Finite Group Databasebeta

← #14655928

Subgroups — #14655928

Order 2816.

598 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 107 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#13079923C211yesmaximal, characteristic
2#13079734C211yesmaximal, characteristic, complemented
3#13079075C211yesmaximal, characteristic, complemented
4#13069568C211yesmaximal, characteristic, complemented
5#13067110C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#1980C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×#66962—22no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C11×#104—22no—
13C4×C11×M16C2211yescharacteristic
14C4×C11×C4⋊C4C2211yescharacteristic
15#10622700—21no—
16#10622691—21no—
17#10622685—21no—
18#10622683—21no—
19#10622651—22no—
20#10622646—22no—
21#10622628—21no—
22#10622620—21no—
23#10622620—22no—
24#10622538C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26#10622328—22no—
27#10622312—21no—
28#10622306—21no—
29#10622167—22no—
30#10622089—22no—
31C2×C11×#41—21no—
32C2×#4339—21no—
33C22×Dic22—21no—
34C2×C11×M16D412yes—
35C11×C4⋊Q8D411yescharacteristic
36C11×#127D411yescharacteristic
37C11×#124—21no—
38C11×#121—21no—
39C11×#121—21no—
40C4×D4×C11—21no—
41C4×D4×C11—21no—
42C2×C11×C4⋊C4—21no—
43C2×C42×C11—21no—
44C2×C42×C11C2311yescharacteristic
45C2×#4323—22no—
46#66983—21no—
47#66983—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C22×C11⋊C8D412yes—
51#66962—44no—
52#66962—44no—
53C2×Dic44—24no—
54C2×#4314—24no—
55#66928—21no—
56#66927D411yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59#66922—21no—
60#66922—21no—
61#66922—21no—
62#66922D412yes—
63#66922D411yescharacteristic
64C11×#104—44no—
65C11×#97—21no—
66C4×C8×C11—21no—
67C11×#95—21no—
68#66896—24no—
69#66896—22no—
70C22⋊(C11⋊C8)D412yes—
71#66873—22no—
72#66871—24no—
73#66871—22no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77C4×C11⋊C8—21no—
78#10204—111nomaximal, Sylow
79C11×#41—42no—
80C11×#41—42no—
81C2×Q8×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—21no—
85C2×D4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C2×C22⋊D11—41no—
92C22×Dic11—41no—
93#4339—42no—
94#4339—42no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—22no—
100C2×Dic22—21no—
101C2×Dic22—41no—
102C2×Dic22—42no—
103C2×Dic22—42no—
104C11×M16—22no—
105C11×M16D814yescomplemented
106C2×C8×C11—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—42no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11#4111yescharacteristic
118#4323—82no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—21no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—42no—
130Dic44—48no—
131#4314—48no—
132#3245—111no—
133#3226—111no—
134#3152—111no—
135#1988—111no—
136#1980D1111yescharacteristic, complemented
137#1502—111no—
138#1283—111no—
139C23×C11—41no—
140C23×C11#12711yescharacteristic
141C22×D11—41no—
142Q8×C11—42no—
143D4×C11—42no—
144D4×C11—41no—
145D4×C11—41no—
146D4×C11—42no—
147D4×C11—81no—
148D4×C11—81no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—82no—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11C2×D812yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C22⋊D11—81no—
166C22⋊D11—81no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—81no—
170C2×Dic11—81no—
171D44—42no—
172D44—41no—
173D44—41no—
174D44—81no—
175C4×D11—82no—
176Dic22—44no—
177Dic22—42no—
178Dic22—82no—
179C8×C11—24no—
180C11⋊C8—42no—
181C11⋊C8—42no—
182C2×#137—222no—
183#532—111no—
184#532C2×D1111yescharacteristic
185C2×C4⋊Q8—111no—
186#500—221no—
187#497—222no—
188#494—221no—
189#492—221no—
190#486—221no—
191#480—222no—
192#474—222no—
193#474—221no—
194#474—221no—
195#466—222no—
196#459—221no—
197#459—221no—
198#431—111no—
199C2×C4⋊C8—111no—
200C2×#104—22no—
201C4×M16C2×D1111yescharacteristic
202C4×C4⋊C4C2×D1111yescharacteristic
203#340—222no—
204#327—222no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—81no—
208C22×C11—81no—
209C22×C11—81no—
210C22×C11#39211yescharacteristic
211C22×C11#49311yescharacteristic
212C22×C11#49611yescharacteristic
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—82no—
220C4×C11—81no—
221C4×C11#44712yes—
222C4×C11#45511yescharacteristic
223C4×C11#45611yescharacteristic
224C4×C11#45912yes—
225Dic11—82no—
226Dic11—81no—
227C2×#41—21no—
228C2×#41—221no—
229C22×Q8—221no—
230#137—444no—
231#137—444no—
232C2×Q16—224no—
233C2×SD16—224no—
234C2×D8—222no—
235C2×M16C22⋊D1112yes—
236C22×C8—112no—
237C4⋊Q8—112no—
238C4⋊Q8—111no—
239C4⋊Q8—221no—
240C4⋊Q8—221no—
241C4⋊Q8—221no—
242C4⋊Q8D4411yescharacteristic
243#127—111no—
244#127D4411yescharacteristic
245#124—21no—
246#124—221no—
247#121—21no—
248#121—21no—
249#121—221no—
250#121—221no—
251C4×D4—21no—
252C4×D4—21no—
253C4×D4—221no—
254C4×D4—221no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—221no—
257C2×C4⋊C4—221no—
258C2×C42—21no—
259C2×C42C22×D1111yescharacteristic
260#107—222no—
261#107—224no—
262C4⋊C8—221no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265#104—44no—
266#102—222no—
267#102—222no—
268#102—224no—
269C22⋊C8—112no—
270#97—21no—
271C4×C8—21no—
272C4×C8—221no—
273#95—21no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—161no—
277C2×C11#200711yescharacteristic
278C2×C11#200911yescharacteristic
279C2×C11#201111yescharacteristic
280D11—161no—
281#41—42no—
282#41—42no—
283#41—442no—
284#41—442no—
285C2×Q8—21no—
286C2×Q8—221no—
287C2×Q8—222no—
288C2×Q8—441no—
289C2×Q8—442no—
290C2×Q8—442no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—441no—
299C22×C4—41no—
300C22×C4—41no—
301C22×C4—441no—
302C22×C4—441no—
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305C22×C4C2×C22⋊D1111yescharacteristic
306Q16—448no—
307SD16—448no—
308D8—882no—
309M16—22no—
310M16#432314yescomplemented
311C2×C8—22no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—442no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—222no—
320C4⋊C4—221no—
321C4⋊C4—222no—
322C4⋊C4—221no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—441no—
328C22⋊C4—441no—
329C42—42no—
330C42C2×D4411yescharacteristic
331C42#433911yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C11#1020411yescharacteristic, complemented, Sylow
335C23—41no—
336C23—441no—
337C23#6699311yescharacteristic
338Q8—42no—
339Q8—444no—
340Q8—442no—
341Q8—882no—
342D4—42no—
343D4—42no—
344D4—41no—
345D4—41no—
346D4—81no—
347D4—81no—
348D4—442no—
349D4—441no—
350D4—441no—
351D4—881no—
352D4—881no—
353D4—881no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—82no—
362C2×C4—441no—
363C2×C4—442no—
364C2×C4—881no—
365C2×C4—881no—
366C2×C4—882no—
367C2×C4#6693511yescharacteristic
368C2×C4#6693511yescharacteristic
369C2×C4#6693711yescharacteristic
370C2×C4#6693711yescharacteristic
371C2×C4#6698311yescharacteristic
372C2×C4C2×#432312yes—
373C2×C4#6699011yescharacteristic
374C2×C4#6700212yes—
375C8—24no—
376C8—442no—
377C8—442no—
378C22—21no—
379C22—21no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—881no—
384C22—881no—
385C22—881no—
386C22#1062257311yescharacteristic
387C22#1062267111yescharacteristic
388C22#1062268611yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—82no—
393C4—81no—
394C4—881no—
395C4—882no—
396C4#1062243811yescharacteristic
397C4#1062243911yescharacteristic
398C4#1062262812yes—
399C4#1062264912yes—
400C2—21no—
401C2—21no—
402C2—161no—
403C2—1761no—
404C2#1306966411yescharacteristic
405C2#1306967711yescharacteristic
406C2#1306968611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1980C2
socleC22×C11#392
prime radical#13079923C2
hypercenter#1980D11
hypocenterC11#10204
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #13079734C2semidirect
3. #13079075C2semidirect
4. #13069568C2semidirect
5. #13067110C2semidirect
6. #13066467C2semidirect
7. C11×#1980C2semidirect
105. C11×M16D8semidirect
136. #1980D11semidirect
310. M16#4323semidirect
334. C11#10204semidirect

Maximal subgroups

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

subgroupindex
#130799232
#130797342
#130790752
#130695682
#130671102
#130664672
C11×#19802
#1020411