Finite Group Databasebeta

← #10595369

Subgroups — #10595369

Order 576.

446 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64153C211yesmaximal, characteristic, complemented
2C3×#946C211yesmaximal, characteristic
3C3×#944C211yesmaximal, characteristic, complemented
4#63896C211yesmaximal, characteristic
5#63887C211yesmaximal, characteristic
6#63878C211yesmaximal, characteristic
7#63877C211yesmaximal, characteristic
8D3×Dic3⋊C4C211yesmaximal, characteristic
9#63870C211yesmaximal, characteristic, complemented
10#63867C211yesmaximal, characteristic, complemented
11#63851C211yesmaximal, characteristic
12#63847C211yesmaximal, characteristic, complemented
13#63846C211yesmaximal, characteristic, complemented
14#63840C211yesmaximal, characteristic, complemented
15#63839C211yesmaximal, characteristic, complemented
16#5729—31nomaximal
17#5623—31nomaximal
18C2×C32×Q8C2211yescharacteristic
19C2×#634C2211yescharacteristic
20C2×C3×C4×D3C2211yescharacteristic
21C2×C3×Dic6C2211yescharacteristic
22C2×#627C2211yescharacteristic
23C2×D3×Dic3C2211yescharacteristic
24C2×D3×Dic3C2211yescharacteristic
25#3750C2211yescharacteristic
26#3750C2211yescharacteristic
27#3750C2211yescharacteristic
28#3750C2211yescharacteristic
29C4×C3⋊Dic3C2211yescharacteristic
30C3×(C2×D3)⋊C4C2211yescharacteristic
31C3×(C2×D3)⋊C4C2211yescharacteristic
32C3×C4⋊Dic3C2211yescharacteristic
33C3×Dic3⋊C4C2211yescharacteristic
34C3×Dic3⋊C4C2211yescharacteristic
35C3×Dic3⋊C4C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×C4×Dic3C2211yescharacteristic
40#3724C2211yescharacteristic
41#3724C2211yescharacteristic
42#3724C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47Dic3⋊Dic3C2211yescharacteristic
48Dic3⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50(C2×D3)⋊Dic3C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×C4⋊Q8—31no—
54C3×C22⋊Q8—31no—
55#946—31no—
56#946D311yescharacteristic
57#944—31no—
58#944—31no—
59#944—31no—
60#944—61no—
61#944D311yescharacteristic, complemented
62#924—31no—
63C2×Dic3⋊C4—31no—
64#896—31no—
65#896—31no—
66#892—31no—
67D3×C4⋊C4—31no—
68#890—31no—
69#889—31no—
70#889—31no—
71#889—31no—
72#889—31no—
73#889—31no—
74#889—31no—
75#888—31no—
76#888—31no—
77#888—31no—
78#878—31no—
79#878—31no—
80#877—31no—
81#877—31no—
82#872—31no—
83#870—31no—
84C22×C3×D3C2311yescharacteristic
85C32×Q8—41no—
86C2×C32×C4C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93#634—41no—
94C2×C3×Dic3C2311yescharacteristic
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C3×C4×D3—41no—
102C3×Dic6—41no—
103#627—41no—
104D3×Dic3—41no—
105D3×Dic3Q814yescomplemented
106#544—91noSylow
107C2×C3×Q8—21no—
108C2×C3×Q8—31no—
109C2×C3×Q8C2×D311yescharacteristic
110C2×C3×Q8C2×D311yescharacteristic
111C22×C3×C4—31no—
112C22×Dic3—31no—
113C22×Dic3—31no—
114C2×C4×D3—31no—
115C2×C4×D3—31no—
116C2×C4×D3C2×D311yescharacteristic
117C2×Dic6—31no—
118C2×Dic6—31no—
119C2×Dic6—31no—
120C2×Dic6—31no—
121C2×Dic6—61no—
122C2×Dic6C2×D311yescharacteristic
123C3×C4⋊C4—31no—
124C3×C4⋊C4—31no—
125C3×C4⋊C4—31no—
126C3×C4⋊C4—31no—
127C3×C4⋊C4—31no—
128C3×C4⋊C4—31no—
129C3×C4⋊C4—31no—
130C3×C22⋊C4—31no—
131C3×C22⋊C4—31no—
132C3×C42—31no—
133#217—31no—
134#217—31no—
135(C2×D3)⋊C4—31no—
136(C2×D3)⋊C4—31no—
137(C2×D3)⋊C4C2×D311yescharacteristic
138(C2×D3)⋊C4C2×D311yescharacteristic
139C4⋊Dic3—31no—
140C4⋊Dic3—31no—
141C4⋊Dic3—31no—
142C4⋊Dic3—31no—
143C4⋊Dic3—31no—
144C4⋊Dic3—31no—
145C4⋊Dic3C2×D311yescharacteristic
146Dic3⋊C4—31no—
147Dic3⋊C4—31no—
148Dic3⋊C4—31no—
149Dic3⋊C4—31no—
150Dic3⋊C4—31no—
151Dic3⋊C4—31no—
152Dic3⋊C4—31no—
153Dic3⋊C4—31no—
154Dic3⋊C4—31no—
155Dic3⋊C4—31no—
156Dic3⋊C4—31no—
157Dic3⋊C4—31no—
158Dic3⋊C4—31no—
159Dic3⋊C4—31no—
160Dic3⋊C4—31no—
161Dic3⋊C4—31no—
162Dic3⋊C4—31no—
163Dic3⋊C4—31no—
164Dic3⋊C4—31no—
165Dic3⋊C4—31no—
166Dic3⋊C4—61no—
167Dic3⋊C4—61no—
168Dic3⋊C4—61no—
169Dic3⋊C4—61no—
170Dic3⋊C4C2×D311yescharacteristic
171Dic3⋊C4C2×D311yescharacteristic
172Dic3⋊C4C2×D311yescharacteristic
173Dic3⋊C4C2×D311yescharacteristic
174Dic3⋊C4C2×D311yescharacteristic
175Dic3⋊C4C2×D311yescharacteristic
176C4×Dic3—31no—
177C4×Dic3—31no—
178C4×Dic3—31no—
179C4×Dic3—31no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C4×Dic3—61no—
183C4×Dic3C2×D311yescharacteristic
184C22×C32C2411yescharacteristic
185C2×C3×D3—21no—
186C2×C3×D3—21no—
187C2×C3×D3C2×Q812yes—
188C32×C4—21no—
189C32×C4—21no—
190C32×C4—21no—
191C3⋊Dic3—21no—
192C3⋊Dic3—21no—
193C3⋊Dic3—21no—
194C3⋊Dic3C2×Q812yes—
195C3×Dic3—21no—
196C3×Dic3—21no—
197C3×Dic3—21no—
198C3×Dic3—21no—
199C3×Dic3—21no—
200C3×Dic3—21no—
201C3×Dic3C2×Q812yes—
202C4⋊Q8—31no—
203C4⋊Q8—91no—
204C4⋊Q8—91no—
205C4⋊Q8—91no—
206#125—91no—
207#125—91no—
208#125—91no—
209#125—91no—
210C22⋊Q8—31no—
211C22⋊Q8—91no—
212C22⋊Q8—91no—
213C22⋊Q8—91no—
214#117—91no—
215#117—91no—
216C2×C4⋊C4—91no—
217C23×C3—31no—
218C22×D3C22×D311yescharacteristic
219C3×Q8—41no—
220C3×Q8—41no—
221C3×Q8—42no—
222C3×Q8—121no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—31no—
232C2×C3×C4—31no—
233C2×C3×C4—121no—
234C2×C3×C4C22×D311yescharacteristic
235C2×C3×C4C22×D311yescharacteristic
236C2×C3×C4C22×D311yescharacteristic
237C2×C3×C4C22×D311yescharacteristic
238C2×C3×C4C22×D311yescharacteristic
239C2×C3×C4C22×D311yescharacteristic
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—34no—
243C2×Dic3—31no—
244C2×Dic3—31no—
245C2×Dic3—31no—
246C2×Dic3—31no—
247C2×Dic3—31no—
248C2×Dic3—31no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—121no—
254C2×Dic3C22×D311yescharacteristic
255C2×Dic3C22×D311yescharacteristic
256C2×Dic3C22×D311yescharacteristic
257C2×Dic3C22×D311yescharacteristic
258C2×Dic3C22×D311yescharacteristic
259C2×Dic3C22×D311yescharacteristic
260C2×Dic3C22×D311yescharacteristic
261C4×D3—34no—
262C4×D3—41no—
263C4×D3—121no—
264Dic6—41no—
265Dic6—121no—
266Dic6—121no—
267Dic6—121no—
268Dic6—121no—
269Dic6—122no—
270C2×C32C22×Q811yescharacteristic
271C2×C32H(5,𝔽2)11yescharacteristic
272C2×C322−1+411yescharacteristic
273C3×D3—22no—
274C2×Q8—31no—
275C2×Q8—91no—
276C2×Q8—91no—
277C2×Q8D3211yescharacteristic
278C22×C4—31no—
279C22×C4—91no—
280C22×C4—91no—
281C4⋊C4—31no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—31no—
286C4⋊C4—31no—
287C4⋊C4—31no—
288C4⋊C4—91no—
289C4⋊C4—91no—
290C4⋊C4—91no—
291C4⋊C4—91no—
292C4⋊C4—91no—
293C4⋊C4—91no—
294C4⋊C4—91no—
295C4⋊C4—91no—
296C4⋊C4—91no—
297C4⋊C4—91no—
298C4⋊C4—91no—
299C4⋊C4—91no—
300C4⋊C4—91no—
301C22⋊C4—31no—
302C22⋊C4—31no—
303C22⋊C4—91no—
304C22⋊C4—91no—
305C42—31no—
306C42—91no—
307C42—91no—
308C42—91no—
309C22×C3—21no—
310C22×C3—32no—
311C22×C3—61no—
312C22×C3—61no—
313C22×C3C23×D311yescharacteristic
314C22×C3C23×D311yescharacteristic
315C2×D3—21no—
316C2×D3—21no—
317C2×D3D3×Q812yes—
318C3×C4—22no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—32no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—61no—
329C3×C4—61no—
330C3×C4—61no—
331C3×C4—61no—
332C3×C4—61no—
333C3×C4—61no—
334Dic3—21no—
335Dic3—21no—
336Dic3—21no—
337Dic3—21no—
338Dic3—21no—
339Dic3—21no—
340Dic3—32no—
341Dic3—32no—
342Dic3—62no—
343Dic3—62no—
344Dic3—61no—
345Dic3—61no—
346Dic3—61no—
347Dic3—61no—
348Dic3—61no—
349Dic3—61no—
350Dic3—121no—
351Dic3—121no—
352Dic3D3×Q812yes—
353C32#54411yescharacteristic, complemented, Sylow
354C23—31no—
355Q8—41no—
356Q8—121no—
357Q8—361no—
358Q8—361no—
359C2×C4—31no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—94no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—121no—
372C2×C4—361no—
373C2×C4C2×D3211yescharacteristic
374C2×C4C2×D3211yescharacteristic
375C2×C4C2×D3211yescharacteristic
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—62no—
380C2×C3#100411yescharacteristic
381C2×C3#100411yescharacteristic
382C2×C3C2×D3×Q811yescharacteristic
383C2×C3C2×D3×Q811yescharacteristic
384C2×C3#100711yescharacteristic
385C2×C3#101011yescharacteristic
386D3—22no—
387C22—32no—
388C22—61no—
389C22—61no—
390C22C22×D3211yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—32no—
395C4—61no—
396C4—61no—
397C4—61no—
398C4—61no—
399C4—61no—
400C4—61no—
401C4—92no—
402C4—181no—
403C4—181no—
404C4—181no—
405C3—21no—
406C3#562311yescharacteristic, complemented
407C3#572911yescharacteristic, complemented
408C2—62no—
409C2#6431511yescharacteristic
410C2D32×Q811yescharacteristic
411C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC2×C32×Q8C22
prime radicalC22×C3×D3C23
hypercenterC2×Q8D32
hypocenterC32#544
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #64153C2semidirect
3. C3×#944C2semidirect
9. #63870C2semidirect
10. #63867C2semidirect
12. #63847C2semidirect
13. #63846C2semidirect
14. #63840C2semidirect
15. #63839C2semidirect
61. #944D3semidirect
105. D3×Dic3Q8semidirect
353. C32#544semidirect
406. C3#5623semidirect
407. C3#5729semidirect

Maximal subgroups

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

subgroupindex
#641532
C3×#9462
C3×#9442
#638962
#638872
#638782
#638772
D3×Dic3⋊C42
#638702
#638672
#638512
#638472
#638462
#638402
#638392
#57293
#56233