Finite Group Databasebeta

← #14736252

Subgroups — #14736252

Order 2816.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078681C212yesmaximal
2C8×#4339C211yesmaximal, characteristic
3#13068043C212yesmaximal, complemented
4#13068036C212yesmaximal, complemented
5#13068007C211yesmaximal, characteristic, complemented
6#13068002C211yesmaximal, characteristic, complemented
7#13067983C211yesmaximal, characteristic, complemented
8#13067978C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067281C212yesmaximal, complemented
11C11×#3170C211yesmaximal, characteristic, complemented
12C11×#533C2212yes—
13C4×#4339C2211yescharacteristic
14C11×#500C2211yescharacteristic
15C11×#494C2211yescharacteristic
16C11×#487C2212yes—
17C11×#467—21no—
18C11×#467—21no—
19C4×C11×Q16—21no—
20C4×C11×Q16—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C8×C22⋊D11—21no—
23C8×C22⋊D11—21no—
24#10622707C2212yes—
25#10622703C2212yes—
26#10622700C2212yes—
27#10622696C2212yes—
28#10622660—22no—
29#10622658—22no—
30C4×#4326—22no—
31C4×#4325—22no—
32#10622538C2211yescharacteristic
33#10622538C2212yes—
34C8×D44C2211yescharacteristic
35C8×D44C2211yescharacteristic
36#10622298—21no—
37C4×C8×D11—21no—
38C8×Dic22C2211yescharacteristic
39C8×Dic22C2211yescharacteristic
40#10622185C2212yes—
41#10622185C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×#4339D411yescharacteristic
48C2×C11×Q16—21no—
49C2×C11×Q16—21no—
50C22×C8×C11D411yescharacteristic
51C22×C8×C11D411yescharacteristic
52C11×C4⋊Q8C2312yes—
53C11×C4⋊Q8C2312yes—
54C11×#125—22no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C11×#117—22no—
60C2×C42×C11C2311yescharacteristic
61C2×#4326—22no—
62C2×#4325—22no—
63C4×C22⋊D11—21no—
64C4×C22⋊D11—21no—
65#66979D411yescharacteristic
66C2×C8×D11—21no—
67C2×C8×D11—21no—
68C4×D44D411yescharacteristic
69C4×D44C2311yescharacteristic
70#66925—21no—
71C42×D11—21no—
72C4×Dic22D411yescharacteristic
73C4×Dic22C2311yescharacteristic
74C11×#107—21no—
75C11×#107—21no—
76C11×#103—22no—
77C11×#103—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—
100C4×C11⋊C8—21no—
101C4×C11⋊C8—22no—
102#19129—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
116C11×Q16—42no—
117C11×Q16—42no—
118C2×C8×C11—22no—
119C2×C8×C11—41no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C22⋊C4—42no—
131C42×C11—42no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11#4111yescharacteristic
135C42×C11C2411yescharacteristic
136C22⋊Dic11—21no—
137#4326—44no—
138#4325—44no—
139(C2×D11)⋊C4—21no—
140(C2×D11)⋊C4—21no—
141C4⋊Dic11C2×D411yescharacteristic
142C4⋊Dic11C2×D411yescharacteristic
143Dic11⋊C4—21no—
144Dic11⋊C4—21no—
145C4×Dic11—21no—
146C4×Dic11—21no—
147C4×Dic11—21no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C8×D11—42no—
153C8×D11—42no—
154#3170D1111yescharacteristic, complemented
155#3107—112no—
156C8×#41—111no—
157#1680—112no—
158#1679—112no—
159#1674—111no—
160#1673—111no—
161#1670—111no—
162#1669—111no—
163#1564—111no—
164#1544—112no—
165C23×C11#12111yescharacteristic
166C22×D11—21no—
167Q8×C11—42no—
168Q8×C11—42no—
169Q8×C11—42no—
170Q8×C11—42no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—22no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C22⋊D11—24no—
185C2×Dic11—21no—
186C2×Dic11—21no—
187C2×Dic11—21no—
188D44—21no—
189D44#13512yes—
190C4×D11—24no—
191C4×D11—41no—
192C4×D11—41no—
193C4×D11—42no—
194Dic22—21no—
195Dic22#13512yes—
196C8×C11—21no—
197C8×C11—21no—
198C8×C11—21no—
199C8×C11#13512yes—
200C11⋊C8—41no—
201C11⋊C8—42no—
202C11⋊C8—42no—
203C11⋊C8—41no—
204#533C2×D1112yes—
205C4×#41—111no—
206#500C2×D1111yescharacteristic
207#494C2×D1111yescharacteristic
208#487C2×D1112yes—
209#485—222no—
210#475—112no—
211#474—112no—
212#467—21no—
213#467—21no—
214#462—112no—
215#461—112no—
216#452—222no—
217C8×Q8—111no—
218C8×Q8—111no—
219C4×Q16—21no—
220C4×Q16—21no—
221C4×Q16—222no—
222C4×SD16—222no—
223C8×D4—111no—
224C8×D4—111no—
225C8×D4—221no—
226C8×D4—221no—
227#431—111no—
228#431—112no—
229#431—221no—
230C2×C4×C8—221no—
231C2×C4×C8C2×D1111yescharacteristic
232#335—111no—
233#335—111no—
234#334—112no—
235#332—112no—
236#332—112no—
237#332—112no—
238#332—112no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11C2×#12111yescharacteristic
243C2×D11—22no—
244C2×D11—41no—
245C2×D11—41no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—82no—
250C4×C11—82no—
251C4×C11#47312yes—
252C4×C11C2×#13511yescharacteristic
253C4×C11C2×#13511yescharacteristic
254C4×C11C2×#13511yescharacteristic
255C4×C11#57511yescharacteristic
256Dic11—22no—
257Dic11—41no—
258Dic11—41no—
259C2×#41—111no—
260C2×Q16—21no—
261C2×Q16—21no—
262C2×Q16—222no—
263C2×SD16—222no—
264C22×C8—221no—
265C22×C8—221no—
266C22×C8C22⋊D1111yescharacteristic
267C22×C8C22⋊D1111yescharacteristic
268C4⋊Q8C22×D1112yes—
269C4⋊Q8C22×D1112yes—
270#125—22no—
271C22⋊Q8—22no—
272C22⋊Q8—22no—
273C4×Q8—22no—
274C4×Q8—22no—
275C4×Q8—111no—
276C4×Q8—111no—
277C4×D4—111no—
278C4×D4—111no—
279C4×D4—221no—
280C4×D4—221no—
281#117—22no—
282#117—111no—
283#117—221no—
284C2×C42—221no—
285C2×C42C22×D1111yescharacteristic
286#107—21no—
287#107—21no—
288#107—222no—
289#106—222no—
290C4⋊C8—111no—
291C4⋊C8—111no—
292C4⋊C8—112no—
293C4⋊C8—112no—
294C4⋊C8—221no—
295C4⋊C8—221no—
296#103—22no—
297#103—22no—
298#103—222no—
299#103—222no—
300#103—222no—
301#102—222no—
302C22⋊C8—222no—
303C22⋊C8—221no—
304C22⋊C8—221no—
305C22⋊C8—221no—
306C4×C8—221no—
307C4×C8—221no—
308C4×C8—222no—
309C4×C8—221no—
310C4×C8C22⋊D1111yescharacteristic
311C4×C8C22⋊D1111yescharacteristic
312C4×C8C22×D1111yescharacteristic
313C4×C8C22×D1111yescharacteristic
314C2×C11—41no—
315C2×C11#303511yescharacteristic
316C2×C11#305011yescharacteristic
317C2×C11C2×#47311yescharacteristic
318D11—42no—
319#41—222no—
320#41—222no—
321C2×Q8—22no—
322C2×Q8—22no—
323C2×Q8—111no—
324C2×D4—111no—
325C2×D4—221no—
326C22×C4—221no—
327C22×C4—221no—
328C22×C4—221no—
329C22×C4D4×D1111yescharacteristic
330C22×C4#434111yescharacteristic
331C22×C4C2×C22⋊D1111yescharacteristic
332Q16—42no—
333Q16—42no—
334Q16—444no—
335SD16—444no—
336C2×C8—22no—
337C2×C8—41no—
338C2×C8—222no—
339C2×C8—222no—
340C2×C8—221no—
341C2×C8—221no—
342C2×C8—442no—
343C2×C8—442no—
344C2×C8C2×C22⋊D1111yescharacteristic
345C2×C8C2×C22⋊D1111yescharacteristic
346C2×C8C2×C22⋊D1111yescharacteristic
347C2×C8C2×C22⋊D1111yescharacteristic
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—111no—
355C4⋊C4—111no—
356C4⋊C4—221no—
357C4⋊C4—221no—
358C22⋊C4—42no—
359C22⋊C4—221no—
360C22⋊C4—221no—
361C22⋊C4—221no—
362C42—42no—
363C42—221no—
364C42—221no—
365C42—221no—
366C42D4×D1111yescharacteristic
367C42#434111yescharacteristic
368C42C2×C22⋊D1111yescharacteristic
369C42C23×D1111yescharacteristic
370C11#1912911yescharacteristic, complemented, Sylow
371C23—221no—
372C23#6699111yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—42no—
376Q8—42no—
377Q8—112no—
378Q8—221no—
379D4—112no—
380D4—224no—
381D4—221no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—224no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—221no—
393C2×C4—442no—
394C2×C4—441no—
395C2×C4—441no—
396C2×C4#6699111yescharacteristic
397C2×C4#6699111yescharacteristic
398C2×C4#6699111yescharacteristic
399C2×C4C2×D4×D1111yescharacteristic
400C2×C4C2×#434111yescharacteristic
401C2×C4C22×C22⋊D1111yescharacteristic
402C8—21no—
403C8—21no—
404C8—21no—
405C8—442no—
406C8—442no—
407C8—441no—
408C8—441no—
409C8#6700312yes—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—222no—
414C22—441no—
415C22—441no—
416C22C2×#6699111yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—82no—
421C4—82no—
422C4—222no—
423C4—441no—
424C4—441no—
425C4#1062280512yes—
426C4D11×#13511yescharacteristic
427C4D11×#13511yescharacteristic
428C4C2×#6700311yescharacteristic
429C4#1062335311yescharacteristic
430C2—41no—
431C2—442no—
432C2#1307806511yescharacteristic
433C2#1307819311yescharacteristic
434C2C2×#1062280511yescharacteristic
subgroupG/H
centerC2×C4#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3170C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenter#3170D11
hypocenterC11#19129
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
3. #13068043C2semidirect
4. #13068036C2semidirect
5. #13068007C2semidirect
6. #13068002C2semidirect
7. #13067983C2semidirect
8. #13067978C2semidirect
9. #13067364C2semidirect
10. #13067281C2semidirect
11. C11×#3170C2semidirect
154. #3170D11semidirect
370. C11#19129semidirect

Maximal subgroups

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

subgroupindex
#130786812
C8×#43392
#130680432
#130680362
#130680072
#130680022
#130679832
#130679782
#130673642
#130672812
C11×#31702
#1912911