Finite Group Databasebeta

← #14737712

Subgroups — #14737712

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#13078772C212yesmaximal
2C8×#4339C211yesmaximal, characteristic
3#13068017C211yesmaximal, characteristic, complemented
4#13068012C211yesmaximal, characteristic, complemented
5#13068007C211yesmaximal, characteristic, complemented
6#13068002C211yesmaximal, characteristic, complemented
7#13067995C212yesmaximal, complemented
8#13067988C212yesmaximal, complemented
9#13067379C211yesmaximal, characteristic, complemented
10#13067326C212yesmaximal, complemented
11C11×#3160C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13C4×#4339C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#500C2211yescharacteristic
16C11×#499—21no—
17C11×#499—21no—
18C11×#498C2212yes—
19C11×#427—21no—
20C11×#427—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C8×C22⋊D11—21no—
23C8×C22⋊D11—21no—
24#10622704C2212yes—
25#10622703C2212yes—
26#10622697C2212yes—
27#10622696C2212yes—
28#10622660—22no—
29#10622658—22no—
30#10622643—22no—
31#10622639—22no—
32#10622539C2212yes—
33#10622538C2211yescharacteristic
34C8×D44C2211yescharacteristic
35C8×D44C2211yescharacteristic
36#10622298—21no—
37C4×C8×D11—21no—
38C8×Dic22C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622184C2212yes—
43#10622184C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×#4339D411yescharacteristic
48C22×C8×C11D411yescharacteristic
49C22×C8×C11D411yescharacteristic
50C11×C4⋊Q8C2312yes—
51C11×C4⋊Q8C2312yes—
52C11×#125—22no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C4×Q8×C11—22no—
56C4×Q8×C11—22no—
57C11×#117—22no—
58C2×C42×C11C2311yescharacteristic
59C2×#4326—22no—
60C2×#4325—22no—
61C4×C22⋊D11—21no—
62C4×C22⋊D11—21no—
63#66979D411yescharacteristic
64C2×C8×D11—21no—
65C2×C8×D11—21no—
66C4×D44D411yescharacteristic
67C4×D44C2311yescharacteristic
68#66925—21no—
69C42×D11—21no—
70C4×Dic22D411yescharacteristic
71C4×Dic22C2311yescharacteristic
72C11×#107—21no—
73C11×#107—21no—
74C11×#107—21no—
75C11×#107—21no—
76C11×#106—22no—
77C11×#106—22no—
78C4×C8×C11D411yescharacteristic
79C4×C8×C11D411yescharacteristic
80C4×C8×C11C2311yescharacteristic
81C4×C8×C11C2311yescharacteristic
82#66899—22no—
83#66899—22no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)—22no—
86(C2×D11)⋊C8—21no—
87(C2×D11)⋊C8—21no—
88Dic11⋊C8—21no—
89Dic11⋊C8—21no—
90C8×Dic11—21no—
91C8×Dic11—21no—
92#66874—22no—
93#66873—22no—
94#66872—22no—
95#66871—22no—
96C4⋊(C11⋊C8)C2311yescharacteristic
97C4⋊(C11⋊C8)C2311yescharacteristic
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100#66867—22no—
101C4×C11⋊C8—21no—
102#19273—111nomaximal, Sylow
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—21no—
109#4339—22no—
110#4339—22no—
111C2×D44C2×D411yescharacteristic
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×Dic22C2×D411yescharacteristic
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C11×C22⋊C4—42no—
129C42×C11—42no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11#4111yescharacteristic
133C42×C11C2411yescharacteristic
134C22⋊Dic11—21no—
135#4326—44no—
136#4325—44no—
137(C2×D11)⋊C4—21no—
138(C2×D11)⋊C4—21no—
139C4⋊Dic11C2×D411yescharacteristic
140C4⋊Dic11C2×D411yescharacteristic
141Dic11⋊C4—21no—
142Dic11⋊C4—21no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145C4×Dic11—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C8×D11—42no—
151C8×D11—42no—
152#3160D1111yescharacteristic, complemented
153#3116—112no—
154C8×#41—111no—
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#12111yescharacteristic
164C22×D11—21no—
165Q8×C11—42no—
166Q8×C11—42no—
167Q8×C11—82no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C22×D411yescharacteristic
180C2×C4×C11C2×#4111yescharacteristic
181C22⋊D11—24no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—21no—
185D44—21no—
186D44#13512yes—
187C4×D11—24no—
188C4×D11—42no—
189C4×D11—41no—
190C4×D11—41no—
191Dic22—21no—
192Dic22#13512yes—
193C8×C11—21no—
194C8×C11—21no—
195C8×C11#13712yes—
196C8×C11#13712yes—
197C11⋊C8—42no—
198C11⋊C8—42no—
199C11⋊C8—41no—
200C11⋊C8—41no—
201#533C2×D1112yes—
202C4×#41—111no—
203#500C2×D1111yescharacteristic
204#500C2×D1111yescharacteristic
205#499—21no—
206#499—21no—
207#498C2×D1112yes—
208#485—222no—
209#477—112no—
210#476—112no—
211#462—112no—
212#461—112no—
213#452—222no—
214C8×Q8—111no—
215C8×Q8—111no—
216#441—222no—
217#440—222no—
218C8×D4—111no—
219C8×D4—111no—
220C8×D4—221no—
221C8×D4—221no—
222#432—112no—
223#431—111no—
224#431—221no—
225#427—21no—
226#427—21no—
227C2×C4×C8—221no—
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—21no—
239C22×C11C2×#12111yescharacteristic
240C2×D11—22no—
241C2×D11—41no—
242C2×D11—41no—
243C4×C11—21no—
244C4×C11—21no—
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—82no—
248C4×C11—82no—
249C4×C11C2×#13511yescharacteristic
250C4×C11C2×#13511yescharacteristic
251C4×C11C2×#13711yescharacteristic
252C4×C11C2×#13711yescharacteristic
253Dic11—22no—
254Dic11—41no—
255Dic11—41no—
256C2×#41—111no—
257C2×Q16—222no—
258C2×SD16—222no—
259C22×C8—221no—
260C22×C8—221no—
261C22×C8C22⋊D1111yescharacteristic
262C22×C8C22⋊D1111yescharacteristic
263C4⋊Q8C22×D1112yes—
264C4⋊Q8C22×D1112yes—
265#125—22no—
266C22⋊Q8—22no—
267C22⋊Q8—22no—
268C4×Q8—22no—
269C4×Q8—22no—
270C4×Q8—111no—
271C4×Q8—111no—
272C4×D4—111no—
273C4×D4—111no—
274C4×D4—221no—
275C4×D4—221no—
276#117—22no—
277#117—111no—
278#117—221no—
279C2×C42—221no—
280C2×C42C22×D1111yescharacteristic
281#107—21no—
282#107—21no—
283#107—21no—
284#107—21no—
285#107—222no—
286#106—22no—
287#106—22no—
288#106—222no—
289C4⋊C8—111no—
290C4⋊C8—111no—
291C4⋊C8—112no—
292C4⋊C8—112no—
293C4⋊C8—221no—
294C4⋊C8—221no—
295#103—222no—
296#103—222no—
297#103—222no—
298#102—222no—
299C22⋊C8—222no—
300C22⋊C8—221no—
301C22⋊C8—221no—
302C22⋊C8—221no—
303#97—222no—
304C4×C8—221no—
305C4×C8—221no—
306C4×C8—221no—
307C4×C8C22⋊D1111yescharacteristic
308C4×C8C22⋊D1111yescharacteristic
309C4×C8C22×D1111yescharacteristic
310C4×C8C22×D1111yescharacteristic
311C2×C11—41no—
312C2×C11#303911yescharacteristic
313C2×C11#305011yescharacteristic
314C2×C11#306711yescharacteristic
315D11—42no—
316#41—222no—
317#41—222no—
318C2×Q8—22no—
319C2×Q8—22no—
320C2×Q8—111no—
321C2×D4—111no—
322C2×D4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4D4×D1111yescharacteristic
327C22×C4#434111yescharacteristic
328C22×C4C2×C22⋊D1111yescharacteristic
329Q16—444no—
330SD16—444no—
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—222no—
334C2×C8—222no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—442no—
338C2×C8—442no—
339C2×C8C2×C22⋊D1111yescharacteristic
340C2×C8C2×C22⋊D1111yescharacteristic
341C2×C8C2×C22⋊D1111yescharacteristic
342C2×C8C2×C22⋊D1111yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—42no—
348C4⋊C4—42no—
349C4⋊C4—111no—
350C4⋊C4—111no—
351C4⋊C4—221no—
352C4⋊C4—221no—
353C22⋊C4—42no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C22⋊C4—221no—
357C42—42no—
358C42—221no—
359C42—221no—
360C42—221no—
361C42D4×D1111yescharacteristic
362C42#434111yescharacteristic
363C42C2×C22⋊D1111yescharacteristic
364C42C23×D1111yescharacteristic
365C11#1927311yescharacteristic, complemented, Sylow
366C23—221no—
367C23#6699111yescharacteristic
368Q8—42no—
369Q8—42no—
370Q8—82no—
371Q8—112no—
372Q8—221no—
373D4—112no—
374D4—224no—
375D4—221no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—224no—
384C2×C4—221no—
385C2×C4—221no—
386C2×C4—221no—
387C2×C4—442no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4#6699111yescharacteristic
391C2×C4#6699111yescharacteristic
392C2×C4#6699111yescharacteristic
393C2×C4C2×D4×D1111yescharacteristic
394C2×C4C2×#434111yescharacteristic
395C2×C4C22×C22⋊D1111yescharacteristic
396C8—21no—
397C8—21no—
398C8—442no—
399C8—442no—
400C8—441no—
401C8—441no—
402C8#6699512yes—
403C8#6699512yes—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—222no—
408C22—441no—
409C22—441no—
410C22C2×#6699111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—82no—
416C4—82no—
417C4—222no—
418C4—441no—
419C4—441no—
420C4D11×#13511yescharacteristic
421C4D11×#13511yescharacteristic
422C4C2×#6699511yescharacteristic
423C4C2×#6699511yescharacteristic
424C2—41no—
425C2—442no—
426C2#1307809911yescharacteristic
427C2#1307819311yescharacteristic
428C2#1307833211yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3160C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3160D11
hypocenterC11#19273
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #13068017C2semidirect
4. #13068012C2semidirect
5. #13068007C2semidirect
6. #13068002C2semidirect
7. #13067995C2semidirect
8. #13067988C2semidirect
9. #13067379C2semidirect
10. #13067326C2semidirect
11. C11×#3160C2semidirect
152. #3160D11semidirect
365. C11#19273semidirect

Maximal subgroups

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

subgroupindex
#130787722
C8×#43392
#130680172
#130680122
#130680072
#130680022
#130679952
#130679882
#130673792
#130673262
C11×#31602
#1927311