Finite Group Databasebeta

← #10594972

Subgroups — #10594972

Order 576.

429 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64133C211yesmaximal, characteristic, complemented
2C3×#929C211yesmaximal, characteristic
3C3×#924C211yesmaximal, characteristic, complemented
4#63969C211yesmaximal, characteristic
5#63959C211yesmaximal, characteristic
6#63956C211yesmaximal, characteristic, complemented
7#63956C211yesmaximal, characteristic, complemented
8#63896C211yesmaximal, characteristic, complemented
9#63887C211yesmaximal, characteristic, complemented
10#63861C211yesmaximal, characteristic, complemented
11#63858C211yesmaximal, characteristic, complemented
12#63847C211yesmaximal, characteristic, complemented
13#63845C211yesmaximal, characteristic, complemented
14#63840C211yesmaximal, characteristic, complemented
15#63839C211yesmaximal, characteristic, complemented
16#5651—31nomaximal
17#5646—31nomaximal
18C22×C32×C4C2211yescharacteristic
19C2×#634C2211yescharacteristic
20C2×C3×#67C2211yescharacteristic
21C2×C3×Dic6C2211yescharacteristic
22C2×#627C2211yescharacteristic
23C2×D3×Dic3C2211yescharacteristic
24#3757C2211yescharacteristic
25#3757C2211yescharacteristic
26C4⋊(C3⋊Dic3)C2211yescharacteristic
27#3750C2211yescharacteristic
28#3750C2211yescharacteristic
29C3×#217C2211yescharacteristic
30C3×#217C2211yescharacteristic
31C3×#217C2211yescharacteristic
32C3×(C2×D3)⋊C4C2211yescharacteristic
33C3×(C2×D3)⋊C4C2211yescharacteristic
34C3×C4⋊Dic3C2211yescharacteristic
35C3×Dic3⋊C4C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39#3724C2211yescharacteristic
40#3724C2211yescharacteristic
41#3724C2211yescharacteristic
42Dic3⋊Dic3C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45Dic3⋊Dic3C2211yescharacteristic
46Dic3⋊Dic3C2211yescharacteristic
47(C2×D3)⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50Dic32C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#123—31no—
54C3×C22⋊Q8—31no—
55#946—31no—
56#944—31no—
57#936—31no—
58#935—31no—
59#929D311yescharacteristic
60#924—31no—
61#924—31no—
62#924—61no—
63#924D311yescharacteristic, complemented
64#898—31no—
65#898—31no—
66#896—31no—
67#890—31no—
68#889—31no—
69#889—31no—
70#889—31no—
71#888—31no—
72#888—31no—
73#888—31no—
74#885—31no—
75#883—31no—
76#879—31no—
77#879—31no—
78#879—31no—
79#879—31no—
80#879—31no—
81#879—31no—
82#878—31no—
83#878—31no—
84C23×C32C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C2×C32×C4—41no—
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93#634—41no—
94C3×#67—41no—
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C2×C3×Dic3C2311yescharacteristic
100C2×C3×Dic3C2311yescharacteristic
101C2×C3×Dic3C2311yescharacteristic
102C3×Dic6—41no—
103#627—41no—
104D3×Dic3—41no—
105#563—91noSylow
106C2×C3×Q8—31no—
107C2×C3×D4—31no—
108C22×C3×C4—21no—
109C22×C3×C4C2×D311yescharacteristic
110C22×C3×C4C2×D311yescharacteristic
111C2×#67C2×D311yescharacteristic
112C22×Dic3—31no—
113C2×C4×D3—31no—
114C2×Dic6—31no—
115C2×Dic6—31no—
116C2×Dic6—31no—
117C2×Dic6—31no—
118C2×Dic6—61no—
119C2×Dic6C2×D311yescharacteristic
120C3×C4⋊C4—31no—
121C3×C4⋊C4—31no—
122C3×C4⋊C4—31no—
123C3×C4⋊C4—31no—
124C3×C4⋊C4—31no—
125C3×C22⋊C4—31no—
126C3×C22⋊C4—31no—
127C3×C22⋊C4—31no—
128C3×C22⋊C4—31no—
129C3×C22⋊C4—31no—
130#217—31no—
131#217—31no—
132#217—31no—
133#217—31no—
134#217—31no—
135#217—31no—
136#217—31no—
137#217—61no—
138#217—61no—
139#217C2×D311yescharacteristic
140#217C2×D311yescharacteristic
141#217C2×D311yescharacteristic
142(C2×D3)⋊C4—31no—
143(C2×D3)⋊C4—31no—
144(C2×D3)⋊C4—31no—
145(C2×D3)⋊C4C2×D311yescharacteristic
146(C2×D3)⋊C4C2×D311yescharacteristic
147C4⋊Dic3—31no—
148C4⋊Dic3—31no—
149C4⋊Dic3—31no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—31no—
154C4⋊Dic3—61no—
155C4⋊Dic3C2×D311yescharacteristic
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—31no—
167Dic3⋊C4—31no—
168Dic3⋊C4—31no—
169Dic3⋊C4—31no—
170Dic3⋊C4—31no—
171Dic3⋊C4—61no—
172Dic3⋊C4—61no—
173Dic3⋊C4C2×D311yescharacteristic
174Dic3⋊C4C2×D311yescharacteristic
175Dic3⋊C4C2×D311yescharacteristic
176Dic3⋊C4C2×D311yescharacteristic
177C4×Dic3—31no—
178C4×Dic3—31no—
179C4×Dic3—31no—
180C4×Dic3—31no—
181C4×Dic3—31no—
182C4×Dic3—31no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32C2411yescharacteristic
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3—21no—
190C32×C4—21no—
191C32×C4—21no—
192C3⋊Dic3—21no—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3⋊Dic3—21no—
196C3×Dic3—21no—
197C3×Dic3—21no—
198C3×Dic3—21no—
199C3×Dic3—21no—
200C3×Dic3—21no—
201C3×Dic3—21no—
202C3×Dic3—21no—
203C4⋊Q8—91no—
204C4⋊Q8—91no—
205#126—91no—
206#126—91no—
207#126—91no—
208#126—91no—
209#125—91no—
210#125—91no—
211#124—91no—
212#123—31no—
213#123—91no—
214C22⋊Q8—31no—
215C22⋊Q8—91no—
216C22⋊Q8—91no—
217C22⋊Q8—91no—
218C23×C3—21no—
219C23×C3—31no—
220C23×C3C22×D311yescharacteristic
221C23×C3C22×D311yescharacteristic
222C22×D3C22×D311yescharacteristic
223C3×Q8—121no—
224C3×D4—121no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
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—31no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—42no—
237C2×C3×C4C22×D311yescharacteristic
238C2×C3×C4C22×D311yescharacteristic
239C2×C3×C4C22×D311yescharacteristic
240C2×C3×C4C22×D311yescharacteristic
241#67—41no—
242C2×Dic3—31no—
243C2×Dic3—31no—
244C2×Dic3—31no—
245C2×Dic3—31no—
246C2×Dic3—31no—
247C2×Dic3—31no—
248C2×Dic3—31no—
249C2×Dic3—31no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—121no—
255C2×Dic3C22×D311yescharacteristic
256C2×Dic3C22×D311yescharacteristic
257C2×Dic3C22×D311yescharacteristic
258C2×Dic3C22×D311yescharacteristic
259C2×Dic3C22×D311yescharacteristic
260C2×Dic3C22×D311yescharacteristic
261C2×Dic3C22×D311yescharacteristic
262C4×D3—121no—
263Dic6—41no—
264Dic6—121no—
265Dic6—121no—
266Dic6—121no—
267Dic6—121no—
268Dic6—122no—
269C2×C32—41no—
270C2×C32H(5,𝔽2)11yescharacteristic
271C2×C322−1+411yescharacteristic
272C2×C322−1+411yescharacteristic
273C3×D3—41no—
274C2×Q8—31no—
275C2×Q8—91no—
276C2×Q8—91no—
277C2×D4—31no—
278C22×C4—91no—
279C22×C4D3211yescharacteristic
280C4⋊C4—31no—
281C4⋊C4—31no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—31no—
285C4⋊C4—91no—
286C4⋊C4—91no—
287C4⋊C4—91no—
288C4⋊C4—91no—
289C4⋊C4—91no—
290C4⋊C4—91no—
291C4⋊C4—91no—
292C4⋊C4—91no—
293C4⋊C4—91no—
294C4⋊C4—91no—
295C4⋊C4—91no—
296C22⋊C4—31no—
297C22⋊C4—31no—
298C22⋊C4—31no—
299C22⋊C4—31no—
300C22⋊C4—31no—
301C22⋊C4—91no—
302C22⋊C4—91no—
303C22⋊C4—91no—
304C22⋊C4—91no—
305C22⋊C4—91no—
306C42—91no—
307C42—91no—
308C42—91no—
309C22×C3—22no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—61no—
320C22×C3—61no—
321C22×C3—61no—
322C22×C3C23×D311yescharacteristic
323C22×C3C23×D311yescharacteristic
324C2×D3—21no—
325C2×D3—21no—
326C2×D3—21no—
327C3×C4—22no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—41no—
333C3×C4—61no—
334C3×C4—61no—
335C3×C4—61no—
336C3×C4—61no—
337C3×C4—61no—
338C3×C4—61no—
339C3×C4—61no—
340Dic3—21no—
341Dic3—21no—
342Dic3—21no—
343Dic3—21no—
344Dic3—21no—
345Dic3—21no—
346Dic3—21no—
347Dic3—61no—
348Dic3—61no—
349Dic3—61no—
350Dic3—61no—
351Dic3—61no—
352Dic3—61no—
353Dic3—61no—
354Dic3—61no—
355Dic3—121no—
356Dic3—121no—
357Dic3—121no—
358Dic3—121no—
359C32#56311yescharacteristic, complemented, Sylow
360C23—31no—
361C23C2×D3211yescharacteristic
362Q8—121no—
363Q8—361no—
364Q8—361no—
365D4—121no—
366C2×C4—31no—
367C2×C4—31no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—31no—
373C2×C4—41no—
374C2×C4—91no—
375C2×C4—91no—
376C2×C4—91no—
377C2×C4—91no—
378C2×C4—361no—
379C2×C4C2×D3211yescharacteristic
380C2×C4C2×D3211yescharacteristic
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—42no—
385C2×C3—41no—
386C2×C3—41no—
387C2×C3—121no—
388C2×C3#100411yescharacteristic
389C2×C3#100411yescharacteristic
390C2×C3#100711yescharacteristic
391C2×C3#101011yescharacteristic
392C2×C3#101011yescharacteristic
393C2×C3#101011yescharacteristic
394D3—41no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—61no—
399C22—61no—
400C22—61no—
401C22C22×D3211yescharacteristic
402C4—21no—
403C4—21no—
404C4—61no—
405C4—61no—
406C4—61no—
407C4—61no—
408C4—61no—
409C4—61no—
410C4—61no—
411C4—181no—
412C4—181no—
413C4—181no—
414C4—181no—
415C3—21no—
416C3#564611yescharacteristic, complemented
417C3#565111yescharacteristic, complemented
418C2—41no—
419C2—121no—
420C2#6429711yescharacteristic
421C2#6429811yescharacteristic
422C2#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC22×C32×C4C22
prime radicalC2×C3×#67C22
hypercenterC22×C4D32
hypocenterC32#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #64133C2semidirect
3. C3×#924C2semidirect
6. #63956C2semidirect
7. #63956C2semidirect
8. #63896C2semidirect
9. #63887C2semidirect
10. #63861C2semidirect
11. #63858C2semidirect
12. #63847C2semidirect
13. #63845C2semidirect
14. #63840C2semidirect
15. #63839C2semidirect
63. #924D3semidirect
359. C32#563semidirect
416. C3#5646semidirect
417. C3#5651semidirect

Maximal subgroups

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

subgroupindex
#641332
C3×#9292
C3×#9242
#639692
#639592
#639562
#638962
#638872
#638612
#638582
#638472
#638452
#638402
#638392
#56513
#56463