Finite Group Databasebeta

← #11780690

Subgroups — #11780690

Order 1152.

427 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 427 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5684C211yesmaximal, characteristic
2C3×#5055C211yesmaximal, characteristic, complemented
3#10590291C211yesmaximal, characteristic, complemented
4#10590280C211yesmaximal, characteristic, complemented
5#10589406C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71954—31nomaximal
9#71246—31nomaximal
10C32×#124C2211yescharacteristic
11C3×#946—21no—
12C3×#939—21no—
13C3×#886—21no—
14C3×#884—21no—
15C3×#883—21no—
16C3×#878—21no—
17C3×#875C2211yescharacteristic
18C3×#870C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63630C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#835—21no—
23C3×#832—21no—
24C3×#803C2211yescharacteristic
25#63565—21no—
26#63565—21no—
27#63565—21no—
28#63562—21no—
29C3×#562—31no—
30#5684D311yescharacteristic
31C3×#489—31no—
32#5089—31no—
33#5082—31no—
34#5069—31no—
35#5055—31no—
36#5055D311yescharacteristic, complemented
37#4543—31no—
38#4540—31no—
39#4540—31no—
40#4540—31no—
41#4540—61no—
42#4465—31no—
43#4464—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D411yescharacteristic
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C2×C3×D12D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×#217—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×Dic3⋊C4—21no—
70C2×C3×C3⋊C8—21no—
71#1662—91noSylow
72C3×C4⋊Q8—31no—
73C3×#125—31no—
74C3×#124—21no—
75C3×#124—31no—
76C3×#124C2×D311yescharacteristic
77C3×#124C2×D311yescharacteristic
78C3×#123—61no—
79C3×#123—61no—
80C3×C22⋊Q8—61no—
81C3×C22⋊Q8—61no—
82C3×#121—61no—
83C3×#121—61no—
84#946—21no—
85#939—21no—
86#886—21no—
87#884—21no—
88#883—21no—
89#878—21no—
90#875C2×D311yescharacteristic
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#103—61no—
94C3×#102—61no—
95C3×#97—31no—
96#835—21no—
97#835—61no—
98#835—61no—
99#835—61no—
100#832—21no—
101#832—61no—
102#810—61no—
103#810—61no—
104#810—61no—
105#809—61no—
106#803—31no—
107#803—31no—
108#803—31no—
109#803—31no—
110#803—61no—
111#803—61no—
112#803C2×D311yescharacteristic
113C23×C32—21no—
114C22×C3×D3—21no—
115C32×Q8—41no—
116C32×D4—41no—
117C2×C32×C4—21no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C3×#67—81no—
122C3×#67—81no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C3×D12—41no—
129C3×C4×D3—81no—
130C3×Dic6—41no—
131C3×Dic6—42no—
132C3⋊(C3⋊C8)—41no—
133C3⋊(C3⋊C8)—41no—
134C3×C3⋊C8—41no—
135#562—31no—
136#491—91no—
137#489—31no—
138#489—91no—
139#330—91no—
140#329—91no—
141#329—91no—
142C2×C3×Q8—21no—
143C2×C3×Q8—31no—
144C2×C3×Q8—61no—
145C2×C3×Q8#6711yescharacteristic
146C2×C3×Q8#6711yescharacteristic
147C2×C3×D4—21no—
148C2×C3×D4—31no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4#6711yescharacteristic
152C2×C3×D4#6711yescharacteristic
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C2×#67—21no—
156C2×#67—21no—
157C22×Dic3—21no—
158C2×D12#6711yescharacteristic
159C2×C4×D3—21no—
160C2×Dic6—21no—
161C2×Dic6#6711yescharacteristic
162C2×C3×C8—61no—
163C3×C4⋊C4—31no—
164C3×C4⋊C4—31no—
165C3×C4⋊C4—61no—
166C3×C4⋊C4—61no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C22⋊C4—21no—
172C3×C22⋊C4—21no—
173C3×C22⋊C4—21no—
174C3×C22⋊C4—21no—
175C3×C22⋊C4—41no—
176C3×C22⋊C4—41no—
177C3×C22⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C42—21no—
182C3×C42C22×D311yescharacteristic
183C3×C42C22×D311yescharacteristic
184#217—21no—
185(C2×D3)⋊C4—21no—
186(C2×D3)⋊C4—21no—
187(C2×D3)⋊C4—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3#6711yescharacteristic
192C4⋊Dic3#6711yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C2×C3⋊C8—61no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—121no—
202C2×C3⋊C8—121no—
203C22×C32—41no—
204C22×C32—41no—
205C22×C32—41no—
206C22×C32#12011yescharacteristic
207C2×C3×D3—41no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—21no—
213C32×C4—41no—
214C3×Dic3—41no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—81no—
218C4⋊Q8—31no—
219#125—31no—
220#124—31no—
221#124D3211yescharacteristic
222#123—61no—
223#123—61no—
224C22⋊Q8—61no—
225C22⋊Q8—61no—
226#121—61no—
227#121—61no—
228#103—61no—
229#103—181no—
230#103—181no—
231#103—181no—
232#102—61no—
233#102—181no—
234#97—31no—
235#97—91no—
236#97—91no—
237C23×C3—21no—
238C23×C3—21no—
239C23×C3—41no—
240C23×C3—61no—
241C22×D3—21no—
242C3×Q8—41no—
243C3×Q8—41no—
244C3×Q8—81no—
245C3×Q8—121no—
246C3×Q8—122no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—81no—
250C3×D4—121no—
251C3×D4—241no—
252C3×D4—241no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—41no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—121no—
263C2×C3×C4—241no—
264C2×C3×C4—241no—
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×#6711yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—81no—
272#67—81no—
273C2×Dic3—21no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—41no—
277C2×Dic3—81no—
278D12—41no—
279C4×D3—81no—
280Dic6—41no—
281Dic6—42no—
282C3×C8—121no—
283C3⋊C8—41no—
284C3⋊C8—121no—
285C3⋊C8—121no—
286C3⋊C8—121no—
287C3⋊C8—121no—
288C3⋊C8—122no—
289C3⋊C8—122no—
290C2×C32—81no—
291C2×C32#45411yescharacteristic
292C2×C32#45511yescharacteristic
293C2×C32#45511yescharacteristic
294C3×D3—81no—
295C2×Q8—31no—
296C2×Q8—61no—
297C2×Q8#62511yescharacteristic
298C2×D4—31no—
299C2×D4—61no—
300C2×D4—61no—
301C2×D4#62511yescharacteristic
302C22×C4—61no—
303C22×C4—61no—
304C2×C8—61no—
305C2×C8—181no—
306C2×C8—181no—
307C4⋊C4—31no—
308C4⋊C4—31no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4—61no—
314C4⋊C4—61no—
315C22⋊C4—21no—
316C22⋊C4—21no—
317C22⋊C4—61no—
318C22⋊C4—61no—
319C22⋊C4—61no—
320C22⋊C4—61no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—41no—
328C22×C3—41no—
329C22×C3—81no—
330C22×C3—81no—
331C22×C3—81no—
332C22×C3—121no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3#93711yescharacteristic
336C22×C3#95311yescharacteristic
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—41no—
347C3×C4—41no—
348C3×C4—41no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—81no—
352C3×C4—121no—
353C3×C4—121no—
354C3×C4—121no—
355C3×C4—241no—
356Dic3—41no—
357Dic3—41no—
358Dic3—41no—
359Dic3—81no—
360C32#166211yescharacteristic, complemented, Sylow
361C23—21no—
362C23—61no—
363Q8—41no—
364Q8—121no—
365Q8—122no—
366D4—41no—
367D4—121no—
368D4—241no—
369D4—241no—
370C2×C4—21no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—121no—
375C2×C4—241no—
376C2×C4—241no—
377C2×C4C2×#62511yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C8—121no—
381C8—361no—
382C8—361no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—81no—
387C2×C3—81no—
388C2×C3—161no—
389C2×C3—241no—
390C2×C3#506111yescharacteristic
391C2×C3#520111yescharacteristic
392C2×C3#520211yescharacteristic
393C2×C3#524211yescharacteristic
394C2×C3#524211yescharacteristic
395C2×C3#524511yescharacteristic
396D3—81no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—121no—
401C22—121no—
402C22—121no—
403C22#6397611yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—121no—
409C4—121no—
410C4—121no—
411C4—241no—
412C3—21no—
413C3#7124611yescharacteristic, complemented
414C3#7195411yescharacteristic, complemented
415C2—81no—
416C2—241no—
417C2#1059151211yescharacteristic
418C2#1059166411yescharacteristic
419C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radicalC3×#5684C2
hypercenter#124D32
hypocenterC32#1662
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C3×#5055C2semidirect
3. #10590291C2semidirect
4. #10590280C2semidirect
5. #10589406C2semidirect
6. #10589088C2semidirect
7. #10589086C2semidirect
36. #5055D3semidirect
360. C32#1662semidirect
413. C3#71246semidirect
414. C3#71954semidirect

Maximal subgroups

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

subgroupindex
C3×#56842
C3×#50552
#105902912
#105902802
#105894062
#105890882
#105890862
#719543
#712463