Finite Group Databasebeta

← #15683646

Subgroups — #15683646

Order 2944.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13093025C211yesmaximal, characteristic, complemented
2#13092889C211yesmaximal, characteristic
3#13092761C211yesmaximal, characteristic, complemented
4#13092756C211yesmaximal, characteristic, complemented
5#13092719C211yesmaximal, characteristic, complemented
6#13092716C211yesmaximal, characteristic, complemented
7#13092621C211yesmaximal, characteristic, complemented
8#13092620C211yesmaximal, characteristic, complemented
9#13092569C211yesmaximal, characteristic
10#13092566C211yesmaximal, characteristic
11#13092517C211yesmaximal, characteristic, complemented
12#13092515C211yesmaximal, characteristic, complemented
13C4×#67263C211yesmaximal, characteristic, complemented
14#13092476C211yesmaximal, characteristic, complemented
15C4×SD16×C23C211yesmaximal, characteristic, complemented
16C2×D4×D23C2211yescharacteristic
17C2×SD16×C23C2211yescharacteristic
18C4×Q8×C23C2211yescharacteristic, complemented
19C4×D4×C23C2211yescharacteristic
20#10625117C2211yescharacteristic
21#10625115C2211yescharacteristic, complemented
22C2×#67274C2211yescharacteristic
23D4×Dic23C2211yescharacteristic
24C2×#67273C2211yescharacteristic
25C4×C22⋊D23—21no—
26C2×(C2×D23)⋊C4—21no—
27C2×#67263C2211yescharacteristic
28#10625069—21no—
29#10625068C2211yescharacteristic
30#10625064C2211yescharacteristic
31#10625063C2211yescharacteristic
32#10625061C2211yescharacteristic, complemented
33#10625060—21no—
34(C22⋊D23)⋊C4—21no—
35C22⋊C4×D23—21no—
36#10625047—21no—
37C4×D92C2211yescharacteristic
38#10625043C2211yescharacteristic
39#10625041—21no—
40C4×Dic46C2211yescharacteristic, complemented
41C23×#106C2211yescharacteristic, complemented
42C23×#103C2211yescharacteristic, complemented
43C23×#102C2211yescharacteristic
44C4×C8×C23C2211yescharacteristic, complemented
45#10625017C2211yescharacteristic, complemented
46#10625014C2211yescharacteristic
47#10625003C2211yescharacteristic
48(C2×D23)⋊C8C2211yescharacteristic
49(C2×D23)⋊C8C2211yescharacteristic
50#10624999C2211yescharacteristic, complemented
51#10624998C2211yescharacteristic, complemented
52Dic23⋊C8C2211yescharacteristic, complemented
53Dic23⋊C8C2211yescharacteristic, complemented
54#10624992C2211yescharacteristic, complemented
55#10624991C2211yescharacteristic
56#10624989C2211yescharacteristic, complemented
57#10624989C2211yescharacteristic, complemented
58#10624985C2211yescharacteristic, complemented
59C23×D23—21no—
60C2×Q8×C23C2311yescharacteristic
61C2×D4×C23C2311yescharacteristic
62C22×C4×C23—21no—
63C2×C22⋊D23—21no—
64C22×Dic23—21no—
65D4×D23—22no—
66D4×D23—22no—
67C2×D92C2311yescharacteristic
68C2×C4×D23—21no—
69C2×C4×D23—21no—
70C2×C4×D23C2311yescharacteristic
71C2×Dic46C2311yescharacteristic
72SD16×C23—22no—
73C2×C8×C23C2311yescharacteristic
74C2×C8×C23C2311yescharacteristic
75C4⋊C4×C23—21no—
76C4⋊C4×C23C2311yescharacteristic
77C4⋊C4×C23C2311yescharacteristic
78C22⋊C4×C23—21no—
79C42×C23—21no—
80C42×C23C2311yescharacteristic
81C22⋊Dic23—21no—
82#67274—22no—
83#67273—22no—
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⋊Dic23—21no—
93C4⋊Dic23C2311yescharacteristic
94C4⋊Dic23C2311yescharacteristic
95Dic23⋊C4—21no—
96Dic23⋊C4—21no—
97Dic23⋊C4—21no—
98Dic23⋊C4—21no—
99Dic23⋊C4—21no—
100Dic23⋊C4D411yescharacteristic
101Dic23⋊C4D411yescharacteristic
102C4×Dic23—21no—
103C4×Dic23—21no—
104C4×Dic23C2311yescharacteristic
105C2×C23⋊C8C2311yescharacteristic
106C2×C23⋊C8C2311yescharacteristic
107#67263—22no—
108C23×C23—21no—
109C22×D23—21no—
110C22×D23—24no—
111C22×D23—81no—
112C22×D23—81no—
113C22×D23C2×D411yescharacteristic
114Q8×C23—21no—
115Q8×C23—21no—
116D4×C23—21no—
117D4×C23#4112yes—
118C2×C4×C23—21no—
119C2×C4×C23—21no—
120C2×C4×C23—21no—
121C2×C4×C23—81no—
122C2×C4×C23C2×D411yescharacteristic
123C2×C4×C23C2×D411yescharacteristic
124C2×C4×C23C2411yescharacteristic
125C22⋊D23—24no—
126C2×Dic23—21no—
127C2×Dic23—21no—
128C2×Dic23—21no—
129C2×Dic23—81no—
130C2×Dic23C2×D411yescharacteristic
131C2×Dic23C2×D411yescharacteristic
132C2×Dic23C2×D411yescharacteristic
133D92—21no—
134D92#4112yes—
135C4×D23—21no—
136C4×D23—21no—
137C4×D23—81no—
138C4×D23—81no—
139Dic46—21no—
140Dic46—21no—
141C8×C23—21no—
142C8×C23—21no—
143C23⋊C8—21no—
144C23⋊C8—21no—
145#3123—231nomaximal, Sylow
146C22×C23—22no—
147C22×C23—41no—
148C22×C23—41no—
149C22×C23C22×D411yescharacteristic
150C2×D23—21no—
151C2×D23—22no—
152C2×D23—21no—
153C2×D23—21no—
154C2×D23—41no—
155C2×D23—41no—
156C2×D23—84no—
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—
169Dic23—41no—
170#541—231no—
171#518—231no—
172#485—231no—
173#485—231no—
174#478—231no—
175#478—231no—
176#461—231no—
177#461—231no—
178#450—231no—
179#450—231no—
180#440—231no—
181#440—231no—
182C4×SD16—231no—
183C4×SD16D2311yescharacteristic, complemented
184#433—231no—
185C2×C23—42no—
186C2×C23#52511yescharacteristic
187C2×C23#57711yescharacteristic
188C2×C23#57711yescharacteristic
189D23—41no—
190D23—42no—
191C22×D4—231no—
192C2×SD16—231no—
193C2×SD16—231no—
194C2×SD16—231no—
195C2×SD16C2×D2311yescharacteristic
196C4⋊Q8—231no—
197#126—461no—
198#126—461no—
199#125—231no—
200#125—461no—
201#125—461no—
202C22⋊Q8—231no—
203C22⋊Q8—231no—
204C4×Q8—231no—
205C4×Q8C2×D2311yescharacteristic, complemented
206C4×D4—231no—
207C4×D4—231no—
208C4×D4—231no—
209C4×D4—461no—
210C4×D4—461no—
211C4×D4C2×D2311yescharacteristic
212#117—231no—
213#117—231no—
214C2×C22⋊C4—461no—
215C2×C22⋊C4—461no—
216#107—231no—
217#107—231no—
218#106—231no—
219#106C2×D2311yescharacteristic, complemented
220C4⋊C8—231no—
221C4⋊C8—231no—
222#103—231no—
223#103—231no—
224#103—231no—
225#103C2×D2311yescharacteristic, complemented
226#102—231no—
227#102—231no—
228#102—231no—
229#102C2×D2311yescharacteristic
230C22⋊C8—231no—
231C22⋊C8—231no—
232#97—231no—
233C4×C8C2×D2311yescharacteristic, complemented
234C23#312311yescharacteristic, complemented, Sylow
235C24—461no—
236C2×Q8—231no—
237C2×Q8C22×D2311yescharacteristic
238C2×D4—231no—
239C2×D4—461no—
240C2×D4—462no—
241C2×D4—462no—
242C2×D4C22×D2311yescharacteristic
243C22×C4—21no—
244C22×C4—231no—
245C22×C4—461no—
246C22×C4—461no—
247C22×C4—461no—
248SD16—22no—
249SD16—462no—
250SD16—462no—
251SD16—462no—
252C2×C8—231no—
253C2×C8—231no—
254C2×C8C22×D2311yescharacteristic
255C2×C8C22×D2311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—231no—
258C4⋊C4—231no—
259C4⋊C4—231no—
260C4⋊C4—231no—
261C4⋊C4—461no—
262C4⋊C4—461no—
263C4⋊C4—461no—
264C4⋊C4—461no—
265C4⋊C4—461no—
266C4⋊C4—461no—
267C4⋊C4—461no—
268C4⋊C4C22×D2311yescharacteristic
269C4⋊C4C22×D2311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—231no—
272C22⋊C4—231no—
273C22⋊C4—461no—
274C22⋊C4—461no—
275C22⋊C4—461no—
276C22⋊C4—461no—
277C22⋊C4—461no—
278C22⋊C4—461no—
279C42—21no—
280C42—231no—
281C42—461no—
282C42—461no—
283C42C22×D2311yescharacteristic
284C23—21no—
285C23—231no—
286C23—464no—
287C23—461no—
288C23—1841no—
289C23—1841no—
290Q8—21no—
291Q8—21no—
292Q8—461no—
293Q8—461no—
294D4—21no—
295D4—232no—
296D4—464no—
297D4—461no—
298D4#6728812yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—231no—
304C2×C4—231no—
305C2×C4—231no—
306C2×C4—461no—
307C2×C4—461no—
308C2×C4—461no—
309C2×C4—461no—
310C2×C4—461no—
311C2×C4—1841no—
312C2×C4—1841no—
313C2×C4—1841no—
314C2×C4D4×D2311yescharacteristic
315C2×C4D4×D2311yescharacteristic
316C2×C4C23×D2311yescharacteristic
317C8—21no—
318C8—21no—
319C8—461no—
320C8—461no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—461no—
325C22—462no—
326C22—461no—
327C22—461no—
328C22—921no—
329C22—921no—
330C22—1844no—
331C22C2×D4×D2311yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—461no—
338C4—461no—
339C4—461no—
340C4—921no—
341C4—921no—
342C4—921no—
343C4C2×#6728811yescharacteristic
344C4#41×D2311yescharacteristic
345C2—42no—
346C2—921no—
347C2—922no—
348C2#1309292611yescharacteristic
349C2#1309322311yescharacteristic
350C2#1309322411yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×SD16×C23C2
socleC22×C23C22×D4
prime radicalC2×D4×D23C22
hypercenterC4×SD16D23
hypocenterC23#3123
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
1. #13093025C2semidirect
3. #13092761C2semidirect
4. #13092756C2semidirect
5. #13092719C2semidirect
6. #13092716C2semidirect
7. #13092621C2semidirect
8. #13092620C2semidirect
11. #13092517C2semidirect
12. #13092515C2semidirect
13. C4×#67263C2semidirect
14. #13092476C2semidirect
15. C4×SD16×C23C2semidirect
18. C4×Q8×C23C22semidirect
21. #10625115C22semidirect
32. #10625061C22semidirect
40. C4×Dic46C22semidirect
41. C23×#106C22semidirect
42. C23×#103C22semidirect
44. C4×C8×C23C22semidirect
45. #10625017C22semidirect
50. #10624999C22semidirect
51. #10624998C22semidirect
52. Dic23⋊C8C22semidirect
53. Dic23⋊C8C22semidirect
54. #10624992C22semidirect
56. #10624989C22semidirect
57. #10624989C22semidirect
58. #10624985C22semidirect
183. C4×SD16D23semidirect
205. C4×Q8C2×D23semidirect
219. #106C2×D23semidirect
225. #103C2×D23semidirect
233. C4×C8C2×D23semidirect
234. C23#3123semidirect

Maximal subgroups

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

subgroupindex
#130930252
#130928892
#130927612
#130927562
#130927192
#130927162
#130926212
#130926202
#130925692
#130925662
#130925172
#130925152
C4×#672632
#130924762
C4×SD16×C232
#312323