Finite Group Databasebeta

← #14910774

Subgroups — #14910774

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#13080964C211yesmaximal, characteristic, complemented
2#13070852C211yesmaximal, characteristic, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070794C211yesmaximal, characteristic, complemented
5#13070768C211yesmaximal, characteristic, complemented
6#13070731C211yesmaximal, characteristic, complemented
7#13070700C211yesmaximal, characteristic, complemented
8#13070668C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070533C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070328C211yesmaximal, characteristic, complemented
14C2×#10622202C211yesmaximal, characteristic, complemented
15C11×#3285C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C11×#548—21no—
19#10623086—21no—
20C11×#495C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#464—21no—
24C11×#452—21no—
25C11×#448—21no—
26C4×C11×Q16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622728C2211yescharacteristic
32#10622728C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622459—21no—
38#10622349—21no—
39#10622349—21no—
40C4×D88C2211yescharacteristic
41#10622295C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×#41—21no—
60C22×Q8×C11—21no—
61C2×#4341—41no—
62C11×#135—22no—
63C11×#135—41no—
64C2×C11×Q16—22no—
65C2×C11×Q16—21no—
66C2×C11×Q16—41no—
67C2×C11×Q16C2311yescharacteristic
68C2×C11×Q16C2311yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×D8C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#124—21no—
75C11×#124—41no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—41no—
78C11×#121—21no—
79C11×#121—41no—
80C4×Q8×C11—21no—
81C4×D4×C11—41no—
82C4×D4×C11D411yescharacteristic
83#66983—21no—
84#66983—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×D88C2311yescharacteristic
88#66950—41no—
89#66939—41no—
90#66939—41no—
91C4×D44—21no—
92#66922—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#103—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66892—22no—
102#66892—41no—
103#66890—41no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882—21no—
109#66882—21no—
110#66882C2311yescharacteristic
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33875—111nomaximal, Sylow
120C11×#41—42no—
121C11×#41—81no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—42no—
125C2×Q8×C11—41no—
126C2×Q8×C11—81no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11D811yescharacteristic
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139#4341—84no—
140C2×D44—21no—
141C2×C4×D11—41no—
142C2×Dic22—41no—
143C11×Q16—21no—
144C11×Q16—21no—
145C11×Q16—21no—
146C11×Q16—42no—
147C11×Q16#4112yescomplemented
148C11×SD16—42no—
149C11×SD16—81no—
150C11×D8—21no—
151C11×D8—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11C2411yescharacteristic
160C11×C4⋊C4—21no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4D811yescharacteristic
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4D811yescharacteristic
169C11×C22⋊C4D811yescharacteristic
170C42×C11—41no—
171C42×C11C2×D411yescharacteristic
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—41no—
179C4⋊Dic11—41no—
180C4⋊Dic11—41no—
181D88—21no—
182D88—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334—111no—
188#3285D1111yescharacteristic, complemented
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#2185—111no—
198#2175—111no—
199#2168—111no—
200#2139—111no—
201C2×#358—111no—
202C23×C11—41no—
203C23×C11C2×D811yescharacteristic
204C23×C11C2×D811yescharacteristic
205C22×D11—41no—
206Q8×C11—22no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—82no—
211D4×C11—22no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—82no—
215D4×C11—82no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—82no—
224C2×C4×C11—82no—
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C22⋊D11—82no—
231C22⋊D11—82no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—82no—
236C2×Dic11—82no—
237D44—41no—
238D44—41no—
239C4×D11—82no—
240Dic22—82no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11—21no—
244C8×C11C2×#4111yescharacteristic
245C8×C11H(5,𝔽2)11yescharacteristic
246C2×#135C2×D1111yescharacteristic
247C22×Q16C2×D1111yescharacteristic
248#548—21no—
249#547—221no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×D16—111no—
253C2×M32—111no—
254C22×C16—111no—
255#500—111no—
256#495C2×D1111yescharacteristic
257#480—221no—
258#480—221no—
259#474—221no—
260#467C2×D1111yescharacteristic
261#466—111no—
262#466—111no—
263#466C2×D1111yescharacteristic
264#464—21no—
265#452—21no—
266#448—21no—
267C4×Q16C2×D1111yescharacteristic
268C4×D8—111no—
269C8×D4C2×D1111yescharacteristic
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#358—111no—
281#358—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286C22⋊C16—111no—
287C22⋊C16—111no—
288#346—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11#50912yes—
298C22×C11C22×D811yescharacteristic
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—81no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—42no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11#54611yescharacteristic
310C4×C11#57711yescharacteristic
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—21no—
315C2×#41—441no—
316C22×Q8—21no—
317#135—22no—
318#135—41no—
319C2×Q16—22no—
320C2×Q16—21no—
321C2×Q16—41no—
322C2×Q16C22×D1111yescharacteristic
323C2×Q16C22×D1111yescharacteristic
324C2×SD16—21no—
325C2×SD16—21no—
326C2×D8—111no—
327C2×D8C22×D1111yescharacteristic
328C22×C8C22×D1111yescharacteristic
329C22×C8C22×D1111yescharacteristic
330C4⋊Q8—221no—
331#124—21no—
332#124—41no—
333#123—441no—
334#123—441no—
335C22⋊Q8—21no—
336C22⋊Q8—41no—
337C22⋊Q8—441no—
338#121—21no—
339#121—41no—
340#121—221no—
341#121—221no—
342C4×Q8—21no—
343C4×D4—41no—
344C4×D4—221no—
345C4×D4C22⋊D1111yescharacteristic
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348SD32—222no—
349SD32—441no—
350D16—441no—
351M32—441no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—111no—
355C2×C16—111no—
356C2×C16—441no—
357#107—111no—
358#107—111no—
359#107—111no—
360#107—221no—
361#107—221no—
362#107—221no—
363#107C22×D1111yescharacteristic
364C4⋊C8C22⋊D1111yescharacteristic
365#103—21no—
366#103—21no—
367#102—21no—
368#102—221no—
369#102—221no—
370#102—221no—
371C22⋊C8C22⋊D1111yescharacteristic
372C22⋊C8C22⋊D1111yescharacteristic
373C4×C8C22×D1111yescharacteristic
374C2×C11—22no—
375C2×C11—41no—
376C2×C11—161no—
377C2×C11#329411yescharacteristic
378C2×C11C2×#50911yescharacteristic
379C2×C11#341711yescharacteristic
380D11—161no—
381#41—42no—
382#41—81no—
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—41no—
393C2×D4—221no—
394C2×D4—441no—
395C2×D4—441no—
396C2×D4#432311yescharacteristic
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1111yescharacteristic
404Q16—21no—
405Q16—21no—
406Q16—21no—
407Q16—42no—
408Q16#434112yescomplemented
409SD16—42no—
410SD16—81no—
411D8—21no—
412D8—21no—
413D8—221no—
414D8—221no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8C2×C22⋊D1111yescharacteristic
420C2×C8C2×C22⋊D1111yescharacteristic
421C2×C8C2×C22⋊D1111yescharacteristic
422C2×C8C23×D1111yescharacteristic
423C4⋊C4—21no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—221no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4—441no—
432C4⋊C4#432311yescharacteristic
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4—441no—
440C22⋊C4#432311yescharacteristic
441C22⋊C4#432311yescharacteristic
442C42—41no—
443C42C2×C22⋊D1111yescharacteristic
444C16—221no—
445C16—221no—
446C16—221no—
447C16—221no—
448C11#3387511yescharacteristic, complemented, Sylow
449C23—41no—
450C23—441no—
451C23C2×#432311yescharacteristic
452C23C2×#432311yescharacteristic
453Q8—22no—
454Q8—41no—
455Q8—41no—
456Q8—41no—
457Q8—82no—
458Q8—882no—
459D4—22no—
460D4—41no—
461D4—41no—
462D4—82no—
463D4—82no—
464D4—441no—
465D4—441no—
466D4—882no—
467D4—882no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—882no—
481C2×C4—882no—
482C2×C4—882no—
483C2×C4C2×#432311yescharacteristic
484C2×C4C2×#432311yescharacteristic
485C2×C4C2×#432311yescharacteristic
486C2×C4C2×#432311yescharacteristic
487C2×C4C22×C22⋊D1111yescharacteristic
488C8—21no—
489C8—21no—
490C8—21no—
491C8C2×#434111yescharacteristic
492C8#6703711yescharacteristic
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22#1062280612yes—
505C22C22×#432311yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—81no—
512C4—81no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062333711yescharacteristic
517C4#1062336711yescharacteristic
518C2—22no—
519C2—41no—
520C2—161no—
521C2—1761no—
522C2#1308042911yescharacteristic
523C2C2×#1062280611yescharacteristic
524C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3285C2
socleC22×C11C22×D8
hypercenter#3285D11
hypocenterC11#33875
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #13080964C2semidirect
2. #13070852C2semidirect
3. #13070816C2semidirect
4. #13070794C2semidirect
5. #13070768C2semidirect
6. #13070731C2semidirect
7. #13070700C2semidirect
8. #13070668C2semidirect
9. #13070539C2semidirect
10. #13070533C2semidirect
11. #13070478C2semidirect
12. #13070442C2semidirect
13. #13070328C2semidirect
14. C2×#10622202C2semidirect
15. C11×#3285C2semidirect
147. C11×Q16#41semidirect
188. #3285D11semidirect
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
#130809642
#130708522
#130708162
#130707942
#130707682
#130707312
#130707002
#130706682
#130705392
#130705332
#130704782
#130704422
#130703282
C2×#106222022
C11×#32852
#3387511