Finite Group Databasebeta

← #11796533

Subgroups — #11796533

Order 1152.

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

normal subgroups only

This group has 492 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×#5675C211yesmaximal, characteristic
2D3×#836C212yesmaximal, complemented
3#10589408C211yesmaximal, characteristic, complemented
4C3×#4542C211yesmaximal, characteristic, complemented
5#10589184C212yesmaximal, complemented
6#71872—31nomaximal
7#69164—31nomaximal
8C2×C3×D3×Q8C2211yescharacteristic
9C2×C3×#237C411yescharacteristic
10C32×#124C2211yescharacteristic
11C3×#944C2211yescharacteristic
12C3×#936C411yescharacteristic
13C3×#883—22no—
14C3×#878—22no—
15C3×#872C411yescharacteristic
16C3×#869C411yescharacteristic
17D3×#208—22no—
18#63663C2212yes—
19C3×#836C2212yes—
20#63560—22no—
21C3×#536—31no—
22#5675D311yescharacteristic
23C2×#836—32no—
24D3×#101—32no—
25C3×#355—31no—
26#4548—32no—
27#4542—31no—
28#4542—31no—
29#4542—61no—
30#4542D311yescharacteristic, complemented
31#4478—32no—
32C2×C32×Q8C2311yescharacteristic
33C2×C32×D4C2×C411yescharacteristic
34C2×C3×#67—21no—
35C22×C3×Dic3—21no—
36C3×D3×Q8—42no—
37C3×#237—42no—
38C2×C3×C4×D3C2×C411yescharacteristic
39C2×C3×C4×D3D412yes—
40C2×C3×Dic6C2×C411yescharacteristic
41C2×C3×Dic6C2×C411yescharacteristic
42C2×C3×Dic6D412yes—
43C32×C22⋊C4—22no—
44C32×C42C2×C411yescharacteristic
45#3748—22no—
46C3×#217—22no—
47C3×(C2×D3)⋊C4—21no—
48C3×C4⋊Dic3—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×D3×Q8C2×D311yescharacteristic
59C2×#237Dic311yescharacteristic
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8—31no—
62C3×#124—21no—
63C3×#124—31no—
64C3×#124C2×D311yescharacteristic
65C3×#124C2×D311yescharacteristic
66C3×#123—62no—
67C3×C22⋊Q8—62no—
68C3×#117—31no—
69#944C2×D311yescharacteristic
70#936Dic311yescharacteristic
71C2×#208—62no—
72D3×M16—62no—
73#883—22no—
74#878—22no—
75#872Dic311yescharacteristic
76#869Dic311yescharacteristic
77C3×#101—32no—
78#836—32no—
79#836—32no—
80#836—62no—
81#836—62no—
82#836C2×D312yes—
83#824—62no—
84C23×C32—21no—
85C22×C3×D3C22⋊C411yescharacteristic
86C32×Q8—41no—
87C32×D4—41no—
88C2×C32×C4—21no—
89C2×C32×C4C22×C411yescharacteristic
90C2×C32×C4C2×D412yes—
91C3×#67—42no—
92C2×C3×Dic3—21no—
93C2×C3×Dic3—21no—
94C2×C3×Dic3—42no—
95C2×C3×Dic3C22⋊C411yescharacteristic
96C2×C3×Dic3C22⋊C412yes—
97C3×C4×D3—22no—
98C3×C4×D3—22no—
99C3×C4×D3—22no—
100C3×Dic6—41no—
101C3×Dic6—42no—
102C3×Dic6—41no—
103C3⋊(C3⋊C8)—42no—
104C3×C3⋊C8—42no—
105#536—31no—
106C2×#101—92no—
107#356—92no—
108#355—31no—
109#355—91no—
110C3×#41—122no—
111C2×C3×Q8—21no—
112C2×C3×Q8—31no—
113C2×C3×Q8—32no—
114C2×C3×Q8—31no—
115C2×C3×Q8—122no—
116C2×C3×Q8C22×D311yescharacteristic
117C2×C3×Q8C22×D311yescharacteristic
118C2×C3×D4—21no—
119C2×C3×D4—61no—
120C2×C3×D4C4×D311yescharacteristic
121C2×C3×D4C2×Dic311yescharacteristic
122C22×C3×C4—31no—
123C22×C3×C4—32no—
124C22×C3×C4—61no—
125C2×#67—21no—
126C22×Dic3—21no—
127D3×Q8—42no—
128#237—42no—
129C2×C4×D3C2×Dic311yescharacteristic
130C2×C4×D3#6712yes—
131C2×Dic6C2×Dic311yescharacteristic
132C2×Dic6C2×Dic311yescharacteristic
133C2×Dic6#6712yes—
134C3×M16—62no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—62no—
137C3×C4⋊C4—62no—
138C3×C22⋊C4—22no—
139C3×C22⋊C4—22no—
140C3×C22⋊C4—42no—
141C3×C22⋊C4—61no—
142C3×C22⋊C4—62no—
143C3×C42—21no—
144C3×C42—31no—
145C3×C42C4×D311yescharacteristic
146C3×C42C2×Dic311yescharacteristic
147#217—22no—
148(C2×D3)⋊C4—21no—
149C4⋊Dic3—22no—
150Dic3⋊C4—22no—
151Dic3⋊C4—21no—
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×C32—42no—
162C22×C32—41no—
163C22×C32C2×C22⋊C411yescharacteristic
164C2×C3×D3—41no—
165C2×C3×D3#9912yes—
166C32×C4—22no—
167C32×C4—21no—
168C32×C4—41no—
169C3×Dic3—21no—
170C3×Dic3—22no—
171C3×Dic3—41no—
172C3×Dic3—41no—
173C2×#41—31no—
174C22×Q8—31no—
175C2×M16—182no—
176C4⋊Q8—31no—
177C4⋊Q8—31no—
178#124—31no—
179#124D3211yescharacteristic
180#123—62no—
181C22⋊Q8—62no—
182#117—31no—
183#101—32no—
184#101—92no—
185#101—182no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—31no—
189C23×C3—41no—
190C22×D3#21711yescharacteristic
191C3×Q8—41no—
192C3×Q8—41no—
193C3×Q8—81no—
194C3×Q8—122no—
195C3×Q8—121no—
196C3×Q8—121no—
197C3×D4—41no—
198C3×D4—41no—
199C3×D4—81no—
200C3×D4—122no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—22no—
205C2×C3×C4—32no—
206C2×C3×C4—31no—
207C2×C3×C4—41no—
208C2×C3×C4—62no—
209C2×C3×C4—62no—
210C2×C3×C4—62no—
211C2×C3×C4—61no—
212C2×C3×C4—61no—
213C2×C3×C4—122no—
214C2×C3×C4C2×C4×D311yescharacteristic
215C2×C3×C4D3×D412yes—
216C2×C3×C4C22×Dic311yescharacteristic
217C2×C3×C4C2×#6712yes—
218#67—42no—
219C2×Dic3—21no—
220C2×Dic3—21no—
221C2×Dic3—42no—
222C2×Dic3#21711yescharacteristic
223C2×Dic3#21712yes—
224C4×D3—22no—
225C4×D3—22no—
226C4×D3—22no—
227Dic6—41no—
228Dic6—42no—
229Dic6—41no—
230C3×C8—122no—
231C3⋊C8—42no—
232C3⋊C8—122no—
233C3⋊C8—122no—
234C3⋊C8—242no—
235C2×C32—21no—
236C2×C32—81no—
237C2×C32C2×#9911yescharacteristic
238C3×D3—22no—
239#41—122no—
240C2×Q8—31no—
241C2×Q8—32no—
242C2×Q8—31no—
243C2×Q8—122no—
244C2×Q8C2×D3211yescharacteristic
245C2×D4—61no—
246C2×D4D3×Dic311yescharacteristic
247C22×C4—31no—
248C22×C4—32no—
249C22×C4—61no—
250M16—62no—
251M16—182no—
252M16—362no—
253C2×C8—362no—
254C4⋊C4—61no—
255C4⋊C4—62no—
256C4⋊C4—62no—
257C22⋊C4—22no—
258C22⋊C4—61no—
259C22⋊C4—62no—
260C42—31no—
261C42D3×Dic311yescharacteristic
262C22×C3—21no—
263C22×C3—32no—
264C22×C3—42no—
265C22×C3—42no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—81no—
269C22×C3—82no—
270C22×C3—121no—
271C22×C3D3×C22⋊C411yescharacteristic
272C22×C3C2×#21711yescharacteristic
273C2×D3—41no—
274C2×D3#83412yes—
275C3×C4—22no—
276C3×C4—21no—
277C3×C4—22no—
278C3×C4—21no—
279C3×C4—42no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—41no—
283C3×C4—61no—
284C3×C4—62no—
285C3×C4—81no—
286C3×C4—121no—
287C3×C4—121no—
288Dic3—21no—
289Dic3—22no—
290Dic3—41no—
291Dic3—41no—
292C32#213311yescharacteristic, complemented, Sylow
293C23—21no—
294C23—31no—
295Q8—41no—
296Q8—122no—
297Q8—121no—
298Q8—121no—
299D4—41no—
300D4—122no—
301C2×C4—21no—
302C2×C4—32no—
303C2×C4—31no—
304C2×C4—62no—
305C2×C4—62no—
306C2×C4—62no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—122no—
310C2×C4C2×D3×Dic311yescharacteristic
311C2×C4D3×#6712yes—
312C8—122no—
313C8—362no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—41no—
318C2×C3—62no—
319C2×C3—81no—
320C2×C3—81no—
321C2×C3—161no—
322C2×C3D3×#9911yescharacteristic
323C2×C3C2×#83411yescharacteristic
324D3—22no—
325C22—32no—
326C22—42no—
327C22—41no—
328C22—121no—
329C22D3×#21711yescharacteristic
330C4—22no—
331C4—21no—
332C4—41no—
333C4—61no—
334C4—62no—
335C4—121no—
336C4—121no—
337C3—21no—
338C3#6916411yescharacteristic, complemented
339C3#7187211yescharacteristic, complemented
340C2—21no—
341C2—62no—
342C2—81no—
343C2D3×#83411yescharacteristic
subgroupG/H
centerC2D3×#834
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC32×#124C22
socleC2×C32C2×#99
prime radicalC2×C3×#237C4
cosocleC2×C32×Q8C23
hypercenter#124D32
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
2. D3×#836C2semidirect
3. #10589408C2semidirect
4. C3×#4542C2semidirect
5. #10589184C2semidirect
30. #4542D3semidirect
292. C32#2133semidirect
338. C3#69164semidirect
339. C3#71872semidirect

Maximal subgroups

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

subgroupindex
C3×#56752
D3×#8362
#105894082
C3×#45422
#105891842
#718723
#691643