Finite Group Databasebeta

← C11×#32898 #14610091

Subgroups — C11×#32898 #14610091

Order 2816.

4360 conjugacy classes of subgroups; only the 370 normal subgroups are shown.

normal subgroups only

This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 370 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
1C22×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×C11×B(4,𝔽2)C214yesmaximal, complemented
3C11×#2403C213yesmaximal, complemented
4C11×#1790C214yesmaximal, complemented
5C11×#1781C213yesmaximal, complemented
6C2×C11×H(5,𝔽2)—216no—
7C2×C11×H(5,𝔽2)—26no—
8C2×C11×H(5,𝔽2)C2214yes—
9C22×C11×#41—23no—
10C23×D4×C11—23no—
11C23×D4×C11C2213yes—
12C23×D4×C11C2211yescharacteristic, complemented
13C2×C11×#120—23no—
14C2×C11×#120C2216yescomplemented
15C11×B(4,𝔽2)—216no—
16C2×C11×#99C22112yescomplemented
17C11×#392—26no—
18C11×#386—23no—
19C11×#386C2216yescomplemented
20C11×#379C2213yescomplemented
21C25×C11—21no—
22C25×C11D413yescomplemented
23C25×C11C2311yescharacteristic
24C25×C11C2311yescharacteristic, complemented
25C11×H(5,𝔽2)—248no—
26C11×H(5,𝔽2)—248no—
27C11×H(5,𝔽2)—224no—
28C11×H(5,𝔽2)D4116yescomplemented
29C2×C11×#41—212no—
30C2×C11×#41—248no—
31C2×C11×#41—212no—
32C22×Q8×C11—21no—
33C22×D4×C11—23no—
34C22×D4×C11—248no—
35C22×D4×C11—212no—
36C22×D4×C11—26no—
37C22×D4×C11—212no—
38C22×D4×C11—26no—
39C22×D4×C11—224no—
40C22×D4×C11—23no—
41C22×D4×C11—23no—
42C22×D4×C11—26no—
43C22×D4×C11—44no—
44C22×D4×C11D416yescomplemented
45C22×D4×C11C2316yes—
46C23×C4×C11—23no—
47C23×C4×C11D413yescomplemented
48C23×C4×C11C2311yescharacteristic, complemented
49C11×#120—224no—
50C11×#120—412no—
51C2×C11×C22⋊C4—23no—
52C2×C11×C22⋊C4—26no—
53C2×C11×C22⋊C4—26no—
54C2×C11×C22⋊C4—23no—
55C2×C11×C22⋊C4C2316yescomplemented
56C11×#99—224no—
57C11×#95—26no—
58#32898C1111yesmaximal, characteristic, direct product factor, Sylow
59C24×C11—28no—
60C24×C11—24no—
61C24×C11—23no—
62C24×C11—23no—
63C24×C11—212no—
64C24×C11—24no—
65C24×C11—23no—
66C24×C11—24no—
67C24×C11—42no—
68C24×C11—42no—
69C24×C11—46no—
70C24×C11—81no—
71C24×C11—81no—
72C24×C11—83no—
73C24×C11—82no—
74C24×C11—82no—
75C24×C11C2×D413yes—
76C24×C11C2×D413yes—
77C24×C11C2×D416yes—
78C24×C11C2411yescharacteristic
79C11×#41—296no—
80C11×#41—248no—
81C11×#41—248no—
82C2×Q8×C11—28no—
83C2×Q8×C11—24no—
84C2×D4×C11—224no—
85C2×D4×C11—248no—
86C2×D4×C11—212no—
87C2×D4×C11—296no—
88C2×D4×C11—248no—
89C2×D4×C11—248no—
90C2×D4×C11—212no—
91C2×D4×C11—248no—
92C2×D4×C11—212no—
93C2×D4×C11—212no—
94C2×D4×C11—212no—
95C2×D4×C11—212no—
96C2×D4×C11—212no—
97C2×D4×C11—46no—
98C2×D4×C11—46no—
99C2×D4×C11—46no—
100C2×D4×C11—43no—
101C2×D4×C11—41no—
102C2×D4×C11—412no—
103C2×D4×C11—412no—
104C2×D4×C11—86no—
105C2×D4×C11C2×D4124yes—
106C22×C4×C11—224no—
107C22×C4×C11—212no—
108C22×C4×C11—23no—
109C22×C4×C11—23no—
110C22×C4×C11—212no—
111C22×C4×C11—23no—
112C22×C4×C11—26no—
113C22×C4×C11—42no—
114C22×C4×C11C2×D416yes—
115C11×C22⋊C4—212no—
116C11×C22⋊C4—412no—
117C11×C22⋊C4—46no—
118C11×C22⋊C4—412no—
119C11×C22⋊C4—83no—
120C22×H(5,𝔽2)C2×C1111yescharacteristic, complemented
121C2×B(4,𝔽2)C2×C1114yescomplemented
122#2403C2×C1113yescomplemented
123#1790C2×C1114yescomplemented
124#1781C2×C1113yescomplemented
125C23×C11—212no—
126C23×C11—212no—
127C23×C11—216no—
128C23×C11—26no—
129C23×C11—26no—
130C23×C11—26no—
131C23×C11—26no—
132C23×C11—26no—
133C23×C11—26no—
134C23×C11—41no—
135C23×C11—43no—
136C23×C11—41no—
137C23×C11—43no—
138C23×C11—43no—
139C23×C11—46no—
140C23×C11—46no—
141C23×C11—46no—
142C23×C11—43no—
143C23×C11—46no—
144C23×C11—46no—
145C23×C11—46no—
146C23×C11—41no—
147C23×C11—83no—
148C23×C11—83no—
149C23×C11—88no—
150C23×C11—88no—
151C23×C11—824no—
152C23×C11—816no—
153C23×C11—84no—
154C23×C11—84no—
155C23×C11#12013yes—
156C23×C11#12011yescharacteristic
157C23×C11#120112yescomplemented
158C23×C11C22×D413yes—
159C23×C11C22×D414yes—
160Q8×C11—216no—
161D4×C11—248no—
162D4×C11—248no—
163D4×C11—248no—
164D4×C11—412no—
165D4×C11—44no—
166D4×C11—824no—
167C2×C4×C11—212no—
168C2×C4×C11—212no—
169C2×C4×C11—248no—
170C2×C4×C11—26no—
171C2×C4×C11—26no—
172C2×C4×C11—26no—
173C2×C4×C11—43no—
174C2×C4×C11—41no—
175C2×C4×C11—46no—
176C2×C4×C11—46no—
177C2×C4×C11—46no—
178C2×C4×C11#120112yescomplemented
179C2×H(5,𝔽2)—216no—
180C2×H(5,𝔽2)—26no—
181C2×H(5,𝔽2)C22×C1114yes—
182C22×#41—23no—
183C23×D4—23no—
184C23×D4C22×C1113yes—
185C23×D4C22×C1111yescharacteristic, complemented
186C2×#120—23no—
187C2×#120C22×C1116yescomplemented
188B(4,𝔽2)—216no—
189C2×#99C22×C11112yescomplemented
190#392—26no—
191#386—23no—
192#386C22×C1116yescomplemented
193#379C22×C1113yescomplemented
194C22×C11—21no—
195C22×C11—23no—
196C22×C11—23no—
197C22×C11—21no—
198C22×C11—23no—
199C22×C11—212no—
200C22×C11—23no—
201C22×C11—23no—
202C22×C11—44no—
203C22×C11—412no—
204C22×C11—412no—
205C22×C11—424no—
206C22×C11—412no—
207C22×C11—46no—
208C22×C11—46no—
209C22×C11—42no—
210C22×C11—86no—
211C22×C11—86no—
212C22×C11—86no—
213C22×C11—812no—
214C22×C11—816no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11B(4,𝔽2)12yescomplemented
218C22×C11C2×#12016yes—
219C22×C11C2×#12011yescharacteristic
220C4×C11—212no—
221C4×C11—42no—
222C4×C11—86no—
223C25—21no—
224C25D4×C1113yescomplemented
225C25C23×C1111yescharacteristic
226C25C23×C1111yescharacteristic, complemented
227H(5,𝔽2)—248no—
228H(5,𝔽2)—248no—
229H(5,𝔽2)—224no—
230H(5,𝔽2)D4×C11116yescomplemented
231C2×#41—212no—
232C2×#41—248no—
233C2×#41—212no—
234C22×Q8—21no—
235C22×D4—23no—
236C22×D4—248no—
237C22×D4—212no—
238C22×D4—26no—
239C22×D4—212no—
240C22×D4—26no—
241C22×D4—224no—
242C22×D4—23no—
243C22×D4—23no—
244C22×D4—26no—
245C22×D4—44no—
246C22×D4D4×C1116yescomplemented
247C22×D4C23×C1116yes—
248C23×C4—23no—
249C23×C4D4×C1113yescomplemented
250C23×C4C23×C1111yescharacteristic, complemented
251#120—224no—
252#120—412no—
253C2×C22⋊C4—23no—
254C2×C22⋊C4—26no—
255C2×C22⋊C4—26no—
256C2×C22⋊C4—23no—
257C2×C22⋊C4C23×C1116yescomplemented
258#99—224no—
259#95—26no—
260C2×C11—26no—
261C2×C11—22no—
262C2×C11—43no—
263C2×C11—412no—
264C2×C11—82no—
265C2×C11#284611yescharacteristic
266C2×C11C2×B(4,𝔽2)11yescharacteristic
267C2×C11#302611yescharacteristic
268C24—28no—
269C24—24no—
270C24—23no—
271C24—23no—
272C24—212no—
273C24—24no—
274C24—23no—
275C24—24no—
276C24—42no—
277C24—42no—
278C24—46no—
279C24—81no—
280C24—81no—
281C24—83no—
282C24—82no—
283C24—82no—
284C24C2×D4×C1113yes—
285C24C2×D4×C1113yes—
286C24C2×D4×C1116yes—
287C24C24×C1111yescharacteristic
288#41—296no—
289#41—248no—
290#41—248no—
291C2×Q8—28no—
292C2×Q8—24no—
293C2×D4—224no—
294C2×D4—248no—
295C2×D4—212no—
296C2×D4—296no—
297C2×D4—248no—
298C2×D4—248no—
299C2×D4—212no—
300C2×D4—248no—
301C2×D4—212no—
302C2×D4—212no—
303C2×D4—212no—
304C2×D4—212no—
305C2×D4—212no—
306C2×D4—46no—
307C2×D4—46no—
308C2×D4—46no—
309C2×D4—43no—
310C2×D4—41no—
311C2×D4—412no—
312C2×D4—412no—
313C2×D4—86no—
314C2×D4C2×D4×C11124yes—
315C22×C4—224no—
316C22×C4—212no—
317C22×C4—23no—
318C22×C4—23no—
319C22×C4—212no—
320C22×C4—23no—
321C22×C4—26no—
322C22×C4—42no—
323C22×C4C2×D4×C1116yes—
324C22⋊C4—212no—
325C22⋊C4—412no—
326C22⋊C4—46no—
327C22⋊C4—412no—
328C22⋊C4—83no—
329C11#3289811yescharacteristic, direct product factor, Sylow
330C23—212no—
331C23—212no—
332C23—216no—
333C23—26no—
334C23—26no—
335C23—26no—
336C23—26no—
337C23—26no—
338C23—26no—
339C23—41no—
340C23—43no—
341C23—41no—
342C23—43no—
343C23—43no—
344C23—46no—
345C23—46no—
346C23—46no—
347C23—43no—
348C23—46no—
349C23—46no—
350C23—46no—
351C23—41no—
352C23—83no—
353C23—83no—
354C23—88no—
355C23—88no—
356C23—824no—
357C23—816no—
358C23—84no—
359C23—84no—
360C23C11×#12013yes—
361C23C11×#12011yescharacteristic
362C23C11×#120112yescomplemented
363C23C22×D4×C1113yes—
364C23C22×D4×C1114yes—
365Q8—216no—
366D4—248no—
367D4—248no—
368D4—248no—
369D4—412no—
370D4—44no—
371D4—824no—
372C2×C4—212no—
373C2×C4—212no—
374C2×C4—248no—
375C2×C4—26no—
376C2×C4—26no—
377C2×C4—26no—
378C2×C4—43no—
379C2×C4—41no—
380C2×C4—46no—
381C2×C4—46no—
382C2×C4—46no—
383C2×C4C11×#120112yescomplemented
384C22—23no—
385C22—23no—
386C22—21no—
387C22—21no—
388C22—23no—
389C22—23no—
390C22—23no—
391C22—212no—
392C22—44no—
393C22—412no—
394C22—412no—
395C22—424no—
396C22—412no—
397C22—46no—
398C22—46no—
399C22—42no—
400C22—86no—
401C22—86no—
402C22—86no—
403C22—812no—
404C22—816no—
405C22—81no—
406C22—81no—
407C22C11×B(4,𝔽2)12yescomplemented
408C22C2×C11×#12016yes—
409C22C2×C11×#12011yescharacteristic
410C4—212no—
411C4—42no—
412C4—86no—
413C2—26no—
414C2—22no—
415C2—43no—
416C2—412no—
417C2—82no—
418C2C11×#284611yescharacteristic
419C2C2×C11×B(4,𝔽2)11yescharacteristic
420C2C11×#302611yescharacteristic
subgroupG/H
center, socleC22×C11C2×#120
commutator, Frattini, cosocleC24C24×C11
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×H(5,𝔽2)C2semidirect
2. C2×C11×B(4,𝔽2)C2semidirect
3. C11×#2403C2semidirect
4. C11×#1790C2semidirect
5. C11×#1781C2semidirect
12. C23×D4×C11C22semidirect
14. C2×C11×#120C22semidirect
16. C2×C11×#99C22semidirect
19. C11×#386C22semidirect
20. C11×#379C22semidirect
22. C25×C11D4semidirect
24. C25×C11C23semidirect
28. C11×H(5,𝔽2)D4semidirect
44. C22×D4×C11D4semidirect
47. C23×C4×C11D4semidirect
48. C23×C4×C11C23semidirect
55. C2×C11×C22⋊C4C23semidirect
58. #32898C11direct (N × H)
120. C22×H(5,𝔽2)C2×C11semidirect
121. C2×B(4,𝔽2)C2×C11semidirect
122. #2403C2×C11semidirect
123. #1790C2×C11semidirect
124. #1781C2×C11semidirect
157. C23×C11#120semidirect
178. C2×C4×C11#120semidirect
185. C23×D4C22×C11semidirect
187. C2×#120C22×C11semidirect
189. C2×#99C22×C11semidirect
192. #386C22×C11semidirect
193. #379C22×C11semidirect
217. C22×C11B(4,𝔽2)semidirect
224. C25D4×C11semidirect
226. C25C23×C11semidirect
230. H(5,𝔽2)D4×C11semidirect
246. C22×D4D4×C11semidirect
249. C23×C4D4×C11semidirect
250. C23×C4C23×C11semidirect
257. C2×C22⋊C4C23×C11semidirect
329. C11#32898direct (N × H)
362. C23C11×#120semidirect
383. C2×C4C11×#120semidirect
407. C22C11×B(4,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C22×C11×H(5,𝔽2)2
C2×C11×B(4,𝔽2)2
C11×#24032
C11×#17902
C11×#17812
#3289811