Finite Group Databasebeta

← #11779181

Subgroups — #11779181

Order 1152.

484 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593861C211yesmaximal, characteristic, complemented
2#10592547C211yesmaximal, characteristic
3#10590367C211yesmaximal, characteristic
4#10590281C211yesmaximal, characteristic
5C3×#4484C211yesmaximal, characteristic, complemented
6C3×#4482C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68456—31nomaximal
9#68252—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63872—21no—
16#63866—21no—
17#63846—22no—
18#63843—21no—
19Dic3×Dic6—21no—
20C2×#3717—21no—
21C32×C4⋊C8C2211yescharacteristic
22#63648—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63564—22no—
26#63564—21no—
27#5721—31no—
28#5570—31no—
29#5088—31no—
30#5027—31no—
31#4848—31no—
32#4848—31no—
33#4848—31no—
34#4848—61no—
35#4694—31no—
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38#4484—31no—
39#4484D311yescharacteristic, complemented
40#4482D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634D411yescharacteristic
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53#3744—42no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D412yes—
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#3717—42no—
66#1626—91noSylow
67C3×C4⋊Q8—31no—
68C3×C4×Q8—31no—
69Q8×Dic3—61no—
70Q8×Dic3—61no—
71#944—61no—
72C2×#215—61no—
73C2×#204—61no—
74C2×#204—61no—
75C2×#204—62no—
76C2×#204—61no—
77#890—61no—
78#890—61no—
79#890—62no—
80#889—62no—
81#887—61no—
82#874—31no—
83#874—31no—
84#874—61no—
85#869—61no—
86#869C2×D311yescharacteristic
87C4×Dic6—31no—
88C4×Dic6—31no—
89C4×Dic6—61no—
90C4×Dic6—61no—
91C4×Dic6C2×D311yescharacteristic
92C3×C4⋊C8—21no—
93C3×C4⋊C8—31no—
94C3×C4⋊C8C2×D311yescharacteristic
95C3×C4⋊C8C2×D311yescharacteristic
96C3×C4×C8—31no—
97#821—61no—
98#821—61no—
99#821—62no—
100#821—62no—
101#821—61no—
102#809—61no—
103#809—62no—
104C4⋊(C3⋊C8)C2×D311yescharacteristic
105C4×C3⋊C8C2×D311yescharacteristic
106C22×C3⋊D3—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—42no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—41no—
117#634—21no—
118#634—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—21no—
122C3×Dic6—21no—
123C3×Dic6—41no—
124C3×Dic6—41no—
125C3×Dic6SD1612yescomplemented
126C32×C8—41no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129#557—91no—
130#486—91no—
131#460—91no—
132#460—91no—
133#332—31no—
134Q8⋊C8—31no—
135Q8⋊C8—91no—
136C2×C3×Q8—31no—
137C2×C3×Q8—61no—
138C2×D12—62no—
139C2×D12—61no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—61no—
145C2×D12—121no—
146C2×D12—121no—
147C2×Dic6—21no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—61no—
151C2×Dic6D1211yescharacteristic
152C2×C3×C8—22no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C3×C4⋊C4—32no—
158C3×C4⋊C4—31no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C42—21no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#215—122no—
166C4⋊Dic3—21no—
167C4⋊Dic3—31no—
168C4⋊Dic3—31no—
169C4⋊Dic3—61no—
170C4⋊Dic3—62no—
171C4⋊Dic3—62no—
172C4⋊Dic3—62no—
173C4⋊Dic3D1211yescharacteristic
174C4⋊Dic3D1212yes—
175Dic3⋊C4—21no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—121no—
182C4×Dic3—21no—
183C4×Dic3—62no—
184C4×Dic3—62no—
185C4×Dic3—61no—
186C4×Dic3—61no—
187C4×Dic3—121no—
188C2×C3⋊C8—21no—
189C2×C3⋊C8—21no—
190#204—124no—
191#204—122no—
192#204—122no—
193#204—122no—
194C22×C32#12011yescharacteristic
195C2×C3⋊D3—81no—
196C2×C3⋊D3—81no—
197C2×C3⋊D3—81no—
198C32×C4—21no—
199C32×C4C2×SD1611yescharacteristic
200C32×C4#13511yescharacteristic
201C32×C4AGL(1,ℤ/8)11yescharacteristic
202C32×C4#13711yescharacteristic
203C3⋊Dic3—41no—
204C3⋊Dic3—41no—
205C3×Dic3—22no—
206C3×Dic3—42no—
207C3×Dic3—41no—
208C2×SD16—181no—
209C2×SD16—181no—
210C4⋊Q8—31no—
211C4⋊Q8—181no—
212#127—91no—
213#125—182no—
214#125—181no—
215C4×Q8—31no—
216C4×Q8—91no—
217C4×Q8—181no—
218C4×Q8—181no—
219C4⋊C8—31no—
220C4⋊C8D3211yescharacteristic
221#102—181no—
222#102—182no—
223#102—181no—
224C4×C8—31no—
225C22×D3—122no—
226C22×D3—121no—
227C22×D3—121no—
228C3×Q8—32no—
229C3×Q8—61no—
230C3×Q8—121no—
231C3×Q8—121no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—61no—
236C2×C3×C4—62no—
237C2×C3×C4—61no—
238C2×C3×C4C2×D1211yescharacteristic
239C2×C3×C4C2×D1211yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—22no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—121no—
252C2×Dic3—121no—
253D12—122no—
254D12—122no—
255D12—122no—
256D12—122no—
257D12—121no—
258D12—121no—
259D12—121no—
260D12—121no—
261D12—121no—
262D12—121no—
263D12—121no—
264D12—121no—
265D12—241no—
266D12—241no—
267D12—242no—
268Dic6—21no—
269Dic6—41no—
270Dic6—41no—
271Dic6—62no—
272Dic6—61no—
273Dic6—61no—
274Dic6—61no—
275Dic6—61no—
276Dic6—121no—
277Dic6#20412yescomplemented
278C3×C8—42no—
279C3×C8—41no—
280C3×C8—41no—
281C3×C8—121no—
282C3×C8—121no—
283C3⋊C8—41no—
284C3⋊C8—41no—
285C2×C32#44811yescharacteristic
286C2×C32#44911yescharacteristic
287C2×C32#45411yescharacteristic
288C3⋊D3—161no—
289C2×Q8—31no—
290C2×Q8—61no—
291C2×Q8—91no—
292C2×D4—181no—
293C2×D4—181no—
294C2×D4—181no—
295SD16—362no—
296SD16—362no—
297C2×C8—21no—
298C2×C8—61no—
299C2×C8—61no—
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#88211yescharacteristic
315C22×C3#88211yescharacteristic
316C2×D3—242no—
317C2×D3—242no—
318C2×D3—242no—
319C2×D3—241no—
320C2×D3—241no—
321C2×D3—241no—
322C2×D3—241no—
323C2×D3—241no—
324C2×D3—241no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—41no—
332C3×C4—62no—
333C3×C4—121no—
334C3×C4—122no—
335C3×C4C2×#20411yescharacteristic
336C3×C4#90911yescharacteristic
337C3×C4#91111yescharacteristic
338C3×C4D3×SD1611yescharacteristic
339C3×C4#91411yescharacteristic
340C3×C4#91611yescharacteristic
341C3×C4#91811yescharacteristic
342C3×C4#91911yescharacteristic
343Dic3—22no—
344Dic3—42no—
345Dic3—41no—
346Dic3—122no—
347Dic3—121no—
348Dic3—121no—
349Dic3—121no—
350Dic3—121no—
351Dic3—241no—
352C32#162611yescharacteristic, complemented, Sylow
353C23—361no—
354Q8—32no—
355Q8—61no—
356Q8—121no—
357Q8—121no—
358Q8—181no—
359Q8—181no—
360D4—362no—
361D4—361no—
362D4—361no—
363D4—361no—
364D4—361no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—62no—
368C2×C4—181no—
369C2×C4—181no—
370C2×C4D3×D1211yescharacteristic
371C2×C4D3×D1211yescharacteristic
372C2×C4#381111yescharacteristic
373C8—41no—
374C8—121no—
375C8—121no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—21no—
379C2×C3#473811yescharacteristic
380C2×C3#475311yescharacteristic
381C2×C3#478111yescharacteristic
382C2×C3#480611yescharacteristic
383C2×C3#481011yescharacteristic
384C2×C3#482711yescharacteristic
385D3—482no—
386D3—481no—
387D3—481no—
388C22—721no—
389C22—721no—
390C22—721no—
391C22#6392311yescharacteristic
392C4—21no—
393C4—62no—
394C4—121no—
395C4—122no—
396C4—361no—
397C4—361no—
398C4D3×#20411yescharacteristic
399C4#6380111yescharacteristic
400C4#6393711yescharacteristic
401C4#6395011yescharacteristic
402C3—21no—
403C3#6825211yescharacteristic, complemented
404C3#6845611yescharacteristic, complemented
405C2—1441no—
406C2#1059061711yescharacteristic
407C2#1059095111yescharacteristic
408C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#1626
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593861C2semidirect
5. C3×#4484C2semidirect
6. C3×#4482C2semidirect
7. #10589085C2semidirect
39. #4484D3semidirect
40. #4482D3semidirect
125. C3×Dic6SD16semidirect
277. Dic6#204semidirect
352. C32#1626semidirect
403. C3#68252semidirect
404. C3#68456semidirect

Maximal subgroups

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

subgroupindex
#105938612
#105925472
#105903672
#105902812
C3×#44842
C3×#44822
#105890852
#684563
#682523