Finite Group Databasebeta

← #14730362

Subgroups — #14730362

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080007C211yesmaximal, characteristic, complemented
2#13078996C211yesmaximal, characteristic, complemented
3#13078687C211yesmaximal, characteristic
4#13067837C212yesmaximal, complemented
5#13067837C212yesmaximal, complemented
6#13067830C212yesmaximal, complemented
7#13067823C212yesmaximal, complemented
8#13067297C211yesmaximal, characteristic, complemented
9#13067055C211yesmaximal, characteristic
10#13067037C211yesmaximal, characteristic, complemented
11C11×#3503C211yesmaximal, characteristic
12Q82×C11C2212yes—
13C11×#557—21no—
14C11×#554—22no—
15C11×#554C2212yes—
16D4×Q8×C11—22no—
17D4×Q8×C11—21no—
18C11×#544—22no—
19C11×#544—21no—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520—21no—
25C4×C11×#41C2211yescharacteristic
26#10623001C2211yescharacteristic
27#10622852—21no—
28#10622838—22no—
29#10622707—21no—
30#10622703—21no—
31#10622695—22no—
32#10622694C2212yes—
33#10622694C2212yes—
34#10622665—22no—
35#10622644C2212yes—
36#10622644C2211yescharacteristic
37C4×#4326—21no—
38#10622633C2212yes—
39#10622633C2211yescharacteristic
40#10622632C2211yescharacteristic
41C4×#4324—21no—
42#10622620C2211yescharacteristic
43#10622609—21no—
44#10622538C2211yescharacteristic
45#10622537C2211yescharacteristic
46C4×#4318C2211yescharacteristic
47#10622184C2212yes—
48#10622184C2212yes—
49Q8⋊(C11⋊C8)C2212yes—
50Q8⋊(C11⋊C8)C2212yes—
51Q8⋊(C11⋊C8)C2212yes—
52D4⋊(C11⋊C8)C2212yes—
53C2×C11×#41D411yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8D412yes—
64C11×C4⋊Q8D411yescharacteristic
65C11×C4⋊Q8D411yescharacteristic
66C11×C4⋊Q8C2312yes—
67C11×#125—22no—
68C11×#125—24no—
69C11×#125—22no—
70C11×#125—21no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—24no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8D412yes—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—21no—
82C4×Q8×C11D411yescharacteristic
83C4×Q8×C11C2311yescharacteristic
84C4×Q8×C11C2312yes—
85C4×D4×C11—24no—
86C4×D4×C11—22no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11D411yescharacteristic
90C4×D4×C11C2311yescharacteristic
91C11×#117—22no—
92C11×#117—21no—
93C11×#117—21no—
94C11×#117D411yescharacteristic
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—22no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×#4326—21no—
102C2×#4326—22no—
103C2×#4324—21no—
104#66979—21no—
105#66977—21no—
106#66977—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109#66923—21no—
110#66922C2311yescharacteristic
111#66922C2311yescharacteristic
112C4×Dic22—21no—
113C4×Dic22—21no—
114#66899—24no—
115#66899—24no—
116#66899—21no—
117#66899—22no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120#66874—21no—
121#66874—21no—
122#66874—22no—
123#66872—21no—
124#66872—22no—
125#66871—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)C2312yes—
128C4⋊(C11⋊C8)C2311yescharacteristic
129C4⋊(C11⋊C8)C2311yescharacteristic
130#66867—21no—
131C4×C11⋊C8—21no—
132C4×C11⋊C8C2312yes—
133#18575—111nomaximal, Sylow
134C11×#41—22no—
135C11×#41—22no—
136C2×Q8×C11—24no—
137C2×Q8×C11—22no—
138C2×Q8×C11—21no—
139C2×Q8×C11—44no—
140C2×Q8×C11—84no—
141C2×Q8×C11C2×D412yes—
142C2×Q8×C11C2×D411yescharacteristic
143C2×Q8×C11C2×D414yes—
144C2×D4×C11—21no—
145C2×D4×C11C2×D411yescharacteristic
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C2×Dic22—21no—
155C2×Dic22—21no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C2×D411yescharacteristic
172C11×C4⋊C4C2×D412yes—
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C22⋊C4—24no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C42×C11—24no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—22no—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D411yescharacteristic
187C42×C11C2411yescharacteristic
188C22⋊Dic11—41no—
189#4326—42no—
190#4326—82no—
191#4324—42no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196Dic11⋊C4—41no—
197Dic11⋊C4—41no—
198C4×Dic11—41no—
199#4318—42no—
200#4318—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205#3503D1111yescharacteristic
206#3255—111no—
207#3139—111no—
208#3107—111no—
209#1645—112no—
210#1645—112no—
211#1644—112no—
212#1643—112no—
213#1548—111no—
214#1489—111no—
215#1485—111no—
216C23×C11—21no—
217C23×C11#12011yescharacteristic
218Q8×C11—21no—
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—44no—
222Q8×C11—44no—
223Q8×C11—42no—
224Q8×C11—84no—
225Q8×C11#13712yes—
226D4×C11—24no—
227D4×C11—21no—
228D4×C11#13712yes—
229C2×C4×C11—24no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11—82no—
245C2×C4×C11—84no—
246C2×C4×C11#12011yescharacteristic
247C2×C4×C11#12011yescharacteristic
248C2×C4×C11#12011yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×Dic11—41no—
253C2×Dic11—41no—
254Dic22—41no—
255Dic22—41no—
256Dic22—41no—
257Dic22—41no—
258C11⋊C8—42no—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—42no—
262Q82C2×D1112yes—
263#557—21no—
264#554—22no—
265#554C2×D1112yes—
266D4×Q8—22no—
267D4×Q8—21no—
268#544—22no—
269#544—21no—
270#533—21no—
271#533—111no—
272#533C2×D1111yescharacteristic
273C2×C4⋊Q8—21no—
274C2×C4⋊Q8C2×D1111yescharacteristic
275#520—21no—
276C4×#41C2×D1111yescharacteristic
277#491—222no—
278#487—112no—
279#487—112no—
280#485—221no—
281#475—111no—
282#475—112no—
283#475—221no—
284#474—111no—
285#470—222no—
286#462—111no—
287#462—112no—
288#462—221no—
289#461—111no—
290#452—221no—
291C4×Q16—221no—
292C4×SD16—221no—
293#431—111no—
294#423—111no—
295#419—222no—
296C4×M16—111no—
297#333—112no—
298#333—112no—
299Q8⋊C8—112no—
300Q8⋊C8—112no—
301Q8⋊C8—112no—
302D4⋊C8—112no—
303C22×C11—21no—
304C22×C11—22no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—41no—
308C22×C11—41no—
309C22×C11C2×#12011yescharacteristic
310C4×C11—21no—
311C4×C11—22no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—41no—
315C4×C11—42no—
316C4×C11—41no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11#45512yes—
320C4×C11C2×#13711yescharacteristic
321C4×C11C2×#13711yescharacteristic
322C4×C11#57711yescharacteristic
323C4×C11#57811yescharacteristic
324Dic11—81no—
325Dic11—81no—
326C2×#41C22⋊D1111yescharacteristic
327C22×Q8—22no—
328C22×Q8C22⋊D1112yes—
329C2×Q16—221no—
330C2×Q16—222no—
331C2×SD16—221no—
332C2×M16—221no—
333C2×M16—221no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—24no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—111no—
342C4⋊Q8—111no—
343C4⋊Q8C22⋊D1112yes—
344C4⋊Q8C22⋊D1111yescharacteristic
345C4⋊Q8C22⋊D1111yescharacteristic
346C4⋊Q8C22×D1112yes—
347#125—22no—
348#125—24no—
349#125—22no—
350#125—21no—
351#125—221no—
352C22⋊Q8—22no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—22no—
356C22⋊Q8—24no—
357C22⋊Q8—21no—
358C22⋊Q8—221no—
359C22⋊Q8—221no—
360C22⋊Q8C22⋊D1112yes—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×Q8—21no—
365C4×Q8—221no—
366C4×Q8—221no—
367C4×Q8C22⋊D1111yescharacteristic
368C4×Q8C22×D1111yescharacteristic
369C4×Q8C22×D1112yes—
370C4×D4—24no—
371C4×D4—22no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C22⋊D1111yescharacteristic
375C4×D4C22×D1111yescharacteristic
376#117—22no—
377#117—21no—
378#117—21no—
379#117—221no—
380#117C22⋊D1111yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C42—21no—
386C2×C42C22×D1111yescharacteristic
387#107—221no—
388#106—221no—
389#106—222no—
390C4⋊C8—112no—
391C4⋊C8—111no—
392C4⋊C8—111no—
393C4⋊C8—221no—
394#103—224no—
395#103—224no—
396#103—221no—
397#103—222no—
398#103—221no—
399#103—221no—
400#103—222no—
401#102—221no—
402C22⋊C8—221no—
403#97—221no—
404C4×C8—112no—
405C4×C8—221no—
406C2×C11—41no—
407C2×C11—42no—
408C2×C11#300411yescharacteristic
409C2×C11#301311yescharacteristic
410C2×C11C2×#45511yescharacteristic
411#41—22no—
412#41—22no—
413C2×Q8—24no—
414C2×Q8—22no—
415C2×Q8—21no—
416C2×Q8—44no—
417C2×Q8—84no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8C2×C22⋊D1112yes—
421C2×Q8C2×C22⋊D1111yescharacteristic
422C2×Q8C2×C22⋊D1114yes—
423C2×D4—21no—
424C2×D4C2×C22⋊D1111yescharacteristic
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433Q16—442no—
434Q16—882no—
435SD16—442no—
436M16—442no—
437M16—881no—
438C2×C8—222no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—441no—
462C4⋊C4—441no—
463C4⋊C4C2×C22⋊D1112yes—
464C4⋊C4C2×C22⋊D1111yescharacteristic
465C4⋊C4C2×C22⋊D1111yescharacteristic
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—441no—
472C42—24no—
473C42—21no—
474C42—21no—
475C42—21no—
476C42—22no—
477C42—441no—
478C42C2×C22⋊D1111yescharacteristic
479C42C2×C22⋊D1111yescharacteristic
480C42C2×C22⋊D1111yescharacteristic
481C42C23×D1111yescharacteristic
482C11#1857511yescharacteristic, complemented, Sylow
483C23—21no—
484C23#6700611yescharacteristic
485Q8—21no—
486Q8—22no—
487Q8—22no—
488Q8—44no—
489Q8—44no—
490Q8—42no—
491Q8—84no—
492Q8—441no—
493Q8—441no—
494Q8—441no—
495Q8—441no—
496Q8#6699512yes—
497D4—24no—
498D4—21no—
499D4#6699512yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—84no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4#6700611yescharacteristic
520C2×C4#6700611yescharacteristic
521C2×C4#6700611yescharacteristic
522C2×C4C22×C22⋊D1111yescharacteristic
523C2×C4C22×C22⋊D1111yescharacteristic
524C2×C4C22×C22⋊D1111yescharacteristic
525C8—442no—
526C8—441no—
527C8—441no—
528C8—442no—
529C22—21no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—41no—
534C22—41no—
535C22C2×#6700611yescharacteristic
536C4—21no—
537C4—22no—
538C4—21no—
539C4—21no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—44no—
544C4—42no—
545C4—881no—
546C4—881no—
547C4#1062285512yes—
548C4C2×#6699511yescharacteristic
549C4C2×#6699511yescharacteristic
550C4#1062336811yescharacteristic
551C4#1062336911yescharacteristic
552C2—41no—
553C2—42no—
554C2#1307785011yescharacteristic
555C2#1307793111yescharacteristic
556C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×C11×#41D4
hypercenter#3503D11
hypocenterC11#18575
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13080007C2semidirect
2. #13078996C2semidirect
4. #13067837C2semidirect
5. #13067837C2semidirect
6. #13067830C2semidirect
7. #13067823C2semidirect
8. #13067297C2semidirect
10. #13067037C2semidirect
482. C11#18575semidirect

Maximal subgroups

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

subgroupindex
#130800072
#130789962
#130786872
#130678372
#130678302
#130678232
#130672972
#130670552
#130670372
C11×#35032
#1857511