Finite Group Databasebeta

← #10594431

Subgroups — #10594431

Order 576.

456 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#64099C211yesmaximal, characteristic, complemented
2C3×#894C211yesmaximal, characteristic
3C3×#889C211yesmaximal, characteristic, complemented
4#63893C211yesmaximal, characteristic, complemented
5#63893C211yesmaximal, characteristic, complemented
6Dic3×D12C211yesmaximal, characteristic
7#63884C211yesmaximal, characteristic
8#63878C211yesmaximal, characteristic, complemented
9#63878C211yesmaximal, characteristic, complemented
10D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
11#63861C211yesmaximal, characteristic, complemented
12#63858C211yesmaximal, characteristic, complemented
13#63845C211yesmaximal, characteristic, complemented
14#63841C211yesmaximal, characteristic, complemented
15#63837C211yesmaximal, characteristic, complemented
16#5694—31nomaximal
17#5650—31nomaximal
18C2×C3×D12C2211yescharacteristic
19C2×C3×C4×D3C2211yescharacteristic
20C2×#627C2211yescharacteristic
21C2×D3×Dic3C2211yescharacteristic
22C2×D3×Dic3C2211yescharacteristic
23C2×D3×Dic3C2211yescharacteristic
24C32×C4⋊C4C2211yescharacteristic
25C4⋊(C3⋊Dic3)C2211yescharacteristic
26C4⋊(C3⋊Dic3)C2211yescharacteristic
27C4⋊(C3⋊Dic3)C2211yescharacteristic
28#3750C2211yescharacteristic
29#3750C2211yescharacteristic
30C4×C3⋊Dic3C2211yescharacteristic
31C3×(C2×D3)⋊C4C2211yescharacteristic
32C3×(C2×D3)⋊C4C2211yescharacteristic
33C3×(C2×D3)⋊C4C2211yescharacteristic
34C3×C4⋊Dic3C2211yescharacteristic
35C3×Dic3⋊C4C2211yescharacteristic
36C3×Dic3⋊C4C2211yescharacteristic
37C3×Dic3⋊C4C2211yescharacteristic
38C3×Dic3⋊C4C2211yescharacteristic
39C3×Dic3⋊C4C2211yescharacteristic
40C3×C4×Dic3C2211yescharacteristic
41#3724C2211yescharacteristic
42Dic3⋊Dic3C2211yescharacteristic
43Dic3⋊Dic3C2211yescharacteristic
44Dic3⋊Dic3C2211yescharacteristic
45(C2×D3)⋊Dic3C2211yescharacteristic
46(C2×D3)⋊Dic3C2211yescharacteristic
47(C2×D3)⋊Dic3C2211yescharacteristic
48(C2×D3)⋊Dic3C2211yescharacteristic
49(C2×D3)⋊Dic3C2211yescharacteristic
50Dic32C2211yescharacteristic
51Dic32C2211yescharacteristic
52Dic32C2211yescharacteristic
53C3×#125—31no—
54C3×#123—31no—
55#935—31no—
56D4×Dic3—31no—
57#926—31no—
58C2×Dic3⋊C4—31no—
59#898—31no—
60#898—31no—
61#897—31no—
62#897—31no—
63#894—31no—
64#894D311yescharacteristic
65#892—31no—
66#892—31no—
67#892—31no—
68D3×C4⋊C4—31no—
69#890—31no—
70#890—31no—
71#890—31no—
72#890—61no—
73#889—31no—
74#889D311yescharacteristic, complemented
75#887—31no—
76#879—31no—
77#879—31no—
78#878—31no—
79#878—31no—
80#877—31no—
81#877—31no—
82C4×D12—31no—
83C4×Dic6—31no—
84C22×C3×D3C2311yescharacteristic
85C22×C3×D3C2311yescharacteristic
86C2×C32×C4C2311yescharacteristic
87C2×C32×C4C2311yescharacteristic
88C2×C32×C4C2311yescharacteristic
89C2×C3⋊Dic3C2311yescharacteristic
90C2×C3⋊Dic3C2311yescharacteristic
91C2×C3⋊Dic3C2311yescharacteristic
92C2×C3⋊Dic3C2311yescharacteristic
93C2×C3×Dic3C2311yescharacteristic
94C2×C3×Dic3C2311yescharacteristic
95C2×C3×Dic3C2311yescharacteristic
96C2×C3×Dic3C2311yescharacteristic
97C2×C3×Dic3C2311yescharacteristic
98C2×C3×Dic3C2311yescharacteristic
99C3×D12—22no—
100C3×C4×D3—22no—
101#627—22no—
102D3×Dic3—22no—
103D3×Dic3—22no—
104D3×Dic3—22no—
105#552—91noSylow
106C2×C3×D4—31no—
107C22×C3×C4—31no—
108C22×Dic3—31no—
109C22×Dic3—31no—
110C22×Dic3—31no—
111C2×D12C2×D311yescharacteristic
112C2×C4×D3—31no—
113C2×C4×D3—31no—
114C2×C4×D3—31no—
115C2×C4×D3C2×D311yescharacteristic
116C2×Dic6—31no—
117C2×Dic6—31no—
118C3×C4⋊C4—21no—
119C3×C4⋊C4—31no—
120C3×C4⋊C4—31no—
121C3×C4⋊C4—31no—
122C3×C4⋊C4—31no—
123C3×C4⋊C4—31no—
124C3×C4⋊C4—31no—
125C3×C4⋊C4C2×D311yescharacteristic
126C3×C4⋊C4C2×D311yescharacteristic
127C3×C22⋊C4—31no—
128C3×C22⋊C4—31no—
129C3×C22⋊C4—31no—
130C3×C42—31no—
131#217—31no—
132#217—31no—
133#217—31no—
134#217—31no—
135#217—31no—
136(C2×D3)⋊C4—31no—
137(C2×D3)⋊C4—31no—
138(C2×D3)⋊C4—31no—
139(C2×D3)⋊C4—31no—
140(C2×D3)⋊C4—31no—
141(C2×D3)⋊C4C2×D311yescharacteristic
142(C2×D3)⋊C4C2×D311yescharacteristic
143(C2×D3)⋊C4C2×D311yescharacteristic
144C4⋊Dic3—31no—
145C4⋊Dic3—31no—
146C4⋊Dic3—31no—
147C4⋊Dic3—31no—
148C4⋊Dic3—31no—
149C4⋊Dic3—31no—
150C4⋊Dic3—31no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
169Dic3⋊C4C2×D311yescharacteristic
170Dic3⋊C4C2×D311yescharacteristic
171Dic3⋊C4C2×D311yescharacteristic
172Dic3⋊C4C2×D311yescharacteristic
173C4×Dic3—31no—
174C4×Dic3—31no—
175C4×Dic3—31no—
176C4×Dic3—31no—
177C4×Dic3—31no—
178C4×Dic3—31no—
179C4×Dic3—31no—
180C4×Dic3—31no—
181C4×Dic3—61no—
182C4×Dic3C2×D311yescharacteristic
183C22×C32C2411yescharacteristic
184C2×C3×D3—21no—
185C2×C3×D3—21no—
186C2×C3×D3—21no—
187C2×C3×D3—21no—
188C2×C3×D3—21no—
189C2×C3×D3#4112yes—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—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#4112yes—
203#126—91no—
204#126—91no—
205#125—31no—
206#125—91no—
207#125—91no—
208#123—31no—
209#123—91no—
210C22⋊Q8—91no—
211C22⋊Q8—91no—
212C4×Q8—91no—
213C4×D4—91no—
214#117—91no—
215#117—91no—
216#117—91no—
217C2×C4⋊C4—91no—
218C23×C3—31no—
219C23×C3—31no—
220C22×D3C22×D311yescharacteristic
221C22×D3C22×D311yescharacteristic
222C3×D4—62no—
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—62no—
233C2×C3×C4C22×D311yescharacteristic
234C2×C3×C4C22×D311yescharacteristic
235C2×C3×C4C22×D311yescharacteristic
236C2×C3×C4C22×D311yescharacteristic
237C2×C3×C4C22×D311yescharacteristic
238C2×C3×C4C22×D311yescharacteristic
239C2×Dic3—31no—
240C2×Dic3—31no—
241C2×Dic3—31no—
242C2×Dic3—31no—
243C2×Dic3—31no—
244C2×Dic3—31no—
245C2×Dic3—31no—
246C2×Dic3—31no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3C22×D311yescharacteristic
255C2×Dic3C22×D311yescharacteristic
256C2×Dic3C22×D311yescharacteristic
257C2×Dic3C22×D311yescharacteristic
258C2×Dic3C22×D311yescharacteristic
259C2×Dic3C22×D311yescharacteristic
260D12—22no—
261C4×D3—22no—
262C4×D3—62no—
263C4×D3—62no—
264C4×D3—62no—
265Dic6—62no—
266Dic6—62no—
267C2×C32C2×#4111yescharacteristic
268C2×C32C2×#4111yescharacteristic
269C2×C322−1+411yescharacteristic
270C3×D3—22no—
271C3×D3—41no—
272C2×Q8—91no—
273C2×D4—31no—
274C22×C4—31no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—91no—
278C4⋊C4—31no—
279C4⋊C4—31no—
280C4⋊C4—31no—
281C4⋊C4—31no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—91no—
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⋊C4D3211yescharacteristic
294C22⋊C4—31no—
295C22⋊C4—31no—
296C22⋊C4—31no—
297C22⋊C4—91no—
298C22⋊C4—91no—
299C22⋊C4—91no—
300C22⋊C4—91no—
301C22⋊C4—91no—
302C42—31no—
303C42—91no—
304C42—91no—
305C42—91no—
306C42—91no—
307C22×C3—21no—
308C22×C3—32no—
309C22×C3—61no—
310C22×C3—61no—
311C22×C3—61no—
312C22×C3—61no—
313C22×C3—61no—
314C22×C3C23×D311yescharacteristic
315C22×C3C23×D311yescharacteristic
316C2×D3—21no—
317C2×D3—21no—
318C2×D3—21no—
319C2×D3—21no—
320C2×D3—21no—
321C2×D3#23712yes—
322C3×C4—22no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—32no—
330C3×C4—41no—
331C3×C4—41no—
332C3×C4—61no—
333C3×C4—61no—
334C3×C4—61no—
335C3×C4—61no—
336C3×C4—61no—
337Dic3—21no—
338Dic3—21no—
339Dic3—21no—
340Dic3—21no—
341Dic3—21no—
342Dic3—61no—
343Dic3—61no—
344Dic3—61no—
345Dic3—61no—
346Dic3—61no—
347Dic3—61no—
348Dic3—61no—
349Dic3—61no—
350Dic3—121no—
351Dic3—121no—
352Dic3—121no—
353Dic3—121no—
354Dic3#23912yes—
355C32#55211yescharacteristic, complemented, Sylow
356C23—31no—
357C23—31no—
358Q8—182no—
359D4—62no—
360C2×C4—31no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—62no—
367C2×C4—91no—
368C2×C4—91no—
369C2×C4—91no—
370C2×C4—91no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4C2×D3211yescharacteristic
375C2×C4C2×D3211yescharacteristic
376C2×C4C2×D3211yescharacteristic
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—62no—
381C2×C3—121no—
382C2×C3C2×#23711yescharacteristic
383C2×C3C2×#23911yescharacteristic
384C2×C3D3×#4111yescharacteristic
385C2×C3D3×#4111yescharacteristic
386C2×C3#101011yescharacteristic
387C2×C3#101011yescharacteristic
388D3—22no—
389D3—41no—
390C22—32no—
391C22—61no—
392C22—61no—
393C22—61no—
394C22—61no—
395C22—61no—
396C22C22×D3211yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—32no—
401C4—61no—
402C4—61no—
403C4—61no—
404C4—61no—
405C4—61no—
406C4—181no—
407C4—181no—
408C4—181no—
409C4—181no—
410C3—21no—
411C3#565011yescharacteristic, complemented
412C3#569411yescharacteristic, complemented
413C2—62no—
414C2—121no—
415C2#6429811yescharacteristic
416C2D3×#23711yescharacteristic
417C2D3×#23911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D32
commutator, socle, cosocleC22×C32C24
FittingC32×C4⋊C4C22
prime radicalC2×C3×D12C22
hypercenterC4⋊C4D32
hypocenterC32#552
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #64099C2semidirect
3. C3×#889C2semidirect
4. #63893C2semidirect
5. #63893C2semidirect
8. #63878C2semidirect
9. #63878C2semidirect
10. D3×Dic3⋊C4C2semidirect
11. #63861C2semidirect
12. #63858C2semidirect
13. #63845C2semidirect
14. #63841C2semidirect
15. #63837C2semidirect
74. #889D3semidirect
355. C32#552semidirect
411. C3#5650semidirect
412. C3#5694semidirect

Maximal subgroups

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

subgroupindex
#640992
C3×#8942
C3×#8892
#638932
Dic3×D122
#638842
#638782
D3×Dic3⋊C42
#638612
#638582
#638452
#638412
#638372
#56943
#56503