Finite Group Databasebeta

← #14655829

Subgroups — #14655829

Order 2816.

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

normal subgroups only

This group has 496 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#13079764C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic
3#13067298C211yesmaximal, 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#10622694—21no—
19#10622691—21no—
20#10622657—22no—
21#10622634—22no—
22#10622620—22no—
23#10622620—22no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28Q8⋊(C11⋊C8)—22no—
29#10622163—22no—
30#10622119—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×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C22×C11⋊C8—21no—
53#66922—21no—
54#66922—21no—
55#66922—21no—
56#66922D412yes—
57C11×#107—22no—
58C11×#106—22no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×#102—22no—
62C11×#102—22no—
63#66899—24no—
64#66896—24no—
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)D412yes—
67#66871—24no—
68#66871—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#10190—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×C11Q1612yes—
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
115C4⋊Dic11—22no—
116C4⋊Dic11—22no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124#3230—111no—
125#3077D1111yescharacteristic
126C2×#474—111no—
127#1548—111no—
128#1481—111no—
129#1460—111no—
130#1301—111no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11#12111yescharacteristic
137Q8×C11—42no—
138Q8×C11—42no—
139D4×C11—22no—
140D4×C11—22no—
141D4×C11—41no—
142D4×C11—41no—
143C2×C4×C11—22no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—82no—
149C2×C4×C11—82no—
150C2×C4×C11—81no—
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12011yescharacteristic
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11#12111yescharacteristic
156C2×C4×C11#12711yescharacteristic
157C2×C4×C11C2×Q1611yescharacteristic
158C2×C4×C11#13511yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×C4×C11#13711yescharacteristic
161C2×Dic11—42no—
162C2×Dic11—82no—
163Dic22—82no—
164Dic22—82no—
165C8×C11—42no—
166C11⋊C8—42no—
167C11⋊C8—42no—
168C11⋊C8—81no—
169#533C2×D1111yescharacteristic
170C2×C4⋊Q8—111no—
171C2×C4×D4C2×D1111yescharacteristic
172#500—221no—
173#487—221no—
174#484—222no—
175#478—22no—
176#477—222no—
177#476—21no—
178#474—21no—
179#474—222no—
180#474—222no—
181#431—111no—
182#431—111no—
183#428—21no—
184C2×#107—221no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8—111no—
187#418—21no—
188C2×#102—221no—
189#333—222no—
190Q8⋊C8—222no—
191#323—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11#39211yescharacteristic
200C22×C11#46711yescharacteristic
201C22×C11#47011yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11#45111yescharacteristic
209C4×C11#45111yescharacteristic
210C4×C11#45211yescharacteristic
211C4×C11#45211yescharacteristic
212C4×C11#47212yes—
213Dic11—82no—
214C22×Q8—221no—
215C22×D4C22⋊D1111yescharacteristic
216C23×C4—21no—
217C2×M16—21no—
218C22×C8—221no—
219C4⋊Q8—112no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8—221no—
223C4⋊Q8C22⋊D1111yescharacteristic
224C4⋊Q8C22⋊D1111yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×D4—21no—
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234#117—21no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4C22⋊D1111yescharacteristic
238C2×C22⋊C4—21no—
239C2×C42C22×D1111yescharacteristic
240#107—22no—
241#107—224no—
242#107—224no—
243#106—22no—
244C4⋊C8—21no—
245C4⋊C8—112no—
246C4⋊C8—221no—
247C4⋊C8—221no—
248C4⋊C8—221no—
249C4⋊C8C22⋊D1112yes—
250#103—224no—
251#102—22no—
252#102—22no—
253#102—224no—
254C22⋊C8—112no—
255C22⋊C8—221no—
256C4×C8—221no—
257C4×C8—221no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—82no—
261C2×C11#200111yescharacteristic
262C2×C11#200911yescharacteristic
263C2×C11#201811yescharacteristic
264C24—21no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—222no—
268C2×Q8—441no—
269C2×Q8—882no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4#432612yes—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—82no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282C22×C4#434111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284M16—41no—
285M16—41no—
286C2×C8—22no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—441no—
290C2×C8—441no—
291C2×C8—441no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C42D4×D1111yescharacteristic
309C42D4×D1111yescharacteristic
310C42C2×C22⋊D1111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C11#1019011yescharacteristic, complemented, Sylow
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23#6699211yescharacteristic
319Q8—42no—
320Q8—42no—
321Q8—882no—
322Q8—882no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4#6699011yescharacteristic
338C2×C4#6699011yescharacteristic
339C2×C4#6699111yescharacteristic
340C2×C4#6699211yescharacteristic
341C2×C4#6699311yescharacteristic
342C2×C4#6699511yescharacteristic
343C2×C4C2×#432611yescharacteristic
344C2×C4#6700311yescharacteristic
345C2×C4#6700411yescharacteristic
346C2×C4#6700611yescharacteristic
347C8—42no—
348C8—442no—
349C8—442no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22#1062266411yescharacteristic
359C22#1062266511yescharacteristic
360C22#1062283611yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—81no—
366C4—81no—
367C4—882no—
368C4#1062266011yescharacteristic
369C4#1062266311yescharacteristic
370C4#1062281212yes—
371C4#1062284111yescharacteristic
372C4#1062285211yescharacteristic
373C2—21no—
374C2—21no—
375C2—82no—
376C2#1306962411yescharacteristic
377C2#1306967311yescharacteristic
378C2#1306972211yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3077C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#3077D11
hypocenterC11#10190
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. #13079764C2semidirect
3. #13067298C2semidirect
4. #13067019C2semidirect
6. #13066511C2semidirect
312. C11#10190semidirect

Maximal subgroups

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

subgroupindex
#130797642
C2×#106226202
#130672982
#130670192
#130669372
#130665112
C11×#30772
#1019011