Finite Group Databasebeta

← #11780693

Subgroups — #11780693

Order 1152.

422 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#10593985C211yesmaximal, characteristic
2C3×#4714C211yesmaximal, characteristic, complemented
3#10590289C211yesmaximal, characteristic, complemented
4#10590280C211yesmaximal, characteristic, complemented
5#10589331C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71246—31nomaximal
9#68358—31nomaximal
10#64079C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×#875C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63891—21no—
15#63891—21no—
16#63887—21no—
17#63887—21no—
18#63885—21no—
19#63885—21no—
20C32×#97C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#821—21no—
23C3×#816—21no—
24C3×#803C2211yescharacteristic
25#63566—21no—
26#63566—21no—
27#63565—21no—
28#63562—21no—
29#5684—31no—
30#5684—31no—
31C3×#489—31no—
32#5089—31no—
33#5082—31no—
34#5055—31no—
35#4714D311yescharacteristic, complemented
36#4703—31no—
37C3×#329—31no—
38#4540—31no—
39#4465—31no—
40#4465—31no—
41#4465—61no—
42#4464—31no—
43#4464D311yescharacteristic, complemented
44C2×C3×D12D411yescharacteristic
45C2×C3×D12D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×C3×Dic6D411yescharacteristic
49C2×#625—21no—
50C2×#625—21no—
51C2×D3×Dic3—21no—
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C4⋊(C3⋊Dic3)D411yescharacteristic
57#3750—21no—
58#3750—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C2×C3×C3⋊C8—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71#1662—91noSylow
72C3×C4⋊Q8—31no—
73C3×#124—31no—
74C3×#124—31no—
75#946—61no—
76#946—61no—
77#939—61no—
78#939—61no—
79#886—61no—
80#886—61no—
81#884—61no—
82#884—61no—
83#883—61no—
84#883—61no—
85#878—61no—
86#878—61no—
87#875C2×D311yescharacteristic
88#875C2×D311yescharacteristic
89#870—31no—
90#870—31no—
91#870—61no—
92#869C2×D311yescharacteristic
93C3×#103—61no—
94C3×#102—61no—
95C3×#97—21no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#835—61no—
100#835—61no—
101#835—61no—
102#832—61no—
103#821—21no—
104#816—21no—
105#816—61no—
106#816—61no—
107#810—61no—
108#809—61no—
109#803—31no—
110#803—31no—
111#803—61no—
112#803C2×D311yescharacteristic
113C22×C3×D3—21no—
114C22×C3×D3—21no—
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—41no—
123C3×D12—41no—
124C3×D12—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×Dic6—42no—
128#625—81no—
129#625—81no—
130D3×Dic3—81no—
131D3×Dic3—81no—
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C3×C3⋊C8—41no—
135#562—91no—
136#491—91no—
137#489—31no—
138#489—91no—
139#330—91no—
140#329—31no—
141#329—91no—
142C2×C3×Q8—31no—
143C2×C3×Q8—31no—
144C2×C3×Q8—61no—
145C2×C3×D4—31no—
146C2×C3×D4—31no—
147C2×#67—61no—
148C2×#67—61no—
149C2×#67—61no—
150C2×#67—61no—
151C22×Dic3—61no—
152C22×Dic3—61no—
153C2×D12D1211yescharacteristic
154C2×D12#6711yescharacteristic
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×Dic6—21no—
158C2×Dic6D1211yescharacteristic
159C2×Dic6#6711yescharacteristic
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—41no—
163C2×C3×C8—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4—61no—
166C3×C22⋊C4—61no—
167C3×C22⋊C4—61no—
168C3×C22⋊C4—61no—
169C3×C22⋊C4—61no—
170C3×C42—21no—
171C3×C42C22×D311yescharacteristic
172C3×C42C22×D311yescharacteristic
173#217—61no—
174#217—61no—
175(C2×D3)⋊C4—21no—
176(C2×D3)⋊C4—21no—
177(C2×D3)⋊C4—21no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—31no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—121no—
198Dic3⋊C4—121no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—61no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—121no—
203C22×C32#12011yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C2×C3×D3—41no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C32×C4—21no—
211C32×C4—21no—
212C32×C4—21no—
213C3⋊Dic3—41no—
214C3⋊Dic3—41no—
215C3×Dic3—41no—
216C3×Dic3—41no—
217C3×Dic3—81no—
218C4⋊Q8—31no—
219#125—91no—
220#124—31no—
221#124—31no—
222#123—181no—
223#123—181no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226#121—181no—
227#121—181no—
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#97D3211yescharacteristic
237C23×C3—61no—
238C23×C3—61no—
239C22×D3—21no—
240C22×D3—21no—
241C3×Q8—121no—
242C3×Q8—121no—
243C3×Q8—122no—
244C3×D4—121no—
245C3×D4—121no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—121no—
252C2×C3×C4C2×D1211yescharacteristic
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258#67—241no—
259#67—241no—
260#67—241no—
261#67—241no—
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—41no—
265C2×Dic3—61no—
266C2×Dic3—61no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—121no—
270C2×Dic3—121no—
271C2×Dic3—241no—
272C2×Dic3—241no—
273D12—41no—
274D12—41no—
275C4×D3—241no—
276C4×D3—241no—
277Dic6—41no—
278Dic6—41no—
279Dic6—42no—
280C3×C8—41no—
281C3×C8—41no—
282C3×C8—42no—
283C3×C8—121no—
284C3⋊C8—41no—
285C3⋊C8—121no—
286C3⋊C8—121no—
287C3⋊C8—122no—
288C2×C32#45411yescharacteristic
289C2×C32#45511yescharacteristic
290C2×C32#45511yescharacteristic
291C3×D3—81no—
292C3×D3—81no—
293C2×Q8—31no—
294C2×Q8—31no—
295C2×Q8—61no—
296C2×D4—31no—
297C2×D4—31no—
298C2×D4—181no—
299C2×D4—181no—
300C22×C4—181no—
301C22×C4—181no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—181no—
305C4⋊C4—61no—
306C4⋊C4—61no—
307C4⋊C4—91no—
308C4⋊C4—91no—
309C4⋊C4—181no—
310C4⋊C4—181no—
311C4⋊C4—181no—
312C4⋊C4—181no—
313C22⋊C4—61no—
314C22⋊C4—61no—
315C22⋊C4—61no—
316C22⋊C4—61no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C42C2×D3211yescharacteristic
320C22×C3—21no—
321C22×C3—121no—
322C22×C3—121no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3—121no—
327C22×C3#88211yescharacteristic
328C22×C3#93711yescharacteristic
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—121no—
345C3×C4—121no—
346C3×C4—241no—
347Dic3—41no—
348Dic3—41no—
349Dic3—81no—
350Dic3—121no—
351Dic3—121no—
352Dic3—121no—
353Dic3—121no—
354Dic3—241no—
355Dic3—241no—
356C32#166211yescharacteristic, complemented, Sylow
357C23—61no—
358C23—61no—
359Q8—121no—
360Q8—121no—
361Q8—122no—
362D4—121no—
363D4—121no—
364D4—721no—
365D4—721no—
366C2×C4—61no—
367C2×C4—61no—
368C2×C4—121no—
369C2×C4—181no—
370C2×C4—181no—
371C2×C4—721no—
372C2×C4—721no—
373C2×C4D3×D1211yescharacteristic
374C2×C4#380211yescharacteristic
375C2×C4D3×#6711yescharacteristic
376C8—41no—
377C8—121no—
378C8—361no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—241no—
383C2×C3—241no—
384C2×C3#474611yescharacteristic
385C2×C3#482511yescharacteristic
386C2×C3#482711yescharacteristic
387C2×C3#506111yescharacteristic
388C2×C3#520111yescharacteristic
389C2×C3#520211yescharacteristic
390D3—81no—
391D3—81no—
392C22—121no—
393C22—121no—
394C22—121no—
395C22—121no—
396C22—121no—
397C22—121no—
398C22#6392211yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—121no—
403C4—121no—
404C4—241no—
405C4—361no—
406C4—361no—
407C3—21no—
408C3#6835811yescharacteristic, complemented
409C3#7124611yescharacteristic, complemented
410C2—241no—
411C2—241no—
412C2#1059039611yescharacteristic
413C2#1059101211yescharacteristic
414C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10593985C2
hypercenter#97D32
hypocenterC32#1662
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. C3×#4714C2semidirect
3. #10590289C2semidirect
4. #10590280C2semidirect
5. #10589331C2semidirect
6. C3×#4464C2semidirect
7. #10589086C2semidirect
35. #4714D3semidirect
43. #4464D3semidirect
356. C32#1662semidirect
408. C3#68358semidirect
409. C3#71246semidirect

Maximal subgroups

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

subgroupindex
#105939852
C3×#47142
#105902892
#105902802
#105893312
C3×#44642
#105890862
#712463
#683583