Finite Group Databasebeta

← #14910322

Subgroups — #14910322

Order 2816.

664 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622792C211yesmaximal, characteristic, complemented
2C22×#66893C211yesmaximal, characteristic, complemented
3#13080359C211yesmaximal, characteristic
4#13070885C211yesmaximal, characteristic, complemented
5#13070722C211yesmaximal, characteristic, complemented
6#13070714C211yesmaximal, characteristic, complemented
7#13070678C211yesmaximal, characteristic, complemented
8#13070663C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070550C211yesmaximal, characteristic, complemented
11#13070549C211yesmaximal, characteristic, complemented
12#13070533C211yesmaximal, characteristic, complemented
13#13070485C211yesmaximal, characteristic, complemented
14#13070442C211yesmaximal, characteristic, complemented
15D4×C11×Q16C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18D4×Q8×C11—21no—
19C22×Dic44C2211yescharacteristic
20C2×#66957C2211yescharacteristic
21#10623083—21no—
22C11×#494C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C11×#467C2211yescharacteristic
25C11×#462—21no—
26C11×#451—21no—
27C11×#451—21no—
28C4×C11×Q16C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic
30C2×#66893—24no—
31C2×#66893C2211yescharacteristic
32C2×#66893C2211yescharacteristic
33C2×#66893C2211yescharacteristic
34C2×#66893C2211yescharacteristic
35C2×#66893C2211yescharacteristic
36C2×#66893C2211yescharacteristic
37#10622792—24no—
38C2×#66892C2211yescharacteristic
39C2×#66892C2211yescharacteristic
40C2×#66892C2211yescharacteristic
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#10622202C2211yescharacteristic
53C22⋊(C11⋊C16)C2211yescharacteristic
54C22⋊(C11⋊C16)C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622128C2211yescharacteristic
59C4⋊(C11⋊C16)C2211yescharacteristic
60#10622099C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—21no—
63C2×#4339—21no—
64C22×Dic22—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—22no—
67C2×C11×Q16—21no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×Q16—41no—
71C2×C11×Q16—41no—
72C2×C11×Q16C2311yescharacteristic
73C2×C11×Q16C2311yescharacteristic
74C2×C11×Q16C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×C4⋊Q8—21no—
78C11×C4⋊Q8—41no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—41no—
82C11×C22⋊Q8—41no—
83C4×Q8×C11—21no—
84C4×D4×C11—41no—
85C4×D4×C11D411yescharacteristic
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×#103—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66893—22no—
113#66893—22no—
114#66893—22no—
115#66893—22no—
116#66893—41no—
117#66893D414yescomplemented
118#66892—22no—
119#66892—22no—
120#66892—41no—
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#33836—111nomaximal, Sylow
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11—41no—
138C2×Q8×C11—41no—
139C2×Q8×C11—81no—
140C2×Q8×C11—81no—
141C2×D4×C11D811yescharacteristic
142C22×C4×C11—41no—
143C22×C4×C11—41no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C22×Dic11—41no—
149#4339—42no—
150#4339—81no—
151C2×D44—21no—
152C2×C4×D11—41no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—42no—
156C2×Dic22—41no—
157C2×Dic22—81no—
158C11×Q16—21no—
159C11×Q16—21no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×Q16—42no—
164C11×Q16—42no—
165C11×Q16—81no—
166C11×Q16C2×D412yes—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
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⋊C4D811yescharacteristic
185C11×C22⋊C4D811yescharacteristic
186C42×C11—41no—
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—
210C22×Q32—111no—
211D4×Q16D1111yescharacteristic, complemented
212#3285—111no—
213#2251—111no—
214#2219—111no—
215#2217—111no—
216#2211—111no—
217#2209—111no—
218#2189—111no—
219#2188—111no—
220#2188—111no—
221#2185—111no—
222#2176—111no—
223#2168—111no—
224C23×C11C2×D811yescharacteristic
225C23×C11C2×D811yescharacteristic
226C22×D11—41no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—82no—
234Q8×C11—82no—
235D4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—82no—
245C2×C4×C11—82no—
246C2×C4×C11C2×D811yescharacteristic
247C2×C4×C11C2×D811yescharacteristic
248C2×C4×C11C2×D811yescharacteristic
249C2×C4×C11C2×D811yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C22⋊D11—82no—
252C22⋊D11—82no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—82no—
257D44—41no—
258D44—41no—
259C4×D11—82no—
260Dic22—22no—
261Dic22—41no—
262Dic22—41no—
263Dic22—41no—
264Dic22—82no—
265C8×C11—21no—
266C8×C11—21no—
267C8×C11—21no—
268C8×C11C22×D411yescharacteristic
269C8×C11H(5,𝔽2)11yescharacteristic
270C2×#135—111no—
271C22×Q16—111no—
272C22×Q16C2×D1111yescharacteristic
273C22×Q16C2×D1111yescharacteristic
274D4×Q8—21no—
275#548—221no—
276#510—224no—
277C2×Q32—111no—
278C2×Q32—111no—
279C2×Q32—111no—
280C2×Q32—111no—
281C2×Q32—111no—
282C2×Q32—111no—
283C2×Q32—224no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×M32—111no—
288C22×C16—111no—
289#495—111no—
290#494C2×D1111yescharacteristic
291#467—111no—
292#467C2×D1111yescharacteristic
293#467C2×D1111yescharacteristic
294#466—111no—
295#464—221no—
296#462—21no—
297#452—221no—
298#451—21no—
299#451—21no—
300#448—221no—
301C4×Q16—111no—
302C4×Q16C2×D1111yescharacteristic
303C8×D4C2×D1111yescharacteristic
304#367—111no—
305C4⋊C16—111no—
306#358—111no—
307#358—111no—
308#358—111no—
309#358—111no—
310#358—111no—
311#357—111no—
312C22⋊C16—111no—
313C22⋊C16—111no—
314#346—111no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11#51012yescomplemented
321C22×C11C22×D811yescharacteristic
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—21no—
328C4×C11—21no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11D4211yescharacteristic
334C4×C11#57611yescharacteristic
335Dic11—42no—
336Dic11—81no—
337Dic11—81no—
338C2×#41—221no—
339C22×Q8—21no—
340C22×Q8—21no—
341C22×Q8—221no—
342#135—222no—
343#135—441no—
344C2×Q16—22no—
345C2×Q16—22no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16—21no—
349C2×Q16—41no—
350C2×Q16—41no—
351C2×Q16—111no—
352C2×Q16—111no—
353C2×Q16—222no—
354C2×Q16—221no—
355C2×Q16—441no—
356C2×Q16C22×D1111yescharacteristic
357C2×Q16C22×D1111yescharacteristic
358C2×Q16C22×D1111yescharacteristic
359C2×SD16—221no—
360C2×SD16—221no—
361C2×D8—111no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—21no—
365C4⋊Q8—41no—
366#124—221no—
367#124—441no—
368C22⋊Q8—21no—
369C22⋊Q8—21no—
370C22⋊Q8—41no—
371C22⋊Q8—41no—
372C22⋊Q8—221no—
373C22⋊Q8—441no—
374#121—221no—
375#121—441no—
376C4×Q8—21no—
377C4×Q8—221no—
378C4×D4—41no—
379C4×D4—441no—
380C4×D4C22⋊D1111yescharacteristic
381Q32—114no—
382Q32—222no—
383Q32—222no—
384Q32—222no—
385Q32—222no—
386Q32—441no—
387SD32—222no—
388SD32—222no—
389SD32—441no—
390M32—222no—
391C2×C16—111no—
392C2×C16—111no—
393C2×C16—111no—
394C2×C16—111no—
395C2×C16—222no—
396#107—111no—
397#107C22×D1111yescharacteristic
398C4⋊C8C22⋊D1111yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—221no—
403#103—221no—
404#102—221no—
405C22⋊C8C22⋊D1111yescharacteristic
406C22⋊C8C22⋊D1111yescharacteristic
407C4×C8C22×D1111yescharacteristic
408C2×C11—22no—
409C2×C11—41no—
410C2×C11D4×D811yescharacteristic
411C2×C11C2×#51011yescharacteristic
412C2×C11#341711yescharacteristic
413D11—161no—
414#41—442no—
415#41—881no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—81no—
424C2×Q8—81no—
425C2×Q8—221no—
426C2×Q8—221no—
427C2×Q8—442no—
428C2×Q8—441no—
429C2×Q8—881no—
430C2×D4—221no—
431C2×D4—441no—
432C2×D4—441no—
433C2×D4#432311yescharacteristic
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—441no—
437C22×C4—441no—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440Q16—21no—
441Q16—21no—
442Q16—21no—
443Q16—21no—
444Q16—21no—
445Q16—42no—
446Q16—42no—
447Q16—81no—
448Q16—112no—
449Q16—221no—
450Q16—221no—
451Q16—221no—
452Q16—442no—
453Q16D4×D1112yes—
454SD16—442no—
455SD16—881no—
456D8—221no—
457D8—221no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8C2×C22⋊D1111yescharacteristic
463C2×C8C2×C22⋊D1111yescharacteristic
464C2×C8C2×C22⋊D1111yescharacteristic
465C2×C8C23×D1111yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—221no—
473C4⋊C4—441no—
474C4⋊C4—441no—
475C4⋊C4#432311yescharacteristic
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—441no—
479C22⋊C4—441no—
480C22⋊C4—441no—
481C22⋊C4—441no—
482C22⋊C4#432311yescharacteristic
483C22⋊C4#432311yescharacteristic
484C42—41no—
485C42—441no—
486C42C2×C22⋊D1111yescharacteristic
487C16—112no—
488C16—221no—
489C16—221no—
490C16—221no—
491C11#3383611yescharacteristic, complemented, Sylow
492C23—441no—
493C23C2×#432311yescharacteristic
494C23C2×#432311yescharacteristic
495Q8—22no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—82no—
502Q8—82no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
506Q8—441no—
507Q8—882no—
508D4—22no—
509D4—441no—
510D4—441no—
511D4—882no—
512D4—882no—
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—82no—
522C2×C4—82no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—882no—
527C2×C4—882no—
528C2×C4C2×#432311yescharacteristic
529C2×C4C2×#432311yescharacteristic
530C2×C4C2×#432311yescharacteristic
531C2×C4C2×#432311yescharacteristic
532C2×C4C22×C22⋊D1111yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8C2×D4×D1111yescharacteristic
537C8#6703711yescharacteristic
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22#1062279212yescomplemented
547C22C22×#432311yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—442no—
557C4—881no—
558C4—881no—
559C4D4×C22⋊D1111yescharacteristic
560C4#1062336611yescharacteristic
561C2—22no—
562C2—41no—
563C2—1761no—
564C2D4×#432311yescharacteristic
565C2C2×#1062279211yescharacteristic
566C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×Q16C2
socleC22×C11C22×D8
prime radical#13080359C2
hypercenterD4×Q16D11
hypocenterC11#33836
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#10622792C2semidirect
2. C22×#66893C2semidirect
4. #13070885C2semidirect
5. #13070722C2semidirect
6. #13070714C2semidirect
7. #13070678C2semidirect
8. #13070663C2semidirect
9. #13070554C2semidirect
10. #13070550C2semidirect
11. #13070549C2semidirect
12. #13070533C2semidirect
13. #13070485C2semidirect
14. #13070442C2semidirect
15. D4×C11×Q16C2semidirect
117. #66893D4semidirect
211. D4×Q16D11semidirect
320. C22×C11#510semidirect
491. C11#33836semidirect
546. C22#10622792semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C22×#668932
#130803592
#130708852
#130707222
#130707142
#130706782
#130706632
#130705542
#130705502
#130705492
#130705332
#130704852
#130704422
D4×C11×Q162
#3383611