Finite Group Databasebeta

← #14654243

Subgroups — #14654243

Order 2816.

594 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 99 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#13079374C211yesmaximal, characteristic
2C2×#10622580C211yesmaximal, characteristic
3#13073097C211yesmaximal, characteristic, complemented
4#13069451C211yesmaximal, characteristic
5#13067187C211yesmaximal, characteristic, complemented
6#13066463C211yesmaximal, characteristic, complemented
7C11×#1823C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622824—22no—
14C4×C22⋊Dic11C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622727—22no—
17#10622595—22no—
18#10622590—21no—
19#10622587—21no—
20#10622580—22no—
21#10622580—22no—
22C2×#66873—21no—
23C2×#66871—21no—
24C2×#66870—22no—
25#10622351—21no—
26#10622348—21no—
27#10622344—21no—
28#10622334—21no—
29C11×#340—22no—
30#10622090—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×D44D411yescharacteristic
35C22×Dic22D411yescharacteristic
36C22×C8×C11D412yes—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C22⋊C4—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11D412yes—
47#66983—21no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×C4⋊Dic11D411yescharacteristic
53C2×C4⋊Dic11D411yescharacteristic
54#66977—21no—
55#66977—21no—
56#66977—21no—
57#66977—21no—
58C2×Dic11⋊C4—21no—
59C2×C4×Dic11—21no—
60C22×C11⋊C8—21no—
61C2×#4314—22no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×#95—21no—
65C11⋊#95—24no—
66C11⋊#95—24no—
67C11⋊#95—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)D412yes—
70#66885—22no—
71#66881—22no—
72#66880—22no—
73#66873—24no—
74#66871—24no—
75#66870—44no—
76#9953—111nomaximal, Sylow
77C24×C11C2×D411yescharacteristic
78C23×D11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—42no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C22×Dic11—22no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—42no—
103C2×Dic22—21no—
104C2×Dic22—21no—
105C2×Dic22—42no—
106C2×C8×C11—22no—
107C2×C8×C11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—42no—
114C22⋊Dic11—22no—
115C22⋊Dic11—22no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126C4×Dic11—42no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—42no—
129#4314—82no—
130#3187—111no—
131C2×#480—111no—
132#2503—111no—
133#1964—111no—
134#1823D1111yescharacteristic, complemented
135#1520—111no—
136#1282—111no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11#12011yescharacteristic
140C23×C11#12111yescharacteristic
141C23×C11#12711yescharacteristic
142C23×C11#13512yes—
143C23×C11AGL(1,ℤ/8)12yes—
144C22×D11—41no—
145C22×D11—42no—
146C22×D11—81no—
147C22×D11—81no—
148C2×C4×C11—22no—
149C2×C4×C11—22no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—44no—
156C2×C4×C11—82no—
157C2×C4×C11—81no—
158C2×C4×C11—81no—
159C2×C4×C11—81no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C22⋊D11—82no—
167C22⋊D11—81no—
168C22⋊D11—81no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178D44—42no—
179D44—42no—
180Dic22—42no—
181Dic22—81no—
182C8×C11—42no—
183C11⋊C8—42no—
184C2×C22⋊Q8—111no—
185C2×#121—111no—
186C22×C4⋊C4C2×D1111yescharacteristic
187#483—221no—
188#481—221no—
189#480—222no—
190#480—222no—
191#465—222no—
192#450—221no—
193#448—221no—
194C2×#107—221no—
195C2×#102—221no—
196C2×#99—222no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1111yescharacteristic
199#400—222no—
200#391—221no—
201#382—221no—
202#381—222no—
203#380C2×D1111yescharacteristic
204C4×C22⋊C4—111no—
205#340—22no—
206#328—222no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11#39211yescharacteristic
216C22×C11#44912yes—
217C22×C11#46312yes—
218C22×C11#49511yescharacteristic
219C22×C11#49611yescharacteristic
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—162no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—82no—
228C4×C11—161no—
229C4×C11#45812yes—
230Dic11—82no—
231Dic11—81no—
232Dic11—81no—
233Dic11—81no—
234C22×Q8—111no—
235C22×D4—111no—
236C22×D4—221no—
237C23×C4—21no—
238C23×C4C22×D1111yescharacteristic
239C2×SD16—222no—
240C22×C8—221no—
241C22×C8C22⋊D1112yes—
242C22⋊Q8—221no—
243C22⋊Q8—221no—
244C22⋊Q8—221no—
245C22⋊Q8—221no—
246#121—221no—
247#121—221no—
248#121—221no—
249#121—221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4D4412yes—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—112no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C42—221no—
265#107—224no—
266#106—222no—
267#103—222no—
268#102—224no—
269#102—222no—
270#99—444no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—112no—
274C22⋊C8—221no—
275#95—21no—
276#95—224no—
277#95—224no—
278#95—221no—
279C2×C11—22no—
280C2×C11—21no—
281C2×C11—22no—
282C2×C11—21no—
283C2×C11#200911yescharacteristic
284C2×C11#201211yescharacteristic
285C2×C11#202211yescharacteristic
286D11—161no—
287C24—221no—
288C24D4×D1111yescharacteristic
289C2×Q8—221no—
290C2×Q8—221no—
291C2×Q8—442no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—442no—
295C2×D4—441no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—441no—
299C22×C4—22no—
300C22×C4—42no—
301C22×C4—41no—
302C22×C4—42no—
303C22×C4—42no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—222no—
307C22×C4—221no—
308C22×C4—221no—
309C22×C4—221no—
310C22×C4C2×D4411yescharacteristic
311C22×C4#433911yescharacteristic
312C22×C4D4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C22×C4C2×C22⋊D1111yescharacteristic
316SD16—882no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—222no—
320C2×C8—442no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—42no—
324C4⋊C4—41no—
325C4⋊C4—41no—
326C4⋊C4—221no—
327C4⋊C4—221no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—441no—
331C4⋊C4—441no—
332C22⋊C4—42no—
333C22⋊C4—222no—
334C22⋊C4—222no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C22⋊C4—441no—
339C42—442no—
340C11#995311yescharacteristic, complemented, Sylow
341C23—41no—
342C23—41no—
343C23—441no—
344C23—442no—
345C23—881no—
346C23—881no—
347C23#6693511yescharacteristic
348C23#6693711yescharacteristic
349C23#6696412yes—
350C23#6696912yes—
351C23#6699311yescharacteristic
352Q8—442no—
353Q8—881no—
354D4—442no—
355D4—442no—
356D4—881no—
357D4—881no—
358D4—882no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—82no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6693511yescharacteristic
383C2×C4#6693711yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4#6699011yescharacteristic
386C8—42no—
387C8—442no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—42no—
395C22—42no—
396C22—881no—
397C22—881no—
398C22—881no—
399C22—1762no—
400C22#1062239412yes—
401C22#1062240012yes—
402C22#1062257311yescharacteristic
403C22#1062276711yescharacteristic
404C22#1062278111yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—82no—
409C4—161no—
410C4—882no—
411C4—881no—
412C4—881no—
413C4—881no—
414C4#1062266612yes—
415C2—21no—
416C2—22no—
417C2—22no—
418C2—21no—
419C2—1761no—
420C2#1306967811yescharacteristic
421C2#1306969511yescharacteristic
422C2#1306974711yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1823C2
socleC22×C11#392
prime radicalC2×#66983C22
hypercenter#1823D11
hypocenterC11#9953
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
3. #13073097C2semidirect
5. #13067187C2semidirect
6. #13066463C2semidirect
7. C11×#1823C2semidirect
134. #1823D11semidirect
340. C11#9953semidirect

Maximal subgroups

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

subgroupindex
#130793742
C2×#106225802
#130730972
#130694512
#130671872
#130664632
C11×#18232
#995311