Finite Group Databasebeta

← #11776140

Subgroups — #11776140

Order 1152.

667 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#10595948C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10589094C212yesmaximal, complemented
5#10589091C212yesmaximal, complemented
6#70772—31nomaximal
7#70431—31nomaximal
8C2×#3828—21no—
9C2×C32×C42C2211yescharacteristic
10#64139—21no—
11#64139C412yes—
12#64084—21no—
13#64083C2211yescharacteristic
14C4×C4⋊(C3⋊D3)—21no—
15C4×C4⋊(C3⋊D3)C412yes—
16#64078C2211yescharacteristic
17C22×C3×C3⋊C8—21no—
18C3×#830—21no—
19C3×C4⋊(C3⋊C8)—21no—
20C3×C4⋊(C3⋊C8)C2212yes—
21C3×C4⋊(C3⋊C8)C2212yes—
22C3×C4×C3⋊C8—21no—
23#5477—31no—
24#5477—31no—
25#5477—61no—
26C3×#431—31no—
27C2×C3×C4⋊C8—31no—
28#4925D311yescharacteristic, complemented
29C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
30#4486—32no—
31#4485—32no—
32#4485—32no—
33#4482—32no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C2×#638—22no—
38#3828—42no—
39#3828—42no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)C2×C412yes—
43C2×C4×C3⋊D3—22no—
44C2×#634—21no—
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42C2311yescharacteristic
49#3752—22no—
50#3752—22no—
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)C2×C412yes—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—22no—
55C2×C3×C3⋊C8—42no—
56#1540—91noSylow
57C2×#235—62no—
58C2×#235—61no—
59C2×#235—61no—
60C22×C3×C8—61no—
61C2×C3×C42—21no—
62C2×C3×C42C2×D311yescharacteristic
63C2×C3×C42C2×D311yescharacteristic
64#930—32no—
65#930—32no—
66#930—62no—
67#930—62no—
68#930—61no—
69#930—61no—
70C22×C3⋊C8—21no—
71#875—62no—
72#875—61no—
73#875—61no—
74#874—31no—
75#874—31no—
76#874—61no—
77C4×D12—32no—
78C4×D12—32no—
79C4×D12—62no—
80C4×D12—62no—
81C4×D12—61no—
82C4×D12—61no—
83#869—31no—
84#869—31no—
85#869—61no—
86C3×C4⋊C8—32no—
87C3×C4⋊C8—32no—
88C3×C4⋊C8—61no—
89C3×C22⋊C8—61no—
90C3×C4×C8—61no—
91#830—21no—
92C4⋊(C3⋊C8)—21no—
93C4⋊(C3⋊C8)C2×D312yes—
94C4⋊(C3⋊C8)C2×D312yes—
95C4×C3⋊C8—21no—
96C23×C32C22⋊C411yescharacteristic
97C22×C3⋊D3—22no—
98C2×C32×C4—22no—
99C2×C32×C4—41no—
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22⋊C411yescharacteristic
103C2×C32×C4D812yes—
104C2×C32×C4SD1612yes—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108#638—44no—
109C2×C3⋊Dic3—22no—
110C4⋊(C3⋊D3)—42no—
111C4⋊(C3⋊D3)—41no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—42no—
114C4×C3⋊D3—44no—
115#634—41no—
116#634—41no—
117C3×C3⋊C8—42no—
118C3×C3⋊C8—42no—
119#532—91no—
120#431—31no—
121C2×C4⋊C8—31no—
122#332—92no—
123#331—92no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4C4×D311yescharacteristic
128C22×C3×C4C4×D311yescharacteristic
129C22×C3×C4D1211yescharacteristic
130C22×C3×C4D1211yescharacteristic
131C22×C3×C4#6711yescharacteristic
132C22×C3×C4#6711yescharacteristic
133C2×#67—64no—
134C2×#67—62no—
135C2×#67—62no—
136#235—124no—
137#235—124no—
138#235—122no—
139#235—122no—
140#235—122no—
141#235—122no—
142C2×D12—32no—
143C2×D12—32no—
144C2×D12—62no—
145C2×D12—62no—
146C2×D12—62no—
147C2×D12—61no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×C4×D3—64no—
152C2×C4×D3—62no—
153C2×C4×D3—62no—
154C2×Dic6—62no—
155C2×Dic6—61no—
156C2×Dic6—61no—
157C2×C3×C8—62no—
158C2×C3×C8—62no—
159C2×C3×C8—122no—
160C3×C42—21no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42C4×D311yescharacteristic
165C3×C42C4×D311yescharacteristic
166C3×C42D1211yescharacteristic
167C3×C42D1211yescharacteristic
168C3×C42#6711yescharacteristic
169C3×C42#6711yescharacteristic
170C3×C42C22×D311yescharacteristic
171C3×C42C22×D311yescharacteristic
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—64no—
174(C2×D3)⋊C4—62no—
175(C2×D3)⋊C4—62no—
176(C2×D3)⋊C4—62no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—32no—
179C4⋊Dic3—32no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C2×C3⋊C8—22no—
185C2×C3⋊C8—22no—
186C2×C3⋊C8—42no—
187C22×C32—21no—
188C22×C32—21no—
189C22×C32#10212yes—
190C22×C32C2×C22⋊C411yescharacteristic
191C2×C3⋊D3—42no—
192C2×C3⋊D3—42no—
193C2×C3⋊D3—42no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4—21no—
197C32×C4#10212yes—
198C32×C4C2×D811yescharacteristic
199C32×C4C2×SD1611yescharacteristic
200C32×C4#13512yes—
201C3⋊Dic3—42no—
202C2×#41—181no—
203C22×C8—61no—
204C4⋊Q8—91no—
205#127—91no—
206#124—181no—
207#121—92no—
208#121—181no—
209C4×D4—92no—
210C4×D4—181no—
211C2×C42D3211yescharacteristic
212C4⋊C8—32no—
213C4⋊C8—32no—
214C4⋊C8—61no—
215C22⋊C8—61no—
216C4×C8—61no—
217C23×C3—21no—
218C23×C3(C2×D3)⋊C411yescharacteristic
219C23×C3(C2×D3)⋊C411yescharacteristic
220C22×D3—64no—
221C22×D3—62no—
222C22×D3—62no—
223C2×C3×C4—22no—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—22no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—42no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—42no—
237C2×C3×C4#20412yes—
238C2×C3×C4D2412yes—
239C2×C3×C4(C2×D3)⋊C411yescharacteristic
240C2×C3×C4(C2×D3)⋊C411yescharacteristic
241C2×C3×C4(C2×D3)⋊C411yescharacteristic
242C2×C3×C4(C2×D3)⋊C411yescharacteristic
243C2×C3×C4(C2×D3)⋊C411yescharacteristic
244C2×C3×C4(C2×D3)⋊C411yescharacteristic
245C2×C3×C4#21312yes—
246C2×C3×C4#21512yes—
247C2×C3×C4C2×C4×D311yescharacteristic
248C2×C3×C4C2×C4×D311yescharacteristic
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4C2×#6711yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253#67—128no—
254#67—124no—
255#67—124no—
256C2×Dic3—64no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259D12—122no—
260D12—122no—
261D12—124no—
262D12—124no—
263D12—122no—
264D12—122no—
265D12—121no—
266D12—121no—
267D12—122no—
268D12—121no—
269D12—121no—
270D12—122no—
271C4×D3—128no—
272C4×D3—124no—
273C4×D3—124no—
274Dic6—122no—
275Dic6—122no—
276Dic6—121no—
277Dic6—121no—
278Dic6—121no—
279Dic6—121no—
280C3×C8—122no—
281C3×C8—122no—
282C3⋊C8—42no—
283C3⋊C8—42no—
284C2×C32—22no—
285C2×C32#41311yescharacteristic
286C2×C32C2×#10211yescharacteristic
287C2×C32#41611yescharacteristic
288C3⋊D3—82no—
289#41—362no—
290#41—362no—
291C2×Q8—181no—
292C2×D4—92no—
293C2×D4—182no—
294C2×D4—181no—
295C2×D4—181no—
296C22×C4—182no—
297C22×C4#62411yescharacteristic
298C22×C4#62611yescharacteristic
299C22×C4#62611yescharacteristic
300C2×C8—62no—
301C2×C8—62no—
302C2×C8—122no—
303C4⋊C4—92no—
304C4⋊C4—181no—
305C22⋊C4—182no—
306C22⋊C4—182no—
307C42#62411yescharacteristic
308C42#62611yescharacteristic
309C42#62611yescharacteristic
310C42C2×D3211yescharacteristic
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3#80912yes—
320C22×C3#82112yes—
321C22×C3C2×(C2×D3)⋊C411yescharacteristic
322C22×C3C2×(C2×D3)⋊C411yescharacteristic
323C2×D3—124no—
324C2×D3—124no—
325C2×D3—124no—
326C2×D3—122no—
327C2×D3—122no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—122no—
331C2×D3—122no—
332C3×C4—22no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—22no—
342C3×C4—21no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4#80912yes—
346C3×C4#82112yes—
347C3×C4C2×#20411yescharacteristic
348C3×C4C2×D2411yescharacteristic
349C3×C4#90412yes—
350C3×C4C2×#21311yescharacteristic
351C3×C4C2×#21511yescharacteristic
352C3×C4#95012yes—
353Dic3—124no—
354Dic3—122no—
355Dic3—122no—
356C32#154011yescharacteristic, complemented, Sylow
357C23—182no—
358C23#372211yescharacteristic
359Q8—361no—
360Q8—361no—
361D4—362no—
362D4—364no—
363D4—361no—
364D4—362no—
365D4—361no—
366C2×C4—22no—
367C2×C4—41no—
368C2×C4—182no—
369C2×C4—364no—
370C2×C4#371412yes—
371C2×C4#371712yes—
372C2×C4#372211yescharacteristic
373C2×C4#372211yescharacteristic
374C2×C4#372211yescharacteristic
375C2×C4C2×#62411yescharacteristic
376C2×C4C2×#62611yescharacteristic
377C2×C4C2×#62611yescharacteristic
378C8—122no—
379C8—122no—
380C2×C3—22no—
381C2×C3—22no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—42no—
386C2×C3C2×#80911yescharacteristic
387C2×C3#500211yescharacteristic
388C2×C3C2×#82111yescharacteristic
389C2×C3#511311yescharacteristic
390C2×C3#513211yescharacteristic
391C2×C3#513211yescharacteristic
392D3—244no—
393D3—242no—
394D3—242no—
395C22—21no—
396C22—21no—
397C22—362no—
398C22—362no—
399C22—362no—
400C22#6356412yes—
401C22C2×#372211yescharacteristic
402C4—21no—
403C4—21no—
404C4—21no—
405C4—362no—
406C4#6356412yes—
407C4C2×#371411yescharacteristic
408C4#6382912yes—
409C4C2×#371711yescharacteristic
410C3—21no—
411C3#7043111yescharacteristic, complemented
412C3#7077211yescharacteristic, complemented
413C2—22no—
414C2—722no—
415C2#1059107811yescharacteristic
416C2C2×#6356411yescharacteristic
417C2#1059110511yescharacteristic
subgroupG/H
centerC2×C4#3722
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595948C2
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1540
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4925C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. #10589094C2semidirect
5. #10589091C2semidirect
28. #4925D3semidirect
29. C2×C4⋊(C3⋊C8)D3semidirect
356. C32#1540semidirect
411. C3#70431semidirect
412. C3#70772semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#49252
C2×C3×C4⋊(C3⋊C8)2
#105890942
#105890912
#707723
#704313