Finite Group Databasebeta

← #15683627

Subgroups — #15683627

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#13093040C211yesmaximal, characteristic
2#13092895C211yesmaximal, characteristic, complemented
3#13092755C211yesmaximal, characteristic, complemented
4#13092742C211yesmaximal, characteristic
5#13092710C211yesmaximal, characteristic, complemented
6#13092700C211yesmaximal, characteristic, complemented
7#13092641C211yesmaximal, characteristic, complemented
8#13092641C211yesmaximal, characteristic, complemented
9#13092556C211yesmaximal, characteristic
10#13092524C211yesmaximal, characteristic, complemented
11#13092520C211yesmaximal, characteristic, complemented
12Q16×Dic23C211yesmaximal, characteristic, complemented
13#13092502C211yesmaximal, characteristic, complemented
14#13092475C211yesmaximal, characteristic, complemented
15C23×#451C211yesmaximal, characteristic, complemented
16C22×Q8×C23C2211yescharacteristic
17C2×Q16×C23C2211yescharacteristic
18C2×Q16×C23C2211yescharacteristic
19C23×C22⋊Q8C2211yescharacteristic
20#10625118C2211yescharacteristic
21Q8×Dic23—21no—
22Q8×Dic23—21no—
23Q8×Dic23C2211yescharacteristic
24Q8×Dic23C2211yescharacteristic
25Q8×Dic23C2211yescharacteristic
26Q8×Dic23C2211yescharacteristic
27Q8×Dic23C2211yescharacteristic
28C2×#67274C2211yescharacteristic
29C2×#67274C2211yescharacteristic
30#10625101C2211yescharacteristic
31#10625097—21no—
32#10625097—21no—
33#10625097C2211yescharacteristic
34#10625097C2211yescharacteristic
35#10625069—21no—
36#10625068—21no—
37#10625064C2211yescharacteristic
38#10625059C2211yescharacteristic
39#10625056—21no—
40#10625054—21no—
41C23×#103C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×C22⋊C8C2211yescharacteristic
44#10625017C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625017C2211yescharacteristic
48C22⋊(C23⋊C8)C2211yescharacteristic
49#10625003C2211yescharacteristic
50#10625003C2211yescharacteristic
51#10625000C2211yescharacteristic
52#10624999C2211yescharacteristic
53#10624997C2211yescharacteristic
54Dic23⋊C8C2211yescharacteristic
55Dic23⋊C8C2211yescharacteristic
56C8×Dic23C2211yescharacteristic
57#10624990C2211yescharacteristic
58#10624989C2211yescharacteristic
59C2×Q8×C23—22no—
60C2×Q8×C23—22no—
61C2×Q8×C23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×Q8×C23C2311yescharacteristic
64C2×Q8×C23C2311yescharacteristic
65C22×C4×C23—21no—
66C22×C4×C23C2311yescharacteristic
67C2×C22⋊D23—21no—
68C2×D92C2311yescharacteristic
69C2×C4×D23—21no—
70C2×Dic46—21no—
71Q16×C23—22no—
72Q16×C23—22no—
73C2×C8×C23C2311yescharacteristic
74C2×C8×C23C2311yescharacteristic
75C4⋊C4×C23—21no—
76C4⋊C4×C23C2311yescharacteristic
77C22⋊C4×C23—21no—
78C22⋊Dic23—21no—
79C22⋊Dic23D411yescharacteristic
80C22⋊Dic23D411yescharacteristic
81#67274—22no—
82#67274—22no—
83(C2×D23)⋊C4—21no—
84(C2×D23)⋊C4—21no—
85(C2×D23)⋊C4—21no—
86(C2×D23)⋊C4—21no—
87C4⋊Dic23—21no—
88C4⋊Dic23—21no—
89C4⋊Dic23—21no—
90C4⋊Dic23—21no—
91C4⋊Dic23—21no—
92C4⋊Dic23D411yescharacteristic
93C4⋊Dic23D411yescharacteristic
94C4⋊Dic23C2311yescharacteristic
95C4⋊Dic23C2311yescharacteristic
96C4⋊Dic23C2311yescharacteristic
97Dic23⋊C4—21no—
98C4×Dic23—21no—
99C4×Dic23—21no—
100C4×Dic23—21no—
101C4×Dic23—21no—
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C4×Dic23C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107C2×C23⋊C8C2311yescharacteristic
108C23×C23C2×D411yescharacteristic
109C22×D23—21no—
110Q8×C23—24no—
111Q8×C23—21no—
112Q8×C23—21no—
113Q8×C23—21no—
114Q8×C23—21no—
115Q8×C23#4112yes—
116Q8×C23#4112yes—
117C2×C4×C23—24no—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—21no—
122C2×C4×C23—21no—
123C2×C4×C23—21no—
124C2×C4×C23C2×D411yescharacteristic
125C2×C4×C23C2411yescharacteristic
126C22⋊D23—81no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—21no—
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133C2×Dic23C2×D411yescharacteristic
134D92—21no—
135D92—21no—
136C4×D23—81no—
137Dic46—81no—
138C8×C23—21no—
139C8×C23—21no—
140C23⋊C8—21no—
141C23⋊C8—21no—
142#3121—231nomaximal, Sylow
143C22×C23—21no—
144C22×C23—21no—
145C22×C23—21no—
146C22×C23C22×D411yescharacteristic
147C2×D23—41no—
148C2×D23—41no—
149C2×D23—41no—
150C4×C23—22no—
151C4×C23—22no—
152C4×C23—21no—
153C4×C23—41no—
154C4×C23—41no—
155C4×C23C2×#4111yescharacteristic
156C4×C23C2×#4111yescharacteristic
157Dic23—21no—
158Dic23—21no—
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#451D2311yescharacteristic, complemented
173#448—231no—
174#441—231no—
175#440—231no—
176C4×Q16—231no—
177C4×SD16—231no—
178#433—231no—
179C2×C23—41no—
180C2×C23#52511yescharacteristic
181C2×C23#57711yescharacteristic
182C2×C23#57811yescharacteristic
183D23—81no—
184C22×Q8C2×D2311yescharacteristic
185C2×Q16C2×D2311yescharacteristic
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—461no—
195C22⋊Q8C2×D2311yescharacteristic
196#121—231no—
197C4×Q8—231no—
198C4×Q8—231no—
199C4×Q8—231no—
200C4×Q8—231no—
201C4×Q8—231no—
202C4×Q8—461no—
203C4×Q8—461no—
204C4×D4—231no—
205#117—231no—
206#117—231no—
207#117—461no—
208#117—461no—
209#107—231no—
210#107—231no—
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⋊C8C2×D2311yescharacteristic
225#97—231no—
226C4×C8—231no—
227C23#312111yescharacteristic, complemented, Sylow
228C2×Q8—22no—
229C2×Q8—22no—
230C2×Q8—21no—
231C2×Q8—461no—
232C2×Q8C22×D2311yescharacteristic
233C2×Q8C22×D2311yescharacteristic
234C2×Q8C22×D2311yescharacteristic
235C2×D4—231no—
236C2×D4—461no—
237C22×C4—21no—
238C22×C4—461no—
239C22×C4C22×D2311yescharacteristic
240Q16—22no—
241Q16—22no—
242SD16—462no—
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—231no—
254C4⋊C4—461no—
255C4⋊C4—461no—
256C4⋊C4—461no—
257C4⋊C4—461no—
258C4⋊C4—461no—
259C4⋊C4—461no—
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—231no—
270C42—231no—
271C42—461no—
272C42—461no—
273C42—461no—
274C42—461no—
275C42—461no—
276C42—461no—
277C23—461no—
278C23D4×D2311yescharacteristic
279Q8—24no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—1841no—
285Q8#6729012yes—
286Q8#6729012yes—
287D4—461no—
288D4—461no—
289D4—1841no—
290C2×C4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—231no—
298C2×C4—231no—
299C2×C4—231no—
300C2×C4—231no—
301C2×C4—461no—
302C2×C4—461no—
303C2×C4—461no—
304C2×C4—1841no—
305C2×C4D4×D2311yescharacteristic
306C2×C4C23×D2311yescharacteristic
307C8—21no—
308C8—21no—
309C8—461no—
310C8—461no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—921no—
315C22—921no—
316C22—921no—
317C22C2×D4×D2311yescharacteristic
318C4—22no—
319C4—22no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—461no—
324C4—461no—
325C4—461no—
326C4—461no—
327C4—921no—
328C4—921no—
329C4—921no—
330C4C2×#6729011yescharacteristic
331C4C2×#6729011yescharacteristic
332C2—41no—
333C2—1841no—
334C2#1309292311yescharacteristic
335C2#1309322611yescharacteristic
336C2#1309323011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#451C2
socleC22×C23C22×D4
prime radical#10625101C22
hypercenter#451D23
hypocenterC23#3121
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #13092895C2semidirect
3. #13092755C2semidirect
5. #13092710C2semidirect
6. #13092700C2semidirect
7. #13092641C2semidirect
8. #13092641C2semidirect
10. #13092524C2semidirect
11. #13092520C2semidirect
12. Q16×Dic23C2semidirect
13. #13092502C2semidirect
14. #13092475C2semidirect
15. C23×#451C2semidirect
172. #451D23semidirect
227. C23#3121semidirect

Maximal subgroups

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

subgroupindex
#130930402
#130928952
#130927552
#130927422
#130927102
#130927002
#130926412
#130925562
#130925242
#130925202
Q16×Dic232
#130925022
#130924752
C23×#4512
#312123