Finite Group Databasebeta

← #11779170

Subgroups — #11779170

Order 1152.

484 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 88 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#10593864C211yesmaximal, characteristic, complemented
2#10592774C211yesmaximal, characteristic
3C3×#5075C211yesmaximal, characteristic
4C3×#5070C211yesmaximal, characteristic
5#10589093C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71204—31nomaximal
9#71034—31nomaximal
10C32×#127C2211yescharacteristic
11C2×#3754—21no—
12C4×#634C2211yescharacteristic
13C2×C3×#214—21no—
14C3×#869C2211yescharacteristic
15C3×C4×Dic6C2211yescharacteristic
16#63873—21no—
17#63869—21no—
18#63847—22no—
19#63844—21no—
20#63843—21no—
21#63659—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#832—22no—
24C3×#832—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27#5721—31no—
28#5567—31no—
29C3×#486—31no—
30C3×#460—31no—
31#5075—31no—
32#5075—31no—
33#5075—61no—
34#5075D311yescharacteristic
35#5070D311yescharacteristic
36#4547—31no—
37#4535—31no—
38#4484—31no—
39#4482—31no—
40#4456—31no—
41#4456—31no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×#634D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C32×C42C2311yescharacteristic
49#3754—42no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#214—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D411yescharacteristic
57C3×C4⋊Dic3D412yes—
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3724—22no—
63#3724—22no—
64Dic3⋊Dic3—22no—
65Dic32—22no—
66#1626—91noSylow
67C2×C3×SD16—61no—
68C3×C4⋊Q8—31no—
69C3×#127—21no—
70C3×#127C2×D311yescharacteristic
71C3×#127C2×D311yescharacteristic
72C3×C4×Q8—31no—
73Q8×Dic3—61no—
74#944—61no—
75#944—61no—
76C2×#214—21no—
77C2×#214—61no—
78C2×#214—61no—
79C2×#214—62no—
80#890—61no—
81#889—62no—
82#889—62no—
83#887—61no—
84#887—61no—
85#870—61no—
86#869C2×D311yescharacteristic
87C4×Dic6—31no—
88C4×Dic6—31no—
89C4×Dic6—61no—
90C4×Dic6—61no—
91C4×Dic6C2×D311yescharacteristic
92C3×C4⋊C8—31no—
93C3×#102—61no—
94C3×#102—62no—
95C3×C4×C8—31no—
96#832—22no—
97#832—21no—
98#832—61no—
99#832—61no—
100#832—62no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—31no—
103C4⋊(C3⋊C8)—61no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4×C3⋊C8C2×D311yescharacteristic
106C23×C32—41no—
107C32×D4—41no—
108C32×D4—41no—
109C32×D4—42no—
110C32×D4—41no—
111C32×D4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117#634—21no—
118#634SD1612yescomplemented
119C2×C3×Dic3—21no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C3×Dic6—21no—
123C3×Dic6—21no—
124C3×Dic6—41no—
125C3×Dic6—41no—
126C3⋊(C3⋊C8)—41no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129#557—91no—
130#486—31no—
131#460—31no—
132#460—91no—
133#332—91no—
134Q8⋊C8—91no—
135Q8⋊C8—91no—
136C2×C3×Q8—31no—
137C2×C3×Q8—61no—
138C2×C3×D4—22no—
139C2×C3×D4—21no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—21no—
143C2×C3×D4—21no—
144C2×C3×D4—21no—
145C2×C3×D4—41no—
146C2×C3×D4—41no—
147C2×Dic6—21no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—61no—
151C2×Dic6#6711yescharacteristic
152C3×SD16—122no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—31no—
156C3×C4⋊C4—32no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C42—21no—
160C3×C42—61no—
161C3×C42C22×D311yescharacteristic
162C3×C42C22×D311yescharacteristic
163#214—42no—
164#214—122no—
165#214—122no—
166#214—124no—
167C4⋊Dic3—21no—
168C4⋊Dic3—31no—
169C4⋊Dic3—31no—
170C4⋊Dic3—61no—
171C4⋊Dic3—62no—
172C4⋊Dic3#6711yescharacteristic
173C4⋊Dic3#6712yes—
174Dic3⋊C4—21no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—62no—
180Dic3⋊C4—61no—
181Dic3⋊C4—61no—
182Dic3⋊C4—121no—
183C4×Dic3—21no—
184C4×Dic3—62no—
185C4×Dic3—62no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—121no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—62no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C22×C32—81no—
195C22×C32—81no—
196C22×C32—81no—
197C22×C32#12011yescharacteristic
198C32×C4—21no—
199C32×C4C2×SD1611yescharacteristic
200C32×C4#13511yescharacteristic
201C32×C4AGL(1,ℤ/8)11yescharacteristic
202C32×C4#13711yescharacteristic
203C3⋊Dic3—22no—
204C3⋊Dic3—41no—
205C3×Dic3—41no—
206C3×Dic3—42no—
207C3×Dic3—41no—
208C2×SD16—61no—
209C2×SD16—181no—
210C4⋊Q8—31no—
211C4⋊Q8—181no—
212#127D3211yescharacteristic
213#125—181no—
214#125—182no—
215C4×Q8—31no—
216C4×Q8—91no—
217C4×Q8—181no—
218C4×Q8—181no—
219C4⋊C8—31no—
220C4⋊C8—91no—
221#102—61no—
222#102—62no—
223#102—181no—
224C4×C8—31no—
225C23×C3—42no—
226C23×C3—41no—
227C23×C3—41no—
228C3×Q8—61no—
229C3×Q8—61no—
230C3×Q8—121no—
231C3×Q8—121no—
232C3×D4—42no—
233C3×D4—42no—
234C3×D4—42no—
235C3×D4—42no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—81no—
245C3×D4—81no—
246C3×D4—82no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—61no—
251C2×C3×C4—62no—
252C2×C3×C4—61no—
253C2×C3×C4D3×D411yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4C2×#6711yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×Dic3—21no—
260C2×Dic3—21no—
261C2×Dic3—22no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—121no—
267C2×Dic3—121no—
268Dic6—21no—
269Dic6—21no—
270Dic6—32no—
271Dic6—32no—
272Dic6—41no—
273Dic6—41no—
274Dic6—62no—
275Dic6—61no—
276Dic6—61no—
277Dic6—121no—
278C3×C8—121no—
279C3×C8—121no—
280C3⋊C8—41no—
281C3⋊C8—41no—
282C3⋊C8—122no—
283C3⋊C8—121no—
284C3⋊C8—121no—
285C2×C32—161no—
286C2×C32#44811yescharacteristic
287C2×C32#44911yescharacteristic
288C2×C32#45411yescharacteristic
289C2×Q8—31no—
290C2×Q8—61no—
291C2×Q8—91no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295SD16—122no—
296SD16—362no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8—181no—
300C4⋊C4—31no—
301C4⋊C4—32no—
302C4⋊C4—61no—
303C4⋊C4—61no—
304C4⋊C4—91no—
305C4⋊C4—182no—
306C4⋊C4—182no—
307C4⋊C4—182no—
308C4⋊C4—181no—
309C42—61no—
310C42—182no—
311C42—181no—
312C42C2×D3211yescharacteristic
313C22×C3—21no—
314C22×C3—82no—
315C22×C3—82no—
316C22×C3—82no—
317C22×C3—81no—
318C22×C3—81no—
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3—81no—
323C22×C3#93711yescharacteristic
324C22×C3#93711yescharacteristic
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—121no—
333C3×C4—122no—
334C3×C4—121no—
335C3×C4#91111yescharacteristic
336C3×C4#91211yescharacteristic
337C3×C4D3×SD1611yescharacteristic
338C3×C4D3×SD1611yescharacteristic
339C3×C4#91511yescharacteristic
340C3×C4#91511yescharacteristic
341C3×C4#93211yescharacteristic
342C3×C4#95011yescharacteristic
343Dic3—42no—
344Dic3—41no—
345Dic3—41no—
346Dic3—62no—
347Dic3—62no—
348Dic3—122no—
349Dic3—121no—
350Dic3—121no—
351Dic3—241no—
352C32#162611yescharacteristic, complemented, Sylow
353C23—41no—
354Q8—61no—
355Q8—61no—
356Q8—92no—
357Q8—121no—
358Q8—121no—
359Q8—181no—
360D4—42no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—41no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—62no—
368C2×C4—181no—
369C2×C4—181no—
370C2×C4D3×#6711yescharacteristic
371C2×C4D3×#6711yescharacteristic
372C2×C4#381111yescharacteristic
373C8—121no—
374C8—121no—
375C8—361no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—162no—
380C2×C3—161no—
381C2×C3—161no—
382C2×C3#503711yescharacteristic
383C2×C3#506211yescharacteristic
384C2×C3#515811yescharacteristic
385C2×C3#517011yescharacteristic
386C2×C3#517011yescharacteristic
387C2×C3#520111yescharacteristic
388C22—81no—
389C22—81no—
390C22—81no—
391C22#6398311yescharacteristic
392C4—21no—
393C4—121no—
394C4—122no—
395C4—121no—
396C4—182no—
397C4—361no—
398C4#6393011yescharacteristic
399C4#6393111yescharacteristic
400C4#6393211yescharacteristic
401C4#6393311yescharacteristic
402C3—21no—
403C3#7103411yescharacteristic, complemented
404C3#7120411yescharacteristic, complemented
405C2—161no—
406C2#1059151811yescharacteristic
407C2#1059151911yescharacteristic
408C2#1059152511yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
Fitting, prime radicalC32×#127C22
socleC22×C32#120
hypercenter#127D32
hypocenterC32#1626
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10593864C2semidirect
5. #10589093C2semidirect
6. #10589085C2semidirect
7. #10589084C2semidirect
118. #634SD16semidirect
352. C32#1626semidirect
403. C3#71034semidirect
404. C3#71204semidirect

Maximal subgroups

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

subgroupindex
#105938642
#105927742
C3×#50752
C3×#50702
#105890932
#105890852
#105890842
#712043
#710343