Finite Group Databasebeta

← #14736495

Subgroups — #14736495

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#13078406C212yesmaximal
3#13077582C211yesmaximal, characteristic
4#13068199C212yesmaximal, complemented
5#13068192C212yesmaximal, complemented
6#13068145C211yesmaximal, characteristic, complemented
7#13068140C211yesmaximal, characteristic, complemented
8#13068111C211yesmaximal, characteristic, complemented
9#13068106C211yesmaximal, characteristic, complemented
10#13067274C212yesmaximal, complemented
11C2×C11×#334C211yesmaximal, characteristic, complemented
12C4×#4339C2211yescharacteristic
13#10623001C2212yes—
14C2×C11×C4⋊C8C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16#10622729—21no—
17#10622729—21no—
18#10622726—22no—
19#10622724—21no—
20#10622724—21no—
21#10622719—22no—
22#10622538C2211yescharacteristic
23#10622464C2212yes—
24#10622463C2212yes—
25#10622460—22no—
26#10622459C2212yes—
27#10622455C2212yes—
28#10622442—22no—
29#10622312C2211yescharacteristic
30C4×Dic44—21no—
31C4×Dic44—21no—
32#10622301C2211yescharacteristic
33#10622301C2211yescharacteristic
34C4×#4313—21no—
35#10622298—21no—
36#10622295C2211yescharacteristic
37#10622294C2212yes—
38#10622292C2211yescharacteristic
39#10622292C2211yescharacteristic
40C11×#334C2211yescharacteristic
41C11×#334C2211yescharacteristic
42C11×#334C2212yes—
43#10622124C2212yes—
44#10622124C2212yes—
45#10622119C2212yes—
46#10622119C2212yes—
47C2×#4339D411yescharacteristic
48C22×C8×C11—22no—
49C22×C8×C11D411yescharacteristic
50C22×C8×C11D411yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C4×C22⋊D11—21no—
53C4×C22⋊D11—21no—
54#66979—22no—
55#66979D411yescharacteristic
56#66977—22no—
57#66977—22no—
58C2×Dic44—21no—
59C2×Dic44—21no—
60C2×#4313—21no—
61C2×#4313—21no—
62C4×D44D411yescharacteristic
63C4×D44C2311yescharacteristic
64#66925—21no—
65C42×D11—21no—
66#66923—22no—
67#66922C2312yes—
68#66922C2312yes—
69C4×Dic22—22no—
70C4×Dic22—22no—
71C4×Dic22D411yescharacteristic
72C4×Dic22C2311yescharacteristic
73C11×C4⋊C8—22no—
74C11×C4⋊C8C2312yes—
75C11×C4⋊C8C2312yes—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80C22⋊(C11⋊C8)—21no—
81#66885—22no—
82#66885—22no—
83(C2×D11)⋊C8—21no—
84(C2×D11)⋊C8—21no—
85#66882—21no—
86#66882—21no—
87#66882—22no—
88#66882—22no—
89#66881—22no—
90#66881—22no—
91#66880—22no—
92#66880—22no—
93#66880—22no—
94#66880—22no—
95#66879—21no—
96#66879—21no—
97Dic11⋊C8—21no—
98Dic11⋊C8—21no—
99C4⋊(C11⋊C8)C2311yescharacteristic
100C4⋊(C11⋊C8)C2311yescharacteristic
101C4×C11⋊C8—21no—
102#19158—111nomaximal, Sylow
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C2×C22⋊D11—21no—
107#4339—24no—
108C2×D44C2×D411yescharacteristic
109C2×C4×D11—21no—
110C2×C4×D11—21no—
111C2×C4×D11—21no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22C2×D411yescharacteristic
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—41no—
119C2×C8×C11—44no—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11C2×D411yescharacteristic
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128C22⋊Dic11—21no—
129C22⋊Dic11—42no—
130(C2×D11)⋊C4—21no—
131(C2×D11)⋊C4—21no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11C2×D411yescharacteristic
137C4⋊Dic11C2×D411yescharacteristic
138Dic11⋊C4—21no—
139Dic11⋊C4—21no—
140Dic11⋊C4—42no—
141Dic11⋊C4—42no—
142C4×Dic11—21no—
143C4×Dic11—21no—
144C4×Dic11—21no—
145C4×Dic11—42no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148Dic44—42no—
149Dic44—42no—
150#4313—42no—
151#4313—42no—
152#3170—111no—
153#3076—112no—
154#2965—111no—
155#1704—112no—
156#1703—112no—
157#1696—111no—
158#1695—111no—
159#1690—111no—
160#1689—111no—
161C2×#334D1111yescharacteristic, complemented
162#1542—112no—
163C23×C11#12111yescharacteristic
164C22×D11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—41no—
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#13714yes—
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C22⋊D11—42no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181D44—22no—
182C4×D11—42no—
183C4×D11—41no—
184C4×D11—41no—
185C4×D11—42no—
186Dic22—22no—
187Dic22—42no—
188Dic22—42no—
189Dic22—82no—
190C8×C11—21no—
191C8×C11—21no—
192C8×C11—21no—
193C8×C11—42no—
194C8×C11—42no—
195C8×C11#13512yes—
196C11⋊C8—41no—
197C11⋊C8—41no—
198#533—112no—
199C4×#41—111no—
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#446—111no—
212#446—111no—
213C4×Q16—221no—
214C4×Q16—221no—
215#436—111no—
216#436—111no—
217#435—221no—
218#435—221no—
219#431—111no—
220#431—221no—
221#427—222no—
222C2×C4⋊C8C2×D1112yes—
223#416—222no—
224C4×M16—221no—
225C2×C4×C8C2×D1111yescharacteristic
226#334C2×D1111yescharacteristic
227#334C2×D1111yescharacteristic
228#334C2×D1112yes—
229#333—112no—
230#333—112no—
231#332—112no—
232#332—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11#47012yes—
236C22×C11C2×#12111yescharacteristic
237C2×D11—41no—
238C2×D11—41no—
239C2×D11—41no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11#47012yes—
244C4×C11C2×#13511yescharacteristic
245C4×C11C2×#13712yes—
246C4×C11#57511yescharacteristic
247Dic11—41no—
248Dic11—41no—
249Dic11—41no—
250Dic11—82no—
251Dic11—82no—
252C2×#41—111no—
253C2×Q16—221no—
254C2×Q16—221no—
255C2×M16—221no—
256C2×M16—221no—
257C22×C8—22no—
258C22×C8D4411yescharacteristic
259C22×C8D4411yescharacteristic
260C4⋊Q8—112no—
261C4⋊Q8—112no—
262#125—222no—
263C22⋊Q8—222no—
264C22⋊Q8—222no—
265C4×Q8—111no—
266C4×Q8—111no—
267C4×Q8—222no—
268C4×Q8—222no—
269C4×D4—111no—
270C4×D4—111no—
271C4×D4—221no—
272C4×D4—221no—
273#117—111no—
274#117—221no—
275#117—222no—
276C2×C42—221no—
277C2×C42C22×D1111yescharacteristic
278#107—222no—
279#107—222no—
280#107—221no—
281#107—221no—
282#106—222no—
283#106—222no—
284C4⋊C8—22no—
285C4⋊C8—111no—
286C4⋊C8—111no—
287C4⋊C8—221no—
288C4⋊C8—221no—
289C4⋊C8C22×D1112yes—
290C4⋊C8C22×D1112yes—
291#103—222no—
292#103—222no—
293#103—222no—
294#103—222no—
295#102—222no—
296#102—222no—
297C22⋊C8—221no—
298C22⋊C8—221no—
299C22⋊C8—221no—
300#97—221no—
301#97—221no—
302C4×C8—221no—
303C4×C8D4411yescharacteristic
304C4×C8D4411yescharacteristic
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1111yescharacteristic
307C2×C11—22no—
308C2×C11#303511yescharacteristic
309C2×C11C2×#47011yescharacteristic
310C2×C11#306711yescharacteristic
311D11—81no—
312#41—224no—
313C2×Q8—111no—
314C2×Q8—222no—
315C2×Q8—222no—
316C2×D4—111no—
317C2×D4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4C2×D4411yescharacteristic
322C22×C4D4×D1111yescharacteristic
323C22×C4#434311yescharacteristic
324Q16—442no—
325Q16—442no—
326M16—442no—
327M16—442no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—41no—
332C2×C8—44no—
333C2×C8—221no—
334C2×C8—221no—
335C2×C8C2×D4411yescharacteristic
336C2×C8C2×D4411yescharacteristic
337C2×C8C2×D4411yescharacteristic
338C2×C8C2×D4411yescharacteristic
339C4⋊C4—111no—
340C4⋊C4—111no—
341C4⋊C4—221no—
342C4⋊C4—221no—
343C4⋊C4—222no—
344C4⋊C4—222no—
345C4⋊C4—222no—
346C4⋊C4—222no—
347C4⋊C4—442no—
348C4⋊C4—442no—
349C22⋊C4—221no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—442no—
353C42—221no—
354C42—221no—
355C42—221no—
356C42—442no—
357C42C2×D4411yescharacteristic
358C42D4×D1111yescharacteristic
359C42#434311yescharacteristic
360C42C23×D1111yescharacteristic
361C11#1915811yescharacteristic, complemented, Sylow
362C23—221no—
363C23#6694811yescharacteristic
364Q8—222no—
365Q8—442no—
366Q8—442no—
367Q8—882no—
368D4—222no—
369D4—442no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—41no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4#6694811yescharacteristic
383C2×C4#6694811yescharacteristic
384C2×C4#6694811yescharacteristic
385C2×C4#6696814yes—
386C2×C4C22×D4411yescharacteristic
387C2×C4C2×D4×D1111yescharacteristic
388C2×C4C2×#434311yescharacteristic
389C8—21no—
390C8—21no—
391C8—21no—
392C8—42no—
393C8—42no—
394C8—441no—
395C8—441no—
396C8#6695712yes—
397C22—21no—
398C22—21no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22#1062248112yes—
403C22C2×#6694811yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—441no—
408C4—441no—
409C4—441no—
410C4—882no—
411C4—882no—
412C4#1062248112yes—
413C4C2×#6695711yescharacteristic
414C4#1062327911yescharacteristic
415C4C2×#6696812yes—
416C2—22no—
417C2—881no—
418C2#1307807311yescharacteristic
419C2C2×#1062248111yescharacteristic
420C2#1307833711yescharacteristic
subgroupG/H
centerC2×C4#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#334C2
socleC22×C11C2×#121
prime radicalC2×#4339D4
hypercenterC2×#334D11
hypocenterC11#19158
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
4. #13068199C2semidirect
5. #13068192C2semidirect
6. #13068145C2semidirect
7. #13068140C2semidirect
8. #13068111C2semidirect
9. #13068106C2semidirect
10. #13067274C2semidirect
11. C2×C11×#334C2semidirect
161. C2×#334D11semidirect
361. C11#19158semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130784062
#130775822
#130681992
#130681922
#130681452
#130681402
#130681112
#130681062
#130672742
C2×C11×#3342
#1915811