Finite Group Databasebeta

← #14909577

Subgroups — #14909577

Order 2816.

588 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622729C211yesmaximal, characteristic, complemented
2#13070824C212yesmaximal, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070799C211yesmaximal, characteristic, complemented
5#13070727C212yesmaximal, complemented
6#13070722C212yesmaximal, complemented
7#13070556C212yesmaximal, complemented
8#13070549C211yesmaximal, characteristic, complemented
9#13070532C211yesmaximal, characteristic, complemented
10#13070227C211yesmaximal, characteristic, complemented
11C11×#3050C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C11×#525—21no—
15C2×#66977—21no—
16C22×Dic44C2211yescharacteristic
17C11×#467C2211yescharacteristic
18C11×#467C2211yescharacteristic
19C11×#466C2211yescharacteristic
20C11×#466C2211yescharacteristic
21C11×#465—21no—
22C11×#465—21no—
23C11×#427C2211yescharacteristic
24C11×#416—21no—
25C2×#66893C2212yescomplemented
26C2×#66891C2212yescomplemented
27#10622729—21no—
28#10622729—21no—
29#10622729C2212yes—
30#10622729C2212yes—
31C2×#66882C2211yescharacteristic
32C2×#66880—21no—
33C2×#66876C2212yes—
34#10622202C2212yescomplemented
35#10622200C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic
37C22⋊(C11⋊C16)C2211yescharacteristic
38C22⋊(C11⋊C16)C2212yes—
39#10622130C2212yescomplemented
40#10622130C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×C11×#41—21no—
44C23×C4×C11D411yescharacteristic
45C22×Dic22—21no—
46C11×#135—42no—
47C2×C11×Q16C2311yescharacteristic
48C2×C11×SD16—21no—
49C2×C11×D8C2311yescharacteristic
50C22×C8×C11—42no—
51C22×C8×C11D411yescharacteristic
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C22×C8×C11C2311yescharacteristic
55C22×C8×C11C2311yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#123—41no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C11×#121—21no—
61C11×#121—21no—
62C11×#120—41no—
63C4×D4×C11—41no—
64C4×D4×C11—41no—
65C11×#117—21no—
66C2×C22⋊Dic11—41no—
67C2×C4⋊Dic11—21no—
68#66977—22no—
69#66977—22no—
70#66977—41no—
71#66977—41no—
72C2×Dic11⋊C4—41no—
73C2×Dic44—21no—
74C2×Dic44—42no—
75C2×Dic44C2312yes—
76C11×#107C2311yescharacteristic
77C11×#107C2311yescharacteristic
78C11×#106—21no—
79C11×#103—21no—
80C11×#103—21no—
81C11×#102—21no—
82C11×#102—21no—
83#66893—42no—
84#66891—42no—
85#66882—21no—
86#66882C2312yes—
87#66880—22no—
88#66880—22no—
89#66876—42no—
90C2×C11⋊C16C2312yes—
91C2×C11⋊C16C2312yes—
92#33762—111nomaximal, Sylow
93C24×C11D811yescharacteristic
94C11×#41—42no—
95C11×#41—42no—
96C2×Q8×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11D811yescharacteristic
105C22×C4×C11D811yescharacteristic
106C22×C4×C11D811yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×Dic11—41no—
111C22×Dic11—41no—
112C2×Dic22—22no—
113C2×Dic22—42no—
114C2×Dic22—42no—
115C2×Dic22—41no—
116C11×Q16—22no—
117C11×SD16—42no—
118C11×D8—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C2×C8×C11—41no—
125C2×C8×C11C2×D411yescharacteristic
126C2×C8×C11C2×D411yescharacteristic
127C2×C8×C11C2×D411yescharacteristic
128C2×C8×C11C2411yescharacteristic
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C42×C11—41no—
139C22⋊Dic11—42no—
140C22⋊Dic11—42no—
141C4⋊Dic11—22no—
142C4⋊Dic11—41no—
143Dic11⋊C4—42no—
144Dic11⋊C4—42no—
145Dic44—22no—
146Dic44—22no—
147Dic44—42no—
148C11⋊C16—22no—
149C11⋊C16—22no—
150#3050D1111yescharacteristic
151C2×#467—111no—
152#2237—112no—
153#2236—111no—
154#2233—111no—
155#2220—112no—
156#2219—112no—
157#2189—112no—
158#2188—111no—
159#2185—111no—
160#2112—111no—
161C23×C11—22no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11C2×D811yescharacteristic
166C23×C11C2×D811yescharacteristic
167C23×C11C2×D811yescharacteristic
168Q8×C11—41no—
169Q8×C11—41no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—82no—
173D4×C11—82no—
174D4×C11—82no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—82no—
188C2×C4×C11C2×D811yescharacteristic
189C2×C4×C11C2×D811yescharacteristic
190C2×C4×C11C2×D811yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—82no—
195C2×Dic11—82no—
196Dic22—42no—
197Dic22—42no—
198Dic22—82no—
199C8×C11—21no—
200C8×C11—21no—
201C8×C11—21no—
202C8×C11H(5,𝔽2)12yes—
203C2×#135C2×D1111yescharacteristic
204C22×Q16—111no—
205C23×C8C2×D1111yescharacteristic
206#525—21no—
207C2×C22⋊Q8—221no—
208C2×Q32—112no—
209C2×SD32—112no—
210C2×M32—112no—
211#467—112no—
212#467—112no—
213#467—221no—
214#467—221no—
215#467C2×D1111yescharacteristic
216#467C2×D1111yescharacteristic
217#466C2×D1111yescharacteristic
218#466C2×D1111yescharacteristic
219#465—21no—
220#465—21no—
221#427C2×D1111yescharacteristic
222C2×#107—111no—
223#416—21no—
224C2×#103—221no—
225#367—112no—
226#366—112no—
227#358—112no—
228#358—112no—
229#358—112no—
230#357—112no—
231C22⋊C16—111no—
232C22⋊C16—111no—
233C22⋊C16—112no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—44no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11#51012yes—
247C22×C11C22×D811yescharacteristic
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—81no—
252C4×C11—81no—
253C4×C11—81no—
254C4×C11#53411yescharacteristic
255C4×C11#57511yescharacteristic
256Dic11—82no—
257Dic11—82no—
258C2×#41—21no—
259C22×Q8—221no—
260C23×C4C22⋊D1111yescharacteristic
261#135—42no—
262C2×Q16—112no—
263C2×Q16—221no—
264C2×Q16—442no—
265C2×Q16C22×D1111yescharacteristic
266C2×SD16—21no—
267C2×D8C22×D1111yescharacteristic
268C22×C8—42no—
269C22×C8C22⋊D1111yescharacteristic
270C22×C8C22⋊D1111yescharacteristic
271C22×C8C22⋊D1111yescharacteristic
272C22×C8C22×D1111yescharacteristic
273C22×C8C22×D1111yescharacteristic
274C22×C8C22×D1111yescharacteristic
275#123—41no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—222no—
279C22⋊Q8—222no—
280C22⋊Q8—441no—
281C22⋊Q8—441no—
282#121—21no—
283#121—21no—
284#120—41no—
285C4×D4—41no—
286C4×D4—41no—
287#117—21no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—441no—
290C2×C22⋊C4—441no—
291Q32—442no—
292SD32—442no—
293M32—442no—
294C2×C16—112no—
295C2×C16—112no—
296#107—112no—
297#107—221no—
298#107C22×D1111yescharacteristic
299#107C22×D1111yescharacteristic
300#106—21no—
301#103—21no—
302#103—21no—
303#103—222no—
304#103—222no—
305#102—21no—
306#102—21no—
307C2×C11—22no—
308C2×C11—41no—
309C2×C11—41no—
310C2×C11—161no—
311C2×C11#318611yescharacteristic
312C2×C11C2×#51011yescharacteristic
313C2×C11#341411yescharacteristic
314C24#432311yescharacteristic
315#41—42no—
316#41—42no—
317C2×Q8—21no—
318C2×Q8—222no—
319C2×Q8—442no—
320C2×Q8—442no—
321C2×Q8—441no—
322C2×D4—21no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—441no—
330C22×C4—441no—
331C22×C4#432311yescharacteristic
332C22×C4#432311yescharacteristic
333C22×C4#432311yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C22×C4C2×C22⋊D1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337Q16—22no—
338Q16—222no—
339Q16—222no—
340Q16—442no—
341SD16—42no—
342D8—22no—
343C2×C8—22no—
344C2×C8—22no—
345C2×C8—22no—
346C2×C8—41no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8C2×C22⋊D1111yescharacteristic
350C2×C8C2×C22⋊D1111yescharacteristic
351C2×C8C2×C22⋊D1111yescharacteristic
352C2×C8C23×D1111yescharacteristic
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—222no—
358C4⋊C4—441no—
359C4⋊C4—442no—
360C4⋊C4—442no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—442no—
367C22⋊C4—442no—
368C42—41no—
369C16—222no—
370C16—222no—
371C11#3376211yescharacteristic, complemented, Sylow
372C23—22no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23C2×#432311yescharacteristic
377C23C2×#432311yescharacteristic
378C23C2×#432311yescharacteristic
379Q8—41no—
380Q8—41no—
381Q8—442no—
382Q8—442no—
383Q8—882no—
384D4—41no—
385D4—41no—
386D4—82no—
387D4—82no—
388D4—82no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—82no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—882no—
405C2×C4—882no—
406C2×C4C2×#432311yescharacteristic
407C2×C4C2×#432311yescharacteristic
408C2×C4C2×#432311yescharacteristic
409C2×C4C22×C22⋊D1111yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8#6703712yes—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—44no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22#1062280812yes—
427C22C22×#432311yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—81no—
432C4—81no—
433C4—81no—
434C4—882no—
435C4—882no—
436C4#1062333511yescharacteristic
437C4#1062335311yescharacteristic
438C2—22no—
439C2—41no—
440C2—41no—
441C2—161no—
442C2#1307936411yescharacteristic
443C2C2×#1062280811yescharacteristic
444C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3050C2
socleC22×C11C22×D8
hypercenter#3050D11
hypocenterC11#33762
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#10622729C2semidirect
2. #13070824C2semidirect
3. #13070816C2semidirect
4. #13070799C2semidirect
5. #13070727C2semidirect
6. #13070722C2semidirect
7. #13070556C2semidirect
8. #13070549C2semidirect
9. #13070532C2semidirect
10. #13070227C2semidirect
25. C2×#66893C22semidirect
26. C2×#66891C22semidirect
34. #10622202C22semidirect
35. #10622200C22semidirect
39. #10622130C22semidirect
40. #10622130C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
371. C11#33762semidirect

Maximal subgroups

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

subgroupindex
C2×#106227292
#130708242
#130708162
#130707992
#130707272
#130707222
#130705562
#130705492
#130705322
#130702272
C11×#30502
#3376211