Finite Group Databasebeta

← #11773798

Subgroups — #11773798

Order 1152.

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

normal subgroups only

This group has 877 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×#64102C211yesmaximal, characteristic
2#10591152C212yesmaximal, complemented
3C3×#4528C212yesmaximal, complemented
4#10589146C212yesmaximal, complemented
5#68143—32nomaximal
6C22×C4⋊(C3⋊D3)C411yescharacteristic
7C22×C4×C3⋊D3C411yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C32×C4⋊C4C2211yescharacteristic
10C2×#3752C411yescharacteristic
11C2×#3752C2211yescharacteristic
12C2×C4×C3⋊Dic3C411yescharacteristic
13#64102—22no—
14#64102—22no—
15C2×#3710—22no—
16C3×#830C2214yes—
17#63557—22no—
18C2×#893—32no—
19C2×#893—61no—
20D3×C22⋊C8—34no—
21C3×#324—32no—
22#4528D312yescomplemented
23#4468—34no—
24C23×C3⋊D3C2×C411yescharacteristic
25C23×C3⋊D3C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2311yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C2×C4⋊(C3⋊D3)—22no—
32C2×C4⋊(C3⋊D3)—22no—
33C2×C4⋊(C3⋊D3)C814yescomplemented
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3D412yes—
39C2×C4×C3⋊D3D412yes—
40C32×C4⋊C4—22no—
41#3752—22no—
42#3752—22no—
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3—21no—
45C2×C3×C3⋊C8—24no—
46#3710—44no—
47#1459—91noSylow
48C22×D12—32no—
49C22×D12—61no—
50C22×C4×D3—32no—
51C22×C4×D3—32no—
52C22×C4×D3—61no—
53C22×C4×D3—61no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4C2×D312yes—
56C2×(C2×D3)⋊C4—32no—
57C2×(C2×D3)⋊C4—32no—
58C2×(C2×D3)⋊C4—61no—
59C2×(C2×D3)⋊C4—61no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—61no—
62C2×D3×C8—64no—
63#893—64no—
64#893—64no—
65#893—64no—
66#893—64no—
67C3×C22⋊C8—34no—
68#830C2×D314yes—
69(C2×D3)⋊C8—64no—
70C23×C32C22×C411yescharacteristic
71C22×C3⋊D3—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—41no—
74C22×C3⋊D3—41no—
75C22×C3⋊D3—41no—
76C22×C3⋊D3—41no—
77C22×C3⋊D3C22⋊C412yes—
78C22×C3⋊D3C2×C812yes—
79C22×C3⋊D3C2×C812yescomplemented
80C22×C3⋊D3M1612yes—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—21no—
84C2×C32×C4—41no—
85C2×C32×C4—41no—
86C2×C32×C4C2×C812yescomplemented
87C2×C32×C4C2×D412yes—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—41no—
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C4⋊(C3⋊D3)—28no—
94C4×C3⋊D3—24no—
95C4×C3⋊D3—42no—
96C4×C3⋊D3—42no—
97C4×C3⋊D3—42no—
98C3×C3⋊C8—44no—
99C2×C4×D4—91no—
100C2×C22⋊C8—92no—
101#324—32no—
102#323—92no—
103C23×D3—32no—
104C23×D3—32no—
105C23×D3—61no—
106C23×D3—61no—
107C22×C3×C4—21no—
108C22×C3×C4—21no—
109C22×C3×C4—21no—
110C22×C3×C4C4×D312yes—
111C22×C3×C4C4×D312yes—
112C22×C3×C4C22×D312yes—
113C22×Dic3—32no—
114C22×Dic3—32no—
115C22×Dic3—61no—
116C22×Dic3—61no—
117C2×D12—38no—
118C2×D12—64no—
119C2×D12—64no—
120C2×D12—64no—
121C2×D12—64no—
122C2×D12—64no—
123C2×C4×D3—34no—
124C2×C4×D3—34no—
125C2×C4×D3—62no—
126C2×C4×D3—62no—
127C2×C4×D3—62no—
128C2×C4×D3—62no—
129C2×C4×D3—62no—
130C2×C4×D3—62no—
131C2×C4×D3—124no—
132C2×C4×D3—124no—
133C2×C4×D3—124no—
134C2×C4×D3—124no—
135C2×C3×C8—64no—
136C3×C4⋊C4—24no—
137C3×C4⋊C4—24no—
138(C2×D3)⋊C4—64no—
139(C2×D3)⋊C4—64no—
140(C2×D3)⋊C4—64no—
141(C2×D3)⋊C4—64no—
142C4×Dic3—62no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C4×Dic3—62no—
146C2×C3⋊C8—24no—
147D3×C8—128no—
148C22×C32—21no—
149C22×C32—21no—
150C22×C32C2×C22⋊C411yescharacteristic
151C22×C32C22×C811yescharacteristic
152C22×C32C2×M1611yescharacteristic
153C2×C3⋊D3—22no—
154C2×C3⋊D3—22no—
155C2×C3⋊D3—22no—
156C2×C3⋊D3—42no—
157C2×C3⋊D3—42no—
158C2×C3⋊D3—42no—
159C2×C3⋊D3—41no—
160C2×C3⋊D3—41no—
161C2×C3⋊D3—42no—
162C2×C3⋊D3C22⋊C814yes—
163C32×C4—22no—
164C32×C4—22no—
165C32×C4—41no—
166C3⋊Dic3—21no—
167C3⋊Dic3—41no—
168C3⋊Dic3#9912yes—
169C22×D4—91no—
170C23×C4—91no—
171C23×C4—91no—
172C22×C8—182no—
173C4×D4—182no—
174C4×D4—182no—
175C2×C4⋊C4D3211yescharacteristic
176C2×C22⋊C4—91no—
177C2×C22⋊C4—91no—
178C2×C42—91no—
179C22⋊C8—34no—
180C22⋊C8—182no—
181C23×C3—21no—
182C23×C3C2×C4×D312yes—
183C22×D3—34no—
184C22×D3—34no—
185C22×D3—34no—
186C22×D3—34no—
187C22×D3—62no—
188C22×D3—62no—
189C22×D3—62no—
190C22×D3—62no—
191C22×D3—62no—
192C22×D3—62no—
193C22×D3—62no—
194C22×D3—62no—
195C22×D3—122no—
196C22×D3—122no—
197C22×D3—122no—
198C22×D3—122no—
199C22×D3—122no—
200C22×D3—122no—
201C22×D3—122no—
202C22×D3—122no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—42no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—42no—
215C2×C3×C4D3×C814yescomplemented
216C2×C3×C4D3×D414yes—
217C2×Dic3—32no—
218C2×Dic3—32no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3—64no—
222C2×Dic3—64no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—122no—
226C2×Dic3—122no—
227D12—616no—
228D12—616no—
229C4×D3—68no—
230C4×D3—124no—
231C4×D3—124no—
232C4×D3—124no—
233C4×D3—124no—
234C4×D3—124no—
235C4×D3—124no—
236C4×D3—124no—
237C3×C8—124no—
238C3⋊C8—44no—
239C2×C32—21no—
240C2×C32—21no—
241C2×C32C2×C22⋊C811yescharacteristic
242C2×C32C2×#9911yescharacteristic
243C2×C32#41311yescharacteristic
244C3⋊D3—24no—
245C3⋊D3—42no—
246C24—91no—
247C24—91no—
248C2×D4—94no—
249C2×D4—182no—
250C2×D4—182no—
251C22×C4—91no—
252C22×C4—92no—
253C22×C4—92no—
254C22×C4—91no—
255C22×C4—181no—
256C22×C4—181no—
257C22×C4—362no—
258C22×C4—362no—
259C22×C4#62411yescharacteristic
260C22×C4#62411yescharacteristic
261C22×C4C2×D3211yescharacteristic
262C2×C8—64no—
263C2×C8—364no—
264C4⋊C4—22no—
265C22⋊C4—182no—
266C22⋊C4—182no—
267C42—181no—
268C42—181no—
269C22×C3—22no—
270C22×C3—22no—
271C22×C3—22no—
272C22×C3—22no—
273C22×C3—21no—
274C22×C3—21no—
275C22×C3—21no—
276C22×C3D3×C22⋊C412yes—
277C22×C3C2×D3×C812yes—
278C22×C3D3×M1612yes—
279C2×D3—38no—
280C2×D3—64no—
281C2×D3—64no—
282C2×D3—64no—
283C2×D3—64no—
284C2×D3—64no—
285C2×D3—122no—
286C2×D3—122no—
287C2×D3—124no—
288C2×D3—124no—
289C2×D3—122no—
290C2×D3—124no—
291C2×D3—124no—
292C2×D3—124no—
293C2×D3—124no—
294C2×D3—124no—
295C2×D3—122no—
296C2×D3—122no—
297C2×D3—122no—
298C2×D3—124no—
299C3×C4—24no—
300C3×C4—24no—
301C3×C4—24no—
302C3×C4—42no—
303C3×C4—42no—
304C3×C4—42no—
305Dic3—34no—
306Dic3—62no—
307Dic3—62no—
308Dic3—62no—
309Dic3—122no—
310Dic3—122no—
311C32#145911yescharacteristic, complemented, Sylow
312C23—92no—
313C23—92no—
314C23—92no—
315C23—92no—
316C23—181no—
317C23—181no—
318C23—361no—
319C23—361no—
320C23—361no—
321C23—361no—
322C23C2×#62411yescharacteristic
323D4—188no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—91no—
330C2×C4—91no—
331C2×C4—184no—
332C2×C4—182no—
333C2×C4—181no—
334C2×C4—362no—
335C2×C4—362no—
336C2×C4—362no—
337C2×C4—361no—
338C2×C4#371012yescomplemented
339C2×C4#381112yes—
340C8—124no—
341C2×C3—22no—
342C2×C3—22no—
343C2×C3—22no—
344C2×C3—22no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3D3×C22⋊C812yes—
349C2×C3D3×#9912yes—
350C2×C3#475112yes—
351D3—68no—
352D3—124no—
353D3—124no—
354D3—124no—
355C22—21no—
356C22—21no—
357C22—94no—
358C22—182no—
359C22—182no—
360C22—182no—
361C22—362no—
362C22—362no—
363C22—362no—
364C22—362no—
365C22—361no—
366C22—361no—
367C22C2×#371011yescharacteristic
368C22#6381811yescharacteristic
369C22#6397411yescharacteristic
370C4—22no—
371C4—22no—
372C4—41no—
373C4—92no—
374C4—181no—
375C4—361no—
376C3—21no—
377C3#6814312yescomplemented
378C2—21no—
379C2—21no—
380C2—184no—
381C2—362no—
382C2#1059115211yescharacteristic
383C2#1059152711yescharacteristic
384C2#1059164011yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C22×C8
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1459
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591152C2semidirect
3. C3×#4528C2semidirect
4. #10589146C2semidirect
22. #4528D3semidirect
33. C2×C4⋊(C3⋊D3)C8semidirect
79. C22×C3⋊D3C2×C8semidirect
86. C2×C32×C4C2×C8semidirect
215. C2×C3×C4D3×C8semidirect
311. C32#1459semidirect
338. C2×C4#3710semidirect
377. C3#68143semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105911522
C3×#45282
#105891462
#681433