Finite Group Databasebeta

← #14737701

Subgroups — #14737701

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622691C211yesmaximal, characteristic, complemented
2#13078104C211yesmaximal, characteristic
3#13078099C211yesmaximal, characteristic
4#13077572C211yesmaximal, characteristic
5#13068009C214yesmaximal, complemented
6#13068004C214yesmaximal, complemented
7#13067374C211yesmaximal, characteristic, complemented
8#13067287C211yesmaximal, characteristic, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66995—21no—
12C2×#66962—21no—
13C4×#4339C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C11×#431C2211yescharacteristic
16C11×#423C2211yescharacteristic
17#10622838—21no—
18#10622733—21no—
19#10622703—21no—
20#10622703C2212yes—
21#10622696—21no—
22#10622696C2212yes—
23#10622691—21no—
24#10622691—21no—
25#10622691C2214yes—
26C2×#66871—22no—
27#10622537C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622462—21no—
30#10622462C2212yes—
31#10622454—21no—
32#10622454C2212yes—
33#10622447C2212yes—
34#10622443C2212yes—
35(C22⋊D11)⋊C8—22no—
36#10622298—21no—
37C4×C8×D11—21no—
38C11×#332C2214yes—
39#10622124C2214yes—
40#10622117C2214yes—
41C22×Q8×C11—21no—
42C2×#4339D411yescharacteristic
43C22×Dic22—21no—
44C2×C11×M16—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4326—22no—
53#66995—44no—
54C2×#4325—22no—
55C4×C22⋊D11—21no—
56C4×C22⋊D11—21no—
57#66979D411yescharacteristic
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×#4318—21no—
61C22×C11⋊C8D412yes—
62#66962—44no—
63C2×Dic44—22no—
64C2×#4314—22no—
65C2×C8×D11—22no—
66C4×D44D411yescharacteristic
67C4×D44C2311yescharacteristic
68#66925—21no—
69C42×D11—21no—
70#66922—21no—
71#66922—21no—
72#66922—21no—
73#66922C2312yes—
74C4×Dic22D411yescharacteristic
75C4×Dic22C2311yescharacteristic
76C11×C4⋊C8—21no—
77C11×C4⋊C8C2312yes—
78C11×C4⋊C8C2312yes—
79C11×C22⋊C8—21no—
80C4×C8×C11—21no—
81#66899—22no—
82#66899—22no—
83(C2×D11)⋊C8—22no—
84#66880—22no—
85#66880—22no—
86Dic11⋊C8—22no—
87C8×Dic11—22no—
88#66871—24no—
89#66871—24no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)C2312yes—
92C4×C11⋊C8D411yescharacteristic
93C4×C11⋊C8D411yescharacteristic
94C4×C11⋊C8C2312yes—
95#19271—111nomaximal, Sylow
96C2×Q8×C11—22no—
97C2×Q8×C11—41no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C2×C22⋊D11—21no—
105C22×Dic11—41no—
106#4339—22no—
107#4339D814yes—
108C2×D44C2×D411yescharacteristic
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×Dic22—22no—
113C2×Dic22—41no—
114C2×Dic22—42no—
115C2×Dic22—42no—
116C2×Dic22C2×D411yescharacteristic
117C11×M16—42no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128C22⋊Dic11—21no—
129#4326—44no—
130#4325—44no—
131(C2×D11)⋊C4—21no—
132(C2×D11)⋊C4—21no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—41no—
136C4⋊Dic11—41no—
137C4⋊Dic11C2×D411yescharacteristic
138C4⋊Dic11C2×D411yescharacteristic
139Dic11⋊C4—21no—
140Dic11⋊C4—21no—
141C4×Dic11—21no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144#4318—42no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8C2×D412yes—
148C2×C11⋊C8C2×D412yes—
149Dic44—44no—
150#4314—44no—
151C8×D11—44no—
152C2×#500—111no—
153#3039—111no—
154#3039—111no—
155C8×#41—111no—
156#1674—114no—
157#1673—114no—
158#1567—111no—
159#1546—111no—
160#1546D1111yescharacteristic, complemented
161C23×C11#12111yescharacteristic
162C22×D11—21no—
163Q8×C11—42no—
164Q8×C11—42no—
165Q8×C11—82no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—42no—
169C2×C4×C11—82no—
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12111yescharacteristic
173C2×C4×C11C2×D812yes—
174C2×C4×C11#13512yes—
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C22⋊D11—24no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—42no—
183C2×Dic11—82no—
184D44—21no—
185D44C2×D812yes—
186C4×D11—24no—
187C4×D11—42no—
188C4×D11—42no—
189Dic22—21no—
190Dic22—42no—
191Dic22—42no—
192Dic22—82no—
193Dic22C2×D812yes—
194C8×C11—42no—
195C8×C11—42no—
196C11⋊C8—22no—
197C11⋊C8—42no—
198C11⋊C8#13714yescomplemented
199C2×#137—221no—
200C2×#137—221no—
201C2×C4⋊Q8—111no—
202C2×C4⋊Q8C2×D1111yescharacteristic
203C4×#41—111no—
204#500—114no—
205#500—221no—
206#500—221no—
207#462—112no—
208#462—112no—
209#462—221no—
210#462—221no—
211#461—112no—
212#461—112no—
213#461—221no—
214#461—221no—
215C8×Q8—112no—
216C8×D4—112no—
217C8×D4—222no—
218#431—221no—
219#431C2×D1111yescharacteristic
220C2×#107—222no—
221#423—111no—
222#423C2×D1111yescharacteristic
223#419—221no—
224#419—221no—
225C2×C4×C8—111no—
226C2×C4×C8—221no—
227#335—114no—
228#332—114no—
229#332C2×D1114yes—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11#46612yes—
233C22×C11C2×#12111yescharacteristic
234C2×D11—22no—
235C2×D11—41no—
236C2×D11—41no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—82no—
240C4×C11#46612yes—
241C4×C11#47312yes—
242C4×C11C22×D811yescharacteristic
243C4×C11C2×#13511yescharacteristic
244C4×C11C2×#13712yes—
245Dic11—22no—
246Dic11—41no—
247Dic11—41no—
248Dic11—82no—
249C2×#41—111no—
250C22×Q8—21no—
251C22×Q8—221no—
252#137—444no—
253#137—444no—
254C2×Q16—222no—
255C2×Q16—222no—
256C2×SD16—222no—
257C2×SD16—222no—
258C2×M16—21no—
259C2×M16—221no—
260C22×C8—112no—
261C22×C8—222no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—112no—
266C4⋊Q8—221no—
267C4⋊Q8—221no—
268C4⋊Q8—221no—
269C4⋊Q8C22×D1112yes—
270C4×Q8—111no—
271C4×Q8—111no—
272C4×D4—111no—
273C4×D4—111no—
274C4×D4—221no—
275C4×D4—221no—
276#117—111no—
277#117—221no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C42—221no—
283C2×C42C22×D1111yescharacteristic
284#107—224no—
285#107—224no—
286C4⋊C8—21no—
287C4⋊C8—112no—
288C4⋊C8—222no—
289C4⋊C8—221no—
290C4⋊C8C22×D1112yes—
291C4⋊C8C22×D1112yes—
292#103—222no—
293#103—222no—
294#103—222no—
295#103—222no—
296C22⋊C8—21no—
297C22⋊C8—222no—
298C4×C8—21no—
299C4×C8—111no—
300C4×C8—111no—
301C4×C8—112no—
302C4×C8—222no—
303C2×C11—22no—
304C2×C11#303911yescharacteristic
305C2×C11C2×#46611yescharacteristic
306C2×C11C2×#47311yescharacteristic
307D11—42no—
308#41—114no—
309#41—222no—
310C2×Q8—22no—
311C2×Q8—41no—
312C2×Q8—42no—
313C2×Q8—42no—
314C2×Q8—111no—
315C2×Q8—222no—
316C2×Q8—441no—
317C2×Q8—442no—
318C2×Q8—442no—
319C2×D4—111no—
320C2×D4—221no—
321C22×C4—41no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—441no—
326C22×C4#433911yescharacteristic
327C22×C4D4×D1111yescharacteristic
328C22×C4D4×D1111yescharacteristic
329Q16—444no—
330Q16—444no—
331SD16—444no—
332SD16—444no—
333M16—42no—
334M16—442no—
335C2×C8—22no—
336C2×C8—22no—
337C2×C8—112no—
338C2×C8—112no—
339C2×C8—224no—
340C2×C8—222no—
341C2×C8—444no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—111no—
347C4⋊C4—111no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—441no—
353C4⋊C4—441no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C22⋊C4—221no—
357C42—221no—
358C42—221no—
359C42—221no—
360C42#433911yescharacteristic
361C42D4×D1111yescharacteristic
362C42D4×D1111yescharacteristic
363C42C23×D1111yescharacteristic
364C11#1927111yescharacteristic, complemented, Sylow
365C23—221no—
366C23#6693711yescharacteristic
367Q8—42no—
368Q8—42no—
369Q8—82no—
370Q8—112no—
371Q8—221no—
372Q8—442no—
373Q8—442no—
374Q8—882no—
375D4—112no—
376D4—224no—
377D4—221no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—82no—
382C2×C4—221no—
383C2×C4—224no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4—882no—
390C2×C4#6693711yescharacteristic
391C2×C4#6693711yescharacteristic
392C2×C4#6693711yescharacteristic
393C2×C4D8×D1112yes—
394C2×C4#6696912yes—
395C2×C4C2×#433911yescharacteristic
396C2×C4C2×D4×D1111yescharacteristic
397C2×C4C2×D4×D1111yescharacteristic
398C8—42no—
399C8—42no—
400C8—114no—
401C8—222no—
402C8—442no—
403C22—21no—
404C22—21no—
405C22—222no—
406C22—441no—
407C22—441no—
408C22#1062238812yes—
409C22C2×#6693711yescharacteristic
410C4—21no—
411C4—21no—
412C4—82no—
413C4—222no—
414C4—441no—
415C4—441no—
416C4—882no—
417C4#1062236812yes—
418C4#1062238812yes—
419C4C2×D8×D1111yescharacteristic
420C4C2×#6696911yescharacteristic
421C4D11×#13712yes—
422C2—22no—
423C2—442no—
424C2#1307810211yescharacteristic
425C2C2×#1062238811yescharacteristic
426C2C2×#1062236811yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#1546D11
hypocenterC11#19271
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
1. C2×#10622691C2semidirect
5. #13068009C2semidirect
6. #13068004C2semidirect
7. #13067374C2semidirect
8. #13067287C2semidirect
9. C11×#1546C2semidirect
160. #1546D11semidirect
198. C11⋊C8#137semidirect
364. C11#19271semidirect

Maximal subgroups

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

subgroupindex
C2×#106226912
#130781042
#130780992
#130775722
#130680092
#130680042
#130673742
#130672872
C11×#15462
#1927111