Finite Group Databasebeta

← #14738648

Subgroups — #14738648

Order 2816.

584 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079846C211yesmaximal, characteristic
2#13079837C211yesmaximal, characteristic
3#13077591C211yesmaximal, characteristic
4#13068195C212yesmaximal, complemented
5#13068188C212yesmaximal, complemented
6#13068071C212yesmaximal, complemented
7#13068064C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067342C211yesmaximal, characteristic, complemented
10#13067333C211yesmaximal, characteristic, complemented
11C2×C11×#487C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623010C2211yescharacteristic
15C11×#487—21no—
16C11×#487—21no—
17C11×#487C2212yes—
18C11×#487C2212yes—
19C2×C11×#103—21no—
20C2×C11×#103—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622707C2212yes—
25#10622704C2212yes—
26#10622702—21no—
27#10622702—21no—
28#10622700C2212yes—
29#10622697C2212yes—
30#10622693—21no—
31#10622693—21no—
32#10622584—21no—
33#10622583—21no—
34#10622581—21no—
35#10622580—21no—
36#10622539C2211yescharacteristic
37#10622539C2211yescharacteristic
38#10622539C2211yescharacteristic
39#10622303—21no—
40#10622302—21no—
41#10622301C2211yescharacteristic
42C8×D44C2211yescharacteristic
43#10622292C2211yescharacteristic
44C8×Dic22C2211yescharacteristic
45#10622185C2212yes—
46#10622185C2212yes—
47#10622184C2212yes—
48#10622184C2212yes—
49#10622096C2212yes—
50#10622095C2212yes—
51C22×Q8×C11—21no—
52C22×Q8×C11—21no—
53C22×C8×C11D411yescharacteristic
54C22×C8×C11D411yescharacteristic
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2312yes—
62C11×C4⋊Q8C2312yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68#66983D411yescharacteristic
69#66982—21no—
70C4×C22⋊D11—21no—
71#66977D411yescharacteristic
72C2×#4313—21no—
73C2×C8×D11—21no—
74#66929—21no—
75#66928D411yescharacteristic
76C4×D44C2311yescharacteristic
77#66925—21no—
78#66923D411yescharacteristic
79C4×Dic22C2311yescharacteristic
80C11×#103—22no—
81C11×#103—22no—
82C11×#103—22no—
83C11×#103—22no—
84C4×C8×C11D411yescharacteristic
85C4×C8×C11D411yescharacteristic
86C4×C8×C11C2311yescharacteristic
87C4×C8×C11C2311yescharacteristic
88C22⋊(C11⋊C8)—21no—
89C22⋊(C11⋊C8)—21no—
90C22⋊(C11⋊C8)—21no—
91(C2×D11)⋊C8—21no—
92(C2×D11)⋊C8—21no—
93#66879—21no—
94Dic11⋊C8—21no—
95Dic11⋊C8—21no—
96C8×Dic11—21no—
97#66874—22no—
98#66874—22no—
99#66873—22no—
100#66873—22no—
101#66872—22no—
102#66872—22no—
103#66871—22no—
104#66871—22no—
105C4⋊(C11⋊C8)C2311yescharacteristic
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109#66867—21no—
110#66867—21no—
111#66867—21no—
112#19365—111nomaximal, Sylow
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11—41no—
118C2×Q8×C11—41no—
119C2×Q8×C11—82no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11#4111yescharacteristic
125C2×C22⋊D11—21no—
126C2×D44C2×D411yescharacteristic
127C2×C4×D11—21no—
128C2×Dic22C2×D411yescharacteristic
129C2×C8×C11—41no—
130C2×C8×C11—41no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11#4111yescharacteristic
146C42×C11C2411yescharacteristic
147C22⋊Dic11—21no—
148(C2×D11)⋊C4—21no—
149(C2×D11)⋊C4—21no—
150(C2×D11)⋊C4—21no—
151(C2×D11)⋊C4—21no—
152C4⋊Dic11C2×D411yescharacteristic
153C4⋊Dic11C2×D411yescharacteristic
154Dic11⋊C4—21no—
155Dic11⋊C4—21no—
156Dic11⋊C4—21no—
157Dic11⋊C4—21no—
158C4×Dic11—21no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163#4313—42no—
164C8×D11—42no—
165#3239—111no—
166#3238—111no—
167C2×#487D1111yescharacteristic, complemented
168#2966—111no—
169#1704—112no—
170#1703—112no—
171#1684—112no—
172#1683—112no—
173#1568—111no—
174#1558—111no—
175#1556—111no—
176C23×C11#12111yescharacteristic
177C22×D11—21no—
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—82no—
181Q8×C11—82no—
182Q8×C11—82no—
183C2×C4×C11—22no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—82no—
190C2×C4×C11—82no—
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C22⋊D11—42no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201D44—22no—
202C4×D11—41no—
203C4×D11—41no—
204Dic22—22no—
205C8×C11—21no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11—21no—
209C11⋊C8—41no—
210C11⋊C8—41no—
211C11⋊C8—42no—
212C11⋊C8—42no—
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×C4⋊Q8C2×D1111yescharacteristic
215#529—111no—
216#501—221no—
217#501—221no—
218#489—221no—
219#489—221no—
220#487—21no—
221#487—21no—
222#487C2×D1112yes—
223#487C2×D1112yes—
224#484—221no—
225#483—221no—
226#481—221no—
227#480—221no—
228#477—112no—
229#476—112no—
230#475—112no—
231#474—112no—
232#446—111no—
233C8×Q8—111no—
234#436—111no—
235#435—221no—
236C8×D4—111no—
237C8×D4—221no—
238#433—221no—
239#432—111no—
240#432—111no—
241#432—111no—
242C2×#103—21no—
243C2×#103—21no—
244#405—221no—
245C2×C4×C8C2×D1111yescharacteristic
246#335—112no—
247#334—112no—
248#333—112no—
249#333—112no—
250#332—112no—
251#332—112no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11#47112yes—
255C22×C11C2×#12111yescharacteristic
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—82no—
264C4×C11—82no—
265C4×C11#57511yescharacteristic
266C4×C11#57511yescharacteristic
267C4×C11#57812yes—
268Dic11—41no—
269Dic11—41no—
270Dic11—41no—
271C22×Q8—21no—
272C22×Q8—21no—
273C2×M16—221no—
274C22×C8—221no—
275C22×C8C22⋊D1111yescharacteristic
276C22×C8C22⋊D1111yescharacteristic
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8C22×D1112yes—
284C4⋊Q8C22×D1112yes—
285#126—221no—
286#125—111no—
287#124—111no—
288#123—221no—
289C22⋊Q8—111no—
290#121—111no—
291C4×Q8—111no—
292C4×D4—111no—
293C4×D4—221no—
294#117—221no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C42C22×D1111yescharacteristic
300#107—222no—
301#107—222no—
302#106—222no—
303#106—222no—
304C4⋊C8—111no—
305C4⋊C8—111no—
306C4⋊C8—112no—
307C4⋊C8—112no—
308C4⋊C8—221no—
309C4⋊C8—221no—
310#103—22no—
311#103—22no—
312#103—22no—
313#103—22no—
314#103—222no—
315#103—222no—
316#102—222no—
317#102—222no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321C22⋊C8—221no—
322C22⋊C8—221no—
323#97—221no—
324#97—221no—
325#97—221no—
326#97—221no—
327C4×C8—221no—
328C4×C8C22⋊D1111yescharacteristic
329C4×C8C22⋊D1111yescharacteristic
330C4×C8C22×D1111yescharacteristic
331C4×C8C22×D1111yescharacteristic
332C2×C11—22no—
333C2×C11#304011yescharacteristic
334C2×C11#305911yescharacteristic
335C2×C11C2×#47111yescharacteristic
336D11—81no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—42no—
340C2×Q8—42no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—82no—
344C2×Q8—111no—
345C2×D4—111no—
346C2×D4—221no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—221no—
350C22×C4D4×D1111yescharacteristic
351C22×C4#434111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353M16—442no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—221no—
359C2×C8—221no—
360C2×C8—442no—
361C2×C8C2×C22⋊D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—111no—
374C4⋊C4—111no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—221no—
383C22⋊C4—221no—
384C42—221no—
385C42D4×D1111yescharacteristic
386C42#434111yescharacteristic
387C42C2×C22⋊D1111yescharacteristic
388C42C23×D1111yescharacteristic
389C11#1936511yescharacteristic, complemented, Sylow
390C23—221no—
391C23#6699111yescharacteristic
392Q8—42no—
393Q8—42no—
394Q8—82no—
395Q8—82no—
396Q8—82no—
397Q8—222no—
398D4—222no—
399D4—442no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—82no—
407C2×C4—82no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4#6699111yescharacteristic
414C2×C4#6699111yescharacteristic
415C2×C4#6699111yescharacteristic
416C2×C4C2×D4×D1111yescharacteristic
417C2×C4C2×#434111yescharacteristic
418C2×C4C22×C22⋊D1111yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—21no—
423C8—442no—
424C8—442no—
425C8—441no—
426C8—441no—
427C22—21no—
428C22—21no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22#1062279012yes—
433C22C2×#6699111yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—82no—
439C4—82no—
440C4—441no—
441C4—441no—
442C4—441no—
443C4#1062329712yes—
444C4#1062335311yescharacteristic
445C4#1062335311yescharacteristic
446C2—22no—
447C2—881no—
448C2#1307810611yescharacteristic
449C2#1307826711yescharacteristic
450C2C2×#1062279011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#487C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenterC2×#487D11
hypocenterC11#19365
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
4. #13068195C2semidirect
5. #13068188C2semidirect
6. #13068071C2semidirect
7. #13068064C2semidirect
8. #13067379C2semidirect
9. #13067342C2semidirect
10. #13067333C2semidirect
11. C2×C11×#487C2semidirect
167. C2×#487D11semidirect
389. C11#19365semidirect

Maximal subgroups

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

subgroupindex
#130798462
#130798372
#130775912
#130681952
#130681882
#130680712
#130680642
#130673792
#130673422
#130673332
C2×C11×#4872
#1936511