Finite Group Databasebeta

← #14736493

Subgroups — #14736493

Order 2816.

596 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#13079202C211yesmaximal, characteristic, complemented
2#13078404C212yesmaximal
3#13068198C212yesmaximal, complemented
4#13068191C212yesmaximal, complemented
5#13068144C211yesmaximal, characteristic, complemented
6#13068139C211yesmaximal, characteristic, complemented
7#13068110C211yesmaximal, characteristic, complemented
8#13068105C211yesmaximal, characteristic, complemented
9C2×#10622095C211yesmaximal, characteristic, complemented
10#13067271C212yesmaximal, complemented
11C11×#2965C211yesmaximal, characteristic
12C4×C11×#41C2211yescharacteristic
13#10623001C2212yes—
14C11×#446C2211yescharacteristic
15C11×#446C2211yescharacteristic
16C11×#436C2211yescharacteristic
17C11×#436C2211yescharacteristic
18C11×#435—21no—
19C11×#435—21no—
20C11×#431—21no—
21C11×#431C2211yescharacteristic
22C4×C11×M16—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622846—22no—
25#10622729—21no—
26#10622729—21no—
27#10622635—22no—
28#10622634C2212yes—
29#10622633C2212yes—
30#10622622—22no—
31#10622621C2212yes—
32#10622620C2212yes—
33#10622611—22no—
34C2×C4⋊(C11⋊C8)C2212yes—
35#10622312C2211yescharacteristic
36C4×Dic44—21no—
37C4×Dic44—21no—
38#10622295C2211yescharacteristic
39#10622294C2212yes—
40#10622120C2212yes—
41#10622120C2212yes—
42#10622119C2212yes—
43#10622119C2212yes—
44#10622095C2211yescharacteristic
45#10622095C2211yescharacteristic
46#10622095C2212yes—
47C2×C11×#41D411yescharacteristic
48C2×C11×M16—21no—
49C2×C11×M16—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
62#66979—22no—
63#66977—22no—
64#66977—22no—
65C22×C11⋊C8—22no—
66C2×Dic44—21no—
67C2×Dic44—21no—
68#66923—22no—
69#66922C2312yes—
70#66922C2312yes—
71C4×Dic22—22no—
72C4×Dic22—22no—
73C11×C4⋊C8—21no—
74C11×C4⋊C8—21no—
75C11×C4⋊C8C2311yescharacteristic
76C11×C4⋊C8C2311yescharacteristic
77C11×C22⋊C8—21no—
78C11×C22⋊C8—21no—
79C11×C22⋊C8—21no—
80C11×#97—21no—
81C11×#97—21no—
82C4×C8×C11—21no—
83C4×C8×C11D411yescharacteristic
84C4×C8×C11D411yescharacteristic
85C4×C8×C11C2311yescharacteristic
86C4×C8×C11C2311yescharacteristic
87#66899—22no—
88#66899—22no—
89#66896—22no—
90#66896—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)—22no—
100C4⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)C2312yes—
102#19158—111nomaximal, Sylow
103C11×#41—24no—
104C2×Q8×C11C2×D411yescharacteristic
105C2×D4×C11—21no—
106C2×D4×C11C2×D411yescharacteristic
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×Dic22—22no—
114C2×Dic22—22no—
115C11×M16—42no—
116C11×M16—42no—
117C2×C8×C11—22no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—41no—
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C2×C8×C11C2×D411yescharacteristic
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4C2×D411yescharacteristic
128C11×C4⋊C4C2×D411yescharacteristic
129C11×C22⋊C4—21no—
130C11×C22⋊C4—21no—
131C11×C22⋊C4—21no—
132C42×C11—21no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11#4111yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11—42no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144Dic11⋊C4—42no—
145Dic11⋊C4—42no—
146C4×Dic11—42no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—44no—
150Dic44—42no—
151Dic44—42no—
152#3170—111no—
153#3076—112no—
154#2965D1111yescharacteristic
155#1704—112no—
156#1703—112no—
157#1696—111no—
158#1695—111no—
159#1690—111no—
160#1689—111no—
161C2×#334—111no—
162#1542—112no—
163C23×C11—21no—
164C23×C11#12111yescharacteristic
165Q8×C11—22no—
166D4×C11—22no—
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—41no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#13714yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×Dic11—42no—
186C2×Dic11—42no—
187Dic22—42no—
188Dic22—42no—
189Dic22—82no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—21no—
193C8×C11—41no—
194C8×C11—41no—
195C8×C11#13512yes—
196C11⋊C8—42no—
197C11⋊C8—42no—
198#533—112no—
199C4×#41C2×D1111yescharacteristic
200#500—111no—
201#494—111no—
202#487—112no—
203#479—222no—
204#478—222no—
205#477—112no—
206#476—112no—
207#475—112no—
208#474—112no—
209#467—221no—
210#467—221no—
211#446C2×D1111yescharacteristic
212#446C2×D1111yescharacteristic
213C4×Q16—221no—
214C4×Q16—221no—
215#436C2×D1111yescharacteristic
216#436C2×D1111yescharacteristic
217#435—21no—
218#435—21no—
219#431—21no—
220#431C2×D1111yescharacteristic
221#427—222no—
222C2×C4⋊C8—112no—
223#416—222no—
224C4×M16—21no—
225C2×C4×C8C2×D1111yescharacteristic
226#334—111no—
227#334—111no—
228#334—112no—
229#333—112no—
230#333—112no—
231#332—112no—
232#332—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11#47012yes—
239C22×C11C2×#12111yescharacteristic
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—41no—
244C4×C11—41no—
245C4×C11—41no—
246C4×C11#47012yes—
247C4×C11C2×#13511yescharacteristic
248C4×C11C2×#13712yes—
249C4×C11#57511yescharacteristic
250Dic11—82no—
251Dic11—82no—
252C2×#41D4411yescharacteristic
253C2×Q16—221no—
254C2×Q16—221no—
255C2×M16—21no—
256C2×M16—21no—
257C22×C8—222no—
258C22×C8C22⋊D1111yescharacteristic
259C22×C8C22⋊D1111yescharacteristic
260C4⋊Q8—112no—
261C4⋊Q8—112no—
262#125—222no—
263C22⋊Q8—222no—
264C22⋊Q8—222no—
265C4×Q8—222no—
266C4×Q8—222no—
267C4×Q8D4411yescharacteristic
268C4×Q8C22×D1111yescharacteristic
269C4×D4—21no—
270C4×D4—21no—
271C4×D4D4411yescharacteristic
272C4×D4C22×D1111yescharacteristic
273#117—21no—
274#117—222no—
275#117D4411yescharacteristic
276C2×C42—21no—
277C2×C42C22×D1111yescharacteristic
278#107—221no—
279#107—221no—
280#107—222no—
281#107—222no—
282#106—222no—
283#106—222no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8—112no—
287C4⋊C8—112no—
288C4⋊C8—222no—
289C4⋊C8C22×D1111yescharacteristic
290C4⋊C8C22×D1111yescharacteristic
291#103—222no—
292#103—222no—
293#103—222no—
294#103—222no—
295#102—222no—
296#102—222no—
297C22⋊C8—21no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300#97—21no—
301#97—21no—
302C4×C8—21no—
303C4×C8C22⋊D1111yescharacteristic
304C4×C8C22⋊D1111yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—22no—
308C2×C11—81no—
309C2×C11#303511yescharacteristic
310C2×C11C2×#47011yescharacteristic
311C2×C11#306711yescharacteristic
312#41—24no—
313C2×Q8—222no—
314C2×Q8—222no—
315C2×Q8C2×D4411yescharacteristic
316C2×D4—21no—
317C2×D4C2×D4411yescharacteristic
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4C2×D4411yescharacteristic
322C22×C4#433911yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324Q16—442no—
325Q16—442no—
326M16—42no—
327M16—42no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—222no—
333C2×C8—222no—
334C2×C8—444no—
335C2×C8C2×C22⋊D1111yescharacteristic
336C2×C8C2×C22⋊D1111yescharacteristic
337C2×C8C2×C22⋊D1111yescharacteristic
338C2×C8C2×C22⋊D1111yescharacteristic
339C4⋊C4—21no—
340C4⋊C4—21no—
341C4⋊C4—222no—
342C4⋊C4—222no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—442no—
346C4⋊C4—442no—
347C4⋊C4C2×D4411yescharacteristic
348C4⋊C4C2×D4411yescharacteristic
349C22⋊C4—21no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—442no—
353C42—21no—
354C42—21no—
355C42—21no—
356C42—442no—
357C42C2×D4411yescharacteristic
358C42#433911yescharacteristic
359C42C2×C22⋊D1111yescharacteristic
360C42C23×D1111yescharacteristic
361C11#1915811yescharacteristic, complemented, Sylow
362C23—21no—
363C23#6698311yescharacteristic
364Q8—22no—
365Q8—442no—
366Q8—442no—
367Q8—882no—
368D4—22no—
369D4—42no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6696214yes—
383C2×C4#6698311yescharacteristic
384C2×C4#6698311yescharacteristic
385C2×C4#6698311yescharacteristic
386C2×C4C22×D4411yescharacteristic
387C2×C4C2×#433911yescharacteristic
388C2×C4C22×C22⋊D1111yescharacteristic
389C8—21no—
390C8—21no—
391C8—21no—
392C8—41no—
393C8—41no—
394C8—442no—
395C8—442no—
396C8#6700312yes—
397C22—21no—
398C22—21no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22#1062275012yes—
403C22C2×#6698311yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—882no—
411C4—882no—
412C4#1062275012yes—
413C4C2×#6696212yes—
414C4C2×#6700311yescharacteristic
415C4#1062335311yescharacteristic
416C2—22no—
417C2—81no—
418C2#1307807111yescharacteristic
419C2C2×#1062275011yescharacteristic
420C2#1307833611yescharacteristic
subgroupG/H
centerC2×C4#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C2×#121
prime radicalC2×C11×#41D4
hypercenter#2965D11
hypocenterC11#19158
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
3. #13068198C2semidirect
4. #13068191C2semidirect
5. #13068144C2semidirect
6. #13068139C2semidirect
7. #13068110C2semidirect
8. #13068105C2semidirect
9. C2×#10622095C2semidirect
10. #13067271C2semidirect
361. C11#19158semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130784042
#130681982
#130681912
#130681442
#130681392
#130681102
#130681052
C2×#106220952
#130672712
C11×#29652
#1915811