Finite Group Databasebeta

← #14775847

Subgroups — #14775847

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078398C211yesmaximal, characteristic
2#13077181C211yesmaximal, characteristic
3#13069594C211yesmaximal, characteristic, complemented
4#13069391C211yesmaximal, characteristic, complemented
5#13069366C212yesmaximal, complemented
6#13069215C212yesmaximal, complemented
7#13068890C212yesmaximal
8#13068471C211yesmaximal, characteristic, complemented
9#13068462C212yesmaximal
10C4×#66889C211yesmaximal, characteristic
11C11×#2962C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×#66954C2212yes—
14C4×#4339C2211yescharacteristic
15C11×#446—22no—
16C11×#446—21no—
17C8×Q8×C11—21no—
18C11×#424C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C11×#405C2212yes—
21C4×C11×M16C2211yescharacteristic
22C2×#66889C2211yescharacteristic
23C2×#66889C2211yescharacteristic
24C2×#66886C2212yes—
25#10622715C2212yes—
26C2×#66879C2212yes—
27#10622707C411yescharacteristic, complemented
28#10622704C411yescharacteristic, complemented
29#10622700C411yescharacteristic, complemented
30#10622697C411yescharacteristic, complemented
31#10622679C412yescomplemented
32#10622676C412yescomplemented
33#10622615C2212yes—
34#10622611C2212yes—
35C42×Dic11C2211yescharacteristic
36#10622537C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38#10622452—22no—
39#10622450—21no—
40D11×C4⋊C8—21no—
41#10622196C2212yes—
42#10622193C2211yescharacteristic
43#10622193C2211yescharacteristic
44#10622188C2212yes—
45#10622170C2212yes—
46#10622170C2212yes—
47C2×#4339C2311yescharacteristic
48C2×C11×M16C2311yescharacteristic
49C2×C11×M16C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8C2×C411yescharacteristic
52C11×C4⋊Q8C2×C411yescharacteristic
53C11×#125C2×C412yes—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11—21no—
58C11×#117C2312yes—
59C2×C42×C11C2311yescharacteristic
60C4×C22⋊D11—21no—
61C4×C22⋊D11—21no—
62#66979C2311yescharacteristic
63C2×C4×Dic11—21no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11C2311yescharacteristic
66C2×C4×Dic11C2311yescharacteristic
67C2×#4318C2312yes—
68C22×C11⋊C8C2312yes—
69#66954—24no—
70#66954—42no—
71C2×#4313—22no—
72C2×C8×D11—22no—
73C4×D44C2×C411yescharacteristic
74C4×D44C2×C411yescharacteristic
75#66925—21no—
76C42×D11—21no—
77C4×Dic22C2×C411yescharacteristic
78C4×Dic22C2×C411yescharacteristic
79C11×C4⋊C8—22no—
80C11×C4⋊C8—22no—
81C11×C4⋊C8D411yescharacteristic
82C11×C4⋊C8D411yescharacteristic
83C11×C4⋊C8D412yes—
84C11×#97—22no—
85C11×#97—21no—
86C4×C8×C11—22no—
87C4×C8×C11—21no—
88#66889—22no—
89#66889Q814yescomplemented
90#66886—42no—
91#66879—42no—
92Dic11⋊C8—22no—
93Dic11⋊C8—22no—
94#66874C2×C412yes—
95#66874C2×C412yes—
96#66873C2×C412yes—
97#66873C2×C412yes—
98#66872C2×C412yes—
99#66872C2×C412yes—
100#66871C2×C412yes—
101#66871C2×C412yes—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)C2×C412yes—
105C4⋊(C11⋊C8)C2×C411yescharacteristic
106C4⋊(C11⋊C8)C2×C411yescharacteristic
107#22983—111nomaximal, Sylow
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116#4339—21no—
117#4339—21no—
118#4339C2×Q812yes—
119#4339#4112yes—
120C2×D44C22×C411yescharacteristic
121C2×C4×D11—21no—
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×Dic22C22×C411yescharacteristic
125C11×M16—21no—
126C11×M16—21no—
127C11×M16—21no—
128C11×M16C2×Q812yes—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11C2×D412yes—
134C2×C8×C11C2×D412yes—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4C22×C412yes—
140C11×C4⋊C4C22×C412yes—
141C11×C22⋊C4—22no—
142C42×C11—22no—
143C42×C11C22×C411yescharacteristic
144C42×C11C22×C411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C22⋊Dic11—21no—
148(C2×D11)⋊C4—21no—
149(C2×D11)⋊C4—21no—
150C4⋊Dic11C22×C411yescharacteristic
151C4⋊Dic11C22×C411yescharacteristic
152Dic11⋊C4—21no—
153Dic11⋊C4—21no—
154C4×Dic11—21no—
155C4×Dic11—21no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C4×Dic11—21no—
159C4×Dic11—21no—
160C4×Dic11—42no—
161C4×Dic11—42no—
162C4×Dic11C2×Q812yes—
163#4318—22no—
164#4318—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8C22×C412yes—
169C2×C11⋊C8C22×C412yes—
170#4313—44no—
171C8×D11—44no—
172#3076—111no—
173#2962D1111yescharacteristic, complemented
174#2906—111no—
175#1994—111no—
176#1950—111no—
177#1946—112no—
178#1922—112no—
179#1866—112no—
180#1767—111no—
181#1765—112no—
182C4×#104—111no—
183C23×C11C2×#4111yescharacteristic
184C22×D11—21no—
185Q8×C11—42no—
186Q8×C11—81no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—41no—
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11C4×D411yescharacteristic
193C2×C4×C11C4×D411yescharacteristic
194C2×C4×C11C4×D411yescharacteristic
195C2×C4×C11C23×C411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×Q811yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C2×C4×C112−1+411yescharacteristic
201C22⋊D11—22no—
202C22⋊D11—22no—
203C2×Dic11—21no—
204C2×Dic11—22no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—22no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212D44—21no—
213D44C4×Q812yes—
214C4×D11—22no—
215C4×D11—22no—
216C4×D11—42no—
217C4×D11—81no—
218Dic22—21no—
219Dic22C4×Q812yes—
220C8×C11—22no—
221C8×C11—22no—
222C8×C11—22no—
223C8×C11—41no—
224C11⋊C8—22no—
225C11⋊C8—22no—
226C11⋊C8—42no—
227C2×#131—112no—
228#533C2×D1111yescharacteristic
229C4×#41—111no—
230#479—112no—
231#478—112no—
232#477—111no—
233#476—111no—
234#475—111no—
235#474—111no—
236#446—22no—
237#446—21no—
238C8×Q8—21no—
239C2×#108—112no—
240#427—112no—
241#424—112no—
242#424—222no—
243#424C2×D1112yes—
244#423—111no—
245#423—221no—
246C2×C4⋊C8—111no—
247C2×C4⋊C8—221no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#104—111no—
250C2×#104—111no—
251#416—112no—
252#405C2×D1112yes—
253C4×M16C2×D1111yescharacteristic
254C2×#97—112no—
255C43—111no—
256#341—112no—
257#339—111no—
258#339—111no—
259#339—112no—
260#339—112no—
261#336—112no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11C2×C4×D411yescharacteristic
265C22×C11#55211yescharacteristic
266C22×C11#55411yescharacteristic
267C2×D11—22no—
268C2×D11—41no—
269C2×D11—41no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—42no—
274C4×C11—42no—
275C4×C11#44412yes—
276C4×C11C2×C4×Q811yescharacteristic
277C4×C11#52011yescharacteristic
278C4×C11#54611yescharacteristic
279C4×C11D4×Q811yescharacteristic
280Dic11—22no—
281Dic11—42no—
282Dic11—42no—
283Dic11—41no—
284Dic11—41no—
285C2×#41—111no—
286#131—224no—
287#131—442no—
288C2×M16—112no—
289C2×M16—222no—
290C2×M16C22×D1111yescharacteristic
291C2×M16C22×D1111yescharacteristic
292C22×C8—112no—
293C22×C8—222no—
294C22×C8C22×D1112yes—
295C4⋊Q8C4×D1111yescharacteristic
296C4⋊Q8C4×D1111yescharacteristic
297#125C4×D1112yes—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—111no—
303C4×Q8—111no—
304C4×D4—111no—
305C4×D4—111no—
306C4×D4—221no—
307C4×D4—221no—
308#117—111no—
309#117—221no—
310#117C22×D1112yes—
311C2×C42—111no—
312C2×C42—111no—
313C2×C42—221no—
314C2×C42—221no—
315C2×C42—221no—
316C2×C42C22×D1111yescharacteristic
317#108—442no—
318#107—112no—
319#107—112no—
320#106—112no—
321#106—112no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—111no—
325C4⋊C8—111no—
326C4⋊C8—112no—
327C4⋊C8—222no—
328C4⋊C8—222no—
329C4⋊C8—221no—
330C4⋊C8—221no—
331C4⋊C8C22⋊D1111yescharacteristic
332C4⋊C8C22⋊D1111yescharacteristic
333C4⋊C8C22⋊D1112yes—
334#104—114no—
335#104—222no—
336#103—112no—
337#103—112no—
338#102—112no—
339#102—112no—
340#97—22no—
341#97—21no—
342#97—442no—
343C4×C8—22no—
344C4×C8—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11#236011yescharacteristic
348C2×C11C2×#44411yescharacteristic
349C2×C11#295611yescharacteristic
350D11—42no—
351#41—112no—
352#41—112no—
353#41—221no—
354#41—221no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—111no—
358C2×D4—111no—
359C2×D4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4#433911yescharacteristic
366C22×C4#433911yescharacteristic
367C22×C4C23×D1111yescharacteristic
368M16—21no—
369M16—21no—
370M16—21no—
371M16—222no—
372M16—222no—
373M16—444no—
374M16Q8×D1112yes—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—112no—
380C2×C8—112no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—444no—
385C2×C8C2×C22⋊D1112yes—
386C2×C8C2×C22⋊D1112yes—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—111no—
392C4⋊C4—111no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4C2×C4×D1112yes—
396C4⋊C4C2×C4×D1112yes—
397C22⋊C4—22no—
398C22⋊C4—221no—
399C22⋊C4—221no—
400C22⋊C4—221no—
401C42—22no—
402C42—112no—
403C42—221no—
404C42—221no—
405C42—221no—
406C42—221no—
407C42—221no—
408C42—221no—
409C42—442no—
410C42—442no—
411C42C2×C4×D1111yescharacteristic
412C42C2×C4×D1111yescharacteristic
413C42C2×C22⋊D1111yescharacteristic
414C42C2×C22⋊D1111yescharacteristic
415C11#2298311yescharacteristic, complemented, Sylow
416C23—221no—
417C23C2×#433911yescharacteristic
418Q8—42no—
419Q8—81no—
420Q8—112no—
421Q8—221no—
422D4—112no—
423D4—222no—
424D4—222no—
425D4—221no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—221no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—222no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—881no—
443C2×C4C4×C22⋊D1111yescharacteristic
444C2×C4C4×C22⋊D1111yescharacteristic
445C2×C4C4×C22⋊D1111yescharacteristic
446C2×C4C4×C22⋊D1111yescharacteristic
447C2×C4C22×C4×D1111yescharacteristic
448C2×C4C2×Q8×D1111yescharacteristic
449C2×C4#6704011yescharacteristic
450C2×C4#41×D1111yescharacteristic
451C2×C4#6704211yescharacteristic
452C2×C4C22×C22⋊D1111yescharacteristic
453C8—22no—
454C8—22no—
455C8—22no—
456C8—41no—
457C8—222no—
458C8—222no—
459C8—442no—
460C22—21no—
461C22—21no—
462C22—222no—
463C22—441no—
464C22—441no—
465C22#1062311011yescharacteristic
466C22#1062311211yescharacteristic
467C22C2×C4×C22⋊D1111yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—42no—
472C4—42no—
473C4—222no—
474C4—442no—
475C4—442no—
476C4—441no—
477C4—441no—
478C4#1062275812yes—
479C4C4×Q8×D1111yescharacteristic
480C4#1062310511yescharacteristic
481C4Q8×C22⋊D1111yescharacteristic
482C4#1062336011yescharacteristic
483C2—21no—
484C2—21no—
485C2—442no—
486C2#1307161711yescharacteristic
487C2C2×#1062275811yescharacteristic
488C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2962C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C23
cosocleC22×C4×C11C24
hypercenter#2962D11
hypocenterC11#22983
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #13069594C2semidirect
4. #13069391C2semidirect
5. #13069366C2semidirect
6. #13069215C2semidirect
8. #13068471C2semidirect
11. C11×#2962C2semidirect
27. #10622707C4semidirect
28. #10622704C4semidirect
29. #10622700C4semidirect
30. #10622697C4semidirect
31. #10622679C4semidirect
32. #10622676C4semidirect
89. #66889Q8semidirect
173. #2962D11semidirect
415. C11#22983semidirect

Maximal subgroups

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

subgroupindex
#130783982
#130771812
#130695942
#130693912
#130693662
#130692152
#130688902
#130684712
#130684622
C4×#668892
C11×#29622
#2298311