Finite Group Databasebeta

← #14737135

Subgroups — #14737135

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079791C212yesmaximal
2#13079202C211yesmaximal, characteristic, complemented
3#13068198C212yesmaximal, complemented
4#13068191C212yesmaximal, complemented
5#13068020C211yesmaximal, characteristic, complemented
6#13068015C211yesmaximal, characteristic, complemented
7#13067986C211yesmaximal, characteristic, complemented
8#13067981C211yesmaximal, characteristic, complemented
9#13067364C211yesmaximal, characteristic, complemented
10#13067327C212yesmaximal, complemented
11C11×#2966C211yesmaximal, characteristic
12C11×#529C2211yescharacteristic
13#10623001C2212yes—
14C11×#446C2211yescharacteristic
15C8×Q8×C11C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#435—21no—
18C8×D4×C11—21no—
19C8×D4×C11C2211yescharacteristic
20C11×#433—21no—
21C11×#432C2211yescharacteristic
22C11×#405—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622729—21no—
25#10622729—21no—
26#10622677—22no—
27#10622669—22no—
28#10622658—22no—
29#10622648—22no—
30#10622634C2212yes—
31#10622633C2212yes—
32#10622621C2212yes—
33#10622620C2212yes—
34#10622538C2212yes—
35#10622312C2211yescharacteristic
36C4×Dic44—21no—
37C4×Dic44—21no—
38#10622295C2211yescharacteristic
39#10622294C2212yes—
40#10622120C2212yes—
41#10622120C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622096C2211yescharacteristic
45#10622096C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×M16—21no—
48C22×C8×C11—21no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C11×#126—21no—
52C11×#125D411yescharacteristic
53C11×#124D411yescharacteristic
54C11×#123—21no—
55C11×C22⋊Q8D411yescharacteristic
56C11×#121D411yescharacteristic
57C4×Q8×C11C2311yescharacteristic
58C4×D4×C11—21no—
59C4×D4×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C42×C11C2311yescharacteristic
62#66979—22no—
63#66977—22no—
64#66977—22no—
65C2×Dic44—21no—
66C2×Dic44—21no—
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—
79C11×#97—21no—
80C11×#97—21no—
81C4×C8×C11—21no—
82C4×C8×C11D411yescharacteristic
83C4×C8×C11D411yescharacteristic
84C4×C8×C11C2311yescharacteristic
85C4×C8×C11C2311yescharacteristic
86#66899—22no—
87#66899—22no—
88#66896—22no—
89#66896—22no—
90C22⋊(C11⋊C8)—22no—
91#66882—21no—
92#66882—21no—
93#66880—22no—
94#66880—22no—
95#66872—22no—
96#66872—22no—
97#66871—22no—
98#66871—22no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C4×C11⋊C8—22no—
102#19220—111nomaximal, Sylow
103C2×Q8×C11C2×D411yescharacteristic
104C2×D4×C11—21no—
105C2×D4×C11C2×D411yescharacteristic
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C2×Dic22—22no—
111C2×Dic22—22no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—41no—
117C2×C8×C11—42no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4C2×D411yescharacteristic
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C22⋊C4—21no—
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C11×C22⋊C4—21no—
133C42×C11—21no—
134C42×C11C2×D411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—42no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143Dic11⋊C4—42no—
144Dic11⋊C4—42no—
145C4×Dic11—42no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148Dic44—42no—
149Dic44—42no—
150#3233—112no—
151#3170—111no—
152#2966D1111yescharacteristic
153#1704—112no—
154#1703—112no—
155#1676—111no—
156#1675—111no—
157#1670—111no—
158#1669—111no—
159#1564—111no—
160#1554—112no—
161C23×C11—21no—
162C23×C11#12111yescharacteristic
163Q8×C11—21no—
164Q8×C11—21no—
165D4×C11—21no—
166D4×C11—21no—
167D4×C11—42no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×Dic11—42no—
185C2×Dic11—42no—
186Dic22—42no—
187Dic22—42no—
188Dic22—82no—
189C8×C11—21no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—41no—
193C8×C11—41no—
194C8×C11#13512yes—
195C11⋊C8—42no—
196C11⋊C8—42no—
197#533—112no—
198#529C2×D1111yescharacteristic
199#500—111no—
200#499—222no—
201#494—111no—
202#488—222no—
203#487—112no—
204#485—222no—
205#482—222no—
206#477—112no—
207#476—112no—
208#475—112no—
209#474—112no—
210#467—221no—
211#467—221no—
212#446C2×D1111yescharacteristic
213C8×Q8C2×D1111yescharacteristic
214C4×Q16—221no—
215C4×Q16—221no—
216#436C2×D1111yescharacteristic
217#435—21no—
218C8×D4—21no—
219C8×D4C2×D1111yescharacteristic
220#433—21no—
221#432C2×D1111yescharacteristic
222#431—112no—
223#405—21no—
224C2×C4×C8C2×D1111yescharacteristic
225#335—111no—
226#335—111no—
227#334—112no—
228#333—112no—
229#333—112no—
230#332—112no—
231#332—112no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11C2×#12111yescharacteristic
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—41no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11C2×#13511yescharacteristic
247C4×C11#57511yescharacteristic
248C4×C11#57811yescharacteristic
249C4×C11#57811yescharacteristic
250Dic11—82no—
251Dic11—82no—
252C2×Q16—221no—
253C2×Q16—221no—
254C2×M16—21no—
255C22×C8—21no—
256C22×C8C22⋊D1111yescharacteristic
257C22×C8C22⋊D1111yescharacteristic
258C4⋊Q8—112no—
259C4⋊Q8—112no—
260#126—21no—
261#125—222no—
262#125D4411yescharacteristic
263#124D4411yescharacteristic
264#123—21no—
265C22⋊Q8—222no—
266C22⋊Q8—222no—
267C22⋊Q8D4411yescharacteristic
268#121D4411yescharacteristic
269C4×Q8—222no—
270C4×Q8—222no—
271C4×Q8C22×D1111yescharacteristic
272C4×D4—21no—
273C4×D4C22×D1111yescharacteristic
274#117—21no—
275#117—222no—
276C2×C42C22×D1111yescharacteristic
277#107—221no—
278#107—221no—
279#107—222no—
280#107—222no—
281#106—222no—
282#106—222no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—112no—
286C4⋊C8—112no—
287C4⋊C8C22×D1111yescharacteristic
288C4⋊C8C22×D1111yescharacteristic
289#103—222no—
290#103—222no—
291#103—222no—
292#103—222no—
293#102—222no—
294#102—222no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—21no—
298C22⋊C8—222no—
299#97—21no—
300#97—21no—
301C4×C8—21no—
302C4×C8—222no—
303C4×C8C22⋊D1111yescharacteristic
304C4×C8C22⋊D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—41no—
308C2×C11—81no—
309C2×C11#303511yescharacteristic
310C2×C11#305911yescharacteristic
311C2×C11#306711yescharacteristic
312C2×Q8—222no—
313C2×Q8—222no—
314C2×Q8C2×D4411yescharacteristic
315C2×D4—21no—
316C2×D4C2×D4411yescharacteristic
317C22×C4—21no—
318C22×C4C2×D4411yescharacteristic
319C22×C4#433911yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321Q16—442no—
322Q16—442no—
323M16—42no—
324C2×C8—22no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—41no—
328C2×C8—42no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8C2×C22⋊D1111yescharacteristic
332C2×C8C2×C22⋊D1111yescharacteristic
333C2×C8C2×C22⋊D1111yescharacteristic
334C2×C8C2×C22⋊D1111yescharacteristic
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—222no—
340C4⋊C4—222no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—442no—
344C4⋊C4—442no—
345C4⋊C4C2×D4411yescharacteristic
346C4⋊C4C2×D4411yescharacteristic
347C22⋊C4—21no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—442no—
353C42—21no—
354C42—442no—
355C42C2×D4411yescharacteristic
356C42#433911yescharacteristic
357C42C2×C22⋊D1111yescharacteristic
358C42C23×D1111yescharacteristic
359C11#1922011yescharacteristic, complemented, Sylow
360C23—21no—
361C23#6698311yescharacteristic
362Q8—21no—
363Q8—21no—
364Q8—442no—
365Q8—442no—
366Q8—882no—
367D4—21no—
368D4—21no—
369D4—42no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6698311yescharacteristic
383C2×C4#6698311yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4C22×D4411yescharacteristic
386C2×C4C2×#433911yescharacteristic
387C2×C4C22×C22⋊D1111yescharacteristic
388C8—21no—
389C8—21no—
390C8—21no—
391C8—41no—
392C8—41no—
393C8—442no—
394C8—442no—
395C8#6700312yes—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22C2×#6698311yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—882no—
411C4—882no—
412C4#1062328411yescharacteristic
413C4#1062328411yescharacteristic
414C4C2×#6700311yescharacteristic
415C4#1062335311yescharacteristic
416C2—41no—
417C2—81no—
418C2#1307807111yescharacteristic
419C2#1307827111yescharacteristic
420C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2966C2
socleC22×C11C2×#121
prime radicalC11×#121D4
hypercenter#2966D11
hypocenterC11#19220
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
2. #13079202C2semidirect
3. #13068198C2semidirect
4. #13068191C2semidirect
5. #13068020C2semidirect
6. #13068015C2semidirect
7. #13067986C2semidirect
8. #13067981C2semidirect
9. #13067364C2semidirect
10. #13067327C2semidirect
359. C11#19220semidirect

Maximal subgroups

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

subgroupindex
#130797912
#130792022
#130681982
#130681912
#130680202
#130680152
#130679862
#130679812
#130673642
#130673272
C11×#29662
#1922011