Finite Group Databasebeta

← #14909142

Subgroups — #14909142

Order 2816.

622 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622487C211yesmaximal, characteristic, complemented
2#13079040C211yesmaximal, characteristic
3#13070854C212yesmaximal, complemented
4#13070851C212yesmaximal, complemented
5#13070842C212yesmaximal, complemented
6#13070838C212yesmaximal, complemented
7#13070329C211yesmaximal, characteristic, complemented
8#13070328C211yesmaximal, characteristic, complemented
9#13070326C211yesmaximal, characteristic, complemented
10M32×Dic11C211yesmaximal, characteristic, complemented
11C11×#2139C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13#10623363—21no—
14C2×#67003—21no—
15C2×#66957C2211yescharacteristic
16C2×#66941—21no—
17C2×C11×M32C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622804C2211yescharacteristic
20#10622794C2211yescharacteristic
21#10622788—21no—
22#10622781—21no—
23#10622768C2211yescharacteristic
24#10622764C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×C8×Dic11C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28C2×#66871—21no—
29#10622487—21no—
30#10622487—21no—
31#10622487C2212yes—
32#10622487C2212yes—
33C11×#358C2212yes—
34C11×#357C2212yes—
35#10622202C2212yes—
36#10622200C2212yes—
37#10622147C2212yes—
38#10622141C2212yes—
39#10622140C2212yes—
40C16×Dic11C2212yes—
41#10622130C2212yes—
42#10622129C2212yes—
43C2×C11×#41—21no—
44C2×#4339—21no—
45C22×Dic22—41no—
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C2×C11×C4⋊C4—21no—
53#67003—44no—
54#67000—21no—
55#66997—21no—
56C2×#4326—21no—
57C2×#4325—21no—
58#66993—21no—
59#66992—41no—
60#66992—41no—
61#66989—21no—
62C2×#4324—21no—
63C2×#4323—21no—
64C4×C22⋊D11—41no—
65C4×C22⋊D11—41no—
66C2×C4⋊Dic11—21no—
67C2×Dic11⋊C4—41no—
68C2×C4×Dic11D411yescharacteristic
69C22×C11⋊C8D411yescharacteristic
70C2×Dic44C2311yescharacteristic
71#66957—22no—
72#66957—22no—
73C2×D88C2311yescharacteristic
74C2×#4314—21no—
75#66941—22no—
76#66941—22no—
77#66941—41no—
78#66941—41no—
79C11×M32—22no—
80C2×C11×C16C2312yes—
81C11×#107—21no—
82C11×#107C2312yes—
83#66882—21no—
84#66882C2312yes—
85C8×Dic11D411yescharacteristic
86C8×Dic11D411yescharacteristic
87C8×Dic11C2311yescharacteristic
88C8×Dic11C2311yescharacteristic
89#66876—22no—
90C2×C11⋊C16C2312yes—
91#66871—22no—
92#66871—22no—
93#33707—111nomaximal, Sylow
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C22×Dic11—41no—
106C22×Dic11D811yescharacteristic
107C22×Dic11D811yescharacteristic
108#4339—42no—
109#4339—42no—
110C2×D44—21no—
111C2×C4×D11—41no—
112C2×Dic22—21no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—84no—
116C11×Q16—21no—
117C11×Q16—21no—
118C11×SD16—42no—
119C11×D8—21no—
120C11×D8—21no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11#4112yes—
123C2×C8×C11#4112yes—
124C2×C8×C11C2411yescharacteristic
125C11×C4⋊C4—22no—
126C11×C4⋊C4—41no—
127C22⋊Dic11—41no—
128C22⋊Dic11—41no—
129#4326—42no—
130#4325—42no—
131#4324—42no—
132#4323—42no—
133(C2×D11)⋊C4—41no—
134(C2×D11)⋊C4—41no—
135C4⋊Dic11—22no—
136C4⋊Dic11—41no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141C4×Dic11D811yescharacteristic
142C4×Dic11D811yescharacteristic
143C4×Dic11C2×D411yescharacteristic
144C4×Dic11C2×D411yescharacteristic
145C2×C11⋊C8SD1614yes—
146C2×C11⋊C8C2×D411yescharacteristic
147C2×C11⋊C8C2×D411yescharacteristic
148Dic44—21no—
149Dic44—21no—
150D88—21no—
151D88—21no—
152#4314—42no—
153C11×C16—22no—
154C11⋊C16—22no—
155C2×#500—111no—
156#3147—111no—
157#2243—112no—
158#2243—112no—
159#2241—112no—
160#2240—112no—
161#2139—111no—
162#2139—111no—
163#2139—111no—
164#2139D1111yescharacteristic, complemented
165C4×M32—111no—
166C23×C11—41no—
167C23×C11C2×D811yescharacteristic
168C22×D11—41no—
169Q8×C11—41no—
170Q8×C11—41no—
171D4×C11—41no—
172D4×C11—41no—
173D4×C11—82no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11#12412yes—
179C2×C4×C11C2×D811yescharacteristic
180C2×C4×C11C2×SD1612yes—
181C2×C4×C11C22×D411yescharacteristic
182C22⋊D11—82no—
183C22⋊D11—82no—
184C22⋊D11—82no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—42no—
188C2×Dic11—41no—
189C2×Dic11—82no—
190C2×Dic11C2×D811yescharacteristic
191C2×Dic11C2×D811yescharacteristic
192C2×Dic11C2×D811yescharacteristic
193C2×Dic11C2×D811yescharacteristic
194D44—41no—
195D44—41no—
196C4×D11—82no—
197Dic22—41no—
198Dic22—41no—
199Dic22—84no—
200Dic22—84no—
201C8×C11#12412yes—
202C8×C11C2×#4111yescharacteristic
203C8×C11C2×#4111yescharacteristic
204C11⋊C8C2×SD1612yes—
205C11⋊C8C2×SD1612yes—
206C2×#135—111no—
207C2×#135—221no—
208C2×#135C2×D1111yescharacteristic
209#532—221no—
210C2×C4⋊Q8—221no—
211C2×M32—111no—
212C2×M32C2×D1111yescharacteristic
213#500—112no—
214#500—112no—
215#500—221no—
216#500—221no—
217#495—111no—
218#495—111no—
219#495—221no—
220#494—111no—
221#493—111no—
222#492—221no—
223C2×#107—111no—
224C2×#107—221no—
225C2×#107C2×D1111yescharacteristic
226C2×C4×C8—111no—
227#358—112no—
228#358—112no—
229#358—112no—
230#358C2×D1112yes—
231#357—112no—
232#357—112no—
233#357—112no—
234#357C2×D1112yes—
235#346—112no—
236C4×C16—112no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11#48612yes—
243C22×C11C22×D811yescharacteristic
244C2×D11—81no—
245C2×D11—81no—
246C2×D11—81no—
247C4×C11—81no—
248C4×C11—82no—
249C4×C11#48612yes—
250C4×C11C2×#12411yescharacteristic
251C4×C11C22×SD1611yescharacteristic
252Dic11—21no—
253Dic11—21no—
254Dic11—81no—
255Dic11—82no—
256Dic11#50912yes—
257Dic11#51012yes—
258C2×#41—21no—
259C2×#41—221no—
260C22×Q8—441no—
261#135—22no—
262#135—22no—
263#135—222no—
264#135—222no—
265#135—444no—
266C2×Q16—111no—
267C2×Q16—221no—
268C2×Q16C22×D1111yescharacteristic
269C2×SD16—21no—
270C2×SD16—221no—
271C2×SD16—221no—
272C2×SD16—221no—
273C2×D8—111no—
274C2×D8—221no—
275C2×D8C22×D1111yescharacteristic
276C22×C8—111no—
277C22×C8C22×D1111yescharacteristic
278C4⋊Q8—222no—
279C4⋊Q8—222no—
280C4⋊Q8—221no—
281C4⋊Q8—441no—
282C4⋊Q8—441no—
283#127—221no—
284#124—221no—
285#124—221no—
286#121—441no—
287#121—441no—
288C4×D4—441no—
289C4×D4—441no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—441no—
293C2×C42—111no—
294M32—22no—
295M32—222no—
296C2×C16—112no—
297C2×C16C22×D1112yes—
298#107—21no—
299#107—112no—
300#107—222no—
301#107—222no—
302#107—221no—
303#107C22×D1112yes—
304C4×C8—111no—
305C4×C8—111no—
306C4×C8—111no—
307C4×C8—111no—
308C2×C11—22no—
309C2×C11—161no—
310C2×C11C2×#48611yescharacteristic
311C2×C11C2×#50911yescharacteristic
312C2×C11C2×#51011yescharacteristic
313D11—161no—
314#41—42no—
315#41—42no—
316#41—442no—
317#41—442no—
318C2×Q8—21no—
319C2×Q8—221no—
320C2×Q8—442no—
321C2×Q8—442no—
322C2×Q8—884no—
323C2×D4—21no—
324C2×D4—41no—
325C2×D4—221no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—441no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—441no—
334C22×C4—441no—
335C22×C4D4×D1111yescharacteristic
336Q16—21no—
337Q16—21no—
338Q16—221no—
339Q16—221no—
340Q16—442no—
341SD16—42no—
342SD16—442no—
343SD16—442no—
344SD16—442no—
345D8—21no—
346D8—21no—
347D8—221no—
348D8—221no—
349D8—442no—
350C2×C8—114no—
351C2×C8—111no—
352C2×C8—111no—
353C2×C8#433912yes—
354C2×C8D4×D1111yescharacteristic
355C2×C8#434112yes—
356C2×C8C23×D1111yescharacteristic
357C4⋊C4—22no—
358C4⋊C4—41no—
359C4⋊C4—222no—
360C4⋊C4—442no—
361C4⋊C4—442no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—441no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C42—111no—
370C42—111no—
371C42—111no—
372C42—111no—
373C16—22no—
374C16—222no—
375C11#3370711yescharacteristic, complemented, Sylow
376C23—41no—
377C23—441no—
378C23D8×D1111yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—441no—
382Q8—441no—
383Q8—884no—
384Q8—884no—
385D4—41no—
386D4—41no—
387D4—82no—
388D4—441no—
389D4—441no—
390D4—882no—
391D4—882no—
392D4—882no—
393C2×C4—41no—
394C2×C4—42no—
395C2×C4—82no—
396C2×C4—82no—
397C2×C4—111no—
398C2×C4—111no—
399C2×C4—111no—
400C2×C4—111no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—441no—
404C2×C4—442no—
405C2×C4—882no—
406C2×C4—882no—
407C2×C4#6693812yes—
408C2×C4D8×D1111yescharacteristic
409C2×C4SD16×D1112yes—
410C2×C4C2×D4×D1111yescharacteristic
411C8—112no—
412C8—112no—
413C8#6693812yes—
414C8C2×#433911yescharacteristic
415C8C2×#434111yescharacteristic
416C22—21no—
417C22—21no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—881no—
422C22—881no—
423C22—881no—
424C22#1062237312yes—
425C22C2×D8×D1111yescharacteristic
426C4—81no—
427C4—82no—
428C4—112no—
429C4—112no—
430C4—221no—
431C4—221no—
432C4—881no—
433C4—882no—
434C4#1062237312yes—
435C4C2×#6693811yescharacteristic
436C4C2×SD16×D1111yescharacteristic
437C2—22no—
438C2—161no—
439C2—1761no—
440C2C2×#1062237311yescharacteristic
441C2D11×#50911yescharacteristic
442C2D11×#51011yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2139C2
socleC22×C11C22×D8
prime radical#13079040C2
hypercenter#2139D11
hypocenterC11#33707
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
1. C2×#10622487C2semidirect
3. #13070854C2semidirect
4. #13070851C2semidirect
5. #13070842C2semidirect
6. #13070838C2semidirect
7. #13070329C2semidirect
8. #13070328C2semidirect
9. #13070326C2semidirect
10. M32×Dic11C2semidirect
11. C11×#2139C2semidirect
164. #2139D11semidirect
375. C11#33707semidirect

Maximal subgroups

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

subgroupindex
C2×#106224872
#130790402
#130708542
#130708512
#130708422
#130708382
#130703292
#130703282
#130703262
M32×Dic112
C11×#21392
#3370711