Finite Group Databasebeta

← #11780688

Subgroups — #11780688

Order 1152.

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

normal subgroups only

This group has 442 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
2#10592754C211yesmaximal, characteristic, complemented
3#10590295C211yesmaximal, characteristic, complemented
4#10590276C211yesmaximal, characteristic, complemented
5C3×#4540C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71954—31nomaximal
9#68358—31nomaximal
10C32×#124C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#946—21no—
13C3×#939—21no—
14C3×#886—21no—
15C3×#884—21no—
16C3×#883—21no—
17C3×#878—21no—
18C3×#875C2211yescharacteristic
19C3×#870C2211yescharacteristic
20#63662—21no—
21#63659—21no—
22#63630C2211yescharacteristic
23C3×#803C2211yescharacteristic
24C3×#803C2211yescharacteristic
25#63567—21no—
26#63567—21no—
27#63566—21no—
28#63563—21no—
29C3×#562—31no—
30#5684D311yescharacteristic
31#5069—31no—
32#5055—31no—
33#5055—31no—
34#5055—31no—
35#5055—61no—
36#4714—31no—
37#4703—31no—
38C3×#329—31no—
39#4543—31no—
40#4540—31no—
41#4540D311yescharacteristic, complemented
42#4465—31no—
43#4464—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D411yescharacteristic
46C2×#634—21no—
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6D411yescharacteristic
53C32×C22⋊C4—21no—
54C32×C22⋊C4—21no—
55C32×C42C2311yescharacteristic
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×#217—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#1662—91noSylow
72C3×#125—31no—
73C3×#124—21no—
74C3×#124—31no—
75C3×#124C2×D311yescharacteristic
76C3×#124C2×D311yescharacteristic
77C3×#123—61no—
78C3×#123—61no—
79C3×C22⋊Q8—61no—
80C3×C22⋊Q8—61no—
81C3×#121—61no—
82C3×#121—61no—
83#946—21no—
84#939—21no—
85#886—21no—
86#884—21no—
87#883—21no—
88#878—21no—
89#875C2×D311yescharacteristic
90#870C2×D311yescharacteristic
91#869—31no—
92#869—31no—
93#869—61no—
94C3×#97—31no—
95C3×#97—31no—
96#835—61no—
97#835—62no—
98#835—61no—
99#835—61no—
100#832—61no—
101#832—62no—
102#832—61no—
103#832—61no—
104#821—61no—
105#816—61no—
106#816—61no—
107#816—61no—
108#810—61no—
109#810—61no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C23×C32—21no—
116C22×C3×D3—21no—
117C32×Q8—41no—
118C32×D4—41no—
119C2×C32×C4—21no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—41no—
124#634—42no—
125C3×#67—81no—
126C3×#67—81no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—81no—
131C3×D12—41no—
132C3×C4×D3—81no—
133C3×Dic6—41no—
134C3⋊(C3⋊C8)—41no—
135C3×C3⋊C8—41no—
136C3×C3⋊C8—41no—
137#562—31no—
138#491—91no—
139#489—91no—
140#489—91no—
141#330—91no—
142#329—31no—
143#329—91no—
144C2×C3×Q8—21no—
145C2×C3×Q8—31no—
146C2×C3×Q8D1211yescharacteristic
147C2×C3×Q8#6711yescharacteristic
148C2×C3×D4—21no—
149C2×C3×D4—31no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C2×C3×D4D1211yescharacteristic
153C2×C3×D4#6711yescharacteristic
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C2×#67—21no—
157C2×#67—21no—
158C22×Dic3—21no—
159C2×D12#6711yescharacteristic
160C2×C4×D3—21no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6—121no—
164C2×Dic6#6711yescharacteristic
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—31no—
168C3×C4⋊C4—31no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C22⋊C4—21no—
174C3×C22⋊C4—21no—
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—41no—
178C3×C22⋊C4—41no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C22⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C42—21no—
184C3×C42C22×D311yescharacteristic
185C3×C42C22×D311yescharacteristic
186#217—21no—
187(C2×D3)⋊C4—21no—
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—62no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—121no—
197C4⋊Dic3#6711yescharacteristic
198C4⋊Dic3#6711yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—62no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32—41no—
210C22×C32#12011yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C32×C4—21no—
217C32×C4—41no—
218C3⋊Dic3—81no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C4⋊Q8—91no—
223#125—31no—
224#124—31no—
225#124D3211yescharacteristic
226#123—61no—
227#123—61no—
228C22⋊Q8—61no—
229C22⋊Q8—61no—
230#121—61no—
231#121—61no—
232#103—181no—
233#103—181no—
234#103—181no—
235#103—181no—
236#102—181no—
237#102—181no—
238#97—31no—
239#97—31no—
240#97—91no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—41no—
244C23×C3—61no—
245C22×D3—21no—
246C3×Q8—41no—
247C3×Q8—41no—
248C3×Q8—42no—
249C3×Q8—121no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—42no—
253C3×D4—121no—
254C3×D4—241no—
255C3×D4—241no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—41no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—241no—
266C2×C3×C4—241no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273#67—81no—
274#67—81no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—81no—
279C2×Dic3—122no—
280C2×Dic3—121no—
281C2×Dic3—121no—
282D12—41no—
283C4×D3—81no—
284Dic6—41no—
285Dic6—122no—
286Dic6—122no—
287Dic6—242no—
288C3×C8—121no—
289C3×C8—121no—
290C3⋊C8—41no—
291C3⋊C8—41no—
292C3⋊C8—122no—
293C3⋊C8—121no—
294C3⋊C8—121no—
295C2×C32—81no—
296C2×C32#45411yescharacteristic
297C2×C32#45511yescharacteristic
298C2×C32#45511yescharacteristic
299C3×D3—81no—
300C2×Q8—31no—
301C2×Q8—181no—
302C2×Q8#62611yescharacteristic
303C2×D4—31no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4#62611yescharacteristic
307C22×C4—61no—
308C22×C4—61no—
309C2×C8—61no—
310C2×C8—61no—
311C2×C8—181no—
312C4⋊C4—31no—
313C4⋊C4—31no—
314C4⋊C4—61no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—61no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—61no—
323C22⋊C4—61no—
324C22⋊C4—61no—
325C22⋊C4—61no—
326C42C2×D3211yescharacteristic
327C22×C3—21no—
328C22×C3—41no—
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—81no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3—121no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3#88211yescharacteristic
341C22×C3#95311yescharacteristic
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C3×C4—22no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—81no—
357C3×C4—121no—
358C3×C4—121no—
359C3×C4—121no—
360Dic3—41no—
361Dic3—41no—
362Dic3—41no—
363Dic3—242no—
364Dic3—241no—
365Dic3—241no—
366C32#166211yescharacteristic, complemented, Sylow
367C23—21no—
368C23—61no—
369Q8—41no—
370Q8—121no—
371Q8—362no—
372D4—41no—
373D4—121no—
374D4—241no—
375D4—241no—
376C2×C4—21no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—61no—
380C2×C4—241no—
381C2×C4—241no—
382C2×C4—361no—
383C2×C4C2×#62611yescharacteristic
384C2×C4D3×#6711yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C8—121no—
387C8—121no—
388C8—361no—
389C2×C3—21no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—81no—
393C2×C3—81no—
394C2×C3—161no—
395C2×C3—241no—
396C2×C3#474611yescharacteristic
397C2×C3#482511yescharacteristic
398C2×C3#482711yescharacteristic
399C2×C3#524211yescharacteristic
400C2×C3#524211yescharacteristic
401C2×C3#524511yescharacteristic
402D3—81no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22#6397711yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—121no—
415C4—121no—
416C4—121no—
417C4—721no—
418C3—21no—
419C3#6835811yescharacteristic, complemented
420C3#7195411yescharacteristic, complemented
421C2—81no—
422C2—241no—
423C2#1059151311yescharacteristic
424C2#1059168511yescharacteristic
425C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
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. #10592754C2semidirect
3. #10590295C2semidirect
4. #10590276C2semidirect
5. C3×#4540C2semidirect
6. #10589088C2semidirect
7. #10589086C2semidirect
41. #4540D3semidirect
366. C32#1662semidirect
419. C3#68358semidirect
420. C3#71954semidirect

Maximal subgroups

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

subgroupindex
C3×#56842
#105927542
#105902952
#105902762
C3×#45402
#105890882
#105890862
#719543
#683583