Finite Group Databasebeta

← #14736873

Subgroups — #14736873

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079746C211yesmaximal, characteristic
2#13079541C211yesmaximal, characteristic
3C2×#10622692C211yesmaximal, characteristic, complemented
4#13077327C211yesmaximal, characteristic
5#13068114C214yesmaximal, complemented
6#13067990C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067298C211yesmaximal, characteristic, complemented
9C11×#1549C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66960—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622840—22no—
17#10622742—21no—
18#10622698—21no—
19#10622696C2214yes—
20#10622694—21no—
21#10622692—21no—
22#10622692—21no—
23#10622692C2212yes—
24#10622692C2212yes—
25C2×#66872—21no—
26C2×#66872—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622455C2214yes—
30#10622451—21no—
31#10622451C2212yes—
32#10622447—21no—
33#10622447C2212yes—
34#10622348—22no—
35#10622307—21no—
36#10622293—21no—
37C11×#332C2214yes—
38#10622119C2214yes—
39#10622118C2212yes—
40#10622117C2212yes—
41C22×Q8×C11—21no—
42C2×#4339—21no—
43C22×Dic22—21no—
44C2×C11×M16—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52C2×#4325—24no—
53#66983—21no—
54#66983D412yes—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C22×C11⋊C8D411yescharacteristic
58C22×C11⋊C8D411yescharacteristic
59#66960—44no—
60C2×#4313—22no—
61C2×C8×D11—22no—
62#66928—21no—
63#66927D411yescharacteristic
64C4×D44—21no—
65C4×D44C2312yes—
66#66922—21no—
67#66922—21no—
68#66922—21no—
69#66922D411yescharacteristic
70#66922C2312yes—
71C11×C4⋊C8—21no—
72C11×C4⋊C8C2312yes—
73C11×C4⋊C8C2312yes—
74C11×C22⋊C8—21no—
75C4×C8×C11—21no—
76#66899—24no—
77C22⋊(C11⋊C8)—21no—
78#66885—24no—
79(C2×D11)⋊C8—22no—
80(C2×D11)⋊C8—22no—
81#66881—24no—
82#66872—22no—
83#66872—22no—
84#66872—22no—
85#66872—22no—
86C4⋊(C11⋊C8)C2312yes—
87C4×C11⋊C8—21no—
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92#19191—111nomaximal, Sylow
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—82no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×C22⋊D11—22no—
101C22×Dic11—41no—
102#4339—42no—
103#4339—42no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44C2×D412yes—
107C2×C4×D11—22no—
108C2×Dic22—21no—
109C2×Dic22—22no—
110C2×Dic22—41no—
111C2×Dic22—82no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123#4325—84no—
124(C2×D11)⋊C4—22no—
125(C2×D11)⋊C4—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130C4⋊Dic11—41no—
131C4⋊Dic11C2×D412yes—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8SD1614yescomplemented
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138C2×C11⋊C8C2×D411yescharacteristic
139#4313—44no—
140C8×D11—44no—
141#3227—111no—
142#3206—111no—
143C2×#498—111no—
144#2931—111no—
145#1691—114no—
146#1671—114no—
147#1564—111no—
148#1549D1111yescharacteristic, complemented
149#1548—111no—
150C23×C11#12111yescharacteristic
151C22×D11—22no—
152Q8×C11—44no—
153Q8×C11—82no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—42no—
157C2×C4×C11—82no—
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11C2×SD1612yes—
162C2×C4×C11#13712yes—
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C2×#4111yescharacteristic
166C22⋊D11—44no—
167C2×Dic11—22no—
168C2×Dic11—42no—
169C2×Dic11—82no—
170D44—24no—
171D44—42no—
172D44—42no—
173C4×D11—42no—
174C4×D11—42no—
175Dic22—42no—
176Dic22—82no—
177Dic22—82no—
178C8×C11—42no—
179C8×C11—42no—
180C11⋊C8—21no—
181C11⋊C8—21no—
182C11⋊C8—42no—
183C11⋊C8C2×SD1612yes—
184C11⋊C8C2×SD1612yes—
185C2×#131—221no—
186#532—111no—
187C2×C4⋊Q8—111no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189#498—112no—
190#498—112no—
191#498—221no—
192#498—221no—
193#498—221no—
194#492—221no—
195#487—221no—
196#486—221no—
197#481—222no—
198#476—114no—
199#461—114no—
200#448—222no—
201#436—112no—
202#436—221no—
203C8×D4—112no—
204C8×D4—221no—
205#431—111no—
206#431C2×D1111yescharacteristic
207C2×#106—221no—
208C2×#106—221no—
209#423C2×D1111yescharacteristic
210#408—221no—
211C2×C4×C8—111no—
212#335—112no—
213#334—112no—
214#333—114no—
215#332C2×D1114yes—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11#46112yes—
219C22×C11C2×#12111yescharacteristic
220C2×D11—42no—
221C2×D11—42no—
222C2×D11—42no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11#46112yes—
227C4×C11#47112yes—
228C4×C11C22×SD1611yescharacteristic
229C4×C11C2×#13711yescharacteristic
230C4×C11#57712yes—
231Dic11—42no—
232Dic11—82no—
233C2×#41—221no—
234C22×Q8—21no—
235C22×Q8—221no—
236C2×SD16—224no—
237#131—444no—
238C2×M16—21no—
239C2×M16—222no—
240C22×C8—111no—
241C22×C8—111no—
242C22×C8—222no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—111no—
247C4⋊Q8—112no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
251C4⋊Q8C22×D1112yes—
252#127—111no—
253#124—221no—
254#121—112no—
255#121—221no—
256C4×D4—112no—
257C4×D4—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C42C22×D1111yescharacteristic
263#106—222no—
264#106—222no—
265#106—222no—
266#106—222no—
267#106—224no—
268C4⋊C8—21no—
269C4⋊C8—112no—
270C4⋊C8C22×D1112yes—
271C4⋊C8C22×D1112yes—
272#103—224no—
273#102—224no—
274C22⋊C8—21no—
275C22⋊C8—222no—
276C22⋊C8—222no—
277C22⋊C8—221no—
278C4×C8—21no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—111no—
283C4×C8—221no—
284C2×C11—22no—
285C2×C11C2×#46111yescharacteristic
286C2×C11#305711yescharacteristic
287C2×C11C2×#47111yescharacteristic
288D11—82no—
289#41—442no—
290#41—442no—
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—82no—
294C2×Q8—221no—
295C2×Q8—222no—
296C2×Q8—441no—
297C2×Q8—882no—
298C2×D4—112no—
299C2×D4—222no—
300C2×D4—221no—
301C2×D4—221no—
302C22×C4—41no—
303C22×C4—222no—
304C22×C4—441no—
305C22×C4#433911yescharacteristic
306C22×C4D4×D1111yescharacteristic
307C22×C4D4×D1111yescharacteristic
308SD16—884no—
309M16—42no—
310M16—444no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8—114no—
314C2×C8—111no—
315C2×C8—111no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—222no—
319C2×C8—222no—
320C2×C8—444no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—112no—
326C4⋊C4—221no—
327C4⋊C4—222no—
328C4⋊C4—222no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C22⋊C4—222no—
332C22⋊C4—222no—
333C42#433911yescharacteristic
334C42D4×D1111yescharacteristic
335C42D4×D1111yescharacteristic
336C42C23×D1111yescharacteristic
337C11#1919111yescharacteristic, complemented, Sylow
338C23—222no—
339C23#6693711yescharacteristic
340Q8—44no—
341Q8—82no—
342Q8—442no—
343Q8—882no—
344Q8—882no—
345D4—224no—
346D4—444no—
347D4—442no—
348D4—442no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4—222no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—882no—
358C2×C4#6693711yescharacteristic
359C2×C4#6693711yescharacteristic
360C2×C4#6693711yescharacteristic
361C2×C4SD16×D1112yes—
362C2×C4#6697112yes—
363C2×C4C2×#433911yescharacteristic
364C2×C4C2×D4×D1111yescharacteristic
365C2×C4C2×D4×D1111yescharacteristic
366C8—42no—
367C8—42no—
368C8—112no—
369C8—112no—
370C8—221no—
371C8—221no—
372C8—442no—
373C22—21no—
374C22—21no—
375C22—442no—
376C22—442no—
377C22—442no—
378C22#1062243112yes—
379C22C2×#6693711yescharacteristic
380C4—21no—
381C4—21no—
382C4—82no—
383C4—442no—
384C4—882no—
385C4#1062236712yes—
386C4#1062243112yes—
387C4C2×SD16×D1111yescharacteristic
388C4C2×#6697111yescharacteristic
389C4#1062330612yes—
390C2—22no—
391C2—882no—
392C2C2×#1062243111yescharacteristic
393C2#1307825411yescharacteristic
394C2C2×#1062236711yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1549D11
hypocenterC11#19191
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. C2×#10622692C2semidirect
5. #13068114C2semidirect
6. #13067990C2semidirect
7. #13067362C2semidirect
8. #13067298C2semidirect
9. C11×#1549C2semidirect
134. C2×C11⋊C8SD16semidirect
148. #1549D11semidirect
337. C11#19191semidirect

Maximal subgroups

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

subgroupindex
#130797462
#130795412
C2×#106226922
#130773272
#130681142
#130679902
#130673622
#130672982
C11×#15492
#1919111