Finite Group Databasebeta

← #15684909

Subgroups — #15684909

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
2C2×SD16×D23C211yesmaximal, characteristic, complemented
3Q8×D92C211yesmaximal, characteristic, complemented
4#13093062C211yesmaximal, characteristic
5#13092811C211yesmaximal, characteristic, complemented
6#13092664C211yesmaximal, characteristic, complemented
7#13092659C211yesmaximal, characteristic, complemented
8#13092639C211yesmaximal, characteristic, complemented
9#13092622C211yesmaximal, characteristic, complemented
10#13092580C211yesmaximal, characteristic, complemented
11#13092574C211yesmaximal, characteristic, complemented
12#13092569C211yesmaximal, characteristic, complemented
13#13092557C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#440C211yesmaximal, characteristic, complemented
16C2×Q8×D23C2211yescharacteristic
17C2×Q8×D23C2211yescharacteristic, complemented
18C2×#67290C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic
21C4×Q8×C23C2211yescharacteristic, complemented
22C4×D4×C23C2211yescharacteristic
23C2×#67275C2211yescharacteristic, complemented
24C2×#67274C2211yescharacteristic
25C2×#67273C2211yescharacteristic
26C2×#67273C2211yescharacteristic
27#10625101—21no—
28C2×(C2×D23)⋊C4—21no—
29#10625086—24no—
30SD16×D23—24no—
31C2×Dic92C2211yescharacteristic, complemented
32C2×Dic92C2211yescharacteristic, complemented
33C2×#67263C2211yescharacteristic
34C2×#67263C2211yescharacteristic
35C2×#67262C2211yescharacteristic, complemented
36C2×C8×D23C2211yescharacteristic
37#10625068—21no—
38#10625068—21no—
39#10625068C2211yescharacteristic
40#10625068C2211yescharacteristic
41#10625068C2211yescharacteristic, complemented
42#10625066C2211yescharacteristic
43#10625057—21no—
44#10625053—21no—
45#10625046C2211yescharacteristic
46C4×D92—21no—
47C4×D92C2211yescharacteristic
48#10625040—21no—
49#10625040C2211yescharacteristic, complemented
50C23×#107C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic
53C23×#97C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624992C2211yescharacteristic, complemented
58#10624992C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic
60C4⋊(C23⋊C8)C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×Q8×C23C2311yescharacteristic
63C2×D4×C23C2311yescharacteristic
64C22×C4×C23—21no—
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C22×Dic23—21no—
68Q8×D23—22no—
69Q8×D23—22no—
70Q8×D23—41no—
71Q8×D23—41no—
72#67290—22no—
73#67290—41no—
74D4×D23—22no—
75D4×D23—41no—
76C2×D92—21no—
77C2×D92D411yescharacteristic
78C2×D92C2311yescharacteristic
79C2×C4×D23—21no—
80C2×C4×D23—21no—
81C2×C4×D23C2311yescharacteristic
82C2×C4×D23C2311yescharacteristic
83C2×Dic46—21no—
84C2×Dic46—21no—
85C2×Dic46C2311yescharacteristic
86C2×Dic46C2311yescharacteristic
87C2×Dic46C2311yescharacteristic
88SD16×C23D414yescomplemented
89C2×C8×C23C2311yescharacteristic
90C2×C8×C23C2311yescharacteristic
91C4⋊C4×C23—21no—
92C4⋊C4×C23C2311yescharacteristic
93C4⋊C4×C23C2311yescharacteristic
94C22⋊C4×C23—21no—
95C42×C23—21no—
96C42×C23C2311yescharacteristic
97#67275—22no—
98#67274—22no—
99#67273—22no—
100#67273—22no—
101(C2×D23)⋊C4—21no—
102(C2×D23)⋊C4—21no—
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4D411yescharacteristic
108(C2×D23)⋊C4D411yescharacteristic
109C4⋊Dic23—21no—
110C4⋊Dic23—21no—
111C4⋊Dic23—21no—
112C4⋊Dic23—21no—
113C4⋊Dic23—21no—
114C4⋊Dic23D411yescharacteristic
115C2×C23⋊C8C2311yescharacteristic
116C2×C23⋊C8C2311yescharacteristic
117Dic92—22no—
118Dic92—41no—
119#67263—22no—
120#67263—41no—
121#67262—22no—
122C8×D23—22no—
123C23×C23—21no—
124C22×D23—21no—
125C22×D23—42no—
126C22×D23—42no—
127C22×D23—81no—
128C22×D23C2×D411yescharacteristic
129C22×D23C2×D411yescharacteristic
130Q8×C23—21no—
131Q8×C23C2×D412yes—
132D4×C23—21no—
133D4×C23C2×D412yes—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23—81no—
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2411yescharacteristic
141C22⋊D23—42no—
142C22⋊D23—42no—
143C2×Dic23—21no—
144C2×Dic23—21no—
145C2×Dic23—21no—
146C2×Dic23—42no—
147C2×Dic23C2×D411yescharacteristic
148C2×Dic23C2×D411yescharacteristic
149D92—22no—
150D92—21no—
151D92—21no—
152D92—81no—
153C4×D23—21no—
154C4×D23—21no—
155C4×D23—21no—
156C4×D23—21no—
157C4×D23—42no—
158C4×D23—42no—
159Dic46—21no—
160Dic46—21no—
161Dic46—21no—
162Dic46—21no—
163Dic46—21no—
164Dic46—21no—
165Dic46—42no—
166Dic46—42no—
167C8×C23—21no—
168C8×C23C2×D412yes—
169C23⋊C8—21no—
170C23⋊C8—21no—
171#3266—231nomaximal, Sylow
172C22×C23—22no—
173C22×C23—41no—
174C22×C23—41no—
175C22×C23C22×D411yescharacteristic
176C2×D23—21no—
177C2×D23—21no—
178C2×D23—21no—
179C2×D23—21no—
180C2×D23—21no—
181C2×D23—41no—
182C2×D23—41no—
183C2×D23—41no—
184C2×D23—84no—
185C2×D23#13712yescomplemented
186C4×C23—22no—
187C4×C23—21no—
188C4×C23—21no—
189C4×C23—41no—
190C4×C23—41no—
191C4×C23C22×D411yescharacteristic
192C4×C23H(5,𝔽2)11yescharacteristic
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#450—231no—
210#448—231no—
211#440D2311yescharacteristic, complemented
212#435—231no—
213C2×C23—42no—
214C2×C23D4211yescharacteristic
215C2×C23C2×#13711yescharacteristic
216C2×C23#57711yescharacteristic
217D23—22no—
218D23—41no—
219D23—81no—
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×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—231no—
244C22⋊Q8—461no—
245C22⋊Q8—461no—
246#121—231no—
247#121—461no—
248#120—461no—
249C4×Q8C2×D2311yescharacteristic, complemented
250C4×D4—231no—
251C4×D4—461no—
252C4×D4C2×D2311yescharacteristic
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#97C2×D2311yescharacteristic, complemented
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—461no—
274C2×Q8—462no—
275C2×Q8—462no—
276C2×Q8—921no—
277C2×Q8—921no—
278C2×Q8C22×D2311yescharacteristic
279C2×D4—231no—
280C2×D4—231no—
281C2×D4—461no—
282C2×D4—461no—
283C2×D4—462no—
284C2×D4—461no—
285C2×D4—921no—
286C2×D4C22×D2311yescharacteristic
287C22×C4—21no—
288C22×C4—231no—
289C22×C4—231no—
290C22×C4—461no—
291C22×C4—461no—
292C22×C4—461no—
293Q16—462no—
294Q16—462no—
295Q16—921no—
296SD16—462no—
297SD16—462no—
298SD16—462no—
299SD16—462no—
300SD16—921no—
301SD16D9214yescomplemented
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—461no—
311C4⋊C4—461no—
312C4⋊C4—461no—
313C4⋊C4—461no—
314C4⋊C4—461no—
315C4⋊C4C22×D2311yescharacteristic
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—21no—
327C42C22×D2311yescharacteristic
328C23—21no—
329C23—231no—
330C23—231no—
331C23—461no—
332C23—922no—
333C23—922no—
334C23—1841no—
335Q8—21no—
336Q8—461no—
337Q8—461no—
338Q8—461no—
339Q8—461no—
340Q8—461no—
341Q8—461no—
342Q8—922no—
343Q8—922no—
344Q8C2×D9212yes—
345D4—21no—
346D4—462no—
347D4—461no—
348D4—461no—
349D4—922no—
350D4—922no—
351D4—1841no—
352D4C2×D9212yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—81no—
357C2×C4—231no—
358C2×C4—231no—
359C2×C4—461no—
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×C4D4×D2311yescharacteristic
370C2×C4D4×D2311yescharacteristic
371C2×C4C23×D2311yescharacteristic
372C8—21no—
373C8—461no—
374C8—461no—
375C8C2×D9212yes—
376C22—22no—
377C22—41no—
378C22—41no—
379C22—232no—
380C22—461no—
381C22—461no—
382C22—461no—
383C22—461no—
384C22—461no—
385C22—921no—
386C22—921no—
387C22—921no—
388C22—1844no—
389C22C2×D4×D2311yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—461no—
396C4—461no—
397C4—921no—
398C4—921no—
399C4—921no—
400C4C22×D9211yescharacteristic
401C4#1062516011yescharacteristic
402C2—42no—
403C2—462no—
404C2—921no—
405C2—1841no—
406C2D4×D9211yescharacteristic
407C2#137×D2311yescharacteristic
408C2#1309322711yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
prime radical#13093062C2
hypercenter#440D23
hypocenterC23#3266
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#10625086C2semidirect
2. C2×SD16×D23C2semidirect
3. Q8×D92C2semidirect
5. #13092811C2semidirect
6. #13092664C2semidirect
7. #13092659C2semidirect
8. #13092639C2semidirect
9. #13092622C2semidirect
10. #13092580C2semidirect
11. #13092574C2semidirect
12. #13092569C2semidirect
13. #13092557C2semidirect
14. #13092490C2semidirect
15. C23×#440C2semidirect
17. C2×Q8×D23C22semidirect
21. C4×Q8×C23C22semidirect
23. C2×#67275C22semidirect
31. C2×Dic92C22semidirect
32. C2×Dic92C22semidirect
35. C2×#67262C22semidirect
41. #10625068C22semidirect
49. #10625040C22semidirect
50. C23×#107C22semidirect
51. C23×#103C22semidirect
53. C23×#97C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. #10624992C22semidirect
57. #10624992C22semidirect
58. #10624992C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
88. SD16×C23D4semidirect
185. C2×D23#137semidirect
211. #440D23semidirect
249. C4×Q8C2×D23semidirect
254. #107C2×D23semidirect
259. #103C2×D23semidirect
264. #97C2×D23semidirect
265. C23#3266semidirect
301. SD16D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250862
C2×SD16×D232
Q8×D922
#130930622
#130928112
#130926642
#130926592
#130926392
#130926222
#130925802
#130925742
#130925692
#130925572
#130924902
C23×#4402
#326623