Finite Group Databasebeta

← #14665998

Subgroups — #14665998

Order 2816.

440 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 59 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#13076873C211yesmaximal, characteristic, complemented
2#13067636C211yesmaximal, characteristic
3#13067568C211yesmaximal, characteristic
4#13066639C211yesmaximal, characteristic, complemented
5#13066636C211yesmaximal, characteristic, complemented
6#13066546C211yesmaximal, characteristic, complemented
7C11×#2022C211yesmaximal, characteristic
8C11×#534C2211yescharacteristic
9C2×C11×#123—21no—
10C2×C11×#99—21no—
11C11×#381C2211yescharacteristic
12#10622825—21no—
13#10622653—21no—
14#10622647—21no—
15#10622562C2211yescharacteristic
16#10622561—21no—
17#10622560C2211yescharacteristic
18#10622274—21no—
19#10622273—21no—
20#10622270—21no—
21#10622269—21no—
22C11×#342C2211yescharacteristic
23#10622175—21no—
24#10622175—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C22×D4×C11—21no—
28C23×C4×C11D411yescharacteristic
29C22×Dic22D411yescharacteristic
30C11×#123—42no—
31C11×#123—41no—
32C11×#123—42no—
33C11×#121—21no—
34C11×#121—21no—
35C11×#120—41no—
36C2×C11×C4⋊C4—41no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—41no—
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C11×C22⋊C4C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×#4324—41no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C11×#99—42no—
52C11×#95—21no—
53C11×#95—21no—
54#66896—41no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C11⋊#95D411yescharacteristic
61C22⋊(C11⋊C8)—21no—
62C22⋊(C11⋊C8)—21no—
63#66874—41no—
64#66872—41no—
65#12125—111nomaximal, Sylow
66C24×C11—21no—
67C24×C11C2×D411yescharacteristic
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11SD1612yescomplemented
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C2×Dic22—41no—
91C2×Dic22—81no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—44no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—41no—
99C11×C22⋊C4—44no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C22⋊Dic11—81no—
103C22⋊Dic11—81no—
104#4324—82no—
105C4⋊Dic11—41no—
106C4⋊Dic11—81no—
107C4⋊Dic11—81no—
108C4⋊Dic11—81no—
109Dic11⋊C4—81no—
110Dic11⋊C4—81no—
111Dic11⋊C4—81no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114#2841—111no—
115#2022D1111yescharacteristic
116#1613—111no—
117#1601—111no—
118#1352—111no—
119#1351—111no—
120#1317—111no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—41no—
124C23×C11—41no—
125C23×C11—41no—
126C23×C11—41no—
127C23×C11—41no—
128C23×C11—81no—
129C23×C11—81no—
130C23×C11#12011yescharacteristic
131C23×C11C2×SD1611yescharacteristic
132C23×C11#13711yescharacteristic
133D4×C11—81no—
134D4×C11—81no—
135D4×C11—81no—
136D4×C11—81no—
137D4×C11—81no—
138D4×C11—81no—
139C2×C4×C11—22no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—81no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169Dic22—42no—
170Dic22—81no—
171C11⋊C8—81no—
172C11⋊C8—81no—
173#534C2×D1111yescharacteristic
174C2×#123—21no—
175#481—221no—
176#448—221no—
177C2×#99—21no—
178#400—221no—
179#399—111no—
180#398—221no—
181#398—221no—
182#396—221no—
183#395—221no—
184#393—111no—
185#381C2×D1111yescharacteristic
186#380—221no—
187#342C2×D1111yescharacteristic
188#327—221no—
189#327—221no—
190#323—111no—
191#323—111no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—21no—
196C22×C11—41no—
197C22×C11—41no—
198C22×C11—41no—
199C22×C11—41no—
200C22×C11—81no—
201C22×C11—82no—
202C22×C11—81no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—161no—
206C22×C11#44811yescharacteristic
207C22×C11#45311yescharacteristic
208C22×C11B(4,𝔽2)11yescharacteristic
209C4×C11—42no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—81no—
213C4×C11—82no—
214C4×C11—81no—
215Dic11—81no—
216Dic11—81no—
217Dic11—81no—
218Dic11—81no—
219C22×Q8—111no—
220C22×D4—21no—
221C23×C4C22⋊D1111yescharacteristic
222C2×SD16—441no—
223#123—42no—
224#123—41no—
225#123—42no—
226#121—21no—
227#121—21no—
228#120—41no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—41no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C22⋊C4C22⋊D1111yescharacteristic
242C2×C22⋊C4C22×D1111yescharacteristic
243#106—441no—
244#103—441no—
245#102—441no—
246#99—42no—
247C22⋊C8—221no—
248C22⋊C8—221no—
249#95—21no—
250#95—21no—
251#95—111no—
252#95—111no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95—221no—
257C2×C11—21no—
258C2×C11—21no—
259C2×C11—41no—
260C2×C11—41no—
261C2×C11—161no—
262C2×C11#159611yescharacteristic
263C2×C11#220011yescharacteristic
264C2×C11#220111yescharacteristic
265C24—21no—
266C24C2×C22⋊D1111yescharacteristic
267C2×Q8—441no—
268C2×Q8—881no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—221no—
288C22×C4#432412yescomplemented
289C22×C4D4×D1111yescharacteristic
290C22×C4D4×D1111yescharacteristic
291SD16—882no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—44no—
297C4⋊C4—441no—
298C4⋊C4—881no—
299C4⋊C4—881no—
300C4⋊C4—881no—
301C4⋊C4—881no—
302C4⋊C4—881no—
303C4⋊C4—881no—
304C22⋊C4—22no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—44no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—881no—
312C22⋊C4—881no—
313C11#1212511yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—81no—
322C23—81no—
323C23C2×#432411yescharacteristic
324C23#6699011yescharacteristic
325C23#6700411yescharacteristic
326Q8—442no—
327Q8—881no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C8—881no—
365C8—881no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—81no—
375C22—82no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—161no—
380C22#1062264511yescharacteristic
381C22#1062265311yescharacteristic
382C22#1062269011yescharacteristic
383C4—42no—
384C4—41no—
385C4—41no—
386C4—81no—
387C4—82no—
388C4—81no—
389C4—881no—
390C4—881no—
391C4—881no—
392C4—881no—
393C2—21no—
394C2—21no—
395C2—41no—
396C2—41no—
397C2—161no—
398C2#1306753811yescharacteristic
399C2#1307062011yescharacteristic
400C2#1307062711yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2022C2
socleC22×C11B(4,𝔽2)
prime radicalC11×#534C22
hypercenter#2022D11
hypocenterC11#12125
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #13076873C2semidirect
4. #13066639C2semidirect
5. #13066636C2semidirect
6. #13066546C2semidirect
83. C22×C4×C11SD16semidirect
288. C22×C4#4324semidirect
313. C11#12125semidirect

Maximal subgroups

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

subgroupindex
#130768732
#130676362
#130675682
#130666392
#130666362
#130665462
C11×#20222
#1212511