Finite Group Databasebeta

← #14910687

Subgroups — #14910687

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081019C211yesmaximal, characteristic, complemented
2#13080359C211yesmaximal, characteristic, complemented
3#13070848C211yesmaximal, characteristic, complemented
4#13070825C211yesmaximal, characteristic, complemented
5#13070802C211yesmaximal, characteristic, complemented
6#13070781C211yesmaximal, characteristic, complemented
7#13070712C211yesmaximal, characteristic, complemented
8#13070702C211yesmaximal, characteristic, complemented
9#13070672C211yesmaximal, characteristic, complemented
10#13070541C211yesmaximal, characteristic, complemented
11#13070535C211yesmaximal, characteristic, complemented
12C4×#66864C211yesmaximal, characteristic, complemented
13#13070324C211yesmaximal, characteristic, complemented
14C2×#10622141C211yesmaximal, characteristic, complemented
15D4×C11×C16C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18#10623096—21no—
19#10623083—21no—
20C22×C11×C16C2211yescharacteristic
21C22×C11×C16C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic
23#10622729C2211yescharacteristic
24#10622728C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622728C2211yescharacteristic
27#10622719C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31C2×D176C2211yescharacteristic
32#10622460—21no—
33#10622458—21no—
34#10622351—21no—
35#10622350—21no—
36#10622348—21no—
37#10622346—21no—
38C4×Dic44C2211yescharacteristic
39#10622309C2211yescharacteristic
40C4×D88C2211yescharacteristic
41#10622296C2211yescharacteristic
42C11×C4⋊C16C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C4×C11×C16C2211yescharacteristic
46#10622147C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×#4339—21no—
60C22×Dic22—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×D4×C11D411yescharacteristic
64#66992—41no—
65#66992—41no—
66#66983—21no—
67#66983—21no—
68#66983—21no—
69#66979—21no—
70C2×C4⋊Dic11—21no—
71#66977—21no—
72C2×Dic44—22no—
73C2×Dic44—21no—
74C2×Dic44—41no—
75C2×Dic44C2311yescharacteristic
76C2×Dic44C2311yescharacteristic
77#66957—22no—
78#66957—41no—
79C2×D88C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82C2×#4314—21no—
83#66951—41no—
84#66949—41no—
85#66938—41no—
86#66936—41no—
87(C22⋊D11)⋊C4—41no—
88(C22⋊D11)⋊C4—41no—
89#66928—21no—
90C4×D44—21no—
91#66923—21no—
92C4×Dic22—21no—
93C2×C11×C16—41no—
94C2×C11×C16—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×C4⋊C8D411yescharacteristic
100C11×C22⋊C8D411yescharacteristic
101C11×C22⋊C8D411yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66885—21no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66882C2311yescharacteristic
112#66881—21no—
113#66881—21no—
114#66880—21no—
115#66880—21no—
116#66864—22no—
117#66864—41no—
118D176—41no—
119#33868—111nomaximal, Sylow
120C2×D4×C11D811yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129#4339—42no—
130#4339—81no—
131C2×D44—21no—
132C2×D44—21no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×Dic22—21no—
136C2×Dic22—21no—
137C2×Dic22—42no—
138C2×Dic22—41no—
139C2×Dic22—81no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4D811yescharacteristic
149C11×C22⋊C4D811yescharacteristic
150C11×C22⋊C4D811yescharacteristic
151C42×C11C2×D411yescharacteristic
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169C4×Dic11—41no—
170C4×Dic11—41no—
171Dic44—21no—
172Dic44—21no—
173Dic44—21no—
174Dic44—42no—
175Dic44#4112yes—
176D88—21no—
177D88—21no—
178D88—21no—
179D88—21no—
180#4314—42no—
181#4314—81no—
182C11×C16—21no—
183C11×C16—21no—
184C11×C16—21no—
185C11×C16—21no—
186#3339—111no—
187#3285—111no—
188#2242—111no—
189#2237—111no—
190#2233—111no—
191#2229—111no—
192#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2185—111no—
197C4×SD32—111no—
198D4×C16D1111yescharacteristic, complemented
199#2138—111no—
200C2×#358—111no—
201C23×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205D4×C11—22no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—82no—
216C22⋊D11—82no—
217C22⋊D11—82no—
218C22⋊D11—161no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—82no—
226C2×Dic11—161no—
227D44—41no—
228D44—41no—
229D44—41no—
230D44—41no—
231C4×D11—82no—
232C4×D11—161no—
233Dic22—22no—
234Dic22—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135—111no—
244C22×Q16—111no—
245#553—221no—
246#548—221no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16—111no—
250C22×C16C2×D1111yescharacteristic
251C22×C16C2×D1111yescharacteristic
252#499—111no—
253#495—111no—
254#482—221no—
255#481—221no—
256#478—221no—
257#467—111no—
258#466—111no—
259#466—111no—
260#466—111no—
261#464—221no—
262#452—221no—
263#448—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4C2×D1111yescharacteristic
267#427—111no—
268C2×#107—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16C2×D1111yescharacteristic
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16C2×D1111yescharacteristic
284C22⋊C16C2×D1111yescharacteristic
285C4×C16C2×D1111yescharacteristic
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11#50812yes—
292C22×C11C22×D811yescharacteristic
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11#54611yescharacteristic
304C4×C11#57711yescharacteristic
305Dic11—42no—
306Dic11—81no—
307Dic11—81no—
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C22×Q8—221no—
313#135—222no—
314#135—441no—
315C2×Q16—111no—
316C2×Q16—111no—
317C2×Q16—222no—
318C2×Q16—221no—
319C2×Q16—441no—
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—111no—
324C22×C8C22×D1111yescharacteristic
325C22×C8C22×D1111yescharacteristic
326#126—441no—
327#125—221no—
328#124—221no—
329#124—441no—
330#123—441no—
331C22⋊Q8—221no—
332C22⋊Q8—441no—
333#121—221no—
334#121—221no—
335#121—221no—
336#121—441no—
337#121—441no—
338C4×Q8—221no—
339C4×D4—221no—
340C4×D4—441no—
341C4×D4—441no—
342C4×D4D4411yescharacteristic
343#117—221no—
344C2×C4⋊C4—221no—
345SD32—222no—
346SD32—441no—
347D16—441no—
348C2×C16—41no—
349C2×C16—41no—
350C2×C16C22×D1111yescharacteristic
351C2×C16C22×D1111yescharacteristic
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—111no—
355#107—111no—
356#107—111no—
357#107—111no—
358#107—221no—
359#106—221no—
360#106—221no—
361C4⋊C8D4411yescharacteristic
362#103—221no—
363#103—221no—
364#102—221no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8D4411yescharacteristic
369C22⋊C8D4411yescharacteristic
370C4×C8C22×D1111yescharacteristic
371C2×C11—22no—
372C2×C11—41no—
373C2×C11#329411yescharacteristic
374C2×C11C2×#50811yescharacteristic
375C2×C11#341611yescharacteristic
376D11—161no—
377D11—161no—
378#41—442no—
379#41—881no—
380C2×Q8—221no—
381C2×Q8—221no—
382C2×Q8—442no—
383C2×Q8—441no—
384C2×Q8—881no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—441no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4D8811yescharacteristic
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4C2×D4411yescharacteristic
397C22×C4C2×D4411yescharacteristic
398Q16—112no—
399Q16—221no—
400Q16—221no—
401Q16—221no—
402Q16—442no—
403SD16—442no—
404SD16—881no—
405D8—221no—
406D8—221no—
407D8—221no—
408D8—221no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8C2×D4411yescharacteristic
414C2×C8C2×D4411yescharacteristic
415C2×C8C2×D4411yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4D8811yescharacteristic
427C22⋊C4—441no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4D8811yescharacteristic
436C22⋊C4D8811yescharacteristic
437C42—441no—
438C42—441no—
439C42C2×D4411yescharacteristic
440C16—21no—
441C16—21no—
442C16—21no—
443C16—21no—
444C11#3386811yescharacteristic, complemented, Sylow
445C23—441no—
446C23—441no—
447C23C2×D8811yescharacteristic
448C23C2×D8811yescharacteristic
449Q8—222no—
450Q8—441no—
451Q8—441no—
452Q8—441no—
453Q8—882no—
454D4—22no—
455D4—441no—
456D4—441no—
457D4—441no—
458D4—441no—
459D4—882no—
460D4—882no—
461D4—882no—
462D4—1761no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—882no—
474C2×C4—882no—
475C2×C4—1761no—
476C2×C4—1761no—
477C2×C4C2×D8811yescharacteristic
478C2×C4C2×D8811yescharacteristic
479C2×C4C2×D8811yescharacteristic
480C2×C4C2×D8811yescharacteristic
481C2×C4C22×D4411yescharacteristic
482C8—21no—
483C8—21no—
484C8—21no—
485C8#6703711yescharacteristic
486C8#41×D1111yescharacteristic
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—881no—
493C22—881no—
494C22—881no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22#1062251712yes—
499C22C22×D8811yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—442no—
505C4—881no—
506C4—881no—
507C4—881no—
508C4—881no—
509C4—881no—
510C4#1062308511yescharacteristic
511C4#1062328211yescharacteristic
512C2—22no—
513C2—41no—
514C2—1761no—
515C2—1761no—
516C2#1308043011yescharacteristic
517C2C2×#1062251711yescharacteristic
518C2#1308176411yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×C16C2
socleC22×C11C22×D8
hypercenterD4×C16D11
hypocenterC11#33868
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13080359C2semidirect
3. #13070848C2semidirect
4. #13070825C2semidirect
5. #13070802C2semidirect
6. #13070781C2semidirect
7. #13070712C2semidirect
8. #13070702C2semidirect
9. #13070672C2semidirect
10. #13070541C2semidirect
11. #13070535C2semidirect
12. C4×#66864C2semidirect
13. #13070324C2semidirect
14. C2×#10622141C2semidirect
15. D4×C11×C16C2semidirect
198. D4×C16D11semidirect
444. C11#33868semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130803592
#130708482
#130708252
#130708022
#130707812
#130707122
#130707022
#130706722
#130705412
#130705352
C4×#668642
#130703242
C2×#106221412
D4×C11×C162
#3386811