Finite Group Databasebeta

← #14655831

Subgroups — #14655831

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#13078413C211yesmaximal, characteristic
3C2×#10622620C211yesmaximal, characteristic
4#13067296C211yesmaximal, 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—21no—
17#10622620—22no—
18#10622620—21no—
19#10622620—22no—
20#10622577—21no—
21C2×#66871—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622463—22no—
25#10622335—22no—
26#10622295—21no—
27#10622294—21no—
28C11×#323—22no—
29#10622119—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—
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×C22⋊C8—21no—
60C11×C22⋊C8D412yes—
61C4×C8×C11—21no—
62C4×C8×C11—21no—
63#66896—24no—
64#66896—22no—
65#66896—22no—
66#66882—24no—
67#66880—24no—
68#66872—22no—
69#66871—24no—
70#66871—22no—
71C4⋊(C11⋊C8)—21no—
72C4⋊(C11⋊C8)—21no—
73C4⋊(C11⋊C8)D412yes—
74C4⋊(C11⋊C8)D412yes—
75#10190—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×C11Q1612yes—
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—21no—
92C2×Dic22—21no—
93C2×Dic22—22no—
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—22no—
108C4⋊Dic11—21no—
109C4⋊Dic11—21no—
110C4⋊Dic11—22no—
111C4⋊Dic11—21no—
112C4⋊Dic11—21no—
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—
124#3230—111no—
125#3077—111no—
126C2×#474—111no—
127#1548—111no—
128#1481—111no—
129#1460D1111yescharacteristic
130#1301—111no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—81no—
135C23×C11—81no—
136C23×C11#12111yescharacteristic
137D4×C11—22no—
138D4×C11—22no—
139D4×C11—41no—
140D4×C11—41no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—41no—
144C2×C4×C11—82no—
145C2×C4×C11—82no—
146C2×C4×C11—81no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12011yescharacteristic
150C2×C4×C11#12111yescharacteristic
151C2×C4×C11#12111yescharacteristic
152C2×C4×C11#12711yescharacteristic
153C2×C4×C11C2×Q1611yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—42no—
160C2×Dic11—82no—
161Dic22—42no—
162Dic22—42no—
163Dic22—82no—
164Dic22—82no—
165C8×C11—42no—
166C8×C11—81no—
167C11⋊C8—42no—
168C11⋊C8—42no—
169#533—111no—
170C2×C4⋊Q8—111no—
171C2×C4×D4C2×D1111yescharacteristic
172#500—221no—
173#487—221no—
174#484—222no—
175#478—222no—
176#477—222no—
177#476—221no—
178#474—222no—
179#474—221no—
180#474—222no—
181#431C2×D1111yescharacteristic
182#431C2×D1111yescharacteristic
183#428—221no—
184C2×#107—221no—
185#423—111no—
186C2×C4⋊C8—111no—
187#418—221no—
188C2×#102—221no—
189#333—222no—
190Q8⋊C8—222no—
191#323—22no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—82no—
196C22×C11—82no—
197C22×C11—81no—
198C22×C11—81no—
199C22×C11#39211yescharacteristic
200C22×C11#46711yescharacteristic
201C22×C11#47011yescharacteristic
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—81no—
206C4×C11#45111yescharacteristic
207C4×C11#45111yescharacteristic
208C4×C11#45211yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#47212yes—
211Dic11—81no—
212Dic11—81no—
213Dic11—82no—
214C22×Q8—221no—
215C22×D4D4411yescharacteristic
216C23×C4—21no—
217C2×M16—221no—
218C22×C8—221no—
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—21no—
231C4×D4—21no—
232C4×D4—21no—
233C4×D4—21no—
234#117—221no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4D4411yescharacteristic
238C2×C22⋊C4—21no—
239C2×C42C22×D1111yescharacteristic
240#107—224no—
241#107—222no—
242#107—224no—
243#106—222no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—112no—
247C4⋊C8—112no—
248C4⋊C8—221no—
249C4⋊C8—221no—
250#103—224no—
251#102—224no—
252#102—222no—
253#102—222no—
254C22⋊C8—21no—
255C22⋊C8C22⋊D1112yes—
256C4×C8—21no—
257C4×C8—21no—
258C2×C11—21no—
259C2×C11—21no—
260C2×C11—82no—
261C2×C11#200111yescharacteristic
262C2×C11#200911yescharacteristic
263C2×C11#201811yescharacteristic
264C24—21no—
265C2×Q8—221no—
266C2×Q8—222no—
267C2×Q8—221no—
268C2×Q8—441no—
269C2×Q8—882no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4Dic4412yes—
276C22×C4—21no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—82no—
280C22×C4—441no—
281C22×C4C2×D4411yescharacteristic
282C22×C4#433911yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284M16—441no—
285M16—441no—
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—441no—
291C2×C8—441no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—221no—
295C4⋊C4—222no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—222no—
299C4⋊C4—221no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—441no—
307C42—441no—
308C42D4×D1111yescharacteristic
309C42D4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42D4×D1111yescharacteristic
312C11#1019011yescharacteristic, complemented, Sylow
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23#6698311yescharacteristic
319Q8—442no—
320Q8—442no—
321Q8—882no—
322Q8—882no—
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—82no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—442no—
336C2×C4—882no—
337C2×C4#6693511yescharacteristic
338C2×C4#6693511yescharacteristic
339C2×C4#6693711yescharacteristic
340C2×C4#6693711yescharacteristic
341C2×C4#6695711yescharacteristic
342C2×C4C2×Dic4411yescharacteristic
343C2×C4#6696211yescharacteristic
344C2×C4#6696211yescharacteristic
345C2×C4#6699011yescharacteristic
346C2×C4#6699311yescharacteristic
347C8—42no—
348C8—81no—
349C8—442no—
350C8—442no—
351C22—21no—
352C22—21no—
353C22—42no—
354C22—82no—
355C22—82no—
356C22—81no—
357C22—81no—
358C22#1062257311yescharacteristic
359C22#1062272911yescharacteristic
360C22#1062275011yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—881no—
366C4—882no—
367C4—881no—
368C4#1062234611yescharacteristic
369C4#1062234611yescharacteristic
370C4#1062235211yescharacteristic
371C4#1062235211yescharacteristic
372C4#1062236212yes—
373C2—21no—
374C2—21no—
375C2—82no—
376C2#1306962611yescharacteristic
377C2#1306967511yescharacteristic
378C2#1306972411yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#1460D11
hypocenterC11#10190
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. #13079769C2semidirect
4. #13067296C2semidirect
5. #13067020C2semidirect
6. #13066512C2semidirect
312. C11#10190semidirect

Maximal subgroups

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

subgroupindex
#130797692
#130784132
C2×#106226202
#130672962
#130670202
#130665122
C11×#14602
#1019011