Finite Group Databasebeta

← #14737718

Subgroups — #14737718

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079130C211yesmaximal, characteristic, complemented
2#13078778C212yesmaximal
3#13068020C211yesmaximal, characteristic, complemented
4#13068015C211yesmaximal, characteristic, complemented
5#13068010C211yesmaximal, characteristic, complemented
6#13068005C211yesmaximal, characteristic, complemented
7#13067998C212yesmaximal, complemented
8#13067991C212yesmaximal, complemented
9#13067379C211yesmaximal, characteristic, complemented
10#13067324C212yesmaximal, complemented
11C8×C11×#41C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13#10623001C2212yes—
14C8×Q8×C11C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C8×D4×C11—21no—
17C8×D4×C11—21no—
18C8×D4×C11C2211yescharacteristic
19C8×D4×C11C2211yescharacteristic
20C11×#431—21no—
21C11×#431C2211yescharacteristic
22C2×C4×C8×C11—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622852—22no—
25#10622719—21no—
26#10622719—21no—
27#10622644C2212yes—
28#10622643—22no—
29#10622634C2212yes—
30#10622632C2212yes—
31#10622631—22no—
32#10622621C2212yes—
33#10622609—22no—
34#10622539C2212yes—
35#10622296—21no—
36#10622296—21no—
37#10622295C2211yescharacteristic
38#10622295C2211yescharacteristic
39#10622293C2212yes—
40#10622124C2212yes—
41#10622124C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41D411yescharacteristic
48C22×C8×C11—21no—
49C22×C8×C11—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C4×Q8×C11D411yescharacteristic
53C4×Q8×C11C2311yescharacteristic
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11D411yescharacteristic
57C4×D4×C11C2311yescharacteristic
58C11×#117—21no—
59C11×#117D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63C2×#4324—22no—
64#66979—22no—
65#66977—22no—
66#66977—22no—
67#66923—22no—
68#66922C2312yes—
69#66922C2312yes—
70C4×Dic22—22no—
71C4×Dic22—22no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8C2311yescharacteristic
75C11×C4⋊C8C2311yescharacteristic
76C11×C22⋊C8—21no—
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C4×C8×C11—21no—
80C4×C8×C11—21no—
81C4×C8×C11—21no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2311yescharacteristic
85C4×C8×C11C2311yescharacteristic
86#66899—22no—
87#66896—22no—
88C22⋊(C11⋊C8)—22no—
89#66882—21no—
90#66882—21no—
91#66882—21no—
92#66882—21no—
93#66881—22no—
94#66881—22no—
95#66874—22no—
96#66874—22no—
97#66872—22no—
98#66871—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101#66867—22no—
102#19273—111nomaximal, Sylow
103C11×#41—22no—
104C11×#41—22no—
105C2×Q8×C11C2×D411yescharacteristic
106C2×D4×C11—21no—
107C2×D4×C11C2×D411yescharacteristic
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—42no—
121C2×C8×C11—42no—
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C2×C8×C11C2×D411yescharacteristic
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4C2×D411yescharacteristic
129C11×C4⋊C4C2×D411yescharacteristic
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140C22⋊Dic11—42no—
141#4326—44no—
142#4324—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—22no—
147Dic11⋊C4—42no—
148Dic11⋊C4—42no—
149C4×Dic11—42no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152#3160—111no—
153#3116—112no—
154C8×#41D1111yescharacteristic
155#1676—111no—
156#1675—111no—
157#1674—111no—
158#1673—111no—
159#1672—112no—
160#1671—112no—
161#1568—111no—
162#1554—112no—
163C23×C11—21no—
164C23×C11#12111yescharacteristic
165Q8×C11—21no—
166Q8×C11#13512yes—
167D4×C11—24no—
168D4×C11—21no—
169D4×C11#13512yes—
170C2×C4×C11—24no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×Dic11—42no—
189C2×Dic11—42no—
190Dic22—42no—
191Dic22—42no—
192Dic22—82no—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11—41no—
196C8×C11—41no—
197C8×C11#13712yes—
198C8×C11#13712yes—
199C11⋊C8—42no—
200C11⋊C8—42no—
201#533—112no—
202C4×#41C2×D1111yescharacteristic
203#500—111no—
204#500—111no—
205#499—221no—
206#499—221no—
207#498—112no—
208#485—222no—
209#477—112no—
210#476—112no—
211#462—112no—
212#461—112no—
213#452—222no—
214C8×Q8C2×D1111yescharacteristic
215C8×Q8C2×D1111yescharacteristic
216#441—222no—
217#440—222no—
218C8×D4—21no—
219C8×D4—21no—
220C8×D4C2×D1111yescharacteristic
221C8×D4C2×D1111yescharacteristic
222#432—112no—
223#431—21no—
224#431C2×D1111yescharacteristic
225#427—221no—
226#427—221no—
227C2×C4×C8—21no—
228C2×C4×C8C2×D1111yescharacteristic
229#335—111no—
230#335—111no—
231#334—112no—
232#333—112no—
233#333—112no—
234#332—112no—
235#332—112no—
236C22×C11—21no—
237C22×C11—21no—
238C22×C11—22no—
239C22×C11—21no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11C2×#12111yescharacteristic
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—22no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—41no—
249C4×C11—41no—
250C4×C11C2×#13511yescharacteristic
251C4×C11C2×#13511yescharacteristic
252C4×C11C2×#13711yescharacteristic
253C4×C11C2×#13711yescharacteristic
254Dic11—82no—
255Dic11—82no—
256C2×#41D4411yescharacteristic
257C2×Q16—222no—
258C2×SD16—222no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8C22⋊D1111yescharacteristic
262C22×C8C22⋊D1111yescharacteristic
263C4⋊Q8—112no—
264C4⋊Q8—112no—
265#125—222no—
266C22⋊Q8—222no—
267C22⋊Q8—222no—
268C4×Q8—222no—
269C4×Q8—222no—
270C4×Q8D4411yescharacteristic
271C4×Q8C22×D1111yescharacteristic
272C4×D4—21no—
273C4×D4—21no—
274C4×D4D4411yescharacteristic
275C4×D4C22×D1111yescharacteristic
276#117—21no—
277#117—222no—
278#117D4411yescharacteristic
279C2×C42—21no—
280C2×C42C22×D1111yescharacteristic
281#107—221no—
282#107—221no—
283#107—221no—
284#107—221no—
285#107—222no—
286#106—222no—
287#106—222no—
288#106—222no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—112no—
292C4⋊C8—112no—
293C4⋊C8C22×D1111yescharacteristic
294C4⋊C8C22×D1111yescharacteristic
295#103—222no—
296#103—222no—
297#103—222no—
298#102—222no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302C22⋊C8—222no—
303#97—222no—
304C4×C8—21no—
305C4×C8—21no—
306C4×C8—21no—
307C4×C8C22⋊D1111yescharacteristic
308C4×C8C22⋊D1111yescharacteristic
309C4×C8C22×D1111yescharacteristic
310C4×C8C22×D1111yescharacteristic
311C2×C11—41no—
312C2×C11—42no—
313C2×C11#303911yescharacteristic
314C2×C11#305011yescharacteristic
315C2×C11#306711yescharacteristic
316#41—22no—
317#41—22no—
318C2×Q8—222no—
319C2×Q8—222no—
320C2×Q8C2×D4411yescharacteristic
321C2×D4—21no—
322C2×D4C2×D4411yescharacteristic
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4C2×D4411yescharacteristic
327C22×C4#433911yescharacteristic
328C22×C4C2×C22⋊D1111yescharacteristic
329Q16—444no—
330SD16—444no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—42no—
336C2×C8—42no—
337C2×C8—222no—
338C2×C8—222no—
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C2×C8C2×C22⋊D1111yescharacteristic
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—442no—
350C4⋊C4—442no—
351C4⋊C4C2×D4411yescharacteristic
352C4⋊C4C2×D4411yescharacteristic
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—442no—
357C42—21no—
358C42—21no—
359C42—21no—
360C42—442no—
361C42C2×D4411yescharacteristic
362C42#433911yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C42C23×D1111yescharacteristic
365C11#1927311yescharacteristic, complemented, Sylow
366C23—21no—
367C23#6698311yescharacteristic
368Q8—21no—
369Q8—442no—
370Q8—442no—
371Q8—882no—
372Q8#6695712yes—
373D4—24no—
374D4—21no—
375D4#6695712yes—
376C2×C4—24no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—442no—
389C2×C4—442no—
390C2×C4#6698311yescharacteristic
391C2×C4#6698311yescharacteristic
392C2×C4#6698311yescharacteristic
393C2×C4C22×D4411yescharacteristic
394C2×C4C2×#433911yescharacteristic
395C2×C4C22×C22⋊D1111yescharacteristic
396C8—21no—
397C8—21no—
398C8—41no—
399C8—41no—
400C8—442no—
401C8—442no—
402C8#6700412yes—
403C8#6700412yes—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—41no—
409C22—41no—
410C22C2×#6698311yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—22no—
416C4—41no—
417C4—41no—
418C4—882no—
419C4—882no—
420C4C2×#6695711yescharacteristic
421C4C2×#6695711yescharacteristic
422C4C2×#6700411yescharacteristic
423C4C2×#6700411yescharacteristic
424C2—41no—
425C2—42no—
426C2#1307810311yescharacteristic
427C2#1307819711yescharacteristic
428C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenterC8×#41D11
hypocenterC11#19273
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #13079130C2semidirect
3. #13068020C2semidirect
4. #13068015C2semidirect
5. #13068010C2semidirect
6. #13068005C2semidirect
7. #13067998C2semidirect
8. #13067991C2semidirect
9. #13067379C2semidirect
10. #13067324C2semidirect
365. C11#19273semidirect

Maximal subgroups

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

subgroupindex
#130791302
#130787782
#130680202
#130680152
#130680102
#130680052
#130679982
#130679912
#130673792
#130673242
C8×C11×#412
#1927311