Finite Group Databasebeta

← #14770877

Subgroups — #14770877

Order 2816.

962 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66899C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic
3#13069309C212yesmaximal, complemented
4#13069247C212yesmaximal, complemented
5#13068884C212yesmaximal, complemented
6#13068704C211yesmaximal, characteristic
7#13068639C211yesmaximal, characteristic
8#13068551C211yesmaximal, characteristic
9#13068446C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic
11Q8×C11×C22⋊C4C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C22×C4⋊Dic11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C11×#391—22no—
17C11×#391C2212yes—
18C11×#380—21no—
19C11×#380C2211yescharacteristic
20C4×C11×C22⋊C4—21no—
21C4×C11×C22⋊C4C2211yescharacteristic
22C2×#66899C418yescomplemented
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66872C2212yes—
32#10622555—21no—
33C22⋊C4×Dic11—21no—
34C4×C4⋊Dic11C2212yes—
35#10622541C2212yes—
36C2×#66867C2212yes—
37#10622267—22no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2212yes—
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—42no—
46C22×Q8×C11C2×C414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C4×Q8×C11—24no—
53C4×Q8×C11—42no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4D411yescharacteristic
58C2×C11×C22⋊C4D411yescharacteristic
59C2×C42×C11—22no—
60C2×C42×C11C2312yes—
61C2×C22⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2×C414yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—22no—
70C22×C11⋊C8—42no—
71C22×C11⋊C8C2×C414yes—
72C22×C11⋊C8C2312yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C11×#95—22no—
76C11×#95—22no—
77C11×#95—21no—
78C11×#95D412yes—
79#66899—24no—
80#66899—42no—
81#66899C2×C414yes—
82#66899C2×C414yes—
83#66899C2×C414yes—
84#66899C2×C414yes—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C22⋊(C11⋊C8)—22no—
89#66872—42no—
90#66867—42no—
91#22567—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—28no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—44no—
101C2×Q8×C11—44no—
102C2×Q8×C11—48no—
103C2×Q8×C11C22×C412yes—
104C2×Q8×C11C22×C412yes—
105C2×Q8×C11#4114yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—24no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4112yes—
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—24no—
120C22×Dic11—21no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—82no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—44no—
127C11×C22⋊C4—22no—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—42no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—44no—
133C22⋊Dic11—42no—
134C4⋊Dic11—24no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—22no—
138C4⋊Dic11—22no—
139C4⋊Dic11C22×C412yes—
140C4⋊Dic11C22×C412yes—
141Dic11⋊C4—82no—
142C4×Dic11—82no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—44no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C22×C412yes—
151C22×#103—111no—
152#2345—111no—
153Q8×C22⋊C4D1111yescharacteristic
154#1935—112no—
155#1927—112no—
156#1865—112no—
157#1824—111no—
158#1807—111no—
159#1787—111no—
160#1763—112no—
161#1752—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C4×D412yes—
165C23×C11#13712yes—
166C23×C11#13712yes—
167C23×C11C22×D411yescharacteristic
168Q8×C11—22no—
169Q8×C11—24no—
170Q8×C11—22no—
171Q8×C11—22no—
172Q8×C11—48no—
173Q8×C11—42no—
174Q8×C11#11714yes—
175C2×C4×C11—22no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—48no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11C4×D412yes—
194C2×C4×C11C23×C411yescharacteristic
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4112yes—
197C2×C4×C11H(5,𝔽2)12yes—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—84no—
206C11⋊C8—22no—
207C11⋊C8—22no—
208C11⋊C8—42no—
209C23×Q8C2×D1111yescharacteristic
210C23×C8—111no—
211C2×C4×Q8C2×D1112yes—
212C22×C4⋊C4—111no—
213C2×#106—112no—
214C2×#103—111no—
215C2×#103—111no—
216C2×#103—111no—
217C2×#103—111no—
218C2×#103—118no—
219C2×#103—112no—
220C2×#103—112no—
221C2×C22⋊C8—111no—
222C2×#97—112no—
223#391—22no—
224#391C2×D1112yes—
225#389—112no—
226#387—222no—
227#380—21no—
228#380—111no—
229#380—221no—
230#380C2×D1111yescharacteristic
231C4×C4⋊C4—112no—
232C4×C22⋊C4—21no—
233C4×C22⋊C4—221no—
234C4×C22⋊C4C2×D1111yescharacteristic
235#340—112no—
236#340—112no—
237#340—112no—
238#336—112no—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—24no—
242C22×C11—24no—
243C22×C11#44114yes—
244C22×C11C2×C4×D411yescharacteristic
245C22×C11#54612yes—
246C22×C11C2×#13711yescharacteristic
247C22×C11C2×#13711yescharacteristic
248C22×C11#57712yes—
249C4×C11—22no—
250C4×C11—24no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11C2×#11711yescharacteristic
256C4×C11#51811yescharacteristic
257C4×C11#55112yes—
258Dic11—42no—
259Dic11—42no—
260Dic11—82no—
261C22×Q8—22no—
262C22×Q8—21no—
263C22×Q8—24no—
264C22×Q8—42no—
265C22×Q8C4×D1114yes—
266C22×Q8C22×D1111yescharacteristic
267C22×Q8C22×D1111yescharacteristic
268C23×C4—21no—
269C23×C4—221no—
270C23×C4C22×D1111yescharacteristic
271C22×C8—111no—
272C22×C8—111no—
273C22×C8—114no—
274C22×C8—112no—
275C22×C8—442no—
276C4×Q8—24no—
277C4×Q8—42no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—114no—
280C2×C4⋊C4—111no—
281C2×C4⋊C4—111no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4—222no—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—21no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4C22⋊D1111yescharacteristic
290C2×C22⋊C4C22⋊D1111yescharacteristic
291C2×C42—22no—
292C2×C42—222no—
293C2×C42C22×D1112yes—
294#106—442no—
295#103—114no—
296#103—114no—
297#103—114no—
298#103—114no—
299#103—224no—
300#103—442no—
301C22⋊C8—222no—
302#97—442no—
303#95—22no—
304#95—22no—
305#95—21no—
306#95—222no—
307#95—222no—
308#95—221no—
309#95C22⋊D1112yes—
310C2×C11—24no—
311C2×C11#234211yescharacteristic
312C2×C11C2×#44111yescharacteristic
313C2×C11#294911yescharacteristic
314C2×C11#331612yes—
315C2×C11#332012yes—
316C24C2×C22⋊D1111yescharacteristic
317C2×Q8—24no—
318C2×Q8—21no—
319C2×Q8—21no—
320C2×Q8—22no—
321C2×Q8—28no—
322C2×Q8—22no—
323C2×Q8—22no—
324C2×Q8—44no—
325C2×Q8—44no—
326C2×Q8—48no—
327C2×Q8C2×C4×D1112yes—
328C2×Q8C2×C4×D1112yes—
329C2×Q8#434114yes—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—44no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—224no—
340C22×C4—222no—
341C22×C4—882no—
342C22×C4C2×C4×D1112yes—
343C22×C4#433912yes—
344C22×C4C2×C22⋊D1112yes—
345C22×C4C2×C22⋊D1112yes—
346C22×C4C2×C22⋊D1111yescharacteristic
347C22×C4C23×D1111yescharacteristic
348C2×C8—112no—
349C2×C8—112no—
350C2×C8—222no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—444no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—44no—
359C4⋊C4—112no—
360C4⋊C4—112no—
361C4⋊C4—224no—
362C4⋊C4—221no—
363C4⋊C4—221no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—882no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—42no—
370C22⋊C4—442no—
371C42—22no—
372C42—22no—
373C42—44no—
374C42—882no—
375C11#2256711yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23C4×C22⋊D1112yes—
379C23#6699512yes—
380C23#6700412yes—
381C23C22×C22⋊D1111yescharacteristic
382Q8—22no—
383Q8—24no—
384Q8—22no—
385Q8—22no—
386Q8—48no—
387Q8—42no—
388Q8#6693014yes—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—48no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—884no—
415C2×C4C4×C22⋊D1112yes—
416C2×C4C22×C4×D1111yescharacteristic
417C2×C4C2×#433911yescharacteristic
418C2×C4C2×#434112yes—
419C2×C4#6703712yes—
420C8—222no—
421C8—222no—
422C8—442no—
423C22—22no—
424C22—24no—
425C22—24no—
426C22—22no—
427C22#1062264314yes—
428C22C2×C4×C22⋊D1111yescharacteristic
429C22#1062333712yes—
430C22C2×#6699511yescharacteristic
431C22C2×#6700411yescharacteristic
432C22#1062336812yes—
433C4—22no—
434C4—24no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4—442no—
440C4—442no—
441C4—882no—
442C4C2×#6693011yescharacteristic
443C4#1062301711yescharacteristic
444C4#1062302612yes—
445C2—24no—
446C2#1307146111yescharacteristic
447C2C2×#1062264311yescharacteristic
448C2#1307747511yescharacteristic
449C2#1308072712yes—
450C2#1308078712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterQ8×C22⋊C4D11
hypocenterC11#22567
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #13069309C2semidirect
4. #13069247C2semidirect
5. #13068884C2semidirect
9. #13068446C2semidirect
22. C2×#66899C4semidirect
375. C11#22567semidirect

Maximal subgroups

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

subgroupindex
C22×#668992
#130714912
#130693092
#130692472
#130688842
#130687042
#130686392
#130685512
#130684462
#130683942
Q8×C11×C22⋊C42
#2256711