Finite Group Databasebeta

← #14737118

Subgroups — #14737118

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079592C212yesmaximal, complemented
2#13077591C211yesmaximal, characteristic, complemented
3#13068181C212yesmaximal, complemented
4#13068174C212yesmaximal, complemented
5#13068007C211yesmaximal, characteristic, complemented
6#13068002C211yesmaximal, characteristic, complemented
7#13067973C211yesmaximal, characteristic, complemented
8#13067968C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067321C212yesmaximal, complemented
11C11×#3169C211yesmaximal, characteristic, complemented
12C11×#532C2212yes—
13#10623010C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16C11×#486C2212yes—
17C11×#466—21no—
18C11×#466—21no—
19C4×C11×D8—21no—
20C4×C11×D8—21no—
21C2×C4×C8×C11C2211yescharacteristic
22#10622852—22no—
23#10622851—22no—
24#10622724—21no—
25C8×C22⋊D11—21no—
26#10622703C2212yes—
27#10622696C2212yes—
28#10622688C2212yes—
29#10622685C2212yes—
30#10622672—22no—
31#10622669—22no—
32#10622539C2211yescharacteristic
33#10622538C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41—22no—
48C2×C11×D8—21no—
49C2×C11×D8—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×C4⋊Q8C2312yes—
53C11×#127C2312yes—
54C11×#124—22no—
55C11×#121—22no—
56C11×#121—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C42×C11C2311yescharacteristic
60C2×#4326—22no—
61C2×#4325—22no—
62C2×#4324—22no—
63C2×#4323—22no—
64#66983D411yescharacteristic
65#66982—21no—
66C4×C22⋊D11—21no—
67#66977D411yescharacteristic
68C2×#4313—21no—
69C2×C8×D11—21no—
70#66929—21no—
71#66928D411yescharacteristic
72C4×D44C2311yescharacteristic
73#66925—21no—
74#66923D411yescharacteristic
75C4×Dic22C2311yescharacteristic
76C11×#107—21no—
77C11×#107—21no—
78C11×#102—22no—
79C11×#102—22no—
80C4×C8×C11D411yescharacteristic
81C4×C8×C11D411yescharacteristic
82C4×C8×C11C2311yescharacteristic
83C4×C8×C11C2311yescharacteristic
84#66899—22no—
85#66899—22no—
86#66896—22no—
87#66896—22no—
88C22⋊(C11⋊C8)—21no—
89C22⋊(C11⋊C8)—22no—
90(C2×D11)⋊C8—21no—
91(C2×D11)⋊C8—21no—
92#66879—21no—
93Dic11⋊C8—21no—
94Dic11⋊C8—21no—
95C8×Dic11—21no—
96C4⋊(C11⋊C8)C2312yes—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2311yescharacteristic
99C4⋊(C11⋊C8)C2311yescharacteristic
100#66867—21no—
101C4×C11⋊C8—22no—
102#19219—111nomaximal, Sylow
103C11×#41—82no—
104C11×#41—82no—
105C2×Q8×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—21no—
115C2×D44C2×D411yescharacteristic
116C2×C4×D11—21no—
117C2×Dic22C2×D411yescharacteristic
118C11×D8—42no—
119C11×D8—42no—
120C2×C8×C11—22no—
121C2×C8×C11—41no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11C2411yescharacteristic
134C22⋊Dic11—21no—
135#4326—82no—
136#4325—82no—
137#4324—82no—
138#4323—82no—
139(C2×D11)⋊C4—21no—
140(C2×D11)⋊C4—21no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143C4⋊Dic11C2×D411yescharacteristic
144C4⋊Dic11C2×D411yescharacteristic
145Dic11⋊C4—21no—
146Dic11⋊C4—21no—
147Dic11⋊C4—21no—
148Dic11⋊C4—21no—
149C4×Dic11—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154#4313—42no—
155C8×D11—42no—
156#3212—112no—
157#3169D1111yescharacteristic, complemented
158#2966—111no—
159#1702—112no—
160#1701—112no—
161#1674—111no—
162#1673—111no—
163#1668—111no—
164#1667—111no—
165#1564—111no—
166#1553—112no—
167C23×C11—42no—
168C23×C11#12111yescharacteristic
169C22×D11—21no—
170Q8×C11—42no—
171Q8×C11—42no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—82no—
177D4×C11—84no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—84no—
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11C22×D411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C22⋊D11—42no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195D44—21no—
196D44—21no—
197C4×D11—41no—
198C4×D11—41no—
199Dic22—21no—
200Dic22—21no—
201C8×C11—21no—
202C8×C11—21no—
203C8×C11—21no—
204C8×C11#13512yes—
205C11⋊C8—41no—
206C11⋊C8—41no—
207C11⋊C8—42no—
208C11⋊C8—42no—
209#532C2×D1112yes—
210#529—111no—
211#500C2×D1111yescharacteristic
212#495—222no—
213#493C2×D1111yescharacteristic
214#488—222no—
215#486C2×D1112yes—
216#466—21no—
217#466—21no—
218#462—112no—
219#461—112no—
220#460—112no—
221#459—112no—
222#452—222no—
223#449—222no—
224#446—111no—
225C8×Q8—111no—
226C4×D8—21no—
227C4×D8—21no—
228#436—111no—
229#435—221no—
230C8×D4—111no—
231C8×D4—221no—
232#433—221no—
233#432—111no—
234#431—112no—
235#405—221no—
236C2×C4×C8C2×D1111yescharacteristic
237#335—111no—
238#335—111no—
239#334—112no—
240#332—112no—
241#332—112no—
242#331—112no—
243#331—112no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—82no—
250C22×C11C2×#12111yescharacteristic
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—41no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—82no—
259C4×C11C2×#13511yescharacteristic
260C4×C11#57511yescharacteristic
261C4×C11#57611yescharacteristic
262C4×C11#57611yescharacteristic
263Dic11—41no—
264Dic11—41no—
265Dic11—41no—
266C2×#41—22no—
267C2×Q16—222no—
268C2×SD16—222no—
269C2×SD16—222no—
270C2×D8—21no—
271C2×D8—21no—
272C2×D8—222no—
273C2×M16—221no—
274C22×C8—221no—
275C22×C8C22⋊D1111yescharacteristic
276C22×C8C22⋊D1111yescharacteristic
277C4⋊Q8C22×D1112yes—
278#127C22×D1112yes—
279#126—221no—
280#125—111no—
281#124—22no—
282#124—111no—
283#123—221no—
284C22⋊Q8—111no—
285#121—22no—
286#121—22no—
287#121—111no—
288C4×Q8—111no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—111no—
292C4×D4—221no—
293#117—221no—
294C2×C42C22×D1111yescharacteristic
295#107—21no—
296#107—21no—
297C4⋊C8—111no—
298C4⋊C8—111no—
299C4⋊C8—112no—
300C4⋊C8—112no—
301C4⋊C8—221no—
302C4⋊C8—221no—
303#103—222no—
304#103—222no—
305#102—22no—
306#102—22no—
307#102—222no—
308#102—222no—
309C22⋊C8—222no—
310C22⋊C8—221no—
311C22⋊C8—221no—
312C22⋊C8—221no—
313#97—221no—
314#97—221no—
315C4×C8—221no—
316C4×C8—222no—
317C4×C8C22⋊D1111yescharacteristic
318C4×C8C22⋊D1111yescharacteristic
319C4×C8C22×D1111yescharacteristic
320C4×C8C22×D1111yescharacteristic
321C2×C11—41no—
322C2×C11—162no—
323C2×C11#303511yescharacteristic
324C2×C11#305811yescharacteristic
325C2×C11#306711yescharacteristic
326D11—81no—
327#41—82no—
328#41—82no—
329C2×Q8—22no—
330C2×Q8—111no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—42no—
335C2×D4—111no—
336C2×D4—221no—
337C22×C4—42no—
338C22×C4—221no—
339C22×C4D4×D1111yescharacteristic
340C22×C4#434111yescharacteristic
341C22×C4C2×C22⋊D1111yescharacteristic
342Q16—882no—
343SD16—882no—
344SD16—882no—
345D8—42no—
346D8—42no—
347D8—882no—
348M16—442no—
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—222no—
352C2×C8—222no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8—442no—
356C2×C8C2×C22⋊D1111yescharacteristic
357C2×C8C2×C22⋊D1111yescharacteristic
358C2×C8C2×C22⋊D1111yescharacteristic
359C2×C8C2×C22⋊D1111yescharacteristic
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—111no—
363C4⋊C4—111no—
364C4⋊C4—221no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—221no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—221no—
371C22⋊C4—221no—
372C22⋊C4—221no—
373C22⋊C4—221no—
374C22⋊C4—221no—
375C42—221no—
376C42D4×D1111yescharacteristic
377C42#434111yescharacteristic
378C42C2×C22⋊D1111yescharacteristic
379C42C23×D1111yescharacteristic
380C11#1921911yescharacteristic, complemented, Sylow
381C23—42no—
382C23—221no—
383C23#6699111yescharacteristic
384Q8—42no—
385Q8—42no—
386Q8—221no—
387Q8—221no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—82no—
393D4—84no—
394D4—221no—
395D4—221no—
396D4—442no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—84no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4#6699111yescharacteristic
410C2×C4#6699111yescharacteristic
411C2×C4#6699111yescharacteristic
412C2×C4C2×D4×D1111yescharacteristic
413C2×C4C2×#434111yescharacteristic
414C2×C4C22×C22⋊D1111yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—442no—
419C8—442no—
420C8—441no—
421C8—441no—
422C8#6700312yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—82no—
427C22—82no—
428C22—82no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22C2×#6699111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—82no—
438C4—441no—
439C4—441no—
440C4—441no—
441C4#1062328811yescharacteristic
442C4#1062328811yescharacteristic
443C4C2×#6700311yescharacteristic
444C4#1062335311yescharacteristic
445C2—41no—
446C2—162no—
447C2—881no—
448C2#1307806511yescharacteristic
449C2#1307826011yescharacteristic
450C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3169C2
socleC22×C11C2×#121
hypercenter#3169D11
hypocenterC11#19219
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #13079592C2semidirect
2. #13077591C2semidirect
3. #13068181C2semidirect
4. #13068174C2semidirect
5. #13068007C2semidirect
6. #13068002C2semidirect
7. #13067973C2semidirect
8. #13067968C2semidirect
9. #13067364C2semidirect
10. #13067321C2semidirect
11. C11×#3169C2semidirect
157. #3169D11semidirect
380. C11#19219semidirect

Maximal subgroups

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

subgroupindex
#130795922
#130775912
#130681812
#130681742
#130680072
#130680022
#130679732
#130679682
#130673642
#130673212
C11×#31692
#1921911