Finite Group Databasebeta

← #11780768

Subgroups — #11780768

Order 1152.

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

normal subgroups only

This group has 403 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×#5672C211yesmaximal, characteristic
2C3×#5055C211yesmaximal, characteristic
3#10590315C211yesmaximal, characteristic, complemented
4#10590291C211yesmaximal, characteristic, complemented
5#10589406C211yesmaximal, characteristic
6#10589088C211yesmaximal, characteristic, complemented
7#10589088C211yesmaximal, characteristic, complemented
8#71957—31nomaximal
9#71247—31nomaximal
10C32×#124C2211yescharacteristic
11C3×#944—21no—
12C3×#935—21no—
13C3×#879—21no—
14C3×#879—21no—
15C3×#878—21no—
16C3×#878—21no—
17C3×#870C2211yescharacteristic
18C3×#870C2211yescharacteristic
19C3×#869C2211yescharacteristic
20#63630C2211yescharacteristic
21#63630C2211yescharacteristic
22C3×#835—21no—
23C3×#832—21no—
24C3×#803C2211yescharacteristic
25#63576—21no—
26#63574—21no—
27#63565—21no—
28#63565—21no—
29C3×#563—31no—
30#5672D311yescharacteristic
31C3×#489—31no—
32#5082—31no—
33#5081—31no—
34#5069—31no—
35#5064—31no—
36#5055D311yescharacteristic
37#4543—31no—
38#4543—31no—
39#4540—31no—
40#4540—31no—
41#4540—61no—
42#4465—31no—
43#4465—31no—
44C2×C32×Q8D411yescharacteristic
45C2×C32×D4D411yescharacteristic
46C22×C3×Dic3—21no—
47C2×C3×Dic6—21no—
48C2×C3×Dic6—21no—
49C32×C22⋊C4—21no—
50C32×C22⋊C4—21no—
51C32×C42C2311yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#217—21no—
55C3×#217—21no—
56C3×#217—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×C4⋊Dic3D411yescharacteristic
61C3×C4⋊Dic3D411yescharacteristic
62C3×C4⋊Dic3D411yescharacteristic
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
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—31no—
77C3×#125—31no—
78C3×#124—21no—
79C3×#124C2×D311yescharacteristic
80C3×#124C2×D311yescharacteristic
81C3×#123—61no—
82C3×C22⋊Q8—61no—
83C3×C22⋊Q8—61no—
84#944—21no—
85#935—21no—
86#879—21no—
87#879—21no—
88#878—21no—
89#878—21no—
90#870C2×D311yescharacteristic
91#870C2×D311yescharacteristic
92#869C2×D311yescharacteristic
93C3×#103—61no—
94C3×#102—61no—
95C3×#97—31no—
96#835—21no—
97#835—61no—
98#835—61no—
99#832—21no—
100#810—61no—
101#810—61no—
102#808—61no—
103#808—61no—
104#807—61no—
105#807—61no—
106#803—31no—
107#803—31no—
108#803—31no—
109#803—31no—
110#803—61no—
111#803—61no—
112#803C2×D311yescharacteristic
113C23×C32—21no—
114C32×Q8—41no—
115C32×D4—41no—
116C2×C32×C4—21no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3×Dic3—21no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—81no—
126C3×Dic6—42no—
127C3×Dic6—81no—
128C3⋊(C3⋊C8)—22no—
129C3⋊(C3⋊C8)—41no—
130C3×C3⋊C8—41no—
131#563—31no—
132#501—91no—
133#491—91no—
134#489—31no—
135#330—91no—
136#330—91no—
137#329—91no—
138C2×C3×Q8—21no—
139C2×C3×Q8—61no—
140C2×C3×Q8—61no—
141C2×C3×Q8#6711yescharacteristic
142C2×C3×Q8#6711yescharacteristic
143C2×C3×D4—21no—
144C2×C3×D4#6711yescharacteristic
145C2×C3×D4#6711yescharacteristic
146C22×C3×C4—61no—
147C22×Dic3—21no—
148C2×Dic6—21no—
149C2×Dic6—21no—
150C2×C3×C8—61no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—31no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C22⋊C4—21no—
164C3×C22⋊C4—21no—
165C3×C22⋊C4—21no—
166C3×C22⋊C4—21no—
167C3×C22⋊C4—41no—
168C3×C22⋊C4—41no—
169C3×C22⋊C4—61no—
170C3×C22⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C42—21no—
173C3×C42—61no—
174C3×C42C22×D311yescharacteristic
175C3×C42C22×D311yescharacteristic
176#217—21no—
177#217—21no—
178#217—21no—
179C4⋊Dic3—21no—
180C4⋊Dic3—21no—
181C4⋊Dic3#6711yescharacteristic
182C4⋊Dic3#6711yescharacteristic
183C4⋊Dic3#6711yescharacteristic
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187Dic3⋊C4—21no—
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—41no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32#12011yescharacteristic
203C32×C4—21no—
204C32×C4—21no—
205C32×C4—21no—
206C32×C4—41no—
207C3×Dic3—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#125—31no—
218#124D3211yescharacteristic
219#123—61no—
220C22⋊Q8—61no—
221C22⋊Q8—61no—
222#107—181no—
223#106—181no—
224#103—61no—
225#103—181no—
226#103—181no—
227#102—61no—
228#97—31no—
229#97—91no—
230#97—91no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—41no—
234C3×Q8—41no—
235C3×Q8—41no—
236C3×Q8—81no—
237C3×Q8—122no—
238C3×Q8—241no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—81no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—41no—
248C2×C3×C4—61no—
249C2×C3×C4—61no—
250C2×C3×C4—61no—
251C2×C3×C4—61no—
252C2×C3×C4—121no—
253C2×C3×C4—241no—
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3—41no—
265C2×Dic3—81no—
266Dic6—42no—
267Dic6—81no—
268C3×C8—121no—
269C3⋊C8—41no—
270C3⋊C8—62no—
271C3⋊C8—62no—
272C3⋊C8—122no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C3⋊C8—122no—
276C2×C32—81no—
277C2×C32#45411yescharacteristic
278C2×C32#45511yescharacteristic
279C2×C32#45611yescharacteristic
280C2×Q8—61no—
281C2×Q8—61no—
282C2×Q8#62511yescharacteristic
283C2×D4#62511yescharacteristic
284C22×C4—61no—
285C2×C8—61no—
286C2×C8—181no—
287C2×C8—181no—
288C4⋊C4—31no—
289C4⋊C4—31no—
290C4⋊C4—31no—
291C4⋊C4—31no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—61no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—61no—
303C22⋊C4—61no—
304C22⋊C4—61no—
305C42—61no—
306C42C2×D3211yescharacteristic
307C22×C3—21no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—81no—
315C22×C3—81no—
316C22×C3—81no—
317C22×C3#93711yescharacteristic
318C22×C3#95311yescharacteristic
319C3×C4—21no—
320C3×C4—21no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—41no—
326C3×C4—41no—
327C3×C4—41no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—81no—
331C3×C4—121no—
332C3×C4—121no—
333C3×C4—121no—
334C3×C4—121no—
335C3×C4—241no—
336Dic3—41no—
337Dic3—41no—
338Dic3—41no—
339Dic3—41no—
340Dic3—81no—
341C32#166411yescharacteristic, complemented, Sylow
342C23—21no—
343Q8—41no—
344Q8—122no—
345Q8—241no—
346D4—41no—
347C2×C4—21no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—121no—
353C2×C4—241no—
354C2×C4C2×#62511yescharacteristic
355C2×C4D3×#6711yescharacteristic
356C2×C4D3×#6711yescharacteristic
357C8—121no—
358C8—182no—
359C8—361no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—81no—
364C2×C3—81no—
365C2×C3—161no—
366C2×C3#506111yescharacteristic
367C2×C3#520111yescharacteristic
368C2×C3#520511yescharacteristic
369C2×C3#524211yescharacteristic
370C2×C3#524511yescharacteristic
371C2×C3#524611yescharacteristic
372C22—41no—
373C22—41no—
374C22—41no—
375C22#6397611yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—121no—
381C4—121no—
382C4—121no—
383C4—121no—
384C4—241no—
385C3—21no—
386C3#7124711yescharacteristic, complemented
387C3#7195711yescharacteristic, complemented
388C2—81no—
389C2#1059151211yescharacteristic
390C2#1059168411yescharacteristic
391C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#124C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#124D32
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #10590315C2semidirect
4. #10590291C2semidirect
6. #10589088C2semidirect
7. #10589088C2semidirect
341. C32#1664semidirect
386. C3#71247semidirect
387. C3#71957semidirect

Maximal subgroups

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

subgroupindex
C3×#56722
C3×#50552
#105903152
#105902912
#105894062
#105890882
#719573
#712473