Finite Group Databasebeta

← #14655775

Subgroups — #14655775

Order 2816.

508 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079566C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic
3C2×#10622621C211yesmaximal, characteristic
4#13067300C211yesmaximal, characteristic, complemented
5#13067020C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1460C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#431C2211yescharacteristic
13#10622828—21no—
14C2×#66896—21no—
15#10622622—22no—
16#10622621—22no—
17#10622621—21no—
18#10622621—22no—
19#10622620—21no—
20#10622577—21no—
21C2×#66872—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622462—22no—
25#10622352—22no—
26#10622312—21no—
27#10622294—21no—
28C11×#323—22no—
29#10622120—22no—
30#10622094—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×Dic22—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C4×D4×C11—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C22⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41#66979—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44#66977—21no—
45#66977—21no—
46C2×#4318—21no—
47C22×C11⋊C8—21no—
48C2×Dic44—24no—
49#66923—21no—
50#66922—21no—
51#66922—21no—
52#66922—21no—
53#66922D412yes—
54#66922D411yescharacteristic
55#66922D411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8D412yes—
62C4×C8×C11—21no—
63C4×C8×C11—21no—
64#66896—24no—
65#66896—22no—
66#66896—22no—
67#66880—24no—
68#66872—24no—
69#66872—22no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75#10182—111nomaximal, Sylow
76C24×C11—21no—
77C2×D4×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11Q1612yescomplemented
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—82no—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—41no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C2×Dic22—82no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4—21no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C22⋊Dic11—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114C4⋊Dic11—41no—
115Dic11⋊C4—41no—
116Dic11⋊C4—41no—
117C4×Dic11—41no—
118#4318—41no—
119#4318—41no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8—41no—
124Dic44—84no—
125#3209—111no—
126#3077—111no—
127C2×#476—111no—
128#1549—111no—
129#1481—111no—
130#1460D1111yescharacteristic
131#1301—111no—
132C23×C11—22no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—81no—
136C23×C11—81no—
137C23×C11#12111yescharacteristic
138D4×C11—22no—
139D4×C11—22no—
140D4×C11—41no—
141D4×C11—41no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—82no—
146C2×C4×C11—82no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12711yescharacteristic
154C2×C4×C11C2×Q1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—82no—
162Dic22—42no—
163Dic22—44no—
164Dic22—42no—
165Dic22—82no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170#533—111no—
171C2×C4⋊Q8—111no—
172C2×C4×D4C2×D1111yescharacteristic
173#494—221no—
174#487—221no—
175#478—222no—
176#476—222no—
177#476—221no—
178#476—222no—
179#474—221no—
180#462—222no—
181#451—222no—
182#431C2×D1111yescharacteristic
183#431C2×D1111yescharacteristic
184#428—221no—
185C2×#106—221no—
186#423—111no—
187C2×C4⋊C8—111no—
188#418—221no—
189C2×#102—221no—
190#332—222no—
191Q8⋊C8—222no—
192#323—22no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—42no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—81no—
199C22×C11—81no—
200C22×C11#39211yescharacteristic
201C22×C11#46711yescharacteristic
202C22×C11#47011yescharacteristic
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—81no—
207C4×C11#45111yescharacteristic
208C4×C11#45111yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#45211yescharacteristic
211C4×C11#47112yes—
212Dic11—82no—
213Dic11—81no—
214Dic11—81no—
215C22×Q8—221no—
216C22×D4D4411yescharacteristic
217C23×C4—21no—
218C2×Q16—224no—
219C2×M16—221no—
220C22×C8—221no—
221C4⋊Q8—112no—
222C4⋊Q8—111no—
223C4⋊Q8—111no—
224C4⋊Q8—221no—
225C4⋊Q8—221no—
226C4⋊Q8—221no—
227#125—221no—
228C22⋊Q8—221no—
229C22⋊Q8—221no—
230C4×Q8—221no—
231C4×Q8—221no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236#117—221no—
237C2×C4⋊C4—221no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4D4411yescharacteristic
240C2×C22⋊C4—21no—
241C2×C42C22×D1111yescharacteristic
242#107—222no—
243#106—224no—
244#106—222no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—112no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251#103—224no—
252#102—224no—
253#102—222no—
254#102—222no—
255C22⋊C8—21no—
256C22⋊C8C22⋊D1112yes—
257C4×C8—21no—
258C4×C8—21no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11—82no—
262C2×C11#200111yescharacteristic
263C2×C11#200811yescharacteristic
264C2×C11#201911yescharacteristic
265C24—21no—
266C2×Q8—221no—
267C2×Q8—222no—
268C2×Q8—221no—
269C2×Q8—441no—
270C2×Q8—882no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4Dic4412yescomplemented
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—82no—
281C22×C4—441no—
282C22×C4C2×D4411yescharacteristic
283C22×C4#433911yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—884no—
286M16—441no—
287M16—441no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—222no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—222no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—441no—
309C42—441no—
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C42D4×D1111yescharacteristic
314C11#1018211yescharacteristic, complemented, Sylow
315C23—22no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23#6698311yescharacteristic
321Q8—442no—
322Q8—444no—
323Q8—442no—
324Q8—882no—
325D4—22no—
326D4—22no—
327D4—41no—
328D4—41no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—882no—
339C2×C4#6693511yescharacteristic
340C2×C4#6693511yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4#6695711yescharacteristic
344C2×C4C2×Dic4411yescharacteristic
345C2×C4#6696211yescharacteristic
346C2×C4#6696211yescharacteristic
347C2×C4#6699011yescharacteristic
348C2×C4#6699311yescharacteristic
349C8—42no—
350C8—81no—
351C8—442no—
352C8—442no—
353C22—21no—
354C22—21no—
355C22—42no—
356C22—82no—
357C22—82no—
358C22—81no—
359C22—81no—
360C22#1062257311yescharacteristic
361C22#1062272911yescharacteristic
362C22#1062275011yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—81no—
367C4—882no—
368C4—881no—
369C4—881no—
370C4#1062234611yescharacteristic
371C4#1062234611yescharacteristic
372C4#1062235211yescharacteristic
373C4#1062235211yescharacteristic
374C4#1062236112yes—
375C2—21no—
376C2—21no—
377C2—82no—
378C2#1306962611yescharacteristic
379C2#1306966811yescharacteristic
380C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#1460D11
hypocenterC11#10182
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #13079566C2semidirect
4. #13067300C2semidirect
5. #13067020C2semidirect
6. #13066512C2semidirect
82. C2×D4×C11Q16semidirect
276. C2×D4Dic44semidirect
314. C11#10182semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130784132
C2×#106226212
#130673002
#130670202
#130665122
C11×#14602
#1018211