Finite Group Databasebeta

← #14812696

Subgroups — #14812696

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#13079152C211yesmaximal, characteristic, complemented
2#13078472C212yesmaximal
3#13077212C211yesmaximal, characteristic
4#13070122C212yesmaximal, complemented
5#13069961C212yesmaximal, complemented
6#13069399C211yesmaximal, characteristic, complemented
7#13069364C211yesmaximal, characteristic, complemented
8#13068841C212yesmaximal
9#13068681C211yesmaximal, characteristic
10#13068453C211yesmaximal, characteristic
11C11×#1845C211yesmaximal, characteristic, complemented
12C2×#66954C2211yescharacteristic
13#10623035C2212yes—
14#10623031C2212yes—
15C2×C11×#107C2212yes—
16C2×C11×#107C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18C2×C4×C8×C11C2211yescharacteristic
19C11×#384C2212yes—
20#10622726C2211yescharacteristic
21C2×#66883C2211yescharacteristic
22#10622719C2211yescharacteristic
23#10622715C2212yes—
24#10622714C2211yescharacteristic
25#10622579C2212yes—
26#10622577C2212yes—
27#10622577C2212yes—
28#10622577C2212yes—
29C2×#66869C2211yescharacteristic
30#10622504—22no—
31#10622503—22no—
32#10622494—22no—
33#10622493—21no—
34D11×#107—21no—
35#10622491—21no—
36#10622490—22no—
37#10622489—22no—
38#10622488—22no—
39#10622487—21no—
40#10622190C2211yescharacteristic
41#10622168C2212yes—
42#10622168C2212yes—
43#10622161C2212yes—
44#10622161C2211yescharacteristic
45C2×#4339C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C2×C11×C4⋊C4—42no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52C4×C22⋊D11—42no—
53#66979C2311yescharacteristic
54#66979C2312yes—
55#66977—42no—
56C2×#4318C2312yes—
57C2×#4318C2311yescharacteristic
58C2×#4318C2311yescharacteristic
59#66954—22no—
60#66954Q814yescomplemented
61C2×#4313—21no—
62C2×C8×D11—21no—
63#66946—22no—
64#66945—22no—
65C4⋊C4×D11—22no—
66#66943—22no—
67#66943—22no—
68#66941—22no—
69#66941—22no—
70#66940—22no—
71C11×#107—21no—
72C11×#107—22no—
73C11×#107—21no—
74C11×#107—22no—
75C11×#107—21no—
76C11×#107—21no—
77C4×C8×C11—22no—
78#66885D411yescharacteristic
79#66885D411yescharacteristic
80#66883—22no—
81#66882D411yescharacteristic
82#66882D411yescharacteristic
83#66881D412yes—
84#66880D411yescharacteristic
85#66880D411yescharacteristic
86#66879—21no—
87Dic11⋊C8—22no—
88Dic11⋊C8—22no—
89C8×Dic11—21no—
90#66874—22no—
91#66873—22no—
92#66872—22no—
93#66872—22no—
94#66872—22no—
95#66871—22no—
96#66871—22no—
97#66871—22no—
98#66869Q814yescomplemented
99#26083—111nomaximal, Sylow
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11C2411yescharacteristic
104C2×C22⋊D11—21no—
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
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11C2×D411yescharacteristic
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×Q812yes—
121C2×C8×C11#4112yes—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—84no—
127C42×C11—21no—
128C42×C11C2×Q812yes—
129C22⋊Dic11—21no—
130C22⋊Dic11—22no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—42no—
133C4⋊Dic11C2×D411yescharacteristic
134C4⋊Dic11C2×D412yes—
135C4⋊Dic11C2×D411yescharacteristic
136C4⋊Dic11C2×D412yes—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139Dic11⋊C4—42no—
140C4×Dic11—21no—
141C4×Dic11—22no—
142C4×Dic11—42no—
143#4318—21no—
144#4318—22no—
145#4318—21no—
146#4318—22no—
147#4318C2×Q812yes—
148#4318C2×Q812yes—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
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#1945—111no—
161#1859—112no—
162#1845D1111yescharacteristic, complemented
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—42no—
171C2×C4×C11—42no—
172C2×C4×C11—82no—
173C2×C4×C11—82no—
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C11C22×Q811yescharacteristic
177C2×C4×C11C22×Q811yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C112−1+411yescharacteristic
180C22⋊D11—22no—
181C22⋊D11—22no—
182C2×Dic11—21no—
183C2×Dic11—22no—
184C2×Dic11—21no—
185C2×Dic11—21no—
186C2×Dic11—22no—
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×C11C22⋊Q812yes—
198C8×C11C22⋊Q812yes—
199C11⋊C8—22no—
200C11⋊C8—22no—
201C11⋊C8—42no—
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×#108—111no—
213#428—112no—
214#428—112no—
215#428—112no—
216#428—222no—
217#427—111no—
218#427—221no—
219C2×#107—221no—
220C2×#107C2×D1112yes—
221C2×#107C2×D1111yescharacteristic
222C2×#107C2×D1111yescharacteristic
223#424—112no—
224C2×#104—111no—
225#417—112no—
226#416—111no—
227#405—111no—
228C2×C4×C8C2×D1111yescharacteristic
229#384C2×D1112yes—
230#343—112no—
231#343—112no—
232#341—111no—
233#339—111no—
234#339—112no—
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—82no—
245C4×C11—82no—
246C4×C11C2×C22⋊Q811yescharacteristic
247C4×C11C2×C4⋊Q811yescharacteristic
248C4×C11#54711yescharacteristic
249C4×C11D4×Q811yescharacteristic
250Dic11—22no—
251Dic11—41no—
252Dic11—42no—
253Dic11—42no—
254Dic11—41no—
255C2×#41—111no—
256#131—114no—
257#131—222no—
258C2×M16—111no—
259C2×M16—111no—
260C2×M16—112no—
261C2×M16—221no—
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—112no—
274#117—111no—
275#117—222no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4C22×D1112yes—
279C2×C4⋊C4C22×D1112yes—
280C2×C42C22×D1111yescharacteristic
281#108—222no—
282#107—21no—
283#107—21no—
284#107—22no—
285#107—22no—
286#107—21no—
287#107—21no—
288#107—111no—
289#107—111no—
290#107—222no—
291#107—222no—
292#107—222no—
293#106—112no—
294#106—222no—
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—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—22no—
325C22×C4—22no—
326C22×C4—221no—
327C22×C4—442no—
328C22×C4C23×D1111yescharacteristic
329M16—112no—
330M16—112no—
331M16—221no—
332M16—221no—
333M16—224no—
334M16—222no—
335M16—222no—
336C2×C8—21no—
337C2×C8—21no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—224no—
341C2×C8—222no—
342C2×C8#433912yes—
343C2×C8D4×D1111yescharacteristic
344C2×C8D4×D1111yescharacteristic
345C2×C8D4×D1111yescharacteristic
346C2×C8D4×D1111yescharacteristic
347C2×C8Q8×D1112yes—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—84no—
353C4⋊C4—111no—
354C4⋊C4—111no—
355C4⋊C4—112no—
356C4⋊C4—112no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4—442no—
360C4⋊C4—442no—
361C22⋊C4—222no—
362C22⋊C4—221no—
363C22⋊C4—442no—
364C42—21no—
365C42—221no—
366C42—222no—
367C42—442no—
368C42Q8×D1112yes—
369C11#2608311yescharacteristic, complemented, Sylow
370C23—221no—
371C23#6703711yescharacteristic
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—42no—
383C2×C4—42no—
384C2×C4—82no—
385C2×C4—82no—
386C2×C4—221no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—222no—
390C2×C4—221no—
391C2×C4—222no—
392C2×C4—221no—
393C2×C4—1762no—
394C2×C4C2×#433911yescharacteristic
395C2×C4C2×D4×D1111yescharacteristic
396C2×C4C2×D4×D1111yescharacteristic
397C2×C4C2×Q8×D1111yescharacteristic
398C2×C4C2×Q8×D1111yescharacteristic
399C2×C4#6704011yescharacteristic
400C8—21no—
401C8—21no—
402C8—222no—
403C8—222no—
404C8—442no—
405C8#6694912yes—
406C8#6694912yes—
407C22—21no—
408C22—21no—
409C22—222no—
410C22—441no—
411C22—441no—
412C22#1062304211yescharacteristic
413C22#1062324811yescharacteristic
414C22#1062326011yescharacteristic
415C4—24no—
416C4—82no—
417C4—82no—
418C4—222no—
419C4—442no—
420C4—441no—
421C4—442no—
422C4—441no—
423C4#1062303811yescharacteristic
424C4C2×#6694911yescharacteristic
425C4D11×C4⋊Q811yescharacteristic
426C4#1062325811yescharacteristic
427C2—21no—
428C2—21no—
429C2—442no—
430C2#1307232111yescharacteristic
431C2#1308041511yescharacteristic
432C2#1308042011yescharacteristic
subgroupG/H
centerC22#10623248
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1845C2
socleC22×C11D42
prime radicalC2×#4339C23
hypercenter#1845D11
hypocenterC11#26083
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1845

Complements

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

NH ≅ G/Ntype
1. #13079152C2semidirect
4. #13070122C2semidirect
5. #13069961C2semidirect
6. #13069399C2semidirect
7. #13069364C2semidirect
11. C11×#1845C2semidirect
60. #66954Q8semidirect
98. #66869Q8semidirect
162. #1845D11semidirect
369. C11#26083semidirect

Maximal subgroups

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

subgroupindex
#130791522
#130784722
#130772122
#130701222
#130699612
#130693992
#130693642
#130688412
#130686812
#130684532
C11×#18452
#2608311