Finite Group Databasebeta

← #14655776

Subgroups — #14655776

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#13078415C211yesmaximal, characteristic
3C2×#10622455C211yesmaximal, characteristic
4#13067302C211yesmaximal, characteristic, complemented
5#13067018C211yesmaximal, characteristic, complemented
6#13066936C211yesmaximal, characteristic
7C11×#1301C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9#10623001C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14#10622744—21no—
15#10622734—21no—
16C2×#66885—21no—
17C2×#66881—21no—
18#10622538C2211yescharacteristic
19#10622462—22no—
20#10622460—22no—
21#10622459—21no—
22#10622455—22no—
23#10622455—21no—
24#10622455—22no—
25#10622352—22no—
26#10622312—21no—
27#10622294—21no—
28#10622124—22no—
29#10622122—22no—
30#10622106—22no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22—21no—
34C2×C11×M16—21no—
35C22×C8×C11—21no—
36C2×C42×C11C2311yescharacteristic
37C2×(C2×D11)⋊C4—21no—
38#66979—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42#66977—21no—
43#66977—21no—
44C2×Dic44—24no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48C4×D44—21no—
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×C4⋊C8—21no—
61C11×C4⋊C8D412yes—
62C11×C4⋊C8D412yes—
63C11×C22⋊C8D412yes—
64C4×C8×C11—21no—
65C22⋊(C11⋊C8)—21no—
66#66885—24no—
67#66885—22no—
68#66885—22no—
69#66882—22no—
70#66881—22no—
71#66881—24no—
72#66880—24no—
73C4⋊(C11⋊C8)—21no—
74C4×C11⋊C8—21no—
75#10182—111nomaximal, Sylow
76C23×D11—21no—
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×Dic11—21no—
81C22×Dic11—41no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44Q1612yescomplemented
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—82no—
91C2×Dic22—22no—
92C2×Dic22—21no—
93C2×Dic22—21no—
94C2×Dic22—41no—
95C2×Dic22—82no—
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—22no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11—41no—
102C2×C8×C11—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C22⋊Dic11—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110C4⋊Dic11—21no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—22no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123C2×C11⋊C8—41no—
124Dic44—84no—
125#3209—111no—
126#3077—111no—
127C2×#476—111no—
128#1549—111no—
129#1481—111no—
130#1460—111no—
131#1301D1111yescharacteristic, complemented
132C23×C11#12111yescharacteristic
133C22×D11—22no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—81no—
137C22×D11—81no—
138C2×C4×C11—22no—
139C2×C4×C11—41no—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11#12711yescharacteristic
146C2×C4×C11C2×Q1611yescharacteristic
147C2×C4×C11#13511yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×C4×C11#13711yescharacteristic
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—82no—
155C2×Dic11—81no—
156D44—22no—
157D44—22no—
158D44—41no—
159D44—41no—
160C4×D11—82no—
161C4×D11—82no—
162Dic22—42no—
163Dic22—44no—
164Dic22—42no—
165Dic22—82no—
166C8×C11—42no—
167C8×C11—42no—
168C8×C11—42no—
169C11⋊C8—81no—
170#533—111no—
171C2×C4⋊Q8—111no—
172C2×C4×D4—111no—
173#494—221no—
174#487—221no—
175#478—222no—
176#476—221no—
177#476—222no—
178#476—222no—
179#474—221no—
180#462—222no—
181#451—222no—
182#431—111no—
183#431C2×D1111yescharacteristic
184#428—221no—
185C2×#106—221no—
186#423C2×D1111yescharacteristic
187C2×C4⋊C8C2×D1111yescharacteristic
188#418—221no—
189C2×#102—221no—
190#332—222no—
191Q8⋊C8—222no—
192#323—222no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#39211yescharacteristic
196C22×C11#46711yescharacteristic
197C22×C11#47011yescharacteristic
198C2×D11—42no—
199C2×D11—82no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—82no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11#45111yescharacteristic
207C4×C11#45111yescharacteristic
208C4×C11#45211yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#47112yes—
211Dic11—82no—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215C22×Q8—221no—
216C22×D4—111no—
217C23×C4—221no—
218C2×Q16—224no—
219C2×M16—21no—
220C22×C8—21no—
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—221no—
233C4×D4—221no—
234C4×D4—221no—
235C4×D4—221no—
236#117—221no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C22⋊C4—221no—
241C2×C42C22×D1111yescharacteristic
242#107—222no—
243#106—224no—
244#106—222no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—221no—
249C4⋊C8D4412yes—
250C4⋊C8D4412yes—
251#103—224no—
252#102—224no—
253#102—222no—
254#102—222no—
255C22⋊C8—221no—
256C22⋊C8D4412yes—
257C4×C8—21no—
258C4×C8—221no—
259C2×C11—21no—
260C2×C11—21no—
261C2×C11#200111yescharacteristic
262C2×C11#200811yescharacteristic
263C2×C11#201911yescharacteristic
264D11—82no—
265C24—221no—
266C2×Q8—222no—
267C2×Q8—221no—
268C2×Q8—221no—
269C2×Q8—441no—
270C2×Q8—882no—
271C2×D4—112no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C22×C4—221no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—882no—
282C22×C4C2×D4411yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4#434311yescharacteristic
285Q16—884no—
286M16—41no—
287M16—41no—
288C2×C8—22no—
289C2×C8—22no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—441no—
294C4⋊C4—222no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C42—441no—
310C42C2×D4411yescharacteristic
311C42C2×D4411yescharacteristic
312C42D4×D1111yescharacteristic
313C42D4×D1111yescharacteristic
314C11#1018211yescharacteristic, complemented, Sylow
315C23—222no—
316C23—441no—
317C23—441no—
318C23—881no—
319C23—881no—
320C23#6694811yescharacteristic
321Q8—442no—
322Q8—444no—
323Q8—442no—
324Q8—882no—
325D4—222no—
326D4—222no—
327D4—441no—
328D4—441no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—441no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—442no—
335C2×C4—882no—
336C2×C4—882no—
337C2×C4—882no—
338C2×C4—881no—
339C2×C4#6692711yescharacteristic
340C2×C4#6693511yescharacteristic
341C2×C4#6693511yescharacteristic
342C2×C4#6693511yescharacteristic
343C2×C4#6694811yescharacteristic
344C2×C4#6694811yescharacteristic
345C2×C4#6696511yescharacteristic
346C2×C4#6696811yescharacteristic
347C2×C4#6696811yescharacteristic
348C2×C4Q16×D1111yescharacteristic
349C8—42no—
350C8—42no—
351C8—42no—
352C8—881no—
353C22—21no—
354C22—21no—
355C22—442no—
356C22—882no—
357C22—882no—
358C22—881no—
359C22—881no—
360C22#1062228411yescharacteristic
361C22#1062248111yescharacteristic
362C22#1062250011yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—882no—
367C4—881no—
368C4—881no—
369C4—881no—
370C4#1062239611yescharacteristic
371C4#1062239611yescharacteristic
372C4#1062242111yescharacteristic
373C4#1062242111yescharacteristic
374C4#1062251112yes—
375C2—21no—
376C2—21no—
377C2—882no—
378C2#1306962711yescharacteristic
379C2#1306967211yescharacteristic
380C2#1306973311yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1301D11
hypocenterC11#10182
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
1. #13079566C2semidirect
4. #13067302C2semidirect
5. #13067018C2semidirect
7. C11×#1301C2semidirect
87. C2×D44Q16semidirect
131. #1301D11semidirect
314. C11#10182semidirect

Maximal subgroups

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

subgroupindex
#130795662
#130784152
C2×#106224552
#130673022
#130670182
#130669362
C11×#13012
#1018211