Finite Group Databasebeta

← #11775432

Subgroups — #11775432

Order 1152.

659 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4#10589151C214yesmaximal, complemented
5#70835—31nomaximal
6#69564—31nomaximal
7C2×#3828—21no—
8C2×C32×C42C2211yescharacteristic
9#64139—21no—
10#64139C2212yes—
11#64084—21no—
12#64083C411yescharacteristic, complemented
13C4×C4⋊(C3⋊D3)—21no—
14C4×C4⋊(C3⋊D3)C412yescomplemented
15#64078C411yescharacteristic, complemented
16C3×C3⋊#95—21no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2212yes—
19C3×#830C2212yes—
20C3×C4⋊(C3⋊C8)—21no—
21C3×#803—21no—
22#5477—31no—
23#5477—31no—
24#5477—61no—
25C3×#432—31no—
26C3×#383—31no—
27#4937D311yescharacteristic, complemented
28#4926D311yescharacteristic, complemented
29#4470—34no—
30#4451—34no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35#3828—44no—
36C2×C4⋊(C3⋊D3)—21no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4⋊(C3⋊D3)C2×C412yes—
39C2×C4×C3⋊D3—22no—
40C2×#634—21no—
41C22×C3×Dic3—22no—
42C32×C42C2×C411yescharacteristic
43C32×C42C2×C411yescharacteristic
44C32×C42D411yescharacteristic
45C32×C42D411yescharacteristic
46#3752—22no—
47#3752—22no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)C2×C412yes—
50C2×C3×C3⋊C8—22no—
51#1514—91noSylow
52C2×#235—62no—
53C2×#235—61no—
54C2×#235—61no—
55C2×C3×C42—21no—
56C2×C3×C42C2×D311yescharacteristic
57C2×C3×C42C2×D311yescharacteristic
58#930—32no—
59#930—32no—
60#930—62no—
61#930—62no—
62#930—61no—
63#930—61no—
64#875—62no—
65#875—61no—
66#875—61no—
67#874—31no—
68#874—31no—
69#874—61no—
70C4×D12—32no—
71C4×D12—32no—
72C4×D12—62no—
73C4×D12—62no—
74C4×D12—61no—
75C4×D12—61no—
76#869—31no—
77#869—31no—
78#869—61no—
79C3×C4⋊C8—61no—
80C3×C22⋊C8—32no—
81C3×#97—61no—
82C3×#95—32no—
83C3×#95—61no—
84C3×#95—61no—
85C3⋊#95—21no—
86C3⋊#95—21no—
87C3⋊#95C2×D312yes—
88#830C2×D312yes—
89C4⋊(C3⋊C8)—21no—
90#803—21no—
91C23×C32C2×D411yescharacteristic
92C22×C3⋊D3—22no—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102#638—44no—
103C2×C3⋊Dic3—22no—
104C4⋊(C3⋊D3)—42no—
105C4⋊(C3⋊D3)—42no—
106C4⋊(C3⋊D3)—42no—
107C4×C3⋊D3—44no—
108#634—42no—
109C2×C3×Dic3—42no—
110C2×C3×Dic3—42no—
111C2×C3×Dic3—42no—
112C3×C3⋊C8—42no—
113#532—91no—
114#432—31no—
115#383—31no—
116#327—94no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4D1211yescharacteristic
122C22×C3×C4D1211yescharacteristic
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4C22×D311yescharacteristic
126C22×C3×C4C22×D311yescharacteristic
127C2×#67—64no—
128C2×#67—62no—
129C2×#67—62no—
130C22×Dic3—22no—
131#235—128no—
132#235—124no—
133#235—124no—
134C2×D12—32no—
135C2×D12—32no—
136C2×D12—62no—
137C2×D12—62no—
138C2×D12—62no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×C4×D3—64no—
144C2×C4×D3—62no—
145C2×C4×D3—62no—
146C2×Dic6—62no—
147C2×Dic6—61no—
148C2×Dic6—61no—
149C2×C3×C8—62no—
150C3×C42—21no—
151C3×C42—21no—
152C3×C42—21no—
153C3×C42—21no—
154C3×C42C4×D311yescharacteristic
155C3×C42C4×D311yescharacteristic
156C3×C42C4×D311yescharacteristic
157C3×C42C4×D311yescharacteristic
158C3×C42D1211yescharacteristic
159C3×C42D1211yescharacteristic
160C3×C42#6711yescharacteristic
161C3×C42#6711yescharacteristic
162(C2×D3)⋊C4—64no—
163(C2×D3)⋊C4—64no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168C4⋊Dic3—32no—
169C4⋊Dic3—32no—
170C4⋊Dic3—62no—
171C4⋊Dic3—62no—
172C4⋊Dic3—61no—
173C4⋊Dic3—61no—
174C2×C3⋊C8—22no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32C2×C22⋊C411yescharacteristic
178C22×C32AGL(1,ℤ/8)12yes—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C32×C4—21no—
183C32×C4—21no—
184C32×C4—21no—
185C32×C4—21no—
186C32×C4—21no—
187C32×C4—21no—
188C3⋊Dic3—42no—
189C3×Dic3—82no—
190C2×#41—181no—
191C4⋊Q8—91no—
192#127—91no—
193#124—181no—
194#121—92no—
195#121—181no—
196C4×D4—92no—
197C4×D4—181no—
198C2×C42D3211yescharacteristic
199C4⋊C8—61no—
200C22⋊C8—32no—
201#97—61no—
202#95—32no—
203#95—61no—
204#95—61no—
205C23×C3—21no—
206C23×C3C2×D1211yescharacteristic
207C23×C3C2×#6711yescharacteristic
208C22×D3—64no—
209C22×D3—62no—
210C22×D3—62no—
211C2×C3×C4—24no—
212C2×C3×C4—22no—
213C2×C3×C4—22no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—42no—
225C2×C3×C4—42no—
226C2×C3×C4—122no—
227C2×C3×C4—122no—
228C2×C3×C4—122no—
229C2×C3×C4(C2×D3)⋊C411yescharacteristic
230C2×C3×C4(C2×D3)⋊C411yescharacteristic
231C2×C3×C4(C2×D3)⋊C411yescharacteristic
232C2×C3×C4(C2×D3)⋊C411yescharacteristic
233C2×C3×C4(C2×D3)⋊C411yescharacteristic
234C2×C3×C4(C2×D3)⋊C411yescharacteristic
235C2×C3×C4(C2×D3)⋊C411yescharacteristic
236C2×C3×C4(C2×D3)⋊C411yescharacteristic
237C2×C3×C4C2×C4×D311yescharacteristic
238C2×C3×C4C2×C4×D311yescharacteristic
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241#67—128no—
242#67—124no—
243#67—124no—
244C2×Dic3—42no—
245C2×Dic3—42no—
246C2×Dic3—42no—
247C2×Dic3—64no—
248C2×Dic3—62no—
249C2×Dic3—62no—
250D12—122no—
251D12—122no—
252D12—124no—
253D12—124no—
254D12—122no—
255D12—122no—
256D12—124no—
257D12—122no—
258D12—122no—
259C4×D3—128no—
260C4×D3—124no—
261C4×D3—124no—
262Dic6—124no—
263Dic6—122no—
264Dic6—122no—
265C3×C8—122no—
266C3⋊C8—42no—
267C2×C32—22no—
268C2×C32#41011yescharacteristic
269C2×C32#41811yescharacteristic
270C2×C32#42111yescharacteristic
271C3⋊D3—82no—
272#41—364no—
273C2×Q8—181no—
274C2×D4—92no—
275C2×D4—182no—
276C2×D4—181no—
277C2×D4—181no—
278C22×C4—62no—
279C22×C4—182no—
280C22×C4#62611yescharacteristic
281C22×C4#62611yescharacteristic
282C22×C4C2×D3211yescharacteristic
283C2×C8—62no—
284C4⋊C4—92no—
285C4⋊C4—181no—
286C22⋊C4—182no—
287C22⋊C4—182no—
288C42#62411yescharacteristic
289C42#62411yescharacteristic
290C42#62611yescharacteristic
291C42#62611yescharacteristic
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—22no—
297C22×C3—21no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3#90812yes—
301C22×C3C2×(C2×D3)⋊C411yescharacteristic
302C22×C3C2×(C2×D3)⋊C411yescharacteristic
303C22×C3#94912yes—
304C2×D3—124no—
305C2×D3—124no—
306C2×D3—124no—
307C2×D3—122no—
308C2×D3—122no—
309C2×D3—122no—
310C2×D3—122no—
311C2×D3—122no—
312C2×D3—122no—
313C3×C4—22no—
314C3×C4—22no—
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—242no—
332Dic3—82no—
333Dic3—124no—
334Dic3—122no—
335Dic3—122no—
336C32#151411yescharacteristic, complemented, Sylow
337C23—182no—
338C23C2×#62611yescharacteristic
339Q8—362no—
340D4—362no—
341D4—362no—
342D4—362no—
343D4—364no—
344C2×C4—22no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—122no—
348C2×C4—122no—
349C2×C4—122no—
350C2×C4—182no—
351C2×C4—364no—
352C2×C4#372211yescharacteristic
353C2×C4#372211yescharacteristic
354C2×C4#372211yescharacteristic
355C2×C4#372211yescharacteristic
356C2×C4C2×#62411yescharacteristic
357C2×C4C2×#62611yescharacteristic
358C8—122no—
359C2×C3—22no—
360C2×C3—22no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—42no—
365C2×C3#500111yescharacteristic
366C2×C3#500511yescharacteristic
367C2×C3#500611yescharacteristic
368C2×C3#500611yescharacteristic
369C2×C3#513111yescharacteristic
370C2×C3#513911yescharacteristic
371D3—244no—
372D3—242no—
373D3—242no—
374C22—21no—
375C22—21no—
376C22—362no—
377C22—362no—
378C22—362no—
379C22#6382512yes—
380C22C2×#372211yescharacteristic
381C4—21no—
382C4—21no—
383C4—21no—
384C4—21no—
385C4—21no—
386C4—21no—
387C4—242no—
388C4—362no—
389C3—21no—
390C3#6956411yescharacteristic, complemented
391C3#7083511yescharacteristic, complemented
392C2—22no—
393C2—722no—
394C2#1059109611yescharacteristic
395C2#1059111311yescharacteristic
396C2#1059123211yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595948C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1514
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4937C2semidirect
3. C3×#4926C2semidirect
4. #10589151C2semidirect
12. #64083C4semidirect
14. C4×C4⋊(C3⋊D3)C4semidirect
15. #64078C4semidirect
27. #4937D3semidirect
28. #4926D3semidirect
336. C32#1514semidirect
390. C3#69564semidirect
391. C3#70835semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#49372
C3×#49262
#105891512
#708353
#695643