Finite Group Databasebeta

← #14655803

Subgroups — #14655803

Order 2816.

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

normal subgroups only

This group has 528 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, complemented
2#13078413C211yesmaximal, characteristic
3C2×#10622632C211yesmaximal, characteristic
4#13067287C211yesmaximal, characteristic, complemented
5#13067020C211yesmaximal, characteristic, complemented
6#13066512C211yesmaximal, characteristic, complemented
7C11×#1460C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4324—21no—
10#10623001C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#431C2211yescharacteristic
13C11×#431C2211yescharacteristic
14#10622828—21no—
15#10622632—22no—
16#10622632—22no—
17#10622622—22no—
18#10622621—21no—
19#10622620—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×#323—22no—
29#10622124—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
41C2×#4324—24no—
42C2×#4324—42no—
43C2×#4324—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#66896—22no—
67#66896—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#10186—111nomaximal, Sylow
78C24×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11SD1612yes—
85C22×C4×C11—21no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—82no—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×Dic11—41no—
93C2×Dic22—22no—
94C2×Dic22—21no—
95C2×Dic22—21no—
96C2×Dic22—41no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22—41no—
100C2×Dic22—41no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C22⋊Dic11—41no—
112#4324—48no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—22no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124#4318—41no—
125#4318—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130#3229—111no—
131#3077—111no—
132C2×#461—111no—
133#1546—111no—
134#1481—111no—
135#1460D1111yescharacteristic
136#1301—111no—
137C23×C11—22no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11#12111yescharacteristic
143D4×C11—22no—
144D4×C11—22no—
145D4×C11—41no—
146D4×C11—41no—
147C2×C4×C11—22no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—82no—
151C2×C4×C11—82no—
152C2×C4×C11—81no—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11#12011yescharacteristic
155C2×C4×C11#12011yescharacteristic
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12711yescharacteristic
159C2×C4×C11C2×SD1611yescharacteristic
160C2×C4×C11#13511yescharacteristic
161C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C11#13711yescharacteristic
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168Dic22—42no—
169Dic22—42no—
170Dic22—42no—
171Dic22—42no—
172Dic22—81no—
173Dic22—81no—
174C8×C11—42no—
175C8×C11—81no—
176C11⋊C8—42no—
177C11⋊C8—42no—
178C22×SD16—221no—
179#533—111no—
180C2×C4⋊Q8—111no—
181C2×C4×D4C2×D1111yescharacteristic
182#498—221no—
183#487—221no—
184#483—222no—
185#478—222no—
186#476—221no—
187#475—222no—
188#474—221no—
189#461—222no—
190#461—222no—
191#431C2×D1111yescharacteristic
192#431C2×D1111yescharacteristic
193#428—221no—
194#423—111no—
195C2×C4⋊C8—111no—
196#418—221no—
197C2×#103—221no—
198#332—222no—
199Q8⋊C8—222no—
200#323—22no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—42no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11—81no—
207C22×C11—81no—
208C22×C11#39211yescharacteristic
209C22×C11#46511yescharacteristic
210C22×C11#46811yescharacteristic
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—81no—
215C4×C11#44811yescharacteristic
216C4×C11#44911yescharacteristic
217C4×C11#45011yescharacteristic
218C4×C11#45211yescharacteristic
219C4×C11#47112yes—
220Dic11—82no—
221Dic11—81no—
222Dic11—81no—
223C22×Q8—221no—
224C22×D4D4411yescharacteristic
225C23×C4—21no—
226C2×SD16—224no—
227C2×SD16—442no—
228C2×SD16—442no—
229C2×M16—221no—
230C22×C8—221no—
231C4⋊Q8—112no—
232C4⋊Q8—111no—
233C4⋊Q8—111no—
234C4⋊Q8—221no—
235C4⋊Q8—221no—
236C4⋊Q8—221no—
237#125—221no—
238C22⋊Q8—221no—
239C22⋊Q8—221no—
240C4×Q8—221no—
241C4×Q8—221no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245C4×D4—21no—
246#117—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4D4411yescharacteristic
250C2×C22⋊C4—21no—
251C2×C42C22×D1111yescharacteristic
252#107—222no—
253#106—222no—
254#106—224no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—112no—
258C4⋊C8—112no—
259C4⋊C8—221no—
260C4⋊C8—221no—
261#103—224no—
262#103—224no—
263#102—222no—
264#102—222no—
265C22⋊C8—21no—
266C22⋊C8C22⋊D1112yes—
267C4×C8—21no—
268C4×C8—21no—
269C2×C11—21no—
270C2×C11—21no—
271C2×C11—82no—
272C2×C11#200011yescharacteristic
273C2×C11#200911yescharacteristic
274C2×C11#201911yescharacteristic
275C24—21no—
276C2×Q8—222no—
277C2×Q8—221no—
278C2×Q8—221no—
279C2×Q8—441no—
280C2×Q8—441no—
281C2×Q8—441no—
282C2×Q8—441no—
283C2×Q8—441no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4#431412yes—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—82no—
294C22×C4—441no—
295C22×C4C2×D4411yescharacteristic
296C22×C4#433911yescharacteristic
297C22×C4C2×C22⋊D1111yescharacteristic
298SD16—448no—
299M16—441no—
300M16—441no—
301C2×C8—22no—
302C2×C8—41no—
303C2×C8—222no—
304C2×C8—222no—
305C2×C8—441no—
306C2×C8—441no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—221no—
310C4⋊C4—221no—
311C4⋊C4—222no—
312C4⋊C4—221no—
313C4⋊C4—222no—
314C4⋊C4—221no—
315C4⋊C4—441no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C22⋊C4—41no—
320C22⋊C4—41no—
321C22⋊C4—441no—
322C42—441no—
323C42D4×D1111yescharacteristic
324C42D4×D1111yescharacteristic
325C42D4×D1111yescharacteristic
326C42D4×D1111yescharacteristic
327C11#1018611yescharacteristic, complemented, Sylow
328C23—22no—
329C23—41no—
330C23—41no—
331C23—81no—
332C23—81no—
333C23#6698311yescharacteristic
334Q8—442no—
335Q8—442no—
336Q8—442no—
337Q8—442no—
338Q8—881no—
339Q8—881no—
340D4—22no—
341D4—22no—
342D4—41no—
343D4—41no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—82no—
348C2×C4—82no—
349C2×C4—81no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4—881no—
354C2×C4—881no—
355C2×C4#6693511yescharacteristic
356C2×C4#6693511yescharacteristic
357C2×C4#6693711yescharacteristic
358C2×C4#6693711yescharacteristic
359C2×C4C2×#431411yescharacteristic
360C2×C4#6695711yescharacteristic
361C2×C4#6696111yescharacteristic
362C2×C4#6696211yescharacteristic
363C2×C4#6699011yescharacteristic
364C2×C4#6699311yescharacteristic
365C8—42no—
366C8—81no—
367C8—442no—
368C8—442no—
369C22—21no—
370C22—21no—
371C22—42no—
372C22—82no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22#1062257311yescharacteristic
377C22#1062272711yescharacteristic
378C22#1062274711yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—81no—
383C4—882no—
384C4—881no—
385C4—881no—
386C4#1062234411yescharacteristic
387C4#1062234611yescharacteristic
388C4#1062234711yescharacteristic
389C4#1062235111yescharacteristic
390C4#1062236112yes—
391C2—21no—
392C2—21no—
393C2—82no—
394C2#1306962111yescharacteristic
395C2#1306967511yescharacteristic
396C2#1306973211yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#392
prime radicalC22×D4×C11D4
hypercenter#1460D11
hypocenterC11#10186
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. #13079762C2semidirect
4. #13067287C2semidirect
5. #13067020C2semidirect
6. #13066512C2semidirect
327. C11#10186semidirect

Maximal subgroups

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

subgroupindex
#130797622
#130784132
C2×#106226322
#130672872
#130670202
#130665122
C11×#14602
#1018611