Finite Group Databasebeta

← #14655754

Subgroups — #14655754

Order 2816.

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

normal subgroups only

This group has 560 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#13079559C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3C2×#10622640C211yesmaximal, characteristic
4#13067283C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1461C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4325—21no—
10C2×#66927C2211yescharacteristic
11#10623001C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622838—21no—
15#10622640—22no—
16#10622640—22no—
17#10622635—22no—
18#10622634—21no—
19#10622633—21no—
20C2×#66873—21no—
21#10622577—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622461—22no—
25#10622344—22no—
26#10622307—21no—
27#10622306—21no—
28C11×#324—22no—
29#10622123—22no—
30#10622094—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D44—21no—
33C22×D44—21no—
34C22×D44—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C4×Q8×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C42×C11—21no—
42C2×C42×C11C2311yescharacteristic
43C2×#4325—24no—
44C2×#4325—42no—
45C2×#4325—42no—
46#66979—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318—21no—
50C22×C11⋊C8—21no—
51C2×#4314—24no—
52#66927—21no—
53#66927—21no—
54#66927—21no—
55#66927D412yes—
56#66923—21no—
57#66922D411yescharacteristic
58#66922D411yescharacteristic
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8D412yes—
65C4×C8×C11—21no—
66C4×C8×C11—21no—
67#66899—22no—
68#66899—22no—
69#66885—24no—
70#66873—24no—
71#66872—22no—
72#66871—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77#10179—111nomaximal, Sylow
78C23×D11—41no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11SD1612yescomplemented
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—82no—
101C2×D44—82no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C11×C4⋊C4—21no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C22⋊Dic11—41no—
117#4325—48no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122Dic11⋊C4—41no—
123Dic11⋊C4—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#3208—111no—
133#3078—111no—
134C2×#460—111no—
135#1545—111no—
136#1481—111no—
137#1461D1111yescharacteristic, complemented
138#1301—111no—
139C23×C11#12111yescharacteristic
140C22×D11—42no—
141C22×D11—82no—
142C22×D11—82no—
143C22×D11—81no—
144C22×D11—81no—
145Q8×C11—22no—
146Q8×C11—22no—
147Q8×C11—41no—
148Q8×C11—41no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11#12011yescharacteristic
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12711yescharacteristic
162C2×C4×C11C2×SD1611yescharacteristic
163C2×C4×C11#13511yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11#13711yescharacteristic
166C2×Dic11—41no—
167C2×Dic11—41no—
168D44—44no—
169D44—42no—
170D44—42no—
171D44—82no—
172D44—82no—
173D44—81no—
174D44—81no—
175D44—82no—
176Dic22—42no—
177Dic22—42no—
178C8×C11—42no—
179C8×C11—81no—
180C11⋊C8—42no—
181C11⋊C8—42no—
182C22×SD16—221no—
183#533—111no—
184C2×#127—111no—
185C2×C4×Q8C2×D1111yescharacteristic
186#492—221no—
187#486—221no—
188#479—222no—
189#477—221no—
190#475—221no—
191#460—222no—
192#460—222no—
193#460—222no—
194#450—222no—
195#431C2×D1111yescharacteristic
196#431C2×D1111yescharacteristic
197#428—221no—
198#423—111no—
199C2×C4⋊C8—111no—
200#419—221no—
201C2×#102—221no—
202#331—222no—
203Q8⋊C8—222no—
204#324—22no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11#39211yescharacteristic
208C22×C11#46511yescharacteristic
209C22×C11#46811yescharacteristic
210C2×D11—82no—
211C2×D11—82no—
212C2×D11—82no—
213C2×D11—162no—
214C2×D11—162no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—42no—
219C4×C11—81no—
220C4×C11#44811yescharacteristic
221C4×C11#44911yescharacteristic
222C4×C11#45011yescharacteristic
223C4×C11#45211yescharacteristic
224C4×C11#47112yes—
225Dic11—81no—
226Dic11—81no—
227C22×Q8D4411yescharacteristic
228C22×D4—221no—
229C22×D4—221no—
230C22×D4—221no—
231C2×SD16—224no—
232C2×SD16—224no—
233C2×SD16—442no—
234C2×SD16—442no—
235C2×M16—221no—
236C22×C8—221no—
237C4⋊Q8—111no—
238C4⋊Q8—111no—
239#127—112no—
240#127—221no—
241#127—221no—
242#127—221no—
243#125—221no—
244C22⋊Q8—221no—
245C22⋊Q8—221no—
246C4×Q8—21no—
247C4×Q8—21no—
248C4×Q8—21no—
249C4×Q8—21no—
250C4×Q8—221no—
251C4×Q8—221no—
252#117—221no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4D4411yescharacteristic
255C2×C42—21no—
256C2×C42C22×D1111yescharacteristic
257#107—222no—
258#106—222no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8—112no—
262C4⋊C8—112no—
263C4⋊C8—221no—
264C4⋊C8—221no—
265#103—222no—
266#103—222no—
267#102—224no—
268#102—224no—
269C22⋊C8—21no—
270C22⋊C8C22⋊D1112yes—
271C4×C8—21no—
272C4×C8—21no—
273C2×C11—21no—
274C2×C11—21no—
275C2×C11#200011yescharacteristic
276C2×C11#200811yescharacteristic
277C2×C11#201911yescharacteristic
278D11—162no—
279C24—441no—
280C2×Q8—21no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—221no—
286C2×Q8—221no—
287C2×Q8#431412yescomplemented
288C2×D4—222no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—441no—
292C2×D4—441no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—882no—
299C2×D4—882no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4C2×D4411yescharacteristic
303C22×C4#433911yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305SD16—448no—
306SD16—884no—
307M16—441no—
308M16—441no—
309C2×C8—22no—
310C2×C8—41no—
311C2×C8—222no—
312C2×C8—222no—
313C2×C8—441no—
314C2×C8—441no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—221no—
320C4⋊C4—221no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C22⋊C4—441no—
326C42—41no—
327C42—41no—
328C42—441no—
329C42D4×D1111yescharacteristic
330C42D4×D1111yescharacteristic
331C42D4×D1111yescharacteristic
332C42D4×D1111yescharacteristic
333C11#1017911yescharacteristic, complemented, Sylow
334C23—442no—
335C23—882no—
336C23—882no—
337C23—881no—
338C23—881no—
339C23#6698311yescharacteristic
340Q8—22no—
341Q8—22no—
342Q8—41no—
343Q8—41no—
344Q8—442no—
345Q8—442no—
346D4—444no—
347D4—442no—
348D4—442no—
349D4—882no—
350D4—882no—
351D4—881no—
352D4—881no—
353D4—882no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—81no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4#6693511yescharacteristic
364C2×C4#6693511yescharacteristic
365C2×C4#6693711yescharacteristic
366C2×C4#6693711yescharacteristic
367C2×C4C2×#431411yescharacteristic
368C2×C4#6695711yescharacteristic
369C2×C4#6696111yescharacteristic
370C2×C4#6696211yescharacteristic
371C2×C4#6699011yescharacteristic
372C2×C4#6699311yescharacteristic
373C8—42no—
374C8—81no—
375C8—442no—
376C8—442no—
377C22—21no—
378C22—21no—
379C22—882no—
380C22—882no—
381C22—882no—
382C22—1762no—
383C22—1762no—
384C22#1062257311yescharacteristic
385C22#1062272711yescharacteristic
386C22#1062274711yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—81no—
392C4—881no—
393C4—881no—
394C4#1062234411yescharacteristic
395C4#1062234611yescharacteristic
396C4#1062234711yescharacteristic
397C4#1062235111yescharacteristic
398C4#1062236712yes—
399C2—21no—
400C2—21no—
401C2—1762no—
402C2#1306962111yescharacteristic
403C2#1306966811yescharacteristic
404C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#392
prime radicalC2×#66927C22
hypercenter#1461D11
hypocenterC11#10179
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. #13078421C2semidirect
5. #13067020C2semidirect
6. #13066512C2semidirect
7. C11×#1461C2semidirect
84. C2×Q8×C11SD16semidirect
137. #1461D11semidirect
287. C2×Q8#4314semidirect
333. C11#10179semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130784212
C2×#106226402
#130672832
#130670202
#130665122
C11×#14612
#1017911