Finite Group Databasebeta

← #11780647

Subgroups — #11780647

Order 1152.

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

normal subgroups only

This group has 461 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×#5700C211yesmaximal, characteristic
2#10592763C211yesmaximal, characteristic, complemented
3#10590372C211yesmaximal, characteristic, complemented
4#10590276C211yesmaximal, characteristic, complemented
5C3×#4543C211yesmaximal, characteristic, complemented
6#10589086C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71953—31nomaximal
9#68373—31nomaximal
10C32×#125C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#896—21no—
13C3×#896—21no—
14C3×#895—21no—
15C3×#895—21no—
16C3×#894—21no—
17C3×#894—21no—
18C3×#875C2211yescharacteristic
19C3×#875C2211yescharacteristic
20C2×#3719—21no—
21C2×#3716—21no—
22#63635—21no—
23#63634—21no—
24#63630C2211yescharacteristic
25C3×#803C2211yescharacteristic
26C3×#803C2211yescharacteristic
27#63566—21no—
28#63563—21no—
29C3×#562—31no—
30#5700D311yescharacteristic
31#5064—31no—
32#5064—31no—
33#5064—61no—
34#5060—31no—
35#5055—31no—
36#4715—31no—
37#4714—31no—
38C3×#330—31no—
39#4543D311yescharacteristic, complemented
40#4540—31no—
41#4540—31no—
42#4464—31no—
43#4464—31no—
44C2×#634—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12D411yescharacteristic
48C2×C3×D12D411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×Dic6D411yescharacteristic
52C2×C3×Dic6D411yescharacteristic
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C42C2311yescharacteristic
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#3719—42no—
72#3716—42no—
73#1661—91noSylow
74C3×#125—21no—
75C3×#125C2×D311yescharacteristic
76C3×#125C2×D311yescharacteristic
77C3×#124—31no—
78C3×#124—31no—
79C3×#123—61no—
80C3×#123—61no—
81C3×C22⋊Q8—61no—
82C3×C22⋊Q8—61no—
83C3×#121—61no—
84C3×#121—61no—
85C2×#216—61no—
86C2×#214—61no—
87C2×Dic12—61no—
88C2×#204—61no—
89#896—21no—
90#896—21no—
91#895—21no—
92#895—21no—
93#894—21no—
94#894—21no—
95#875C2×D311yescharacteristic
96#875C2×D311yescharacteristic
97#869—31no—
98#869—31no—
99#869—61no—
100C3×#97—31no—
101C3×#97—31no—
102#835—61no—
103#832—61no—
104#821—61no—
105#816—61no—
106#808—62no—
107#808—61no—
108#808—61no—
109#807—62no—
110#807—61no—
111#807—61no—
112#803—31no—
113#803—31no—
114#803—61no—
115#803C2×D311yescharacteristic
116#803C2×D311yescharacteristic
117C22×C3×D3—21no—
118C22×C3×D3—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3⋊Dic3—41no—
125#634—41no—
126#634—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C3×D12—41no—
130C3×D12—41no—
131C3×D12—81no—
132C3×D12—81no—
133C3×C4×D3—81no—
134C3×C4×D3—81no—
135C3×Dic6—41no—
136C3×Dic6—41no—
137C3⋊(C3⋊C8)—22no—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—41no—
140#562—31no—
141#501—91no—
142#497—91no—
143#489—91no—
144#330—31no—
145#329—91no—
146#329—91no—
147C2×C3×Q8—31no—
148C2×C3×Q8—31no—
149C2×C3×D4—31no—
150C2×C3×D4—31no—
151C2×C3×D4—61no—
152C2×C3×D4—61no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12#6711yescharacteristic
158C2×D12#6711yescharacteristic
159C2×C4×D3—21no—
160C2×C4×D3—21no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6—121no—
164C2×Dic6#6711yescharacteristic
165C2×Dic6#6711yescharacteristic
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—41no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4D1211yescharacteristic
179C3×C4⋊C4D1211yescharacteristic
180C3×C4⋊C4#6711yescharacteristic
181C3×C4⋊C4#6711yescharacteristic
182C3×C22⋊C4—61no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—21no—
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D311yescharacteristic
191#216—122no—
192#214—122no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—21no—
198(C2×D3)⋊C4—21no—
199C4⋊Dic3—62no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—121no—
205Dic3⋊C4—21no—
206Dic3⋊C4—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212Dic12—122no—
213#204—122no—
214C22×C32#12011yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3—41no—
221C32×C4—21no—
222C32×C4—21no—
223C32×C4—21no—
224C32×C4—41no—
225C32×C4—41no—
226C3⋊Dic3—81no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×Q16—181no—
230C2×SD16—181no—
231C4⋊Q8—91no—
232#125D3211yescharacteristic
233#124—31no—
234#124—31no—
235#123—61no—
236#123—61no—
237C22⋊Q8—61no—
238C22⋊Q8—61no—
239#121—61no—
240#121—61no—
241#107—181no—
242#106—181no—
243#103—181no—
244#102—181no—
245#97—31no—
246#97—31no—
247#97—91no—
248C23×C3—61no—
249C23×C3—61no—
250C22×D3—21no—
251C22×D3—21no—
252C3×Q8—121no—
253C3×Q8—121no—
254C3×D4—121no—
255C3×D4—121no—
256C3×D4—241no—
257C3×D4—241no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—241no—
270C2×C3×C4—241no—
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×C3×C4C2×#6711yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—122no—
280C2×Dic3—121no—
281C2×Dic3—121no—
282D12—41no—
283D12—41no—
284D12—81no—
285D12—81no—
286C4×D3—81no—
287C4×D3—81no—
288Dic6—41no—
289Dic6—41no—
290Dic6—121no—
291Dic6—121no—
292Dic6—121no—
293Dic6—121no—
294Dic6—241no—
295Dic6—241no—
296C3×C8—62no—
297C3×C8—121no—
298C3⋊C8—22no—
299C3⋊C8—41no—
300C3⋊C8—64no—
301C3⋊C8—62no—
302C3⋊C8—62no—
303C2×C32#45311yescharacteristic
304C2×C32#45511yescharacteristic
305C2×C32#45611yescharacteristic
306C3×D3—81no—
307C3×D3—81no—
308C2×Q8—31no—
309C2×Q8—31no—
310C2×Q8—181no—
311C2×D4—31no—
312C2×D4—31no—
313C2×D4—61no—
314C2×D4—61no—
315C22×C4—61no—
316C22×C4—61no—
317Q16—362no—
318SD16—362no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—181no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4#62611yescharacteristic
329C4⋊C4#62611yescharacteristic
330C22⋊C4—61no—
331C22⋊C4—61no—
332C22⋊C4—61no—
333C22⋊C4—61no—
334C22⋊C4—61no—
335C22⋊C4—61no—
336C42C2×D3211yescharacteristic
337C22×C3—21no—
338C22×C3—121no—
339C22×C3—121no—
340C22×C3—121no—
341C22×C3—121no—
342C22×C3—121no—
343C22×C3—121no—
344C22×C3#88211yescharacteristic
345C22×C3#95311yescharacteristic
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—41no—
352C3×C4—22no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—41no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—41no—
365C3×C4—81no—
366C3×C4—81no—
367C3×C4—121no—
368C3×C4—121no—
369Dic3—41no—
370Dic3—41no—
371Dic3—242no—
372Dic3—241no—
373Dic3—241no—
374C32#166111yescharacteristic, complemented, Sylow
375C23—61no—
376C23—61no—
377Q8—121no—
378Q8—121no—
379Q8—361no—
380Q8—361no—
381D4—121no—
382D4—121no—
383D4—241no—
384D4—241no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—61no—
388C2×C4—61no—
389C2×C4—241no—
390C2×C4—241no—
391C2×C4—361no—
392C2×C4C2×#62611yescharacteristic
393C2×C4D3×#6711yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—62no—
396C8—121no—
397C8—182no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—241no—
402C2×C3—241no—
403C2×C3#475211yescharacteristic
404C2×C3#482211yescharacteristic
405C2×C3#482511yescharacteristic
406C2×C3#524111yescharacteristic
407C2×C3#524211yescharacteristic
408C2×C3#524611yescharacteristic
409D3—81no—
410D3—81no—
411C22—121no—
412C22—121no—
413C22—121no—
414C22—121no—
415C22—121no—
416C22—121no—
417C22#6397711yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—41no—
422C4—41no—
423C4—121no—
424C4—121no—
425C4—721no—
426C3—21no—
427C3#6837311yescharacteristic, complemented
428C3#7195311yescharacteristic, complemented
429C2—241no—
430C2—241no—
431C2#1059164911yescharacteristic
432C2#1059166611yescharacteristic
433C2#1059168811yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32#120
prime radicalC3×#5700C2
hypercenter#125D32
hypocenterC32#1661
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #10592763C2semidirect
3. #10590372C2semidirect
4. #10590276C2semidirect
5. C3×#4543C2semidirect
6. #10589086C2semidirect
7. #10589086C2semidirect
39. #4543D3semidirect
374. C32#1661semidirect
427. C3#68373semidirect
428. C3#71953semidirect

Maximal subgroups

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

subgroupindex
C3×#57002
#105927632
#105903722
#105902762
C3×#45432
#105890862
#719533
#683733