Finite Group Databasebeta

← #15684943

Subgroups — #15684943

Order 2944.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10625082C211yesmaximal, characteristic, complemented
2C2×#10625083C211yesmaximal, characteristic, complemented
3#13093087C211yesmaximal, characteristic, complemented
4#13093062C211yesmaximal, characteristic, complemented
5#13092804C211yesmaximal, characteristic, complemented
6#13092662C211yesmaximal, characteristic, complemented
7#13092652C211yesmaximal, characteristic, complemented
8#13092640C211yesmaximal, characteristic, complemented
9#13092580C211yesmaximal, characteristic, complemented
10#13092563C211yesmaximal, characteristic, complemented
11#13092559C211yesmaximal, characteristic, complemented
12#13092549C211yesmaximal, characteristic, complemented
13#13092517C211yesmaximal, characteristic, complemented
14#13092487C211yesmaximal, characteristic, complemented
15C23×#459C211yesmaximal, characteristic, complemented
16C2×#67290C2211yescharacteristic
17C2×#67290C2211yescharacteristic
18C2×#67290C2211yescharacteristic, complemented
19C2×D4×D23C2211yescharacteristic
20C2×D8×C23C2211yescharacteristic
21C2×D8×C23C2211yescharacteristic
22C23×#127C2211yescharacteristic, complemented
23C4×D4×C23C2211yescharacteristic
24#10625111—21no—
25#10625110—21no—
26#10625110—21no—
27#10625109C2211yescharacteristic
28#10625109C2211yescharacteristic, complemented
29D4×Dic23—21no—
30C2×#67273C2211yescharacteristic
31C2×#67273C2211yescharacteristic, complemented
32C2×#67273C2211yescharacteristic, complemented
33C2×#67272C2211yescharacteristic
34C2×#67272C2211yescharacteristic
35#10625101—21no—
36C2×(C2×D23)⋊C4—21no—
37#10625083—24no—
38#10625082—24no—
39C2×Dic92C2211yescharacteristic, complemented
40C2×#67263C2211yescharacteristic
41C2×#67262C2211yescharacteristic
42C2×C8×D23C2211yescharacteristic, complemented
43#10625068C2211yescharacteristic
44#10625066C2211yescharacteristic
45#10625057—21no—
46#10625053—21no—
47#10625046C2211yescharacteristic
48C4×D92C2211yescharacteristic
49C4×Dic46C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×#102C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic, complemented
53#10625014C2211yescharacteristic
54#10625003C2211yescharacteristic
55(C2×D23)⋊C8C2211yescharacteristic
56(C2×D23)⋊C8C2211yescharacteristic, complemented
57#10624998C2211yescharacteristic, complemented
58#10624992C2211yescharacteristic, complemented
59#10624989C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×D4×C23—21no—
63C2×D4×C23—21no—
64C2×D4×C23C2311yescharacteristic
65C2×D4×C23C2311yescharacteristic
66C2×D4×C23C2311yescharacteristic
67C22×C4×C23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71C2×C22⋊D23—21no—
72C2×C22⋊D23—21no—
73C2×C22⋊D23—21no—
74C22×Dic23—21no—
75C22×Dic23—21no—
76C22×Dic23—21no—
77#67290—22no—
78#67290—22no—
79#67290—22no—
80#67290—41no—
81#67290—41no—
82#67290—41no—
83D4×D23—22no—
84D4×D23—41no—
85C2×D92—21no—
86C2×D92D411yescharacteristic
87C2×D92C2311yescharacteristic
88C2×C4×D23C2311yescharacteristic
89C2×C4×D23C2311yescharacteristic
90C2×Dic46C2311yescharacteristic
91C2×Dic46C2311yescharacteristic
92D8×C23—22no—
93D8×C23—22no—
94C2×C8×C23C2311yescharacteristic
95C2×C8×C23C2311yescharacteristic
96C4⋊C4×C23C2311yescharacteristic
97C22⋊C4×C23—21no—
98C42×C23C2311yescharacteristic
99C22⋊Dic23—21no—
100C22⋊Dic23—21no—
101#67273—22no—
102#67273—41no—
103#67273D414yescomplemented
104#67272—22no—
105#67272—41no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4D411yescharacteristic
111(C2×D23)⋊C4D411yescharacteristic
112C4⋊Dic23—21no—
113C4⋊Dic23D411yescharacteristic
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116C4×Dic23—21no—
117C2×C23⋊C8C2311yescharacteristic
118C2×C23⋊C8C2311yescharacteristic
119Dic92—22no—
120#67263—22no—
121#67262—22no—
122C8×D23—22no—
123C23×C23—21no—
124C23×C23—21no—
125C23×C23—21no—
126C22×D23—21no—
127C22×D23—42no—
128C22×D23—42no—
129C22×D23—81no—
130C22×D23C2×D411yescharacteristic
131C22×D23C2×D411yescharacteristic
132D4×C23—21no—
133D4×C23—21no—
134D4×C23—21no—
135D4×C23—21no—
136D4×C23—21no—
137D4×C23—42no—
138D4×C23—81no—
139D4×C23C2×D412yes—
140C2×C4×C23—21no—
141C2×C4×C23—81no—
142C2×C4×C23C2×D411yescharacteristic
143C2×C4×C23C2×D411yescharacteristic
144C2×C4×C23C2411yescharacteristic
145C22⋊D23—42no—
146C22⋊D23—42no—
147C22⋊D23—42no—
148C22⋊D23—42no—
149C22⋊D23—81no—
150C22⋊D23—81no—
151C2×Dic23—21no—
152C2×Dic23—21no—
153C2×Dic23—21no—
154C2×Dic23—42no—
155C2×Dic23—42no—
156C2×Dic23—42no—
157C2×Dic23C2×D411yescharacteristic
158C2×Dic23C2×D411yescharacteristic
159D92—21no—
160D92—21no—
161D92—41no—
162D92—81no—
163C4×D23—21no—
164C4×D23—21no—
165C4×D23—21no—
166C4×D23—21no—
167Dic46—21no—
168Dic46—21no—
169Dic46—21no—
170Dic46C2×D412yes—
171C8×C23—21no—
172C8×C23—21no—
173C23⋊C8—21no—
174C23⋊C8C2×D412yes—
175#3268—231nomaximal, Sylow
176C22×C23—22no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23—41no—
180C22×C23—41no—
181C22×C23—41no—
182C22×C23—41no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23C22×D411yescharacteristic
186C2×D23—21no—
187C2×D23—21no—
188C2×D23—21no—
189C2×D23—21no—
190C2×D23—21no—
191C2×D23—21no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—84no—
196C4×C23—21no—
197C4×C23—21no—
198C4×C23—41no—
199C4×C23C22×D411yescharacteristic
200C4×C23H(5,𝔽2)11yescharacteristic
201Dic23—22no—
202Dic23—21no—
203Dic23—21no—
204Dic23—41no—
205Dic23—41no—
206C2×AGL(1,ℤ/8)—231no—
207C2×#135—231no—
208#550—231no—
209#546—231no—
210#496—231no—
211#468—231no—
212#466—231no—
213#464—231no—
214#459D2311yescharacteristic, complemented
215#452—231no—
216#449—231no—
217#449—231no—
218#447—231no—
219#440—231no—
220#435—231no—
221C2×C23—42no—
222C2×C23—81no—
223C2×C23—81no—
224C2×C23D4211yescharacteristic
225C2×C23#57511yescharacteristic
226C2×C23#57611yescharacteristic
227D23—41no—
228D23—41no—
229D23—81no—
230C2×#41—231no—
231C2×#41—231no—
232C2×#41—231no—
233C22×D4—231no—
234AGL(1,ℤ/8)—464no—
235#135—464no—
236C2×Q16—231no—
237C2×SD16—231no—
238C2×SD16—231no—
239C2×SD16—231no—
240C2×SD16—231no—
241C2×D8—231no—
242C2×D8—231no—
243C2×D8C2×D2311yescharacteristic
244C2×D8C2×D2311yescharacteristic
245C2×M16—231no—
246C22×C8—231no—
247#127—461no—
248#127C2×D2311yescharacteristic, complemented
249#124—231no—
250#123—461no—
251C22⋊Q8—231no—
252#121—231no—
253#121—231no—
254#121—231no—
255#121—461no—
256#121—461no—
257#121—461no—
258#120—461no—
259C4×Q8—231no—
260C4×D4—231no—
261C4×D4—461no—
262C4×D4C2×D2311yescharacteristic
263C2×C22⋊C4—461no—
264#107—231no—
265C4⋊C8C2×D2311yescharacteristic, complemented
266#103—231no—
267#103—231no—
268#102—231no—
269#102—231no—
270#102C2×D2311yescharacteristic, complemented
271#102C2×D2311yescharacteristic, complemented
272C22⋊C8—231no—
273C22⋊C8—231no—
274#97—231no—
275C23#326811yescharacteristic, complemented, Sylow
276C24—461no—
277#41—462no—
278#41—462no—
279#41—462no—
280#41—921no—
281#41—921no—
282#41—921no—
283C2×Q8—231no—
284C2×Q8—231no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—461no—
290C2×D4—461no—
291C2×D4—462no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—921no—
298C2×D4C22×D2311yescharacteristic
299C2×D4C22×D2311yescharacteristic
300C2×D4C22×D2311yescharacteristic
301C22×C4—21no—
302C22×C4—231no—
303C22×C4—231no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4—461no—
307Q16—462no—
308SD16—234no—
309SD16—462no—
310SD16—462no—
311SD16—921no—
312D8—22no—
313D8—22no—
314D8—462no—
315D8—921no—
316M16—462no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—462no—
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—231no—
323C4⋊C4—231no—
324C4⋊C4—461no—
325C4⋊C4—461no—
326C4⋊C4C22×D2311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—231no—
329C22⋊C4—231no—
330C22⋊C4—461no—
331C22⋊C4—461no—
332C22⋊C4—461no—
333C22⋊C4—461no—
334C22⋊C4—461no—
335C22⋊C4—461no—
336C42—461no—
337C42C22×D2311yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—231no—
342C23—231no—
343C23—461no—
344C23—922no—
345C23—922no—
346C23—1841no—
347Q8—232no—
348Q8—461no—
349Q8—461no—
350Q8—461no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—461no—
359D4—461no—
360D4—921no—
361D4—922no—
362D4—922no—
363D4—922no—
364D4—922no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368D4D4×D2312yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—231no—
372C2×C4—231no—
373C2×C4—461no—
374C2×C4—461no—
375C2×C4—461no—
376C2×C4—461no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—461no—
380C2×C4—922no—
381C2×C4—922no—
382C2×C4—922no—
383C2×C4D4×D2311yescharacteristic
384C2×C4D4×D2311yescharacteristic
385C2×C4C23×D2311yescharacteristic
386C8—21no—
387C8—21no—
388C8—232no—
389C8—461no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—461no—
400C22—461no—
401C22—461no—
402C22—461no—
403C22—461no—
404C22—461no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22—1844no—
409C22C2×D4×D2311yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—461no—
414C4—461no—
415C4—462no—
416C4—921no—
417C4—921no—
418C4C2×D4×D2311yescharacteristic
419C4#1062516011yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—921no—
424C2—921no—
425C2—1841no—
426C2#1309305111yescharacteristic
427C2#1309321311yescharacteristic
428C2#1309321811yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#459C2
socleC22×C23C22×D4
hypercenter#459D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#10625082C2semidirect
2. C2×#10625083C2semidirect
3. #13093087C2semidirect
4. #13093062C2semidirect
5. #13092804C2semidirect
6. #13092662C2semidirect
7. #13092652C2semidirect
8. #13092640C2semidirect
9. #13092580C2semidirect
10. #13092563C2semidirect
11. #13092559C2semidirect
12. #13092549C2semidirect
13. #13092517C2semidirect
14. #13092487C2semidirect
15. C23×#459C2semidirect
18. C2×#67290C22semidirect
22. C23×#127C22semidirect
28. #10625109C22semidirect
31. C2×#67273C22semidirect
32. C2×#67273C22semidirect
39. C2×Dic92C22semidirect
42. C2×C8×D23C22semidirect
49. C4×Dic46C22semidirect
50. C23×C4⋊C8C22semidirect
51. C23×#102C22semidirect
52. C23×#102C22semidirect
56. (C2×D23)⋊C8C22semidirect
57. #10624998C22semidirect
58. #10624992C22semidirect
59. #10624989C22semidirect
60. #10624985C22semidirect
103. #67273D4semidirect
214. #459D23semidirect
248. #127C2×D23semidirect
265. C4⋊C8C2×D23semidirect
270. #102C2×D23semidirect
271. #102C2×D23semidirect
275. C23#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#106250822
C2×#106250832
#130930872
#130930622
#130928042
#130926622
#130926522
#130926402
#130925802
#130925632
#130925592
#130925492
#130925172
#130924872
C23×#4592
#326823