Finite Group Databasebeta

← #11790788

Subgroups — #11790788

Order 1152.

849 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 849 conjugacy classes of subgroups — too many to draw. Only its 136 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
2C42×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#805C212yesmaximal, complemented
4#10591120C211yesmaximal, characteristic, complemented
5C2×#63568C212yesmaximal, complemented
6#70356—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×C42C2211yescharacteristic
9C2×C4×C3⋊Dic3—22no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×#208C2212yes—
13#63980—22no—
14#63914C411yescharacteristic, complemented
15C4×#625—22no—
16#63873C411yescharacteristic, complemented
17#63863C412yescomplemented
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—
26C42×Dic3—32no—
27C42×Dic3—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—28no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D412yes—
49C4×C3⋊Dic3D412yescomplemented
50C3×#208—22no—
51C3×#208—22no—
52C2×C3×C3⋊C8—22no—
53#3724—22no—
54(C2×D3)⋊Dic3—24no—
55#1962—91noSylow
56C2×C3×#41—32no—
57C2×#235C2×D312yes—
58C2×C3×M16—32no—
59C2×C3×C42—21no—
60C2×C3×C42C2×D312yes—
61#947—32no—
62#944—32no—
63#940—32no—
64#939—64no—
65#936—32no—
66C4×#67—64no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—64no—
72C2×C4×Dic3—64no—
73C2×#208C2×D312yes—
74C3×#104—64no—
75#837—64no—
76#825—64no—
77Dic3⋊C8—64no—
78#805—24no—
79C23×C32C2×D411yescharacteristic
80C22×C3×D3—22no—
81C2×C32×C4—24no—
82C2×C32×C4—22no—
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4#4111yescharacteristic
88C2×C32×C4#4111yescharacteristic
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3C22⋊C412yes—
93C2×C3⋊Dic3C22⋊C412yes—
94C3×#67—42no—
95C3×#67—42no—
96C2×C3×Dic3—22no—
97C3×D12—22no—
98C3×D12—22no—
99C3×C4×D3—42no—
100C3×C4×D3—42no—
101C3×Dic6—22no—
102C3×Dic6—22no—
103#625—44no—
104C3×C3⋊C8—42no—
105#532—91no—
106#423—91no—
107C2×#104—32no—
108C2×#104—92no—
109C43—91no—
110C3×#41—62no—
111C3×#41—62no—
112C3×#41—62no—
113C3×#41—62no—
114C2×C3×Q8—32no—
115C2×C3×D4—32no—
116C2×C3×D4—62no—
117C22×C3×C4—22no—
118C22×C3×C4—22no—
119C22×C3×C4—21no—
120C22×C3×C4—62no—
121C22×C3×C4C22×D312yes—
122C2×#67—22no—
123C2×#67—64no—
124C22×Dic3—34no—
125C22×Dic3—62no—
126C22×Dic3—62no—
127C22×Dic3—62no—
128#235—22no—
129#235—22no—
130#235—22no—
131#235—22no—
132C2×D12C4×D312yes—
133C2×C4×D3—22no—
134C2×Dic6C4×D312yes—
135C3×M16—62no—
136C3×M16—62no—
137C2×C3×C8—62no—
138C3×C42—22no—
139C3×C42—22no—
140C3×C42—22no—
141C3×C42#6714yescomplemented
142#217—64no—
143(C2×D3)⋊C4—64no—
144Dic3⋊C4—64no—
145C4×Dic3—32no—
146C4×Dic3—32no—
147C4×Dic3—34no—
148C4×Dic3—34no—
149C4×Dic3—61no—
150C4×Dic3—61no—
151C4×Dic3—62no—
152C4×Dic3—62no—
153C4×Dic3—616no—
154C4×Dic3—616no—
155C4×Dic3—62no—
156C4×Dic3—62no—
157#208—22no—
158#208—22no—
159C2×C3⋊C8—22no—
160C22×C32—22no—
161C22×C32C2×C22⋊C411yescharacteristic
162C22×C32#12111yescharacteristic
163C22×C32#12111yescharacteristic
164C2×C3×D3—42no—
165C2×C3×D3—44no—
166C32×C4—24no—
167C32×C4C4×D411yescharacteristic
168C32×C4C4×D411yescharacteristic
169C32×C4#12411yescharacteristic
170C32×C4#12711yescharacteristic
171C3⋊Dic3—24no—
172C3⋊Dic3—22no—
173C3⋊Dic3#10414yescomplemented
174C3×Dic3—42no—
175C2×#41—32no—
176C2×M16—32no—
177C4⋊Q8—91no—
178#127—91no—
179#124—92no—
180#121—182no—
181C4×D4—182no—
182C2×C42—91no—
183C2×C42—91no—
184C2×C42—182no—
185C2×C42D3211yescharacteristic
186C4⋊C8—182no—
187#104—64no—
188#104—184no—
189C23×C3—21no—
190C23×C3—62no—
191C23×C3D3×D412yes—
192C22×D3—22no—
193C3×Q8—62no—
194C3×Q8—62no—
195C3×D4—62no—
196C3×D4—62no—
197C3×D4—122no—
198C3×D4—122no—
199C2×C3×C4—28no—
200C2×C3×C4—28no—
201C2×C3×C4—24no—
202C2×C3×C4—24no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—62no—
210C2×C3×C4—122no—
211C2×C3×C4—122no—
212C2×C3×C4C2×C4×D312yes—
213C2×C3×C4#23512yes—
214C2×C3×C4D3×D412yes—
215C2×C3×C4D3×D412yes—
216C2×C3×C4#23712yes—
217C2×C3×C4C2×#6712yes—
218#67—42no—
219#67—42no—
220#67—128no—
221C2×Dic3—22no—
222C2×Dic3—34no—
223C2×Dic3—34no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—68no—
227C2×Dic3—68no—
228C2×Dic3—68no—
229C2×Dic3—68no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232D12—22no—
233D12—22no—
234C4×D3—42no—
235C4×D3—42no—
236Dic6—22no—
237Dic6—22no—
238C3×C8—122no—
239C3⋊C8—42no—
240C2×C32—21no—
241C2×C32—21no—
242C2×C32#39011yescharacteristic
243C2×C32C2×#10412yes—
244C3×D3—82no—
245#41—62no—
246#41—62no—
247#41—62no—
248#41—62no—
249C2×Q8—32no—
250C2×D4—32no—
251C2×D4—62no—
252C2×D4—182no—
253C22×C4—21no—
254C22×C4—62no—
255C22×C4—92no—
256C22×C4—181no—
257C22×C4C2×D3211yescharacteristic
258M16—62no—
259M16—62no—
260C2×C8—62no—
261C4⋊C4—182no—
262C22⋊C4—184no—
263C42—21no—
264C42—91no—
265C42—91no—
266C42—92no—
267C42—92no—
268C42—188no—
269C42—181no—
270C42#62512yescomplemented
271C22×C3—24no—
272C22×C3—24no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3—122no—
277C22×C3—124no—
278C22×C3D3×C22⋊C412yes—
279C22×C3#88412yes—
280C22×C3#93912yes—
281C2×D3—42no—
282C2×D3—44no—
283C3×C4—28no—
284C3×C4—28no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—122no—
290C3×C4#67⋊C412yes—
291C3×C4#88512yes—
292C3×C4C4×#6712yes—
293C3×C4#94012yes—
294Dic3—38no—
295Dic3—42no—
296Dic3—64no—
297Dic3—68no—
298Dic3—68no—
299Dic3—64no—
300Dic3—64no—
301C32#196211yescharacteristic, complemented, Sylow
302C23—62no—
303C23#381111yescharacteristic
304Q8—62no—
305Q8—62no—
306D4—62no—
307D4—62no—
308D4—122no—
309D4—122no—
310D4—364no—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—62no—
314C2×C4—92no—
315C2×C4—92no—
316C2×C4—122no—
317C2×C4—122no—
318C2×C4—184no—
319C2×C4—184no—
320C2×C4—182no—
321C2×C4#379811yescharacteristic
322C2×C4C4×D3211yescharacteristic
323C2×C4#380211yescharacteristic
324C2×C4#380211yescharacteristic
325C2×C4#380511yescharacteristic
326C2×C4C2×#62511yescharacteristic
327C8—122no—
328C2×C3—22no—
329C2×C3—22no—
330C2×C3—22no—
331C2×C3—22no—
332C2×C3—21no—
333C2×C3—22no—
334C2×C3—242no—
335C2×C3D3×#10414yes—
336C2×C3#495712yes—
337D3—82no—
338C22—22no—
339C22—122no—
340C22—124no—
341C22#6391211yescharacteristic
342C22#6392111yescharacteristic
343C22#6398011yescharacteristic
344C4—24no—
345C4—94no—
346C4—122no—
347C4—184no—
348C4—182no—
349C4C4×#62511yescharacteristic
350C4#6390211yescharacteristic
351C4#6391411yescharacteristic
352C4#6391511yescharacteristic
353C3—21no—
354C3#7035612yescomplemented
355C2—21no—
356C2—21no—
357C2—242no—
358C2#1059039312yes—
359C2#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#1962
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. C42×C3⋊Dic3C2semidirect
3. C2×C3×#805C2semidirect
4. #10591120C2semidirect
5. C2×#63568C2semidirect
14. #63914C4semidirect
16. #63873C4semidirect
17. #63863C4semidirect
28. C2×#805D3semidirect
43. C32×C42D4semidirect
49. C4×C3⋊Dic3D4semidirect
141. C3×C42#67semidirect
173. C3⋊Dic3#104semidirect
270. C42#625semidirect
301. C32#1962semidirect
354. C3#70356semidirect

Maximal subgroups

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

subgroupindex
#105950322
C42×C3⋊Dic32
C2×C3×#8052
#105911202
C2×#635682
#703563