Finite Group Databasebeta

← #14657250

Subgroups — #14657250

Order 2816.

444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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#13069586C211yesmaximal, characteristic, complemented
2#13069433C211yesmaximal, characteristic
3#13068749C211yesmaximal, characteristic, complemented
4C2×#10622181C211yesmaximal, characteristic, complemented
5C2×#10622178C211yesmaximal, characteristic
6#13066497C211yesmaximal, characteristic, complemented
7C11×#2820C211yesmaximal, characteristic
8C2×C11×#125C2211yescharacteristic
9C2×C11×#124C2211yescharacteristic
10C11×#399—21no—
11C11×#397—21no—
12C11×#396—21no—
13C11×#396—21no—
14C11×#395—21no—
15C11×#394—21no—
16C11×#382C2211yescharacteristic
17C2×#66899—21no—
18C2×#66896—21no—
19#10622548C2211yescharacteristic
20C2×#66867C2211yescharacteristic
21C2×#66867C2211yescharacteristic
22C2×#66867C2211yescharacteristic
23#10622181—22no—
24#10622178—22no—
25#10622167—21no—
26#10622167—21no—
27#10622167—21no—
28#10622167—21no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C11×#125—21no—
32C11×#125—21no—
33C11×#125—21no—
34C11×#125—21no—
35C11×#124—21no—
36C11×#124—21no—
37C11×#124—21no—
38C11×#124—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#66899—42no—
65#66896—42no—
66#66867—21no—
67#66867—21no—
68#66867—21no—
69#66867—21no—
70#66867—21no—
71#66867D412yes—
72#10426—111nomaximal, Sylow
73C24×C11—21no—
74C2×Q8×C11—21no—
75C2×Q8×C11—21no—
76C2×Q8×C11—41no—
77C2×Q8×C11—41no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—41no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C11×C4⋊C4—41no—
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—81no—
102C11×C4⋊C4—81no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—81no—
108C11×C22⋊C4—81no—
109C11×C22⋊C4—81no—
110C11×C22⋊C4—81no—
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114C42×C11#4111yescharacteristic
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C2×C11⋊C8—22no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128#2820D1111yescharacteristic
129#1992—111no—
130#1959—111no—
131#1836—111no—
132C2×#330—111no—
133C2×#329—111no—
134#1295—111no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—41no—
141C23×C11—41no—
142C23×C11#12011yescharacteristic
143Q8×C11—42no—
144Q8×C11—81no—
145D4×C11—42no—
146D4×C11—81no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12311yescharacteristic
172C2×C4×C11#12311yescharacteristic
173C2×C4×C11#12411yescharacteristic
174C2×Dic11—81no—
175C2×Dic11—81no—
176C2×Dic11—81no—
177C11⋊C8—42no—
178C11⋊C8—42no—
179C11⋊C8—42no—
180C2×#125C2×D1111yescharacteristic
181C2×#124C2×D1111yescharacteristic
182C2×#103—221no—
183C2×#102—221no—
184C2×#97—111no—
185C2×#97—111no—
186C2×#97—111no—
187#399—21no—
188#397—21no—
189#396—21no—
190#396—21no—
191#395—21no—
192#394—21no—
193#384—111no—
194#382C2×D1111yescharacteristic
195#340—221no—
196#340—221no—
197#340—221no—
198#340—221no—
199#330—222no—
200#329—222no—
201C22×C11—81no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39411yescharacteristic
209C22×C11#45311yescharacteristic
210C22×C11#45411yescharacteristic
211C22×C11#45411yescharacteristic
212C22×C11#45511yescharacteristic
213C22×C11#45511yescharacteristic
214C22×C11#45611yescharacteristic
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—81no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11—81no—
225C4×C11—81no—
226Dic11—161no—
227C22×Q8C22⋊D1111yescharacteristic
228C22×D4C22⋊D1111yescharacteristic
229C22×C8—221no—
230C22×C8—221no—
231C22×C8—221no—
232#125—21no—
233#125—21no—
234#125—21no—
235#125—21no—
236#124—21no—
237#124—21no—
238#124—21no—
239#124—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4C22⋊D1111yescharacteristic
248C2×C4⋊C4C22⋊D1111yescharacteristic
249C2×C4⋊C4C22⋊D1111yescharacteristic
250C2×C4⋊C4C22⋊D1111yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4—21no—
257C2×C42C22×D1111yescharacteristic
258#103—442no—
259#102—442no—
260#97—112no—
261#97—221no—
262#97—221no—
263#97—221no—
264#97—221no—
265#97—221no—
266#95—21no—
267#95—21no—
268#95—21no—
269#95—21no—
270C2×C11—161no—
271C2×C11#165711yescharacteristic
272C2×C11#166111yescharacteristic
273C2×C11#166211yescharacteristic
274C2×C11#166411yescharacteristic
275C2×C11#203711yescharacteristic
276C2×C11#203811yescharacteristic
277C2×C11#204011yescharacteristic
278C24—21no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—441no—
293C22×C4C2×C22⋊D1111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296C2×C8—222no—
297C2×C8—222no—
298C2×C8—222no—
299C2×C8—441no—
300C2×C8—441no—
301C2×C8—441no—
302C2×C8—441no—
303C2×C8—441no—
304C2×C8—441no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—81no—
316C4⋊C4—81no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—442no—
320C4⋊C4—442no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—81no—
326C22⋊C4—81no—
327C22⋊C4—81no—
328C22⋊C4—81no—
329C42D4×D1111yescharacteristic
330C42#434111yescharacteristic
331C42#434111yescharacteristic
332C42#434111yescharacteristic
333C11#1042611yescharacteristic, complemented, Sylow
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23#6700611yescharacteristic
342Q8—42no—
343Q8—81no—
344D4—42no—
345D4—81no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—881no—
368C2×C4—881no—
369C2×C4—881no—
370C2×C4#6698811yescharacteristic
371C2×C4#6698811yescharacteristic
372C2×C4#6698911yescharacteristic
373C2×C4#6699111yescharacteristic
374C2×C4#6699211yescharacteristic
375C2×C4#6699211yescharacteristic
376C8—442no—
377C8—442no—
378C8—442no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22#1062283511yescharacteristic
387C22#1062285411yescharacteristic
388C22#1062285511yescharacteristic
389C22#1062285511yescharacteristic
390C22#1062285811yescharacteristic
391C22#1062285811yescharacteristic
392C22#1062285911yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—21no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4—81no—
403C4—81no—
404C4—1761no—
405C2—161no—
406C2#1306791411yescharacteristic
407C2#1306793311yescharacteristic
408C2#1306793911yescharacteristic
409C2#1306795011yescharacteristic
410C2#1306982311yescharacteristic
411C2#1306983011yescharacteristic
412C2#1306984211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2820C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2820D11
hypocenterC11#10426
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2820

Complements

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

NH ≅ G/Ntype
1. #13069586C2semidirect
3. #13068749C2semidirect
4. C2×#10622181C2semidirect
6. #13066497C2semidirect
333. C11#10426semidirect

Maximal subgroups

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

subgroupindex
#130695862
#130694332
#130687492
C2×#106221812
C2×#106221782
#130664972
C11×#28202
#1042611