Finite Group Databasebeta

← #11796509

Subgroups — #11796509

Order 1152.

655 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 655 conjugacy classes of subgroups — too many to draw. Only its 108 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#10596303C211yesmaximal, characteristic
2C3×#5237C212yesmaximal, complemented
3#10589185C212yesmaximal, complemented
4#10589183C212yesmaximal, complemented
5#70148—32nomaximal
6C2×C32×#41C2211yescharacteristic
7C2×#3828C411yescharacteristic
8#64156C2211yescharacteristic
9#64153C2211yescharacteristic
10#64149C411yescharacteristic
11#64148—22no—
12#64145C411yescharacteristic
13C4×#638—22no—
14C2×C4×C3⋊Dic3C411yescharacteristic
15C2×C3×#208—22no—
16C3×#836C2214yes—
17C3×#833—22no—
18#5832—32no—
19#5832—61no—
20C3×#413—32no—
21#5237D312yescomplemented
22#4478—34no—
23#4477—34no—
24C32×#41—41no—
25C32×#41—41no—
26C2×C32×Q8C2311yescharacteristic
27C2×C32×D4C2×C411yescharacteristic
28C2×C32×D4D412yes—
29C22×C32×C4C2×C411yescharacteristic
30C22×C32×C4D412yes—
31C2×#638—21no—
32C2×#638—22no—
33C22×C3⋊Dic3—21no—
34#3828—41no—
35#3828—41no—
36C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×#634C2×C411yescharacteristic
39#3757—22no—
40#3752—22no—
41#3750—22no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3C2×C411yescharacteristic
44C4×C3⋊Dic3C2×C411yescharacteristic
45C3×#208—24no—
46C3×#208—42no—
47C2×C3×C3⋊C8—42no—
48#2132—91noSylow
49C2×C3×#41—21no—
50C2×C3×#41C2×D312yes—
51C2×#235—32no—
52C2×#235—61no—
53C2×C3×M16—62no—
54#947—32no—
55#947—61no—
56#944—32no—
57#944—61no—
58#940—32no—
59#940—61no—
60#939—64no—
61#939—62no—
62#939—62no—
63#936—32no—
64#936—61no—
65C4×#67—64no—
66C4×#67—62no—
67C4×#67—62no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C2×#208—22no—
71C3×#101—34no—
72C3×#100—62no—
73#836C2×D314yes—
74#833—22no—
75C23×C32C22⋊C412yes—
76C23×C32C22⋊C411yescharacteristic
77C22×C3⋊D3—21no—
78C32×Q8—41no—
79C32×D4—41no—
80C32×D4—42no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22×C411yescharacteristic
87C2×C32×C4C2×D412yes—
88#638—44no—
89#638—42no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—42no—
94C4⋊(C3⋊D3)—41no—
95C4×C3⋊D3—41no—
96C4×C3⋊D3—41no—
97#634—41no—
98C3×C3⋊C8—44no—
99#532—91no—
100#413—32no—
101#356—92no—
102#355—92no—
103C3×#41—42no—
104C3×#41—42no—
105C3×#41—42no—
106C3×#41—42no—
107C2×C3×Q8—21no—
108C2×C3×Q8C22×D312yes—
109C2×C3×D4—21no—
110C2×C3×D4—22no—
111C2×C3×D4C4×D312yes—
112C2×C3×D4D1212yes—
113C2×C3×D4#6712yes—
114C22×C3×C4—21no—
115C22×C3×C4—22no—
116C22×C3×C4C4×D312yes—
117C22×C3×C4D1212yes—
118C22×C3×C4#6712yes—
119C2×#67—64no—
120C2×#67—62no—
121C2×#67—62no—
122C2×#67—62no—
123C2×#67—62no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126#235—122no—
127#235—122no—
128#235—122no—
129#235—122no—
130C2×D12—32no—
131C2×D12—61no—
132C2×C4×D3—62no—
133C2×C4×D3—62no—
134C2×Dic6—32no—
135C2×Dic6—61no—
136C3×M16—64no—
137C3×M16—122no—
138C2×C3×C8—122no—
139#217—64no—
140#217—62no—
141#217—62no—
142(C2×D3)⋊C4—64no—
143(C2×D3)⋊C4—62no—
144(C2×D3)⋊C4—62no—
145Dic3⋊C4—64no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148C4×Dic3—32no—
149C4×Dic3—32no—
150C4×Dic3—61no—
151C4×Dic3—61no—
152C4×Dic3—62no—
153C4×Dic3—62no—
154#208—24no—
155#208—42no—
156C2×C3⋊C8—42no—
157C22×C32—21no—
158C22×C32—22no—
159C22×C32—41no—
160C22×C32—42no—
161C22×C32C2×C22⋊C411yescharacteristic
162C2×C3⋊D3—42no—
163C2×C3⋊D3—41no—
164C32×C4—21no—
165C32×C4—22no—
166C32×C4#9911yescharacteristic
167C32×C4#9911yescharacteristic
168C3⋊Dic3—22no—
169C3⋊Dic3—41no—
170C3⋊Dic3—41no—
171C2×#41—91no—
172C2×#41D3211yescharacteristic
173C2×M16—62no—
174C4⋊Q8—91no—
175#127—91no—
176#124—91no—
177#124—91no—
178#121—182no—
179C4×D4—182no—
180C2×C42—91no—
181#101—34no—
182#100—62no—
183C23×C3—21no—
184C23×C3—22no—
185C23×C3(C2×D3)⋊C412yes—
186C23×C3(C2×D3)⋊C412yes—
187C23×C3(C2×D3)⋊C412yes—
188C22×D3—62no—
189C22×D3—62no—
190C3×Q8—42no—
191C3×Q8—42no—
192C3×D4—42no—
193C3×D4—42no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—44no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—22no—
208C2×C3×C4—42no—
209C2×C3×C4—42no—
210C2×C3×C4(C2×D3)⋊C412yes—
211C2×C3×C4C2×C4×D312yes—
212C2×C3×C4C2×D1212yes—
213C2×C3×C4C2×#6712yes—
214#67—124no—
215#67—124no—
216#67—128no—
217#67—124no—
218#67—124no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—124no—
226C2×Dic3—124no—
227D12—122no—
228D12—122no—
229C4×D3—122no—
230C4×D3—122no—
231C4×D3—122no—
232C4×D3—122no—
233Dic6—122no—
234Dic6—122no—
235C3×C8—124no—
236C3⋊C8—44no—
237C2×C32—21no—
238C2×C32—41no—
239C2×C32—42no—
240C2×C32C2×#9911yescharacteristic
241C3⋊D3—81no—
242#41—41no—
243#41—41no—
244#41—361no—
245#41—361no—
246C2×Q8—91no—
247C2×Q8C2×D3211yescharacteristic
248C2×D4—91no—
249C2×D4—182no—
250C2×D4—181no—
251C2×D4#62411yescharacteristic
252C2×D4#62612yes—
253C22×C4—181no—
254C22×C4—181no—
255C22×C4#62411yescharacteristic
256C22×C4#62612yes—
257M16—64no—
258M16—122no—
259C2×C8—122no—
260C4⋊C4—182no—
261C22⋊C4—182no—
262C22⋊C4—182no—
263C42—91no—
264C42—91no—
265C42—181no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—42no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3—42no—
275C22×C3—42no—
276C22×C3—44no—
277C22×C3C2×(C2×D3)⋊C412yes—
278C2×D3—122no—
279C2×D3—124no—
280C2×D3—122no—
281C2×D3—122no—
282C2×D3—122no—
283C3×C4—22no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—42no—
290C3×C4#80612yes—
291C3×C4#80612yes—
292Dic3—64no—
293Dic3—64no—
294Dic3—122no—
295Dic3—122no—
296Dic3—122no—
297Dic3—122no—
298C32#213211yescharacteristic, complemented, Sylow
299C23—181no—
300C23#372212yes—
301C23#372211yescharacteristic
302Q8—41no—
303Q8—361no—
304D4—41no—
305D4—42no—
306D4—361no—
307D4—364no—
308D4—362no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—181no—
314C2×C4—181no—
315C2×C4—181no—
316C2×C4—362no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4#372211yescharacteristic
320C2×C4C2×#62411yescharacteristic
321C2×C4C2×#62612yes—
322C8—124no—
323C2×C3—22no—
324C2×C3—22no—
325C2×C3—21no—
326C2×C3—42no—
327C2×C3—42no—
328C2×C3—42no—
329C2×C3—42no—
330C2×C3—82no—
331C2×C3C2×#80612yes—
332D3—242no—
333D3—242no—
334C22—21no—
335C22—22no—
336C22—41no—
337C22—42no—
338C22—362no—
339C22—361no—
340C22C2×#372211yescharacteristic
341C4—22no—
342C4—21no—
343C4—182no—
344C4—361no—
345C4—361no—
346C4#6358111yescharacteristic
347C4#6358111yescharacteristic
348C3—21no—
349C3#7014812yescomplemented
350C2—21no—
351C2—41no—
352C2—42no—
353C2—721no—
354C2C2×#6358111yescharacteristic
subgroupG/H
centerC4#63581
commutatorC2×C32×C4C22×C4
FrattiniC2×Q8C2×D32
FittingC2×C32×#41C22
socleC2×C32C2×#99
prime radical#10596303C2
cosocleC2×C32×Q8C23
hypercenterC2×#41D32
hypocenterC32#2132
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#5237C2semidirect
3. #10589185C2semidirect
4. #10589183C2semidirect
21. #5237D3semidirect
298. C32#2132semidirect
349. C3#70148semidirect

Maximal subgroups

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

subgroupindex
#105963032
C3×#52372
#105891852
#105891832
#701483