Finite Group Databasebeta

← #15683622

Subgroups — #15683622

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#13093032C211yesmaximal, characteristic
2#13092893C211yesmaximal, characteristic, complemented
3#13092761C211yesmaximal, characteristic, complemented
4#13092739C211yesmaximal, characteristic
5#13092710C211yesmaximal, characteristic, complemented
6#13092701C211yesmaximal, characteristic, complemented
7#13092638C211yesmaximal, characteristic, complemented
8#13092637C211yesmaximal, characteristic, complemented
9#13092574C211yesmaximal, characteristic, complemented
10#13092554C211yesmaximal, characteristic
11#13092522C211yesmaximal, characteristic, complemented
12#13092517C211yesmaximal, characteristic, complemented
13C4×Dic92C211yesmaximal, characteristic, complemented
14#13092476C211yesmaximal, characteristic, complemented
15C4×SD16×C23C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19C4×D4×C23C2211yescharacteristic
20Q8×Dic23C2211yescharacteristic
21C2×#67275C2211yescharacteristic
22#10625109C2211yescharacteristic
23#10625107C2211yescharacteristic
24C2×#67273C2211yescharacteristic
25#10625100—21no—
26#10625095—21no—
27C2×Dic92C2211yescharacteristic
28#10625068C2211yescharacteristic
29#10625063—21no—
30#10625063C2211yescharacteristic
31#10625059C2211yescharacteristic
32#10625058—21no—
33#10625058C2211yescharacteristic
34#10625056—21no—
35#10625050—21no—
36#10625043—21no—
37#10625043C2211yescharacteristic
38C4×Dic46—21no—
39C4×Dic46C2211yescharacteristic
40C4×Dic46C2211yescharacteristic
41C23×#106C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×#102C2211yescharacteristic
44C4×C8×C23C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625014C2211yescharacteristic
47(C2×D23)⋊C8C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49#10625000C2211yescharacteristic
50#10624998C2211yescharacteristic
51#10624998C2211yescharacteristic
52Dic23⋊C8C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54#10624992C2211yescharacteristic
55#10624992C2211yescharacteristic
56#10624990C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×D4×C23C2311yescharacteristic
61C22×C4×C23—21no—
62C2×C22⋊D23—21no—
63Q8×D23—22no—
64Q8×D23—22no—
65C2×C4×D23—21no—
66C2×C4×D23C2311yescharacteristic
67C2×Dic46—21no—
68C2×Dic46—21no—
69C2×Dic46C2311yescharacteristic
70C2×Dic46C2311yescharacteristic
71SD16×C23—22no—
72C2×C8×C23C2311yescharacteristic
73C2×C8×C23C2311yescharacteristic
74C4⋊C4×C23—21no—
75C4⋊C4×C23C2311yescharacteristic
76C4⋊C4×C23C2311yescharacteristic
77C22⋊C4×C23—21no—
78C42×C23—21no—
79C42×C23C2311yescharacteristic
80C22⋊Dic23—21no—
81C22⋊Dic23—21no—
82C22⋊Dic23—21no—
83#67275—22no—
84#67273—22no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4D411yescharacteristic
88(C2×D23)⋊C4D411yescharacteristic
89C4⋊Dic23—21no—
90C4⋊Dic23—21no—
91C4⋊Dic23C2311yescharacteristic
92C4⋊Dic23C2311yescharacteristic
93Dic23⋊C4—21no—
94Dic23⋊C4—21no—
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4D411yescharacteristic
98Dic23⋊C4D411yescharacteristic
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107Dic92—22no—
108C23×C23—21no—
109C22×D23C2×D411yescharacteristic
110Q8×C23—21no—
111Q8×C23#4112yes—
112D4×C23—21no—
113D4×C23—21no—
114C2×C4×C23—21no—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—81no—
118C2×C4×C23C2×D411yescharacteristic
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2411yescharacteristic
121C22⋊D23—81no—
122C2×Dic23—21no—
123C2×Dic23—21no—
124C2×Dic23—21no—
125C2×Dic23—21no—
126C2×Dic23C2×D411yescharacteristic
127C2×Dic23C2×D411yescharacteristic
128C2×Dic23C2×D411yescharacteristic
129C4×D23—24no—
130C4×D23—21no—
131C4×D23—21no—
132Dic46—24no—
133Dic46—21no—
134Dic46—21no—
135Dic46—21no—
136Dic46—81no—
137Dic46#4112yes—
138C8×C23—21no—
139C8×C23—21no—
140C23⋊C8—21no—
141C23⋊C8—21no—
142#3121—231nomaximal, Sylow
143C22×C23—41no—
144C22×C23—41no—
145C22×C23—41no—
146C22×C23C22×D411yescharacteristic
147C2×D23—21no—
148C2×D23—21no—
149C2×D23—21no—
150C4×C23—22no—
151C4×C23—21no—
152C4×C23—21no—
153C4×C23—41no—
154C4×C23—41no—
155C4×C23C2×#4111yescharacteristic
156C4×C23C2×#4111yescharacteristic
157Dic23—21no—
158Dic23—22no—
159Dic23—21no—
160Dic23—21no—
161Dic23—41no—
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×Q16—231no—
177C4×SD16D2311yescharacteristic, complemented
178#433—231no—
179C2×C23—81no—
180C2×C23#52511yescharacteristic
181C2×C23#57711yescharacteristic
182C2×C23#57811yescharacteristic
183D23—41no—
184C22×Q8—231no—
185C2×Q16—231no—
186C2×Q16—231no—
187C2×SD16—231no—
188C2×SD16C2×D2311yescharacteristic
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—231no—
201C4×Q8—461no—
202C4×Q8—461no—
203C4×Q8C2×D2311yescharacteristic
204C4×D4C2×D2311yescharacteristic
205#117—231no—
206#117—231no—
207#117—461no—
208#117—461no—
209#107—231no—
210#107—231no—
211#106—231no—
212#106C2×D2311yescharacteristic
213C4⋊C8—231no—
214C4⋊C8—231no—
215#103—231no—
216#103—231no—
217#103—231no—
218#103—231no—
219#103—231no—
220#103C2×D2311yescharacteristic
221#102—231no—
222#102C2×D2311yescharacteristic
223C22⋊C8—231no—
224C22⋊C8—231no—
225#97—231no—
226C4×C8C2×D2311yescharacteristic
227C23#312111yescharacteristic, complemented, Sylow
228C2×Q8—231no—
229C2×Q8—231no—
230C2×Q8—461no—
231C2×Q8—461no—
232C2×Q8—462no—
233C2×Q8—462no—
234C2×Q8C22×D2311yescharacteristic
235C2×D4—461no—
236C2×D4C22×D2311yescharacteristic
237C22×C4—21no—
238C22×C4—231no—
239C22×C4—461no—
240Q16—462no—
241Q16—462no—
242SD16—22no—
243SD16—462no—
244C2×C8—231no—
245C2×C8—231no—
246C2×C8C22×D2311yescharacteristic
247C2×C8C22×D2311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—231no—
250C4⋊C4—231no—
251C4⋊C4—231no—
252C4⋊C4—231no—
253C4⋊C4—461no—
254C4⋊C4—461no—
255C4⋊C4—461no—
256C4⋊C4—461no—
257C4⋊C4—461no—
258C4⋊C4—461no—
259C4⋊C4C22×D2311yescharacteristic
260C4⋊C4C22×D2311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—231no—
263C22⋊C4—231no—
264C22⋊C4—461no—
265C22⋊C4—461no—
266C22⋊C4—461no—
267C22⋊C4—461no—
268C22⋊C4—461no—
269C42—21no—
270C42—231no—
271C42—461no—
272C42—461no—
273C42—461no—
274C42—461no—
275C42—461no—
276C42C22×D2311yescharacteristic
277C23—21no—
278C23—231no—
279Q8—21no—
280Q8—232no—
281Q8—464no—
282Q8—461no—
283Q8—461no—
284Q8—461no—
285Q8—1841no—
286Q8#6728812yes—
287D4—21no—
288D4—21no—
289D4—1841no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
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—461no—
304C2×C4D4×D2311yescharacteristic
305C2×C4D4×D2311yescharacteristic
306C2×C4C23×D2311yescharacteristic
307C8—21no—
308C8—21no—
309C8—461no—
310C8—461no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—461no—
315C22—461no—
316C22—461no—
317C22C2×D4×D2311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—461no—
324C4—462no—
325C4—461no—
326C4—461no—
327C4—921no—
328C4—921no—
329C4—921no—
330C4C2×#6728811yescharacteristic
331C4#41×D2311yescharacteristic
332C2—81no—
333C2—921no—
334C2#1309292611yescharacteristic
335C2#1309322311yescharacteristic
336C2#1309323111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×SD16×C23C2
socleC22×C23C22×D4
prime radical#10625109C22
hypercenterC4×SD16D23
hypocenterC23#3121
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #13092893C2semidirect
3. #13092761C2semidirect
5. #13092710C2semidirect
6. #13092701C2semidirect
7. #13092638C2semidirect
8. #13092637C2semidirect
9. #13092574C2semidirect
11. #13092522C2semidirect
12. #13092517C2semidirect
13. C4×Dic92C2semidirect
14. #13092476C2semidirect
15. C4×SD16×C23C2semidirect
177. C4×SD16D23semidirect
227. C23#3121semidirect

Maximal subgroups

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

subgroupindex
#130930322
#130928932
#130927612
#130927392
#130927102
#130927012
#130926382
#130926372
#130925742
#130925542
#130925222
#130925172
C4×Dic922
#130924762
C4×SD16×C232
#312123