Finite Group Databasebeta

← #14735652

Subgroups — #14735652

Order 2816.

822 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 171 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079834C212yesmaximal, complemented
2C2×#10622682C211yesmaximal, characteristic, complemented
3#13067950C214yesmaximal, complemented
4#13067944C212yesmaximal, complemented
5#13067939C212yesmaximal, complemented
6#13067243C211yesmaximal, characteristic, complemented
7#13067236C212yesmaximal, complemented
8C11×#3553C211yesmaximal, characteristic
9C11×#564C2211yescharacteristic
10C11×#563C2212yes—
11C11×#562C2211yescharacteristic
12C11×#554—22no—
13C11×#553—22no—
14C11×#552—22no—
15C11×#541—22no—
16C11×#539—22no—
17C11×#539—22no—
18C11×#529C2212yes—
19C2×C11×#125C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21#10622682—22no—
22#10622682C2212yes—
23#10622682C2212yes—
24#10622678C2214yes—
25#10622668C2214yes—
26#10622656—22no—
27#10622646—22no—
28#10622634—22no—
29#10622621—22no—
30C2×#66874—22no—
31#10622539C2212yes—
32C2×#66867C2211yescharacteristic
33#10622181C2212yes—
34#10622181C2214yes—
35#10622181C2212yes—
36#10622178C2214yes—
37C22×Dic22—21no—
38C11×C4⋊Q8—22no—
39C11×#126—22no—
40C11×#126—22no—
41C11×#126—22no—
42C11×#126—22no—
43C11×#126—22no—
44C11×#125—22no—
45C11×#125—22no—
46C11×#125—22no—
47C11×#125—22no—
48C11×#125—22no—
49C11×#125—22no—
50C11×#125D412yes—
51C11×#125C2311yescharacteristic
52C11×#125C2311yescharacteristic
53C11×#125C2312yes—
54C11×#124C2312yes—
55C11×#123—22no—
56C11×#123—22no—
57C11×#123—22no—
58C11×#123—22no—
59C11×#123—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×C22⋊Q8D412yes—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121D412yes—
70C4×Q8×C11—22no—
71C4×Q8×C11D412yes—
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C4×D4×C11D412yes—
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4D412yes—
82C2×C42×C11C2311yescharacteristic
83C2×C4⋊Dic11—22no—
84C22×C11⋊C8—21no—
85#66922—22no—
86#66922—21no—
87#66922C2312yes—
88#66899—24no—
89#66896—24no—
90C22⋊(C11⋊C8)—22no—
91#66874—24no—
92#66874—24no—
93#66872—24no—
94#66871—24no—
95C4⋊(C11⋊C8)—22no—
96#66867—21no—
97#66867C2312yes—
98#66867C2314yes—
99#19060—111nomaximal, Sylow
100C2×Q8×C11—22no—
101C2×Q8×C11C2×D412yes—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11C2×D412yes—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×Dic11—41no—
112C2×Dic22—22no—
113C2×Dic22—44no—
114C2×Dic22—41no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4C2×D412yes—
131C11×C4⋊C4C2×D412yes—
132C11×C4⋊C4C2×D412yes—
133C11×C4⋊C4C2×D412yes—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—22no—
138C11×C22⋊C4—22no—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C11×C22⋊C4—22no—
142C11×C22⋊C4—22no—
143C42×C11—22no—
144C42×C11—22no—
145C42×C11—22no—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D412yes—
148C42×C11C2411yescharacteristic
149C4⋊Dic11—24no—
150C4⋊Dic11—42no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—24no—
153C2×C11⋊C8—42no—
154#3553D1111yescharacteristic
155#3238—112no—
156C2×#491—111no—
157#1664—114no—
158#1663—112no—
159#1662—112no—
160#1534—111no—
161#1532—112no—
162C23×C11—22no—
163C23×C11#12011yescharacteristic
164Q8×C11—42no—
165Q8×C11—82no—
166D4×C11—42no—
167D4×C11—44no—
168D4×C11—82no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—42no—
176C2×C4×C11—82no—
177C2×C4×C11—82no—
178C2×C4×C11—82no—
179C2×C4×C11—82no—
180C2×C4×C11#12012yes—
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11C22×D412yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×Dic11—42no—
185C2×Dic11—82no—
186Dic22—44no—
187Dic22—82no—
188C11⋊C8—44no—
189C11⋊C8—42no—
190#564C2×D1111yescharacteristic
191#563C2×D1112yes—
192#562C2×D1111yescharacteristic
193#554—22no—
194#553—22no—
195#552—22no—
196#541—22no—
197#539—22no—
198#539—22no—
199C2×C4⋊Q8—111no—
200#529C2×D1112yes—
201C2×#125C2×D1111yescharacteristic
202#501—114no—
203#491—112no—
204#491—112no—
205#491—222no—
206#489—114no—
207#483—222no—
208#480—222no—
209#477—222no—
210#476—222no—
211#432—112no—
212C2×#103—222no—
213C2×#97—111no—
214#330—112no—
215#330—114no—
216#330—112no—
217#329—114no—
218C22×C11—22no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11#45412yes—
223C22×C11C2×#12011yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—42no—
229C4×C11—42no—
230C4×C11—42no—
231C4×C11—42no—
232C4×C11—42no—
233Dic11—82no—
234C22×Q8—221no—
235C22×C8—221no—
236C4⋊Q8—22no—
237C4⋊Q8—112no—
238C4⋊Q8—222no—
239C4⋊Q8—221no—
240#126—22no—
241#126—22no—
242#126—22no—
243#126—22no—
244#126—22no—
245#125—22no—
246#125—22no—
247#125—22no—
248#125—22no—
249#125—22no—
250#125—22no—
251#125C22⋊D1112yes—
252#125C22×D1111yescharacteristic
253#125C22×D1111yescharacteristic
254#125C22×D1112yes—
255#124C22×D1112yes—
256#123—22no—
257#123—22no—
258#123—22no—
259#123—22no—
260#123—22no—
261C22⋊Q8—22no—
262C22⋊Q8—22no—
263C22⋊Q8—22no—
264C22⋊Q8—22no—
265C22⋊Q8—22no—
266C22⋊Q8—22no—
267C22⋊Q8C22⋊D1112yes—
268#121—22no—
269#121—22no—
270#121C22⋊D1112yes—
271C4×Q8—22no—
272C4×Q8C22⋊D1112yes—
273C4×D4—22no—
274C4×D4—22no—
275C4×D4—22no—
276C4×D4—22no—
277C4×D4C22⋊D1112yes—
278#117—22no—
279#117—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4C22⋊D1112yes—
284C2×C42C22×D1111yescharacteristic
285#107—224no—
286#106—224no—
287C4⋊C8—222no—
288#103—224no—
289#103—224no—
290#103—224no—
291#102—224no—
292C22⋊C8—222no—
293#97—112no—
294#97—114no—
295#97—221no—
296C2×C11—22no—
297C2×C11—82no—
298C2×C11C2×#45411yescharacteristic
299C2×C11#302212yes—
300C2×Q8—22no—
301C2×Q8—222no—
302C2×Q8—444no—
303C2×Q8—441no—
304C2×Q8C2×C22⋊D1112yes—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4C2×C22⋊D1112yes—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—441no—
313C22×C4C2×C22⋊D1111yescharacteristic
314C22×C4C2×C22⋊D1112yes—
315C2×C8—222no—
316C2×C8—224no—
317C2×C8—442no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—224no—
334C4⋊C4—442no—
335C4⋊C4C2×C22⋊D1112yes—
336C4⋊C4C2×C22⋊D1112yes—
337C4⋊C4C2×C22⋊D1112yes—
338C4⋊C4C2×C22⋊D1112yes—
339C22⋊C4—22no—
340C22⋊C4—22no—
341C22⋊C4—22no—
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C42—22no—
349C42—22no—
350C42—22no—
351C42C2×C22⋊D1111yescharacteristic
352C42C2×C22⋊D1112yes—
353C42C23×D1111yescharacteristic
354C11#1906011yescharacteristic, complemented, Sylow
355C23—22no—
356C23#6700611yescharacteristic
357Q8—42no—
358Q8—82no—
359Q8—444no—
360Q8—882no—
361D4—42no—
362D4—44no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4—82no—
375C2×C4—442no—
376C2×C4—882no—
377C2×C4#6700612yes—
378C2×C4#6700611yescharacteristic
379C2×C4C22×C22⋊D1111yescharacteristic
380C2×C4C22×C22⋊D1112yes—
381C8—442no—
382C8—444no—
383C22—22no—
384C22—42no—
385C22—42no—
386C22—42no—
387C22#1062285812yes—
388C22C2×#6700611yescharacteristic
389C4—21no—
390C4—21no—
391C4—22no—
392C4—22no—
393C4—42no—
394C4—42no—
395C4—42no—
396C4—42no—
397C4—42no—
398C4—882no—
399C2—22no—
400C2—82no—
401C2C2×#1062285811yescharacteristic
402C2#1307799512yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3553C2
socleC22×C11C2×#120
hypercenter#3553D11
hypocenterC11#19060
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3553

Complements

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

NH ≅ G/Ntype
1. #13079834C2semidirect
2. C2×#10622682C2semidirect
3. #13067950C2semidirect
4. #13067944C2semidirect
5. #13067939C2semidirect
6. #13067243C2semidirect
7. #13067236C2semidirect
354. C11#19060semidirect

Maximal subgroups

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

subgroupindex
#130798342
C2×#106226822
#130679502
#130679442
#130679392
#130672432
#130672362
C11×#35532
#1906011