Finite Group Databasebeta

← #11791438

Subgroups — #11791438

Order 1152.

793 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 793 conjugacy classes of subgroups — too many to draw. Only its 172 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×#64153C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal
3#10591274C211yesmaximal, characteristic
4C2×#63572C211yesmaximal, characteristic
5C2×#63567C212yesmaximal
6#70229—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C22×#634C2211yescharacteristic
9#64153—22no—
10#64153C414yescomplemented
11C2×#3750—21no—
12C2×#3750—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2212yes—
15C22×C3×C3⋊C8C2212yes—
16C2×Dic32—21no—
17C3×#835—24no—
18#63579—21no—
19#63572—22no—
20#63567—24no—
21C2×#944—32no—
22C2×#944—61no—
23C2×C3×#103—32no—
24C2×#835D312yes—
25C2×#816—32no—
26C2×Dic3⋊C8—32no—
27Dic3×C4⋊C4—32no—
28C2×#810—32no—
29C2×C32×Q8—21no—
30C2×C32×Q8—22no—
31C2×C32×Q8—22no—
32C2×C32×Q8C2×C412yes—
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×#634—22no—
39C2×#634—22no—
40C2×#634—21no—
41C2×#634C2×C412yes—
42C22×C3×Dic3—22no—
43#3750—24no—
44#3750—24no—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3D412yes—
47C3×C4⋊Dic3—22no—
48C3×C4⋊Dic3D414yes—
49C2×C3×C3⋊C8—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52Dic32—42no—
53#1981—91noSylow
54C22×C3×Q8—21no—
55C22×C3×Q8C2×D312yes—
56C22×Dic6—32no—
57C22×Dic6—61no—
58C22×C3×C8—32no—
59C2×C3×C4⋊C4—32no—
60#944—38no—
61#944—64no—
62#944—64no—
63#944—64no—
64C2×C4⋊Dic3C2×D312yes—
65C2×Dic3⋊C4—62no—
66C2×Dic3⋊C4—62no—
67C2×Dic3⋊C4—62no—
68C2×Dic3⋊C4—62no—
69C2×C4×Dic3—32no—
70C2×C4×Dic3—61no—
71C2×C4×Dic3—62no—
72C22×C3⋊C8C2×D312yes—
73C3×#103—64no—
74#835—24no—
75C3⋊#95—62no—
76#816—64no—
77Dic3⋊C8—64no—
78#810—64no—
79C23×C32C2×D411yescharacteristic
80C32×Q8—24no—
81C32×Q8—41no—
82C32×Q8—41no—
83C2×C32×C4—22no—
84C2×C32×C4—42no—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D412yes—
88C2×C32×C4#4112yes—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3—22no—
91C2×C3⋊Dic3—42no—
92C2×C3⋊Dic3C22⋊C412yes—
93C2×C3⋊Dic3C22⋊C412yes—
94C2×C3⋊Dic3SD1612yes—
95C2×C3⋊Dic3Q1612yes—
96#634—24no—
97#634—41no—
98#634—41no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3—42no—
102C3×C3⋊C8—42no—
103C2×C4⋊Q8—91no—
104C2×C4⋊C8—91no—
105C2×#103—32no—
106C2×#103—92no—
107C4×C4⋊C4—91no—
108C2×C3×Q8—22no—
109C2×C3×Q8—22no—
110C2×C3×Q8—22no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8—22no—
114C2×C3×Q8—22no—
115C2×C3×Q8—42no—
116C2×C3×Q8—42no—
117C2×C3×Q8C4×D314yes—
118C22×C3×C4—22no—
119C22×C3×C4—22no—
120C22×C3×C4—21no—
121C22×C3×C4—62no—
122C22×C3×C4C22×D312yes—
123C22×Dic3—22no—
124C22×Dic3—32no—
125C22×Dic3—32no—
126C22×Dic3—61no—
127C22×Dic3—61no—
128C22×Dic3—62no—
129C22×Dic3—62no—
130C2×Dic6—34no—
131C2×Dic6—62no—
132C2×Dic6—62no—
133C2×Dic6—62no—
134C2×Dic6—62no—
135C2×Dic6—62no—
136C2×Dic6—62no—
137C2×Dic6—62no—
138C2×Dic6—122no—
139C2×Dic6—122no—
140C2×C3×C8—62no—
141C2×C3×C8—62no—
142C2×C3×C8—62no—
143C3×C4⋊C4—34no—
144C3×C4⋊C4—62no—
145C4⋊Dic3—22no—
146C4⋊Dic3#6714yes—
147Dic3⋊C4—68no—
148Dic3⋊C4—68no—
149Dic3⋊C4—68no—
150Dic3⋊C4—68no—
151C4×Dic3—34no—
152C4×Dic3—34no—
153C4×Dic3—62no—
154C4×Dic3—62no—
155C4×Dic3—124no—
156C2×C3⋊C8—22no—
157C2×C3⋊C8—22no—
158C2×C3⋊C8—22no—
159C22×C32C2×C22⋊C411yescharacteristic
160C22×C32#12112yes—
161C22×C32C2×SD1611yescharacteristic
162C22×C32C2×Q1611yescharacteristic
163C22×C32#13712yes—
164C32×C4—42no—
165C32×C4C4×D412yes—
166C32×C4#12411yescharacteristic
167C32×C4#12711yescharacteristic
168C3⋊Dic3—22no—
169C3⋊Dic3—42no—
170C3⋊Dic3#10314yescomplemented
171C3×Dic3—44no—
172C22×Q8—91no—
173C22×Q8D3211yescharacteristic
174C22×C8—32no—
175C4⋊Q8—94no—
176C4⋊Q8—182no—
177C2×C4⋊C4—32no—
178C2×C4⋊C4—181no—
179C2×C4⋊C4—181no—
180C2×C42—91no—
181C2×C42—181no—
182C4⋊C8—182no—
183#103—64no—
184#103—184no—
185#95—181no—
186C23×C3—21no—
187C23×C3D3×D412yes—
188C3×Q8—24no—
189C3×Q8—24no—
190C3×Q8—44no—
191C3×Q8—42no—
192C3×Q8—42no—
193C3×Q8—42no—
194C3×Q8—42no—
195C2×C3×C4—24no—
196C2×C3×C4—24no—
197C2×C3×C4—22no—
198C2×C3×C4—21no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—44no—
202C2×C3×C4—42no—
203C2×C3×C4—42no—
204C2×C3×C4—64no—
205C2×C3×C4—122no—
206C2×C3×C4—122no—
207C2×C3×C4C2×C4×D312yes—
208C2×C3×C4#23512yes—
209C2×C3×C4D3×D412yes—
210C2×C3×C4D3×D412yes—
211C2×C3×C4#23712yes—
212C2×C3×C4C2×#6712yes—
213C2×Dic3—24no—
214C2×Dic3—34no—
215C2×Dic3—34no—
216C2×Dic3—34no—
217C2×Dic3—34no—
218C2×Dic3—42no—
219C2×Dic3—42no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—64no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—64no—
228C2×Dic3—64no—
229C2×Dic3—124no—
230C2×Dic3—122no—
231C2×Dic3—122no—
232Dic6—64no—
233Dic6—64no—
234Dic6—124no—
235Dic6—122no—
236Dic6—122no—
237Dic6—122no—
238Dic6—122no—
239C3×C8—122no—
240C3⋊C8—42no—
241C2×C32#39011yescharacteristic
242C2×C32C2×#10311yescharacteristic
243C2×C32#41911yescharacteristic
244C2×C32#46112yes—
245C2×C32#46212yes—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—92no—
250C2×Q8—181no—
251C2×Q8—182no—
252C2×Q8—182no—
253C2×Q8#62412yes—
254C22×C4—21no—
255C22×C4—62no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—181no—
259C22×C4C2×D3211yescharacteristic
260C2×C8—62no—
261C2×C8—62no—
262C2×C8—62no—
263C4⋊C4—34no—
264C4⋊C4—62no—
265C4⋊C4—184no—
266C4⋊C4—184no—
267C42—92no—
268C42—92no—
269C42—362no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3—22no—
273C22×C3—22no—
274C22×C3—21no—
275C22×C3D3×C22⋊C412yes—
276C22×C3#88412yes—
277C22×C3D3×SD1612yes—
278C22×C3#91512yes—
279C22×C3D3×Q1612yes—
280C22×C3#91812yes—
281C22×C3#93912yes—
282C3×C4—22no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—44no—
286C3×C4—44no—
287C3×C4—124no—
288C3×C4#67⋊C412yes—
289C3×C4#88512yes—
290C3×C4C4×#6712yes—
291C3×C4#94012yes—
292Dic3—38no—
293Dic3—44no—
294Dic3—64no—
295Dic3—64no—
296Dic3—64no—
297Dic3—124no—
298Dic3—124no—
299C32#198111yescharacteristic, complemented, Sylow
300C23#381111yescharacteristic
301Q8—24no—
302Q8—41no—
303Q8—41no—
304Q8—184no—
305Q8—361no—
306Q8—361no—
307C2×C4—22no—
308C2×C4—42no—
309C2×C4—64no—
310C2×C4—92no—
311C2×C4—92no—
312C2×C4—92no—
313C2×C4—92no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4—182no—
317C2×C4—182no—
318C2×C4—362no—
319C2×C4#380412yes—
320C2×C4C2×#62411yescharacteristic
321C2×C4D3×#6712yes—
322C2×C4#381111yescharacteristic
323C8—122no—
324C2×C3—21no—
325C2×C3—21no—
326C2×C3—22no—
327C2×C3—22no—
328C2×C3—21no—
329C2×C3#479512yes—
330C2×C3D3×#10312yes—
331C2×C3#480212yes—
332C2×C3#481812yes—
333C2×C3#495712yes—
334C2×C3#516212yes—
335C2×C3#518212yes—
336C22#6394011yescharacteristic
337C22#6394411yescharacteristic
338C22#6395112yes—
339C22#6397112yes—
340C22#6397411yescharacteristic
341C4—42no—
342C4—94no—
343C4—124no—
344C4—182no—
345C4—362no—
346C4#6395212yes—
347C4#6395311yescharacteristic
348C4#6397911yescharacteristic
349C3—21no—
350C3#7022912yescomplemented
351C2#1059155211yescharacteristic
352C2#1059156211yescharacteristic
353C2#1059156912yes—
354C2#1059158012yes—
355C2#1059170411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1981
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
10. #64153C4semidirect
170. C3⋊Dic3#103semidirect
299. C32#1981semidirect
350. C3#70229semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C2×C3×#8352
#105912742
C2×#635722
C2×#635672
#702293