Finite Group Databasebeta

← #14910302

Subgroups — #14910302

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622808C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic, complemented
3#13080359C211yesmaximal, characteristic, complemented
4#13070885C211yesmaximal, characteristic, complemented
5#13070731C211yesmaximal, characteristic, complemented
6#13070705C211yesmaximal, characteristic, complemented
7#13070671C211yesmaximal, characteristic, complemented
8#13070663C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070554C211yesmaximal, characteristic, complemented
11#13070549C211yesmaximal, characteristic, complemented
12#13070539C211yesmaximal, characteristic, complemented
13#13070480C211yesmaximal, characteristic, complemented
14#13070442C211yesmaximal, characteristic, complemented
15C11×#3283C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C2×C11×#135C2211yescharacteristic
18C11×#547—21no—
19C22×Dic44C2211yescharacteristic
20C2×#66957C2211yescharacteristic
21#10623083—21no—
22C11×#494C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C11×#467C2211yescharacteristic
25C11×#461—21no—
26C11×#452—21no—
27C11×#452—21no—
28C4×C11×D8C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic
30#10622808—24no—
31#10622807—24no—
32C2×#66893C2211yescharacteristic
33C2×#66893C2211yescharacteristic
34C2×#66893C2211yescharacteristic
35C2×#66893C2211yescharacteristic
36C2×#66892C2211yescharacteristic
37C2×#66892C2211yescharacteristic
38C2×#66891C2211yescharacteristic
39C2×#66891C2211yescharacteristic
40C2×#66890C2211yescharacteristic
41#10622729C2211yescharacteristic
42#10622728C2211yescharacteristic
43C2×#66876C2211yescharacteristic
44C22×C11⋊C16C2211yescharacteristic
45#10622458—21no—
46#10622351—21no—
47#10622346—21no—
48C4×Dic44C2211yescharacteristic
49#10622309C2211yescharacteristic
50#10622202C2211yescharacteristic
51#10622202C2211yescharacteristic
52#10622200C2211yescharacteristic
53C22⋊(C11⋊C16)C2211yescharacteristic
54C22⋊(C11⋊C16)C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622127C2211yescharacteristic
59C4⋊(C11⋊C16)C2211yescharacteristic
60#10622099C2211yescharacteristic
61C2×C11×#41—21no—
62C2×C11×#41—21no—
63C2×#4339—21no—
64C22×Dic22—21no—
65C11×#135—22no—
66C11×#135—22no—
67C11×#135—41no—
68C11×#135—41no—
69C2×C11×Q16—21no—
70C2×C11×Q16C2311yescharacteristic
71C2×C11×Q16C2311yescharacteristic
72C2×C11×SD16—21no—
73C2×C11×SD16—21no—
74C2×C11×D8C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—21no—
78C11×#123—41no—
79C11×#123—41no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×#121—41no—
83C4×D4×C11—21no—
84C4×D4×C11D411yescharacteristic
85C2×C11×C4⋊C4—41no—
86#66992—41no—
87#66983—21no—
88#66977—21no—
89C2×Dic44—22no—
90C2×Dic44—21no—
91C2×Dic44—41no—
92C2×Dic44C2311yescharacteristic
93C2×Dic44C2311yescharacteristic
94#66957—22no—
95#66957—41no—
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C2×#4314—21no—
99#66949—41no—
100#66938—41no—
101(C22⋊D11)⋊C4—41no—
102#66928—21no—
103C4×Dic22—21no—
104C11×#107C2311yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×#103—21no—
107C11×#103—21no—
108C11×#102—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66893—22no—
113#66893—22no—
114#66893—22no—
115#66893—41no—
116#66892—22no—
117#66892—41no—
118#66891—22no—
119#66891D414yescomplemented
120#66890—22no—
121#66885—21no—
122#66882C2311yescharacteristic
123#66880—21no—
124#66880—21no—
125#66876—22no—
126C2×C11⋊C16—22no—
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131#33835—111nomaximal, Sylow
132C11×#41—42no—
133C11×#41—42no—
134C11×#41—81no—
135C11×#41—81no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11D811yescharacteristic
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C22×Dic11—41no—
150#4339—42no—
151#4339—81no—
152C2×D44—21no—
153C2×C4×D11—41no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—42no—
157C2×Dic22—41no—
158C2×Dic22—81no—
159C11×Q16—21no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×Q16—81no—
164C11×SD16—42no—
165C11×SD16—42no—
166C11×D8—21no—
167C11×D8C2×D412yes—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4D811yescharacteristic
182C11×C22⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4D811yescharacteristic
186C11×C22⋊C4D811yescharacteristic
187C42×C11C2×D411yescharacteristic
188C22⋊Dic11—41no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—41no—
191(C2×D11)⋊C4—41no—
192C4⋊Dic11—21no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195C4×Dic11—41no—
196Dic44—21no—
197Dic44—21no—
198Dic44—21no—
199Dic44—42no—
200Dic44C2×D412yes—
201D88—21no—
202D88—21no—
203#4314—42no—
204#4314—81no—
205C11⋊C16—21no—
206C11⋊C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#510—111no—
210C2×#508—111no—
211#3285—111no—
212#3283D1111yescharacteristic, complemented
213#2251—111no—
214#2220—111no—
215#2216—111no—
216#2210—111no—
217#2209—111no—
218#2189—111no—
219#2189—111no—
220#2188—111no—
221#2186—111no—
222#2175—111no—
223#2168—111no—
224C23×C11—41no—
225C23×C11C2×D811yescharacteristic
226C23×C11C2×D811yescharacteristic
227C22×D11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232D4×C11—22no—
233D4×C11—41no—
234D4×C11—41no—
235D4×C11—82no—
236D4×C11—82no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—82no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11C2×D811yescharacteristic
248C2×C4×C11C2×D811yescharacteristic
249C2×C4×C11C2×D811yescharacteristic
250C2×C4×C11C2×D811yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C22⋊D11—82no—
253C22⋊D11—82no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—82no—
258D44—41no—
259D44—41no—
260C4×D11—82no—
261Dic22—22no—
262Dic22—41no—
263Dic22—41no—
264Dic22—41no—
265Dic22—82no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11C22×D411yescharacteristic
270C8×C11H(5,𝔽2)11yescharacteristic
271C2×#135—111no—
272C2×#135C2×D1111yescharacteristic
273C2×#135C2×D1111yescharacteristic
274C22×Q16—111no—
275#548—221no—
276#547—21no—
277#510—224no—
278#508—224no—
279C2×Q32—111no—
280C2×Q32—111no—
281C2×Q32—111no—
282C2×Q32—111no—
283C2×SD32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×D16—111no—
288C2×M32—111no—
289C22×C16—111no—
290#495—111no—
291#494C2×D1111yescharacteristic
292#467—111no—
293#467C2×D1111yescharacteristic
294#467C2×D1111yescharacteristic
295#466—111no—
296#464—221no—
297#461—21no—
298#452—21no—
299#452—21no—
300#452—221no—
301#448—221no—
302C4×Q16—111no—
303C4×D8C2×D1111yescharacteristic
304C8×D4C2×D1111yescharacteristic
305#366—111no—
306C4⋊C16—111no—
307#358—111no—
308#358—111no—
309#358—111no—
310#358—111no—
311#357—111no—
312#357—111no—
313C22⋊C16—111no—
314C22⋊C16—111no—
315#346—111no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11C22×D811yescharacteristic
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11D4211yescharacteristic
337C4×C11#57611yescharacteristic
338Dic11—42no—
339Dic11—81no—
340Dic11—81no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—221no—
344C22×Q8—221no—
345#135—22no—
346#135—22no—
347#135—41no—
348#135—41no—
349#135—222no—
350#135—441no—
351C2×Q16—21no—
352C2×Q16—111no—
353C2×Q16—111no—
354C2×Q16—222no—
355C2×Q16—221no—
356C2×Q16—441no—
357C2×Q16C22×D1111yescharacteristic
358C2×Q16C22×D1111yescharacteristic
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—111no—
364C2×D8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C4⋊Q8—21no—
368#124—221no—
369#124—441no—
370#123—41no—
371#123—41no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—221no—
375C22⋊Q8—441no—
376#121—41no—
377#121—221no—
378#121—441no—
379C4×Q8—221no—
380C4×D4—21no—
381C4×D4—441no—
382C4×D4C22⋊D1111yescharacteristic
383C2×C4⋊C4—41no—
384Q32—222no—
385Q32—222no—
386Q32—222no—
387Q32—441no—
388SD32—114no—
389SD32—222no—
390SD32—222no—
391SD32—441no—
392D16—222no—
393M32—222no—
394C2×C16—111no—
395C2×C16—111no—
396C2×C16—111no—
397C2×C16—111no—
398C2×C16—222no—
399#107—111no—
400#107C22×D1111yescharacteristic
401C4⋊C8C22⋊D1111yescharacteristic
402#103—21no—
403#103—21no—
404#103—221no—
405#103—221no—
406#102—21no—
407#102—221no—
408C22⋊C8C22⋊D1111yescharacteristic
409C22⋊C8C22⋊D1111yescharacteristic
410C4×C8C22×D1111yescharacteristic
411C2×C11—41no—
412C2×C11—41no—
413C2×C11—82no—
414C2×C11D4×D811yescharacteristic
415C2×C11#341411yescharacteristic
416C2×C11#341711yescharacteristic
417D11—161no—
418#41—42no—
419#41—42no—
420#41—81no—
421#41—81no—
422#41—442no—
423#41—881no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—442no—
429C2×Q8—441no—
430C2×Q8—881no—
431C2×D4—21no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—221no—
435C2×D4—441no—
436C2×D4—441no—
437C2×D4#432311yescharacteristic
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445Q16—21no—
446Q16—21no—
447Q16—21no—
448Q16—21no—
449Q16—81no—
450Q16—112no—
451Q16—221no—
452Q16—221no—
453Q16—221no—
454Q16—442no—
455SD16—42no—
456SD16—42no—
457SD16—442no—
458SD16—881no—
459D8—21no—
460D8—221no—
461D8—221no—
462D8D4×D1112yes—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8C2×C22⋊D1111yescharacteristic
468C2×C8C2×C22⋊D1111yescharacteristic
469C2×C8C2×C22⋊D1111yescharacteristic
470C2×C8C23×D1111yescharacteristic
471C4⋊C4—21no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—221no—
477C4⋊C4—441no—
478C4⋊C4—441no—
479C4⋊C4#432311yescharacteristic
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—441no—
484C22⋊C4—441no—
485C22⋊C4—441no—
486C22⋊C4—441no—
487C22⋊C4#432311yescharacteristic
488C22⋊C4#432311yescharacteristic
489C42—441no—
490C42C2×C22⋊D1111yescharacteristic
491C16—112no—
492C16—221no—
493C16—221no—
494C16—221no—
495C11#3383511yescharacteristic, complemented, Sylow
496C23—41no—
497C23—441no—
498C23C2×#432311yescharacteristic
499C23C2×#432311yescharacteristic
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—222no—
505Q8—441no—
506Q8—441no—
507Q8—441no—
508Q8—882no—
509D4—22no—
510D4—41no—
511D4—41no—
512D4—82no—
513D4—82no—
514D4—441no—
515D4—441no—
516D4—882no—
517D4—882no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—882no—
532C2×C4—882no—
533C2×C4C2×#432311yescharacteristic
534C2×C4C2×#432311yescharacteristic
535C2×C4C2×#432311yescharacteristic
536C2×C4C2×#432311yescharacteristic
537C2×C4C22×C22⋊D1111yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8C2×D4×D1111yescharacteristic
542C8#6703711yescharacteristic
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—42no—
550C22—81no—
551C22—81no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22C22×#432311yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—442no—
564C4—881no—
565C4—881no—
566C4D4×C22⋊D1111yescharacteristic
567C4#1062336611yescharacteristic
568C2—41no—
569C2—41no—
570C2—82no—
571C2—1761no—
572C2D4×#432311yescharacteristic
573C2#1308175011yescharacteristic
574C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3283C2
socleC22×C11C22×D8
hypercenter#3283D11
hypocenterC11#33835
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3283

Complements

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

NH ≅ G/Ntype
1. C2×#10622808C2semidirect
2. C2×#10622807C2semidirect
3. #13080359C2semidirect
4. #13070885C2semidirect
5. #13070731C2semidirect
6. #13070705C2semidirect
7. #13070671C2semidirect
8. #13070663C2semidirect
9. #13070556C2semidirect
10. #13070554C2semidirect
11. #13070549C2semidirect
12. #13070539C2semidirect
13. #13070480C2semidirect
14. #13070442C2semidirect
15. C11×#3283C2semidirect
119. #66891D4semidirect
212. #3283D11semidirect
495. C11#33835semidirect

Maximal subgroups

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

subgroupindex
C2×#106228082
C2×#106228072
#130803592
#130708852
#130707312
#130707052
#130706712
#130706632
#130705562
#130705542
#130705492
#130705392
#130704802
#130704422
C11×#32832
#3383511