Finite Group Databasebeta

← #11780692

Subgroups — #11780692

Order 1152.

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

normal subgroups only

This group has 427 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#10593953C211yesmaximal, characteristic
2C3×#4703C211yesmaximal, characteristic, complemented
3#10590294C211yesmaximal, characteristic, complemented
4#10590280C211yesmaximal, characteristic, complemented
5#10589330C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71251—31nomaximal
9#68358—31nomaximal
10#64084C2211yescharacteristic
11C3×#875C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63910—21no—
15#63896—21no—
16#63890—21no—
17#63888—21no—
18#63886—21no—
19#63854—21no—
20C32×#97C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#816—21no—
23C3×#816—21no—
24C3×#803C2211yescharacteristic
25#63567—21no—
26#63565—21no—
27#63564—21no—
28#63562—21no—
29#5700—31no—
30#5684—31no—
31C3×#491—31no—
32#5089—31no—
33#5089—31no—
34#5055—31no—
35#4714—31no—
36#4703D311yescharacteristic, complemented
37C3×#329—31no—
38#4543—31no—
39#4465—31no—
40#4464—31no—
41#4464—31no—
42#4464—61no—
43#4464D311yescharacteristic, complemented
44C2×C4⋊(C3⋊D3)D411yescharacteristic
45C2×#634D411yescharacteristic
46C2×C3×D12D411yescharacteristic
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C2×#626—21no—
50C2×#626—21no—
51C2×#624—21no—
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54C32×C42C2311yescharacteristic
55#3752—21no—
56#3752—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3D411yescharacteristic
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C2×C3×C3⋊C8—21no—
67#3724—21no—
68Dic3⋊Dic3—21no—
69#3722—21no—
70(C2×D3)⋊Dic3—21no—
71#1662—91noSylow
72C3×C4⋊Q8—31no—
73C3×#125—31no—
74C3×#124—31no—
75#946—61no—
76#939—61no—
77#896—61no—
78#896—61no—
79#895—61no—
80#895—61no—
81#894—61no—
82#894—61no—
83#886—61no—
84#884—61no—
85#883—61no—
86#878—61no—
87#875—31no—
88#875—31no—
89#875—61no—
90#875C2×D311yescharacteristic
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#103—61no—
94C3×#103—61no—
95C3×#97—21no—
96C3×#97—31no—
97C3×#97C2×D311yescharacteristic
98C3×#97C2×D311yescharacteristic
99#835—61no—
100#832—61no—
101#821—61no—
102#816—21no—
103#816—21no—
104#816—61no—
105#810—61no—
106#810—61no—
107#809—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—
119C4⋊(C3⋊D3)—41no—
120#634—41no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—41no—
125C3×D12—41no—
126C3×Dic6—41no—
127C3×Dic6—42no—
128#626—81no—
129#626—81no—
130#624—81no—
131D3×Dic3—81no—
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C3×C3⋊C8—41no—
135#562—91no—
136#491—31no—
137#489—91no—
138#489—91no—
139#330—91no—
140#329—31no—
141#329—91no—
142C2×C3×Q8—31no—
143C2×C3×Q8—61no—
144C2×C3×D4—31no—
145C2×#67—61no—
146C2×#67—61no—
147C22×Dic3—61no—
148C2×D12—31no—
149C2×D12—31no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12D1211yescharacteristic
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×Dic6—21no—
158C2×Dic6—31no—
159C2×Dic6—31no—
160C2×Dic6—61no—
161C2×Dic6D1211yescharacteristic
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—41no—
165C2×C3×C8—61no—
166C3×C4⋊C4—31no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C42—21no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177#217—61no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—121no—
188(C2×D3)⋊C4—121no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—61no—
192C4⋊Dic3#6711yescharacteristic
193C4⋊Dic3#6711yescharacteristic
194Dic3⋊C4—21no—
195Dic3⋊C4—21no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
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—31no—
220#124—31no—
221#124—91no—
222#123—181no—
223#123—181no—
224C22⋊Q8—181no—
225C22⋊Q8—181no—
226#121—181no—
227#121—181no—
228#103—61no—
229#103—61no—
230#103—181no—
231#103—181no—
232#102—181no—
233#102—181no—
234#97—31no—
235#97—91no—
236#97D3211yescharacteristic
237C23×C3—61no—
238C22×D3—21no—
239C22×D3—61no—
240C22×D3—61no—
241C22×D3—121no—
242C3×Q8—121no—
243C3×Q8—122no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—61no—
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—
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—21no—
263C2×Dic3—41no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—121no—
267C2×Dic3—241no—
268D12—41no—
269D12—121no—
270D12—121no—
271D12—241no—
272D12—241no—
273D12—241no—
274C4×D3—241no—
275C4×D3—241no—
276C4×D3—241no—
277Dic6—41no—
278Dic6—42no—
279Dic6—121no—
280Dic6—121no—
281Dic6—241no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—42no—
285C3×C8—121no—
286C3⋊C8—41no—
287C3⋊C8—121no—
288C3⋊C8—121no—
289C3⋊C8—122no—
290C2×C32#45411yescharacteristic
291C2×C32#45511yescharacteristic
292C2×C32#45511yescharacteristic
293C3⋊D3—81no—
294C3×D3—81no—
295C2×Q8—31no—
296C2×Q8—61no—
297C2×Q8—91no—
298C2×D4—31no—
299C2×D4—91no—
300C2×D4—181no—
301C2×D4—181no—
302C22×C4—181no—
303C22×C4—181no—
304C2×C8—21no—
305C2×C8—61no—
306C2×C8—181no—
307C4⋊C4—31no—
308C4⋊C4—31no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4—61no—
312C4⋊C4—61no—
313C4⋊C4—181no—
314C4⋊C4—181no—
315C22⋊C4—61no—
316C22⋊C4—61no—
317C22⋊C4—181no—
318C22⋊C4—181no—
319C22⋊C4—181no—
320C22⋊C4—181no—
321C42C2×D3211yescharacteristic
322C22×C3—21no—
323C22×C3—121no—
324C22×C3—121no—
325C22×C3—121no—
326C22×C3#88211yescharacteristic
327C22×C3#93711yescharacteristic
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—121no—
332C2×D3—121no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—121no—
336C2×D3—121no—
337C2×D3—241no—
338C2×D3—241no—
339C2×D3—241no—
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—121no—
350C3×C4—121no—
351C3×C4—121no—
352C3×C4—241no—
353Dic3—41no—
354Dic3—41no—
355Dic3—41no—
356Dic3—81no—
357Dic3—121no—
358Dic3—121no—
359Dic3—241no—
360C32#166211yescharacteristic, complemented, Sylow
361C23—61no—
362C23—181no—
363Q8—121no—
364Q8—122no—
365Q8—361no—
366D4—121no—
367D4—361no—
368D4—721no—
369D4—721no—
370C2×C4—61no—
371C2×C4—61no—
372C2×C4—61no—
373C2×C4—121no—
374C2×C4—181no—
375C2×C4—721no—
376C2×C4—721no—
377C2×C4D3×D1211yescharacteristic
378C2×C4#380211yescharacteristic
379C2×C4D3×#6711yescharacteristic
380C8—41no—
381C8—121no—
382C8—361no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—241no—
387C2×C3#474611yescharacteristic
388C2×C3#482511yescharacteristic
389C2×C3#482711yescharacteristic
390C2×C3#506211yescharacteristic
391C2×C3#520211yescharacteristic
392C2×C3#520211yescharacteristic
393D3—81no—
394D3—241no—
395D3—241no—
396D3—481no—
397C22—121no—
398C22—121no—
399C22—121no—
400C22—361no—
401C22—361no—
402C22—361no—
403C22#6392211yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—121no—
408C4—121no—
409C4—121no—
410C4—241no—
411C4—361no—
412C3—21no—
413C3#6835811yescharacteristic, complemented
414C3#7125111yescharacteristic, complemented
415C2—241no—
416C2—721no—
417C2#1059040011yescharacteristic
418C2#1059101111yescharacteristic
419C2#1059101211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#97C22
socleC22×C32#120
prime radical#10593953C2
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×#4703C2semidirect
3. #10590294C2semidirect
4. #10590280C2semidirect
5. #10589330C2semidirect
6. C3×#4464C2semidirect
7. #10589088C2semidirect
36. #4703D3semidirect
43. #4464D3semidirect
360. C32#1662semidirect
413. C3#68358semidirect
414. C3#71251semidirect

Maximal subgroups

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

subgroupindex
#105939532
C3×#47032
#105902942
#105902802
#105893302
C3×#44642
#105890882
#712513
#683583