Finite Group Databasebeta

← #14910780

Subgroups — #14910780

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#13080354C211yesmaximal, characteristic, complemented
3#13070851C211yesmaximal, characteristic, complemented
4#13070820C211yesmaximal, characteristic, complemented
5#13070794C211yesmaximal, characteristic, complemented
6#13070767C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070669C211yesmaximal, characteristic, complemented
9#13070536C211yesmaximal, characteristic, complemented
10#13070532C211yesmaximal, characteristic, complemented
11#13070477C211yesmaximal, characteristic, complemented
12#13070441C211yesmaximal, characteristic, complemented
13#13070325C211yesmaximal, characteristic, complemented
14C2×#10622141C211yesmaximal, characteristic, complemented
15C11×#2215C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18#10623142—21no—
19#10623129—21no—
20C2×C11×D16C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#466C2211yescharacteristic
24#10622770C2211yescharacteristic
25#10622768C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66891C2211yescharacteristic
28C2×#66891C2211yescharacteristic
29C8×C22⋊D11C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31#10622653—21no—
32#10622646—21no—
33C2×#66862C2211yescharacteristic
34#10622500C2211yescharacteristic
35D11×#107C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622396—21no—
39#10622387—21no—
40#10622380—21no—
41#10622372—21no—
42C11×#366C2211yescharacteristic
43C11×#357C2211yescharacteristic
44C11×#357C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622141C2211yescharacteristic
53#10622140C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×#4341—21no—
60C2×#4341—41no—
61C22×Dic22—21no—
62C2×C11×D8C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#121—21no—
66C11×#121—21no—
67#66992—41no—
68#66991—21no—
69#66989—21no—
70#66988—41no—
71D4×Dic11—21no—
72D4×Dic11—41no—
73C2×#4324—21no—
74C2×#4324—21no—
75C4×C22⋊D11D411yescharacteristic
76C2×C4⋊Dic11—21no—
77#66965—22no—
78#66965—41no—
79C2×Dic44—22no—
80C2×Dic44—21no—
81C2×Dic44—41no—
82C2×Dic44C2311yescharacteristic
83C2×Dic44C2311yescharacteristic
84C2×C8×D11C2311yescharacteristic
85#66950—21no—
86C4⋊C4×D11—21no—
87#66941—21no—
88#66940—21no—
89#66938—41no—
90#66936—41no—
91#66931—41no—
92#66931—41no—
93C11×D16—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#102—21no—
100C11×#102—21no—
101#66896—21no—
102#66896—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66891—22no—
105#66891—41no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110Dic11⋊C8D411yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66874—21no—
115#66874—21no—
116#66871—21no—
117#66871—21no—
118#66862—41no—
119#33875—111nomaximal, Sylow
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11D811yescharacteristic
128C22×Dic11—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132#4341—42no—
133#4341—81no—
134#4341—84no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C2×Dic22—21no—
138C2×Dic22—21no—
139C2×Dic22—42no—
140C2×Dic22—41no—
141C2×Dic22—41no—
142C2×Dic22—81no—
143C11×D8—21no—
144C11×D8—21no—
145C11×D8—21no—
146C11×D8—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11C2×D411yescharacteristic
150C2×C8×C11C2411yescharacteristic
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C22⋊Dic11—41no—
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158C22⋊Dic11—41no—
159C22⋊Dic11D811yescharacteristic
160#4324—42no—
161#4324—81no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4D811yescharacteristic
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4D811yescharacteristic
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176Dic44—21no—
177Dic44—21no—
178Dic44—21no—
179Dic44—42no—
180Dic44#4112yescomplemented
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#2215D1111yescharacteristic, complemented
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×C11—41no—
204C23×C11C2×D811yescharacteristic
205C22×D11C2×D811yescharacteristic
206D4×C11—41no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—82no—
211D4×C11—82no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—22no—
219C22⋊D11—82no—
220C22⋊D11—82no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—82no—
226C2×Dic11—82no—
227C2×Dic11—82no—
228C2×Dic11—82no—
229C2×Dic11C2×D811yescharacteristic
230C2×Dic11C2×D811yescharacteristic
231C2×Dic11C2×D811yescharacteristic
232C4×D11—21no—
233C4×D11—21no—
234C4×D11—82no—
235Dic22—22no—
236Dic22—41no—
237Dic22—41no—
238Dic22—41no—
239Dic22—82no—
240Dic22—82no—
241C8×C11—21no—
242C8×C11C2×#4111yescharacteristic
243C8×C11H(5,𝔽2)11yescharacteristic
244C11⋊C8—21no—
245C11⋊C8—21no—
246C2×#135—111no—
247C22×Q16—111no—
248#548—221no—
249#547—221no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×D16C2×D1111yescharacteristic
253C2×M32—111no—
254C22×C16C2×D1111yescharacteristic
255#500—111no—
256#495—111no—
257#480—221no—
258#480—221no—
259#474—221no—
260#467—111no—
261#466—111no—
262#466C2×D1111yescharacteristic
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#366C2×D1111yescharacteristic
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#357C2×D1111yescharacteristic
285#357C2×D1111yescharacteristic
286C22⋊C16—111no—
287C22⋊C16—111no—
288#346—111no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11#50912yes—
298C22×C11C22×D811yescharacteristic
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C4×C11—21no—
303C4×C11—81no—
304C4×C11—81no—
305C4×C11#54611yescharacteristic
306C4×C11#57711yescharacteristic
307Dic11—21no—
308Dic11—21no—
309Dic11—21no—
310Dic11—42no—
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C2×#41—441no—
316C22×Q8—221no—
317#135—222no—
318#135—441no—
319C2×Q16—111no—
320C2×Q16—111no—
321C2×Q16—222no—
322C2×Q16—221no—
323C2×Q16—441no—
324C2×SD16—221no—
325C2×SD16—221no—
326C2×D8C22×D1111yescharacteristic
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—21no—
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—222no—
349SD32—441no—
350D16—41no—
351M32—441no—
352C2×C16—41no—
353C2×C16—111no—
354C2×C16—111no—
355C2×C16C22×D1111yescharacteristic
356C2×C16C22×D1111yescharacteristic
357#107—111no—
358#107—111no—
359#107—221no—
360#107—221no—
361#107—221no—
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364C4⋊C8—111no—
365#103—221no—
366#103—221no—
367#102—21no—
368#102—21no—
369#102—221no—
370#102—221no—
371C22⋊C8—111no—
372C22⋊C8—111no—
373C4×C8—111no—
374C2×C11—22no—
375C2×C11—161no—
376C2×C11—161no—
377C2×C11#329411yescharacteristic
378C2×C11C2×#50911yescharacteristic
379C2×C11#341711yescharacteristic
380D11—41no—
381#41—442no—
382#41—881no—
383#41—884no—
384C2×Q8—221no—
385C2×Q8—221no—
386C2×Q8—442no—
387C2×Q8—441no—
388C2×Q8—441no—
389C2×Q8—881no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—111no—
395C2×D4—441no—
396C2×D4—441no—
397C22×C4—111no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4—441no—
402C22×C4—441no—
403C22×C4D4×D1111yescharacteristic
404Q16—112no—
405Q16—221no—
406Q16—221no—
407Q16—221no—
408Q16—442no—
409SD16—442no—
410SD16—881no—
411D8—21no—
412D8—21no—
413D8—21no—
414D8—21no—
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—21no—
425C4⋊C4—111no—
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—41no—
435C22⋊C4—111no—
436C22⋊C4—111no—
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—41no—
451C23—111no—
452C23D8×D1111yescharacteristic
453Q8—222no—
454Q8—441no—
455Q8—441no—
456Q8—441no—
457Q8—882no—
458Q8—882no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—82no—
464D4—82no—
465D4—222no—
466D4—882no—
467D4—882no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—111no—
473C2×C4—111no—
474C2×C4—111no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—882no—
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—
491C8#6703711yescharacteristic
492C8#41×D1111yescharacteristic
493C22—21no—
494C22—21no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—221no—
502C22—221no—
503C22—221no—
504C22#1062252412yes—
505C22C2×D8×D1111yescharacteristic
506C4—21no—
507C4—81no—
508C4—81no—
509C4—221no—
510C4—221no—
511C4—221no—
512C4—442no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062314111yescharacteristic
517C4#1062330111yescharacteristic
518C2—22no—
519C2—161no—
520C2—161no—
521C2—441no—
522C2#1308042411yescharacteristic
523C2C2×#1062252411yescharacteristic
524C2#1308176611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33875
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. #13080960C2semidirect
2. #13080354C2semidirect
3. #13070851C2semidirect
4. #13070820C2semidirect
5. #13070794C2semidirect
6. #13070767C2semidirect
7. #13070728C2semidirect
8. #13070669C2semidirect
9. #13070536C2semidirect
10. #13070532C2semidirect
11. #13070477C2semidirect
12. #13070441C2semidirect
13. #13070325C2semidirect
14. C2×#10622141C2semidirect
15. C11×#2215C2semidirect
180. Dic44#41semidirect
194. #2215D11semidirect
448. C11#33875semidirect

Maximal subgroups

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

subgroupindex
#130809602
#130803542
#130708512
#130708202
#130707942
#130707672
#130707282
#130706692
#130705362
#130705322
#130704772
#130704412
#130703252
C2×#106221412
C11×#22152
#3387511