Finite Group Databasebeta

← #11779027

Subgroups — #11779027

Order 1152.

507 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5579C211yesmaximal, characteristic, complemented
2C3×#5027C211yesmaximal, characteristic, complemented
3#10590375C211yesmaximal, characteristic, complemented
4#10590347C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71923—31nomaximal
9#71028—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×#215—21no—
13C3×#896—22no—
14C3×D3×C4⋊C4—21no—
15C3×#874C2211yescharacteristic
16C3×C4×D12—21no—
17C3×C4×D12C2211yescharacteristic
18C3×#870—21no—
19C3×#869C2211yescharacteristic
20C2×#3715—22no—
21C2×#3713—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#809—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26#63562—21no—
27C3×#554—31no—
28#5579D311yescharacteristic, complemented
29C3×#460—31no—
30#5085—31no—
31#5076—31no—
32#5072—31no—
33#5027D311yescharacteristic, complemented
34#5015—31no—
35#4546—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39D4⋊(C3⋊C8)—31no—
40#4483—31no—
41#4481—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4D411yescharacteristic
52C32×C42—21no—
53C32×C42C2311yescharacteristic
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#215—42no—
57C3×(C2×D3)⋊C4—22no—
58C3×(C2×D3)⋊C4—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—22no—
64C2×C3×C3⋊C8—21no—
65#3715—44no—
66#3713—42no—
67#1622—91noSylow
68C2×C3×SD16—61no—
69C3×C4⋊Q8—31no—
70C3×#127—31no—
71C3×#125—61no—
72C3×C22⋊Q8—62no—
73C3×C22⋊Q8—61no—
74C3×C4×Q8—21no—
75C3×C4×Q8C2×D311yescharacteristic
76C3×C4×Q8C2×D311yescharacteristic
77C3×C4×D4—31no—
78C3×C4×D4—61no—
79C2×C3×C4⋊C4—61no—
80#946—21no—
81C2×#215—21no—
82C2×#215—62no—
83C2×#214—62no—
84C2×#213—61no—
85C2×#213—61no—
86#896—22no—
87D3×C4⋊C4—21no—
88#874C2×D311yescharacteristic
89C4×D12—21no—
90C4×D12C2×D311yescharacteristic
91#870—21no—
92#869C2×D311yescharacteristic
93C3×C4⋊C8—31no—
94C3×#102—61no—
95#832—61no—
96#809—21no—
97#809—61no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—31no—
103C4×C3⋊C8—31no—
104C4×C3⋊C8—61no—
105C22×C3×D3—21no—
106C22×C3×D3—41no—
107C32×Q8—21no—
108C32×Q8—21no—
109C2×C32×C4—21no—
110C2×C32×C4—21no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C3×Dic3—21no—
115C2×C3×Dic3—22no—
116C3×D12—21no—
117C3×D12—42no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×D12—41no—
122C3×D12SD1612yescomplemented
123C3×C4×D3—41no—
124C3×C4×D3—41no—
125C3×C4×D3—82no—
126C3×Dic6—42no—
127C3⋊(C3⋊C8)—22no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—41no—
130#554—31no—
131#492—91no—
132#460—31no—
133#459—91no—
134#333—91no—
135Q8⋊C8—91no—
136D4⋊C8—91no—
137C2×C3×Q8—21no—
138C2×C3×Q8—32no—
139C2×C3×Q8#6711yescharacteristic
140C2×C3×Q8#6711yescharacteristic
141C2×C3×D4—31no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C22×C3×C4—62no—
146C22×C3×C4—61no—
147C2×D12—21no—
148C2×D12—21no—
149C2×D12—21no—
150C2×D12#6711yescharacteristic
151C2×C4×D3—21no—
152C2×C4×D3—22no—
153C2×Dic6#6712yes—
154C3×SD16—122no—
155C2×C3×C8—61no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4—21no—
159C3×C4⋊C4—31no—
160C3×C4⋊C4—41no—
161C3×C4⋊C4—62no—
162C3×C4⋊C4—62no—
163C3×C4⋊C4—61no—
164C3×C4⋊C4—61no—
165C3×C4⋊C4#6711yescharacteristic
166C3×C4⋊C4#6711yescharacteristic
167C3×C22⋊C4—62no—
168C3×C22⋊C4—61no—
169C3×C42—21no—
170C3×C42—21no—
171C3×C42—21no—
172C3×C42—41no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#215—42no—
176#215—124no—
177#214—124no—
178#213—122no—
179#213—122no—
180(C2×D3)⋊C4—22no—
181(C2×D3)⋊C4—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3#6711yescharacteristic
185Dic3⋊C4—22no—
186Dic3⋊C4—22no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—61no—
189C2×C3⋊C8—61no—
190C2×C3⋊C8—61no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—121no—
193C2×C3⋊C8—121no—
194C22×C32#12011yescharacteristic
195C2×C3×D3—22no—
196C2×C3×D3—41no—
197C2×C3×D3—41no—
198C2×C3×D3—81no—
199C2×C3×D3—81no—
200C2×C3×D3—81no—
201C32×C4—21no—
202C32×C4—41no—
203C32×C4—41no—
204C32×C4C2×SD1611yescharacteristic
205C32×C4#13511yescharacteristic
206C32×C4AGL(1,ℤ/8)11yescharacteristic
207C32×C4#13711yescharacteristic
208C3×Dic3—41no—
209C3×Dic3—42no—
210C2×SD16—61no—
211C2×SD16—182no—
212C2×D8—181no—
213C4⋊Q8—31no—
214#127—31no—
215#125—61no—
216C22⋊Q8—62no—
217C22⋊Q8—61no—
218C4×Q8D3211yescharacteristic
219C4×D4—31no—
220C4×D4—61no—
221C2×C4⋊C4—61no—
222C4⋊C8—31no—
223C4⋊C8—91no—
224#102—61no—
225#102—181no—
226C4×C8—91no—
227C23×C3—61no—
228C23×C3—121no—
229C22×D3—21no—
230C22×D3—41no—
231C3×Q8—22no—
232C3×Q8—21no—
233C3×Q8—21no—
234C3×Q8—21no—
235C3×Q8—21no—
236C3×Q8—41no—
237C3×Q8—122no—
238C3×D4—32no—
239C3×D4—61no—
240C3×D4—122no—
241C3×D4—121no—
242C3×D4—121no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—62no—
256C2×C3×C4—121no—
257C2×C3×C4—121no—
258C2×C3×C4—242no—
259C2×C3×C4D3×D411yescharacteristic
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×C3×C4C2×#6711yescharacteristic
263C2×C3×C4C2×#6711yescharacteristic
264C2×C3×C4C2×#6711yescharacteristic
265C2×Dic3—21no—
266C2×Dic3—22no—
267D12—21no—
268D12—42no—
269D12—41no—
270D12—41no—
271D12—41no—
272D12—41no—
273D12#21512yescomplemented
274C4×D3—41no—
275C4×D3—41no—
276C4×D3—82no—
277Dic6—42no—
278C3×C8—121no—
279C3⋊C8—41no—
280C3⋊C8—62no—
281C3⋊C8—62no—
282C3⋊C8—122no—
283C3⋊C8—121no—
284C3⋊C8—121no—
285C3⋊C8—241no—
286C2×C32#44811yescharacteristic
287C2×C32#44911yescharacteristic
288C2×C32#45311yescharacteristic
289C3×D3—42no—
290C3×D3—161no—
291C2×Q8—32no—
292C2×Q8#62511yescharacteristic
293C2×D4—31no—
294C2×D4—61no—
295C2×D4—61no—
296C2×D4—61no—
297C22×C4—62no—
298C22×C4—61no—
299SD16—122no—
300SD16—364no—
301D8—362no—
302C2×C8—61no—
303C2×C8—181no—
304C2×C8—181no—
305C4⋊C4—21no—
306C4⋊C4—31no—
307C4⋊C4—62no—
308C4⋊C4—62no—
309C4⋊C4—61no—
310C4⋊C4—61no—
311C4⋊C4#62511yescharacteristic
312C22⋊C4—62no—
313C22⋊C4—61no—
314C42—21no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—62no—
318C22×C3—121no—
319C22×C3—121no—
320C22×C3—241no—
321C22×C3—241no—
322C22×C3—241no—
323C22×C3#93711yescharacteristic
324C22×C3#95311yescharacteristic
325C2×D3—22no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—81no—
329C2×D3—81no—
330C2×D3—81no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—41no—
338C3×C4—42no—
339C3×C4—41no—
340C3×C4—41no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—81no—
344C3×C4—122no—
345C3×C4—121no—
346C3×C4D3×SD1611yescharacteristic
347C3×C4#91511yescharacteristic
348C3×C4#93211yescharacteristic
349C3×C4C2×#21511yescharacteristic
350C3×C4#94211yescharacteristic
351C3×C4#94911yescharacteristic
352C3×C4#95011yescharacteristic
353C3×C4#95011yescharacteristic
354Dic3—41no—
355Dic3—42no—
356C32#162211yescharacteristic, complemented, Sylow
357C23—61no—
358C23—121no—
359Q8—21no—
360Q8—21no—
361Q8—122no—
362D4—32no—
363D4—61no—
364D4—122no—
365D4—121no—
366D4—121no—
367D4—121no—
368D4—121no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—61no—
372C2×C4—62no—
373C2×C4—121no—
374C2×C4—121no—
375C2×C4—242no—
376C2×C4C2×#62511yescharacteristic
377C2×C4D3×#6711yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—121no—
380C8—182no—
381C8—361no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—122no—
386C2×C3—481no—
387C2×C3#503711yescharacteristic
388C2×C3#517011yescharacteristic
389C2×C3#519811yescharacteristic
390C2×C3#522711yescharacteristic
391C2×C3#523811yescharacteristic
392C2×C3#524111yescharacteristic
393D3—42no—
394D3—161no—
395C22—62no—
396C22—121no—
397C22—121no—
398C22—241no—
399C22—241no—
400C22—241no—
401C22#6397611yescharacteristic
402C4—21no—
403C4—41no—
404C4—41no—
405C4—122no—
406C4—121no—
407C4#6382211yescharacteristic
408C4#6382311yescharacteristic
409C4D3×#21511yescharacteristic
410C4#6394611yescharacteristic
411C3—21no—
412C3#7102811yescharacteristic, complemented
413C3#7192311yescharacteristic, complemented
414C2—122no—
415C2—481no—
416C2#1059116111yescharacteristic
417C2#1059158311yescharacteristic
418C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radical#10590347C2
hypercenterC4×Q8D32
hypocenterC32#1622
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5579C2semidirect
2. C3×#5027C2semidirect
3. #10590375C2semidirect
5. #10589401C2semidirect
6. #10589095C2semidirect
7. #10589080C2semidirect
28. #5579D3semidirect
33. #5027D3semidirect
122. C3×D12SD16semidirect
273. D12#215semidirect
356. C32#1622semidirect
412. C3#71028semidirect
413. C3#71923semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×#50272
#105903752
#105903472
#105894012
#105890952
#105890802
#719233
#710283