Finite Group Databasebeta

← #14655765

Subgroups — #14655765

Order 2816.

530 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079541C211yesmaximal, characteristic
2C2×#10622704C211yesmaximal, characteristic, complemented
3#13078090C211yesmaximal, characteristic
4#13067016C211yesmaximal, characteristic
5#13066939C211yesmaximal, characteristic, complemented
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1549C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66962—21no—
10#10623008C2211yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#423C2211yescharacteristic
14#10622840—22no—
15#10622746—21no—
16#10622704—22no—
17#10622704—22no—
18#10622698—21no—
19#10622696—22no—
20#10622694—21no—
21C2×#66874—21no—
22C2×#66871—21no—
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622462—21no—
26#10622461—21no—
27#10622458—22no—
28C11×#332—22no—
29#10622107—22no—
30#10622097—22no—
31C22×Q8×C11—21no—
32C2×#4339—21no—
33C22×Dic22D411yescharacteristic
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4325—24no—
43#66983—21no—
44#66983—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48C22×C11⋊C8—21no—
49#66962—42no—
50#66962—42no—
51C2×Dic44—22no—
52C2×#4314—22no—
53#66928—21no—
54#66927D411yescharacteristic
55C4×D44—21no—
56C4×D44—21no—
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C4×Dic22—21no—
62C11×C4⋊C8—21no—
63C11×C4⋊C8—21no—
64C11×C4⋊C8D412yes—
65C11×C22⋊C8—21no—
66C4×C8×C11—21no—
67#66899—24no—
68C22⋊(C11⋊C8)D412yes—
69#66885—22no—
70#66880—22no—
71#66874—24no—
72#66871—24no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4×C11⋊C8—21no—
77#10181—111nomaximal, Sylow
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C2×Q8×C11—82no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—41no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88#4339—41no—
89#4339—41no—
90#4339—41no—
91#4339—41no—
92C2×D44—21no—
93C2×D44—21no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—21no—
99C2×Dic22—21no—
100C2×Dic22—21no—
101C2×Dic22—21no—
102C2×Dic22SD1612yescomplemented
103C11×M16—41no—
104C11×M16—41no—
105C2×C8×C11—22no—
106C2×C8×C11—41no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115#4325—84no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122Dic11⋊C4—41no—
123Dic11⋊C4—41no—
124C4×Dic11—41no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130Dic44—44no—
131#4314—44no—
132#3206—111no—
133C2×#477—111no—
134#3037—111no—
135#1549D1111yescharacteristic, complemented
136#1480—111no—
137#1461—111no—
138#1301—111no—
139C23×C11#12111yescharacteristic
140C22×D11—41no—
141Q8×C11—44no—
142Q8×C11—82no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—82no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C22⋊D11—81no—
158C22⋊D11—81no—
159C2×Dic11—22no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—81no—
165D44—42no—
166D44—41no—
167D44—41no—
168D44—42no—
169C4×D11—81no—
170C4×D11—81no—
171Dic22—22no—
172Dic22—22no—
173Dic22—41no—
174Dic22—41no—
175Dic22—41no—
176Dic22—41no—
177C8×C11—42no—
178C8×C11—81no—
179C11⋊C8—42no—
180C11⋊C8—42no—
181C2×#137—221no—
182#532—111no—
183C2×C4⋊Q8C2×D1111yescharacteristic
184C2×C4×Q8—111no—
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#431—111no—
195#431C2×D1111yescharacteristic
196C2×#107—221no—
197#423C2×D1111yescharacteristic
198C2×C4⋊C8—111no—
199#417—221no—
200C2×#103—221no—
201#332—22no—
202D4⋊C8—222no—
203#324—222no—
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—82no—
216C4×C11#44811yescharacteristic
217C4×C11#44911yescharacteristic
218C4×C11#45011yescharacteristic
219C4×C11#45211yescharacteristic
220C4×C11#47312yes—
221Dic11—42no—
222Dic11—81no—
223Dic11—81no—
224C2×#41—221no—
225C22×Q8—21no—
226C22×Q8—111no—
227#137—442no—
228#137—442no—
229C2×Q16—222no—
230C2×SD16—222no—
231C2×SD16—224no—
232C2×M16—21no—
233C22×C8—221no—
234C4⋊Q8—21no—
235C4⋊Q8—21no—
236C4⋊Q8—21no—
237C4⋊Q8—111no—
238C4⋊Q8D4412yes—
239#127—111no—
240#124—221no—
241#121—221no—
242#121—221no—
243C4×Q8—221no—
244C4×Q8—221no—
245C4×Q8—221no—
246C4×Q8—221no—
247C4×D4—221no—
248C4×D4—221no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—221no—
253C2×C42—221no—
254C2×C42C22×D1111yescharacteristic
255#107—224no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—112no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261C4⋊C8C22⋊D1112yes—
262#103—224no—
263#103—222no—
264#103—224no—
265#102—222no—
266C22⋊C8—21no—
267C22⋊C8—112no—
268C4×C8—21no—
269C4×C8—221no—
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—22no—
281C2×Q8—41no—
282C2×Q8—82no—
283C2×Q8—112no—
284C2×Q8—221no—
285C2×Q8—221no—
286C2×Q8—221no—
287C2×Q8—221no—
288C2×Q8—221no—
289C2×Q8—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—441no—
294C22×C4—41no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4—441no—
298C22×C4#433911yescharacteristic
299C22×C4D4×D1111yescharacteristic
300C22×C4D4×D1111yescharacteristic
301Q16—444no—
302SD16—444no—
303SD16—884no—
304M16—41no—
305M16—41no—
306C2×C8—22no—
307C2×C8—41no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8—441no—
311C2×C8—441no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—221no—
317C4⋊C4—221no—
318C4⋊C4—221no—
319C4⋊C4—221no—
320C4⋊C4—441no—
321C4⋊C4—441no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C42—441no—
325C42—441no—
326C42C2×D4411yescharacteristic
327C42D4×D1111yescharacteristic
328C42D4×D1111yescharacteristic
329C42C2×C22⋊D1111yescharacteristic
330C11#1018111yescharacteristic, complemented, Sylow
331C23—441no—
332C23#6693711yescharacteristic
333Q8—44no—
334Q8—82no—
335Q8—222no—
336Q8—222no—
337Q8—441no—
338Q8—441no—
339Q8—441no—
340Q8—441no—
341D4—442no—
342D4—441no—
343D4—441no—
344D4—442no—
345D4—881no—
346D4—881no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—222no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4—881no—
359C2×C4#6693511yescharacteristic
360C2×C4#6693511yescharacteristic
361C2×C4#6693711yescharacteristic
362C2×C4SD16×D1111yescharacteristic
363C2×C4#6696711yescharacteristic
364C2×C4#6697111yescharacteristic
365C2×C4#6697211yescharacteristic
366C2×C4#6698311yescharacteristic
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#1062242011yescharacteristic
379C22#1062242511yescharacteristic
380C22#1062257311yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—442no—
386C4—881no—
387C4—881no—
388C4#1062236812yes—
389C4#1062241911yescharacteristic
390C4#1062242411yescharacteristic
391C4#1062278211yescharacteristic
392C4#1062280011yescharacteristic
393C2—21no—
394C2—21no—
395C2—1761no—
396C2#1306961811yescharacteristic
397C2#1306967111yescharacteristic
398C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1549C2
socleC22×C11#392
prime radical#10623008C22
hypercenter#1549D11
hypocenterC11#10181
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
2. C2×#10622704C2semidirect
5. #13066939C2semidirect
6. #13066511C2semidirect
7. C11×#1549C2semidirect
102. C2×Dic22SD16semidirect
135. #1549D11semidirect
330. C11#10181semidirect

Maximal subgroups

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

subgroupindex
#130795412
C2×#106227042
#130780902
#130670162
#130669392
#130665112
C11×#15492
#1018111