Finite Group Databasebeta

← #14666557

Subgroups — #14666557

Order 2816.

578 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 59 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#13072282C211yesmaximal, characteristic
2#13067641C211yesmaximal, characteristic, complemented
3#13067573C211yesmaximal, characteristic, complemented
4#13066639C211yesmaximal, characteristic, complemented
5#13066636C211yesmaximal, characteristic, complemented
6#13066544C211yesmaximal, characteristic
7C11×#2029C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C22×C22⋊Dic11—21no—
10C2×#66931—21no—
11C11×#379—21no—
12C11×#379C2211yescharacteristic
13#10622663—21no—
14#10622657—21no—
15#10622563—21no—
16#10622562C2211yescharacteristic
17#10622561—21no—
18#10622560C2211yescharacteristic
19#10622559—21no—
20#10622555—21no—
21C11×#342—21no—
22C11×#342C2211yescharacteristic
23#10622176—21no—
24#10622176—21no—
25#10622163C2211yescharacteristic
26#10622163C2211yescharacteristic
27C25×C11D411yescharacteristic
28C23×Dic11—21no—
29C23×Dic11—21no—
30C22×Dic22D411yescharacteristic
31C11×C22⋊Q8—21no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—41no—
34C11×C22⋊Q8—41no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—41no—
40C2×C11×C22⋊C4—41no—
41C2×C11×C22⋊C4D411yescharacteristic
42C2×C11×C22⋊C4C2311yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45C2×C22⋊Dic11—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—44no—
48C2×#4326—41no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11D411yescharacteristic
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54#66931—44no—
55#66899—41no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95D411yescharacteristic
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66874—41no—
63#66871—41no—
64#12214—111nomaximal, Sylow
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—42no—
68C24×C11—41no—
69C24×C11—42no—
70C24×C11—41no—
71C24×C11Q1612yescomplemented
72C24×C11C2×D411yescharacteristic
73C2×Q8×C11—21no—
74C2×Q8×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×Dic11—21no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—42no—
86C22×Dic11—42no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89C22×Dic11—81no—
90C22×Dic11—81no—
91C2×Dic22—41no—
92C2×Dic22—42no—
93C11×C4⋊C4—21no—
94C11×C4⋊C4—21no—
95C11×C4⋊C4—41no—
96C11×C4⋊C4—41no—
97C11×C22⋊C4—41no—
98C11×C22⋊C4—42no—
99C11×C22⋊C4—42no—
100C11×C22⋊C4—41no—
101C11×C22⋊C4—41no—
102C11×C22⋊C4—41no—
103C11×C22⋊C4—41no—
104C11×C22⋊C4—41no—
105C11×C22⋊C4—82no—
106C11×C22⋊C4—82no—
107C22⋊Dic11—24no—
108C22⋊Dic11—42no—
109C22⋊Dic11—42no—
110C22⋊Dic11—42no—
111#4326—82no—
112C4⋊Dic11—41no—
113C4⋊Dic11—42no—
114Dic11⋊C4—42no—
115Dic11⋊C4—42no—
116Dic11⋊C4—81no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119#2437—111no—
120#2029D1111yescharacteristic
121#1614—111no—
122#1602—111no—
123#1352—111no—
124#1351—111no—
125#1316—111no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—44no—
135C23×C11—42no—
136C23×C11—41no—
137C23×C11—44no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11—42no—
141C23×C11—42no—
142C23×C11—81no—
143C23×C11—84no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11#12011yescharacteristic
147C23×C11C2×Q1611yescharacteristic
148C23×C11#13711yescharacteristic
149Q8×C11—81no—
150Q8×C11—81no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—84no—
178C2×Dic11—84no—
179Dic22—42no—
180Dic22—81no—
181C11⋊C8—81no—
182C11⋊C8—81no—
183#543C2×D1111yescharacteristic
184C2×C22⋊Q8—221no—
185C22×C22⋊C4—221no—
186#484—221no—
187#451—221no—
188#399—111no—
189#396—221no—
190#393—111no—
191#385—221no—
192#385—221no—
193#380—221no—
194#379—21no—
195#379C2×D1111yescharacteristic
196#342—21no—
197#342C2×D1111yescharacteristic
198#328—221no—
199#328—221no—
200#323—111no—
201#323—111no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—24no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—42no—
210C22×C11—42no—
211C22×C11—42no—
212C22×C11—44no—
213C22×C11—42no—
214C22×C11—41no—
215C22×C11—42no—
216C22×C11—41no—
217C22×C11—42no—
218C22×C11—81no—
219C22×C11—82no—
220C22×C11—82no—
221C22×C11—82no—
222C22×C11#45111yescharacteristic
223C22×C11#45511yescharacteristic
224C22×C11B(4,𝔽2)11yescharacteristic
225C4×C11—41no—
226C4×C11—41no—
227C4×C11—81no—
228C4×C11—81no—
229C4×C11—81no—
230C4×C11—161no—
231Dic11—42no—
232Dic11—42no—
233Dic11—81no—
234Dic11—81no—
235C25C22⋊D1111yescharacteristic
236C22×Q8—111no—
237C23×C4—221no—
238C23×C4—221no—
239C2×Q16—441no—
240C22⋊Q8—21no—
241C22⋊Q8—21no—
242C22⋊Q8—41no—
243C22⋊Q8—41no—
244C22⋊Q8—444no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—221no—
247C2×C4⋊C4—221no—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—41no—
255C2×C22⋊C4—41no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—444no—
261C2×C22⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4C22×D1111yescharacteristic
263#107—441no—
264#103—441no—
265#103—441no—
266C22⋊C8—221no—
267C22⋊C8—221no—
268#95—111no—
269#95—111no—
270#95—221no—
271#95—221no—
272C2×C11—21no—
273C2×C11—21no—
274C2×C11—41no—
275C2×C11—44no—
276C2×C11—41no—
277C2×C11#160211yescharacteristic
278C2×C11#219611yescharacteristic
279C2×C11#219711yescharacteristic
280C24—21no—
281C24—21no—
282C24—41no—
283C24—42no—
284C24—42no—
285C24—41no—
286C24#432612yescomplemented
287C24C2×C22⋊D1111yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—441no—
291C2×Q8—442no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—41no—
296C22×C4—221no—
297C22×C4—221no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—442no—
301C22×C4—442no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—881no—
305C22×C4—881no—
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308Q16—882no—
309C2×C8—441no—
310C2×C8—441no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—441no—
316C4⋊C4—442no—
317C4⋊C4—442no—
318C4⋊C4—442no—
319C4⋊C4—881no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—82no—
329C22⋊C4—82no—
330C22⋊C4—224no—
331C22⋊C4—442no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C11#1221411yescharacteristic, complemented, Sylow
335C23—22no—
336C23—22no—
337C23—21no—
338C23—22no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—44no—
344C23—42no—
345C23—41no—
346C23—44no—
347C23—41no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—81no—
352C23—84no—
353C23—81no—
354C23—81no—
355C23#6699011yescharacteristic
356C23C2×#432611yescharacteristic
357C23#6700411yescharacteristic
358Q8—81no—
359Q8—81no—
360Q8—442no—
361Q8—881no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—884no—
389C2×C4—884no—
390C8—881no—
391C8—881no—
392C22—21no—
393C22—21no—
394C22—24no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—42no—
400C22—42no—
401C22—42no—
402C22—44no—
403C22—41no—
404C22—42no—
405C22—41no—
406C22—42no—
407C22—42no—
408C22—81no—
409C22—82no—
410C22—82no—
411C22—82no—
412C22#1062264511yescharacteristic
413C22#1062266311yescharacteristic
414C22#1062267411yescharacteristic
415C4—41no—
416C4—41no—
417C4—81no—
418C4—81no—
419C4—81no—
420C4—161no—
421C4—442no—
422C4—442no—
423C4—881no—
424C4—881no—
425C2—21no—
426C2—21no—
427C2—41no—
428C2—44no—
429C2—41no—
430C2#1306757211yescharacteristic
431C2#1307059811yescharacteristic
432C2#1307060411yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2029C2
socleC22×C11B(4,𝔽2)
prime radicalC25×C11D4
hypercenter#2029D11
hypocenterC11#12214
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2029

Complements

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

NH ≅ G/Ntype
2. #13067641C2semidirect
3. #13067573C2semidirect
4. #13066639C2semidirect
5. #13066636C2semidirect
71. C24×C11Q16semidirect
286. C24#4326semidirect
334. C11#12214semidirect

Maximal subgroups

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

subgroupindex
#130722822
#130676412
#130675732
#130666392
#130666362
#130665442
C11×#20292
#1221411