Finite Group Databasebeta

← #11774015

Subgroups — #11774015

Order 1152.

768 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 768 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#64094C211yesmaximal, characteristic
2#10592418C211yesmaximal, characteristic, complemented
3#10592417C211yesmaximal, characteristic, complemented
4C32×#323C211yesmaximal, characteristic, complemented
5#10589391C211yesmaximal, characteristic, complemented
6#10589334C211yesmaximal, characteristic, complemented
7#10589334C211yesmaximal, characteristic, complemented
8#68104—34nomaximal
9C22×#638C411yescharacteristic
10C22×#634C411yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C411yescharacteristic
13C2×#3752C411yescharacteristic
14C2×#3752C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64094—21no—
17#64094—21no—
18#64094—21no—
19#64094—21no—
20C32×C22⋊C8C2211yescharacteristic
21C32×C22⋊C8C2211yescharacteristic
22#63657C2211yescharacteristic
23#63657C2211yescharacteristic
24#63642—21no—
25#63641—21no—
26#63641—21no—
27C8×C3⋊Dic3—21no—
28C2×#885—34no—
29#4719—34no—
30#4718—34no—
31C3×#323D314yescomplemented
32#4525—34no—
33#4468—34no—
34#4468—34no—
35C24×C32C2×C411yescharacteristic
36C23×C3⋊D3C2×C411yescharacteristic
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40C2×#638—21no—
41C2×#638—42no—
42C22×C3⋊Dic3C2×C411yescharacteristic
43C22×C3⋊Dic3C2×C411yescharacteristic
44C22×C3⋊Dic3C2×C411yescharacteristic
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—42no—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C32×C22⋊C4—21no—
51C32×C22⋊C4—21no—
52#3757—21no—
53#3757—21no—
54#3752—21no—
55#3752—21no—
56#3752—21no—
57#3752—21no—
58C4×C3⋊Dic3D411yescharacteristic
59C4×C3⋊Dic3D411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64#1469—91noSylow
65C22×#67—34no—
66C22×Dic6—34no—
67C2×C3×C22⋊C4C2×D314yes—
68C2×#217—34no—
69C2×(C2×D3)⋊C4—34no—
70C2×(C2×D3)⋊C4—34no—
71C2×C4×Dic3—34no—
72#885—64no—
73#885—64no—
74#885—64no—
75#885—64no—
76C3×C22⋊C8C2×D314yes—
77C3×C22⋊C8C2×D314yes—
78#830—34no—
79#830—34no—
80#815—64no—
81Dic3⋊C8—64no—
82Dic3⋊C8—64no—
83C8×Dic3—64no—
84C23×C32—21no—
85C23×C32—21no—
86C23×C32—21no—
87C23×C32—41no—
88C23×C32—41no—
89C23×C32C22×C411yescharacteristic
90C22×C3⋊D3—21no—
91C22×C3⋊D3—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—41no—
94C22×C3⋊D3—41no—
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100#638—42no—
101#638—42no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C2×C3⋊Dic3C22⋊C411yescharacteristic
110C2×C3⋊Dic3C22⋊C411yescharacteristic
111#634—42no—
112#634—42no—
113C32×C8—41no—
114C32×C8—41no—
115C3⋊(C3⋊C8)—41no—
116C3⋊(C3⋊C8)—41no—
117C2×#124—91no—
118#432—91no—
119#431—91no—
120#323—91no—
121#323—91no—
122#323—91no—
123#323C3⋊D311yescharacteristic, complemented
124C24×C3C4×D314yes—
125C23×D3—34no—
126C22×C3×C4C4×D314yes—
127C22×C3×C4C22×D314yes—
128C2×#67—64no—
129C2×#67—64no—
130C2×#67—128no—
131C22×Dic3—34no—
132C22×Dic3—34no—
133C22×Dic3—34no—
134C2×Dic6—64no—
135C2×Dic6—64no—
136C2×Dic6—128no—
137C2×C3×C8—24no—
138C2×C3×C8—24no—
139C3×C22⋊C4—24no—
140C3×C22⋊C4—24no—
141#217—64no—
142#217—64no—
143(C2×D3)⋊C4—64no—
144(C2×D3)⋊C4—64no—
145(C2×D3)⋊C4—64no—
146(C2×D3)⋊C4—64no—
147C4×Dic3—34no—
148C4×Dic3—34no—
149C4×Dic3—34no—
150C4×Dic3—34no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8—64no—
153C22×C32—21no—
154C22×C32—21no—
155C22×C32—41no—
156C22×C32—41no—
157C22×C32—41no—
158C22×C32—81no—
159C22×C32—81no—
160C22×C32C2×C22⋊C411yescharacteristic
161C22×C32#13111yescharacteristic
162C22×C32#13111yescharacteristic
163C2×C3⋊D3—41no—
164C2×C3⋊D3—41no—
165C2×C3⋊D3—41no—
166C2×C3⋊D3—81no—
167C2×C3⋊D3—81no—
168C32×C4—21no—
169C32×C4—21no—
170C32×C4—41no—
171C3⋊Dic3—21no—
172C3⋊Dic3—21no—
173C3⋊Dic3—21no—
174C3⋊Dic3—41no—
175C3⋊Dic3#10012yes—
176C22×Q8—91no—
177C22×D4—91no—
178#124—181no—
179#124—181no—
180#124—181no—
181#124—181no—
182C2×C22⋊C4—91no—
183C2×C22⋊C4—91no—
184C2×C22⋊C4—91no—
185C2×C22⋊C4C2×C3⋊D311yescharacteristic
186C2×C42—91no—
187C4⋊C8—181no—
188C4⋊C8—181no—
189C22⋊C8—91no—
190C22⋊C8—91no—
191C22⋊C8C2×C3⋊D311yescharacteristic
192C22⋊C8C2×C3⋊D311yescharacteristic
193#97—181no—
194C4×C8—181no—
195C23×C3—24no—
196C23×C3—24no—
197C23×C3—24no—
198C23×C3—44no—
199C23×C3—44no—
200C23×C3C2×C4×D314yes—
201C22×D3—64no—
202C22×D3—64no—
203C22×D3—64no—
204C22×D3—124no—
205C22×D3—124no—
206C2×C3×C4—24no—
207C2×C3×C4—44no—
208C2×C3×C4—44no—
209C2×C3×C4D3×D414yes—
210C2×C3×C4D3×D414yes—
211#67—128no—
212#67—128no—
213C2×Dic3—34no—
214C2×Dic3—34no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—68no—
218C2×Dic3—64no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—124no—
222Dic6—128no—
223Dic6—128no—
224C3×C8—44no—
225C3×C8—44no—
226C3⋊C8—124no—
227C3⋊C8—124no—
228C2×C32—21no—
229C2×C32—21no—
230C2×C32—81no—
231C2×C32#40811yescharacteristic
232C2×C32#41011yescharacteristic
233C2×C32C2×#10011yescharacteristic
234C3⋊D3—81no—
235C24—91no—
236C24C4×C3⋊D311yescharacteristic
237C2×Q8—181no—
238C2×Q8—181no—
239C2×Q8—362no—
240C2×D4—181no—
241C2×D4—181no—
242C2×D4—362no—
243C22×C4—91no—
244C22×C4—91no—
245C22×C4—91no—
246C22×C4C4×C3⋊D311yescharacteristic
247C22×C4C22×C3⋊D311yescharacteristic
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—181no—
251C2×C8—181no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—181no—
255C22⋊C4—181no—
256C22⋊C4—181no—
257C22⋊C4—181no—
258C22⋊C4—181no—
259C22⋊C4—181no—
260C42—91no—
261C42—91no—
262C42—91no—
263C42—91no—
264C22×C3—24no—
265C22×C3—24no—
266C22×C3—44no—
267C22×C3—44no—
268C22×C3—44no—
269C22×C3—84no—
270C22×C3—84no—
271C22×C3D3×C22⋊C414yes—
272C22×C3#90114yes—
273C22×C3#90714yes—
274C2×D3—124no—
275C2×D3—124no—
276C2×D3—124no—
277C2×D3—244no—
278C2×D3—244no—
279C3×C4—24no—
280C3×C4—24no—
281C3×C4—44no—
282Dic3—38no—
283Dic3—64no—
284Dic3—64no—
285Dic3—64no—
286Dic3—124no—
287C32#146911yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—181no—
294C23—181no—
295C23—181no—
296C23—361no—
297C23—361no—
298C23C2×C4×C3⋊D311yescharacteristic
299Q8—362no—
300Q8—362no—
301D4—362no—
302D4—362no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—91no—
309C2×C4—91no—
310C2×C4—182no—
311C2×C4—181no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—361no—
315C2×C4D4×C3⋊D311yescharacteristic
316C2×C4D4×C3⋊D311yescharacteristic
317C8—41no—
318C8—41no—
319C8—361no—
320C8—361no—
321C2×C3—24no—
322C2×C3—24no—
323C2×C3—84no—
324C2×C3#472714yes—
325C2×C3#474014yes—
326C2×C3D3×#10014yes—
327D3—244no—
328C22—21no—
329C22—21no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—361no—
336C22—361no—
337C22—361no—
338C22—721no—
339C22—721no—
340C22C22⋊C4×C3⋊D311yescharacteristic
341C22#6411011yescharacteristic
342C22#6411611yescharacteristic
343C4—21no—
344C4—21no—
345C4—41no—
346C4—92no—
347C4—181no—
348C4—181no—
349C4—181no—
350C4—361no—
351C3#6810414yescomplemented
352C2—21no—
353C2—21no—
354C2—81no—
355C2—721no—
356C2#1059242611yescharacteristic
357C2#1059243911yescharacteristic
358C2C3⋊D3×#10011yescharacteristic
subgroupG/H
centerC22C22⋊C4×C3⋊D3
commutatorC23×C32C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#323C2
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenter#323C3⋊D3
hypocenterC32#1469
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #10592418C2semidirect
3. #10592417C2semidirect
4. C32×#323C2semidirect
5. #10589391C2semidirect
6. #10589334C2semidirect
7. #10589334C2semidirect
31. C3×#323D3semidirect
123. #323C3⋊D3semidirect
287. C32#1469semidirect
351. C3#68104semidirect

Maximal subgroups

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

subgroupindex
C2×#640942
#105924182
#105924172
C32×#3232
#105893912
#105893342
#681043