Finite Group Databasebeta

← #14808161

Subgroups — #14808161

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622677C211yesmaximal, characteristic, complemented
2C2×#10622695C211yesmaximal, characteristic, complemented
3#13074446C211yesmaximal, characteristic
4#13069816C212yesmaximal
5#13069809C212yesmaximal
6#13069586C211yesmaximal, characteristic, complemented
7#13069419C211yesmaximal, characteristic, complemented
8#13068884C212yesmaximal, complemented
9#13068870C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic
11C2×C11×#541C211yesmaximal, characteristic
12C11×#541—24no—
13C11×#541—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—22no—
16C2×C11×#125—22no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622825C2212yes—
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622695—24no—
30#10622677—24no—
31#10622597—22no—
32C2×#66872C2212yes—
33C2×#66871C2212yes—
34#10622561—22no—
35#10622548C2211yescharacteristic
36#10622541C2212yes—
37C2×#66867C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2211yescharacteristic
42#10622162C2211yescharacteristic
43C22×Q8×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8D414yes—
47C11×#126—216no—
48C11×#125—216no—
49C11×#125—22no—
50C11×#125D414yes—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C4×Q8×C11—24no—
54C4×Q8×C11—24no—
55C11×#117—22no—
56C11×#117—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4D412yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D412yes—
65C2×C42×C11—22no—
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78#66923—22no—
79#66923—22no—
80#66899—24no—
81#66899—24no—
82#66899—24no—
83#66899—24no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C22⋊(C11⋊C8)—22no—
87C22⋊(C11⋊C8)—22no—
88#66872—24no—
89#66871—24no—
90#66867—22no—
91C4×C11⋊C8—22no—
92#25683—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11C2×D414yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—22no—
113C22×Dic11—22no—
114C11×C4⋊C4—28no—
115C11×C4⋊C4—28no—
116C11×C4⋊C4—28no—
117C11×C4⋊C4—28no—
118C11×C4⋊C4—24no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4C2×D414yes—
121C11×C22⋊C4—28no—
122C11×C22⋊C4—24no—
123C42×C11—28no—
124C42×C11—21no—
125C42×C11—21no—
126C42×C11C2×D412yes—
127C42×C11C2×D412yes—
128C22⋊Dic11—82no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—22no—
132C4⋊Dic11—22no—
133C4⋊Dic11—82no—
134Dic11⋊C4—44no—
135Dic11⋊C4—82no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—21no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8—21no—
146C2×C11⋊C8#4112yes—
147C2×C11⋊C8#4112yes—
148C2×#541D1111yescharacteristic
149C2×#499—111no—
150C2×#491—111no—
151#2629—111no—
152#2036—112no—
153#2035—112no—
154#1992—111no—
155#1956—111no—
156#1865—112no—
157#1863—112no—
158#1750—111no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11C22×D411yescharacteristic
165Q8×C11—24no—
166Q8×C11—24no—
167Q8×C11—42no—
168Q8×C11—42no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11#12014yes—
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C112−1+411yescharacteristic
193C2×C4×C112−1+411yescharacteristic
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C11⋊C8—22no—
201C11⋊C8—22no—
202C11⋊C8—41no—
203C11⋊C8—41no—
204#541—24no—
205#541—24no—
206C2×C4⋊Q8C2×D1111yescharacteristic
207C2×#126—22no—
208C2×#125—22no—
209C2×#125—111no—
210C2×#125C2×D1111yescharacteristic
211C2×C22⋊Q8C2×D1112yes—
212C2×C4×Q8C2×D1112yes—
213C2×#117C2×D1111yescharacteristic
214#499—224no—
215#491—224no—
216C2×#107—112no—
217C2×#106—112no—
218C2×#103—112no—
219C2×#103—112no—
220C2×#103—112no—
221C2×#103—112no—
222C2×C22⋊C8—111no—
223C2×C22⋊C8—111no—
224C2×#97—111no—
225C2×C4×C8—111no—
226#398—222no—
227#396—222no—
228#389—112no—
229#384—111no—
230#380—112no—
231#340—112no—
232#340—112no—
233#336—111no—
234#336—111no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—42no—
239C22×C11—42no—
240C22×C11C2×#12011yescharacteristic
241C22×C11#53211yescharacteristic
242C22×C11#53611yescharacteristic
243C22×C11#57712yes—
244C22×C11#57812yes—
245C4×C11—24no—
246C4×C11—41no—
247C4×C11—44no—
248C4×C11—42no—
249C4×C11—44no—
250C4×C11#54711yescharacteristic
251C4×C11#54711yescharacteristic
252C4×C11#54811yescharacteristic
253C4×C11#54811yescharacteristic
254Dic11—82no—
255Dic11—82no—
256C22×Q8C22×D1112yes—
257C23×C4C22×D1111yescharacteristic
258C22×C8—111no—
259C22×C8—111no—
260C22×C8—111no—
261C22×C8—111no—
262C4⋊Q8—22no—
263C4⋊Q8C22⋊D1114yes—
264#126—216no—
265#125—216no—
266#125—22no—
267#125—222no—
268#125—222no—
269#125C22⋊D1114yes—
270C22⋊Q8—24no—
271C22⋊Q8—24no—
272C4×Q8—24no—
273C4×Q8—24no—
274#117—22no—
275#117—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—112no—
281C2×C4⋊C4—112no—
282C2×C4⋊C4—222no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4C22⋊D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4C22⋊D1112yes—
290C2×C42—22no—
291C2×C42C22×D1111yescharacteristic
292C2×C42C22×D1111yescharacteristic
293#107—224no—
294#106—224no—
295#103—224no—
296#103—224no—
297#103—224no—
298#103—224no—
299C22⋊C8—222no—
300C22⋊C8—222no—
301#97—222no—
302C4×C8—222no—
303#95—222no—
304#95—222no—
305C2×C11—81no—
306C2×C11#243211yescharacteristic
307C2×C11#301312yes—
308C2×C11#317411yescharacteristic
309C2×C11#317711yescharacteristic
310C2×C11#324212yes—
311C24C2×C22⋊D1111yescharacteristic
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—22no—
315C2×Q8—22no—
316C2×Q8—22no—
317C2×Q8C2×C22⋊D1114yes—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4C2×C22⋊D1111yescharacteristic
329C22×C4C2×C22⋊D1112yes—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C23×D1111yescharacteristic
332C2×C8—112no—
333C2×C8—112no—
334C2×C8—221no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—221no—
343C2×C8—221no—
344C4⋊C4—28no—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—24no—
349C4⋊C4—22no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—444no—
355C4⋊C4—882no—
356C4⋊C4—882no—
357C4⋊C4C2×C22⋊D1114yes—
358C22⋊C4—28no—
359C22⋊C4—24no—
360C22⋊C4—882no—
361C42—28no—
362C42—21no—
363C42—21no—
364C42C2×C22⋊D1112yes—
365C42C2×C22⋊D1112yes—
366C11#2568311yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23—21no—
372C23C22×C22⋊D1111yescharacteristic
373Q8—24no—
374Q8—24no—
375Q8—42no—
376Q8—42no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—21no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4#6700614yes—
402C2×C4#41×D1111yescharacteristic
403C2×C4#41×D1111yescharacteristic
404C2×C4#6704311yescharacteristic
405C2×C4#6704311yescharacteristic
406C2×C4C22×C22⋊D1111yescharacteristic
407C2×C4C22×C22⋊D1111yescharacteristic
408C8—222no—
409C8—222no—
410C8—441no—
411C8—441no—
412C22—42no—
413C22—41no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22#1062335611yescharacteristic
418C22#1062336311yescharacteristic
419C22#1062336812yes—
420C22#1062336912yes—
421C22C2×#6700611yescharacteristic
422C4—24no—
423C4—41no—
424C4—44no—
425C4—42no—
426C4—44no—
427C4—882no—
428C4—882no—
429C4#1062335511yescharacteristic
430C4#1062335511yescharacteristic
431C4#1062336211yescharacteristic
432C4#1062336211yescharacteristic
433C2—81no—
434C2#1307224011yescharacteristic
435C2#1307793112yes—
436C2#1307924511yescharacteristic
437C2#1307926911yescharacteristic
438C2#1307987812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#541C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#541D11
hypocenterC11#25683
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×#10622677C2semidirect
2. C2×#10622695C2semidirect
6. #13069586C2semidirect
7. #13069419C2semidirect
8. #13068884C2semidirect
9. #13068870C2semidirect
366. C11#25683semidirect

Maximal subgroups

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

subgroupindex
C2×#106226772
C2×#106226952
#130744462
#130698162
#130698092
#130695862
#130694192
#130688842
#130688702
#130683822
C2×C11×#5412
#2568311