Finite Group Databasebeta

← #11775182

Subgroups — #11775182

Order 1152.

567 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 567 conjugacy classes of subgroups — too many to draw. Only its 94 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#10596093C211yesmaximal, characteristic
2#10591252C211yesmaximal, characteristic
3#10591066C211yesmaximal, characteristic
4C3×#4538C212yesmaximal
5#10589154C212yesmaximal
6#68310—32nomaximal
7C32×C22⋊Q8C2211yescharacteristic
8Q8×C3⋊Dic3C411yescharacteristic, complemented
9#64153C411yescharacteristic, complemented
10#64133C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12#64098—21no—
13#64097C411yescharacteristic, complemented
14#64096—21no—
15#64096C411yescharacteristic, complemented
16#64087—21no—
17#64086—21no—
18C2×Dic32—21no—
19C3×C3⋊#95C2212yes—
20C3×#830C2212yes—
21#63579—21no—
22#63572—21no—
23#63555—21no—
24#5622—32no—
25#5622—61no—
26#4719—32no—
27#4648—32no—
28C3×#328—32no—
29#4538D312yes—
30#4467—32no—
31#4452—32no—
32C2×C32×Q8C2×C411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35C22×C3⋊Dic3D411yescharacteristic
36C2×#634—21no—
37C2×#634C2×C411yescharacteristic
38C22×C3×Dic3—22no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4C2×C411yescharacteristic
41C32×C22⋊C4—21no—
42#3757—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C411yescharacteristic
45#3750—21no—
46#3750—21no—
47#3750—21no—
48#3750—21no—
49#3750—21no—
50C4×C3⋊Dic3—21no—
51C4×C3⋊Dic3—21no—
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3C2×C411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C4×C3⋊Dic3D411yescharacteristic
56C2×C3×C3⋊C8—22no—
57Dic32—24no—
58#1506—91noSylow
59C3×C22⋊Q8—21no—
60C3×C22⋊Q8C2×D312yes—
61Q8×Dic3—32no—
62Q8×Dic3—61no—
63#944—32no—
64#944—61no—
65#924—32no—
66#924—61no—
67C2×C4×Dic3—32no—
68C2×C4×Dic3—61no—
69C2×C4×Dic3—62no—
70#889—62no—
71#889—62no—
72#888—32no—
73#888—61no—
74#887—32no—
75#887—61no—
76#887—62no—
77#887—62no—
78#878—62no—
79#878—62no—
80#877—62no—
81#877—62no—
82C3×C22⋊C8—32no—
83C3×#95—32no—
84C3⋊#95—62no—
85C3⋊#95C2×D312yes—
86#830C2×D312yes—
87#815—62no—
88Dic3⋊C8—62no—
89C23×C32C2×D411yescharacteristic
90C32×Q8—41no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—41no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C3⋊Dic3—22no—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—22no—
100C2×C3⋊Dic3C22⋊C411yescharacteristic
101C2×C3⋊Dic3C22⋊C411yescharacteristic
102C2×C3⋊Dic3C22⋊C411yescharacteristic
103C2×C3⋊Dic3C22⋊C411yescharacteristic
104#634—42no—
105#634—41no—
106C2×C3×Dic3—24no—
107C2×C3×Dic3—42no—
108C2×C3×Dic3—42no—
109C3×C3⋊C8—42no—
110#533—91no—
111#432—91no—
112#376—91no—
113#328—32no—
114#328—92no—
115C2×C3×Q8—21no—
116C2×C3×Q8C4×D312yes—
117C22×C3×C4—21no—
118C22×C3×C4—62no—
119C22×C3×C4C22×D312yes—
120C22×Dic3—22no—
121C22×Dic3—32no—
122C22×Dic3—32no—
123C22×Dic3—61no—
124C22×Dic3—61no—
125C2×Dic6—32no—
126C2×Dic6—61no—
127C2×Dic6—62no—
128C2×Dic6—62no—
129C2×C3×C8—62no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—22no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4C4×D312yes—
134C3×C22⋊C4—22no—
135C3×C22⋊C4—22no—
136#217—62no—
137#217—62no—
138C4⋊Dic3—32no—
139C4⋊Dic3—61no—
140C4⋊Dic3—62no—
141C4⋊Dic3—62no—
142Dic3⋊C4—62no—
143Dic3⋊C4—62no—
144Dic3⋊C4—62no—
145Dic3⋊C4—62no—
146Dic3⋊C4—62no—
147Dic3⋊C4—62no—
148Dic3⋊C4—62no—
149Dic3⋊C4—62no—
150Dic3⋊C4—62no—
151Dic3⋊C4—62no—
152C4×Dic3—32no—
153C4×Dic3—32no—
154C4×Dic3—32no—
155C4×Dic3—32no—
156C4×Dic3—61no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—61no—
160C4×Dic3—68no—
161C4×Dic3—62no—
162C4×Dic3—62no—
163C4×Dic3—62no—
164C4×Dic3—62no—
165C2×C3⋊C8—22no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32C2×C22⋊C411yescharacteristic
169C22×C32#13712yes—
170C32×C4—21no—
171C32×C4—21no—
172C32×C4—41no—
173C32×C4—41no—
174C3⋊Dic3—21no—
175C3⋊Dic3—21no—
176C3⋊Dic3—21no—
177C3⋊Dic3—41no—
178C3⋊Dic3—41no—
179C3⋊Dic3#10412yes—
180C3×Dic3—44no—
181C4⋊Q8—91no—
182C4⋊Q8—91no—
183#125—181no—
184C22⋊Q8—91no—
185C22⋊Q8—181no—
186C22⋊Q8D3211yescharacteristic
187C4×Q8—91no—
188C4×Q8—91no—
189C4×Q8—181no—
190#117—181no—
191C2×C42—91no—
192C2×C42—181no—
193C4⋊C8—181no—
194C22⋊C8—32no—
195#97—181no—
196#95—32no—
197#95—181no—
198C23×C3—21no—
199C23×C3D3×D412yes—
200C3×Q8—42no—
201C3×Q8—42no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—42no—
209C2×C3×C4—42no—
210C2×C3×C4—64no—
211C2×C3×C4—122no—
212C2×C3×C4—122no—
213C2×C3×C4C2×C4×D312yes—
214C2×C3×C4D3×D412yes—
215C2×Dic3—24no—
216C2×Dic3—32no—
217C2×Dic3—32no—
218C2×Dic3—32no—
219C2×Dic3—32no—
220C2×Dic3—42no—
221C2×Dic3—42no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—64no—
227C2×Dic3—64no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—62no—
232C2×Dic3—62no—
233C2×Dic3—62no—
234C2×Dic3—122no—
235Dic6—124no—
236Dic6—124no—
237Dic6—122no—
238Dic6—122no—
239C3×C8—122no—
240C3⋊C8—42no—
241C2×C32—22no—
242C2×C32#41011yescharacteristic
243C2×C32#41911yescharacteristic
244C2×C32C2×#10411yescharacteristic
245C2×Q8—91no—
246C2×Q8—181no—
247C2×Q8#62411yescharacteristic
248C22×C4—62no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4C2×D3211yescharacteristic
252C2×C8—62no—
253C4⋊C4—21no—
254C4⋊C4—91no—
255C4⋊C4—181no—
256C4⋊C4—181no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C4⋊C4—181no—
260C4⋊C4—181no—
261C4⋊C4#62411yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—181no—
264C42—91no—
265C42—91no—
266C42—91no—
267C42—91no—
268C42—181no—
269C42—181no—
270C42—184no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3D3×C22⋊C412yes—
278C22×C3#91512yes—
279C22×C3#91812yes—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—22no—
283C3×C4—41no—
284C3×C4—42no—
285C3×C4—42no—
286C3×C4—42no—
287C3×C4—42no—
288C3×C4—124no—
289Dic3—34no—
290Dic3—44no—
291Dic3—62no—
292Dic3—62no—
293Dic3—62no—
294Dic3—62no—
295Dic3—62no—
296Dic3—62no—
297Dic3—121no—
298Dic3—122no—
299Dic3—122no—
300Dic3—122no—
301Dic3—122no—
302C32#150611yescharacteristic, complemented, Sylow
303C23#381111yescharacteristic
304Q8—41no—
305Q8—361no—
306Q8—362no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—64no—
311C2×C4—91no—
312C2×C4—91no—
313C2×C4—91no—
314C2×C4—91no—
315C2×C4—122no—
316C2×C4—122no—
317C2×C4—182no—
318C2×C4—182no—
319C2×C4—181no—
320C2×C4—181no—
321C2×C4C2×#62411yescharacteristic
322C2×C4#381111yescharacteristic
323C8—122no—
324C2×C3—22no—
325C2×C3—22no—
326C2×C3—21no—
327C2×C3—21no—
328C2×C3—21no—
329C2×C3—42no—
330C2×C3#474012yes—
331C2×C3#480212yes—
332C2×C3D3×#10412yes—
333C22—21no—
334C22—21no—
335C22#6395112yes—
336C22#6397411yescharacteristic
337C4—21no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—92no—
342C4—124no—
343C4—181no—
344C4—181no—
345C4—181no—
346C4—361no—
347C4—361no—
348C3—21no—
349C3#6831012yescomplemented
350C2—22no—
351C2#1059152911yescharacteristic
352C2#1059156211yescharacteristic
353C2#1059167111yescharacteristic
subgroupG/H
centerC22#63974
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1506
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
8. Q8×C3⋊Dic3C4semidirect
9. #64153C4semidirect
13. #64097C4semidirect
15. #64096C4semidirect
302. C32#1506semidirect
349. C3#68310semidirect

Maximal subgroups

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

subgroupindex
#105960932
#105912522
#105910662
C3×#45382
#105891542
#683103