Finite Group Databasebeta

← #15684933

Subgroups — #15684933

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×#10625103C211yesmaximal, characteristic, complemented
2C2×#10625121C211yesmaximal, characteristic, complemented
3#13093088C211yesmaximal, characteristic, complemented
4#13092807C211yesmaximal, characteristic, complemented
5#13092665C211yesmaximal, characteristic, complemented
6#13092651C211yesmaximal, characteristic, complemented
7#13092636C211yesmaximal, characteristic, complemented
8#13092612C211yesmaximal, characteristic, complemented
9#13092577C211yesmaximal, characteristic, complemented
10#13092562C211yesmaximal, characteristic, complemented
11#13092560C211yesmaximal, characteristic, complemented
12#13092551C211yesmaximal, characteristic, complemented
13#13092517C211yesmaximal, characteristic, complemented
14#13092489C211yesmaximal, characteristic, complemented
15C23×#546C211yesmaximal, characteristic, complemented
16C2×#41×C23C2211yescharacteristic
17C22×D4×C23C2211yescharacteristic
18C2×#67288C2211yescharacteristic
19C2×#67288C2211yescharacteristic, complemented
20C23×#124C2211yescharacteristic
21C23×#123—21no—
22C23×C22⋊Q8C2211yescharacteristic
23C23×#121—21no—
24C23×#121C2211yescharacteristic
25C23×#120—21no—
26C4×D4×C23C2211yescharacteristic
27C4×D4×C23C2211yescharacteristic
28C2×C22⋊C4×C23—21no—
29#10625121—24no—
30C2×#67275C2211yescharacteristic, complemented
31C2×#67274C2211yescharacteristic, complemented
32C2×#67274C2211yescharacteristic, complemented
33#10625111—21no—
34C2×#67273C2211yescharacteristic
35C2×#67273C2211yescharacteristic
36#10625103—24no—
37C2×#67272C2211yescharacteristic
38C2×#67272C2211yescharacteristic
39C2×#67272C2211yescharacteristic
40C2×#67272C2211yescharacteristic
41#10625101C2211yescharacteristic
42#10625101C2211yescharacteristic, complemented
43C2×#67267C2211yescharacteristic
44C22×C23⋊C8C2211yescharacteristic, complemented
45#10625064—21no—
46#10625055—21no—
47#10625055—21no—
48#10625045C2211yescharacteristic, complemented
49C4×Dic46C2211yescharacteristic, complemented
50#10625017C2211yescharacteristic, complemented
51#10625014C2211yescharacteristic
52#10625014C2211yescharacteristic
53C22⋊(C23⋊C8)C2211yescharacteristic
54C22⋊(C23⋊C8)C2211yescharacteristic, complemented
55#10624992C2211yescharacteristic, complemented
56#10624991C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic, complemented
58#10624989C2211yescharacteristic, complemented
59C4⋊(C23⋊C8)C2211yescharacteristic, complemented
60#10624985C2211yescharacteristic, complemented
61C24×C23—21no—
62#41×C23—22no—
63#41×C23—41no—
64C2×Q8×C23C2311yescharacteristic
65C2×D4×C23—22no—
66C2×D4×C23—21no—
67C2×D4×C23—21no—
68C2×D4×C23—21no—
69C2×D4×C23—41no—
70C2×D4×C23D411yescharacteristic
71C2×D4×C23C2311yescharacteristic
72C2×D4×C23C2311yescharacteristic
73C22×C4×C23—21no—
74C22×C4×C23—21no—
75C22×C4×C23C2311yescharacteristic
76C22×C4×C23C2311yescharacteristic
77C2×C22⋊D23—21no—
78C2×C22⋊D23—21no—
79C2×C22⋊D23—21no—
80C2×C22⋊D23—21no—
81#67288—22no—
82#67288—22no—
83#67288—41no—
84#67288—41no—
85C2×D92—21no—
86C2×D92—21no—
87C2×D92C2311yescharacteristic
88C2×D92C2311yescharacteristic
89C2×C4×D23—21no—
90C2×C4×D23—21no—
91C2×Dic46C2311yescharacteristic
92C4⋊C4×C23—21no—
93C4⋊C4×C23D411yescharacteristic
94C4⋊C4×C23C2311yescharacteristic
95C22⋊C4×C23—21no—
96C22⋊C4×C23—21no—
97C22⋊C4×C23—21no—
98C22⋊C4×C23—21no—
99C22⋊C4×C23—21no—
100C22⋊C4×C23D411yescharacteristic
101C22⋊C4×C23D411yescharacteristic
102C42×C23C2311yescharacteristic
103#67275—22no—
104#67274—22no—
105#67274—41no—
106#67273—22no—
107#67273D414yescomplemented
108#67272—22no—
109#67272—22no—
110#67272—22no—
111#67272—41no—
112(C2×D23)⋊C4—21no—
113(C2×D23)⋊C4—21no—
114C4⋊Dic23C2311yescharacteristic
115Dic23⋊C4—21no—
116C4×Dic23—21no—
117#67267—22no—
118C2×C23⋊C8—22no—
119C2×C23⋊C8C2311yescharacteristic
120C2×C23⋊C8C2311yescharacteristic
121C2×C23⋊C8C2311yescharacteristic
122C2×C23⋊C8C2311yescharacteristic
123C23×C23—21no—
124C23×C23—21no—
125C23×C23—42no—
126C23×C23—42no—
127C23×C23—81no—
128C23×C23C2×D411yescharacteristic
129C23×C23C2×D411yescharacteristic
130C22×D23—21no—
131C22×D23—21no—
132Q8×C23—21no—
133Q8×C23—21no—
134D4×C23—21no—
135D4×C23—21no—
136D4×C23—21no—
137D4×C23—41no—
138D4×C23—42no—
139D4×C23—42no—
140D4×C23—81no—
141D4×C23C2×D412yes—
142C2×C4×C23—21no—
143C2×C4×C23—21no—
144C2×C4×C23—21no—
145C2×C4×C23—21no—
146C2×C4×C23—21no—
147C2×C4×C23—21no—
148C2×C4×C23—42no—
149C2×C4×C23—81no—
150C2×C4×C23C2×D411yescharacteristic
151C2×C4×C23C2×D411yescharacteristic
152C2×C4×C23C2×D411yescharacteristic
153C2×C4×C23C2×D411yescharacteristic
154C2×C4×C23C2411yescharacteristic
155C22⋊D23—42no—
156C22⋊D23—42no—
157C22⋊D23—81no—
158C22⋊D23—81no—
159C2×Dic23—21no—
160C2×Dic23—21no—
161D92—21no—
162D92—21no—
163D92—21no—
164D92—21no—
165D92—42no—
166D92—81no—
167C4×D23—42no—
168C4×D23—42no—
169Dic46—21no—
170Dic46C2×D412yes—
171C23⋊C8—21no—
172C23⋊C8—21no—
173C23⋊C8—21no—
174C23⋊C8C2×D412yes—
175#3268—231nomaximal, Sylow
176C22×C23—21no—
177C22×C23—21no—
178C22×C23—22no—
179C22×C23—21no—
180C22×C23—21no—
181C22×C23—21no—
182C22×C23—21no—
183C22×C23—41no—
184C22×C23—41no—
185C22×C23—41no—
186C22×C23—41no—
187C22×C23—41no—
188C22×C23—84no—
189C22×C23C22×D411yescharacteristic
190C2×D23—41no—
191C2×D23—41no—
192C2×D23—41no—
193C2×D23—41no—
194C2×D23—41no—
195C2×D23—41no—
196C4×C23—21no—
197C4×C23—21no—
198C4×C23—21no—
199C4×C23—21no—
200C4×C23—41no—
201C4×C23—41no—
202C4×C23C22×D411yescharacteristic
203C4×C23H(5,𝔽2)11yescharacteristic
204Dic23—22no—
205Dic23—41no—
206C2×AGL(1,ℤ/8)—231no—
207C2×#135—231no—
208#550—231no—
209#546D2311yescharacteristic, complemented
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#435—231no—
221C2×C23—41no—
222C2×C23—41no—
223C2×C23—42no—
224C2×C23—81no—
225C2×C23D4211yescharacteristic
226C2×C23#57511yescharacteristic
227C2×C23#57611yescharacteristic
228D23—81no—
229D23—81no—
230C2×#41—231no—
231C2×#41—231no—
232C2×#41C2×D2311yescharacteristic
233C22×D4C2×D2311yescharacteristic
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×M16—231no—
246C22×C8—231no—
247#127—231no—
248#127—461no—
249#124C2×D2311yescharacteristic
250#123—21no—
251C22⋊Q8C2×D2311yescharacteristic
252#121—21no—
253#121—231no—
254#121—231no—
255#121—461no—
256#121—461no—
257#121C2×D2311yescharacteristic
258#120—21no—
259C4×Q8—231no—
260C4×D4—461no—
261C4×D4C2×D2311yescharacteristic
262C4×D4C2×D2311yescharacteristic
263C2×C22⋊C4—21no—
264#107—231no—
265C4⋊C8—231no—
266#103—231no—
267#103—231no—
268#102—231no—
269#102—231no—
270#102—231no—
271#102—231no—
272C22⋊C8—231no—
273C22⋊C8—231no—
274#97—231no—
275C23#326811yescharacteristic, complemented, Sylow
276C24—21no—
277#41—22no—
278#41—41no—
279#41—462no—
280#41—462no—
281#41—921no—
282#41—921no—
283C2×Q8—231no—
284C2×Q8C22×D2311yescharacteristic
285C2×D4—22no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—41no—
290C2×D4—231no—
291C2×D4—231no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—461no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4C22⋊D2311yescharacteristic
299C2×D4C22×D2311yescharacteristic
300C2×D4C22×D2311yescharacteristic
301C22×C4—21no—
302C22×C4—21no—
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—462no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—231no—
320C2×C8—231no—
321C2×C8—462no—
322C4⋊C4—21no—
323C4⋊C4—231no—
324C4⋊C4—461no—
325C4⋊C4C22⋊D2311yescharacteristic
326C4⋊C4C22×D2311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C22⋊C4—21no—
332C22⋊C4—461no—
333C22⋊C4—461no—
334C22⋊C4C22⋊D2311yescharacteristic
335C22⋊C4C22⋊D2311yescharacteristic
336C42—461no—
337C42C22×D2311yescharacteristic
338C23—21no—
339C23—21no—
340C23—42no—
341C23—42no—
342C23—81no—
343C23—461no—
344C23—461no—
345C23C2×C22⋊D2311yescharacteristic
346C23C2×C22⋊D2311yescharacteristic
347Q8—21no—
348Q8—21no—
349Q8—232no—
350Q8—461no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—41no—
355D4—42no—
356D4—42no—
357D4—81no—
358D4—461no—
359D4—461no—
360D4—461no—
361D4—461no—
362D4—922no—
363D4—922no—
364D4—922no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368D4D4×D2312yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—42no—
376C2×C4—81no—
377C2×C4—461no—
378C2×C4—461no—
379C2×C4—922no—
380C2×C4—922no—
381C2×C4C2×C22⋊D2311yescharacteristic
382C2×C4C2×C22⋊D2311yescharacteristic
383C2×C4C2×C22⋊D2311yescharacteristic
384C2×C4C2×C22⋊D2311yescharacteristic
385C2×C4C23×D2311yescharacteristic
386C8—232no—
387C8—461no—
388C8—461no—
389C8—461no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—22no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—84no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22—921no—
409C22C22×C22⋊D2311yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—462no—
417C4—921no—
418C4C2×D4×D2311yescharacteristic
419C4#1062515511yescharacteristic
420C2—41no—
421C2—41no—
422C2—42no—
423C2—81no—
424C2—1841no—
425C2—1841no—
426C2D4×C22⋊D2311yescharacteristic
427C2#1309321511yescharacteristic
428C2#1309322011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#546C2
socleC22×C23C22×D4
hypercenter#546D23
hypocenterC23#3268
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#10625103C2semidirect
2. C2×#10625121C2semidirect
3. #13093088C2semidirect
4. #13092807C2semidirect
5. #13092665C2semidirect
6. #13092651C2semidirect
7. #13092636C2semidirect
8. #13092612C2semidirect
9. #13092577C2semidirect
10. #13092562C2semidirect
11. #13092560C2semidirect
12. #13092551C2semidirect
13. #13092517C2semidirect
14. #13092489C2semidirect
15. C23×#546C2semidirect
19. C2×#67288C22semidirect
30. C2×#67275C22semidirect
31. C2×#67274C22semidirect
32. C2×#67274C22semidirect
42. #10625101C22semidirect
44. C22×C23⋊C8C22semidirect
48. #10625045C22semidirect
49. C4×Dic46C22semidirect
50. #10625017C22semidirect
54. C22⋊(C23⋊C8)C22semidirect
55. #10624992C22semidirect
56. #10624991C22semidirect
57. #10624991C22semidirect
58. #10624989C22semidirect
59. C4⋊(C23⋊C8)C22semidirect
60. #10624985C22semidirect
107. #67273D4semidirect
209. #546D23semidirect
275. C23#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#106251032
C2×#106251212
#130930882
#130928072
#130926652
#130926512
#130926362
#130926122
#130925772
#130925622
#130925602
#130925512
#130925172
#130924892
C23×#5462
#326823