Finite Group Databasebeta

← #15684914

Subgroups — #15684914

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×#10625080C211yesmaximal, characteristic, complemented
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3#13093080C211yesmaximal, characteristic, complemented
4#13093064C211yesmaximal, characteristic
5#13092808C211yesmaximal, characteristic, complemented
6#13092659C211yesmaximal, characteristic, complemented
7#13092638C211yesmaximal, characteristic, complemented
8#13092621C211yesmaximal, characteristic, complemented
9#13092577C211yesmaximal, characteristic, complemented
10#13092574C211yesmaximal, characteristic, complemented
11#13092569C211yesmaximal, characteristic, complemented
12#13092555C211yesmaximal, characteristic, complemented
13#13092516C211yesmaximal, characteristic, complemented
14#13092486C211yesmaximal, characteristic, complemented
15C23×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×D4×D23C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C22×Dic46C2211yescharacteristic, complemented
20C2×SD16×C23C2211yescharacteristic
21C2×M16×C23C2211yescharacteristic, complemented
22C23×C22⋊Q8C2211yescharacteristic, complemented
23C23×#121C2211yescharacteristic
24#10625115C2211yescharacteristic, complemented
25C2×#67275C2211yescharacteristic, complemented
26C2×#67274C2211yescharacteristic
27#10625109—21no—
28#10625108—21no—
29#10625107C2211yescharacteristic
30C2×#67273C2211yescharacteristic
31C2×#67273C2211yescharacteristic
32C4×C22⋊D23C2211yescharacteristic
33SD16×D23—24no—
34#10625080—24no—
35C2×Dic92C2211yescharacteristic, complemented
36C2×Dic92C2211yescharacteristic, complemented
37C2×#67263C2211yescharacteristic
38C2×#67263C2211yescharacteristic
39C2×C8×D23C2211yescharacteristic
40#10625068C2211yescharacteristic
41#10625068C2211yescharacteristic
42#10625067—21no—
43#10625064C2211yescharacteristic
44#10625059—21no—
45#10625058C2211yescharacteristic, complemented
46#10625054—21no—
47(C22⋊D23)⋊C4—21no—
48C22⋊C4×D23—21no—
49#10625049—21no—
50C23×#107C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic
53C22⋊(C23⋊C8)C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic
55#10624997C2211yescharacteristic, complemented
56Dic23⋊C8C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624992C2211yescharacteristic, complemented
59#10624992C2211yescharacteristic, complemented
60#10624991C2211yescharacteristic
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C22×C4×C23C2311yescharacteristic
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23D411yescharacteristic
69C22×Dic23—21no—
70Q8×D23—22no—
71Q8×D23—41no—
72D4×D23—22no—
73D4×D23—41no—
74#67288—22no—
75#67288—41no—
76C2×D92C2311yescharacteristic
77C2×C4×D23—21no—
78C2×C4×D23—21no—
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—
89M16×C23—22no—
90C2×C8×C23C2311yescharacteristic
91C2×C8×C23C2311yescharacteristic
92C4⋊C4×C23—21no—
93C4⋊C4×C23C2311yescharacteristic
94C4⋊C4×C23C2311yescharacteristic
95C22⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊Dic23—21no—
98C22⋊Dic23—21no—
99C22⋊Dic23D411yescharacteristic
100#67275—41no—
101#67274—22no—
102#67273—22no—
103#67273—41no—
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4D411yescharacteristic
108C4⋊Dic23—21no—
109C4⋊Dic23—21no—
110Dic23⋊C4—21no—
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113Dic23⋊C4D411yescharacteristic
114C4×Dic23—21no—
115C4×Dic23C2311yescharacteristic
116C2×C23⋊C8C2311yescharacteristic
117C2×C23⋊C8C2311yescharacteristic
118Dic92—22no—
119Dic92—22no—
120#67263—22no—
121#67263D414yescomplemented
122C8×D23—22no—
123C23×C23—21no—
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23—42no—
127C22×D23—42no—
128C22×D23—81no—
129C22×D23C2×D411yescharacteristic
130Q8×C23—21no—
131Q8×C23—21no—
132D4×C23—21no—
133D4×C23—21no—
134D4×C23—81no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—21no—
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—22no—
143C22⋊D23—42no—
144C22⋊D23—42no—
145C2×Dic23—21no—
146C2×Dic23—21no—
147C2×Dic23—21no—
148C2×Dic23—42no—
149C2×Dic23C2×D411yescharacteristic
150C2×Dic23C2×D411yescharacteristic
151C2×Dic23C2×D411yescharacteristic
152D92—21no—
153D92C2×D412yes—
154C4×D23—21no—
155C4×D23—21no—
156C4×D23—42no—
157C4×D23—42no—
158C4×D23—81no—
159Dic46—21no—
160Dic46—21no—
161Dic46—21no—
162Dic46—21no—
163Dic46—21no—
164Dic46—42no—
165Dic46—42no—
166Dic46C2×D412yes—
167C8×C23—21no—
168C8×C23C2×D412yes—
169C23⋊C8—21no—
170C23⋊C8—21no—
171#3266—231nomaximal, Sylow
172C22×C23—21no—
173C22×C23—21no—
174C22×C23—21no—
175C22×C23—41no—
176C22×C23—41no—
177C22×C23—41no—
178C22×C23C22×D411yescharacteristic
179C2×D23—21no—
180C2×D23—21no—
181C2×D23—22no—
182C2×D23—41no—
183C2×D23—41no—
184C2×D23—84no—
185C2×D23#13712yescomplemented
186C4×C23—21no—
187C4×C23—41no—
188C4×C23—41no—
189C4×C23—41no—
190C4×C23C22×D411yescharacteristic
191C4×C23H(5,𝔽2)11yescharacteristic
192Dic23—22no—
193Dic23—21no—
194Dic23—21no—
195Dic23—21no—
196Dic23—41no—
197Dic23—41no—
198C2×#137—231no—
199C22×SD16—231no—
200D4×Q8—231no—
201#546—231no—
202#497—231no—
203#468D2311yescharacteristic, complemented
204#467—231no—
205#464—231no—
206#461—231no—
207#452—231no—
208#451—231no—
209#450—231no—
210#448—231no—
211#440—231no—
212#435—231no—
213C2×C23—41no—
214C2×C23—81no—
215C2×C23D4211yescharacteristic
216C2×C23C2×#13711yescharacteristic
217C2×C23#57711yescharacteristic
218D23—22no—
219D23—42no—
220C2×#41—231no—
221C22×Q8—231no—
222C22×Q8—231no—
223C22×D4—231no—
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—231no—
233C2×SD16—464no—
234C2×SD16C2×D2311yescharacteristic
235C2×M16C2×D2311yescharacteristic, complemented
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, complemented
246#121—461no—
247#121C2×D2311yescharacteristic
248#120—461no—
249C4×Q8—231no—
250C4×D4—231no—
251C4×D4—231no—
252C4×D4—461no—
253C2×C22⋊C4—461no—
254#107C2×D2311yescharacteristic, complemented
255C4⋊C8—231no—
256#103—231no—
257#103—231no—
258#103—231no—
259#103C2×D2311yescharacteristic, complemented
260#102—231no—
261#102C2×D2311yescharacteristic
262C22⋊C8—231no—
263C22⋊C8—231no—
264#97—231no—
265C23#326611yescharacteristic, complemented, Sylow
266C24—461no—
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—21no—
280C2×D4—231no—
281C2×D4—231no—
282C2×D4—461no—
283C2×D4—462no—
284C2×D4—461no—
285C2×D4—921no—
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—234no—
298SD16—462no—
299SD16—462no—
300SD16—462no—
301SD16—921no—
302M16—22no—
303C2×C8—231no—
304C2×C8—231no—
305C2×C8—462no—
306C2×C8C22×D2311yescharacteristic
307C2×C8C22×D2311yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—231no—
310C4⋊C4—461no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4—461no—
314C4⋊C4—461no—
315C4⋊C4C22×D2311yescharacteristic
316C4⋊C4C22×D2311yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—231no—
320C22⋊C4—231no—
321C22⋊C4—461no—
322C22⋊C4—461no—
323C22⋊C4—461no—
324C22⋊C4—461no—
325C22⋊C4—461no—
326C42—231no—
327C42—461no—
328C23—21no—
329C23—231no—
330C23—461no—
331C23—922no—
332C23—922no—
333C23—1841no—
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—81no—
348D4—232no—
349D4—462no—
350D4—461no—
351D4—922no—
352D4—922no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—231no—
359C2×C4—231no—
360C2×C4—231no—
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—461no—
374C8—461no—
375C8D4×D2312yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—232no—
383C22—461no—
384C22—461no—
385C22—462no—
386C22—921no—
387C22—921no—
388C22—1844no—
389C22C2×D4×D2311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—461no—
395C4—461no—
396C4—461no—
397C4—462no—
398C4—921no—
399C4—921no—
400C4C2×D4×D2311yescharacteristic
401C4#1062516011yescharacteristic
402C2—41no—
403C2—81no—
404C2—462no—
405C2—922no—
406C2#1309305111yescharacteristic
407C2#137×D2311yescharacteristic
408C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#468C2
socleC22×C23C22×D4
prime radical#13093064C2
hypercenter#468D23
hypocenterC23#3266
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#10625080C2semidirect
2. C2×SD16×D23C2semidirect
3. #13093080C2semidirect
5. #13092808C2semidirect
6. #13092659C2semidirect
7. #13092638C2semidirect
8. #13092621C2semidirect
9. #13092577C2semidirect
10. #13092574C2semidirect
11. #13092569C2semidirect
12. #13092555C2semidirect
13. #13092516C2semidirect
14. #13092486C2semidirect
15. C23×#468C2semidirect
19. C22×Dic46C22semidirect
21. C2×M16×C23C22semidirect
22. C23×C22⋊Q8C22semidirect
24. #10625115C22semidirect
25. C2×#67275C22semidirect
35. C2×Dic92C22semidirect
36. C2×Dic92C22semidirect
45. #10625058C22semidirect
50. C23×#107C22semidirect
51. C23×#103C22semidirect
53. C22⋊(C23⋊C8)C22semidirect
55. #10624997C22semidirect
56. Dic23⋊C8C22semidirect
57. #10624992C22semidirect
58. #10624992C22semidirect
59. #10624992C22semidirect
121. #67263D4semidirect
185. C2×D23#137semidirect
203. #468D23semidirect
235. C2×M16C2×D23semidirect
245. C22⋊Q8C2×D23semidirect
254. #107C2×D23semidirect
259. #103C2×D23semidirect
265. C23#3266semidirect

Maximal subgroups

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

subgroupindex
C2×#106250802
C2×SD16×D232
#130930802
#130930642
#130928082
#130926592
#130926382
#130926212
#130925772
#130925742
#130925692
#130925552
#130925162
#130924862
C23×#4682
#326623