Finite Group Databasebeta

← #11796375

Subgroups — #11796375

Order 1152.

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

normal subgroups only

This group has 671 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×#5240C212yesmaximal, complemented
3#10589181C212yesmaximal, complemented
4#10589179C212yesmaximal, complemented
5#70060—32nomaximal
6C2×C32×#41C2211yescharacteristic
7C2×#3828C411yescharacteristic, complemented
8#64156C411yescharacteristic, complemented
9#64153C411yescharacteristic, complemented
10#64149C2211yescharacteristic
11#64148—22no—
12#64145C2211yescharacteristic
13C4×#638—22no—
14C2×C4×C3⋊Dic3C411yescharacteristic, complemented
15C3×#926—22no—
16C3×#834—22no—
17C3×#834C2214yes—
18#5832—32no—
19#5832—61no—
20C3×#410—32no—
21#5240D312yescomplemented
22#4474—34no—
23#4473—34no—
24C32×#41—41no—
25C32×#41—41no—
26C2×C32×Q8C2×C411yescharacteristic
27C2×C32×D4D412yes—
28C2×C32×D4C2311yescharacteristic
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×#217—24no—
46C3×C4⋊Dic3—42no—
47C3×C4×Dic3—42no—
48#2126—91noSylow
49C2×C3×#41—21no—
50C2×C3×#41C2×D312yes—
51C2×#235—32no—
52C2×#235—61no—
53C3×#117—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—
68#926—22no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C3×#99—34no—
72C3×#99—62no—
73#834—22no—
74#834C2×D314yes—
75C23×C32C22⋊C411yescharacteristic
76C23×C32C2×D412yes—
77C22×C3⋊D3—21no—
78C32×Q8—41no—
79C32×D4—42no—
80C32×D4—41no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4C22⋊C412yes—
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C22×C411yescharacteristic
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—
98C2×C3×Dic3—44no—
99#532—91no—
100#410—32no—
101#354—92no—
102#353—92no—
103C3×#41—42no—
104C3×#41—42no—
105C3×#41—42no—
106C3×#41—42no—
107C2×C3×Q8—21no—
108C2×C3×Q8C4×D312yes—
109C2×C3×D4—22no—
110C2×C3×D4—21no—
111C2×C3×D4D1212yes—
112C2×C3×D4#6712yes—
113C2×C3×D4C22×D312yes—
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×C4⋊C4—122no—
137C3×C22⋊C4—64no—
138C3×C42—122no—
139#217—24no—
140#217—64no—
141#217—62no—
142#217—62no—
143(C2×D3)⋊C4—64no—
144(C2×D3)⋊C4—62no—
145(C2×D3)⋊C4—62no—
146C4⋊Dic3—42no—
147Dic3⋊C4—64no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150C4×Dic3—32no—
151C4×Dic3—32no—
152C4×Dic3—42no—
153C4×Dic3—61no—
154C4×Dic3—61no—
155C4×Dic3—62no—
156C4×Dic3—62no—
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—
171C3×Dic3—84no—
172C2×#41—91no—
173C2×#41D3211yescharacteristic
174C4⋊Q8—91no—
175#127—91no—
176#124—91no—
177#124—91no—
178#121—182no—
179C4×D4—182no—
180#117—62no—
181C2×C42—91no—
182#99—34no—
183#99—62no—
184C23×C3—21no—
185C23×C3—22no—
186C23×C3(C2×D3)⋊C412yes—
187C23×C3C2×D1212yes—
188C23×C3C2×#6712yes—
189C22×D3—62no—
190C22×D3—62no—
191C3×Q8—42no—
192C3×Q8—42no—
193C3×D4—42no—
194C3×D4—42no—
195C3×D4—42no—
196C3×D4—42no—
197C3×D4—44no—
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—22no—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—42no—
210C2×C3×C4—42no—
211C2×C3×C4—124no—
212C2×C3×C4(C2×D3)⋊C412yes—
213C2×C3×C4(C2×D3)⋊C412yes—
214C2×C3×C4(C2×D3)⋊C412yes—
215C2×C3×C4C2×C4×D312yes—
216#67—124no—
217#67—124no—
218#67—128no—
219#67—124no—
220#67—124no—
221C2×Dic3—44no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—124no—
229C2×Dic3—124no—
230D12—122no—
231D12—122no—
232C4×D3—122no—
233C4×D3—122no—
234C4×D3—122no—
235C4×D3—122no—
236Dic6—122no—
237Dic6—122no—
238C2×C32—21no—
239C2×C32—41no—
240C2×C32—42no—
241C2×C32C2×#9911yescharacteristic
242C3⋊D3—81no—
243#41—41no—
244#41—41no—
245#41—361no—
246#41—361no—
247C2×Q8—91no—
248C2×Q8#62411yescharacteristic
249C2×D4—91no—
250C2×D4—181no—
251C2×D4—182no—
252C2×D4#62612yes—
253C2×D4C2×D3211yescharacteristic
254C22×C4—181no—
255C22×C4—181no—
256C22×C4#62411yescharacteristic
257C22×C4#62612yes—
258C4⋊C4—122no—
259C4⋊C4—182no—
260C22⋊C4—64no—
261C22⋊C4—182no—
262C22⋊C4—182no—
263C42—91no—
264C42—91no—
265C42—122no—
266C42—181no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—21no—
272C22×C3—42no—
273C22×C3—42no—
274C22×C3—42no—
275C22×C3—42no—
276C22×C3—42no—
277C22×C3—44no—
278C22×C3C2×(C2×D3)⋊C412yes—
279C2×D3—122no—
280C2×D3—124no—
281C2×D3—122no—
282C2×D3—122no—
283C2×D3—122no—
284C3×C4—22no—
285C3×C4—22no—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—42no—
291C3×C4—244no—
292C3×C4#80612yes—
293C3×C4#80612yes—
294Dic3—64no—
295Dic3—64no—
296Dic3—84no—
297Dic3—122no—
298Dic3—122no—
299Dic3—122no—
300Dic3—122no—
301C32#212611yescharacteristic, complemented, Sylow
302C23—181no—
303C23#372211yescharacteristic
304C23C2×#62612yes—
305Q8—41no—
306Q8—361no—
307D4—42no—
308D4—41no—
309D4—361no—
310D4—364no—
311D4—362no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—124no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—362no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4#372212yes—
324C2×C4#372211yescharacteristic
325C2×C4C2×#62411yescharacteristic
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3—42no—
330C2×C3—42no—
331C2×C3—42no—
332C2×C3—42no—
333C2×C3—82no—
334C2×C3C2×#80612yes—
335D3—242no—
336D3—242no—
337C22—22no—
338C22—21no—
339C22—41no—
340C22—42no—
341C22—362no—
342C22—361no—
343C22C2×#372211yescharacteristic
344C4—22no—
345C4—21no—
346C4—182no—
347C4—244no—
348C4—361no—
349C4—361no—
350C4#6358111yescharacteristic
351C4#6358111yescharacteristic
352C3—21no—
353C3#7006012yescomplemented
354C2—21no—
355C2—42no—
356C2—41no—
357C2—721no—
358C2C2×#6358111yescharacteristic
subgroupG/H
centerC4#63581
commutatorC2×C32×C4C22×C4
FrattiniC2×D4C2×D32
FittingC2×C32×#41C22
socleC2×C32C2×#99
prime radical#10596303C2
cosocleC2×C32×D4C23
hypercenterC2×#41D32
hypocenterC32#2126
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×#5240C2semidirect
3. #10589181C2semidirect
4. #10589179C2semidirect
7. C2×#3828C4semidirect
8. #64156C4semidirect
9. #64153C4semidirect
14. C2×C4×C3⋊Dic3C4semidirect
21. #5240D3semidirect
301. C32#2126semidirect
353. C3#70060semidirect

Maximal subgroups

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

subgroupindex
#105963032
C3×#52402
#105891812
#105891792
#700603