Finite Group Databasebeta

← #14669303

Subgroups — #14669303

Order 2816.

1000 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 135 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#13070262C214yesmaximal, complemented
2#13068544C211yesmaximal, characteristic, complemented
3#13068534C211yesmaximal, characteristic, complemented
4C11×#3485C211yesmaximal, characteristic
5C2×C11×H(5,𝔽2)C411yescharacteristic, complemented
6C22×C11×#41C2211yescharacteristic
7C11×#547—24no—
8C11×#546—24no—
9C11×#536—21no—
10C11×#534—21no—
11C11×#534C2212yes—
12C11×#525—21no—
13C2×C11×#123—21no—
14C2×C11×#123C412yescomplemented
15C11×#518C411yescharacteristic, complemented
16C2×#66900—21no—
17C2×#66898—21no—
18C2×#66898C2212yescomplemented
19C2×#66897C2212yescomplemented
20#10622824—21no—
21#10622820—21no—
22#10622177—24no—
23#10622174—24no—
24C11×H(5,𝔽2)—42no—
25C11×H(5,𝔽2)—42no—
26C2×C11×#41—24no—
27C2×C11×#41—21no—
28C2×C11×#41—22no—
29C2×C11×#41—42no—
30C2×C11×#41—42no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—22no—
34C22×D4×C11C2×C411yescharacteristic
35C22×D4×C11C2×C412yes—
36C22×D4×C11D411yescharacteristic
37C22×D4×C11C2311yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C11×C4⋊Q8—22no—
42C11×#124—22no—
43C11×#123—24no—
44C11×#123—22no—
45C11×#123—22no—
46C11×#123—22no—
47C11×#123—22no—
48C11×#123—24no—
49C11×#123D414yes—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—24no—
52C11×#121—22no—
53C11×#121—24no—
54C11×#121—24no—
55C11×#120—22no—
56C11×#120—22no—
57C11×#120D414yes—
58C4×D4×C11—24no—
59C4×D4×C11—24no—
60C11×#117—21no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4C2×C412yes—
67C2×C22⋊Dic11—22no—
68C2×#4318—22no—
69#66900—42no—
70#66898—24no—
71#66898—42no—
72#66897—24no—
73C11⋊#95—42no—
74C22⋊(C11⋊C8)—42no—
75#12706—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11C22⋊C411yescharacteristic
78C24×C11C22⋊C412yes—
79C24×C11C22×C411yescharacteristic
80C24×C11C2×D411yescharacteristic
81C11×#41—42no—
82C11×#41—416no—
83C11×#41—48no—
84C11×#41—42no—
85C2×Q8×C11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—22no—
88C2×Q8×C11—41no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—21no—
93C2×D4×C11—22no—
94C2×D4×C11—22no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—24no—
98C2×D4×C11—22no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—48no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C2×D4×C11C2×D414yes—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11C22⋊C411yescharacteristic
122C22×C4×C11C22⋊C411yescharacteristic
123C22×C4×C11C22⋊C411yescharacteristic
124C22×C4×C11C22⋊C412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×Dic11—42no—
127C11×C4⋊C4—24no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—22no—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—24no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4C22⋊C414yes—
138C42×C11—22no—
139C22⋊Dic11—42no—
140C22⋊Dic11—42no—
141#4318—42no—
142#4318—42no—
143C2×C11⋊C8—42no—
144#3485D1111yescharacteristic
145#2121—114no—
146#1785—111no—
147#1782—111no—
148C23×C11—21no—
149C23×C11—21no—
150C23×C11—21no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—22no—
155C23×C11—42no—
156C23×C11—42no—
157C23×C11—81no—
158C23×C11—81no—
159C23×C11—81no—
160C23×C11—82no—
161C23×C11—82no—
162C23×C11#9912yes—
163C23×C11C2×C22⋊C412yes—
164C23×C11C2×C22⋊C411yescharacteristic
165C23×C11#12012yes—
166Q8×C11—44no—
167Q8×C11—42no—
168D4×C11—28no—
169D4×C11—44no—
170D4×C11—42no—
171D4×C11—44no—
172D4×C11—44no—
173D4×C11—44no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—84no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—24no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—44no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—82no—
196C2×C4×C11—82no—
197C2×C4×C11#9912yes—
198C2×C4×C11#12012yes—
199C2×Dic11—82no—
200C2×Dic11—84no—
201C11⋊C8—82no—
202C2×H(5,𝔽2)Dic1111yescharacteristic, complemented
203C22×#41C2×D1111yescharacteristic
204#547—24no—
205#546—24no—
206#536—21no—
207#534—21no—
208#534C2×D1112yes—
209#525—21no—
210C2×#123—21no—
211C2×#123Dic1112yescomplemented
212#518Dic1111yescharacteristic, complemented
213C2×#101—221no—
214C2×#100—112no—
215C2×#99—112no—
216C2×#99—221no—
217#407—221no—
218#381—221no—
219#352—224no—
220AΣL(1,𝔽16)—224no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—22no—
224C22×C11—41no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—44no—
231C22×C11—42no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—81no—
235C22×C11—81no—
236C22×C11—162no—
237C22×C11—162no—
238C22×C11#37911yescharacteristic
239C22×C11C2×#9911yescharacteristic
240C22×C11C2×#9911yescharacteristic
241C4×C11—22no—
242C4×C11—22no—
243C4×C11—44no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11—42no—
247Dic11—162no—
248H(5,𝔽2)—42no—
249H(5,𝔽2)—42no—
250C2×#41—24no—
251C2×#41—21no—
252C2×#41—22no—
253C2×#41—42no—
254C2×#41—42no—
255C22×Q8C22⋊D1111yescharacteristic
256C22×D4—21no—
257C22×D4—22no—
258C22×D4C2×Dic1111yescharacteristic
259C22×D4C2×Dic1112yes—
260C22×D4C22⋊D1111yescharacteristic
261C22×D4C22×D1111yescharacteristic
262C23×C4C2×Dic1111yescharacteristic
263C23×C4C22⋊D1111yescharacteristic
264C23×C4C22⋊D1111yescharacteristic
265C2×M16—222no—
266C4⋊Q8—22no—
267#124—22no—
268#123—24no—
269#123—22no—
270#123—22no—
271#123—22no—
272#123—22no—
273#123—24no—
274#123C22⋊D1114yes—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277#121—22no—
278#121—24no—
279#121—24no—
280#120—22no—
281#120—22no—
282#120C22⋊D1114yes—
283C4×D4—24no—
284C4×D4—24no—
285#117—21no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—22no—
291C2×C22⋊C4—222no—
292C2×C22⋊C4C2×Dic1112yes—
293#101—442no—
294#100—224no—
295#99—224no—
296#99—442no—
297C22⋊C8—442no—
298#95—442no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—42no—
303C2×C11—42no—
304C2×C11—42no—
305C2×C11—82no—
306C2×C11#178111yescharacteristic
307C24—21no—
308C24C22⋊Dic1111yescharacteristic
309C24C22⋊Dic1112yes—
310C24C22×Dic1111yescharacteristic
311C24C2×C22⋊D1111yescharacteristic
312#41—42no—
313#41—416no—
314#41—48no—
315#41—42no—
316C2×Q8—21no—
317C2×Q8—22no—
318C2×Q8—22no—
319C2×Q8—41no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—21no—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—22no—
327C2×D4—22no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—41no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—48no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4C2×C22⋊D1114yes—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—442no—
353C22×C4C22⋊Dic1111yescharacteristic
354C22×C4C22⋊Dic1111yescharacteristic
355C22×C4C22⋊Dic1111yescharacteristic
356C22×C4C22⋊Dic1112yes—
357C22×C4C2×C22⋊D1111yescharacteristic
358M16—442no—
359M16—442no—
360C2×C8—442no—
361C4⋊C4—24no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—22no—
367C22⋊C4—24no—
368C22⋊C4—22no—
369C22⋊C4—24no—
370C22⋊C4—24no—
371C22⋊C4—442no—
372C22⋊C4—442no—
373C22⋊C4C22⋊Dic1114yes—
374C42—22no—
375C11#1270611yescharacteristic, complemented, Sylow
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—22no—
383C23—42no—
384C23—42no—
385C23—81no—
386C23—81no—
387C23—81no—
388C23—82no—
389C23—82no—
390C23#6689812yes—
391C23C2×C22⋊Dic1112yes—
392C23C2×C22⋊Dic1111yescharacteristic
393C23#6700612yes—
394Q8—44no—
395Q8—42no—
396D4—28no—
397D4—44no—
398D4—42no—
399D4—44no—
400D4—44no—
401D4—44no—
402D4—42no—
403D4—42no—
404D4—84no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4—82no—
425C2×C4—882no—
426C2×C4—884no—
427C2×C4#6689812yes—
428C2×C4#6700612yes—
429C8—882no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—41no—
434C22—42no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—44no—
440C22—42no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—162no—
446C22—162no—
447C22C2×#6689811yescharacteristic
448C22C2×#6689811yescharacteristic
449C22#1062286011yescharacteristic
450C4—22no—
451C4—22no—
452C4—44no—
453C4—41no—
454C4—41no—
455C4—42no—
456C4—1762no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—42no—
461C2—42no—
462C2—42no—
463C2—82no—
464C2#1306853111yescharacteristic
subgroupG/H
centerC2#13068531
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC11×#3485C2
socleC2×C11#1781
cosocleC22×D4×C11C23
hypercenter#3485D11
hypocenterC11#12706
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C23 ◁ C22×#41 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #13070262C2semidirect
2. #13068544C2semidirect
3. #13068534C2semidirect
5. C2×C11×H(5,𝔽2)C4semidirect
14. C2×C11×#123C4semidirect
15. C11×#518C4semidirect
18. C2×#66898C22semidirect
19. C2×#66897C22semidirect
202. C2×H(5,𝔽2)Dic11semidirect
211. C2×#123Dic11semidirect
212. #518Dic11semidirect
375. C11#12706semidirect

Maximal subgroups

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

subgroupindex
#130702622
#130685442
#130685342
C11×#34852
#1270611