Finite Group Databasebeta

← #11796537

Subgroups — #11796537

Order 1152.

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

normal subgroups only

This group has 490 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×#5724C211yesmaximal, characteristic
2D3×#836C212yesmaximal, complemented
3#10589414C211yesmaximal, characteristic, complemented
4C3×#4548C211yesmaximal, characteristic, complemented
5#10589182C212yesmaximal, complemented
6#71872—31nomaximal
7#69171—31nomaximal
8C2×C3×#239C411yescharacteristic
9C2×C3×D3×Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C3×#947C2211yescharacteristic
12C3×#944C411yescharacteristic
13C3×#896—22no—
14C3×#894—22no—
15C3×#875C411yescharacteristic
16C3×#872C411yescharacteristic
17D3×#208—22no—
18#63663C2212yes—
19C3×#836C2212yes—
20#63560—22no—
21C3×#536—31no—
22#5724D311yescharacteristic
23C2×#836—32no—
24D3×#101—32no—
25C3×#356—31no—
26#4548—31no—
27#4548—31no—
28#4548—61no—
29#4548D311yescharacteristic, complemented
30#4542—32no—
31#4477—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×Q8C2311yescharacteristic
34C3×#239—42no—
35C3×D3×Q8—42no—
36C2×C3×D12—21no—
37C2×C3×D12C2×C411yescharacteristic
38C2×C3×C4×D3—21no—
39C2×C3×C4×D3C2×C411yescharacteristic
40C2×C3×C4×D3D412yes—
41C2×C3×Dic6C2×C411yescharacteristic
42C2×C3×Dic6D412yes—
43C32×C4⋊C4—22no—
44C32×C42C2×C411yescharacteristic
45#3748—22no—
46C3×(C2×D3)⋊C4—21no—
47C3×(C2×D3)⋊C4—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×Dic3⋊C4—22no—
50C3×Dic3⋊C4—21no—
51C3×C4×Dic3C2×C411yescharacteristic
52C3×#208—22no—
53#3711—42no—
54D3×C3⋊C8—42no—
55#2133—91noSylow
56C2×C3×#41—31no—
57C22×C3×Q8—31no—
58C2×#239Dic311yescharacteristic
59C2×D3×Q8C2×D311yescharacteristic
60C3×C4⋊Q8—21no—
61C3×C4⋊Q8—31no—
62C3×C4⋊Q8C2×D311yescharacteristic
63C3×C4⋊Q8C2×D311yescharacteristic
64C3×#124—31no—
65C3×#124—31no—
66C3×#123—62no—
67C3×C22⋊Q8—62no—
68C3×#117—31no—
69#947C2×D311yescharacteristic
70#944Dic311yescharacteristic
71C2×#208—62no—
72D3×M16—62no—
73#896—22no—
74#894—22no—
75#875Dic311yescharacteristic
76#872Dic311yescharacteristic
77C3×#101—32no—
78#836—32no—
79#836—32no—
80#836—62no—
81#836—62no—
82#836C2×D312yes—
83#824—62no—
84C22×C3×D3—21no—
85C22×C3×D3C22⋊C411yescharacteristic
86C32×Q8—41no—
87C32×Q8—41no—
88C2×C32×C4—21no—
89C2×C32×C4—21no—
90C2×C32×C4C22×C411yescharacteristic
91C2×C32×C4C2×D412yes—
92C2×C3×Dic3—21no—
93C2×C3×Dic3C22⋊C412yes—
94C2×C3×Dic3C22⋊C411yescharacteristic
95C3×D12—41no—
96C3×D12—42no—
97C3×C4×D3—22no—
98C3×C4×D3—22no—
99C3×C4×D3—22no—
100C3×C4×D3—42no—
101C3×Dic6—41no—
102C3×Dic6—42no—
103C3⋊(C3⋊C8)—42no—
104C3×C3⋊C8—42no—
105#536—31no—
106C2×#101—92no—
107#356—31no—
108#356—91no—
109#355—92no—
110C3×#41—122no—
111C2×C3×Q8—21no—
112C2×C3×Q8—21no—
113C2×C3×Q8—31no—
114C2×C3×Q8—32no—
115C2×C3×Q8—122no—
116C2×C3×Q8C4×D311yescharacteristic
117C2×C3×Q8C2×Dic311yescharacteristic
118C2×C3×Q8C22×D311yescharacteristic
119C2×C3×Q8C22×D311yescharacteristic
120C2×C3×D4—31no—
121C2×C3×D4—61no—
122C22×C3×C4—31no—
123C22×C3×C4—32no—
124C22×C3×C4—61no—
125#239—42no—
126D3×Q8—42no—
127C2×D12—21no—
128C2×D12C2×Dic311yescharacteristic
129C2×C4×D3—21no—
130C2×C4×D3C2×Dic311yescharacteristic
131C2×C4×D3#6712yes—
132C2×Dic6C2×Dic311yescharacteristic
133C2×Dic6#6712yes—
134C3×M16—62no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—42no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—62no—
140C3×C22⋊C4—62no—
141C3×C22⋊C4—61no—
142C3×C22⋊C4—62no—
143C3×C42—21no—
144C3×C42—31no—
145C3×C42C4×D311yescharacteristic
146C3×C42C2×Dic311yescharacteristic
147(C2×D3)⋊C4—21no—
148(C2×D3)⋊C4—22no—
149(C2×D3)⋊C4—22no—
150Dic3⋊C4—21no—
151Dic3⋊C4—22no—
152C4×Dic3C2×Dic311yescharacteristic
153#208—22no—
154#208—62no—
155#208—62no—
156#208—122no—
157#208—122no—
158C2×C3⋊C8—122no—
159ΓL(1,𝔽25)—122no—
160D3×C8—122no—
161C22×C32C2×C22⋊C411yescharacteristic
162C2×C3×D3—41no—
163C2×C3×D3—42no—
164C2×C3×D3—41no—
165C2×C3×D3#9912yes—
166C32×C4—22no—
167C32×C4—21no—
168C32×C4—41no—
169C32×C4—41no—
170C3×Dic3—21no—
171C3×Dic3—22no—
172C3×Dic3—41no—
173C2×#41—31no—
174C22×Q8—31no—
175C2×M16—182no—
176C4⋊Q8—31no—
177C4⋊Q8D3211yescharacteristic
178#124—31no—
179#124—31no—
180#123—62no—
181C22⋊Q8—62no—
182#117—31no—
183#101—32no—
184#101—92no—
185#101—182no—
186C23×C3—31no—
187C23×C3—61no—
188C22×D3—21no—
189C22×D3#21711yescharacteristic
190C3×Q8—41no—
191C3×Q8—41no—
192C3×Q8—41no—
193C3×Q8—41no—
194C3×Q8—81no—
195C3×Q8—81no—
196C3×Q8—122no—
197C3×Q8—121no—
198C3×D4—121no—
199C3×D4—122no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—32no—
207C2×C3×C4—31no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—62no—
211C2×C3×C4—62no—
212C2×C3×C4—62no—
213C2×C3×C4—61no—
214C2×C3×C4—122no—
215C2×C3×C4C2×C4×D311yescharacteristic
216C2×C3×C4D3×D412yes—
217C2×C3×C4C22×Dic311yescharacteristic
218C2×C3×C4C2×#6712yes—
219C2×Dic3—21no—
220C2×Dic3#21712yes—
221C2×Dic3#21711yescharacteristic
222D12—41no—
223D12—42no—
224C4×D3—22no—
225C4×D3—22no—
226C4×D3—22no—
227C4×D3—42no—
228Dic6—41no—
229Dic6—42no—
230C3×C8—122no—
231C3⋊C8—42no—
232C3⋊C8—122no—
233C3⋊C8—122no—
234C3⋊C8—242no—
235C2×C32—21no—
236C2×C32C2×#9911yescharacteristic
237C3×D3—22no—
238C3×D3—81no—
239#41—122no—
240C2×Q8—31no—
241C2×Q8—32no—
242C2×Q8—122no—
243C2×Q8D3×Dic311yescharacteristic
244C2×Q8C2×D3211yescharacteristic
245C2×D4—31no—
246C2×D4—61no—
247C22×C4—31no—
248C22×C4—32no—
249C22×C4—61no—
250M16—62no—
251M16—182no—
252M16—362no—
253C2×C8—362no—
254C4⋊C4—22no—
255C4⋊C4—61no—
256C4⋊C4—62no—
257C22⋊C4—62no—
258C22⋊C4—61no—
259C22⋊C4—62no—
260C42—31no—
261C42D3×Dic311yescharacteristic
262C22×C3—21no—
263C22×C3—32no—
264C22×C3—121no—
265C22×C3—122no—
266C22×C3—121no—
267C22×C3D3×C22⋊C411yescharacteristic
268C22×C3C2×#21711yescharacteristic
269C2×D3—41no—
270C2×D3—42no—
271C2×D3—41no—
272C2×D3#83412yes—
273C3×C4—22no—
274C3×C4—21no—
275C3×C4—22no—
276C3×C4—21no—
277C3×C4—42no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—42no—
282C3×C4—41no—
283C3×C4—41no—
284C3×C4—61no—
285C3×C4—62no—
286C3×C4—81no—
287C3×C4—121no—
288Dic3—21no—
289Dic3—22no—
290Dic3—41no—
291C32#213311yescharacteristic, complemented, Sylow
292C23—31no—
293C23—61no—
294Q8—41no—
295Q8—41no—
296Q8—122no—
297Q8—121no—
298D4—121no—
299D4—122no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—32no—
303C2×C4—31no—
304C2×C4—62no—
305C2×C4—62no—
306C2×C4—62no—
307C2×C4—61no—
308C2×C4—122no—
309C2×C4C2×D3×Dic311yescharacteristic
310C2×C4D3×#6712yes—
311C8—122no—
312C8—362no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—41no—
317C2×C3—62no—
318C2×C3—241no—
319C2×C3D3×#9911yescharacteristic
320C2×C3C2×#83411yescharacteristic
321D3—22no—
322D3—81no—
323C22—32no—
324C22—121no—
325C22—122no—
326C22—121no—
327C22D3×#21711yescharacteristic
328C4—22no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—61no—
333C4—62no—
334C4—121no—
335C3—21no—
336C3#6917111yescharacteristic, complemented
337C3#7187211yescharacteristic, complemented
338C2—21no—
339C2—62no—
340C2—241no—
341C2D3×#83411yescharacteristic
subgroupG/H
centerC2D3×#834
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×C4⋊Q8C22
socleC2×C32C2×#99
prime radicalC2×C3×#239C4
cosocleC2×C32×Q8C23
hypercenterC4⋊Q8D32
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. D3×#836C2semidirect
3. #10589414C2semidirect
4. C3×#4548C2semidirect
5. #10589182C2semidirect
29. #4548D3semidirect
291. C32#2133semidirect
336. C3#69171semidirect
337. C3#71872semidirect

Maximal subgroups

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

subgroupindex
C3×#57242
D3×#8362
#105894142
C3×#45482
#105891822
#718723
#691713