic11#4112yes—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—42no—
177Dic11⋊C4—81no—
178C4×Dic11—42no—
179C4×Dic11—81no—
180C4×Dic11—81no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8C2×Q812yes—
193#2454D1111yescharacteristic
194#2370—111no—
195#2067—111no—
196#2059—111no—
197#2059—111no—
198#2025—111no—
199#1989—111no—
200#1944—111no—
201#1926—111no—
202#1925—111no—
203#1919—111no—
204#1918—111no—
205#1917—111no—
206#1864—111no—
207#1762—111no—
208C23×C11—22no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11C22×D411yescharacteristic
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—41no—
219D4×C11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
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×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—84no—
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
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—
266C11⋊C8—22no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C2×#125—111no—
271C2×#125C2×D1111yescharacteristic
272C2×C4×D4C2×D1111yescharacteristic
273C2×#107—111no—
274C2×#107—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×#102—111no—
279C2×#102—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#97—111no—
283#399—21no—
284#396—21no—
285#390C2×D1111yescharacteristic
286#390C2×D1111yescharacteristic
287#389—111no—
288#389—111no—
289#389—221no—
290#389C2×D1111yescharacteristic
291#389C2×D1111yescharacteristic
292#387—221no—
293#387—221no—
294#385—21no—
295#380—21no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4—221no—
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11#52511yescharacteristic
321C22×C11#54611yescharacteristic
322C22×C11D4×Q811yescharacteristic
323C22×C11#57511yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57611yescharacteristic
326C22×C11#57711yescharacteristic
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—41no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11#53311yescharacteristic
337C4×C11#54211yescharacteristic
338C4×C11#55411yescharacteristic
339C4×C11#55611yescharacteristic
340Dic11—42no—
341Dic11—42no—
342Dic11—42no—
343Dic11—81no—
344C22×D4C22×D1111yescharacteristic
345C23×C4—21no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—111no—
349C22×C8—111no—
350#125—22no—
351#125—41no—
352#125—222no—
353#125—222no—
354C4×D4—22no—
355C4×D4—41no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22⋊D1111yescharacteristic
369C2×C4⋊C4C22⋊D1111yescharacteristic
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382C2×C42C22×D1111yescharacteristic
383C2×C42C22×D1111yescharacteristic
384#107—222no—
385#107—441no—
386#106—222no—
387#106—222no—
388C4⋊C8—441no—
389#102—114no—
390#102—222no—
391#102—222no—
392#102—441no—
393#97—441no—
394#95—21no—
395#95—21no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95C22⋊D1111yescharacteristic
402#95C22⋊D1111yescharacteristic
403C2×C11—82no—
404C2×C11#246511yescharacteristic
405C2×C11#311111yescharacteristic
406C2×C11#311911yescharacteristic
407C2×C11#330911yescharacteristic
408C2×C11#332311yescharacteristic
409C2×C11#338811yescharacteristic
410C2×C11#338911yescharacteristic
411C24—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4Q8×D1112yes—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—81no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—112no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—42no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—112no—
461C4⋊C4—224no—
462C4⋊C4—224no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—442no—
469C4⋊C4—881no—
470C4⋊C4#434112yes—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—442no—
483C42—881no—
484C42—881no—
485C11#2702711yescharacteristic, complemented, Sylow
486C23—22no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23C22×C22⋊D1111yescharacteristic
494D4—22no—
495D4—22no—
496D4—41no—
497D4—41no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4C2×#434111yescharacteristic
539C2×C4#6703711yescharacteristic
540C2×C4C2×Q8×D1111yescharacteristic
541C2×C4#6704011yescharacteristic
542C2×C4#41×D1111yescharacteristic
543C2×C4#41×D1111yescharacteristic
544C8—222no—
545C8—441no—
546C8—441no—
547C8—441no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22#1062333711yescharacteristic
556C22Q8×C22⋊D1111yescharacteristic
557C22#1062335311yescharacteristic
558C22#1062335311yescharacteristic
559C22#1062335911yescharacteristic
560C22#1062336611yescharacteristic
561C22#1062336711yescharacteristic
562C4—41no—
563C4—41no—
564C4—42no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—442no—
572C4—442no—
573C4—442no—
574C4—881no—
575C4#1062315311yescharacteristic
576C4#1062316711yescharacteristic
577C4#1062317111yescharacteristic
578C4#1062317211yescharacteristic
579C2—82no—
580C2#1307263311yescharacteristic
581C2#1307871911yescharacteristic
582C2#1307880911yescharacteristic
583C2#1308062211yescharacteristic
584C2#1308083211yescharacteristic
585C2#1308156111yescharacteristic
586C2#1308157011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2454C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2454D11
hypocenterC11#27027
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2454

Complements

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

NH ≅ G/Ntype
1. #13071710C2semidirect
3. #13069954C2semidirect
4. #13069951C2semidirect
6. #13069574C2semidirect
7. #13069356C2semidirect
10. #13069191C2semidirect
11. #13069184C2semidirect
12. #13069182C2semidirect
485. C11#27027semidirect

Maximal subgroups

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

subgroupindex
#130717102
#130700042
#130699542
#130699512
#130697622
#130695742
#130693562
#130692402
#130692332
#130691912
#130691842
#130691822
#130688772
#130684412
C11×#24542
#2702711