Finite Group Databasebeta

← #14908166

Subgroups — #14908166

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C212yesmaximal, complemented
2#13079044C211yesmaximal, characteristic, complemented
3#13070697C212yesmaximal, complemented
4#13070692C212yesmaximal, complemented
5#13070685C214yesmaximal, complemented
6C2×#10622101C211yesmaximal, characteristic, complemented
7#13070363C212yesmaximal, complemented
8C2×C11×#443C211yesmaximal, characteristic, complemented
9C2×C11×#135C2211yescharacteristic
10C2×C11×#131—21no—
11C2×#66957—21no—
12C2×#66957C2212yes—
13#10623008—21no—
14C11×#443—21no—
15C11×#443—21no—
16C11×#443C2212yes—
17C11×#443C2212yes—
18C2×C11×#108C2211yescharacteristic
19C2×C11×#104—21no—
20C2×C4×C8×C11C2211yescharacteristic
21#10622808C2214yes—
22#10622807—24no—
23#10622806C2214yes—
24#10622792—22no—
25#10622760—22no—
26C2×#66876C2212yes—
27#10622312C2211yescharacteristic, complemented
28#10622309—21no—
29#10622309C2212yescomplemented
30#10622308C2211yescharacteristic, complemented
31#10622306—21no—
32#10622134C2214yescomplemented
33#10622133C2214yescomplemented
34#10622101C2212yescomplemented
35#10622101C2212yescomplemented
36C2×C11×#41—21no—
37C2×#4339—22no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135D412yescomplemented
41C11×#135C2312yes—
42C2×C11×Q16D411yescharacteristic, complemented
43C2×C11×SD16—21no—
44C2×C11×D8D411yescharacteristic, complemented
45C11×#131—22no—
46C11×#131—22no—
47C11×#131—41no—
48C11×#131—41no—
49C2×C11×M16—21no—
50C2×C11×M16—41no—
51C22×C8×C11—41no—
52C22×C8×C11D411yescharacteristic
53C22×C8×C11C2311yescharacteristic
54C2×C42×C11D411yescharacteristic
55#66983—42no—
56C2×Dic44—21no—
57C2×Dic44C2312yes—
58#66957—22no—
59#66957—22no—
60#66957—22no—
61#66957—22no—
62#66957—41no—
63#66957—41no—
64#66957—41no—
65#66957—41no—
66C2×D88—21no—
67C2×D88C2312yes—
68C2×#4314—22no—
69C2×#4314—22no—
70#66928—22no—
71#66927—21no—
72C4×D44—42no—
73#66922—21no—
74C11×#108—21no—
75C11×#108C2312yes—
76C11×#104—22no—
77C11×#104—22no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66893—24no—
83#66892—24no—
84#66891—24no—
85#66890—24no—
86#66876—22no—
87#66876C2314yes—
88C2×C11⋊C16—22no—
89#33594—111nomaximal, Sylow
90C11×#41—22no—
91C11×#41—22no—
92C11×#41—41no—
93C11×#41—41no—
94C2×Q8×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C22×C4×C11—21no—
98C22×C4×C11—41no—
99C22×C4×C11C2×D411yescharacteristic
100C2×C22⋊D11—42no—
101#4339—42no—
102#4339—42no—
103#4339—42no—
104#4339—42no—
105C2×D44—22no—
106C2×D44—42no—
107C2×C4×D11—42no—
108C2×Dic22—22no—
109C11×Q16—21no—
110C11×Q16C2×D412yes—
111C11×SD16—22no—
112C11×SD16—22no—
113C11×D8—21no—
114C11×D8C2×D412yes—
115C11×M16—22no—
116C11×M16—42no—
117C11×M16—42no—
118C11×M16—41no—
119C2×C8×C11—42no—
120C2×C8×C11—42no—
121C2×C8×C11—41no—
122C2×C8×C11D811yescharacteristic
123C2×C8×C11D811yescharacteristic
124C2×C8×C11D811yescharacteristic
125C2×C8×C11D811yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11#4111yescharacteristic
132C2×C8×C11#4111yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C42×C11—21no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137(C2×D11)⋊C4—44no—
138C4⋊Dic11—42no—
139Dic44—22no—
140Dic44—22no—
141Dic44—41no—
142Dic44—41no—
143D88—22no—
144D88—22no—
145D88—41no—
146D88—41no—
147#4314—42no—
148#4314—42no—
149#4314—42no—
150#4314—42no—
151C11⋊C16—24no—
152#3414—112no—
153#3147—111no—
154C2×#443D1111yescharacteristic, complemented
155#2214—112no—
156#2213—112no—
157#2212—114no—
158C2×#364—111no—
159#2148—112no—
160C23×C11—41no—
161C23×C11AGL(1,ℤ/8)11yescharacteristic
162C22×D11—42no—
163Q8×C11—22no—
164Q8×C11—41no—
165D4×C11—22no—
166D4×C11—42no—
167D4×C11—42no—
168D4×C11—41no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11C2×D811yescharacteristic
178C2×C4×C11C2×D811yescharacteristic
179C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C11C22×D411yescharacteristic
181C22⋊D11—82no—
182C22⋊D11—82no—
183C2×Dic11—42no—
184D44—42no—
185D44—42no—
186D44—84no—
187C4×D11—82no—
188C4×D11—82no—
189Dic22—42no—
190Dic22—42no—
191C8×C11—42no—
192C8×C11#12111yescharacteristic
193C8×C11#12111yescharacteristic
194C8×C11C2×D811yescharacteristic
195C8×C11C2×D811yescharacteristic
196C8×C11C2×D811yescharacteristic
197C8×C11C2×D811yescharacteristic
198C8×C11C22×D411yescharacteristic
199C8×C11C2×#4111yescharacteristic
200C2×#135—112no—
201C2×#135—221no—
202C2×#135C2×D1111yescharacteristic
203C2×#131—21no—
204#532—221no—
205#510—114no—
206#510—222no—
207#509—114no—
208#509—222no—
209#508—224no—
210C2×M32—112no—
211#495—112no—
212#495—221no—
213#494—111no—
214#493—111no—
215#492—221no—
216#443—21no—
217#443—21no—
218#443C2×D1112yes—
219#443C2×D1112yes—
220C2×#108C2×D1111yescharacteristic
221C2×#104—21no—
222C2×C4×C8C2×D1111yescharacteristic
223#364—112no—
224#364—112no—
225#362—114no—
226#361—114no—
227C22×C11—41no—
228C22×C11—42no—
229C22×C11—82no—
230C22×C11#45911yescharacteristic
231C22×C11#45911yescharacteristic
232C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
233C2×D11—84no—
234C2×D11—82no—
235C4×C11—22no—
236C4×C11—41no—
237C4×C11—42no—
238C4×C11#45911yescharacteristic
239C4×C11#45911yescharacteristic
240C4×C11C2×#12111yescharacteristic
241C4×C11C22×D811yescharacteristic
242Dic11—82no—
243C2×#41—21no—
244C2×#41—222no—
245#135—21no—
246#135—21no—
247#135—222no—
248#135—222no—
249#135—222no—
250#135—222no—
251#135—441no—
252#135—441no—
253#135—441no—
254#135—441no—
255#135D4412yescomplemented
256#135C22×D1112yes—
257C2×Q16—112no—
258C2×Q16—221no—
259C2×Q16D4411yescharacteristic, complemented
260C2×SD16—21no—
261C2×SD16—222no—
262C2×SD16—222no—
263C2×D8—112no—
264C2×D8—221no—
265C2×D8D4411yescharacteristic, complemented
266#131—22no—
267#131—22no—
268#131—41no—
269#131—41no—
270C2×M16—21no—
271C2×M16—41no—
272C22×C8—41no—
273C22×C8C22⋊D1111yescharacteristic
274C22×C8C22×D1111yescharacteristic
275C4⋊Q8—221no—
276#127—221no—
277#124—222no—
278#121—442no—
279C4×D4—442no—
280C2×C42C22⋊D1111yescharacteristic
281Q32—224no—
282SD32—224no—
283SD32—224no—
284D16—224no—
285M32—114no—
286M32—222no—
287C2×C16—222no—
288#108—21no—
289#108C22×D1112yes—
290#104—22no—
291#104—22no—
292C4×C8C22⋊D1111yescharacteristic
293C4×C8C22⋊D1111yescharacteristic
294C4×C8C22×D1111yescharacteristic
295C4×C8C22×D1111yescharacteristic
296C2×C11—21no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—82no—
300C2×C11C2×#45911yescharacteristic
301D11—162no—
302#41—22no—
303#41—22no—
304#41—41no—
305#41—41no—
306#41—442no—
307#41—442no—
308#41—442no—
309#41—442no—
310C2×Q8—21no—
311C2×Q8—222no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—222no—
315C2×D4—442no—
316C2×D4—442no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—442no—
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—21no—
322Q16—222no—
323Q16—222no—
324Q16—441no—
325Q16—441no—
326Q16C2×D4412yes—
327SD16—22no—
328SD16—22no—
329SD16—442no—
330SD16—442no—
331SD16—442no—
332SD16—442no—
333D8—21no—
334D8—222no—
335D8—222no—
336D8—441no—
337D8—441no—
338D8C2×D4412yes—
339M16—22no—
340M16—41no—
341M16—42no—
342M16—42no—
343C2×C8—41no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8#432311yescharacteristic
347C2×C8#432311yescharacteristic
348C2×C8#432311yescharacteristic
349C2×C8#432311yescharacteristic
350C2×C8C2×D4411yescharacteristic
351C2×C8C2×D4411yescharacteristic
352C2×C8#433911yescharacteristic
353C2×C8#433911yescharacteristic
354C2×C8C2×C22⋊D1111yescharacteristic
355C2×C8C2×C22⋊D1111yescharacteristic
356C2×C8C2×C22⋊D1111yescharacteristic
357C2×C8C23×D1111yescharacteristic
358C4⋊C4—442no—
359C22⋊C4—444no—
360C42—21no—
361C42C2×C22⋊D1111yescharacteristic
362C42C2×C22⋊D1111yescharacteristic
363C16—224no—
364C11#3359411yescharacteristic, complemented, Sylow
365C23—41no—
366C23—442no—
367C23#6700211yescharacteristic
368Q8—22no—
369Q8—41no—
370Q8—442no—
371Q8—442no—
372D4—22no—
373D4—42no—
374D4—42no—
375D4—41no—
376D4—442no—
377D4—442no—
378D4—884no—
379D4—882no—
380D4—882no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—442no—
388C2×C4—882no—
389C2×C4—882no—
390C2×C4#6698311yescharacteristic
391C2×C4#6698311yescharacteristic
392C2×C4C2×#432311yescharacteristic
393C2×C4C2×#432311yescharacteristic
394C2×C4#6700211yescharacteristic
395C2×C4C22×C22⋊D1111yescharacteristic
396C8—42no—
397C8#6698311yescharacteristic
398C8#6698311yescharacteristic
399C8C2×#432311yescharacteristic
400C8C2×#432311yescharacteristic
401C8C2×#432311yescharacteristic
402C8C2×#432311yescharacteristic
403C8C22×D4411yescharacteristic
404C8C2×#433911yescharacteristic
405C22—41no—
406C22—42no—
407C22—82no—
408C22—884no—
409C22—882no—
410C22#1062262811yescharacteristic
411C22#1062262811yescharacteristic
412C22C2×#6700211yescharacteristic
413C4—22no—
414C4—41no—
415C4—42no—
416C4—882no—
417C4#1062262811yescharacteristic
418C4#1062262811yescharacteristic
419C4C2×#6698311yescharacteristic
420C4C22×#432311yescharacteristic
421C2—21no—
422C2—21no—
423C2—21no—
424C2—82no—
425C2—1762no—
426C2C2×#1062262811yescharacteristic
subgroupG/H
centerC4#10622628
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#443C2
socleC2×C11C2×#459
hypercenterC2×#443D11
hypocenterC11#33594
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
1. #13081750C2semidirect
2. #13079044C2semidirect
3. #13070697C2semidirect
4. #13070692C2semidirect
5. #13070685C2semidirect
6. C2×#10622101C2semidirect
7. #13070363C2semidirect
8. C2×C11×#443C2semidirect
27. #10622312C22semidirect
29. #10622309C22semidirect
30. #10622308C22semidirect
32. #10622134C22semidirect
33. #10622133C22semidirect
34. #10622101C22semidirect
35. #10622101C22semidirect
40. C11×#135D4semidirect
42. C2×C11×Q16D4semidirect
44. C2×C11×D8D4semidirect
154. C2×#443D11semidirect
255. #135D44semidirect
259. C2×Q16D44semidirect
265. C2×D8D44semidirect
364. C11#33594semidirect

Maximal subgroups

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

subgroupindex
#130817502
#130790442
#130706972
#130706922
#130706852
C2×#106221012
#130703632
C2×C11×#4432
#3359411