Finite Group Databasebeta

← #15684911

Subgroups — #15684911

Order 2944.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625086C211yesmaximal, characteristic, complemented
2C22×#67273C211yesmaximal, characteristic, complemented
3#13093080C211yesmaximal, characteristic, complemented
4#13093061C211yesmaximal, characteristic
5#13092808C211yesmaximal, characteristic, complemented
6#13092662C211yesmaximal, characteristic, complemented
7#13092656C211yesmaximal, characteristic, complemented
8#13092638C211yesmaximal, characteristic, complemented
9#13092620C211yesmaximal, characteristic, complemented
10#13092580C211yesmaximal, characteristic, complemented
11#13092575C211yesmaximal, characteristic, complemented
12#13092554C211yesmaximal, characteristic, complemented
13#13092514C211yesmaximal, characteristic, complemented
14#13092485C211yesmaximal, characteristic, complemented
15C23×#450C211yesmaximal, characteristic, complemented
16C22×D4×C23C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic, complemented
18C2×#67290C2211yescharacteristic
19C22×Dic46C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic
21C2×SD16×C23C2211yescharacteristic
22C23×C22⋊Q8C2211yescharacteristic
23#10625124—21no—
24C2×C22⋊Dic23—21no—
25#10625115C2211yescharacteristic, complemented
26C2×#67275C2211yescharacteristic, complemented
27#10625110—21no—
28#10625109C2211yescharacteristic
29#10625107C2211yescharacteristic
30#10625106—21no—
31D4×Dic23C2211yescharacteristic
32C2×#67273—24no—
33C2×#67273C2211yescharacteristic
34C2×#67273C2211yescharacteristic
35C2×#67273C2211yescharacteristic
36C2×#67273C2211yescharacteristic
37C4×C22⋊D23C2211yescharacteristic
38#10625095C2211yescharacteristic
39C22×C23⋊C8C2211yescharacteristic
40#10625086—24no—
41C2×Dic92C2211yescharacteristic, complemented
42C2×Dic92C2211yescharacteristic, complemented
43C2×#67262C2211yescharacteristic, complemented
44#10625068C2211yescharacteristic, complemented
45#10625067—21no—
46#10625059—21no—
47#10625058C2211yescharacteristic, complemented
48(C22⋊D23)⋊C4—21no—
49#10625049—21no—
50C23×#102C2211yescharacteristic
51C23×#102C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic
53#10625017C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic, complemented
55#10624998C2211yescharacteristic, complemented
56#10624998C2211yescharacteristic, complemented
57#10624997C2211yescharacteristic, complemented
58Dic23⋊C8C2211yescharacteristic, complemented
59#10624992C2211yescharacteristic, complemented
60#10624989C2211yescharacteristic, complemented
61C24×C23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—22no—
64C2×D4×C23—21no—
65C2×D4×C23—41no—
66C2×D4×C23C2311yescharacteristic
67C2×D4×C23C2311yescharacteristic
68C22×C4×C23C2311yescharacteristic
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23D411yescharacteristic
72C22×Dic23—21no—
73C22×Dic23—21no—
74C22×Dic23—21no—
75Q8×D23—22no—
76Q8×D23—41no—
77#67290—22no—
78#67290—41no—
79C2×C4×D23—21no—
80C2×C4×D23C2311yescharacteristic
81C2×Dic46—22no—
82C2×Dic46—21no—
83C2×Dic46—21no—
84C2×Dic46—41no—
85C2×Dic46C2311yescharacteristic
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88SD16×C23—22no—
89SD16×C23—41no—
90C2×C8×C23C2311yescharacteristic
91C2×C8×C23C2311yescharacteristic
92C4⋊C4×C23—21no—
93C4⋊C4×C23C2311yescharacteristic
94C22⋊C4×C23—21no—
95C22⋊Dic23—21no—
96C22⋊Dic23—21no—
97C22⋊Dic23—21no—
98C22⋊Dic23—21no—
99C22⋊Dic23—21no—
100C22⋊Dic23D411yescharacteristic
101#67275—22no—
102#67273—22no—
103#67273—22no—
104#67273—22no—
105#67273D414yescomplemented
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4D411yescharacteristic
108C4⋊Dic23—21no—
109C4⋊Dic23C2311yescharacteristic
110Dic23⋊C4—21no—
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113Dic23⋊C4—21no—
114Dic23⋊C4D411yescharacteristic
115C4×Dic23—21no—
116C4×Dic23C2311yescharacteristic
117C2×C23⋊C8—22no—
118C2×C23⋊C8C2311yescharacteristic
119C2×C23⋊C8C2311yescharacteristic
120Dic92—22no—
121Dic92—41no—
122#67262—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23—42no—
126C23×C23—42no—
127C23×C23—81no—
128C23×C23C2×D411yescharacteristic
129C22×D23C2×D411yescharacteristic
130Q8×C23—21no—
131Q8×C23—21no—
132D4×C23—21no—
133D4×C23—21no—
134D4×C23—21no—
135D4×C23—42no—
136D4×C23C2×D412yes—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23—21no—
141C2×C4×C23C2×D411yescharacteristic
142C2×C4×C23C2411yescharacteristic
143C22⋊D23—22no—
144C22⋊D23—42no—
145C22⋊D23—81no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—42no—
151C2×Dic23—42no—
152C2×Dic23—81no—
153C2×Dic23C2×D411yescharacteristic
154C2×Dic23C2×D411yescharacteristic
155C2×Dic23C2×D411yescharacteristic
156C4×D23—21no—
157C4×D23—21no—
158C4×D23—42no—
159Dic46—21no—
160Dic46—21no—
161Dic46—21no—
162Dic46—21no—
163Dic46—21no—
164Dic46—42no—
165Dic46—42no—
166Dic46C2×D412yes—
167C8×C23—21no—
168C8×C23—21no—
169C23⋊C8—21no—
170C23⋊C8C2×D412yes—
171#3266—231nomaximal, Sylow
172C22×C23—21no—
173C22×C23—21no—
174C22×C23—22no—
175C22×C23—41no—
176C22×C23—41no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23—41no—
180C22×C23—84no—
181C22×C23#13712yescomplemented
182C22×C23C22×D411yescharacteristic
183C2×D23—21no—
184C2×D23—21no—
185C2×D23—21no—
186C4×C23—21no—
187C4×C23—41no—
188C4×C23—41no—
189C4×C23C22×D411yescharacteristic
190C4×C23H(5,𝔽2)11yescharacteristic
191Dic23—22no—
192Dic23—21no—
193Dic23—21no—
194Dic23—21no—
195Dic23—41no—
196Dic23—41no—
197Dic23—41no—
198C2×#137—231no—
199C22×SD16—231no—
200D4×Q8—231no—
201#546—231no—
202#497—231no—
203#468—231no—
204#467—231no—
205#464—231no—
206#461—231no—
207#452—231no—
208#451—231no—
209#450D2311yescharacteristic, complemented
210#448—231no—
211#440—231no—
212#435—231no—
213C2×C23—22no—
214C2×C23—42no—
215C2×C23—81no—
216C2×C23D4211yescharacteristic
217C2×C23C2×#13711yescharacteristic
218C2×C23#57711yescharacteristic
219D23—41no—
220C2×#41—231no—
221C22×Q8—231no—
222C22×Q8—231no—
223C22×D4C2×D2311yescharacteristic
224#137—464no—
225C2×Q16—231no—
226C2×Q16—231no—
227C2×Q16—231no—
228C2×SD16—231no—
229C2×SD16—231no—
230C2×SD16—231no—
231C2×SD16—231no—
232C2×SD16—464no—
233C2×SD16C2×D2311yescharacteristic
234C2×SD16C2×D2311yescharacteristic
235C2×M16—231no—
236C22×C8—231no—
237C4⋊Q8—231no—
238C4⋊Q8—461no—
239#124—231no—
240#123—461no—
241C22⋊Q8—231no—
242C22⋊Q8—231no—
243C22⋊Q8—461no—
244C22⋊Q8—461no—
245C22⋊Q8C2×D2311yescharacteristic
246#121—231no—
247#121—461no—
248#120—461no—
249C4×Q8—231no—
250C4×D4—231no—
251C4×D4—231no—
252C4×D4—461no—
253C2×C22⋊C4—461no—
254#107—231no—
255C4⋊C8—231no—
256#103—231no—
257#103—231no—
258#103—231no—
259#103—231no—
260#102C2×D2311yescharacteristic
261#102C2×D2311yescharacteristic
262C22⋊C8—231no—
263C22⋊C8C2×D2311yescharacteristic
264#97—231no—
265C23#326611yescharacteristic, complemented, Sylow
266C24—21no—
267#41—462no—
268#41—921no—
269C2×Q8—231no—
270C2×Q8—231no—
271C2×Q8—231no—
272C2×Q8—461no—
273C2×Q8—462no—
274C2×Q8—461no—
275C2×Q8—462no—
276C2×Q8—921no—
277C2×Q8—921no—
278C2×Q8C22×D2311yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—41no—
282C2×D4—231no—
283C2×D4—461no—
284C2×D4—461no—
285C2×D4C22×D2311yescharacteristic
286C2×D4C22×D2311yescharacteristic
287C22×C4—231no—
288C22×C4—461no—
289C22×C4—461no—
290C22×C4—461no—
291C22×C4—461no—
292C22×C4C22×D2311yescharacteristic
293Q16—462no—
294Q16—462no—
295Q16—921no—
296SD16—22no—
297SD16—41no—
298SD16—234no—
299SD16—462no—
300SD16—462no—
301SD16—462no—
302M16—462no—
303C2×C8—231no—
304C2×C8—231no—
305C2×C8—462no—
306C2×C8C22×D2311yescharacteristic
307C2×C8C22×D2311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—231no—
310C4⋊C4—231no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4—461no—
314C4⋊C4—461no—
315C4⋊C4—461no—
316C4⋊C4C22×D2311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—231no—
319C22⋊C4—231no—
320C22⋊C4—461no—
321C22⋊C4—461no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C42—231no—
327C42—461no—
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23—231no—
334C23D4×D2311yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—232no—
338Q8—461no—
339Q8—461no—
340Q8—461no—
341Q8—461no—
342Q8—461no—
343Q8—922no—
344Q8—922no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—42no—
349D4—462no—
350D4—922no—
351D4—1841no—
352D4D4×D2312yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—231no—
358C2×C4—231no—
359C2×C4—231no—
360C2×C4—461no—
361C2×C4—461no—
362C2×C4—461no—
363C2×C4—461no—
364C2×C4—461no—
365C2×C4—461no—
366C2×C4—922no—
367C2×C4—922no—
368C2×C4—922no—
369C2×C4—1841no—
370C2×C4D4×D2311yescharacteristic
371C2×C4C23×D2311yescharacteristic
372C8—21no—
373C8—21no—
374C8—232no—
375C8—461no—
376C22—21no—
377C22—21no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—84no—
385C22—461no—
386C22—461no—
387C22—461no—
388C22#1062508612yescomplemented
389C22C2×D4×D2311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—461no—
394C4—461no—
395C4—461no—
396C4—462no—
397C4—921no—
398C4—921no—
399C4—921no—
400C4C2×D4×D2311yescharacteristic
401C4#1062515511yescharacteristic
402C2—22no—
403C2—42no—
404C2—81no—
405C2—921no—
406C2#1309304911yescharacteristic
407C2C2×#1062508611yescharacteristic
408C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#450C2
socleC22×C23C22×D4
prime radical#13093061C2
hypercenter#450D23
hypocenterC23#3266
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×#10625086C2semidirect
2. C22×#67273C2semidirect
3. #13093080C2semidirect
5. #13092808C2semidirect
6. #13092662C2semidirect
7. #13092656C2semidirect
8. #13092638C2semidirect
9. #13092620C2semidirect
10. #13092580C2semidirect
11. #13092575C2semidirect
12. #13092554C2semidirect
13. #13092514C2semidirect
14. #13092485C2semidirect
15. C23×#450C2semidirect
17. C2×Q8×D23C22semidirect
25. #10625115C22semidirect
26. C2×#67275C22semidirect
41. C2×Dic92C22semidirect
42. C2×Dic92C22semidirect
43. C2×#67262C22semidirect
44. #10625068C22semidirect
47. #10625058C22semidirect
53. #10625017C22semidirect
54. (C2×D23)⋊C8C22semidirect
55. #10624998C22semidirect
56. #10624998C22semidirect
57. #10624997C22semidirect
58. Dic23⋊C8C22semidirect
59. #10624992C22semidirect
60. #10624989C22semidirect
105. #67273D4semidirect
181. C22×C23#137semidirect
209. #450D23semidirect
265. C23#3266semidirect
388. C22#10625086semidirect

Maximal subgroups

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

subgroupindex
C2×#106250862
C22×#672732
#130930802
#130930612
#130928082
#130926622
#130926562
#130926382
#130926202
#130925802
#130925752
#130925542
#130925142
#130924852
C23×#4502
#326623