Finite Group Databasebeta

← #14812695

Subgroups — #14812695

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079155C211yesmaximal, characteristic, complemented
2#13078466C212yesmaximal
3#13077212C211yesmaximal, characteristic
4#13070125C212yesmaximal, complemented
5#13069959C212yesmaximal, complemented
6#13069362C211yesmaximal, characteristic, complemented
7#13068845C212yesmaximal
8#13068774C211yesmaximal, characteristic, complemented
9#13068677C211yesmaximal, characteristic
10#13068455C211yesmaximal, characteristic
11C11×#1952C211yesmaximal, characteristic, complemented
12C2×#66954C2211yescharacteristic
13#10623050C2212yes—
14#10623035C2212yes—
15C2×C11×#108C2211yescharacteristic
16C11×#428C2212yes—
17C2×C11×#107C2211yescharacteristic
18C11×#405C2211yescharacteristic
19C2×#66889C2211yescharacteristic
20#10622746C2212yes—
21#10622734C2212yes—
22#10622732C2212yes—
23#10622719C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×C8×Dic11C2211yescharacteristic
26#10622615C2211yescharacteristic
27#10622589C2212yes—
28#10622577C2212yes—
29C2×#66871C2212yes—
30#10622503—22no—
31#10622494—22no—
32#10622493—21no—
33D11×#107—21no—
34#10622488—22no—
35#10622484—22no—
36#10622470—22no—
37#10622315—22no—
38#10622296—21no—
39#10622295—21no—
40C11×#343C2212yes—
41#10622196C2211yescharacteristic
42#10622193C2212yes—
43#10622192C2212yes—
44#10622170C2211yescharacteristic
45C2×#4339C2311yescharacteristic
46C2×C11×M16C2312yes—
47C2×C11×M16C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#117C2311yescharacteristic
50C2×C11×C4⋊C4C2312yes—
51C4×C22⋊D11—42no—
52#66979C2312yes—
53C2×C4⋊Dic11C2312yes—
54C2×Dic11⋊C4—42no—
55C2×C4×Dic11C2311yescharacteristic
56C2×#4318C2311yescharacteristic
57C22×C11⋊C8C2311yescharacteristic
58#66954—22no—
59#66954Q814yescomplemented
60C2×#4313—21no—
61C2×C8×D11—21no—
62#66946—22no—
63#66945—22no—
64C4⋊C4×D11—22no—
65#66943—22no—
66#66941—22no—
67#66940—22no—
68#66931—42no—
69#66923—22no—
70#66922—22no—
71C11×#108—22no—
72C11×#107—21no—
73C11×#107—21no—
74C11×#107—22no—
75C11×#106—22no—
76C11×#97—21no—
77C4×C8×C11—21no—
78#66889Q814yescomplemented
79#66885—22no—
80#66882—21no—
81#66882—21no—
82#66882—22no—
83#66882D411yescharacteristic
84#66882D411yescharacteristic
85#66881—22no—
86#66881D412yes—
87#66880—22no—
88Dic11⋊C8—22no—
89Dic11⋊C8—22no—
90C8×Dic11—22no—
91#66874D411yescharacteristic
92#66874D411yescharacteristic
93#66873D411yescharacteristic
94#66873D411yescharacteristic
95#66872—22no—
96#66871—22no—
97#66871—22no—
98#66871—22no—
99#26083—111nomaximal, Sylow
100C22×C4×C11—22no—
101C22×C4×C11C2411yescharacteristic
102C2×C22⋊D11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105#4339—21no—
106#4339—21no—
107#4339C2×Q812yes—
108#4339C2×Q812yes—
109C2×D44C2×D411yescharacteristic
110C2×C4×D11—21no—
111C2×C4×D11—42no—
112C2×Dic22—42no—
113C2×Dic22C2×D411yescharacteristic
114C11×M16—22no—
115C11×M16—21no—
116C11×M16—22no—
117C11×M16C2×Q812yes—
118C2×C8×C11—21no—
119C2×C8×C11—22no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×Q812yes—
123C2×C8×C11#4112yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C22⋊C4—21no—
129C42×C11—21no—
130C22⋊Dic11—22no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—42no—
135C4⋊Dic11C2×D412yes—
136C4⋊Dic11C2×D412yes—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139Dic11⋊C4—42no—
140Dic11⋊C4—84no—
141C4×Dic11—22no—
142C4×Dic11—21no—
143C4×Dic11—42no—
144C4×Dic11C2×Q812yes—
145#4318—21no—
146#4318C2×Q812yes—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C2×D411yescharacteristic
151C2×C11⋊C8C2×D411yescharacteristic
152#4313—24no—
153C8×D11—24no—
154#3164—111no—
155#3083—112no—
156#2913—111no—
157#2089—112no—
158#2060—112no—
159#1952D1111yescharacteristic, complemented
160#1945—111no—
161#1859—112no—
162#1845—111no—
163#1816—111no—
164#1764—111no—
165C23×C11H(5,𝔽2)11yescharacteristic
166C22×D11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—42no—
170C2×C4×C11—82no—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×Q811yescharacteristic
174C2×C4×C11C22×Q811yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C2×C4×C112−1+411yescharacteristic
177C22⋊D11—22no—
178C22⋊D11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—21no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—42no—
186C2×Dic11—82no—
187D44—21no—
188D44C4⋊Q812yes—
189C4×D11—22no—
190C4×D11—22no—
191C4×D11—162no—
192Dic22—21no—
193Dic22—162no—
194Dic22C4⋊Q812yes—
195C8×C11—22no—
196C8×C11—42no—
197C8×C11C22⋊Q812yes—
198C8×C11C22⋊Q812yes—
199C11⋊C8—22no—
200C11⋊C8—21no—
201C11⋊C8—21no—
202C2×#131—111no—
203#544—112no—
204#520—112no—
205#501—222no—
206#500—221no—
207#499—221no—
208#479—222no—
209#478—222no—
210#477—222no—
211#474—222no—
212C2×#108C2×D1111yescharacteristic
213#428—112no—
214#428—112no—
215#428—222no—
216#428C2×D1112yes—
217#427—111no—
218#427—221no—
219C2×#107—111no—
220C2×#107—112no—
221C2×#107—221no—
222C2×#107C2×D1111yescharacteristic
223#424—112no—
224C2×#104—111no—
225#417—112no—
226#416—111no—
227#405C2×D1111yescharacteristic
228C2×C4×C8—111no—
229#384—112no—
230#343—112no—
231#343C2×D1112yes—
232#341—111no—
233#339—112no—
234#339—111no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11#54411yescharacteristic
238C22×C11D4211yescharacteristic
239C22×C11#55411yescharacteristic
240C2×D11—22no—
241C2×D11—41no—
242C2×D11—41no—
243C4×C11—41no—
244C4×C11—41no—
245C4×C11—82no—
246C4×C11C2×C22⋊Q811yescharacteristic
247C4×C11C2×C4⋊Q811yescharacteristic
248C4×C11#54711yescharacteristic
249C4×C11D4×Q811yescharacteristic
250Dic11—24no—
251Dic11—22no—
252Dic11—42no—
253Dic11—42no—
254Dic11—82no—
255C2×#41—111no—
256#131—114no—
257#131—222no—
258C2×M16—111no—
259C2×M16—221no—
260C2×M16C22×D1112yes—
261C2×M16C22×D1111yescharacteristic
262C22×C8—111no—
263C22×C8—221no—
264C22×C8C22×D1111yescharacteristic
265C4⋊Q8—222no—
266C4⋊Q8—222no—
267#125—222no—
268#125—222no—
269C22⋊Q8—442no—
270C4×Q8—222no—
271C4×D4—222no—
272C4×D4—442no—
273#117—112no—
274#117—222no—
275#117C22×D1111yescharacteristic
276C2×C4⋊C4—112no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—442no—
279C2×C4⋊C4C22×D1112yes—
280C2×C42—111no—
281#108—22no—
282#107—21no—
283#107—21no—
284#107—22no—
285#107—111no—
286#107—111no—
287#107—222no—
288#107—222no—
289#107—222no—
290#107—222no—
291#107—221no—
292#107—221no—
293#106—22no—
294#106—112no—
295#106—222no—
296#106—222no—
297C4⋊C8—222no—
298C4⋊C8—222no—
299#104—114no—
300#103—111no—
301#103—111no—
302#103—222no—
303#102—111no—
304#102—111no—
305#102—222no—
306#97—21no—
307C4×C8—21no—
308C4×C8—222no—
309C2×C11—21no—
310C2×C11—21no—
311C2×C11#244011yescharacteristic
312C2×C11#329211yescharacteristic
313C2×C11#329311yescharacteristic
314D11—42no—
315#41—112no—
316#41—112no—
317#41—221no—
318#41—221no—
319C2×Q8—111no—
320C2×Q8—442no—
321C2×D4—111no—
322C2×D4—221no—
323C22×C4—22no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—222no—
327C22×C4—442no—
328C22×C4C23×D1111yescharacteristic
329M16—21no—
330M16—22no—
331M16—22no—
332M16—112no—
333M16—221no—
334M16—224no—
335M16Q8×D1112yes—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—111no—
339C2×C8—111no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—221no—
343C2×C8—224no—
344C2×C8#433912yes—
345C2×C8D4×D1111yescharacteristic
346C2×C8D4×D1111yescharacteristic
347C2×C8Q8×D1112yes—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—112no—
351C4⋊C4—112no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—442no—
355C4⋊C4—442no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—884no—
359C4⋊C4D4×D1111yescharacteristic
360C4⋊C4D4×D1111yescharacteristic
361C22⋊C4—21no—
362C22⋊C4—222no—
363C22⋊C4—442no—
364C42—21no—
365C42—112no—
366C42—221no—
367C42—222no—
368C42—442no—
369C11#2608311yescharacteristic, complemented, Sylow
370C23—221no—
371C23#6704211yescharacteristic
372Q8—112no—
373Q8—221no—
374Q8—1762no—
375D4—112no—
376D4—222no—
377D4—222no—
378D4—221no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—82no—
383C2×C4—222no—
384C2×C4—222no—
385C2×C4—222no—
386C2×C4—221no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—442no—
392C2×C4—882no—
393C2×C4—1762no—
394C2×C4C2×#433911yescharacteristic
395C2×C4C2×D4×D1111yescharacteristic
396C2×C4C2×D4×D1111yescharacteristic
397C2×C4C2×Q8×D1111yescharacteristic
398C2×C4C2×Q8×D1111yescharacteristic
399C2×C4#6704311yescharacteristic
400C8—22no—
401C8—42no—
402C8—222no—
403C8—221no—
404C8—221no—
405C8#6694912yes—
406C8#6694912yes—
407C22—21no—
408C22—21no—
409C22—222no—
410C22—441no—
411C22—441no—
412C22#1062311011yescharacteristic
413C22#1062314011yescharacteristic
414C22#1062322011yescharacteristic
415C4—41no—
416C4—41no—
417C4—82no—
418C4—224no—
419C4—222no—
420C4—442no—
421C4—442no—
422C4—882no—
423C4C2×#6694911yescharacteristic
424C4#1062308211yescharacteristic
425C4#1062316311yescharacteristic
426C4D11×C4⋊Q811yescharacteristic
427C2—21no—
428C2—21no—
429C2—442no—
430C2#1307232011yescharacteristic
431C2#1308041411yescharacteristic
432C2#1308041911yescharacteristic
subgroupG/H
centerC22#10623140
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1952C2
socleC22×C11D42
prime radicalC2×#4339C23
hypercenter#1952D11
hypocenterC11#26083
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1952

Complements

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

NH ≅ G/Ntype
1. #13079155C2semidirect
4. #13070125C2semidirect
5. #13069959C2semidirect
6. #13069362C2semidirect
8. #13068774C2semidirect
11. C11×#1952C2semidirect
59. #66954Q8semidirect
78. #66889Q8semidirect
159. #1952D11semidirect
369. C11#26083semidirect

Maximal subgroups

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

subgroupindex
#130791552
#130784662
#130772122
#130701252
#130699592
#130693622
#130688452
#130687742
#130686772
#130684552
C11×#19522
#2608311