Finite Group Databasebeta

← #11790815

Subgroups — #11790815

Order 1152.

729 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 729 conjugacy classes of subgroups — too many to draw. Only its 132 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#10595032C211yesmaximal, characteristic
2#10592631C211yesmaximal, characteristic, complemented
3C2×C3×#805C212yesmaximal, complemented
4#10591120C211yesmaximal, characteristic, complemented
5C2×#63568C212yesmaximal, complemented
6#70357—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×C42C2211yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C3×#208C2212yes—
12#63980—22no—
13#63914C411yescharacteristic, complemented
14C4×#625—22no—
15#63873C411yescharacteristic, complemented
16#63863C412yescomplemented
17#63658—22no—
18C3×#805—24no—
19#63572—22no—
20#63568—24no—
21#5832—32no—
22C2×C3×#104—32no—
23C2×#837—32no—
24C2×#825—32no—
25#5118—32no—
26#4932—32no—
27#4932—61no—
28C2×#805D312yescomplemented
29C22×C32×C4—21no—
30C22×C32×C4C2311yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3D412yes—
33C2×C3×#67—22no—
34C3×#235—22no—
35C3×#235—22no—
36C3×#235—22no—
37C3×#235—22no—
38C2×C3×D12C2×C412yes—
39C2×C3×C4×D3—22no—
40C2×C3×Dic6C2×C412yes—
41C2×#625—22no—
42C32×C42—21no—
43C32×C42D412yescomplemented
44C4×C3⋊Dic3—21no—
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3D412yes—
48C4×C3⋊Dic3D412yescomplemented
49C3×#208—22no—
50C3×#208—22no—
51C2×C3×C3⋊C8—22no—
52#3724—22no—
53(C2×D3)⋊Dic3—24no—
54#1963—91noSylow
55C2×C3×#41—32no—
56C2×#235C2×D312yes—
57C2×C3×M16—32no—
58C2×C3×C42—21no—
59C2×C3×C42C2×D312yes—
60#947—32no—
61#944—32no—
62#940—32no—
63#939—64no—
64#936—32no—
65C4×#67—64no—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—61no—
69C2×C4×Dic3—61no—
70C2×#208C2×D312yes—
71C3×#104—64no—
72#837—64no—
73C3⋊#95—64no—
74C3⋊#95—64no—
75#825—64no—
76Dic3⋊C8—64no—
77#805—24no—
78C23×C32C2×D411yescharacteristic
79C22×C3×D3—22no—
80C2×C32×C4—22no—
81C2×C32×C4—42no—
82C2×C32×C4C22×C411yescharacteristic
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4#4111yescharacteristic
87C2×C32×C4#4111yescharacteristic
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—42no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3C22⋊C412yes—
92C2×C3⋊Dic3C22⋊C412yes—
93C3×#67—42no—
94C3×#67—42no—
95C2×C3×Dic3—22no—
96C3×D12—22no—
97C3×D12—22no—
98C3×C4×D3—42no—
99C3×C4×D3—42no—
100C3×Dic6—22no—
101C3×Dic6—22no—
102#625—44no—
103C3×C3⋊C8—42no—
104#532—91no—
105#423—91no—
106C2×#104—32no—
107C2×#104—92no—
108#376—91no—
109C3×#41—62no—
110C3×#41—62no—
111C3×#41—62no—
112C3×#41—62no—
113C2×C3×Q8—32no—
114C2×C3×D4—32no—
115C2×C3×D4—62no—
116C22×C3×C4—22no—
117C22×C3×C4—22no—
118C22×C3×C4—21no—
119C22×C3×C4—62no—
120C22×C3×C4C22×D312yes—
121C2×#67—22no—
122C2×#67—64no—
123C22×Dic3—34no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127#235—22no—
128#235—22no—
129#235—22no—
130#235—22no—
131C2×D12C4×D312yes—
132C2×C4×D3—22no—
133C2×Dic6C4×D312yes—
134C3×M16—62no—
135C3×M16—62no—
136C2×C3×C8—62no—
137C3×C42—22no—
138C3×C42—22no—
139C3×C42—22no—
140C3×C42#6714yescomplemented
141#217—64no—
142(C2×D3)⋊C4—64no—
143Dic3⋊C4—64no—
144C4×Dic3—32no—
145C4×Dic3—32no—
146C4×Dic3—34no—
147C4×Dic3—34no—
148C4×Dic3—61no—
149C4×Dic3—61no—
150C4×Dic3—62no—
151C4×Dic3—62no—
152C4×Dic3—62no—
153C4×Dic3—62no—
154#208—22no—
155#208—22no—
156C2×C3⋊C8—22no—
157C22×C32—22no—
158C22×C32C2×C22⋊C411yescharacteristic
159C22×C32#12111yescharacteristic
160C22×C32#12111yescharacteristic
161C2×C3×D3—42no—
162C2×C3×D3—44no—
163C32×C4—42no—
164C32×C4C4×D411yescharacteristic
165C32×C4C4×D411yescharacteristic
166C32×C4#12411yescharacteristic
167C32×C4#12711yescharacteristic
168C3⋊Dic3—22no—
169C3⋊Dic3—22no—
170C3⋊Dic3—42no—
171C3×Dic3—42no—
172C2×#41—32no—
173C2×M16—32no—
174C4⋊Q8—91no—
175#127—91no—
176#124—92no—
177#121—182no—
178C4×D4—182no—
179C2×C42—91no—
180C2×C42—91no—
181C2×C42D3211yescharacteristic
182C4⋊C8—182no—
183#104—64no—
184#104—184no—
185#95—182no—
186C23×C3—21no—
187C23×C3—62no—
188C23×C3D3×D412yes—
189C22×D3—22no—
190C3×Q8—62no—
191C3×Q8—62no—
192C3×D4—62no—
193C3×D4—62no—
194C3×D4—122no—
195C3×D4—122no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—62no—
207C2×C3×C4—122no—
208C2×C3×C4—122no—
209C2×C3×C4C2×C4×D312yes—
210C2×C3×C4#23512yes—
211C2×C3×C4D3×D412yes—
212C2×C3×C4D3×D412yes—
213C2×C3×C4#23712yes—
214C2×C3×C4C2×#6712yes—
215#67—42no—
216#67—42no—
217#67—128no—
218C2×Dic3—22no—
219C2×Dic3—34no—
220C2×Dic3—34no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—64no—
224C2×Dic3—64no—
225C2×Dic3—124no—
226C2×Dic3—124no—
227C2×Dic3—124no—
228C2×Dic3—124no—
229D12—22no—
230D12—22no—
231C4×D3—42no—
232C4×D3—42no—
233Dic6—22no—
234Dic6—22no—
235C3×C8—122no—
236C3⋊C8—42no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32#39011yescharacteristic
240C2×C32#42112yes—
241C3×D3—82no—
242#41—62no—
243#41—62no—
244#41—62no—
245#41—62no—
246C2×Q8—32no—
247C2×D4—32no—
248C2×D4—62no—
249C2×D4—182no—
250C22×C4—21no—
251C22×C4—62no—
252C22×C4—92no—
253C22×C4—181no—
254C22×C4C2×D3211yescharacteristic
255M16—62no—
256M16—62no—
257C2×C8—62no—
258C4⋊C4—182no—
259C22⋊C4—184no—
260C42—21no—
261C42—91no—
262C42—91no—
263C42—92no—
264C42—92no—
265C42—181no—
266C42#62512yescomplemented
267C22×C3—24no—
268C22×C3—24no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—122no—
273C22×C3—124no—
274C22×C3D3×C22⋊C412yes—
275C22×C3#88412yes—
276C22×C3#93912yes—
277C2×D3—42no—
278C2×D3—44no—
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—44no—
284C3×C4—44no—
285C3×C4—122no—
286C3×C4#67⋊C412yes—
287C3×C4#88512yes—
288C3×C4C4×#6712yes—
289C3×C4#94012yes—
290Dic3—42no—
291Dic3—64no—
292Dic3—64no—
293Dic3—122no—
294Dic3—122no—
295Dic3—124no—
296Dic3—124no—
297C32#196311yescharacteristic, complemented, Sylow
298C23—62no—
299C23#381111yescharacteristic
300Q8—62no—
301Q8—62no—
302D4—62no—
303D4—62no—
304D4—122no—
305D4—122no—
306D4—364no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—62no—
310C2×C4—92no—
311C2×C4—92no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4—182no—
315C2×C4—362no—
316C2×C4—362no—
317C2×C4#379811yescharacteristic
318C2×C4C4×D3211yescharacteristic
319C2×C4#380211yescharacteristic
320C2×C4#380211yescharacteristic
321C2×C4#380511yescharacteristic
322C2×C4C2×#62511yescharacteristic
323C8—122no—
324C2×C3—22no—
325C2×C3—22no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3—22no—
330C2×C3—242no—
331C2×C3#482114yes—
332C2×C3#495712yes—
333D3—82no—
334C22—22no—
335C22—122no—
336C22—124no—
337C22#6391211yescharacteristic
338C22#6392111yescharacteristic
339C22#6398011yescharacteristic
340C4—42no—
341C4—122no—
342C4—182no—
343C4—182no—
344C4—362no—
345C4C4×#62511yescharacteristic
346C4#6390211yescharacteristic
347C4#6391411yescharacteristic
348C4#6391511yescharacteristic
349C3—21no—
350C3#7035712yescomplemented
351C2—21no—
352C2—21no—
353C2—242no—
354C2#1059039412yes—
355C2#1059138511yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1963
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592631C2semidirect
3. C2×C3×#805C2semidirect
4. #10591120C2semidirect
5. C2×#63568C2semidirect
13. #63914C4semidirect
15. #63873C4semidirect
16. #63863C4semidirect
28. C2×#805D3semidirect
43. C32×C42D4semidirect
48. C4×C3⋊Dic3D4semidirect
140. C3×C42#67semidirect
266. C42#625semidirect
297. C32#1963semidirect
350. C3#70357semidirect

Maximal subgroups

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

subgroupindex
#105950322
#105926312
C2×C3×#8052
#105911202
C2×#635682
#703573