Finite Group Databasebeta

← #14666659

Subgroups — #14666659

Order 2816.

412 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076715C211yesmaximal, characteristic
2#13069968C211yesmaximal, characteristic, complemented
3#13067641C211yesmaximal, characteristic, complemented
4#13066641C211yesmaximal, characteristic, complemented
5#13066613C211yesmaximal, characteristic
6#13066565C211yesmaximal, characteristic, complemented
7C11×#1596C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C11×#450—21no—
10C11×#392C2211yescharacteristic
11#10622835—21no—
12#10622835—21no—
13#10622833—21no—
14#10622657—21no—
15#10622565—21no—
16#10622562C2211yescharacteristic
17#10622561—21no—
18#10622559—21no—
19#10622559C2211yescharacteristic
20#10622271—21no—
21C11×#328—21no—
22C11×#323C2211yescharacteristic
23#10622176—21no—
24#10622164—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C22×D4×C11—21no—
28C22×D4×C11D411yescharacteristic
29C23×Dic11D411yescharacteristic
30C2×C11×SD16—41no—
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—41no—
34C11×C22⋊Q8—41no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4C2311yescharacteristic
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11—21no—
40C2×C22⋊Dic11—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—41no—
50C11×#102—41no—
51C11×C22⋊C8—21no—
52C11×#95D411yescharacteristic
53#66899—41no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—41no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66871—41no—
62#12231—111nomaximal, Sylow
63C24×C11—21no—
64C24×C11C2×D411yescharacteristic
65C2×Q8×C11—21no—
66C2×Q8×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—81no—
71C2×D4×C11—81no—
72C2×D4×C11—81no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×Dic11—21no—
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—81no—
85C11×SD16—82no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C11×C22⋊C4—81no—
95C22⋊Dic11—22no—
96C22⋊Dic11—21no—
97C22⋊Dic11—21no—
98C22⋊Dic11—41no—
99C22⋊Dic11—81no—
100C22⋊Dic11—81no—
101C22⋊Dic11—81no—
102C22⋊Dic11—81no—
103C22⋊Dic11—81no—
104C4⋊Dic11—41no—
105Dic11⋊C4—81no—
106Dic11⋊C4—81no—
107Dic11⋊C4—81no—
108Dic11⋊C4—82no—
109C2×C11⋊C8—41no—
110#2826—111no—
111#2062—111no—
112#1614—111no—
113#1596D1111yescharacteristic
114#1352—111no—
115#1343—111no—
116#1326—111no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—41no—
120C23×C11—41no—
121C23×C11—41no—
122C23×C11—41no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11#12011yescharacteristic
129C23×C11#13511yescharacteristic
130C23×C11#13711yescharacteristic
131Q8×C11—81no—
132Q8×C11—81no—
133D4×C11—42no—
134D4×C11—81no—
135D4×C11—82no—
136D4×C11—82no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
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—81no—
147C2×C4×C11—81no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—42no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—81no—
163C2×Dic11—81no—
164C2×Dic11—81no—
165C8×C11—81no—
166C11⋊C8—81no—
167#543C2×D1111yescharacteristic
168#484—221no—
169#450—21no—
170#400—221no—
171#399—111no—
172#397—221no—
173#396—221no—
174#394—221no—
175#394—221no—
176#392C2×D1111yescharacteristic
177#386—221no—
178#385—111no—
179#385—221no—
180#342—111no—
181#342—221no—
182#328—21no—
183#328—221no—
184#323—111no—
185#323C2×D1111yescharacteristic
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—81no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11—81no—
201C22×C11—81no—
202C22×C11#45211yescharacteristic
203C22×C11#45611yescharacteristic
204C22×C11B(4,𝔽2)11yescharacteristic
205C4×C11—41no—
206C4×C11—41no—
207C4×C11—81no—
208C4×C11—81no—
209C4×C11—81no—
210Dic11—81no—
211Dic11—81no—
212Dic11—82no—
213Dic11—81no—
214Dic11—81no—
215C22×D4—21no—
216C22×D4C22⋊D1111yescharacteristic
217C23×C4—111no—
218C2×SD16—41no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221C22⋊Q8—41no—
222C22⋊Q8—41no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—221no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—441no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—111no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C22⋊C4C22×D1111yescharacteristic
238#107—441no—
239#103—441no—
240#102—41no—
241C22⋊C8—21no—
242C22⋊C8—221no—
243#95—111no—
244#95—221no—
245#95—221no—
246#95—221no—
247#95—221no—
248#95—441no—
249#95C22⋊D1111yescharacteristic
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—41no—
253C2×C11—41no—
254C2×C11—161no—
255C2×C11#160311yescharacteristic
256C2×C11#220011yescharacteristic
257C2×C11#220011yescharacteristic
258C24—21no—
259C24D4×D1111yescharacteristic
260C2×Q8—21no—
261C2×Q8—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—81no—
266C2×D4—81no—
267C2×D4—81no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—441no—
276C22×C4—441no—
277C22×C4—881no—
278C22×C4D4×D1111yescharacteristic
279C22×C4C2×C22⋊D1111yescharacteristic
280SD16—82no—
281C2×C8—41no—
282C2×C8—441no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—441no—
288C4⋊C4—881no—
289C4⋊C4—881no—
290C4⋊C4—881no—
291C4⋊C4—882no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—81no—
296C22⋊C4—222no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—441no—
300C22⋊C4—881no—
301C22⋊C4—881no—
302C22⋊C4—881no—
303C22⋊C4—881no—
304C22⋊C4—881no—
305C11#1223111yescharacteristic, complemented, Sylow
306C23—21no—
307C23—21no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23#6696811yescharacteristic
318C23#6696911yescharacteristic
319C23#6699011yescharacteristic
320Q8—81no—
321Q8—81no—
322D4—42no—
323D4—81no—
324D4—82no—
325D4—82no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—442no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—881no—
352C2×C4—881no—
353C2×C4—881no—
354C8—81no—
355C8—881no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22#1062264511yescharacteristic
373C22#1062278611yescharacteristic
374C22#1062281811yescharacteristic
375C4—41no—
376C4—41no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4—881no—
381C4—881no—
382C4—882no—
383C4—881no—
384C4—881no—
385C2—21no—
386C2—21no—
387C2—41no—
388C2—41no—
389C2—161no—
390C2#1306757611yescharacteristic
391C2#1307062111yescharacteristic
392C2#1307062211yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1596C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#392C22
hypercenter#1596D11
hypocenterC11#12231
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1596

Complements

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

NH ≅ G/Ntype
2. #13069968C2semidirect
3. #13067641C2semidirect
4. #13066641C2semidirect
6. #13066565C2semidirect
305. C11#12231semidirect

Maximal subgroups

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

subgroupindex
#130767152
#130699682
#130676412
#130666412
#130666132
#130665652
C11×#15962
#1223111