Finite Group Databasebeta

← #11780759

Subgroups — #11780759

Order 1152.

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

normal subgroups only

This group has 398 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×#5699C211yesmaximal, characteristic
2C3×#5064C211yesmaximal, characteristic, complemented
3#10590291C211yesmaximal, characteristic, complemented
4#10590280C211yesmaximal, characteristic
5#10589409C211yesmaximal, characteristic, complemented
6#10589088C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic
8#71957—31nomaximal
9#71394—31nomaximal
10C32×#125C2211yescharacteristic
11C3×#898—21no—
12C3×#898—21no—
13C3×#897—21no—
14C3×#896—21no—
15C3×#894—21no—
16C3×#888—21no—
17C3×#875C2211yescharacteristic
18C3×#870C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63630C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#808—21no—
23C3×#807—21no—
24C3×#803C2211yescharacteristic
25#63565—21no—
26#63565—21no—
27#63565—21no—
28#63562—21no—
29C3×#563—31no—
30#5699D311yescharacteristic
31C3×#501—31no—
32#5089—31no—
33#5082—31no—
34#5069—31no—
35#5064D311yescharacteristic, complemented
36#5055—31no—
37#4543—31no—
38#4543—31no—
39#4543—31no—
40#4543—61no—
41#4540—31no—
42#4465—31no—
43#4464—31no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6D411yescharacteristic
49C32×C4⋊C4—21no—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C4⋊C4D411yescharacteristic
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D411yescharacteristic
65C3×C4⋊Dic3D411yescharacteristic
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×Dic3⋊C4—21no—
69C3×C4×Dic3—21no—
70C2×C3×C3⋊C8—21no—
71#1664—91noSylow
72C3×C4⋊Q8—31no—
73C3×C4⋊Q8—61no—
74C3×#126—61no—
75C3×#126—61no—
76C3×#125—21no—
77C3×#125—31no—
78C3×#125C2×D311yescharacteristic
79C3×#125C2×D311yescharacteristic
80C3×#124—31no—
81C3×#123—61no—
82C3×C22⋊Q8—61no—
83C3×C22⋊Q8—61no—
84#898—21no—
85#898—21no—
86#897—21no—
87#896—21no—
88#894—21no—
89#888—21no—
90#875C2×D311yescharacteristic
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#107—61no—
94C3×#106—61no—
95C3×#97—31no—
96#835—61no—
97#835—61no—
98#835—61no—
99#832—61no—
100#810—61no—
101#810—61no—
102#810—61no—
103#809—61no—
104#808—21no—
105#807—21no—
106#803—31no—
107#803—31no—
108#803—31no—
109#803—31no—
110#803—61no—
111#803—61no—
112#803C2×D311yescharacteristic
113C22×C3×D3—21no—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—41no—
123C3×D12—41no—
124C3×C4×D3—81no—
125C3×Dic6—41no—
126C3×Dic6—42no—
127C3×Dic6—81no—
128C3⋊(C3⋊C8)—41no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—22no—
131#563—31no—
132#501—31no—
133#491—91no—
134#489—91no—
135#330—91no—
136#330—91no—
137#329—91no—
138C2×C3×Q8—31no—
139C2×C3×Q8—61no—
140C2×C3×Q8—61no—
141C2×C3×D4—31no—
142C22×C3×C4—61no—
143C2×D12#6711yescharacteristic
144C2×C4×D3—21no—
145C2×Dic6—21no—
146C2×Dic6—21no—
147C2×Dic6#6711yescharacteristic
148C2×C3×C8—61no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—31no—
157C3×C4⋊C4—41no—
158C3×C4⋊C4—41no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4#6711yescharacteristic
166C3×C4⋊C4#6711yescharacteristic
167C3×C4⋊C4#6711yescharacteristic
168C3×C4⋊C4#6711yescharacteristic
169C3×C22⋊C4—61no—
170C3×C22⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C22⋊C4—61no—
173C3×C22⋊C4—61no—
174C3×C42—21no—
175C3×C42—61no—
176C3×C42C22×D311yescharacteristic
177C3×C42C22×D311yescharacteristic
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—21no—
181(C2×D3)⋊C4—21no—
182(C2×D3)⋊C4—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3#6711yescharacteristic
187C4⋊Dic3#6711yescharacteristic
188Dic3⋊C4—21no—
189Dic3⋊C4—21no—
190Dic3⋊C4—21no—
191C4×Dic3—21no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—121no—
198C2×C3⋊C8—121no—
199C22×C32#12011yescharacteristic
200C2×C3×D3—41no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C32×C4—21no—
204C32×C4—21no—
205C32×C4—21no—
206C32×C4—41no—
207C32×C4—41no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C3×Dic3—81no—
212C4⋊Q8—31no—
213C4⋊Q8—61no—
214#126—61no—
215#126—61no—
216#125—31no—
217#125D3211yescharacteristic
218#124—31no—
219#123—61no—
220C22⋊Q8—61no—
221C22⋊Q8—61no—
222#107—61no—
223#106—61no—
224#103—181no—
225#103—181no—
226#103—181no—
227#102—181no—
228#97—31no—
229#97—91no—
230#97—91no—
231C23×C3—61no—
232C22×D3—21no—
233C3×Q8—121no—
234C3×Q8—122no—
235C3×Q8—241no—
236C3×D4—121no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—121no—
250C2×C3×C4—241no—
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4C2×#6711yescharacteristic
254C2×C3×C4C2×#6711yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×Dic3—21no—
258C2×Dic3—21no—
259C2×Dic3—21no—
260C2×Dic3—41no—
261D12—41no—
262C4×D3—81no—
263Dic6—41no—
264Dic6—42no—
265Dic6—81no—
266C3×C8—62no—
267C3⋊C8—22no—
268C3⋊C8—121no—
269C3⋊C8—121no—
270C3⋊C8—121no—
271C3⋊C8—121no—
272C3⋊C8—122no—
273C3⋊C8—122no—
274C2×C32#45411yescharacteristic
275C2×C32#45511yescharacteristic
276C2×C32#45611yescharacteristic
277C3×D3—81no—
278C2×Q8—31no—
279C2×Q8—61no—
280C2×Q8—61no—
281C2×D4—31no—
282C22×C4—61no—
283C2×C8—61no—
284C2×C8—181no—
285C2×C8—181no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—31no—
289C4⋊C4—31no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4#62511yescharacteristic
297C4⋊C4#62511yescharacteristic
298C22⋊C4—61no—
299C22⋊C4—61no—
300C22⋊C4—61no—
301C22⋊C4—61no—
302C22⋊C4—61no—
303C42—61no—
304C42C2×D3211yescharacteristic
305C22×C3—21no—
306C22×C3—121no—
307C22×C3—121no—
308C22×C3—121no—
309C22×C3#93711yescharacteristic
310C22×C3#95311yescharacteristic
311C2×D3—41no—
312C2×D3—41no—
313C2×D3—41no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—21no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—41no—
325C3×C4—41no—
326C3×C4—41no—
327C3×C4—81no—
328C3×C4—81no—
329C3×C4—121no—
330C3×C4—121no—
331C3×C4—121no—
332C3×C4—241no—
333Dic3—41no—
334Dic3—41no—
335Dic3—41no—
336Dic3—81no—
337C32#166411yescharacteristic, complemented, Sylow
338C23—61no—
339Q8—121no—
340Q8—122no—
341Q8—241no—
342D4—121no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—121no—
349C2×C4—241no—
350C2×C4C2×#62511yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C2×C4D3×#6711yescharacteristic
353C8—62no—
354C8—361no—
355C8—361no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—241no—
360C2×C3#509511yescharacteristic
361C2×C3#520111yescharacteristic
362C2×C3#520211yescharacteristic
363C2×C3#524211yescharacteristic
364C2×C3#524511yescharacteristic
365C2×C3#524611yescharacteristic
366D3—81no—
367C22—121no—
368C22—121no—
369C22—121no—
370C22#6397611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—41no—
375C4—41no—
376C4—121no—
377C4—121no—
378C4—121no—
379C4—241no—
380C3—21no—
381C3#7139411yescharacteristic, complemented
382C3#7195711yescharacteristic, complemented
383C2—241no—
384C2#1059164811yescharacteristic
385C2#1059166411yescharacteristic
386C2#1059168411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenter#125D32
hypocenterC32#1664
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. C3×#5064C2semidirect
3. #10590291C2semidirect
5. #10589409C2semidirect
6. #10589088C2semidirect
35. #5064D3semidirect
337. C32#1664semidirect
381. C3#71394semidirect
382. C3#71957semidirect

Maximal subgroups

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

subgroupindex
C3×#56992
C3×#50642
#105902912
#105902802
#105894092
#105890882
#105890862
#719573
#713943