Finite Group Databasebeta

← #14642917

Subgroups — #14642917

Order 2816.

422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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#13070159C211yesmaximal, characteristic, complemented
2#13070024C211yesmaximal, characteristic, complemented
3#13070019C211yesmaximal, characteristic
4#13066442C211yesmaximal, characteristic, complemented
5#13066442C211yesmaximal, characteristic, complemented
6#13066437C211yesmaximal, characteristic
7C11×#2804C211yesmaximal, characteristic
8C11×#400—21no—
9C11×#393—21no—
10C11×#393—21no—
11C11×#391C2211yescharacteristic
12C11×#391C2211yescharacteristic
13C11×#390C2211yescharacteristic
14C11×#386—21no—
15C11×#385—21no—
16C11×#385—21no—
17C2×#66899—21no—
18C2×#66899—21no—
19C2×#66896—21no—
20C2×#66872—21no—
21#10622548C2211yescharacteristic
22#10622167—21no—
23#10622167—21no—
24#10622162C2211yescharacteristic
25#10622162C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×Q8×C11D411yescharacteristic
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C2×C11×C4⋊C4—21no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46C22×C11⋊C8—21no—
47C11×#95—21no—
48C11×#95—21no—
49C11×#95—21no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54#66899—42no—
55#66899—42no—
56#66896—42no—
57#66872—42no—
58#7804—111nomaximal, Sylow
59C24×C11—21no—
60C2×Q8×C11—21no—
61C2×Q8×C11—21no—
62C2×Q8×C11—21no—
63C2×Q8×C11—21no—
64C2×Q8×C11—41no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11SD1612yes—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—81no—
78C22×C4×C11—81no—
79C22×C4×C11—81no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×Dic11—41no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—81no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—81no—
93C11×C22⋊C4—81no—
94C11×C22⋊C4—81no—
95C42×C11—41no—
96C4⋊Dic11—41no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—41no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—41no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8—41no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2804D1111yescharacteristic
112#2096—111no—
113#2072—111no—
114#2071—111no—
115#1272—111no—
116#1272—111no—
117#1270—111no—
118C23×C11—22no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11#12011yescharacteristic
126Q8×C11—42no—
127Q8×C11—42no—
128Q8×C11—81no—
129Q8×C11—81no—
130D4×C11—42no—
131D4×C11—81no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—84no—
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13511yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11#13711yescharacteristic
159C2×C4×C11#13711yescharacteristic
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166C2×#106—221no—
167C2×#103—221no—
168C2×#103—221no—
169C2×#102—221no—
170#400—21no—
171#393—21no—
172#393—21no—
173#391C2×D1111yescharacteristic
174#391C2×D1111yescharacteristic
175#390C2×D1111yescharacteristic
176#386—21no—
177#385—21no—
178#385—21no—
179#384—111no—
180#340—221no—
181#340—221no—
182#336—111no—
183#336—111no—
184#336—111no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—81no—
189C22×C11—81no—
190C22×C11—81no—
191C22×C11—81no—
192C22×C11#44811yescharacteristic
193C22×C11#44911yescharacteristic
194C22×C11#45211yescharacteristic
195C22×C11#45311yescharacteristic
196C22×C11#45511yescharacteristic
197C22×C11#45511yescharacteristic
198C22×C11#45811yescharacteristic
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11—81no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210Dic11—161no—
211C22×Q8C22⋊D1111yescharacteristic
212C22×Q8C22⋊D1111yescharacteristic
213C22×D4C22⋊D1111yescharacteristic
214C23×C4—21no—
215C22×C8—221no—
216C22×C8—221no—
217C22×C8—221no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—221no—
222C2×C4⋊C4C22⋊D1111yescharacteristic
223C2×C4⋊C4C22⋊D1111yescharacteristic
224C2×C4⋊C4C22⋊D1111yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C42C22×D1111yescharacteristic
231#106—442no—
232#103—442no—
233#103—442no—
234#102—442no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95—21no—
242C2×C11—82no—
243C2×C11#160811yescharacteristic
244C2×C11#161211yescharacteristic
245C2×C11#161811yescharacteristic
246C2×C11#162211yescharacteristic
247C2×C11#164011yescharacteristic
248C2×C11#164311yescharacteristic
249C2×C11#165911yescharacteristic
250C24—21no—
251C2×Q8—21no—
252C2×Q8—21no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×D4—21no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4#432512yes—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—81no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4—441no—
272C22×C4C2×C22⋊D1111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274C22×C4C2×C22⋊D1111yescharacteristic
275C2×C8—222no—
276C2×C8—441no—
277C2×C8—441no—
278C2×C8—441no—
279C2×C8—441no—
280C2×C8—441no—
281C2×C8—441no—
282C2×C8—441no—
283C2×C8—441no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—81no—
288C4⋊C4—441no—
289C4⋊C4—441no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—441no—
293C4⋊C4—441no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—81no—
299C22⋊C4—81no—
300C22⋊C4—81no—
301C42—41no—
302C11#780411yescharacteristic, complemented, Sylow
303C23—22no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23#6700611yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—81no—
314Q8—81no—
315D4—42no—
316D4—81no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—84no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4C2×#432511yescharacteristic
343C2×C4#6699511yescharacteristic
344C2×C4#6700211yescharacteristic
345C2×C4#6700311yescharacteristic
346C2×C4#6700311yescharacteristic
347C2×C4#6700411yescharacteristic
348C8—442no—
349C8—881no—
350C8—881no—
351C22—42no—
352C22—42no—
353C22—42no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22#1062284011yescharacteristic
359C22#1062285111yescharacteristic
360C22#1062285211yescharacteristic
361C22#1062285411yescharacteristic
362C22#1062285511yescharacteristic
363C22#1062285511yescharacteristic
364C22#1062285611yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—81no—
372C4—81no—
373C4—81no—
374C4—81no—
375C4—81no—
376C4—1761no—
377C2—82no—
378C2#1306760711yescharacteristic
379C2#1306763011yescharacteristic
380C2#1306766411yescharacteristic
381C2#1306768811yescharacteristic
382C2#1306780211yescharacteristic
383C2#1306782311yescharacteristic
384C2#1306792211yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2804C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2804D11
hypocenterC11#7804
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2804

Complements

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

NH ≅ G/Ntype
1. #13070159C2semidirect
2. #13070024C2semidirect
4. #13066442C2semidirect
5. #13066442C2semidirect
302. C11#7804semidirect

Maximal subgroups

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

subgroupindex
#130701592
#130700242
#130700192
#130664422
#130664372
C11×#28042
#780411