Finite Group Databasebeta

← #15683665

Subgroups — #15683665

Order 2944.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093039C211yesmaximal, characteristic, complemented
2#13092899C211yesmaximal, characteristic, complemented
3#13092751C211yesmaximal, characteristic, complemented
4#13092732C211yesmaximal, characteristic, complemented
5#13092710C211yesmaximal, characteristic, complemented
6#13092696C211yesmaximal, characteristic, complemented
7#13092641C211yesmaximal, characteristic, complemented
8#13092635C211yesmaximal, characteristic, complemented
9#13092578C211yesmaximal, characteristic, complemented
10#13092565C211yesmaximal, characteristic
11#13092515C211yesmaximal, characteristic, complemented
12#13092515C211yesmaximal, characteristic, complemented
13C4×D184C211yesmaximal, characteristic, complemented
14#13092476C211yesmaximal, characteristic, complemented
15C4×Q16×C23C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×Q16×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic
19C4×Q8×C23C2211yescharacteristic
20#10625118C2211yescharacteristic
21#10625117C2211yescharacteristic
22Q8×Dic23C2211yescharacteristic
23C2×#67274C2211yescharacteristic
24C2×#67274C2211yescharacteristic
25C2×D184C2211yescharacteristic
26#10625067—21no—
27#10625066C2211yescharacteristic
28#10625065—21no—
29#10625064—21no—
30#10625064C2211yescharacteristic
31C4⋊C4×D23—21no—
32C4⋊C4×D23C2211yescharacteristic
33#10625059C2211yescharacteristic
34#10625047—21no—
35#10625046—21no—
36C4×D92—21no—
37C4×D92C2211yescharacteristic
38C4×D92C2211yescharacteristic
39#10625043—21no—
40#10625043C2211yescharacteristic
41C23×#107C2211yescharacteristic
42C23×#103C2211yescharacteristic
43C23×#103C2211yescharacteristic
44C4×C8×C23C2211yescharacteristic
45#10625017C2211yescharacteristic
46#10625017C2211yescharacteristic
47#10625003C2211yescharacteristic
48#10625003C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50(C2×D23)⋊C8C2211yescharacteristic
51#10625000C2211yescharacteristic
52Dic23⋊C8C2211yescharacteristic
53Dic23⋊C8C2211yescharacteristic
54#10624991C2211yescharacteristic
55#10624991C2211yescharacteristic
56#10624989C2211yescharacteristic
57#10624989C2211yescharacteristic
58#10624985C2211yescharacteristic
59C2×Q8×C23C2311yescharacteristic
60C2×Q8×C23C2311yescharacteristic
61#67292—22no—
62#67292—22no—
63C2×D92—21no—
64C2×D92—21no—
65C2×D92C2311yescharacteristic
66C2×D92C2311yescharacteristic
67C2×C4×D23—21no—
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23—21no—
71C2×C4×D23—21no—
72C2×C4×D23C2311yescharacteristic
73C2×Dic46—21no—
74Q16×C23—22no—
75C2×C8×C23C2311yescharacteristic
76C2×C8×C23C2311yescharacteristic
77C4⋊C4×C23—21no—
78C4⋊C4×C23—21no—
79C4⋊C4×C23C2311yescharacteristic
80C4⋊C4×C23C2311yescharacteristic
81C42×C23—21no—
82C42×C23—21no—
83C42×C23C2311yescharacteristic
84#67274—22no—
85#67274—22no—
86(C2×D23)⋊C4—21no—
87(C2×D23)⋊C4—21no—
88(C2×D23)⋊C4—21no—
89(C2×D23)⋊C4—21no—
90(C2×D23)⋊C4—21no—
91(C2×D23)⋊C4—21no—
92(C2×D23)⋊C4—21no—
93(C2×D23)⋊C4D411yescharacteristic
94(C2×D23)⋊C4D411yescharacteristic
95C4⋊Dic23—21no—
96C4⋊Dic23C2311yescharacteristic
97C4⋊Dic23C2311yescharacteristic
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4—21no—
101Dic23⋊C4D411yescharacteristic
102Dic23⋊C4D411yescharacteristic
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107D184—22no—
108C22×D23—21no—
109C22×D23—21no—
110C22×D23C2×D411yescharacteristic
111Q8×C23—21no—
112Q8×C23—21no—
113Q8×C23—21no—
114Q8×C23#4112yes—
115C2×C4×C23—21no—
116C2×C4×C23—21no—
117C2×C4×C23—21no—
118C2×C4×C23—21no—
119C2×C4×C23C2×D411yescharacteristic
120C2×C4×C23C2×D411yescharacteristic
121C2×C4×C23C2411yescharacteristic
122C2×Dic23—21no—
123C2×Dic23—21no—
124C2×Dic23C2×D411yescharacteristic
125C2×Dic23C2×D411yescharacteristic
126C2×Dic23C2×D411yescharacteristic
127D92—24no—
128D92—21no—
129D92—21no—
130D92—21no—
131D92—81no—
132D92#4112yes—
133C4×D23—24no—
134C4×D23—21no—
135C4×D23—21no—
136C4×D23—81no—
137C4×D23—81no—
138C4×D23—81no—
139C4×D23—81no—
140Dic46—81no—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3124—231nomaximal, Sylow
146C22×C23C22×D411yescharacteristic
147C2×D23—21no—
148C2×D23—22no—
149C2×D23—21no—
150C2×D23—21no—
151C2×D23—41no—
152C2×D23—41no—
153C2×D23—41no—
154C2×D23—41no—
155C2×D23—41no—
156C4×C23—22no—
157C4×C23—21no—
158C4×C23—21no—
159C4×C23—41no—
160C4×C23—41no—
161C4×C23—41no—
162C4×C23C2×#4111yescharacteristic
163C4×C23C2×#4111yescharacteristic
164Dic23—21no—
165Dic23—21no—
166Dic23—21no—
167Dic23—41no—
168Dic23—41no—
169#542—231no—
170#520—231no—
171#484—231no—
172#480—231no—
173#477—231no—
174#474—231no—
175#464—231no—
176#463—231no—
177#452—231no—
178#449—231no—
179#440—231no—
180#440—231no—
181C4×Q16D2311yescharacteristic, complemented
182C4×D8—231no—
183#433—231no—
184C2×C23#52511yescharacteristic
185C2×C23#57611yescharacteristic
186C2×C23#57811yescharacteristic
187D23—41no—
188D23—42no—
189D23—81no—
190C2×#41—231no—
191C2×Q16C2×D2311yescharacteristic
192C2×SD16—231no—
193C2×SD16—231no—
194C2×D8—231no—
195C4⋊Q8—231no—
196#126—461no—
197#124—231no—
198#124—461no—
199#123—461no—
200C22⋊Q8—231no—
201C22⋊Q8—461no—
202#121—231no—
203C4×Q8—231no—
204C4×Q8C2×D2311yescharacteristic
205C4×Q8C2×D2311yescharacteristic
206C4×D4—231no—
207C4×D4—231no—
208C4×D4—231no—
209C4×D4—461no—
210C4×D4—461no—
211#117—231no—
212#117—461no—
213C2×C4⋊C4—231no—
214C2×C4⋊C4—461no—
215#107—231no—
216#107—231no—
217#107—231no—
218#107C2×D2311yescharacteristic
219C4⋊C8—231no—
220C4⋊C8—231no—
221#103—231no—
222#103—231no—
223#103C2×D2311yescharacteristic
224#103C2×D2311yescharacteristic
225#102—231no—
226#102—231no—
227#102—231no—
228#102—231no—
229C22⋊C8—231no—
230C22⋊C8—231no—
231#97—231no—
232C4×C8C2×D2311yescharacteristic
233C23#312411yescharacteristic, complemented, Sylow
234#41—462no—
235#41—462no—
236C2×Q8—461no—
237C2×Q8C22×D2311yescharacteristic
238C2×Q8C22×D2311yescharacteristic
239C2×D4—231no—
240C2×D4—231no—
241C2×D4—461no—
242C2×D4—461no—
243C22×C4—231no—
244C22×C4—461no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4—461no—
248C22×C4—461no—
249Q16—22no—
250SD16—462no—
251SD16—462no—
252D8—462no—
253C2×C8—231no—
254C2×C8—231no—
255C2×C8C22×D2311yescharacteristic
256C2×C8C22×D2311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—231no—
260C4⋊C4—231no—
261C4⋊C4—231no—
262C4⋊C4—231no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4C22×D2311yescharacteristic
268C4⋊C4C22×D2311yescharacteristic
269C22⋊C4—231no—
270C22⋊C4—231no—
271C22⋊C4—461no—
272C22⋊C4—461no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C42—21no—
279C42—21no—
280C42—231no—
281C42—461no—
282C42C22×D2311yescharacteristic
283C23—231no—
284C23—461no—
285C23—461no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—1841no—
290Q8#6728812yes—
291D4—232no—
292D4—464no—
293D4—461no—
294D4—461no—
295D4—461no—
296D4—1841no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—231no—
302C2×C4—231no—
303C2×C4—231no—
304C2×C4—464no—
305C2×C4—461no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—1841no—
310C2×C4—1841no—
311C2×C4—1841no—
312C2×C4—1841no—
313C2×C4D4×D2311yescharacteristic
314C2×C4D4×D2311yescharacteristic
315C2×C4C23×D2311yescharacteristic
316C8—21no—
317C8—21no—
318C8—461no—
319C8—461no—
320C22—462no—
321C22—461no—
322C22—461no—
323C22—461no—
324C22—921no—
325C22—921no—
326C22—921no—
327C22—921no—
328C22—921no—
329C22C2×D4×D2311yescharacteristic
330C4—22no—
331C4—21no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—461no—
337C4—461no—
338C4—461no—
339C4—921no—
340C4—921no—
341C4C2×#6728811yescharacteristic
342C4#41×D2311yescharacteristic
343C2—921no—
344C2—922no—
345C2—1841no—
346C2#1309292611yescharacteristic
347C2#1309321911yescharacteristic
348C2#1309323011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×Q16×C23C2
socleC22×C23C22×D4
prime radical#13092565C2
hypercenterC4×Q16D23
hypocenterC23#3124
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
1. #13093039C2semidirect
2. #13092899C2semidirect
3. #13092751C2semidirect
4. #13092732C2semidirect
5. #13092710C2semidirect
6. #13092696C2semidirect
7. #13092641C2semidirect
8. #13092635C2semidirect
9. #13092578C2semidirect
11. #13092515C2semidirect
12. #13092515C2semidirect
13. C4×D184C2semidirect
14. #13092476C2semidirect
15. C4×Q16×C23C2semidirect
181. C4×Q16D23semidirect
233. C23#3124semidirect

Maximal subgroups

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

subgroupindex
#130930392
#130928992
#130927512
#130927322
#130927102
#130926962
#130926412
#130926352
#130925782
#130925652
#130925152
C4×D1842
#130924762
C4×Q16×C232
#312423