Finite Group Databasebeta

← #14737632

Subgroups — #14737632

Order 2816.

628 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#13079175C211yesmaximal, characteristic
2#13078746C211yesmaximal, characteristic, complemented
3#13078738C211yesmaximal, characteristic
4#13068074C212yesmaximal, complemented
5#13068060C212yesmaximal, complemented
6#13067998C212yesmaximal, complemented
7#13067964C212yesmaximal, complemented
8#13067379C211yesmaximal, characteristic, complemented
9#13067314C211yesmaximal, characteristic, complemented
10#13067309C211yesmaximal, characteristic
11C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623008C2211yescharacteristic
14#10623001C2211yescharacteristic
15C8×Q8×C11—21no—
16C8×Q8×C11—21no—
17C8×Q8×C11C2212yes—
18C8×Q8×C11C2212yes—
19C2×C11×C4⋊C8—21no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C11—21no—
22C2×C4×C8×C11C2211yescharacteristic
23#10622841—21no—
24#10622840—21no—
25#10622727—21no—
26#10622727—21no—
27#10622644C2212yes—
28#10622643—22no—
29#10622640C2212yes—
30#10622639—22no—
31#10622634C2212yes—
32#10622633C2212yes—
33#10622584—21no—
34#10622580—21no—
35#10622539C2211yescharacteristic
36#10622539C2211yescharacteristic
37#10622307C2211yescharacteristic
38#10622306C2211yescharacteristic
39C4×#4314—21no—
40C4×#4314—21no—
41#10622294C2211yescharacteristic
42#10622293C2211yescharacteristic
43#10622124C2212yes—
44#10622123C2212yes—
45#10622120C2212yes—
46#10622119C2212yes—
47#10622096C2212yes—
48#10622095C2212yes—
49C22×Q8×C11D411yescharacteristic
50C2×#4339—21no—
51C22×C8×C11—21no—
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11D412yes—
57C4×Q8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4325—22no—
64#66983—21no—
65#66983—21no—
66#66979—21no—
67#66977—21no—
68#66977—21no—
69C2×#4314—21no—
70C2×#4314—21no—
71#66928—21no—
72#66927C2311yescharacteristic
73C4×D44—21no—
74C4×D44—21no—
75#66923—21no—
76#66922C2311yescharacteristic
77#66922C2311yescharacteristic
78#66922C2311yescharacteristic
79C4×Dic22—21no—
80C4×Dic22—21no—
81C11×C4⋊C8—22no—
82C11×C4⋊C8—22no—
83C11×C4⋊C8—21no—
84C11×C4⋊C8C2312yes—
85C4×C8×C11—22no—
86C4×C8×C11—22no—
87C4×C8×C11D411yescharacteristic
88C4×C8×C11D411yescharacteristic
89C4×C8×C11C2311yescharacteristic
90C4×C8×C11C2311yescharacteristic
91#66899—22no—
92#66899—22no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95#66885—21no—
96#66885—21no—
97#66881—21no—
98#66881—21no—
99#66880—21no—
100#66880—21no—
101#66874—22no—
102#66873—22no—
103#66872—22no—
104#66871—22no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107#66867—21no—
108#66867—21no—
109#19263—111nomaximal, Sylow
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11C2×D412yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C2×C22⋊D11—41no—
119#4339—82no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×C4×D11—41no—
124C2×Dic22—21no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C2×C8×C11—41no—
130C2×C8×C11—42no—
131C2×C8×C11C2×D411yescharacteristic
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C2×D412yes—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11#4111yescharacteristic
144C42×C11C2411yescharacteristic
145C22⋊Dic11—41no—
146#4326—44no—
147#4325—44no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158C4×Dic11—41no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161#4314—42no—
162#4314—42no—
163#3167—111no—
164#3113—111no—
165#3112—111no—
166C2×C8×Q8D1111yescharacteristic, complemented
167#1684—112no—
168#1682—112no—
169#1672—112no—
170#1666—112no—
171#1568—111no—
172#1552—111no—
173#1551—111no—
174C23×C11#12111yescharacteristic
175C22×D11—41no—
176Q8×C11—24no—
177Q8×C11—22no—
178Q8×C11#13514yes—
179C2×C4×C11—24no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—22no—
186C2×C4×C11—42no—
187C2×C4×C11#12111yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C22⋊D11—82no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197D44—42no—
198D44—41no—
199D44—41no—
200D44—81no—
201C4×D11—82no—
202Dic22—42no—
203Dic22—41no—
204Dic22—41no—
205Dic22—81no—
206C8×C11—21no—
207C8×C11—21no—
208C8×C11—21no—
209C8×C11—42no—
210C8×C11#13712yes—
211C11⋊C8—42no—
212C11⋊C8—42no—
213#533—111no—
214#532—111no—
215C2×C4×Q8C2×D1111yescharacteristic
216#498—111no—
217#492—111no—
218#487—111no—
219#486—111no—
220#483—221no—
221#480—221no—
222#477—112no—
223#475—112no—
224#465—221no—
225#465—221no—
226#462—112no—
227#460—112no—
228#451—221no—
229#448—221no—
230C8×Q8—21no—
231C8×Q8—21no—
232C8×Q8C2×D1112yes—
233C8×Q8C2×D1112yes—
234#441—222no—
235#440—222no—
236C4×SD16—221no—
237C4×SD16—221no—
238#432—111no—
239#432—111no—
240C2×C4⋊C8—21no—
241C2×C4⋊C8C2×D1111yescharacteristic
242C2×C4×C8—21no—
243C2×C4×C8C2×D1111yescharacteristic
244#335—112no—
245#334—112no—
246#333—112no—
247#332—112no—
248#332—112no—
249#331—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11#47112yes—
253C22×C11C2×#12111yescharacteristic
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C4×C11—21no—
258C4×C11—24no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—42no—
263C4×C11C2×#13512yes—
264C4×C11C2×#13711yescharacteristic
265C4×C11#57511yescharacteristic
266Dic11—81no—
267Dic11—81no—
268Dic11—81no—
269C2×#41—221no—
270C22×Q8D4411yescharacteristic
271C2×Q16—222no—
272C2×SD16—222no—
273C2×SD16—221no—
274C2×SD16—221no—
275C22×C8—21no—
276C22×C8C22⋊D1111yescharacteristic
277C22×C8C22⋊D1111yescharacteristic
278C4⋊Q8—111no—
279C4⋊Q8—111no—
280C4⋊Q8—111no—
281#127—111no—
282#125—221no—
283#124—221no—
284C22⋊Q8—221no—
285C22⋊Q8—221no—
286#121—221no—
287#121—221no—
288C4×Q8—21no—
289C4×Q8—21no—
290C4×Q8—221no—
291C4×Q8—221no—
292C4×Q8D4412yes—
293C4×Q8C22×D1112yes—
294C4×D4—221no—
295C4×D4—221no—
296#117—221no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4D4411yescharacteristic
299C2×C42—21no—
300C2×C42C22×D1111yescharacteristic
301#107—222no—
302#106—221no—
303#106—221no—
304#106—222no—
305C4⋊C8—22no—
306C4⋊C8—22no—
307C4⋊C8—21no—
308C4⋊C8—112no—
309C4⋊C8—112no—
310C4⋊C8C22×D1112yes—
311#103—222no—
312#103—222no—
313#103—221no—
314#103—221no—
315#103—222no—
316#102—221no—
317#102—221no—
318#102—222no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321#97—221no—
322#97—221no—
323C4×C8—22no—
324C4×C8—22no—
325C4×C8C22⋊D1111yescharacteristic
326C4×C8C22⋊D1111yescharacteristic
327C4×C8C22×D1111yescharacteristic
328C4×C8C22×D1111yescharacteristic
329C2×C11—22no—
330C2×C11#303711yescharacteristic
331C2×C11#305011yescharacteristic
332C2×C11C2×#47111yescharacteristic
333D11—161no—
334#41—882no—
335C2×Q8—24no—
336C2×Q8—21no—
337C2×Q8—221no—
338C2×Q8—221no—
339C2×Q8—221no—
340C2×Q8C2×D4412yes—
341C2×D4—221no—
342C2×D4—221no—
343C2×D4—221no—
344C2×D4—441no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—441no—
348C22×C4C2×D4411yescharacteristic
349C22×C4#433911yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351Q16—444no—
352SD16—442no—
353SD16—444no—
354SD16—442no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—42no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8C2×C22⋊D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C2×C22⋊D1111yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—22no—
368C4⋊C4—221no—
369C4⋊C4—221no—
370C4⋊C4—221no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—441no—
375C4⋊C4—441no—
376C4⋊C4C2×D4412yes—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C22⋊C4—441no—
380C42—22no—
381C42—22no—
382C42—441no—
383C42C2×D4411yescharacteristic
384C42#433911yescharacteristic
385C42C2×C22⋊D1111yescharacteristic
386C42C23×D1111yescharacteristic
387C11#1926311yescharacteristic, complemented, Sylow
388C23—441no—
389C23#6698311yescharacteristic
390Q8—24no—
391Q8—22no—
392Q8—442no—
393Q8—441no—
394Q8—441no—
395Q8—881no—
396Q8#6695714yes—
397D4—442no—
398D4—441no—
399D4—441no—
400D4—881no—
401D4—882no—
402C2×C4—24no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—441no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—882no—
414C2×C4#6698311yescharacteristic
415C2×C4#6698311yescharacteristic
416C2×C4#6698311yescharacteristic
417C2×C4C22×D4411yescharacteristic
418C2×C4C2×#433911yescharacteristic
419C2×C4C22×C22⋊D1111yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8—42no—
424C8—442no—
425C8—442no—
426C8#6699512yes—
427C22—21no—
428C22—21no—
429C22—881no—
430C22—881no—
431C22—881no—
432C22#1062275412yes—
433C22C2×#6698311yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—24no—
438C4—21no—
439C4—42no—
440C4—881no—
441C4—881no—
442C4—881no—
443C4C2×#6695712yes—
444C4C2×#6699511yescharacteristic
445C4#1062335311yescharacteristic
446C2—22no—
447C2—1761no—
448C2#1307808811yescharacteristic
449C2#1307819711yescharacteristic
450C2C2×#1062275411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C8×Q8×C11C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×C8×Q8D11
hypocenterC11#19263
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. #13078746C2semidirect
4. #13068074C2semidirect
5. #13068060C2semidirect
6. #13067998C2semidirect
7. #13067964C2semidirect
8. #13067379C2semidirect
9. #13067314C2semidirect
11. C2×C8×Q8×C11C2semidirect
166. C2×C8×Q8D11semidirect
387. C11#19263semidirect

Maximal subgroups

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

subgroupindex
#130791752
#130787462
#130787382
#130680742
#130680602
#130679982
#130679642
#130673792
#130673142
#130673092
C2×C8×Q8×C112
#1926311