Finite Group Databasebeta

← #14655768

Subgroups — #14655768

Order 2816.

530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079543C211yesmaximal, characteristic
2C2×#10622634C211yesmaximal, characteristic, complemented
3#13078088C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic, complemented
5#13067016C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×#66995—21no—
10#10623008C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14C2×#66899—21no—
15#10622644—21no—
16#10622641—22no—
17#10622640—21no—
18#10622634—22no—
19#10622634—22no—
20#10622579—21no—
21C2×#66871—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622454—22no—
25#10622351—22no—
26#10622306—21no—
27#10622294—21no—
28C11×#324—22no—
29#10622120—22no—
30#10622097—22no—
31C22×Q8×C11D411yescharacteristic
32C2×#4339—21no—
33C22×Dic22—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4326—22no—
43#66995—42no—
44#66995—42no—
45C2×#4325—22no—
46#66983—21no—
47#66983—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11—21no—
50C2×#4318—21no—
51C22×C11⋊C8—21no—
52C2×#4314—24no—
53#66928—21no—
54#66927D411yescharacteristic
55C4×D44—21no—
56C4×D44—21no—
57#66922—21no—
58#66922—21no—
59#66922—21no—
60#66922D412yes—
61#66922D411yescharacteristic
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8D412yes—
66C4×C8×C11—21no—
67C4×C8×C11—21no—
68#66899—24no—
69#66880—24no—
70#66874—22no—
71#66873—22no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77#10181—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11SD1612yescomplemented
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—41no—
90C22×Dic11—41no—
91#4339—41no—
92#4339—41no—
93#4339—41no—
94#4339—41no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×C4×D11—41no—
99C2×Dic22—21no—
100C2×Dic22—22no—
101C2×Dic22—41no—
102C2×Dic22—82no—
103C2×C8×C11—22no—
104C2×C8×C11—41no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C42×C11—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115#4326—44no—
116#4325—44no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11—21no—
121C4⋊Dic11—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125#4318—41no—
126#4318—41no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—41no—
130C2×C11⋊C8—41no—
131#4314—84no—
132#3206—111no—
133C2×#477—111no—
134#3037—111no—
135#1549—111no—
136#1480—111no—
137#1461D1111yescharacteristic, complemented
138#1301—111no—
139C23×C11#12111yescharacteristic
140C22×D11—41no—
141Q8×C11—22no—
142Q8×C11—22no—
143Q8×C11—41no—
144Q8×C11—41no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—81no—
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12711yescharacteristic
158C2×C4×C11C2×SD1611yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C22⋊D11—81no—
163C22⋊D11—81no—
164C2×Dic11—42no—
165C2×Dic11—41no—
166C2×Dic11—82no—
167D44—42no—
168D44—41no—
169D44—41no—
170D44—42no—
171C4×D11—81no—
172C4×D11—81no—
173Dic22—44no—
174Dic22—41no—
175Dic22—41no—
176Dic22—82no—
177C8×C11—42no—
178C8×C11—81no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C2×#137—221no—
182#532—111no—
183C2×C4⋊Q8—111no—
184C2×C4×Q8C2×D1111yescharacteristic
185#492—221no—
186#487—221no—
187#477—222no—
188#477—222no—
189#464—222no—
190#462—221no—
191#461—222no—
192#460—221no—
193#448—222no—
194#431C2×D1111yescharacteristic
195#431C2×D1111yescharacteristic
196C2×#107—221no—
197#423—111no—
198C2×C4⋊C8—111no—
199#417—221no—
200C2×#103—221no—
201#332—222no—
202D4⋊C8—222no—
203#324—22no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11#39211yescharacteristic
207C22×C11#46511yescharacteristic
208C22×C11#46811yescharacteristic
209C2×D11—81no—
210C2×D11—81no—
211C2×D11—81no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—81no—
217C4×C11#44811yescharacteristic
218C4×C11#44911yescharacteristic
219C4×C11#45011yescharacteristic
220C4×C11#45211yescharacteristic
221C4×C11#47312yes—
222Dic11—81no—
223Dic11—82no—
224C2×#41—221no—
225C22×Q8—221no—
226C22×Q8D4411yescharacteristic
227#137—442no—
228#137—442no—
229C2×Q16—222no—
230C2×SD16—224no—
231C2×SD16—222no—
232C2×M16—221no—
233C22×C8—221no—
234C4⋊Q8—112no—
235C4⋊Q8—111no—
236C4⋊Q8—221no—
237C4⋊Q8—221no—
238C4⋊Q8—221no—
239#127—111no—
240#124—221no—
241#121—221no—
242#121—221no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×D4—221no—
248C4×D4—221no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—221no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4D4411yescharacteristic
253C2×C42—21no—
254C2×C42C22×D1111yescharacteristic
255#107—224no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—112no—
259C4⋊C8—112no—
260C4⋊C8—221no—
261C4⋊C8—221no—
262#103—222no—
263#103—224no—
264#103—224no—
265#102—222no—
266C22⋊C8—21no—
267C22⋊C8C22⋊D1112yes—
268C4×C8—21no—
269C4×C8—21no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11#200011yescharacteristic
273C2×C11#200811yescharacteristic
274C2×C11#202011yescharacteristic
275D11—161no—
276#41—441no—
277#41—441no—
278#41—441no—
279#41—441no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—221no—
286C2×Q8—222no—
287C2×Q8—441no—
288C2×Q8—882no—
289C2×Q8#431412yescomplemented
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—441no—
297C22×C4—441no—
298C22×C4C2×D4411yescharacteristic
299C22×C4#433911yescharacteristic
300C22×C4C2×C22⋊D1111yescharacteristic
301Q16—444no—
302SD16—444no—
303SD16—884no—
304M16—441no—
305M16—441no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8—441no—
311C2×C8—441no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—222no—
317C4⋊C4—222no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C42—41no—
325C42—41no—
326C42D4×D1111yescharacteristic
327C42D4×D1111yescharacteristic
328C42D4×D1111yescharacteristic
329C42D4×D1111yescharacteristic
330C11#1018111yescharacteristic, complemented, Sylow
331C23—441no—
332C23#6698311yescharacteristic
333Q8—22no—
334Q8—22no—
335Q8—41no—
336Q8—41no—
337Q8—444no—
338Q8—441no—
339Q8—441no—
340Q8—882no—
341D4—442no—
342D4—441no—
343D4—441no—
344D4—442no—
345D4—881no—
346D4—881no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—441no—
355C2×C4—442no—
356C2×C4—882no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4#6693511yescharacteristic
360C2×C4#6693511yescharacteristic
361C2×C4#6693711yescharacteristic
362C2×C4#6693711yescharacteristic
363C2×C4C2×#431411yescharacteristic
364C2×C4#6695711yescharacteristic
365C2×C4#6696111yescharacteristic
366C2×C4#6696211yescharacteristic
367C2×C4#6699011yescharacteristic
368C2×C4#6699311yescharacteristic
369C8—42no—
370C8—81no—
371C8—442no—
372C8—442no—
373C22—21no—
374C22—21no—
375C22—881no—
376C22—881no—
377C22—881no—
378C22#1062257311yescharacteristic
379C22#1062272711yescharacteristic
380C22#1062274711yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—42no—
385C4—81no—
386C4—881no—
387C4—882no—
388C4#1062234411yescharacteristic
389C4#1062234611yescharacteristic
390C4#1062234711yescharacteristic
391C4#1062235111yescharacteristic
392C4#1062236812yes—
393C2—21no—
394C2—21no—
395C2—1761no—
396C2#1306962111yescharacteristic
397C2#1306966811yescharacteristic
398C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1461D11
hypocenterC11#10181
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
2. C2×#10622634C2semidirect
4. #13067300C2semidirect
6. #13066512C2semidirect
7. C11×#1461C2semidirect
83. C2×Q8×C11SD16semidirect
137. #1461D11semidirect
289. C2×Q8#4314semidirect
330. C11#10181semidirect

Maximal subgroups

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

subgroupindex
#130795432
C2×#106226342
#130780882
#130673002
#130670162
#130665122
C11×#14612
#1018111