Finite Group Databasebeta

← #14655832

Subgroups — #14655832

Order 2816.

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

normal subgroups only

This group has 496 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#13079769C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic
3C2×#10622459C211yesmaximal, characteristic
4#13067298C211yesmaximal, 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×#66882—21no—
18#10622538C2211yescharacteristic
19#10622463—22no—
20#10622460—22no—
21#10622459—22no—
22#10622459—21no—
23#10622459—22no—
24#10622455—21no—
25#10622335—22no—
26#10622295—21no—
27#10622294—21no—
28#10622122—22no—
29#10622119—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—
44C4×D44—21no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44—21no—
48#66923—21no—
49#66922—21no—
50#66922—21no—
51#66922—21no—
52#66922D412yes—
53#66922D411yescharacteristic
54#66922D411yescharacteristic
55C4×Dic22—21no—
56C4×Dic22—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×C4⋊C8D412yes—
62C11×C22⋊C8D412yes—
63C4×C8×C11—21no—
64C22⋊(C11⋊C8)—21no—
65#66885—24no—
66#66885—22no—
67#66885—22no—
68#66882—22no—
69#66882—24no—
70#66882—24no—
71#66881—22no—
72#66880—24no—
73C4⋊(C11⋊C8)—21no—
74C4×C11⋊C8—21no—
75#10190—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×D44Q1612yes—
88C2×C4×D11—41no—
89C2×C4×D11—41no—
90C2×C4×D11—82no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—22no—
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—22no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123C2×C11⋊C8—41no—
124#3230—111no—
125#3077—111no—
126C2×#474—111no—
127#1548—111no—
128#1481—111no—
129#1460—111no—
130#1301D1111yescharacteristic, complemented
131C23×C11#12111yescharacteristic
132C22×D11—22no—
133C22×D11—41no—
134C22×D11—41no—
135C22×D11—81no—
136C22×D11—81no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12711yescharacteristic
145C2×C4×C11C2×Q1611yescharacteristic
146C2×C4×C11#13511yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—42no—
152C2×Dic11—41no—
153C2×Dic11—82no—
154C2×Dic11—81no—
155D44—22no—
156D44—22no—
157D44—41no—
158D44—41no—
159C4×D11—82no—
160C4×D11—82no—
161Dic22—42no—
162Dic22—42no—
163Dic22—82no—
164Dic22—82no—
165C8×C11—42no—
166C8×C11—42no—
167C8×C11—42no—
168C11⋊C8—81no—
169#533—111no—
170C2×C4⋊Q8—111no—
171C2×C4×D4—111no—
172#500—221no—
173#487—221no—
174#484—222no—
175#478—222no—
176#477—222no—
177#476—221no—
178#474—221no—
179#474—222no—
180#474—222no—
181#431—111no—
182#431C2×D1111yescharacteristic
183#428—221no—
184C2×#107—221no—
185#423C2×D1111yescharacteristic
186C2×C4⋊C8C2×D1111yescharacteristic
187#418—221no—
188C2×#102—221no—
189#333—222no—
190Q8⋊C8—222no—
191#323—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11#39211yescharacteristic
195C22×C11#46711yescharacteristic
196C22×C11#47011yescharacteristic
197C2×D11—42no—
198C2×D11—82no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—82no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11#45111yescharacteristic
206C4×C11#45111yescharacteristic
207C4×C11#45211yescharacteristic
208C4×C11#45211yescharacteristic
209C4×C11#47212yes—
210Dic11—81no—
211Dic11—81no—
212Dic11—82no—
213Dic11—81no—
214C22×Q8—221no—
215C22×D4—111no—
216C23×C4—221no—
217C2×M16—21no—
218C22×C8—21no—
219C4⋊Q8—112no—
220C4⋊Q8—111no—
221C4⋊Q8—111no—
222C4⋊Q8—221no—
223C4⋊Q8—221no—
224C4⋊Q8—221no—
225#125—221no—
226C22⋊Q8—221no—
227C22⋊Q8—221no—
228C4×Q8—221no—
229C4×Q8—221no—
230C4×D4—221no—
231C4×D4—221no—
232C4×D4—221no—
233C4×D4—221no—
234#117—221no—
235C2×C4⋊C4—111no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C42C22×D1111yescharacteristic
240#107—224no—
241#107—222no—
242#107—224no—
243#106—222no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—221no—
248C4⋊C8D4412yes—
249C4⋊C8D4412yes—
250#103—224no—
251#102—224no—
252#102—222no—
253#102—222no—
254C22⋊C8—221no—
255C22⋊C8D4412yes—
256C4×C8—21no—
257C4×C8—221no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11#200111yescharacteristic
261C2×C11#200911yescharacteristic
262C2×C11#201811yescharacteristic
263D11—82no—
264C24—221no—
265C2×Q8—221no—
266C2×Q8—221no—
267C2×Q8—222no—
268C2×Q8—441no—
269C2×Q8—882no—
270C2×D4—112no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C22×C4—221no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—882no—
281C22×C4C2×D4411yescharacteristic
282C22×C4D4×D1111yescharacteristic
283C22×C4#434311yescharacteristic
284M16—41no—
285M16—41no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—441no—
292C4⋊C4—221no—
293C4⋊C4—222no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—441no—
305C22⋊C4—441no—
306C22⋊C4—441no—
307C42—441no—
308C42C2×D4411yescharacteristic
309C42C2×D4411yescharacteristic
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C11#1019011yescharacteristic, complemented, Sylow
313C23—222no—
314C23—441no—
315C23—441no—
316C23—881no—
317C23—881no—
318C23#6694811yescharacteristic
319Q8—442no—
320Q8—442no—
321Q8—882no—
322Q8—882no—
323D4—222no—
324D4—222no—
325D4—441no—
326D4—441no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—442no—
333C2×C4—882no—
334C2×C4—882no—
335C2×C4—882no—
336C2×C4—881no—
337C2×C4#6692711yescharacteristic
338C2×C4#6693511yescharacteristic
339C2×C4#6693511yescharacteristic
340C2×C4#6693511yescharacteristic
341C2×C4#6694811yescharacteristic
342C2×C4#6694811yescharacteristic
343C2×C4#6696511yescharacteristic
344C2×C4#6696811yescharacteristic
345C2×C4#6696811yescharacteristic
346C2×C4Q16×D1111yescharacteristic
347C8—42no—
348C8—42no—
349C8—42no—
350C8—881no—
351C22—21no—
352C22—21no—
353C22—442no—
354C22—882no—
355C22—882no—
356C22—881no—
357C22—881no—
358C22#1062228411yescharacteristic
359C22#1062248111yescharacteristic
360C22#1062250011yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—881no—
365C4—881no—
366C4—882no—
367C4—881no—
368C4#1062239611yescharacteristic
369C4#1062239611yescharacteristic
370C4#1062242111yescharacteristic
371C4#1062242111yescharacteristic
372C4#1062251012yes—
373C2—21no—
374C2—21no—
375C2—882no—
376C2#1306962711yescharacteristic
377C2#1306967911yescharacteristic
378C2#1306972611yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1301C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1301D11
hypocenterC11#10190
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. #13079769C2semidirect
4. #13067298C2semidirect
5. #13067018C2semidirect
7. C11×#1301C2semidirect
130. #1301D11semidirect
312. C11#10190semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130784152
C2×#106224592
#130672982
#130670182
#130669362
C11×#13012
#1019011