Finite Group Databasebeta

← #15683081

Subgroups — #15683081

Order 2944.

472 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625086C211yesmaximal, characteristic, complemented
2C2×#10625072C211yesmaximal, characteristic, complemented
3#13092996C211yesmaximal, characteristic
4#13092990C211yesmaximal, characteristic, complemented
5#13092676C211yesmaximal, characteristic, complemented
6#13092673C211yesmaximal, characteristic, complemented
7#13092661C211yesmaximal, characteristic, complemented
8#13092660C211yesmaximal, characteristic, complemented
9#13092658C211yesmaximal, characteristic, complemented
10#13092657C211yesmaximal, characteristic, complemented
11#13092645C211yesmaximal, characteristic, complemented
12#13092456C211yesmaximal, characteristic, complemented
13#13092410C211yesmaximal, characteristic, complemented
14#103×D23C211yesmaximal, characteristic, complemented
15C23×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C2×SD16×C23C2211yescharacteristic
20C22×C8×C23C2211yescharacteristic
21C23×C22⋊Q8C2211yescharacteristic
22C23×#121C2211yescharacteristic
23#10625117C2211yescharacteristic
24C2×#67275C2211yescharacteristic
25#10625110—21no—
26#10625109—21no—
27#10625109C2211yescharacteristic
28C2×#67273C2211yescharacteristic
29#10625095C2211yescharacteristic
30#10625095C2211yescharacteristic
31C2×#67267C2211yescharacteristic
32#10625086—24no—
33C2×Dic92C2211yescharacteristic
34#10625072—24no—
35C2×#67262C2211yescharacteristic
36C2×#67262C2211yescharacteristic
37C2×C8×D23C2211yescharacteristic
38C2×C8×D23C2211yescharacteristic
39#10625068C2211yescharacteristic
40#10625068C2211yescharacteristic
41#10625065—21no—
42#10625063C2211yescharacteristic
43C4⋊C4×D23C2211yescharacteristic
44#10625059—21no—
45#10625056—21no—
46#10625055—21no—
47#10625054—21no—
48#10625049—21no—
49C23×#106C2211yescharacteristic
50C23×#103C2211yescharacteristic
51C23×#102C2211yescharacteristic
52#10625017C2211yescharacteristic
53#10625014C2211yescharacteristic
54#10625000C2211yescharacteristic
55#10624998C2211yescharacteristic
56#10624998C2211yescharacteristic
57#10624992C2211yescharacteristic
58#10624992C2211yescharacteristic
59#10624990C2211yescharacteristic
60#10624989C2211yescharacteristic
61C2×Q8×C23C2311yescharacteristic
62C2×D4×C23—21no—
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23D411yescharacteristic
68C2×C22⋊D23D411yescharacteristic
69C22×Dic23—21no—
70Q8×D23—22no—
71Q8×D23—22no—
72#67290—22no—
73#67290—22no—
74#67288—22no—
75#67288—22no—
76C2×D92D411yescharacteristic
77C2×C4×D23—21no—
78C2×C4×D23—21no—
79C2×C4×D23C2311yescharacteristic
80C2×C4×D23C2311yescharacteristic
81C2×Dic46—21no—
82C2×Dic46D411yescharacteristic
83C2×Dic46C2311yescharacteristic
84C2×Dic46C2311yescharacteristic
85SD16×C23—22no—
86C2×C8×C23—22no—
87C2×C8×C23C2311yescharacteristic
88C2×C8×C23C2311yescharacteristic
89C4⋊C4×C23—21no—
90C4⋊C4×C23C2311yescharacteristic
91C4⋊C4×C23C2311yescharacteristic
92C22⋊C4×C23—21no—
93C22⋊C4×C23—21no—
94C22⋊Dic23—21no—
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97#67275—22no—
98#67273—22no—
99(C2×D23)⋊C4—21no—
100(C2×D23)⋊C4—21no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103C4⋊Dic23—21no—
104C4⋊Dic23—21no—
105C4⋊Dic23C2311yescharacteristic
106C4⋊Dic23C2311yescharacteristic
107Dic23⋊C4—21no—
108Dic23⋊C4—21no—
109Dic23⋊C4—21no—
110Dic23⋊C4—21no—
111C4×Dic23—21no—
112#67267—22no—
113C2×C23⋊C8C2311yescharacteristic
114C2×C23⋊C8C2311yescharacteristic
115Dic92—22no—
116#67262—22no—
117#67262D414yescomplemented
118C8×D23—22no—
119C8×D23—22no—
120C23×C23—21no—
121C23×C23C2×D411yescharacteristic
122C22×D23C2×D411yescharacteristic
123C22×D23C2×D411yescharacteristic
124Q8×C23—21no—
125Q8×C23—21no—
126D4×C23—21no—
127D4×C23—21no—
128D4×C23—81no—
129C2×C4×C23—21no—
130C2×C4×C23—21no—
131C2×C4×C23—21no—
132C2×C4×C23—21no—
133C2×C4×C23—21no—
134C2×C4×C23C2×D411yescharacteristic
135C2×C4×C23C2411yescharacteristic
136C22⋊D23—22no—
137C22⋊D23—22no—
138C22⋊D23—42no—
139C22⋊D23—81no—
140C2×Dic23—21no—
141C2×Dic23—21no—
142C2×Dic23—21no—
143C2×Dic23—21no—
144C2×Dic23—42no—
145C2×Dic23C2×D411yescharacteristic
146C2×Dic23C2×D411yescharacteristic
147D92—22no—
148C4×D23—21no—
149C4×D23—21no—
150C4×D23—42no—
151C4×D23—81no—
152C4×D23C2×D412yes—
153C4×D23#4112yes—
154Dic46—22no—
155Dic46—21no—
156Dic46—21no—
157Dic46—21no—
158Dic46—21no—
159Dic46—42no—
160C8×C23—21no—
161C8×C23C2×D412yes—
162C23⋊C8—21no—
163C23⋊C8C2×D412yes—
164#3063—231nomaximal, Sylow
165C22×C23—21no—
166C22×C23—21no—
167C22×C23—21no—
168C22×C23—41no—
169C22×C23—41no—
170C22×C23—41no—
171C22×C23C22×D411yescharacteristic
172C2×D23—21no—
173C2×D23—21no—
174C2×D23—21no—
175C2×D23—21no—
176C2×D23—21no—
177C2×D23#12112yes—
178C4×C23—21no—
179C4×C23—41no—
180C4×C23—41no—
181C4×C23—41no—
182C4×C23C22×D411yescharacteristic
183C4×C23C2×#4111yescharacteristic
184Dic23—21no—
185Dic23—41no—
186Dic23—41no—
187Dic23—41no—
188Dic23—41no—
189Dic23#12112yes—
190C2×#137—231no—
191C2×#131—231no—
192#537—231no—
193#536—231no—
194#470—231no—
195#470—231no—
196#468—231no—
197#468—231no—
198#467—231no—
199#467—231no—
200#465—231no—
201#465D2311yescharacteristic, complemented
202#428—231no—
203#416—231no—
204C2×#103—231no—
205C2×C23—41no—
206C2×C23—81no—
207C2×C23C2×#12111yescharacteristic
208C2×C23#57711yescharacteristic
209C2×C23#57811yescharacteristic
210D23—22no—
211D23—41no—
212C2×#41—231no—
213C2×#41—231no—
214C22×Q8—231no—
215#137—464no—
216C2×Q16—231no—
217C2×Q16—231no—
218C2×SD16—231no—
219C2×SD16C2×D2311yescharacteristic
220#131—464no—
221C2×M16—231no—
222C2×M16—231no—
223C2×M16—231no—
224C22×C8—231no—
225C22×C8—231no—
226C22×C8C2×D2311yescharacteristic
227C4⋊Q8—461no—
228#124—461no—
229#123—461no—
230#123—461no—
231C22⋊Q8—231no—
232C22⋊Q8—231no—
233C22⋊Q8—231no—
234C22⋊Q8—231no—
235C22⋊Q8—231no—
236C22⋊Q8—461no—
237C22⋊Q8C2×D2311yescharacteristic
238#121—231no—
239#121—461no—
240#121—461no—
241#121—461no—
242#121C2×D2311yescharacteristic
243#117—231no—
244C2×C4⋊C4—231no—
245#107—231no—
246#107—231no—
247#106—231no—
248#106C2×D2311yescharacteristic
249#103—231no—
250#103—231no—
251#103—231no—
252#103—231no—
253#103—231no—
254#103C2×D2311yescharacteristic
255#102—231no—
256#102C2×D2311yescharacteristic
257C23#306311yescharacteristic, complemented, Sylow
258#41—462no—
259#41—462no—
260#41—462no—
261#41—462no—
262C2×Q8—231no—
263C2×Q8—231no—
264C2×Q8—231no—
265C2×Q8—461no—
266C2×Q8—462no—
267C2×Q8—462no—
268C2×Q8C22×D2311yescharacteristic
269C2×D4—21no—
270C2×D4—231no—
271C2×D4—231no—
272C2×D4—231no—
273C2×D4—461no—
274C2×D4—461no—
275C2×D4C22×D2311yescharacteristic
276C22×C4—231no—
277C22×C4—231no—
278C22×C4—461no—
279C22×C4—461no—
280C22×C4—461no—
281C22×C4C22×D2311yescharacteristic
282Q16—462no—
283Q16—462no—
284SD16—22no—
285SD16—462no—
286M16—234no—
287M16—462no—
288M16—462no—
289C2×C8—22no—
290C2×C8—231no—
291C2×C8—231no—
292C2×C8—462no—
293C2×C8—462no—
294C2×C8C22×D2311yescharacteristic
295C2×C8C22×D2311yescharacteristic
296C4⋊C4—21no—
297C4⋊C4—231no—
298C4⋊C4—231no—
299C4⋊C4—461no—
300C4⋊C4—461no—
301C4⋊C4—461no—
302C4⋊C4—461no—
303C4⋊C4—461no—
304C4⋊C4—461no—
305C4⋊C4C22×D2311yescharacteristic
306C4⋊C4C22×D2311yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—461no—
310C22⋊C4—461no—
311C22⋊C4—461no—
312C22⋊C4—461no—
313C22⋊C4—461no—
314C22⋊C4—461no—
315C22⋊C4—461no—
316C42—461no—
317C23—21no—
318C23—231no—
319C23—231no—
320C23D4×D2311yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—462no—
324Q8—461no—
325Q8—461no—
326Q8—461no—
327Q8—461no—
328Q8—922no—
329D4—21no—
330D4—21no—
331D4—81no—
332D4—462no—
333D4—462no—
334D4—462no—
335D4—922no—
336D4—1841no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—231no—
343C2×C4—232no—
344C2×C4—232no—
345C2×C4—231no—
346C2×C4—461no—
347C2×C4—461no—
348C2×C4—461no—
349C2×C4—461no—
350C2×C4—461no—
351C2×C4—461no—
352C2×C4—922no—
353C2×C4—922no—
354C2×C4—1841no—
355C2×C4D4×D2311yescharacteristic
356C2×C4C23×D2311yescharacteristic
357C8—21no—
358C8—232no—
359C8—461no—
360C8D4×D2312yes—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—232no—
368C22—461no—
369C22—461no—
370C22—461no—
371C22—461no—
372C22—461no—
373C22C2×D4×D2311yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—232no—
379C4—461no—
380C4—921no—
381C4—921no—
382C4—921no—
383C4—921no—
384C4C2×D4×D2311yescharacteristic
385C4#41×D2311yescharacteristic
386C2—41no—
387C2—81no—
388C2—462no—
389C2—921no—
390C2#121×D2311yescharacteristic
391C2#1309322311yescharacteristic
392C2#1309323111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#465C2
socleC22×C23C22×D4
prime radical#13092996C2
hypercenter#465D23
hypocenterC23#3063
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#10625086C2semidirect
2. C2×#10625072C2semidirect
4. #13092990C2semidirect
5. #13092676C2semidirect
6. #13092673C2semidirect
7. #13092661C2semidirect
8. #13092660C2semidirect
9. #13092658C2semidirect
10. #13092657C2semidirect
11. #13092645C2semidirect
12. #13092456C2semidirect
13. #13092410C2semidirect
14. #103×D23C2semidirect
15. C23×#465C2semidirect
117. #67262D4semidirect
201. #465D23semidirect
257. C23#3063semidirect

Maximal subgroups

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

subgroupindex
C2×#106250862
C2×#106250722
#130929962
#130929902
#130926762
#130926732
#130926612
#130926602
#130926582
#130926572
#130926452
#130924562
#130924102
#103×D232
C23×#4652
#306323