Finite Group Databasebeta

← #15683632

Subgroups — #15683632

Order 2944.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093039C211yesmaximal, characteristic
2#13092893C211yesmaximal, characteristic, complemented
3#13092756C211yesmaximal, characteristic, complemented
4#13092744C211yesmaximal, characteristic
5#13092711C211yesmaximal, characteristic, complemented
6#13092700C211yesmaximal, characteristic, complemented
7#13092642C211yesmaximal, characteristic, complemented
8#13092641C211yesmaximal, characteristic, complemented
9#13092571C211yesmaximal, characteristic, complemented
10#13092557C211yesmaximal, characteristic
11#13092522C211yesmaximal, characteristic, complemented
12#13092515C211yesmaximal, characteristic, complemented
13C4×#67263C211yesmaximal, characteristic, complemented
14#13092476C211yesmaximal, characteristic, complemented
15C4×Q16×C23C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×Q16×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20#10625118C2211yescharacteristic
21#10625117C2211yescharacteristic
22Q8×Dic23C2211yescharacteristic
23C2×#67275C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25C2×#67263C2211yescharacteristic
26#10625067—21no—
27#10625066C2211yescharacteristic
28#10625065—21no—
29#10625063—21no—
30#10625063C2211yescharacteristic
31#10625059C2211yescharacteristic
32#10625058—21no—
33#10625058C2211yescharacteristic
34#10625047—21no—
35#10625046—21no—
36C4×D92C2211yescharacteristic
37#10625043—21no—
38#10625043C2211yescharacteristic
39C4×Dic46—21no—
40C4×Dic46C2211yescharacteristic
41C23×#107C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C4×C8×C23C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625003C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50#10624999C2211yescharacteristic
51#10624998C2211yescharacteristic
52Dic23⋊C8C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61Q8×D23—22no—
62Q8×D23—22no—
63C2×D92—21no—
64C2×D92C2311yescharacteristic
65C2×C4×D23—21no—
66C2×C4×D23—21no—
67C2×C4×D23C2311yescharacteristic
68C2×Dic46—21no—
69C2×Dic46—21no—
70C2×Dic46C2311yescharacteristic
71Q16×C23—22no—
72C2×C8×C23C2311yescharacteristic
73C2×C8×C23C2311yescharacteristic
74C4⋊C4×C23—21no—
75C4⋊C4×C23—21no—
76C4⋊C4×C23C2311yescharacteristic
77C4⋊C4×C23C2311yescharacteristic
78C42×C23—21no—
79C42×C23—21no—
80C42×C23C2311yescharacteristic
81#67275—22no—
82#67274—22no—
83(C2×D23)⋊C4—21no—
84(C2×D23)⋊C4—21no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4D411yescharacteristic
90(C2×D23)⋊C4D411yescharacteristic
91C4⋊Dic23—21no—
92C4⋊Dic23C2311yescharacteristic
93C4⋊Dic23C2311yescharacteristic
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4D411yescharacteristic
99Dic23⋊C4D411yescharacteristic
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107#67263—22no—
108C22×D23—21no—
109C22×D23C2×D411yescharacteristic
110Q8×C23—21no—
111Q8×C23—21no—
112Q8×C23—21no—
113Q8×C23#4112yes—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23C2×D411yescharacteristic
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2411yescharacteristic
121C2×Dic23—21no—
122C2×Dic23—21no—
123C2×Dic23—21no—
124C2×Dic23C2×D411yescharacteristic
125C2×Dic23C2×D411yescharacteristic
126C2×Dic23C2×D411yescharacteristic
127D92—21no—
128D92—21no—
129D92—81no—
130C4×D23—24no—
131C4×D23—21no—
132C4×D23—21no—
133C4×D23—81no—
134Dic46—24no—
135Dic46—21no—
136Dic46—81no—
137Dic46#4112yes—
138C8×C23—21no—
139C8×C23—21no—
140C23⋊C8—21no—
141C23⋊C8—21no—
142#3121—231nomaximal, Sylow
143C22×C23C22×D411yescharacteristic
144C2×D23—21no—
145C2×D23—21no—
146C2×D23—21no—
147C2×D23—41no—
148C2×D23—41no—
149C2×D23—41no—
150C4×C23—22no—
151C4×C23—21no—
152C4×C23—21no—
153C4×C23—41no—
154C4×C23—41no—
155C4×C23—41no—
156C4×C23C2×#4111yescharacteristic
157C4×C23C2×#4111yescharacteristic
158Dic23—21no—
159Dic23—22no—
160Dic23—21no—
161Dic23—21no—
162Dic23—41no—
163Dic23—41no—
164#542—231no—
165#519—231no—
166#485—231no—
167#482—231no—
168#477—231no—
169#475—231no—
170#464—231no—
171#464—231no—
172#451—231no—
173#448—231no—
174#441—231no—
175#440—231no—
176C4×Q16D2311yescharacteristic, complemented
177C4×SD16—231no—
178#433—231no—
179C2×C23#52511yescharacteristic
180C2×C23#57711yescharacteristic
181C2×C23#57811yescharacteristic
182D23—41no—
183D23—81no—
184C22×Q8—231no—
185C2×Q16—231no—
186C2×Q16C2×D2311yescharacteristic
187C2×SD16—231no—
188C2×SD16—231no—
189C4⋊Q8—231no—
190#126—461no—
191#124—231no—
192#124—461no—
193#123—461no—
194C22⋊Q8—231no—
195C22⋊Q8—461no—
196#121—231no—
197C4×Q8—231no—
198C4×Q8—231no—
199C4×Q8—231no—
200C4×Q8—461no—
201C4×Q8—461no—
202C4×Q8C2×D2311yescharacteristic
203C4×Q8C2×D2311yescharacteristic
204C4×D4—231no—
205#117—231no—
206#117—231no—
207#117—461no—
208#117—461no—
209#107—231no—
210#107C2×D2311yescharacteristic
211#106—231no—
212#106—231no—
213C4⋊C8—231no—
214C4⋊C8—231no—
215#103—231no—
216#103—231no—
217#103—231no—
218#103—231no—
219#103C2×D2311yescharacteristic
220#103C2×D2311yescharacteristic
221#102—231no—
222#102—231no—
223C22⋊C8—231no—
224C22⋊C8—231no—
225#97—231no—
226C4×C8C2×D2311yescharacteristic
227C23#312111yescharacteristic, complemented, Sylow
228C2×Q8—231no—
229C2×Q8—461no—
230C2×Q8—461no—
231C2×Q8—462no—
232C2×Q8—462no—
233C2×Q8C22×D2311yescharacteristic
234C2×Q8C22×D2311yescharacteristic
235C2×D4—231no—
236C2×D4—461no—
237C22×C4—231no—
238C22×C4—461no—
239C22×C4—461no—
240Q16—22no—
241Q16—462no—
242SD16—462no—
243SD16—462no—
244C2×C8—231no—
245C2×C8—231no—
246C2×C8C22×D2311yescharacteristic
247C2×C8C22×D2311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—231no—
251C4⋊C4—231no—
252C4⋊C4—231no—
253C4⋊C4—231no—
254C4⋊C4—461no—
255C4⋊C4—461no—
256C4⋊C4—461no—
257C4⋊C4—461no—
258C4⋊C4—461no—
259C4⋊C4C22×D2311yescharacteristic
260C4⋊C4C22×D2311yescharacteristic
261C22⋊C4—231no—
262C22⋊C4—231no—
263C22⋊C4—461no—
264C22⋊C4—461no—
265C22⋊C4—461no—
266C22⋊C4—461no—
267C22⋊C4—461no—
268C22⋊C4—461no—
269C42—21no—
270C42—21no—
271C42—231no—
272C42—461no—
273C42—461no—
274C42—461no—
275C42—461no—
276C42C22×D2311yescharacteristic
277C23—231no—
278C23—461no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—232no—
283Q8—464no—
284Q8—461no—
285Q8—1841no—
286Q8#6728812yes—
287D4—461no—
288D4—461no—
289D4—1841no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—231no—
295C2×C4—231no—
296C2×C4—231no—
297C2×C4—464no—
298C2×C4—461no—
299C2×C4—461no—
300C2×C4—461no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—1841no—
304C2×C4D4×D2311yescharacteristic
305C2×C4D4×D2311yescharacteristic
306C2×C4C23×D2311yescharacteristic
307C8—21no—
308C8—21no—
309C8—461no—
310C8—461no—
311C22—461no—
312C22—461no—
313C22—461no—
314C22—921no—
315C22—921no—
316C22—921no—
317C22C2×D4×D2311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—461no—
325C4—462no—
326C4—461no—
327C4—461no—
328C4—921no—
329C4—921no—
330C4C2×#6728811yescharacteristic
331C4#41×D2311yescharacteristic
332C2—921no—
333C2—1841no—
334C2#1309292611yescharacteristic
335C2#1309322411yescharacteristic
336C2#1309323011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×Q16×C23C2
socleC22×C23C22×D4
prime radical#10625066C22
hypercenterC4×Q16D23
hypocenterC23#3121
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #13092893C2semidirect
3. #13092756C2semidirect
5. #13092711C2semidirect
6. #13092700C2semidirect
7. #13092642C2semidirect
8. #13092641C2semidirect
9. #13092571C2semidirect
11. #13092522C2semidirect
12. #13092515C2semidirect
13. C4×#67263C2semidirect
14. #13092476C2semidirect
15. C4×Q16×C23C2semidirect
176. C4×Q16D23semidirect
227. C23#3121semidirect

Maximal subgroups

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

subgroupindex
#130930392
#130928932
#130927562
#130927442
#130927112
#130927002
#130926422
#130926412
#130925712
#130925572
#130925222
#130925152
C4×#672632
#130924762
C4×Q16×C232
#312123