Finite Group Databasebeta

← #15684939

Subgroups — #15684939

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×#10625085C211yesmaximal, characteristic, complemented
2C2×#10625087C211yesmaximal, characteristic, complemented
3#13093089C211yesmaximal, characteristic, complemented
4#13093062C211yesmaximal, characteristic, complemented
5#13092806C211yesmaximal, characteristic, complemented
6#13092664C211yesmaximal, characteristic, complemented
7#13092654C211yesmaximal, characteristic, complemented
8#13092639C211yesmaximal, characteristic, complemented
9#13092612C211yesmaximal, characteristic, complemented
10#13092582C211yesmaximal, characteristic, complemented
11#13092565C211yesmaximal, characteristic, complemented
12#13092563C211yesmaximal, characteristic, complemented
13#13092552C211yesmaximal, characteristic, complemented
14#13092490C211yesmaximal, characteristic, complemented
15C23×#440C211yesmaximal, characteristic, complemented
16C2×#67292C2211yescharacteristic
17C2×#67292C2211yescharacteristic, complemented
18C2×#67290C2211yescharacteristic
19C2×D4×D23C2211yescharacteristic
20C2×SD16×C23C2211yescharacteristic
21C4×Q8×C23C2211yescharacteristic, complemented
22C4×D4×C23C2211yescharacteristic
23C2×#67275C2211yescharacteristic, complemented
24C2×#67274C2211yescharacteristic
25C2×#67272C2211yescharacteristic
26C2×#67272C2211yescharacteristic
27#10625101—21no—
28C2×(C2×D23)⋊C4—21no—
29#10625087—24no—
30#10625085—24no—
31C2×D184C2211yescharacteristic
32C2×D184C2211yescharacteristic
33C2×#67263C2211yescharacteristic, complemented
34C2×#67263C2211yescharacteristic, complemented
35C2×#67262C2211yescharacteristic
36C2×C8×D23C2211yescharacteristic, complemented
37#10625068C2211yescharacteristic
38#10625066—21no—
39#10625066—21no—
40#10625066C2211yescharacteristic
41#10625066C2211yescharacteristic
42#10625066C2211yescharacteristic, complemented
43#10625057—21no—
44#10625053—21no—
45#10625046C2211yescharacteristic
46#10625045—21no—
47#10625045C2211yescharacteristic, complemented
48C4×D92—21no—
49C4×D92C2211yescharacteristic
50C23×#107C2211yescharacteristic, complemented
51C23×#103C2211yescharacteristic, complemented
52C23×#102C2211yescharacteristic
53C23×#97C2211yescharacteristic, complemented
54(C2×D23)⋊C8C2211yescharacteristic
55(C2×D23)⋊C8C2211yescharacteristic, complemented
56#10624992C2211yescharacteristic, complemented
57#10624991C2211yescharacteristic
58#10624991C2211yescharacteristic, complemented
59#10624991C2211yescharacteristic, complemented
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—
68#67292—22no—
69#67292—22no—
70#67292—41no—
71#67292—41no—
72#67290—22no—
73#67290—41no—
74D4×D23—22no—
75D4×D23—41no—
76C2×D92—21no—
77C2×D92—21no—
78C2×D92—21no—
79C2×D92—21no—
80C2×D92—21no—
81C2×D92—21no—
82C2×D92—21no—
83C2×D92D411yescharacteristic
84C2×D92C2311yescharacteristic
85C2×D92C2311yescharacteristic
86C2×D92C2311yescharacteristic
87C2×C4×D23—21no—
88C2×C4×D23—21no—
89C2×C4×D23C2311yescharacteristic
90C2×C4×D23C2311yescharacteristic
91C2×Dic46C2311yescharacteristic
92SD16×C23D414yescomplemented
93C2×C8×C23C2311yescharacteristic
94C2×C8×C23C2311yescharacteristic
95C4⋊C4×C23—21no—
96C4⋊C4×C23C2311yescharacteristic
97C4⋊C4×C23C2311yescharacteristic
98C22⋊C4×C23—21no—
99C42×C23—21no—
100C42×C23C2311yescharacteristic
101#67275—22no—
102#67274—22no—
103#67272—22no—
104#67272—22no—
105(C2×D23)⋊C4—21no—
106(C2×D23)⋊C4—21no—
107(C2×D23)⋊C4—21no—
108(C2×D23)⋊C4—21no—
109(C2×D23)⋊C4—21no—
110(C2×D23)⋊C4—21no—
111(C2×D23)⋊C4D411yescharacteristic
112(C2×D23)⋊C4D411yescharacteristic
113C4⋊Dic23—21no—
114C4⋊Dic23D411yescharacteristic
115C2×C23⋊C8C2311yescharacteristic
116C2×C23⋊C8C2311yescharacteristic
117D184—22no—
118D184—41no—
119#67263—22no—
120#67263—41no—
121#67262—22no—
122C8×D23—22no—
123C23×C23—21no—
124C22×D23—21no—
125C22×D23—21no—
126C22×D23—21no—
127C22×D23—42no—
128C22×D23—42no—
129C22×D23—81no—
130C22×D23C2×D411yescharacteristic
131C22×D23C2×D411yescharacteristic
132Q8×C23—21no—
133Q8×C23C2×D412yes—
134D4×C23—21no—
135D4×C23C2×D412yes—
136C2×C4×C23—21no—
137C2×C4×C23—21no—
138C2×C4×C23—21no—
139C2×C4×C23—81no—
140C2×C4×C23C2×D411yescharacteristic
141C2×C4×C23C2×D411yescharacteristic
142C2×C4×C23C2411yescharacteristic
143C22⋊D23—42no—
144C22⋊D23—42no—
145C2×Dic23—21no—
146C2×Dic23—42no—
147C2×Dic23C2×D411yescharacteristic
148C2×Dic23C2×D411yescharacteristic
149D92—21no—
150D92—21no—
151D92—21no—
152D92—21no—
153D92—21no—
154D92—21no—
155D92—41no—
156D92—42no—
157D92—42no—
158D92—42no—
159D92—81no—
160D92—81no—
161D92—81no—
162D92—81no—
163C4×D23—21no—
164C4×D23—21no—
165C4×D23—21no—
166C4×D23—21no—
167C4×D23—42no—
168C4×D23—42no—
169Dic46—21no—
170Dic46—21no—
171C8×C23—21no—
172C8×C23C2×D412yes—
173C23⋊C8—21no—
174C23⋊C8—21no—
175#3268—231nomaximal, Sylow
176C22×C23—22no—
177C22×C23—41no—
178C22×C23—41no—
179C22×C23C22×D411yescharacteristic
180C2×D23—21no—
181C2×D23—21no—
182C2×D23—21no—
183C2×D23—21no—
184C2×D23—21no—
185C2×D23—21no—
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—22no—
197C4×C23—21no—
198C4×C23—21no—
199C4×C23—41no—
200C4×C23—41no—
201C4×C23C22×D411yescharacteristic
202C4×C23H(5,𝔽2)11yescharacteristic
203Dic23—21no—
204Dic23—21no—
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#440D2311yescharacteristic, complemented
220#435—231no—
221C2×C23—42no—
222C2×C23D4211yescharacteristic
223C2×C23#57511yescharacteristic
224C2×C23#57611yescharacteristic
225D23—41no—
226D23—41no—
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×SD16C2×D2311yescharacteristic
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#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×Q8C2×D2311yescharacteristic, complemented
260C4×D4—231no—
261C4×D4—461no—
262C4×D4C2×D2311yescharacteristic
263C2×C22⋊C4—461no—
264#107C2×D2311yescharacteristic, complemented
265C4⋊C8—231no—
266#103—231no—
267#103C2×D2311yescharacteristic, complemented
268#102—231no—
269#102—231no—
270#102—231no—
271#102C2×D2311yescharacteristic
272C22⋊C8—231no—
273C22⋊C8—231no—
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×Q8C22×D2311yescharacteristic
285C2×D4—231no—
286C2×D4—231no—
287C2×D4—231no—
288C2×D4—231no—
289C2×D4—461no—
290C2×D4—461no—
291C2×D4—461no—
292C2×D4—461no—
293C2×D4—461no—
294C2×D4—461no—
295C2×D4—462no—
296C2×D4—461no—
297C2×D4—461no—
298C2×D4—461no—
299C2×D4—921no—
300C2×D4C22×D2311yescharacteristic
301C22×C4—21no—
302C22×C4—231no—
303C22×C4—231no—
304C22×C4—461no—
305C22×C4—461no—
306C22×C4—461no—
307Q16—462no—
308SD16—462no—
309SD16—462no—
310SD16—921no—
311SD16D9214yescomplemented
312D8—462no—
313D8—462no—
314D8—462no—
315D8—921no—
316M16—462no—
317C2×C8—231no—
318C2×C8—231no—
319C2×C8—462no—
320C2×C8C22×D2311yescharacteristic
321C2×C8C22×D2311yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—231no—
324C4⋊C4—461no—
325C4⋊C4C22×D2311yescharacteristic
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—21no—
337C42C22×D2311yescharacteristic
338C23—21no—
339C23—231no—
340C23—231no—
341C23—461no—
342C23—461no—
343C23—461no—
344C23—922no—
345C23—922no—
346C23—1841no—
347Q8—21no—
348Q8—461no—
349Q8—461no—
350Q8C2×D9212yes—
351D4—21no—
352D4—461no—
353D4—461no—
354D4—461no—
355D4—461no—
356D4—461no—
357D4—461no—
358D4—921no—
359D4—922no—
360D4—922no—
361D4—922no—
362D4—922no—
363D4—922no—
364D4—1841no—
365D4—1841no—
366D4—1841no—
367D4—1841no—
368D4C2×D9212yes—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—231no—
374C2×C4—231no—
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—461no—
388C8—461no—
389C8C2×D9212yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—461no—
394C22—461no—
395C22—461no—
396C22—461no—
397C22—461no—
398C22—461no—
399C22—921no—
400C22—921no—
401C22—921no—
402C22—921no—
403C22—921no—
404C22—921no—
405C22—921no—
406C22—921no—
407C22—921no—
408C22—1844no—
409C22C2×D4×D2311yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—461no—
416C4—461no—
417C4—921no—
418C4C22×D9211yescharacteristic
419C4#1062516011yescharacteristic
420C2—42no—
421C2—921no—
422C2—921no—
423C2—1841no—
424C2—1841no—
425C2—1841no—
426C2D4×D9211yescharacteristic
427C2#1309321611yescharacteristic
428C2#1309322111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
hypercenter#440D23
hypocenterC23#3268
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×#10625085C2semidirect
2. C2×#10625087C2semidirect
3. #13093089C2semidirect
4. #13093062C2semidirect
5. #13092806C2semidirect
6. #13092664C2semidirect
7. #13092654C2semidirect
8. #13092639C2semidirect
9. #13092612C2semidirect
10. #13092582C2semidirect
11. #13092565C2semidirect
12. #13092563C2semidirect
13. #13092552C2semidirect
14. #13092490C2semidirect
15. C23×#440C2semidirect
17. C2×#67292C22semidirect
21. C4×Q8×C23C22semidirect
23. C2×#67275C22semidirect
33. C2×#67263C22semidirect
34. C2×#67263C22semidirect
36. C2×C8×D23C22semidirect
42. #10625066C22semidirect
47. #10625045C22semidirect
50. C23×#107C22semidirect
51. C23×#103C22semidirect
53. C23×#97C22semidirect
55. (C2×D23)⋊C8C22semidirect
56. #10624992C22semidirect
58. #10624991C22semidirect
59. #10624991C22semidirect
60. C4⋊(C23⋊C8)C22semidirect
92. SD16×C23D4semidirect
219. #440D23semidirect
259. C4×Q8C2×D23semidirect
264. #107C2×D23semidirect
267. #103C2×D23semidirect
274. #97C2×D23semidirect
275. C23#3268semidirect
311. SD16D92semidirect

Maximal subgroups

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

subgroupindex
C2×#106250852
C2×#106250872
#130930892
#130930622
#130928062
#130926642
#130926542
#130926392
#130926122
#130925822
#130925652
#130925632
#130925522
#130924902
C23×#4402
#326823