Finite Group Databasebeta

← #11775156

Subgroups — #11775156

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C3×#4932C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4#10589151C214yesmaximal, complemented
5#70832—31nomaximal
6#69432—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
16C2×C3×C4×Dic3—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×#376—31no—
27#4932D311yescharacteristic, 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—
50C3×C4×Dic3—24no—
51C2×C3×C3⋊C8—22no—
52#1505—91noSylow
53C2×#235—62no—
54C2×#235—61no—
55C2×#235—61no—
56C2×C3×C42—21no—
57C2×C3×C42—61no—
58C2×C3×C42C2×D311yescharacteristic
59C2×C3×C42C2×D311yescharacteristic
60#930—32no—
61#930—32no—
62#930—62no—
63#930—62no—
64#930—61no—
65#930—61no—
66C2×C4×Dic3—21no—
67#875—62no—
68#875—61no—
69#875—61no—
70#874—31no—
71#874—31no—
72#874—61no—
73C4×D12—32no—
74C4×D12—32no—
75C4×D12—62no—
76C4×D12—62no—
77C4×D12—61no—
78C4×D12—61no—
79#869—31no—
80#869—31no—
81#869—61no—
82C3×C4⋊C8—61no—
83C3×C22⋊C8—32no—
84C3×#97—61no—
85C3×#95—32no—
86C3×#95—61no—
87C3⋊#95—21no—
88C3⋊#95C2×D312yes—
89#830C2×D312yes—
90C4⋊(C3⋊C8)—21no—
91#803—21no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—41no—
97C2×C32×C4C22⋊C411yescharacteristic
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103#638—44no—
104C2×C3⋊Dic3—22no—
105C4⋊(C3⋊D3)—42no—
106C4⋊(C3⋊D3)—42no—
107C4⋊(C3⋊D3)—42no—
108C4×C3⋊D3—44no—
109#634—42no—
110C2×C3×Dic3—24no—
111C2×C3×Dic3—42no—
112C2×C3×Dic3—42no—
113C3×C3⋊C8—42no—
114#532—91no—
115#432—31no—
116#376—31no—
117#327—94no—
118C22×C3×C4—21no—
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—62no—
122C22×C3×C4D1211yescharacteristic
123C22×C3×C4D1211yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4#6711yescharacteristic
126C22×C3×C4C22×D311yescharacteristic
127C22×C3×C4C22×D311yescharacteristic
128C2×#67—64no—
129C2×#67—62no—
130C2×#67—62no—
131C22×Dic3—22no—
132#235—128no—
133#235—124no—
134#235—124no—
135C2×D12—32no—
136C2×D12—32no—
137C2×D12—62no—
138C2×D12—62no—
139C2×D12—62no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×C4×D3—64no—
145C2×C4×D3—62no—
146C2×C4×D3—62no—
147C2×Dic6—62no—
148C2×Dic6—61no—
149C2×Dic6—61no—
150C2×C3×C8—62no—
151C3×C42—21no—
152C3×C42—21no—
153C3×C42—21no—
154C3×C42—21no—
155C3×C42—64no—
156C3×C42C4×D311yescharacteristic
157C3×C42C4×D311yescharacteristic
158C3×C42C4×D311yescharacteristic
159C3×C42C4×D311yescharacteristic
160C3×C42D1211yescharacteristic
161C3×C42D1211yescharacteristic
162C3×C42#6711yescharacteristic
163C3×C42#6711yescharacteristic
164(C2×D3)⋊C4—64no—
165(C2×D3)⋊C4—64no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169(C2×D3)⋊C4—62no—
170C4⋊Dic3—32no—
171C4⋊Dic3—32no—
172C4⋊Dic3—62no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4×Dic3—24no—
177C2×C3⋊C8—22no—
178C22×C32—21no—
179C22×C32—21no—
180C22×C32C2×C22⋊C411yescharacteristic
181C22×C32AGL(1,ℤ/8)12yes—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C32×C4—21no—
186C32×C4—21no—
187C32×C4—21no—
188C32×C4—21no—
189C32×C4—21no—
190C32×C4#10412yes—
191C3⋊Dic3—42no—
192C3×Dic3—44no—
193C2×#41—181no—
194C4⋊Q8—91no—
195#127—91no—
196#124—181no—
197#121—92no—
198#121—181no—
199C4×D4—92no—
200C4×D4—181no—
201C2×C42—61no—
202C2×C42D3211yescharacteristic
203C4⋊C8—61no—
204C22⋊C8—32no—
205#97—61no—
206#95—32no—
207#95—61no—
208C23×C3—21no—
209C23×C3C2×D1211yescharacteristic
210C23×C3C2×#6711yescharacteristic
211C22×D3—64no—
212C22×D3—62no—
213C22×D3—62no—
214C2×C3×C4—24no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—22no—
218C2×C3×C4—22no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—42no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—42no—
229C2×C3×C4—64no—
230C2×C3×C4—122no—
231C2×C3×C4—122no—
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×C4(C2×D3)⋊C411yescharacteristic
238C2×C3×C4(C2×D3)⋊C411yescharacteristic
239C2×C3×C4(C2×D3)⋊C411yescharacteristic
240C2×C3×C4C2×C4×D311yescharacteristic
241C2×C3×C4C2×C4×D311yescharacteristic
242C2×C3×C4C2×D1211yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244#67—128no—
245#67—124no—
246#67—124no—
247C2×Dic3—24no—
248C2×Dic3—42no—
249C2×Dic3—42no—
250C2×Dic3—64no—
251C2×Dic3—62no—
252C2×Dic3—62no—
253D12—122no—
254D12—122no—
255D12—124no—
256D12—124no—
257D12—124no—
258D12—122no—
259D12—122no—
260D12—122no—
261D12—122no—
262C4×D3—128no—
263C4×D3—124no—
264C4×D3—124no—
265Dic6—124no—
266Dic6—122no—
267Dic6—122no—
268C3×C8—122no—
269C3⋊C8—42no—
270C2×C32—22no—
271C2×C32#41011yescharacteristic
272C2×C32#41811yescharacteristic
273C2×C32C2×#10411yescharacteristic
274C3⋊D3—82no—
275#41—364no—
276C2×Q8—181no—
277C2×D4—92no—
278C2×D4—182no—
279C2×D4—181no—
280C2×D4—181no—
281C22×C4—62no—
282C22×C4—182no—
283C22×C4#62611yescharacteristic
284C22×C4#62611yescharacteristic
285C22×C4C2×D3211yescharacteristic
286C2×C8—62no—
287C4⋊C4—92no—
288C4⋊C4—181no—
289C22⋊C4—182no—
290C22⋊C4—182no—
291C42—64no—
292C42#62411yescharacteristic
293C42#62411yescharacteristic
294C42#62611yescharacteristic
295C42#62611yescharacteristic
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—22no—
301C22×C3—21no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3#90812yes—
305C22×C3C2×(C2×D3)⋊C411yescharacteristic
306C22×C3C2×(C2×D3)⋊C411yescharacteristic
307C22×C3#94912yes—
308C2×D3—124no—
309C2×D3—124no—
310C2×D3—124no—
311C2×D3—122no—
312C2×D3—122no—
313C2×D3—122no—
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—122no—
317C3×C4—22no—
318C3×C4—22no—
319C3×C4—22no—
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—21no—
330C3×C4—22no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—124no—
334C3×C4#80512yes—
335C3×C4#82512yes—
336Dic3—44no—
337Dic3—124no—
338Dic3—122no—
339Dic3—122no—
340C32#150511yescharacteristic, complemented, Sylow
341C23—182no—
342C23C2×#62611yescharacteristic
343Q8—362no—
344D4—362no—
345D4—362no—
346D4—364no—
347D4—362no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—64no—
352C2×C4—122no—
353C2×C4—122no—
354C2×C4—182no—
355C2×C4—364no—
356C2×C4#372211yescharacteristic
357C2×C4#372211yescharacteristic
358C2×C4#372211yescharacteristic
359C2×C4#372211yescharacteristic
360C2×C4C2×#62411yescharacteristic
361C2×C4C2×#62611yescharacteristic
362C8—122no—
363C2×C3—22no—
364C2×C3—22no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—42no—
369C2×C3C2×#80511yescharacteristic
370C2×C3#500111yescharacteristic
371C2×C3#500611yescharacteristic
372C2×C3#500611yescharacteristic
373C2×C3#513111yescharacteristic
374C2×C3C2×#82511yescharacteristic
375D3—244no—
376D3—242no—
377D3—242no—
378C22—21no—
379C22—21no—
380C22—362no—
381C22—362no—
382C22—362no—
383C22#6382512yes—
384C22C2×#372211yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—124no—
391C4—362no—
392C4#6357012yes—
393C3—21no—
394C3#6943211yescharacteristic, complemented
395C3#7083211yescharacteristic, complemented
396C2—22no—
397C2—722no—
398C2#1059109611yescharacteristic
399C2C2×#6357011yescharacteristic
400C2#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#1505
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×#4932C2semidirect
3. C3×#4926C2semidirect
4. #10589151C2semidirect
12. #64083C4semidirect
14. C4×C4⋊(C3⋊D3)C4semidirect
15. #64078C4semidirect
27. #4932D3semidirect
28. #4926D3semidirect
340. C32#1505semidirect
394. C3#69432semidirect
395. C3#70832semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#49322
C3×#49262
#105891512
#708323
#694323