Finite Group Databasebeta

← #14649828

Subgroups — #14649828

Order 2816.

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

normal subgroups only

This group has 516 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#13074431C211yesmaximal, characteristic
2#13071218C211yesmaximal, characteristic
3#13067188C211yesmaximal, characteristic
4C2×#10622107C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic
6#13066483C211yesmaximal, characteristic
7C11×#1520C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12#10622842C412yescomplemented
13#10622825C2211yescharacteristic
14#10622825C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622597—22no—
17#10622595C412yescomplemented
18#10622591—22no—
19#10622559—21no—
20#10622556—21no—
21#10622556—21no—
22C22⋊C4×Dic11—21no—
23#10622268—22no—
24C11×#328—22no—
25#10622176—22no—
26#10622107—22no—
27C22×Q8×C11C2×C411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C23×Dic11D411yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×C8×C11—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—22no—
50C2×Dic11⋊C4C2×C412yes—
51C2×Dic11⋊C4D412yes—
52C2×C4×Dic11—22no—
53C22×C11⋊C8—21no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95D412yes—
57C11⋊#95—22no—
58C11⋊#95—24no—
59C11⋊#95—22no—
60C11⋊#95—22no—
61C11⋊#95—22no—
62C11⋊#95C2×C412yes—
63C11⋊#95D412yes—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#9202—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C2×Q8×C11—21no—
69C2×Q8×C11—21no—
70C2×Q8×C11—81no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—22no—
74C22×C4×C11—81no—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×Dic11—22no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—22no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—81no—
92C22×Dic11C22⋊C412yes—
93C22×Dic11C22⋊C412yes—
94C2×C8×C11—41no—
95C2×C8×C11—81no—
96C11×C4⋊C4—21no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—81no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C22⋊Dic11—41no—
106C22⋊Dic11—41no—
107C22⋊Dic11—41no—
108C22⋊Dic11—41no—
109C4⋊Dic11—81no—
110C4⋊Dic11—81no—
111Dic11⋊C4—22no—
112Dic11⋊C4—22no—
113Dic11⋊C4—22no—
114Dic11⋊C4—22no—
115Dic11⋊C4—82no—
116C4×Dic11—82no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—81no—
119#2627—111no—
120#2313—111no—
121#1520—111no—
122#1520D1111yescharacteristic
123C2×#324—111no—
124#1289—111no—
125#1289—111no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11#12011yescharacteristic
130C23×C11#12311yescharacteristic
131C23×C11#13511yescharacteristic
132C23×C11#13511yescharacteristic
133C23×C11#13711yescharacteristic
134C23×C11#13711yescharacteristic
135Q8×C11—81no—
136Q8×C11—81no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—42no—
150C2×C4×C11C4×D411yescharacteristic
151C2×C4×C11C4×D411yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—42no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—81no—
171C8×C11—81no—
172C11⋊C8—81no—
173C2×C22⋊Q8C2×D1111yescharacteristic
174C22×C4⋊C4—111no—
175C2×C22⋊C8—111no—
176C2×C22⋊C8C2×D1111yescharacteristic
177#400—112no—
178#398—222no—
179#395—112no—
180#387—222no—
181#387—222no—
182#385—221no—
183#381—221no—
184#381—221no—
185#380—111no—
186#380—111no—
187#380C2×D1111yescharacteristic
188C4×C22⋊C4—221no—
189#328—22no—
190#328—222no—
191#324—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—41no—
201C22×C11—41no—
202C22×C11#38611yescharacteristic
203C22×C11#41611yescharacteristic
204C22×C11#41911yescharacteristic
205C22×C11#45211yescharacteristic
206C22×C11#45211yescharacteristic
207C22×C11#48511yescharacteristic
208C22×C11#48511yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—82no—
214C4×C11—81no—
215C4×C11—81no—
216Dic11—42no—
217Dic11—42no—
218Dic11—82no—
219Dic11—82no—
220C22×Q8C4×D1111yescharacteristic
221C23×C4—111no—
222C23×C4—111no—
223C23×C4C22×D1111yescharacteristic
224C22×C8—21no—
225C22×C8—221no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C22⋊Q8—21no—
229C22⋊Q8—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—112no—
233C2×C4⋊C4—112no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—222no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4C4×D1111yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—221no—
245C2×C22⋊C4—221no—
246C2×C42—222no—
247C22⋊C8—21no—
248C22⋊C8—21no—
249C22⋊C8—221no—
250C22⋊C8—221no—
251#95—112no—
252#95—112no—
253#95—222no—
254#95—222no—
255#95—222no—
256#95—222no—
257#95—224no—
258#95C22⋊D1112yes—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11—21no—
263C2×C11—21no—
264C2×C11—21no—
265C2×C11#187311yescharacteristic
266C2×C11#191211yescharacteristic
267C2×C11#191311yescharacteristic
268C24D4×D1111yescharacteristic
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—81no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—22no—
275C22×C4—81no—
276C22×C4—112no—
277C22×C4—112no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—222no—
287C22×C4—222no—
288C22×C4—881no—
289C22×C4C2×C4×D1111yescharacteristic
290C22×C4#433911yescharacteristic
291C22×C4D4×D1111yescharacteristic
292C22×C4D4×D1111yescharacteristic
293C22×C4#434111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295C2×C8—41no—
296C2×C8—81no—
297C2×C8—441no—
298C2×C8—881no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—81no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—222no—
308C4⋊C4—882no—
309C4⋊C4—881no—
310C4⋊C4—881no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C22⋊C4—441no—
319C42—882no—
320C11#920211yescharacteristic, complemented, Sylow
321C23—41no—
322C23—41no—
323C23C22⋊C4×D1111yescharacteristic
324C23#6693611yescharacteristic
325C23#6696811yescharacteristic
326C23#6696911yescharacteristic
327C23#6697111yescharacteristic
328C23#6697211yescharacteristic
329C23#6699011yescharacteristic
330Q8—81no—
331Q8—81no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—222no—
346C2×C4—222no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—442no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—442no—
358C2×C4—442no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—881no—
362C2×C4(C22⋊D11)⋊C411yescharacteristic
363C2×C4#6693711yescharacteristic
364C2×C4C4×C22⋊D1111yescharacteristic
365C2×C4#6699111yescharacteristic
366C8—81no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22#1062241511yescharacteristic
379C22#1062241711yescharacteristic
380C22#1062242711yescharacteristic
381C22#1062242811yescharacteristic
382C22#1062256911yescharacteristic
383C22#1062278611yescharacteristic
384C22#1062280011yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—81no—
391C4—81no—
392C4—442no—
393C4—442no—
394C4—882no—
395C4—882no—
396C2—21no—
397C2—21no—
398C2—21no—
399C2—21no—
400C2—21no—
401C2—21no—
402C2#1306892511yescharacteristic
403C2#1306915011yescharacteristic
404C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#386
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1520D11
hypocenterC11#9202
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
12. #10622842C4semidirect
17. #10622595C4semidirect
320. C11#9202semidirect

Maximal subgroups

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

subgroupindex
#130744312
#130712182
#130671882
C2×#106221072
#130664842
#130664832
C11×#15202
#920211