Finite Group Databasebeta

← #14738542

Subgroups — #14738542

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079972C212yesmaximal, complemented
2#13077591C211yesmaximal, characteristic, complemented
3#13068107C211yesmaximal, characteristic, complemented
4#13068102C211yesmaximal, characteristic, complemented
5#13068097C211yesmaximal, characteristic, complemented
6#13068092C211yesmaximal, characteristic, complemented
7#13067961C212yesmaximal, complemented
8#13067954C212yesmaximal, complemented
9#13067372C211yesmaximal, characteristic, complemented
10#13067338C212yesmaximal, complemented
11C11×#3147C211yesmaximal, characteristic, complemented
12C2×C11×#135—21no—
13C2×C11×#135—21no—
14C11×#532C2212yes—
15#10623010C2211yescharacteristic
16C11×#495—21no—
17C11×#495—21no—
18C11×#494C2211yescharacteristic
19C11×#493C2211yescharacteristic
20C11×#492C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622724—21no—
23C8×C22⋊D11—21no—
24#10622707C2212yes—
25#10622700C2212yes—
26#10622688C2212yes—
27#10622685C2212yes—
28#10622655—22no—
29#10622652—22no—
30#10622629—22no—
31#10622622—22no—
32#10622539C2211yescharacteristic
33#10622537C2212yes—
34#10622303—21no—
35#10622302—21no—
36#10622301C2211yescharacteristic
37C8×D44C2211yescharacteristic
38#10622292C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622182C2212yes—
43#10622182C2212yes—
44#10622095C2211yescharacteristic
45#10622095C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41—22no—
48C11×#135—44no—
49C11×#135—44no—
50C2×C11×Q16—21no—
51C2×C11×Q16—21no—
52C2×C11×SD16—22no—
53C2×C11×SD16—22no—
54C2×C11×D8—21no—
55C2×C11×D8—21no—
56C22×C8×C11D411yescharacteristic
57C22×C8×C11D411yescharacteristic
58C11×C4⋊Q8C2312yes—
59C11×#127C2312yes—
60C11×#124—22no—
61C11×#121—22no—
62C11×#121—22no—
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C2×C42×C11C2311yescharacteristic
66C2×#4324—22no—
67C2×#4323—22no—
68#66983D411yescharacteristic
69#66982—21no—
70C4×C22⋊D11—21no—
71#66977D411yescharacteristic
72C2×#4318—22no—
73C2×#4313—21no—
74C2×C8×D11—21no—
75#66929—21no—
76#66928D411yescharacteristic
77C4×D44C2311yescharacteristic
78#66925—21no—
79#66923D411yescharacteristic
80C4×Dic22C2311yescharacteristic
81C4×C8×C11D411yescharacteristic
82C4×C8×C11D411yescharacteristic
83C4×C8×C11C2311yescharacteristic
84C4×C8×C11C2311yescharacteristic
85#66896—22no—
86#66896—22no—
87C22⋊(C11⋊C8)—21no—
88(C2×D11)⋊C8—21no—
89(C2×D11)⋊C8—21no—
90#66879—21no—
91Dic11⋊C8—21no—
92Dic11⋊C8—21no—
93C8×Dic11—21no—
94#66874—22no—
95#66873—22no—
96#66872—22no—
97#66871—22no—
98C4⋊(C11⋊C8)—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2311yescharacteristic
102C4⋊(C11⋊C8)C2311yescharacteristic
103#66867—21no—
104#19355—111nomaximal, Sylow
105C11×#41—44no—
106C11×#41—44no—
107C2×Q8×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—22no—
111C2×D4×C11—42no—
112C22×C4×C11—42no—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C2×C22⋊D11—21no—
117C2×D44C2×D411yescharacteristic
118C2×C4×D11—21no—
119C2×Dic22C2×D411yescharacteristic
120C11×Q16—42no—
121C11×Q16—42no—
122C11×SD16—44no—
123C11×SD16—44no—
124C11×D8—42no—
125C11×D8—42no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11C2×D411yescharacteristic
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11C2×D411yescharacteristic
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C22⋊C4—42no—
135C11×C22⋊C4—42no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140C22⋊Dic11—21no—
141#4324—82no—
142#4323—82no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145(C2×D11)⋊C4—21no—
146(C2×D11)⋊C4—21no—
147C4⋊Dic11C2×D411yescharacteristic
148C4⋊Dic11C2×D411yescharacteristic
149Dic11⋊C4—21no—
150Dic11⋊C4—21no—
151Dic11⋊C4—21no—
152Dic11⋊C4—21no—
153C4×Dic11—21no—
154#4318—82no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159#4313—42no—
160C8×D11—42no—
161#3251—112no—
162#3147D1111yescharacteristic, complemented
163#2966—111no—
164#1690—111no—
165#1689—111no—
166#1688—111no—
167#1687—111no—
168#1666—112no—
169#1665—112no—
170#1566—111no—
171#1557—112no—
172C23×C11—42no—
173C23×C11#12111yescharacteristic
174C22×D11—21no—
175Q8×C11—42no—
176Q8×C11—42no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—42no—
180D4×C11—42no—
181D4×C11—82no—
182D4×C11—84no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—84no—
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C22⋊D11—42no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199D44—22no—
200C4×D11—41no—
201C4×D11—41no—
202Dic22—22no—
203C8×C11—21no—
204C8×C11—21no—
205C8×C11AGL(1,ℤ/8)12yes—
206C8×C11AGL(1,ℤ/8)12yes—
207C11⋊C8—41no—
208C11⋊C8—41no—
209C11⋊C8—42no—
210C11⋊C8—42no—
211C2×#135—21no—
212C2×#135—21no—
213#532C2×D1112yes—
214#529—111no—
215#495—21no—
216#495—21no—
217#494C2×D1111yescharacteristic
218#493C2×D1111yescharacteristic
219#492C2×D1112yes—
220#478—222no—
221#475—112no—
222#474—112no—
223#469—222no—
224#468—222no—
225#463—222no—
226#460—112no—
227#459—112no—
228#446—111no—
229C8×Q8—111no—
230#436—111no—
231#435—221no—
232C8×D4—111no—
233C8×D4—221no—
234#433—221no—
235#432—111no—
236#423—112no—
237#405—221no—
238C2×C4×C8C2×D1111yescharacteristic
239#334—112no—
240#334—111no—
241#334—111no—
242#332—112no—
243#332—112no—
244#331—112no—
245#331—112no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C2×#12111yescharacteristic
253C2×D11—41no—
254C2×D11—41no—
255C2×D11—41no—
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—82no—
261C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
262C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C4×C11#57712yes—
264Dic11—41no—
265Dic11—41no—
266Dic11—41no—
267C2×#41—22no—
268#135—44no—
269#135—44no—
270C2×Q16—21no—
271C2×Q16—21no—
272C2×SD16—22no—
273C2×SD16—22no—
274C2×SD16—222no—
275C2×D8—21no—
276C2×D8—21no—
277C2×D8—222no—
278C2×M16—222no—
279C2×M16—221no—
280C22×C8—221no—
281C22×C8C22⋊D1111yescharacteristic
282C22×C8C22⋊D1111yescharacteristic
283C4⋊Q8C22×D1112yes—
284#127C22×D1112yes—
285#126—221no—
286#125—111no—
287#124—22no—
288#124—111no—
289#123—221no—
290C22⋊Q8—111no—
291#121—22no—
292#121—22no—
293#121—111no—
294C4×Q8—111no—
295C4×D4—22no—
296C4×D4—22no—
297C4×D4—111no—
298C4×D4—221no—
299#117—221no—
300C2×C42C22×D1111yescharacteristic
301#107—222no—
302#106—222no—
303C4⋊C8—111no—
304C4⋊C8—111no—
305C4⋊C8—112no—
306C4⋊C8—112no—
307C4⋊C8—221no—
308C4⋊C8—221no—
309C4⋊C8—222no—
310#103—222no—
311#102—222no—
312#102—222no—
313#102—222no—
314C22⋊C8—221no—
315C22⋊C8—221no—
316C22⋊C8—221no—
317#97—221no—
318#97—221no—
319C4×C8—221no—
320C4×C8C22⋊D1111yescharacteristic
321C4×C8C22⋊D1111yescharacteristic
322C4×C8C22×D1111yescharacteristic
323C4×C8C22×D1111yescharacteristic
324C2×C11—41no—
325C2×C11—162no—
326C2×C11#303811yescharacteristic
327C2×C11#306011yescharacteristic
328C2×C11#306711yescharacteristic
329D11—81no—
330#41—44no—
331#41—44no—
332C2×Q8—22no—
333C2×Q8—111no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—42no—
338C2×D4—111no—
339C2×D4—221no—
340C22×C4—42no—
341C22×C4—221no—
342C22×C4D4×D1111yescharacteristic
343C22×C4#434111yescharacteristic
344C22×C4C2×C22⋊D1111yescharacteristic
345Q16—42no—
346Q16—42no—
347SD16—44no—
348SD16—44no—
349SD16—882no—
350D8—42no—
351D8—42no—
352D8—882no—
353M16—442no—
354M16—882no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—221no—
360C2×C8—221no—
361C2×C8—442no—
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C2×C8C2×C22⋊D1111yescharacteristic
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—111no—
369C4⋊C4—111no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C22⋊C4—42no—
375C22⋊C4—42no—
376C22⋊C4—221no—
377C22⋊C4—221no—
378C22⋊C4—221no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C42—221no—
382C42D4×D1111yescharacteristic
383C42#434111yescharacteristic
384C42C2×C22⋊D1111yescharacteristic
385C42C23×D1111yescharacteristic
386C11#1935511yescharacteristic, complemented, Sylow
387C23—42no—
388C23—221no—
389C23#6699111yescharacteristic
390Q8—42no—
391Q8—42no—
392Q8—222no—
393D4—42no—
394D4—42no—
395D4—42no—
396D4—42no—
397D4—82no—
398D4—84no—
399D4—222no—
400D4—442no—
401C2×C4—22no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—84no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4#6699111yescharacteristic
413C2×C4#6699111yescharacteristic
414C2×C4#6699111yescharacteristic
415C2×C4C2×D4×D1111yescharacteristic
416C2×C4C2×#434111yescharacteristic
417C2×C4C22×C22⋊D1111yescharacteristic
418C8—21no—
419C8—21no—
420C8—442no—
421C8—442no—
422C8—441no—
423C8—441no—
424C8#6698512yes—
425C8#6698512yes—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—82no—
430C22—82no—
431C22—82no—
432C22—441no—
433C22—441no—
434C22—441no—
435C22C2×#6699111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—82no—
441C4—441no—
442C4—441no—
443C4—441no—
444C4#1062330112yes—
445C4C2×#6698511yescharacteristic
446C4C2×#6698511yescharacteristic
447C2—41no—
448C2—162no—
449C2—881no—
450C2#1307809211yescharacteristic
451C2#1307827411yescharacteristic
452C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3147C2
socleC22×C11C2×#121
hypercenter#3147D11
hypocenterC11#19355
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. #13079972C2semidirect
2. #13077591C2semidirect
3. #13068107C2semidirect
4. #13068102C2semidirect
5. #13068097C2semidirect
6. #13068092C2semidirect
7. #13067961C2semidirect
8. #13067954C2semidirect
9. #13067372C2semidirect
10. #13067338C2semidirect
11. C11×#3147C2semidirect
162. #3147D11semidirect
386. C11#19355semidirect

Maximal subgroups

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

subgroupindex
#130799722
#130775912
#130681072
#130681022
#130680972
#130680922
#130679612
#130679542
#130673722
#130673382
C11×#31472
#1935511