Finite Group Databasebeta

← #14737203

Subgroups — #14737203

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079795C212yesmaximal
2#13077591C211yesmaximal, characteristic
3#13068141C211yesmaximal, characteristic, complemented
4#13068136C211yesmaximal, characteristic, complemented
5#13068107C211yesmaximal, characteristic, complemented
6#13068102C211yesmaximal, characteristic, complemented
7#13068071C212yesmaximal, complemented
8#13068064C212yesmaximal, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067326C212yesmaximal, complemented
11C11×#3170C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13#10623010C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16C11×#487C2212yes—
17C11×#467—21no—
18C11×#467—21no—
19C4×C11×Q16—21no—
20C4×C11×Q16—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622707C2212yes—
25#10622704C2212yes—
26#10622700C2212yes—
27#10622697C2212yes—
28#10622681—22no—
29#10622677—22no—
30#10622616—22no—
31#10622609—22no—
32#10622539C2211yescharacteristic
33#10622538C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622184C2212yes—
43#10622184C2212yes—
44#10622096C2212yes—
45#10622095C2211yescharacteristic
46#10622095C2211yescharacteristic
47C2×C11×Q16—21no—
48C2×C11×Q16—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×C4⋊Q8C2312yes—
52C11×C4⋊Q8C2312yes—
53C11×#125—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—22no—
56C4×Q8×C11—22no—
57C4×Q8×C11—22no—
58C11×#117—22no—
59C2×C42×C11C2311yescharacteristic
60#66983D411yescharacteristic
61#66982—21no—
62C4×C22⋊D11—21no—
63#66977D411yescharacteristic
64C2×#4313—21no—
65C2×C8×D11—21no—
66#66929—21no—
67#66928D411yescharacteristic
68C4×D44C2311yescharacteristic
69#66925—21no—
70#66923D411yescharacteristic
71C4×Dic22C2311yescharacteristic
72C11×#107—21no—
73C11×#107—21no—
74C11×#103—22no—
75C11×#103—22no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)—22no—
82(C2×D11)⋊C8—21no—
83(C2×D11)⋊C8—21no—
84#66879—21no—
85Dic11⋊C8—21no—
86Dic11⋊C8—21no—
87C8×Dic11—21no—
88#66874—22no—
89#66874—22no—
90#66873—22no—
91#66873—22no—
92#66872—22no—
93#66872—22no—
94#66871—22no—
95#66871—22no—
96C4⋊(C11⋊C8)C2312yes—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867—21no—
101C4×C11⋊C8—22no—
102#19226—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—21no—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×Dic22C2×D411yescharacteristic
112C11×Q16—42no—
113C11×Q16—42no—
114C2×C8×C11—22no—
115C2×C8×C11—41no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—42no—
126C11×C22⋊C4—42no—
127C42×C11—42no—
128C42×C11C2×D411yescharacteristic
129C42×C11C2×D411yescharacteristic
130C42×C11#4111yescharacteristic
131C42×C11C2411yescharacteristic
132C22⋊Dic11—21no—
133(C2×D11)⋊C4—21no—
134(C2×D11)⋊C4—21no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—21no—
137C4⋊Dic11C2×D411yescharacteristic
138C4⋊Dic11C2×D411yescharacteristic
139Dic11⋊C4—21no—
140Dic11⋊C4—21no—
141Dic11⋊C4—21no—
142Dic11⋊C4—21no—
143C4×Dic11—21no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148#4313—42no—
149C8×D11—42no—
150#3233—112no—
151#3170D1111yescharacteristic, complemented
152#2966—111no—
153#1696—111no—
154#1695—111no—
155#1690—111no—
156#1689—111no—
157#1684—112no—
158#1683—112no—
159#1564—111no—
160#1554—112no—
161C23×C11#12111yescharacteristic
162C22×D11—21no—
163Q8×C11—42no—
164Q8×C11—42no—
165Q8×C11—82no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—22no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11#12111yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C22⋊D11—42no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182D44—22no—
183C4×D11—41no—
184C4×D11—41no—
185Dic22—22no—
186C8×C11—21no—
187C8×C11—21no—
188C8×C11—21no—
189C8×C11#13512yes—
190C11⋊C8—41no—
191C11⋊C8—41no—
192C11⋊C8—42no—
193C11⋊C8—42no—
194#533C2×D1112yes—
195#529—111no—
196#500C2×D1111yescharacteristic
197#499—222no—
198#494C2×D1111yescharacteristic
199#488—222no—
200#487C2×D1112yes—
201#485—222no—
202#482—222no—
203#477—112no—
204#476—112no—
205#475—112no—
206#474—112no—
207#467—21no—
208#467—21no—
209#446—111no—
210C8×Q8—111no—
211C4×Q16—21no—
212C4×Q16—21no—
213#436—111no—
214#435—221no—
215C8×D4—111no—
216C8×D4—221no—
217#433—221no—
218#432—111no—
219#431—112no—
220#405—221no—
221C2×C4×C8C2×D1111yescharacteristic
222#335—112no—
223#334—111no—
224#334—111no—
225#333—112no—
226#333—112no—
227#332—112no—
228#332—112no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11C2×#12111yescharacteristic
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—82no—
241C4×C11—82no—
242C4×C11C2×#13511yescharacteristic
243C4×C11#57511yescharacteristic
244C4×C11#57812yes—
245Dic11—41no—
246Dic11—41no—
247Dic11—41no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×M16—221no—
251C22×C8—221no—
252C22×C8C22⋊D1111yescharacteristic
253C22×C8C22⋊D1111yescharacteristic
254C4⋊Q8C22×D1112yes—
255C4⋊Q8C22×D1112yes—
256#126—221no—
257#125—22no—
258#125—111no—
259#124—111no—
260#123—221no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263C22⋊Q8—111no—
264#121—111no—
265C4×Q8—22no—
266C4×Q8—22no—
267C4×Q8—111no—
268C4×D4—111no—
269C4×D4—221no—
270#117—22no—
271#117—221no—
272C2×C42C22×D1111yescharacteristic
273#107—21no—
274#107—21no—
275#107—222no—
276#107—222no—
277#106—222no—
278#106—222no—
279C4⋊C8—111no—
280C4⋊C8—111no—
281C4⋊C8—112no—
282C4⋊C8—112no—
283C4⋊C8—221no—
284C4⋊C8—221no—
285#103—22no—
286#103—22no—
287#103—222no—
288#103—222no—
289#102—222no—
290#102—222no—
291C22⋊C8—222no—
292C22⋊C8—221no—
293C22⋊C8—221no—
294C22⋊C8—221no—
295#97—221no—
296#97—221no—
297C4×C8—221no—
298C4×C8—222no—
299C4×C8C22⋊D1111yescharacteristic
300C4×C8C22⋊D1111yescharacteristic
301C4×C8C22×D1111yescharacteristic
302C4×C8C22×D1111yescharacteristic
303C2×C11—41no—
304C2×C11#303511yescharacteristic
305C2×C11#305911yescharacteristic
306C2×C11#306711yescharacteristic
307D11—81no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—111no—
311C2×D4—111no—
312C2×D4—221no—
313C22×C4—221no—
314C22×C4D4×D1111yescharacteristic
315C22×C4#434111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317Q16—42no—
318Q16—42no—
319M16—442no—
320C2×C8—22no—
321C2×C8—41no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—221no—
325C2×C8—221no—
326C2×C8—442no—
327C2×C8C2×C22⋊D1111yescharacteristic
328C2×C8C2×C22⋊D1111yescharacteristic
329C2×C8C2×C22⋊D1111yescharacteristic
330C2×C8C2×C22⋊D1111yescharacteristic
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—42no—
336C4⋊C4—42no—
337C4⋊C4—111no—
338C4⋊C4—111no—
339C4⋊C4—221no—
340C4⋊C4—221no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C22⋊C4—42no—
344C22⋊C4—221no—
345C22⋊C4—221no—
346C22⋊C4—221no—
347C22⋊C4—221no—
348C22⋊C4—221no—
349C42—42no—
350C42—221no—
351C42D4×D1111yescharacteristic
352C42#434111yescharacteristic
353C42C2×C22⋊D1111yescharacteristic
354C42C23×D1111yescharacteristic
355C11#1922611yescharacteristic, complemented, Sylow
356C23—221no—
357C23#6699111yescharacteristic
358Q8—42no—
359Q8—42no—
360Q8—82no—
361Q8—222no—
362D4—222no—
363D4—442no—
364C2×C4—22no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—221no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4#6699111yescharacteristic
376C2×C4#6699111yescharacteristic
377C2×C4#6699111yescharacteristic
378C2×C4C2×D4×D1111yescharacteristic
379C2×C4C2×#434111yescharacteristic
380C2×C4C22×C22⋊D1111yescharacteristic
381C8—21no—
382C8—21no—
383C8—21no—
384C8—442no—
385C8—442no—
386C8—441no—
387C8—441no—
388C8#6700312yes—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22C2×#6699111yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—82no—
401C4—82no—
402C4—441no—
403C4—441no—
404C4—441no—
405C4#1062329712yes—
406C4C2×#6700311yescharacteristic
407C4#1062335311yescharacteristic
408C2—41no—
409C2—881no—
410C2#1307806511yescharacteristic
411C2#1307826711yescharacteristic
412C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3170D11
hypocenterC11#19226
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068141C2semidirect
4. #13068136C2semidirect
5. #13068107C2semidirect
6. #13068102C2semidirect
7. #13068071C2semidirect
8. #13068064C2semidirect
9. #13067364C2semidirect
10. #13067326C2semidirect
11. C11×#3170C2semidirect
151. #3170D11semidirect
355. C11#19226semidirect

Maximal subgroups

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

subgroupindex
#130797952
#130775912
#130681412
#130681362
#130681072
#130681022
#130680712
#130680642
#130673642
#130673262
C11×#31702
#1922611