Finite Group Databasebeta

← #11773817

Subgroups — #11773817

Order 1152.

837 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 837 conjugacy classes of subgroups — too many to draw. Only its 116 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×#64090C211yesmaximal, characteristic
2#10591061C212yesmaximal, complemented
3C3×#4525C212yesmaximal, complemented
4#10589146C212yesmaximal, complemented
5#68101—32nomaximal
6C22×#638C411yescharacteristic
7C23×C3⋊Dic3C411yescharacteristic
8C22×C4×C3⋊D3C411yescharacteristic
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3752C2211yescharacteristic
11C2×#3750C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64090—22no—
14#64090—22no—
15C3×#830C2214yes—
16#63572—22no—
17#63553—22no—
18C2×#67⋊C4—32no—
19C2×#67⋊C4—61no—
20#4718—34no—
21C3×#323—32no—
22#4525D312yescomplemented
23#4468—34no—
24C24×C32C2×C411yescharacteristic
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2311yescharacteristic
28C2×#638—22no—
29C2×#638—22no—
30C2×#638C814yescomplemented
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3—42no—
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3C2×C411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×C4×C3⋊D3—21no—
39C2×C4×C3⋊D3—42no—
40C32×C22⋊C4—22no—
41#3752—22no—
42#3750—22no—
43C4×C3⋊Dic3D412yes—
44C4×C3⋊Dic3D412yes—
45C2×C3×C3⋊C8—24no—
46#1460—91noSylow
47C22×#67—32no—
48C22×#67—61no—
49C23×Dic3—32no—
50C23×Dic3—61no—
51C22×C4×D3—32no—
52C22×C4×D3—61no—
53C2×C3×C22⋊C4—21no—
54C2×C3×C22⋊C4C2×D312yes—
55C2×(C2×D3)⋊C4—32no—
56C2×(C2×D3)⋊C4—61no—
57C2×Dic3⋊C4—32no—
58C2×Dic3⋊C4—61no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—61no—
61#67⋊C4—64no—
62#67⋊C4—64no—
63#67⋊C4—64no—
64#67⋊C4—64no—
65C3×C22⋊C8—34no—
66#830C2×D314yes—
67Dic3⋊C8—64no—
68C8×Dic3—64no—
69C23×C32—21no—
70C23×C32—21no—
71C23×C32—41no—
72C23×C32—41no—
73C23×C32C2×C812yes—
74C23×C32C22×C411yescharacteristic
75C22×C3⋊D3—21no—
76C22×C3⋊D3—21no—
77C22×C3⋊D3—41no—
78C22×C3⋊D3—41no—
79C22×C3⋊D3C2×C812yes—
80C2×C32×C4—21no—
81C2×C32×C4—41no—
82C2×C32×C4—41no—
83C2×C32×C4C2×D412yes—
84#638—28no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—42no—
88C2×C3⋊Dic3—42no—
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3C22⋊C411yescharacteristic
91C2×C3⋊Dic3C22⋊C412yes—
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C2×C812yes—
94C2×C3⋊Dic3M1612yes—
95C4×C3⋊D3—42no—
96C4×C3⋊D3—42no—
97C3×C3⋊C8—44no—
98C2×C4×D4—91no—
99#431—92no—
100#323—32no—
101#323—92no—
102C24×C3—21no—
103C24×C3C4×D312yes—
104C23×D3—32no—
105C23×D3—61no—
106C22×C3×C4—21no—
107C22×C3×C4—21no—
108C22×C3×C4C4×D312yes—
109C22×C3×C4C22×D312yes—
110C2×#67—38no—
111C2×#67—64no—
112C2×#67—64no—
113C2×#67—64no—
114C2×#67—64no—
115C2×#67—64no—
116C22×Dic3—32no—
117C22×Dic3—32no—
118C22×Dic3—32no—
119C22×Dic3—61no—
120C22×Dic3—61no—
121C22×Dic3—61no—
122C22×Dic3—62no—
123C22×Dic3—62no—
124C22×Dic3—62no—
125C22×Dic3—62no—
126C22×Dic3—124no—
127C22×Dic3—124no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—62no—
132C2×C4×D3—124no—
133C2×C4×D3—124no—
134C2×C3×C8—64no—
135C3×C22⋊C4—24no—
136C3×C22⋊C4—24no—
137(C2×D3)⋊C4—64no—
138(C2×D3)⋊C4—64no—
139Dic3⋊C4—64no—
140Dic3⋊C4—64no—
141C4×Dic3—34no—
142C4×Dic3—34no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C2×C3⋊C8—24no—
146C22×C32—21no—
147C22×C32—21no—
148C22×C32—22no—
149C22×C32—42no—
150C22×C32—42no—
151C22×C32—41no—
152C22×C32—41no—
153C22×C32C2×C22⋊C411yescharacteristic
154C22×C32C22×C811yescharacteristic
155C22×C32C2×M1611yescharacteristic
156C2×C3⋊D3—22no—
157C2×C3⋊D3—42no—
158C2×C3⋊D3—41no—
159C2×C3⋊D3—41no—
160C2×C3⋊D3—42no—
161C32×C4—22no—
162C32×C4—41no—
163C3⋊Dic3—21no—
164C3⋊Dic3—41no—
165C3⋊Dic3C22⋊C814yes—
166C3⋊Dic3#10012yes—
167C22×D4—91no—
168C23×C4—91no—
169C23×C4—91no—
170C4×D4—182no—
171C4×D4—182no—
172C2×C4⋊C4—91no—
173C2×C22⋊C4—91no—
174C2×C22⋊C4D3211yescharacteristic
175C2×C42—91no—
176C4⋊C8—182no—
177C22⋊C8—34no—
178C4×C8—182no—
179C23×C3—22no—
180C23×C3—22no—
181C23×C3—22no—
182C23×C3—22no—
183C23×C3—22no—
184C23×C3—21no—
185C23×C3—42no—
186C23×C3—42no—
187C23×C3—42no—
188C23×C3—42no—
189C23×C3D3×C814yes—
190C23×C3C2×C4×D312yes—
191C22×D3—34no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—62no—
195C22×D3—62no—
196C22×D3—62no—
197C22×D3—122no—
198C22×D3—122no—
199C22×D3—122no—
200C22×D3—122no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—42no—
207C2×C3×C4—42no—
208C2×C3×C4D3×D414yes—
209#67—616no—
210#67—616no—
211C2×Dic3—34no—
212C2×Dic3—32no—
213C2×Dic3—34no—
214C2×Dic3—34no—
215C2×Dic3—32no—
216C2×Dic3—62no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—124no—
226C2×Dic3—124no—
227C2×Dic3—124no—
228C2×Dic3—124no—
229C2×Dic3—122no—
230C2×Dic3—122no—
231C4×D3—124no—
232C4×D3—124no—
233C4×D3—124no—
234C4×D3—124no—
235C3×C8—124no—
236C3⋊C8—44no—
237C2×C32—21no—
238C2×C32—21no—
239C2×C32—42no—
240C2×C32C2×C22⋊C811yescharacteristic
241C2×C32#41011yescharacteristic
242C2×C32C2×#10011yescharacteristic
243C3⋊D3—42no—
244C24—91no—
245C24#62411yescharacteristic
246C2×D4—94no—
247C2×D4—182no—
248C2×D4—182no—
249C22×C4—91no—
250C22×C4—91no—
251C22×C4—91no—
252C22×C4—181no—
253C22×C4—181no—
254C22×C4—181no—
255C22×C4—181no—
256C22×C4—362no—
257C22×C4—362no—
258C22×C4#62411yescharacteristic
259C22×C4C2×D3211yescharacteristic
260C2×C8—64no—
261C4⋊C4—182no—
262C22⋊C4—22no—
263C22⋊C4—182no—
264C42—92no—
265C42—92no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—24no—
271C22×C3—24no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—44no—
276C22×C3—42no—
277C22×C3—44no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3—42no—
281C22×C3—42no—
282C22×C3—42no—
283C22×C3D3×C22⋊C412yes—
284C22×C3C2×D3×C812yes—
285C22×C3D3×M1612yes—
286C2×D3—64no—
287C2×D3—64no—
288C2×D3—122no—
289C2×D3—124no—
290C2×D3—124no—
291C2×D3—124no—
292C2×D3—122no—
293C2×D3—122no—
294C2×D3—122no—
295C2×D3—124no—
296C3×C4—24no—
297C3×C4—42no—
298C3×C4—42no—
299C3×C4—42no—
300Dic3—38no—
301Dic3—34no—
302Dic3—62no—
303Dic3—64no—
304Dic3—62no—
305Dic3—62no—
306Dic3—122no—
307Dic3—122no—
308C32#146011yescharacteristic, complemented, Sylow
309C23—21no—
310C23—21no—
311C23—41no—
312C23—41no—
313C23—92no—
314C23—181no—
315C23—181no—
316C23—361no—
317C23—361no—
318C23#371012yes—
319C23C2×#62411yescharacteristic
320D4—188no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—92no—
327C2×C4—91no—
328C2×C4—91no—
329C2×C4—182no—
330C2×C4—181no—
331C2×C4—362no—
332C2×C4—362no—
333C2×C4—362no—
334C2×C4—362no—
335C2×C4—361no—
336C2×C4#381112yes—
337C8—124no—
338C2×C3—22no—
339C2×C3—22no—
340C2×C3—22no—
341C2×C3—22no—
342C2×C3—21no—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3—44no—
346C2×C3—44no—
347C2×C3D3×C22⋊C812yes—
348C2×C3#474012yes—
349C2×C3D3×#10012yes—
350D3—124no—
351D3—124no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—42no—
357C22—41no—
358C22—41no—
359C22—182no—
360C22—362no—
361C22—362no—
362C22—361no—
363C22—361no—
364C22C2×#371011yescharacteristic
365C22#6381811yescharacteristic
366C22#6397411yescharacteristic
367C4—22no—
368C4—41no—
369C4—92no—
370C4—94no—
371C4—181no—
372C4—361no—
373C3—21no—
374C3#6810112yescomplemented
375C2—21no—
376C2—21no—
377C2—42no—
378C2—362no—
379C2#1059115211yescharacteristic
380C2#1059150311yescharacteristic
381C2#1059152911yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C32×C4C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1460
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591061C2semidirect
3. C3×#4525C2semidirect
4. #10589146C2semidirect
22. #4525D3semidirect
30. C2×#638C8semidirect
308. C32#1460semidirect
374. C3#68101semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
#105910612
C3×#45252
#105891462
#681013