Finite Group Databasebeta

← #14910778

Subgroups — #14910778

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080960C211yesmaximal, characteristic, complemented
2#13080357C211yesmaximal, characteristic, complemented
3#13070854C211yesmaximal, characteristic, complemented
4#13070817C211yesmaximal, characteristic, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070766C211yesmaximal, characteristic, complemented
7#13070726C211yesmaximal, characteristic, complemented
8#13070700C211yesmaximal, characteristic, complemented
9#13070673C211yesmaximal, characteristic, complemented
10#13070538C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12#13070438C211yesmaximal, characteristic, complemented
13#13070327C211yesmaximal, characteristic, complemented
14C2×#10622202C211yesmaximal, characteristic, complemented
15C11×#2185C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17#10623348—21no—
18C2×#66972C2211yescharacteristic
19#10623142—21no—
20C2×C11×SD32C2211yescharacteristic
21C2×C11×SD32C2211yescharacteristic
22C11×#466C2211yescharacteristic
23#10622840—21no—
24#10622804C2211yescharacteristic
25#10622801C2211yescharacteristic
26#10622800—21no—
27#10622798—21no—
28Q16×Dic11C2211yescharacteristic
29#10622770C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622728C2211yescharacteristic
33C8×C22⋊D11C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36#10622646—21no—
37C2×#66862C2211yescharacteristic
38D11×#107C2211yescharacteristic
39#10622487C2211yescharacteristic
40#10622387—21no—
41#10622372—21no—
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic
53#10622142C2211yescharacteristic
54#10622142C2211yescharacteristic
55#10622140C2211yescharacteristic
56Dic11⋊C16C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622127C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×#4343—21no—
61C2×#4341—41no—
62C2×C11×Q16—22no—
63C2×C11×Q16—21no—
64C2×C11×Q16—41no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—21no—
70#67000—21no—
71#67000—41no—
72#66999—21no—
73#66999—41no—
74Q8×Dic11—21no—
75C2×#4325—21no—
76C2×#4325—21no—
77#66991—21no—
78#66988—41no—
79D4×Dic11—21no—
80#66983—21no—
81#66983—41no—
82C4×C22⋊D11—41no—
83C4×C22⋊D11D411yescharacteristic
84C2×C4⋊Dic11—21no—
85#66972—22no—
86#66972—41no—
87C2×D88C2311yescharacteristic
88C2×C8×D11C2311yescharacteristic
89C4⋊C4×D11—21no—
90#66941—21no—
91#66936—41no—
92#66931—41no—
93C11×SD32—22no—
94C11×SD32—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#102—21no—
99#66899—21no—
100#66899—21no—
101#66896—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66890—41no—
105#66885—21no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111Dic11⋊C8D411yescharacteristic
112C8×Dic11C2311yescharacteristic
113C2×C11⋊C16—41no—
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#66871—21no—
117#66871—21no—
118#66862—41no—
119#33875—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—42no—
123C2×Q8×C11—41no—
124C2×Q8×C11—81no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11D811yescharacteristic
132C22×Dic11—41no—
133C22×Dic11—41no—
134#4343—42no—
135#4343—81no—
136#4341—84no—
137C2×D44—21no—
138C2×D44—41no—
139C2×C4×D11—41no—
140C2×C4×D11—41no—
141C2×C4×D11C2×D411yescharacteristic
142C2×Dic22—41no—
143C11×Q16—21no—
144C11×Q16—21no—
145C11×Q16—21no—
146C11×Q16—42no—
147C11×Q16#4112yescomplemented
148C11×D8—21no—
149C11×D8—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2411yescharacteristic
154C11×C4⋊C4—21no—
155C11×C22⋊C4—41no—
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11D811yescharacteristic
159#4325—42no—
160#4325—81no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4D811yescharacteristic
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—41no—
170C4⋊Dic11—41no—
171Dic11⋊C4—41no—
172Dic11⋊C4—41no—
173Dic11⋊C4—41no—
174Dic11⋊C4D811yescharacteristic
175C4×Dic11—41no—
176C4×Dic11C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179D88—21no—
180D88—21no—
181C8×D11—21no—
182C8×D11—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334—111no—
188#3285—111no—
189#2243—111no—
190#2236—111no—
191#2232—111no—
192#2227—111no—
193#2220—111no—
194#2215—111no—
195#2210—111no—
196#2186—111no—
197#2185D1111yescharacteristic, complemented
198#2175—111no—
199#2168—111no—
200#2139—111no—
201C2×#358—111no—
202C23×C11—41no—
203C23×C11C2×D811yescharacteristic
204C22×D11—41no—
205C22×D11C2×D811yescharacteristic
206Q8×C11—22no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—82no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—82no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—82no—
220C2×C4×C11C2×D811yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C22⋊D11—22no—
223C22⋊D11—82no—
224C22⋊D11—82no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—82no—
229C2×Dic11—82no—
230C2×Dic11C2×D811yescharacteristic
231C2×Dic11C2×D811yescharacteristic
232C2×Dic11C2×D811yescharacteristic
233D44—41no—
234D44—41no—
235D44—82no—
236C4×D11—21no—
237C4×D11—21no—
238C4×D11—82no—
239C4×D11—82no—
240Dic22—82no—
241C8×C11—21no—
242C8×C11C2×#4111yescharacteristic
243C8×C11H(5,𝔽2)11yescharacteristic
244C11⋊C8—21no—
245C11⋊C8—21no—
246C2×#135—111no—
247C22×Q16C2×D1111yescharacteristic
248#548—221no—
249#547—221no—
250C2×SD32C2×D1111yescharacteristic
251C2×SD32C2×D1111yescharacteristic
252C2×D16—111no—
253C2×M32—111no—
254C22×C16—111no—
255#500—111no—
256#495—111no—
257#480—221no—
258#480—221no—
259#474—221no—
260#467—111no—
261#466—111no—
262#466—111no—
263#466C2×D1111yescharacteristic
264#464—221no—
265#452—221no—
266#448—221no—
267C4×Q16—111no—
268C4×D8—111no—
269C8×D4—111no—
270C2×#107—111no—
271C2×#107—111no—
272#366—111no—
273#366—111no—
274#366—111no—
275C4⋊C16—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#358—111no—
280#358C2×D1111yescharacteristic
281#358C2×D1111yescharacteristic
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286C22⋊C16—111no—
287C22⋊C16C2×D1111yescharacteristic
288#346—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11#50912yes—
295C22×C11C22×D811yescharacteristic
296C2×D11—21no—
297C2×D11—21no—
298C2×D11—21no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C4×C11—21no—
303C4×C11—42no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—21no—
309Dic11—21no—
310Dic11—21no—
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C2×#41—441no—
316C22×Q8—21no—
317#135—222no—
318#135—441no—
319C2×Q16—22no—
320C2×Q16—21no—
321C2×Q16—41no—
322C2×Q16C22×D1111yescharacteristic
323C2×Q16C22×D1111yescharacteristic
324C2×SD16—221no—
325C2×SD16—221no—
326C2×D8—111no—
327C2×D8C22×D1111yescharacteristic
328C22×C8—111no—
329C22×C8C22×D1111yescharacteristic
330C4⋊Q8—221no—
331#124—221no—
332#124—441no—
333#123—441no—
334#123—441no—
335C22⋊Q8—221no—
336C22⋊Q8—441no—
337C22⋊Q8—441no—
338#121—21no—
339#121—221no—
340#121—221no—
341#121—441no—
342C4×Q8—221no—
343C4×D4—111no—
344C4×D4—221no—
345C4×D4—441no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348SD32—22no—
349SD32—41no—
350D16—441no—
351M32—441no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—441no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—111no—
360#107—221no—
361#107—221no—
362#107—221no—
363#107C22×D1111yescharacteristic
364C4⋊C8—111no—
365#103—221no—
366#103—221no—
367#102—21no—
368#102—221no—
369#102—221no—
370#102—221no—
371C22⋊C8—111no—
372C22⋊C8—111no—
373C4×C8—111no—
374C2×C11—22no—
375C2×C11—161no—
376C2×C11#329411yescharacteristic
377C2×C11C2×#50911yescharacteristic
378C2×C11#341711yescharacteristic
379D11—41no—
380D11—161no—
381#41—442no—
382#41—881no—
383#41—884no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—42no—
387C2×Q8—41no—
388C2×Q8—81no—
389C2×Q8—441no—
390C2×D4—21no—
391C2×D4—41no—
392C2×D4—111no—
393C2×D4—221no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4—441no—
397C22×C4—41no—
398C22×C4—111no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4D4×D1111yescharacteristic
404Q16—21no—
405Q16—21no—
406Q16—21no—
407Q16—42no—
408Q16#434112yescomplemented
409SD16—442no—
410SD16—881no—
411D8—21no—
412D8—21no—
413D8—221no—
414D8—221no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—111no—
418C2×C8—111no—
419C2×C8—221no—
420C2×C8—221no—
421C2×C8D4×D1111yescharacteristic
422C2×C8C23×D1111yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—111no—
425C4⋊C4—221no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4—441no—
433C22⋊C4—41no—
434C22⋊C4—111no—
435C22⋊C4—111no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4—441no—
441C22⋊C4—441no—
442C42—111no—
443C42—441no—
444C16—21no—
445C16—21no—
446C16—221no—
447C16—221no—
448C11#3387511yescharacteristic, complemented, Sylow
449C23—41no—
450C23—111no—
451C23—441no—
452C23D8×D1111yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—882no—
459D4—41no—
460D4—41no—
461D4—82no—
462D4—222no—
463D4—441no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—882no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4—111no—
475C2×C4—111no—
476C2×C4—111no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—882no—
483C2×C4—882no—
484C2×C4—882no—
485C2×C4—882no—
486C2×C4D8×D1111yescharacteristic
487C2×C4C2×D4×D1111yescharacteristic
488C8—21no—
489C8—221no—
490C8—221no—
491C8C2×#434111yescharacteristic
492C8#6703711yescharacteristic
493C22—21no—
494C22—21no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—221no—
499C22—221no—
500C22—221no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22#1062252712yes—
505C22C2×D8×D1111yescharacteristic
506C4—21no—
507C4—42no—
508C4—81no—
509C4—81no—
510C4—221no—
511C4—221no—
512C4—221no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062312211yescharacteristic
517C4#1062330611yescharacteristic
518C2—22no—
519C2—161no—
520C2—441no—
521C2—1761no—
522C2#1308042211yescharacteristic
523C2C2×#1062252711yescharacteristic
524C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2185C2
socleC22×C11C22×D8
hypercenter#2185D11
hypocenterC11#33875
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2185

Complements

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

NH ≅ G/Ntype
1. #13080960C2semidirect
2. #13080357C2semidirect
3. #13070854C2semidirect
4. #13070817C2semidirect
5. #13070797C2semidirect
6. #13070766C2semidirect
7. #13070726C2semidirect
8. #13070700C2semidirect
9. #13070673C2semidirect
10. #13070538C2semidirect
11. #13070481C2semidirect
12. #13070438C2semidirect
13. #13070327C2semidirect
14. C2×#10622202C2semidirect
15. C11×#2185C2semidirect
147. C11×Q16#41semidirect
197. #2185D11semidirect
408. Q16#4341semidirect
448. C11#33875semidirect

Maximal subgroups

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

subgroupindex
#130809602
#130803572
#130708542
#130708172
#130707972
#130707662
#130707262
#130707002
#130706732
#130705382
#130704812
#130704382
#130703272
C2×#106222022
C11×#21852
#3387511