Finite Group Databasebeta

← #14812691

Subgroups — #14812691

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#13079156C211yesmaximal, characteristic, complemented
2#13078469C212yesmaximal
3#13077213C211yesmaximal, characteristic
4#13070121C212yesmaximal, complemented
5#13069960C212yesmaximal, complemented
6#13069402C211yesmaximal, characteristic, complemented
7#13068843C212yesmaximal
8#13068776C211yesmaximal, characteristic, complemented
9#13068677C211yesmaximal, characteristic
10#13068453C211yesmaximal, characteristic
11C11×#1945C211yesmaximal, characteristic, complemented
12C2×#66954C2211yescharacteristic
13#10623054C2212yes—
14#10623050C2212yes—
15C2×C11×#108C2211yescharacteristic
16C11×#427C2211yescharacteristic
17C11×#424C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19#10622746C2212yes—
20#10622734C2212yes—
21#10622726C2211yescharacteristic
22C2×#66882C2212yes—
23C2×#66882C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25#10622714C2211yescharacteristic
26#10622608C2212yes—
27#10622608C2212yes—
28#10622548C2212yes—
29C2×#66869C2211yescharacteristic
30#10622493—21no—
31D11×#107—21no—
32#10622491—21no—
33#10622487—21no—
34#10622474—22no—
35#10622469—22no—
36#10622463—22no—
37#10622460—22no—
38#10622459—22no—
39#10622442—22no—
40C11×#339C2212yes—
41#10622192C2212yes—
42#10622192C2212yes—
43#10622190C2211yescharacteristic
44#10622161C2211yescharacteristic
45C2×#4339C2311yescharacteristic
46C2×C11×M16C2312yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×#117C2312yes—
50C2×C42×C11C2311yescharacteristic
51#66979C2311yescharacteristic
52C2×C4⋊Dic11—42no—
53C2×C4⋊Dic11C2312yes—
54C2×C4⋊Dic11C2312yes—
55C2×#4318C2311yescharacteristic
56C2×#4318C2311yescharacteristic
57#66954—22no—
58#66954Q814yescomplemented
59C2×#4313—21no—
60C2×C8×D11—21no—
61#66945—22no—
62C4⋊C4×D11—22no—
63#66943—22no—
64#66941—22no—
65(C22⋊D11)⋊C4—42no—
66#66931—42no—
67C4×D44—22no—
68#66923—22no—
69#66922—22no—
70C4×Dic22—22no—
71C11×#108—22no—
72C11×#107D411yescharacteristic
73C11×#107D411yescharacteristic
74C11×#106D412yes—
75C11×C4⋊C8—22no—
76C11×C4⋊C8—22no—
77C4×C8×C11—22no—
78#66885—22no—
79#66885D411yescharacteristic
80#66885D411yescharacteristic
81#66882—21no—
82#66882—21no—
83#66882—21no—
84#66882—21no—
85#66882—22no—
86#66882—22no—
87#66882—22no—
88#66881—22no—
89#66880—22no—
90#66880D411yescharacteristic
91#66880D411yescharacteristic
92#66879—21no—
93C8×Dic11—21no—
94#66872—22no—
95#66872—22no—
96#66871—22no—
97#66871—22no—
98#66869Q814yescomplemented
99#26083—111nomaximal, Sylow
100C22×C4×C11—21no—
101C22×C4×C11C2411yescharacteristic
102C2×C22⋊D11—21no—
103C22×Dic11—22no—
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—22no—
116C2×C8×C11—22no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×Q812yes—
124C2×C8×C11#4112yes—
125C11×C4⋊C4C2×D412yes—
126C11×C4⋊C4C2×D412yes—
127C11×C22⋊C4—22no—
128C42×C11—22no—
129C42×C11—21no—
130C42×C11C2×Q812yes—
131C22⋊Dic11—21no—
132(C2×D11)⋊C4—42no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—42no—
138C4⋊Dic11—84no—
139C4⋊Dic11C2×D411yescharacteristic
140C4⋊Dic11C2×D411yescharacteristic
141Dic11⋊C4—42no—
142Dic11⋊C4—42no—
143Dic11⋊C4—42no—
144C4×Dic11—21no—
145C4×Dic11—42no—
146#4318—21no—
147#4318—21no—
148#4318C2×Q812yes—
149#4318C2×Q812yes—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152#4313—24no—
153C8×D11—24no—
154#3164—111no—
155#3083—112no—
156#2913—111no—
157#2089—112no—
158#2060—112no—
159#1952—111no—
160#1945D1111yescharacteristic, complemented
161#1859—112no—
162#1845—111no—
163#1816—111no—
164#1764—111no—
165C23×C11H(5,𝔽2)11yescharacteristic
166C22×D11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×Q811yescharacteristic
175C2×C4×C11C22×Q811yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C112−1+411yescharacteristic
178C22⋊D11—22no—
179C22⋊D11—22no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—82no—
186C2×Dic11—82no—
187D44—21no—
188D44C4⋊Q812yes—
189C4×D11—22no—
190C4×D11—22no—
191C4×D11—162no—
192Dic22—21no—
193Dic22—162no—
194Dic22C4⋊Q812yes—
195C8×C11—21no—
196C8×C11—21no—
197C8×C11—42no—
198C8×C11C22⋊Q812yes—
199C8×C11C22⋊Q812yes—
200C11⋊C8—22no—
201C11⋊C8—22no—
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—112no—
216#428—222no—
217#427—221no—
218#427C2×D1111yescharacteristic
219C2×#107—112no—
220C2×#107—111no—
221C2×#107—111no—
222C2×#107—221no—
223#424C2×D1112yes—
224C2×#104—111no—
225#417—112no—
226#416—111no—
227#405—111no—
228C2×C4×C8C2×D1111yescharacteristic
229#384—112no—
230#343—112no—
231#343—112no—
232#341—111no—
233#339—111no—
234#339C2×D1112yes—
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—24no—
244C4×C11—42no—
245C4×C11—42no—
246C4×C11C2×C22⋊Q811yescharacteristic
247C4×C11C2×C4⋊Q811yescharacteristic
248C4×C11#54711yescharacteristic
249C4×C11D4×Q811yescharacteristic
250Dic11—22no—
251Dic11—41no—
252Dic11—41no—
253Dic11—82no—
254Dic11—82no—
255C2×#41—111no—
256#131—114no—
257#131—222no—
258C2×M16—111no—
259C2×M16—111no—
260C2×M16—221no—
261C2×M16C22×D1112yes—
262C22×C8—221no—
263C22×C8C22×D1111yescharacteristic
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—111no—
274#117—222no—
275#117C22×D1112yes—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—442no—
280C2×C42C22×D1111yescharacteristic
281#108—22no—
282#107—222no—
283#107—221no—
284#107—221no—
285#107—221no—
286#107—221no—
287#107—222no—
288#107—222no—
289#107—222no—
290#107—222no—
291#107D4411yescharacteristic
292#107D4411yescharacteristic
293#106—222no—
294#106—222no—
295#106—222no—
296#106D4412yes—
297C4⋊C8—22no—
298C4⋊C8—22no—
299#104—114no—
300#103—111no—
301#103—111no—
302#103—222no—
303#102—111no—
304#102—111no—
305#102—222no—
306#97—221no—
307C4×C8—22no—
308C4×C8—221no—
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—21no—
324C22×C4—221no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4—442no—
328C22×C4C23×D1111yescharacteristic
329M16—22no—
330M16—22no—
331M16—112no—
332M16—112no—
333M16—221no—
334M16—221no—
335M16—224no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—22no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—224no—
342C2×C8C2×D4411yescharacteristic
343C2×C8C2×D4411yescharacteristic
344C2×C8D4×D1111yescharacteristic
345C2×C8D4×D1111yescharacteristic
346C2×C8#434112yes—
347C2×C8Q8×D1112yes—
348C4⋊C4—111no—
349C4⋊C4—111no—
350C4⋊C4—222no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—442no—
355C4⋊C4—442no—
356C4⋊C4—442no—
357C4⋊C4—442no—
358C4⋊C4—884no—
359C4⋊C4C2×D4412yes—
360C4⋊C4C2×D4412yes—
361C22⋊C4—22no—
362C22⋊C4—221no—
363C22⋊C4—442no—
364C42—22no—
365C42—21no—
366C42—221no—
367C42—442no—
368C42Q8×D1112yes—
369C11#2608311yescharacteristic, complemented, Sylow
370C23—221no—
371C23#6704211yescharacteristic
372Q8—112no—
373Q8—221no—
374Q8—1762no—
375D4—112no—
376D4—222no—
377D4—222no—
378D4—221no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—221no—
385C2×C4—222no—
386C2×C4—222no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—442no—
390C2×C4—442no—
391C2×C4—882no—
392C2×C4—882no—
393C2×C4—1762no—
394C2×C4C22×D4411yescharacteristic
395C2×C4C2×D4×D1111yescharacteristic
396C2×C4C2×#434111yescharacteristic
397C2×C4C2×Q8×D1111yescharacteristic
398C2×C4C2×Q8×D1111yescharacteristic
399C2×C4#6704311yescharacteristic
400C8—21no—
401C8—21no—
402C8—42no—
403C8—222no—
404C8—222no—
405C8#6695012yes—
406C8#6695012yes—
407C22—21no—
408C22—21no—
409C22—222no—
410C22—441no—
411C22—441no—
412C22D4×D4411yescharacteristic
413C22#1062316611yescharacteristic
414C22#1062322011yescharacteristic
415C4—24no—
416C4—42no—
417C4—42no—
418C4—222no—
419C4—441no—
420C4—441no—
421C4—882no—
422C4—882no—
423C4C2×#6695011yescharacteristic
424C4Q8×D4411yescharacteristic
425C4#1062314211yescharacteristic
426C4D11×C4⋊Q811yescharacteristic
427C2—21no—
428C2—21no—
429C2—442no—
430C2#1307231611yescharacteristic
431C2#1308041611yescharacteristic
432C2#1308042111yescharacteristic
subgroupG/H
centerC22D4×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1945C2
socleC22×C11D42
prime radicalC2×#4339C23
hypercenter#1945D11
hypocenterC11#26083
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1945

Complements

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

NH ≅ G/Ntype
1. #13079156C2semidirect
4. #13070121C2semidirect
5. #13069960C2semidirect
6. #13069402C2semidirect
8. #13068776C2semidirect
11. C11×#1945C2semidirect
58. #66954Q8semidirect
98. #66869Q8semidirect
160. #1945D11semidirect
369. C11#26083semidirect

Maximal subgroups

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

subgroupindex
#130791562
#130784692
#130772132
#130701212
#130699602
#130694022
#130688432
#130687762
#130686772
#130684532
C11×#19452
#2608311