Finite Group Databasebeta

← #14655810

Subgroups — #14655810

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#13079762C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic
3C2×#10622644C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic
5#13067020C211yesmaximal, characteristic
6#13066512C211yesmaximal, characteristic
7C11×#1461C211yesmaximal, characteristic
8C2×C4×Q8×C11C2211yescharacteristic
9C22×#4326—21no—
10#10623001C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622838—21no—
15#10622644—22no—
16#10622644—22no—
17#10622635—22no—
18#10622634—21no—
19#10622633—21no—
20C2×#66874—21no—
21#10622577—21no—
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622464—22no—
25#10622334—22no—
26#10622294—21no—
27#10622293—21no—
28C11×#324—22no—
29#10622124—22no—
30#10622094—22no—
31C22×Q8×C11D411yescharacteristic
32C22×Dic22—21no—
33C4×Q8×C11—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C42×C11—21no—
40C2×C42×C11C2311yescharacteristic
41C2×#4326—24no—
42C2×#4326—42no—
43C2×#4326—42no—
44#66979—21no—
45C2×C4⋊Dic11—21no—
46C2×C4⋊Dic11—21no—
47#66977—21no—
48#66977—21no—
49C2×#4318—21no—
50C22×C11⋊C8—21no—
51#66923—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55#66922D412yes—
56#66922D411yescharacteristic
57#66922D411yescharacteristic
58C4×Dic22—21no—
59C4×Dic22—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8D412yes—
64C4×C8×C11—21no—
65C4×C8×C11—21no—
66#66899—22no—
67#66899—22no—
68#66881—24no—
69#66880—24no—
70#66874—24no—
71#66872—22no—
72#66871—22no—
73C4⋊(C11⋊C8)—21no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)D412yes—
76C4⋊(C11⋊C8)D412yes—
77#10187—111nomaximal, Sylow
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11SD1612yes—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×Dic11—41no—
90C2×Dic22—22no—
91C2×Dic22—21no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×Dic22—41no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×C8×C11—22no—
99C2×C8×C11—41no—
100C11×C4⋊C4—21no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—41no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C22⋊Dic11—41no—
111#4326—48no—
112C4⋊Dic11—21no—
113C4⋊Dic11—21no—
114C4⋊Dic11—22no—
115C4⋊Dic11—21no—
116C4⋊Dic11—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120Dic11⋊C4—41no—
121Dic11⋊C4—41no—
122C4×Dic11—41no—
123#4318—41no—
124#4318—41no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129#3229—111no—
130#3078—111no—
131C2×#462—111no—
132#1546—111no—
133#1481—111no—
134#1461D1111yescharacteristic
135#1301—111no—
136C23×C11#12111yescharacteristic
137Q8×C11—22no—
138Q8×C11—22no—
139Q8×C11—41no—
140Q8×C11—41no—
141C2×C4×C11—22no—
142C2×C4×C11—22no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
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×SD1611yescharacteristic
155C2×C4×C11#13511yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11#13711yescharacteristic
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—42no—
161C2×Dic11—81no—
162C2×Dic11—81no—
163Dic22—42no—
164Dic22—42no—
165Dic22—42no—
166Dic22—42no—
167Dic22—81no—
168Dic22—81no—
169C8×C11—42no—
170C8×C11—81no—
171C11⋊C8—42no—
172C11⋊C8—42no—
173C22×Q16—221no—
174#533—111no—
175C2×C4⋊Q8—111no—
176C2×C4×Q8C2×D1111yescharacteristic
177#498—221no—
178#487—221no—
179#483—222no—
180#479—222no—
181#477—221no—
182#475—222no—
183#475—221no—
184#462—222no—
185#462—222no—
186#431C2×D1111yescharacteristic
187#431C2×D1111yescharacteristic
188#428—221no—
189#423—111no—
190C2×C4⋊C8—111no—
191#419—221no—
192C2×#103—221no—
193#332—222no—
194Q8⋊C8—222no—
195#324—22no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11#39211yescharacteristic
199C22×C11#46511yescharacteristic
200C22×C11#46811yescharacteristic
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—42no—
205C4×C11—81no—
206C4×C11#44811yescharacteristic
207C4×C11#44911yescharacteristic
208C4×C11#45011yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#47312yes—
211Dic11—82no—
212Dic11—81no—
213Dic11—81no—
214C22×Q8—221no—
215C22×Q8D4411yescharacteristic
216C2×Q16—224no—
217C2×Q16—442no—
218C2×Q16—442no—
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—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233C4×Q8—21no—
234C4×Q8—221no—
235C4×Q8—221no—
236#117—221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4D4411yescharacteristic
241C2×C42—21no—
242C2×C42C22×D1111yescharacteristic
243#107—222no—
244#106—222no—
245#106—224no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—112no—
249C4⋊C8—112no—
250C4⋊C8—221no—
251C4⋊C8—221no—
252#103—224no—
253#103—224no—
254#103—222no—
255#103—222no—
256C22⋊C8—21no—
257C22⋊C8C22⋊D1112yes—
258C4×C8—21no—
259C4×C8—21no—
260C2×C11—21no—
261C2×C11—21no—
262C2×C11#200011yescharacteristic
263C2×C11#200911yescharacteristic
264C2×C11#202011yescharacteristic
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—21no—
270C2×Q8—222no—
271C2×Q8—221no—
272C2×Q8—221no—
273C2×Q8—441no—
274C2×Q8—441no—
275C2×Q8—441no—
276C2×Q8—441no—
277C2×Q8—441no—
278C2×Q8#431412yes—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—441no—
282C22×C4C2×D4411yescharacteristic
283C22×C4#433911yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285Q16—448no—
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—41no—
297C4⋊C4—41no—
298C4⋊C4—221no—
299C4⋊C4—221no—
300C4⋊C4—222no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C22⋊C4—441no—
309C42—41no—
310C42—41no—
311C42—441no—
312C42D4×D1111yescharacteristic
313C42D4×D1111yescharacteristic
314C42D4×D1111yescharacteristic
315C42D4×D1111yescharacteristic
316C11#1018711yescharacteristic, complemented, Sylow
317C23#6698311yescharacteristic
318Q8—22no—
319Q8—22no—
320Q8—41no—
321Q8—41no—
322Q8—442no—
323Q8—442no—
324Q8—442no—
325Q8—442no—
326Q8—881no—
327Q8—881no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4#6693511yescharacteristic
341C2×C4#6693511yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4#6693711yescharacteristic
344C2×C4C2×#431411yescharacteristic
345C2×C4#6695711yescharacteristic
346C2×C4#6696111yescharacteristic
347C2×C4#6696211yescharacteristic
348C2×C4#6699011yescharacteristic
349C2×C4#6699311yescharacteristic
350C8—42no—
351C8—81no—
352C8—442no—
353C8—442no—
354C22—21no—
355C22—21no—
356C22#1062257311yescharacteristic
357C22#1062272711yescharacteristic
358C22#1062274711yescharacteristic
359C4—21no—
360C4—21no—
361C4—21no—
362C4—42no—
363C4—81no—
364C4—882no—
365C4—881no—
366C4—881no—
367C4#1062234411yescharacteristic
368C4#1062234611yescharacteristic
369C4#1062234711yescharacteristic
370C4#1062235111yescharacteristic
371C4#1062236812yes—
372C2—21no—
373C2—21no—
374C2#1306962111yescharacteristic
375C2#1306967511yescharacteristic
376C2#1306973611yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1461C2
socleC22×C11#392
prime radicalC23×C11#121
hypercenter#1461D11
hypocenterC11#10187
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
316. C11#10187semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130784212
C2×#106226442
#130672872
#130670202
#130665122
C11×#14612
#1018711