Finite Group Databasebeta

← #11781937

Subgroups — #11781937

Order 1152.

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

normal subgroups only

This group has 392 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#10592718C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic
3C3×#5012C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71041—31nomaximal
9#70873—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3754—21no—
12#64078C2211yescharacteristic
13C2×C3×#214—21no—
14C2×C3×#208—21no—
15C3×#869C2211yescharacteristic
16#63637—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#830—21no—
19C3×#810—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63575—21no—
24#63575—21no—
25C3×#461—31no—
26C3×#436—31no—
27#5078—31no—
28#5019—31no—
29#5019—31no—
30#5019—61no—
31#5019D311yescharacteristic
32#5012D311yescharacteristic
33#4682—31no—
34#4547—31no—
35#4486—31no—
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47#3754—42no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×#214—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×#208—42no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#1693—91noSylow
60C2×C3×SD16—61no—
61C2×C3×M16—61no—
62C3×C4⋊Q8—31no—
63C3×C4×D4—21no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C2×D311yescharacteristic
66C2×#214—21no—
67C2×#214—62no—
68C2×#214—61no—
69C2×#214—61no—
70C2×#208—21no—
71#869—31no—
72#869—31no—
73#869—61no—
74#869C2×D311yescharacteristic
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#103—61no—
78C3×C22⋊C8—61no—
79C3×C4×C8—31no—
80#830—21no—
81#818—61no—
82#818—61no—
83#810—21no—
84#810—62no—
85#810—61no—
86#810—61no—
87#807—61no—
88#807—61no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C23×C32—21no—
96C32×D4—21no—
97C32×D4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—41no—
105#634—41no—
106#634—41no—
107C2×C3×Dic3—41no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8SD1612yescomplemented
115#500—91no—
116#461—31no—
117#461—91no—
118#436—31no—
119#334—91no—
120#332—91no—
121#332—91no—
122C2×C3×Q8—61no—
123C2×C3×D4—21no—
124C2×C3×D4D1211yescharacteristic
125C2×C3×D4#6711yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—41no—
129C2×Dic6—21no—
130C2×Dic6—62no—
131C2×Dic6—61no—
132C2×Dic6—61no—
133C3×SD16—122no—
134C3×M16—122no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—61no—
138C2×C3×C8—61no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—61no—
141C3×C4⋊C4—61no—
142C3×C4⋊C4D1211yescharacteristic
143C3×C4⋊C4#6711yescharacteristic
144C3×C22⋊C4—21no—
145C3×C22⋊C4—21no—
146C3×C22⋊C4—41no—
147C3×C42—21no—
148C3×C42C22×D311yescharacteristic
149C3×C42C22×D311yescharacteristic
150#214—42no—
151#214—124no—
152#214—122no—
153#214—122no—
154C4⋊Dic3—21no—
155C4⋊Dic3—21no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—61no—
160C4⋊Dic3—121no—
161C4⋊Dic3—121no—
162#208—42no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—62no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8#6711yescharacteristic
169C2×C3⋊C8#6711yescharacteristic
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—41no—
173C22×C32#12111yescharacteristic
174C32×C4—21no—
175C32×C4—41no—
176C32×C4C2×SD1611yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C32×C4AGL(1,ℤ/8)11yescharacteristic
179C32×C4#13711yescharacteristic
180C3⋊Dic3—81no—
181C3×Dic3—81no—
182C2×SD16—61no—
183C2×SD16—181no—
184C2×M16—61no—
185C4⋊Q8—31no—
186C4⋊Q8—91no—
187C4×D4D3211yescharacteristic
188#107—181no—
189#107—181no—
190C4⋊C8—31no—
191C4⋊C8—31no—
192C4⋊C8—91no—
193#103—61no—
194#103—181no—
195C22⋊C8—61no—
196C4×C8—31no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—41no—
200C3×Q8—121no—
201C3×Q8—121no—
202C3×D4—22no—
203C3×D4—21no—
204C3×D4—21no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—41no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—81no—
219C2×C3×C4—81no—
220C2×C3×C4—121no—
221C2×C3×C4C2×D1211yescharacteristic
222C2×C3×C4#23511yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4#23711yescharacteristic
225C2×C3×C4C2×#6711yescharacteristic
226C2×C3×C4C2×#6711yescharacteristic
227C2×Dic3—41no—
228C2×Dic3—122no—
229C2×Dic3—121no—
230C2×Dic3—121no—
231Dic6—41no—
232Dic6—41no—
233Dic6—122no—
234Dic6—122no—
235Dic6—121no—
236Dic6—121no—
237Dic6—121no—
238Dic6—121no—
239C3×C8—32no—
240C3×C8—61no—
241C3×C8—121no—
242C3×C8—121no—
243C3⋊C8—21no—
244C3⋊C8—41no—
245C3⋊C8—41no—
246C3⋊C8—122no—
247C3⋊C8—121no—
248C3⋊C8—121no—
249C3⋊C8#21412yescomplemented
250C2×C32—81no—
251C2×C32#46111yescharacteristic
252C2×C32#46911yescharacteristic
253C2×C32#47311yescharacteristic
254C2×Q8—61no—
255C2×Q8—181no—
256C2×D4#62611yescharacteristic
257C22×C4—21no—
258SD16—122no—
259SD16—362no—
260M16—122no—
261C2×C8—31no—
262C2×C8—31no—
263C2×C8—61no—
264C2×C8—61no—
265C2×C8—181no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—181no—
269C4⋊C4—181no—
270C4⋊C4#62611yescharacteristic
271C22⋊C4—21no—
272C42C2×D3211yescharacteristic
273C22×C3—21no—
274C22×C3—42no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—41no—
281C22×C3—81no—
282C22×C3—81no—
283C22×C3#93011yescharacteristic
284C22×C3#93911yescharacteristic
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—41no—
294C3×C4—81no—
295C3×C4—241no—
296C3×C4#90811yescharacteristic
297C3×C4#90811yescharacteristic
298C3×C4D3×SD1611yescharacteristic
299C3×C4#91511yescharacteristic
300C3×C4#93211yescharacteristic
301C3×C4C2×#21411yescharacteristic
302C3×C4#94911yescharacteristic
303C3×C4#95111yescharacteristic
304Dic3—81no—
305Dic3—242no—
306Dic3—241no—
307Dic3—241no—
308C32#169311yescharacteristic, complemented, Sylow
309C23—21no—
310Q8—121no—
311Q8—121no—
312Q8—361no—
313Q8—361no—
314D4—21no—
315D4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—121no—
320C2×C4—361no—
321C2×C4#380411yescharacteristic
322C2×C4C2×#62611yescharacteristic
323C2×C4D3×#6711yescharacteristic
324C8—32no—
325C8—61no—
326C8—121no—
327C8—121no—
328C8—361no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—82no—
333C2×C3—81no—
334C2×C3—81no—
335C2×C3#501911yescharacteristic
336C2×C3#503911yescharacteristic
337C2×C3#513511yescharacteristic
338C2×C3#514311yescharacteristic
339C2×C3#516211yescharacteristic
340C2×C3#520411yescharacteristic
341C22—41no—
342C22—41no—
343C22—41no—
344C22#6397811yescharacteristic
345C4—21no—
346C4—41no—
347C4—241no—
348C4—721no—
349C4#6382511yescharacteristic
350C4#6383011yescharacteristic
351C4D3×#21411yescharacteristic
352C4#6392911yescharacteristic
353C3—21no—
354C3#7087311yescharacteristic, complemented
355C3#7104111yescharacteristic, complemented
356C2—81no—
357C2#1059116511yescharacteristic
358C2#1059148911yescharacteristic
359C2#1059168211yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1693
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10590311C2semidirect
5. #10589097C2semidirect
6. #10589094C2semidirect
7. #10589092C2semidirect
114. C3×C3⋊C8SD16semidirect
249. C3⋊C8#214semidirect
308. C32#1693semidirect
354. C3#70873semidirect
355. C3#71041semidirect

Maximal subgroups

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

subgroupindex
#105927182
C3×#50192
C3×#50122
#105903112
#105890972
#105890942
#105890922
#710413
#708733