Finite Group Databasebeta

← #14655772

Subgroups — #14655772

Order 2816.

508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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#13079564C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic
3C2×#10622697C211yesmaximal, characteristic
4#13067020C211yesmaximal, characteristic, complemented
5#13066936C211yesmaximal, characteristic
6#13066511C211yesmaximal, characteristic, complemented
7C11×#1549C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D44C2211yescharacteristic
10#10623001C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622841—22no—
14#10622744—21no—
15#10622734—21no—
16#10622705—21no—
17#10622703—22no—
18#10622697—22no—
19#10622697—22no—
20#10622694—21no—
21C2×#66873—21no—
22C2×#66872—21no—
23#10622538C2211yescharacteristic
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25#10622460—22no—
26#10622459—21no—
27#10622455—21no—
28C11×#332—22no—
29#10622106—22no—
30#10622094—22no—
31C22×Q8×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C2×C11×M16—21no—
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8D412yes—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11C2311yescharacteristic
42C2×#4326—24no—
43C2×(C2×D11)⋊C4—21no—
44#66979—21no—
45C2×C4⋊Dic11D411yescharacteristic
46#66977—21no—
47#66977—21no—
48C22×C11⋊C8—21no—
49C4×D44—21no—
50C4×D44—21no—
51C4×D44—21no—
52C4×D44—21no—
53#66923—21no—
54#66922D411yescharacteristic
55#66922D411yescharacteristic
56C4×Dic22—21no—
57C4×Dic22—21no—
58C11×C4⋊C8—21no—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×C22⋊C8—21no—
62C4×C8×C11—21no—
63#66899—24no—
64C22⋊(C11⋊C8)D412yes—
65#66885—22no—
66#66885—22no—
67#66882—22no—
68#66881—22no—
69#66873—24no—
70#66872—24no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4×C11⋊C8—21no—
75#10182—111nomaximal, Sylow
76C23×D11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—41no—
79C2×Q8×C11—82no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×Dic11—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44—21no—
88C2×D44—21no—
89C2×D44—21no—
90C2×D44Q1612yescomplemented
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×C4×D11—82no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C11×M16—41no—
97C11×M16—41no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C22⋊Dic11—41no—
109#4326—84no—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—41no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118Dic11⋊C4—41no—
119Dic11⋊C4—41no—
120C4×Dic11—41no—
121C2×C11⋊C8—22no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125#3209—111no—
126#3077—111no—
127C2×#476—111no—
128#1549D1111yescharacteristic, complemented
129#1481—111no—
130#1460—111no—
131#1301—111no—
132C23×C11#12111yescharacteristic
133C22×D11—22no—
134C22×D11—41no—
135C22×D11—41no—
136C22×D11—81no—
137C22×D11—81no—
138Q8×C11—44no—
139Q8×C11—82no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—82no—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12711yescharacteristic
150C2×C4×C11C2×Q1611yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11#13711yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—81no—
158D44—22no—
159D44—22no—
160D44—41no—
161D44—41no—
162C4×D11—82no—
163C4×D11—82no—
164Dic22—42no—
165Dic22—42no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—42no—
170#533—111no—
171C2×C4⋊Q8C2×D1111yescharacteristic
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⋊C8—111no—
188#418—221no—
189C2×#102—221no—
190#332—22no—
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—82no—
207C4×C11#45111yescharacteristic
208C4×C11#45111yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#45211yescharacteristic
211C4×C11#47112yes—
212Dic11—81no—
213Dic11—81no—
214Dic11—81no—
215C22×Q8—21no—
216C22×D4—111no—
217C23×C4—221no—
218C2×Q16—224no—
219C2×M16—21no—
220C22×C8—221no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—111no—
225C4⋊Q8—111no—
226C4⋊Q8D4412yes—
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—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—111no—
240C2×C22⋊C4—221no—
241C2×C42C22×D1111yescharacteristic
242#107—222no—
243#106—224no—
244#106—222no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—112no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250C4⋊C8C22⋊D1112yes—
251#103—224no—
252#102—224no—
253#102—222no—
254#102—222no—
255C22⋊C8—21no—
256C22⋊C8—112no—
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—22no—
267C2×Q8—41no—
268C2×Q8—82no—
269C2×Q8—221no—
270C2×Q8—221no—
271C2×D4—112no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C22×C4—41no—
278C22×C4—221no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—882no—
282C22×C4#433911yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4D4×D1111yescharacteristic
285Q16—884no—
286M16—41no—
287M16—41no—
288C2×C8—22no—
289C2×C8—41no—
290C2×C8—222no—
291C2×C8—222no—
292C2×C8—441no—
293C2×C8—441no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C22⋊C4—441no—
307C22⋊C4—441no—
308C22⋊C4—441no—
309C42—441no—
310C42C2×D4411yescharacteristic
311C42D4×D1111yescharacteristic
312C42D4×D1111yescharacteristic
313C42C2×C22⋊D1111yescharacteristic
314C11#1018211yescharacteristic, complemented, Sylow
315C23—222no—
316C23—441no—
317C23—441no—
318C23—881no—
319C23—881no—
320C23#6693711yescharacteristic
321Q8—44no—
322Q8—82no—
323Q8—442no—
324Q8—442no—
325D4—222no—
326D4—222no—
327D4—441no—
328D4—441no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—441no—
336C2×C4—882no—
337C2×C4—882no—
338C2×C4—881no—
339C2×C4#6693511yescharacteristic
340C2×C4#6693511yescharacteristic
341C2×C4#6693711yescharacteristic
342C2×C4#6696811yescharacteristic
343C2×C4#6696911yescharacteristic
344C2×C4Q16×D1111yescharacteristic
345C2×C4#6697111yescharacteristic
346C2×C4#6698311yescharacteristic
347C2×C4#6699011yescharacteristic
348C2×C4#6699311yescharacteristic
349C8—42no—
350C8—81no—
351C8—442no—
352C8—442no—
353C22—21no—
354C22—21no—
355C22—442no—
356C22—882no—
357C22—882no—
358C22—881no—
359C22—881no—
360C22#1062242611yescharacteristic
361C22#1062242911yescharacteristic
362C22#1062257311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—881no—
368C4—881no—
369C4—881no—
370C4#1062236712yes—
371C4#1062242111yescharacteristic
372C4#1062242311yescharacteristic
373C4#1062278611yescharacteristic
374C4#1062279911yescharacteristic
375C2—21no—
376C2—21no—
377C2—882no—
378C2#1306962511yescharacteristic
379C2#1306967111yescharacteristic
380C2#1306972911yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1549C2
socleC22×C11#392
prime radicalC22×D44D4
hypercenter#1549D11
hypocenterC11#10182
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
1. #13079564C2semidirect
4. #13067020C2semidirect
6. #13066511C2semidirect
7. C11×#1549C2semidirect
90. C2×D44Q16semidirect
128. #1549D11semidirect
314. C11#10182semidirect

Maximal subgroups

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

subgroupindex
#130795642
#130784152
C2×#106226972
#130670202
#130669362
#130665112
C11×#15492
#1018211