Finite Group Databasebeta

← #15684942

Subgroups — #15684942

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×#10625079C211yesmaximal, characteristic, complemented
2C2×#10625075C211yesmaximal, characteristic, complemented
3#13093088C211yesmaximal, characteristic, complemented
4#13093063C211yesmaximal, characteristic, complemented
5#13092806C211yesmaximal, characteristic, complemented
6#13092663C211yesmaximal, characteristic, complemented
7#13092653C211yesmaximal, characteristic, complemented
8#13092640C211yesmaximal, characteristic, complemented
9#13092613C211yesmaximal, characteristic, complemented
10#13092581C211yesmaximal, characteristic, complemented
11#13092564C211yesmaximal, characteristic, complemented
12#13092564C211yesmaximal, characteristic, complemented
13#13092553C211yesmaximal, characteristic, complemented
14#13092519C211yesmaximal, characteristic, complemented
15C23×#435C211yesmaximal, characteristic, complemented
16C2×#67288C2211yescharacteristic
17C2×#67288C2211yescharacteristic
18C2×#67288C2211yescharacteristic, complemented
19C22×D92C2211yescharacteristic
20C2×M16×C23C2211yescharacteristic
21C22×C8×C23C2211yescharacteristic, complemented
22C4×D4×C23C2211yescharacteristic
23#10625111—21no—
24#10625108—21no—
25#10625101C2211yescharacteristic
26#10625101C2211yescharacteristic
27#10625101C2211yescharacteristic, complemented
28#10625095C2211yescharacteristic
29#10625079—24no—
30C2×Dic92C2211yescharacteristic, complemented
31#10625075—24no—
32C2×D184C2211yescharacteristic
33C2×D184C2211yescharacteristic
34C2×D184C2211yescharacteristic
35C2×D184C2211yescharacteristic
36C2×#67263C2211yescharacteristic
37C2×#67263C2211yescharacteristic
38C2×#67263C2211yescharacteristic, complemented
39C2×#67263C2211yescharacteristic, complemented
40#10625065—21no—
41#10625064—21no—
42#10625055—21no—
43#10625055—21no—
44#10625055—21no—
45C22⋊C4×D23—21no—
46#10625046C2211yescharacteristic
47#10625045C2211yescharacteristic, complemented
48C4×D92C2211yescharacteristic
49C4×Dic46C2211yescharacteristic, complemented
50C23×C4⋊C8C2211yescharacteristic, complemented
51C23×C22⋊C8C2211yescharacteristic
52C23×C22⋊C8C2211yescharacteristic, complemented
53C23×#97C2211yescharacteristic, complemented
54#10625003C2211yescharacteristic
55#10625003C2211yescharacteristic
56#10625003C2211yescharacteristic, complemented
57#10625003C2211yescharacteristic, complemented
58#10625000C2211yescharacteristic, complemented
59#10624998C2211yescharacteristic, complemented
60#10624998C2211yescharacteristic, complemented
61C23×D23—21no—
62C2×D4×C23D411yescharacteristic
63C22×C4×C23C2311yescharacteristic
64C22×C4×C23C2311yescharacteristic
65C2×C22⋊D23—21no—
66C2×C22⋊D23—21no—
67C2×C22⋊D23—21no—
68C2×C22⋊D23—21no—
69C2×C22⋊D23—21no—
70C2×C22⋊D23—21no—
71#67288—22no—
72#67288—22no—
73#67288—22no—
74#67288—41no—
75#67288—41no—
76#67288—41no—
77C2×D92—22no—
78C2×D92—21no—
79C2×D92—21no—
80C2×D92—21no—
81C2×D92—41no—
82C2×D92C2311yescharacteristic
83C2×D92C2311yescharacteristic
84C2×D92C2311yescharacteristic
85C2×D92C2311yescharacteristic
86C2×C4×D23—21no—
87C2×C4×D23—21no—
88C2×C4×D23—21no—
89C2×C4×D23—21no—
90C2×Dic46C2311yescharacteristic
91C2×Dic46C2311yescharacteristic
92M16×C23—22no—
93C2×C8×C23—22no—
94C2×C8×C23C2311yescharacteristic
95C2×C8×C23C2311yescharacteristic
96C2×C8×C23C2311yescharacteristic
97C2×C8×C23C2311yescharacteristic
98C4⋊C4×C23D411yescharacteristic
99C22⋊C4×C23D411yescharacteristic
100C22⋊C4×C23D411yescharacteristic
101C42×C23C2311yescharacteristic
102C22⋊Dic23—21no—
103(C2×D23)⋊C4—21no—
104(C2×D23)⋊C4—21no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109C4⋊Dic23C2311yescharacteristic
110C4⋊Dic23C2311yescharacteristic
111Dic23⋊C4—21no—
112Dic23⋊C4—21no—
113C4×Dic23—21no—
114Dic92—22no—
115D184—22no—
116D184—22no—
117D184—22no—
118D184—41no—
119#67263—22no—
120#67263—22no—
121#67263—41no—
122#67263D414yescomplemented
123C23×C23C2×D411yescharacteristic
124C23×C23C2×D411yescharacteristic
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—21no—
128C22×D23—21no—
129C22×D23—42no—
130C22×D23—42no—
131C22×D23—81no—
132D4×C23—41no—
133C2×C4×C23—21no—
134C2×C4×C23—21no—
135C2×C4×C23—21no—
136C2×C4×C23—21no—
137C2×C4×C23C2×D411yescharacteristic
138C2×C4×C23C2×D411yescharacteristic
139C2×C4×C23C2×D411yescharacteristic
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2411yescharacteristic
142C22⋊D23—42no—
143C22⋊D23—42no—
144C22⋊D23—42no—
145C22⋊D23—81no—
146C22⋊D23—81no—
147C22⋊D23—81no—
148C2×Dic23—21no—
149C2×Dic23—21no—
150C2×Dic23—21no—
151C2×Dic23—21no—
152D92—21no—
153D92—21no—
154D92—21no—
155D92—21no—
156D92—21no—
157D92—21no—
158D92—21no—
159D92—42no—
160D92—42no—
161D92—81no—
162D92C2×D412yes—
163C4×D23—42no—
164C4×D23—42no—
165C4×D23—42no—
166C4×D23—81no—
167Dic46—21no—
168Dic46—21no—
169Dic46—21no—
170Dic46C2×D412yes—
171C8×C23—21no—
172C8×C23—21no—
173C8×C23—21no—
174C8×C23C2×D412yes—
175#3268—231nomaximal, Sylow
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—21no—
179C22×C23—21no—
180C22×C23—21no—
181C22×C23—21no—
182C22×C23C22×D411yescharacteristic
183C2×D23—22no—
184C2×D23—41no—
185C2×D23—41no—
186C2×D23—41no—
187C2×D23—41no—
188C2×D23—41no—
189C2×D23—41no—
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—84no—
196C4×C23—21no—
197C4×C23—21no—
198C4×C23—21no—
199C4×C23—21no—
200C4×C23C22×D411yescharacteristic
201C4×C23H(5,𝔽2)11yescharacteristic
202Dic23—22no—
203Dic23—41no—
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#459—231no—
215#452—231no—
216#449—231no—
217#449—231no—
218#447—231no—
219#440—231no—
220#435D2311yescharacteristic, complemented
221C2×C23—41no—
222C2×C23—41no—
223C2×C23D4211yescharacteristic
224C2×C23#57511yescharacteristic
225C2×C23#57611yescharacteristic
226D23—42no—
227D23—81no—
228D23—81no—
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×D8—231no—
244C2×D8—231no—
245C2×M16C2×D2311yescharacteristic
246C22×C8C2×D2311yescharacteristic, complemented
247#127—231no—
248#127—461no—
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#102—231no—
271#102—231no—
272C22⋊C8C2×D2311yescharacteristic
273C22⋊C8C2×D2311yescharacteristic, complemented
274#97C2×D2311yescharacteristic, complemented
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—231no—
286C2×D4—231no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—462no—
290C2×D4—461no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—921no—
300C2×D4D9211yescharacteristic
301C22×C4—461no—
302C22×C4—461no—
303C22×C4—461no—
304C22×C4—461no—
305C22×C4C22×D2311yescharacteristic
306C22×C4C22×D2311yescharacteristic
307Q16—462no—
308SD16—234no—
309SD16—462no—
310SD16—462no—
311SD16—921no—
312D8—462no—
313D8—462no—
314D8—462no—
315D8—921no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D2311yescharacteristic
319C2×C8C22×D2311yescharacteristic
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—231no—
323C4⋊C4—231no—
324C4⋊C4—461no—
325C4⋊C4—461no—
326C4⋊C4D9211yescharacteristic
327C22⋊C4—461no—
328C22⋊C4—461no—
329C22⋊C4—461no—
330C22⋊C4—461no—
331C22⋊C4—461no—
332C22⋊C4—461no—
333C22⋊C4—461no—
334C22⋊C4D9211yescharacteristic
335C22⋊C4D9211yescharacteristic
336C42—461no—
337C42C22×D2311yescharacteristic
338C23—461no—
339C23—461no—
340C23—461no—
341C23—461no—
342C23—922no—
343C23—922no—
344C23—1841no—
345C23C2×D9211yescharacteristic
346C23C2×D9211yescharacteristic
347Q8—232no—
348Q8—461no—
349Q8—461no—
350Q8—461no—
351D4—41no—
352D4—232no—
353D4—461no—
354D4—461no—
355D4—461no—
356D4—461no—
357D4—461no—
358D4—461no—
359D4—461no—
360D4—922no—
361D4—922no—
362D4—922no—
363D4—922no—
364D4—922no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368D4—1841no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—461no—
374C2×C4—461no—
375C2×C4—461no—
376C2×C4—461no—
377C2×C4—922no—
378C2×C4—922no—
379C2×C4—922no—
380C2×C4—1841no—
381C2×C4C2×D9211yescharacteristic
382C2×C4C2×D9211yescharacteristic
383C2×C4C2×D9211yescharacteristic
384C2×C4C2×D9211yescharacteristic
385C2×C4C23×D2311yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D2312yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—462no—
397C22—921no—
398C22—921no—
399C22—921no—
400C22—921no—
401C22—921no—
402C22—921no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22—1844no—
409C22C22×D9211yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—462no—
415C4—921no—
416C4—921no—
417C4—921no—
418C4C2×D4×D2311yescharacteristic
419C4#1062516011yescharacteristic
420C2—41no—
421C2—41no—
422C2—922no—
423C2—1841no—
424C2—1841no—
425C2—1841no—
426C2D4×D9211yescharacteristic
427C2#1309321711yescharacteristic
428C2#1309322211yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#435C2
socleC22×C23C22×D4
hypercenter#435D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. C2×#10625075C2semidirect
3. #13093088C2semidirect
4. #13093063C2semidirect
5. #13092806C2semidirect
6. #13092663C2semidirect
7. #13092653C2semidirect
8. #13092640C2semidirect
9. #13092613C2semidirect
10. #13092581C2semidirect
11. #13092564C2semidirect
12. #13092564C2semidirect
13. #13092553C2semidirect
14. #13092519C2semidirect
15. C23×#435C2semidirect
18. C2×#67288C22semidirect
21. C22×C8×C23C22semidirect
27. #10625101C22semidirect
30. C2×Dic92C22semidirect
38. C2×#67263C22semidirect
39. C2×#67263C22semidirect
47. #10625045C22semidirect
49. C4×Dic46C22semidirect
50. C23×C4⋊C8C22semidirect
52. C23×C22⋊C8C22semidirect
53. C23×#97C22semidirect
56. #10625003C22semidirect
57. #10625003C22semidirect
58. #10625000C22semidirect
59. #10624998C22semidirect
60. #10624998C22semidirect
122. #67263D4semidirect
220. #435D23semidirect
246. C22×C8C2×D23semidirect
265. C4⋊C8C2×D23semidirect
273. C22⋊C8C2×D23semidirect
274. #97C2×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×#106250792
C2×#106250752
#130930882
#130930632
#130928062
#130926632
#130926532
#130926402
#130926132
#130925812
#130925642
#130925532
#130925192
C23×#4352
#326823