Finite Group Databasebeta

← #14655773

Subgroups — #14655773

Order 2816.

508 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 105 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#13079561C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic
3#13067302C211yesmaximal, characteristic, complemented
4#13067019C211yesmaximal, characteristic, complemented
5#13066937C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic, complemented
7C11×#3077C211yesmaximal, characteristic
8C11×#533C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#478—22no—
12C11×#476—21no—
13C11×#474—21no—
14C11×#428—21no—
15C11×#423C2211yescharacteristic
16C11×#418—21no—
17C2×#66896—21no—
18#10622706—21no—
19#10622705—21no—
20#10622663—22no—
21#10622644—22no—
22#10622621—22no—
23#10622621—22no—
24C2×#66872—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28Q8⋊(C11⋊C8)—22no—
29#10622163—22no—
30#10622124—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8D411yescharacteristic
36C11×C4⋊Q8D411yescharacteristic
37C11×#125—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C4×Q8×C11—21no—
41C4×Q8×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C11×#117—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4326—24no—
51C2×C4⋊Dic11—21no—
52C2×C4⋊Dic11—21no—
53C22×C11⋊C8—21no—
54#66922—21no—
55#66922—21no—
56#66922—21no—
57#66922D412yes—
58C11×#107—22no—
59C11×#106—22no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×#102—22no—
63C11×#102—22no—
64#66896—24no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)D412yes—
67#66874—24no—
68#66872—24no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)—21no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)D412yes—
73C4×C11⋊C8—21no—
74C4×C11⋊C8—21no—
75#10182—111nomaximal, Sylow
76C24×C11—21no—
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11Q1612yescomplemented
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—82no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—41no—
93C2×Dic22—22no—
94C2×Dic22—41no—
95C2×Dic22—82no—
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11—41no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115#4326—84no—
116C4⋊Dic11—22no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#3209—111no—
126#3077D1111yescharacteristic
127C2×#476—111no—
128#1549—111no—
129#1481—111no—
130#1460—111no—
131#1301—111no—
132C23×C11—22no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—81no—
136C23×C11—81no—
137C23×C11#12111yescharacteristic
138Q8×C11—42no—
139Q8×C11—42no—
140D4×C11—22no—
141D4×C11—22no—
142D4×C11—41no—
143D4×C11—41no—
144C2×C4×C11—22no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—82no—
150C2×C4×C11—82no—
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×Q1611yescharacteristic
159C2×C4×C11#13511yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×C4×C11#13711yescharacteristic
162C2×Dic11—42no—
163C2×Dic11—82no—
164Dic22—44no—
165Dic22—82no—
166C8×C11—42no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170#533C2×D1111yescharacteristic
171C2×C4⋊Q8—111no—
172C2×C4×D4C2×D1111yescharacteristic
173#494—221no—
174#487—221no—
175#478—22no—
176#476—21no—
177#476—222no—
178#476—222no—
179#474—21no—
180#462—222no—
181#451—222no—
182#431—111no—
183#431—111no—
184#428—21no—
185C2×#106—221no—
186#423C2×D1111yescharacteristic
187C2×C4⋊C8—111no—
188#418—21no—
189C2×#102—221no—
190#332—222no—
191Q8⋊C8—222no—
192#323—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—42no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#46711yescharacteristic
202C22×C11#47011yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11#45111yescharacteristic
210C4×C11#45111yescharacteristic
211C4×C11#45211yescharacteristic
212C4×C11#45211yescharacteristic
213C4×C11#47112yes—
214Dic11—82no—
215C22×Q8—221no—
216C22×D4C22⋊D1111yescharacteristic
217C23×C4—21no—
218C2×Q16—224no—
219C2×M16—21no—
220C22×C8—221no—
221C4⋊Q8—112no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225C4⋊Q8C22⋊D1111yescharacteristic
226C4⋊Q8C22⋊D1111yescharacteristic
227#125—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236#117—21no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4C22⋊D1111yescharacteristic
240C2×C22⋊C4—21no—
241C2×C42C22×D1111yescharacteristic
242#107—22no—
243#106—22no—
244#106—224no—
245C4⋊C8—21no—
246C4⋊C8—112no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8C22⋊D1112yes—
251#103—224no—
252#102—22no—
253#102—22no—
254#102—224no—
255C22⋊C8—112no—
256C22⋊C8—221no—
257C4×C8—221no—
258C4×C8—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—82no—
262C2×C11#200111yescharacteristic
263C2×C11#200811yescharacteristic
264C2×C11#201911yescharacteristic
265C24—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—222no—
269C2×Q8—441no—
270C2×Q8—882no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4#432612yescomplemented
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—82no—
281C22×C4—441no—
282C22×C4D4×D1111yescharacteristic
283C22×C4#434111yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—884no—
286M16—41no—
287M16—41no—
288C2×C8—22no—
289C2×C8—222no—
290C2×C8—222no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—222no—
303C4⋊C4—222no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—41no—
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C42C2×C22⋊D1111yescharacteristic
313C42C2×C22⋊D1111yescharacteristic
314C11#1018211yescharacteristic, complemented, Sylow
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23#6699211yescharacteristic
321Q8—42no—
322Q8—42no—
323Q8—444no—
324Q8—882no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—442no—
338C2×C4—882no—
339C2×C4#6699011yescharacteristic
340C2×C4#6699011yescharacteristic
341C2×C4#6699111yescharacteristic
342C2×C4#6699211yescharacteristic
343C2×C4#6699311yescharacteristic
344C2×C4#6699511yescharacteristic
345C2×C4C2×#432611yescharacteristic
346C2×C4#6700311yescharacteristic
347C2×C4#6700411yescharacteristic
348C2×C4#6700611yescharacteristic
349C8—42no—
350C8—442no—
351C8—442no—
352C8—881no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22#1062266411yescharacteristic
361C22#1062266511yescharacteristic
362C22#1062283611yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—882no—
370C4#1062266011yescharacteristic
371C4#1062266311yescharacteristic
372C4#1062281312yes—
373C4#1062284111yescharacteristic
374C4#1062285211yescharacteristic
375C2—21no—
376C2—21no—
377C2—82no—
378C2#1306962411yescharacteristic
379C2#1306966611yescharacteristic
380C2#1306973011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3077C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#3077D11
hypocenterC11#10182
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079561C2semidirect
3. #13067302C2semidirect
4. #13067019C2semidirect
6. #13066511C2semidirect
84. C2×D4×C11Q16semidirect
276. C2×D4#4326semidirect
314. C11#10182semidirect

Maximal subgroups

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

subgroupindex
#130795612
C2×#106226212
#130673022
#130670192
#130669372
#130665112
C11×#30772
#1018211