Finite Group Databasebeta

← #11779063

Subgroups — #11779063

Order 1152.

520 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 92 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#10593856C211yesmaximal, characteristic, complemented
2#10592547C211yesmaximal, characteristic
3#10590373C211yesmaximal, characteristic
4#10590367C211yesmaximal, characteristic
5C3×#4484C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#68504—31nomaximal
9#68264—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63919—21no—
16#63918—21no—
17#63844—21no—
18#63843—21no—
19#63839—22no—
20C2×#3717—21no—
21C2×#3717—22no—
22C32×C4⋊C8C2211yescharacteristic
23#63648—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25C3×C4×C3⋊C8C2211yescharacteristic
26#63564—21no—
27#5722—31no—
28Q8×Dic6—31no—
29#5085—31no—
30#5027—31no—
31#4848—31no—
32#4848—31no—
33#4848—31no—
34#4848—61no—
35#4693—31no—
36C3×#333—31no—
37C3×Q8⋊C8—31no—
38#4484—31no—
39#4484D311yescharacteristic, complemented
40#4481D311yescharacteristic, complemented
41#4456—31no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×#634D411yescharacteristic
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D412yes—
48C2×#627—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54#3744—42no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62#3724—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#3717—44no—
66#3717—42no—
67#1623—91noSylow
68C3×C4⋊Q8—31no—
69C3×C4×Q8—31no—
70Q8×Dic3—61no—
71#944—62no—
72C2×#215—61no—
73C2×#215—62no—
74C2×#204—61no—
75C2×#204—61no—
76C2×#204—62no—
77C2×#204—62no—
78C2×#204—61no—
79#888—61no—
80#888—61no—
81#888—62no—
82#888—61no—
83#887—61no—
84#887—61no—
85#874—31no—
86#874—31no—
87#874—61no—
88#869—61no—
89#869C2×D311yescharacteristic
90C4×Dic6—31no—
91C4×Dic6—31no—
92C4×Dic6—61no—
93C4×Dic6—61no—
94C4×Dic6C2×D311yescharacteristic
95C3×C4⋊C8—21no—
96C3×C4⋊C8—31no—
97C3×C4⋊C8C2×D311yescharacteristic
98C3×C4⋊C8C2×D311yescharacteristic
99C3×C4×C8—31no—
100#821—61no—
101#821—61no—
102#821—62no—
103#821—61no—
104#809—61no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊D3—41no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115C4⋊(C3⋊D3)—42no—
116C4⋊(C3⋊D3)—41no—
117C4⋊(C3⋊D3)—41no—
118#634—21no—
119#634SD1612yescomplemented
120C2×C3×Dic3—21no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C3×Dic6—21no—
124C3×Dic6—42no—
125C3×Dic6SD1612yescomplemented
126#627—82no—
127C32×C8—41no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—41no—
130Q82—91no—
131#492—91no—
132#460—91no—
133#460—91no—
134#333—31no—
135Q8⋊C8—31no—
136Q8⋊C8—91no—
137C2×C3×Q8—31no—
138C2×C3×Q8—32no—
139C2×D12—62no—
140C2×D12—61no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—61no—
144C2×D12—61no—
145C2×D12—61no—
146C2×D12—121no—
147C2×D12—121no—
148C2×Dic6—31no—
149C2×Dic6—31no—
150C2×Dic6—61no—
151C2×Dic6—62no—
152C2×Dic6—62no—
153C2×Dic6D1211yescharacteristic
154C2×Dic6D1212yes—
155C2×C3×C8—22no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C3×C4⋊C4—31no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—61no—
164C3×C42—21no—
165C3×C42—61no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#215—124no—
169#215—122no—
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—31no—
173C4⋊Dic3—31no—
174C4⋊Dic3—61no—
175C4⋊Dic3—62no—
176C4⋊Dic3D1211yescharacteristic
177Dic3⋊C4—21no—
178Dic3⋊C4—62no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—121no—
184C4×Dic3—21no—
185C4×Dic3—62no—
186C4×Dic3—62no—
187C4×Dic3—61no—
188C4×Dic3—61no—
189C4×Dic3—121no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—21no—
192#204—122no—
193#204—122no—
194#204—124no—
195#204—124no—
196#204—122no—
197C22×C32#12011yescharacteristic
198C2×C3⋊D3—81no—
199C2×C3⋊D3—81no—
200C2×C3⋊D3—81no—
201C32×C4—21no—
202C32×C4C2×SD1611yescharacteristic
203C32×C4C2×SD1611yescharacteristic
204C32×C4#13711yescharacteristic
205C32×C4#13711yescharacteristic
206C3⋊Dic3—22no—
207C3⋊Dic3—41no—
208C3×Dic3—22no—
209C3×Dic3—41no—
210C3×Dic3—42no—
211C2×SD16—181no—
212C2×SD16—181no—
213C2×SD16—182no—
214C4⋊Q8—31no—
215C4⋊Q8—181no—
216C4⋊Q8—181no—
217C4⋊Q8—182no—
218#127—91no—
219C4×Q8—31no—
220C4×Q8—91no—
221C4×Q8—181no—
222C4×Q8—181no—
223C4⋊C8—31no—
224C4⋊C8D3211yescharacteristic
225#102—181no—
226#102—181no—
227C4×C8—31no—
228C22×D3—122no—
229C22×D3—121no—
230C22×D3—121no—
231C3×Q8—32no—
232C3×Q8—61no—
233C3×Q8—122no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—61no—
238C2×C3×C4—62no—
239C2×C3×C4—61no—
240C2×C3×C4C2×D1211yescharacteristic
241C2×C3×C4C2×D1211yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—22no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—121no—
254C2×Dic3—121no—
255D12—122no—
256D12—122no—
257D12—122no—
258D12—122no—
259D12—121no—
260D12—121no—
261D12—121no—
262D12—121no—
263D12—121no—
264D12—121no—
265D12—121no—
266D12—121no—
267D12—241no—
268D12—241no—
269D12—242no—
270Dic6—21no—
271Dic6—32no—
272Dic6—32no—
273Dic6—42no—
274Dic6—62no—
275Dic6—61no—
276Dic6—61no—
277Dic6—121no—
278Dic6—242no—
279Dic6—242no—
280Dic6#20412yescomplemented
281C3×C8—42no—
282C3×C8—41no—
283C3×C8—41no—
284C3×C8—62no—
285C3×C8—121no—
286C3⋊C8—22no—
287C3⋊C8—41no—
288C2×C32#44811yescharacteristic
289C2×C32#44811yescharacteristic
290C2×C32#45311yescharacteristic
291C3⋊D3—161no—
292C2×Q8—31no—
293C2×Q8—32no—
294C2×Q8—91no—
295C2×Q8—182no—
296C2×D4—181no—
297C2×D4—181no—
298C2×D4—181no—
299SD16—362no—
300SD16—364no—
301SD16—362no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—61no—
305C4⋊C4—31no—
306C4⋊C4—61no—
307C4⋊C4—61no—
308C4⋊C4—61no—
309C4⋊C4—91no—
310C4⋊C4—182no—
311C4⋊C4—182no—
312C4⋊C4—181no—
313C42—61no—
314C42—182no—
315C42—181no—
316C42C2×D3211yescharacteristic
317C22×C3—21no—
318C22×C3#88211yescharacteristic
319C22×C3#88211yescharacteristic
320C2×D3—242no—
321C2×D3—242no—
322C2×D3—242no—
323C2×D3—241no—
324C2×D3—241no—
325C2×D3—241no—
326C2×D3—241no—
327C2×D3—241no—
328C2×D3—241no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—62no—
337C3×C4—121no—
338C3×C4—122no—
339C3×C4C2×#20411yescharacteristic
340C3×C4#90911yescharacteristic
341C3×C4D3×SD1611yescharacteristic
342C3×C4D3×SD1611yescharacteristic
343C3×C4D3×SD1611yescharacteristic
344C3×C4#91811yescharacteristic
345C3×C4#91811yescharacteristic
346C3×C4#91811yescharacteristic
347Dic3—22no—
348Dic3—42no—
349Dic3—41no—
350Dic3—62no—
351Dic3—62no—
352Dic3—122no—
353Dic3—121no—
354Dic3—121no—
355Dic3—241no—
356C32#162311yescharacteristic, complemented, Sylow
357C23—361no—
358Q8—32no—
359Q8—61no—
360Q8—92no—
361Q8—122no—
362Q8—181no—
363Q8—722no—
364D4—362no—
365D4—361no—
366D4—361no—
367D4—361no—
368D4—361no—
369C2×C4—61no—
370C2×C4—61no—
371C2×C4—62no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4D3×D1211yescharacteristic
375C2×C4D3×D1211yescharacteristic
376C2×C4#381111yescharacteristic
377C8—41no—
378C8—62no—
379C8—121no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3#473811yescharacteristic
384C2×C3#474711yescharacteristic
385C2×C3#480611yescharacteristic
386C2×C3#480611yescharacteristic
387C2×C3#480611yescharacteristic
388C2×C3#482211yescharacteristic
389D3—482no—
390D3—481no—
391D3—481no—
392C22—721no—
393C22—721no—
394C22—721no—
395C22#6392311yescharacteristic
396C4—21no—
397C4—62no—
398C4—122no—
399C4—121no—
400C4—182no—
401C4—361no—
402C4D3×#20411yescharacteristic
403C4#6380111yescharacteristic
404C4#6393011yescharacteristic
405C4#6394511yescharacteristic
406C3—21no—
407C3#6826411yescharacteristic, complemented
408C3#6850411yescharacteristic, complemented
409C2—1441no—
410C2#1059060611yescharacteristic
411C2#1059095111yescharacteristic
412C2#1059101511yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#1623
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. #10593856C2semidirect
5. C3×#4484C2semidirect
6. C3×#4481C2semidirect
7. #10589085C2semidirect
39. #4484D3semidirect
40. #4481D3semidirect
119. #634SD16semidirect
125. C3×Dic6SD16semidirect
280. Dic6#204semidirect
356. C32#1623semidirect
407. C3#68264semidirect
408. C3#68504semidirect

Maximal subgroups

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

subgroupindex
#105938562
#105925472
#105903732
#105903672
C3×#44842
C3×#44812
#105890852
#685043
#682643