Finite Group Databasebeta

← #11786361

Subgroups — #11786361

Order 1152.

606 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 606 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C22×#3787C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic, complemented
3C2×#63778C211yesmaximal, characteristic
4C2×C4⋊#622C211yesmaximal, characteristic, complemented
5#10592365C211yesmaximal, characteristic
6#10590207C211yesmaximal, characteristic, complemented
7#10590207C211yesmaximal, characteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×#622C2211yescharacteristic
10C22×#622C2211yescharacteristic
11C22×#622C2211yescharacteristic
12C22×#622C2211yescharacteristic
13C2×#3787—22no—
14C2×#3787—22no—
15C2×#3787—22no—
16C2×#3752C411yescharacteristic
17C2×#3752C411yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#63779—22no—
21#63778—22no—
22C4⋊#622—22no—
23C32×#95C411yescharacteristic
24#63658C411yescharacteristic
25#4666—62no—
26C23×C3⋊D3C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C32×C4C2×C411yescharacteristic
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2×C411yescharacteristic
32C22×C3⋊Dic3C2311yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3D412yes—
38C2×C4×C3⋊D3Q812yes—
39C2×#622—21no—
40C2×#622—21no—
41C2×#622—21no—
42C2×#622—21no—
43C2×#622—21no—
44C2×#622—21no—
45C2×#622—21no—
46C2×#622—21no—
47C2×#622—21no—
48C2×#622—21no—
49C2×#622D412yes—
50C2×#622D412yes—
51#3787—28no—
52#3752—22no—
53#3752C814yescomplemented
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58#1850—91nomaximal, Sylow
59C22×C4×D3—62no—
60C2×(C2×D3)⋊C4—62no—
61C2×(C2×D3)⋊C4—62no—
62C2×C4×Dic3—62no—
63C2×C4×Dic3—62no—
64C3×#95—22no—
65C3⋊#95—62no—
66C23×C32C22×C411yescharacteristic
67C22×C3⋊D3—21no—
68C22×C3⋊D3—21no—
69C22×C3⋊D3—21no—
70C22×C3⋊D3—21no—
71C22×C3⋊D3C4⋊C412yes—
72C22×C3⋊D3C2×C812yes—
73C22×C3⋊D3M1612yes—
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4—21no—
81C2×C32×C4C4⋊C412yes—
82C2×C32×C4C2×C812yescomplemented
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—21no—
86C2×C3⋊Dic3—21no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3C2×C812yescomplemented
89C2×C3⋊Dic3C2×D411yescharacteristic
90C2×C3⋊Dic3C2×D411yescharacteristic
91C2×C3⋊Dic3C2×D411yescharacteristic
92C2×C3⋊Dic3C2×Q811yescharacteristic
93C2×C3⋊Dic3#4111yescharacteristic
94C2×C3⋊Dic3#4111yescharacteristic
95C4×C3⋊D3—22no—
96C4×C3⋊D3—22no—
97C4×C3⋊D3—22no—
98C4×C3⋊D3—22no—
99#622—22no—
100#622—22no—
101#622—41no—
102#622—41no—
103C23×C8—91no—
104C2×C4⋊C8—91no—
105C2×C4⋊C8—91no—
106C2×C22⋊C8—91no—
107C4×C22⋊C4—91no—
108#336—91no—
109#336—91no—
110C23×D3—62no—
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×C3×C4—22no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—122no—
120C2×C4×D3—122no—
121C2×C4×D3—122no—
122C2×C4×D3—122no—
123(C2×D3)⋊C4—68no—
124(C2×D3)⋊C4—68no—
125C4×Dic3—122no—
126C4×Dic3—122no—
127C4×Dic3—122no—
128C4×Dic3—122no—
129C22×C32C2×C4⋊C411yescharacteristic
130C22×C32C4×D411yescharacteristic
131C22×C32C4×D411yescharacteristic
132C22×C32C22×C811yescharacteristic
133C22×C32C2×M1611yescharacteristic
134C22×C32#13111yescharacteristic
135C22×C32#13111yescharacteristic
136C2×C3⋊D3—22no—
137C2×C3⋊D3—22no—
138C2×C3⋊D3—22no—
139C2×C3⋊D3—22no—
140C2×C3⋊D3—22no—
141C2×C3⋊D3—22no—
142C2×C3⋊D3C4⋊C814yescomplemented
143C32×C4—22no—
144C32×C4—22no—
145C32×C4—41no—
146C3⋊Dic3—22no—
147C3⋊Dic3—41no—
148C3⋊Dic3#12011yescharacteristic
149C3⋊Dic3C22⋊Q811yescharacteristic
150C3⋊Dic3C22⋊Q811yescharacteristic
151C3⋊Dic3#12311yescharacteristic
152C23×C4—91no—
153C22×C8—91no—
154C22×C8—91no—
155C22×C8—91no—
156C22×C8—91no—
157C22×C8—182no—
158C22×C8—182no—
159C22×C8—182no—
160C2×C22⋊C4—91no—
161C2×C22⋊C4—91no—
162C2×C42—91no—
163C2×C42—91no—
164C4⋊C8—182no—
165C4⋊C8—182no—
166C22⋊C8—182no—
167#95—91no—
168#95#15711yescharacteristic
169C23×C3—22no—
170C22×D3—64no—
171C22×D3—64no—
172C22×D3—64no—
173C22×D3—122no—
174C22×D3—122no—
175C22×D3—122no—
176C22×D3—122no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—24no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—42no—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C2×Dic3—62no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—62no—
192C2×Dic3—64no—
193C2×Dic3—64no—
194C2×Dic3—122no—
195C2×Dic3—122no—
196C2×Dic3—122no—
197C2×Dic3—122no—
198C4×D3—124no—
199C4×D3—124no—
200C4×D3—124no—
201C4×D3—124no—
202C2×C32#38511yescharacteristic
203C2×C32C2×C4⋊C811yescharacteristic
204C2×C32#42411yescharacteristic
205C2×C32C8×D411yescharacteristic
206C2×C32C8×D411yescharacteristic
207C2×C32#43511yescharacteristic
208C2×C32#43511yescharacteristic
209C3⋊D3—24no—
210C24—91no—
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—92no—
214C22×C4—92no—
215C22×C4—91no—
216C22×C4—181no—
217C22×C4—181no—
218C22×C4—181no—
219C22×C4—181no—
220C22×C4C2×#15711yescharacteristic
221C22×C4C2×#15711yescharacteristic
222C22×C4C2×#15711yescharacteristic
223C2×C8—92no—
224C2×C8—92no—
225C2×C8—181no—
226C2×C8—181no—
227C2×C8—181no—
228C2×C8—181no—
229C2×C8—188no—
230C2×C8—181no—
231C2×C8—181no—
232C2×C8—181no—
233C2×C8—181no—
234C2×C8—181no—
235C2×C8—181no—
236C22⋊C4—94no—
237C22⋊C4—182no—
238C42—181no—
239C42—181no—
240C42—181no—
241C42—181no—
242C22×C3—22no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C2×D3—68no—
250C2×D3—124no—
251C2×D3—124no—
252C2×D3—124no—
253C2×D3—124no—
254C2×D3—124no—
255C2×D3—124no—
256C3×C4—44no—
257C3×C4—44no—
258C3×C4—44no—
259Dic3—62no—
260Dic3—62no—
261Dic3—62no—
262Dic3—62no—
263Dic3—124no—
264Dic3—124no—
265C32#185011yescharacteristic, complemented, Sylow
266C23—92no—
267C23—92no—
268C23—92no—
269C23—181no—
270C23—181no—
271C23—181no—
272C23—181no—
273C23C22×#15711yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—91no—
286C2×C4—91no—
287C2×C4—92no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—181no—
295C2×C4—181no—
296C2×C4—181no—
297C2×C4#378712yescomplemented
298C2×C4C4⋊#15712yes—
299C8—182no—
300C8—182no—
301C8—361no—
302C8—361no—
303C2×C3—22no—
304C2×C3—22no—
305C2×C3—22no—
306C2×C3—22no—
307C2×C3—22no—
308C2×C3—22no—
309C2×C3—22no—
310D3—128no—
311C22—94no—
312C22—182no—
313C22—182no—
314C22—182no—
315C22—182no—
316C22—182no—
317C22—182no—
318C22C2×#378711yescharacteristic
319C22#6428311yescharacteristic
320C22C2×C4⋊#15711yescharacteristic
321C22#6428711yescharacteristic
322C22D4×#15711yescharacteristic
323C22D4×#15711yescharacteristic
324C22#6428911yescharacteristic
325C4—22no—
326C4—22no—
327C4—41no—
328C4—91no—
329C4—91no—
330C4—91no—
331C4—91no—
332C4—182no—
333C4—361no—
334C3—22no—
335C2—184no—
336C2#1059372611yescharacteristic
337C2#1059373911yescharacteristic
338C2#1059374111yescharacteristic
339C2#1059374611yescharacteristic
340C2#1059374911yescharacteristic
341C2#1059375111yescharacteristic
342C2#1059375511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C22×C8
FittingC32×#95C4
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C3⋊Dic3C23
hypercenter#95#157
hypocenterC32#1850
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63779C2semidirect
4. C2×C4⋊#622C2semidirect
6. #10590207C2semidirect
7. #10590207C2semidirect
53. #3752C8semidirect
82. C2×C32×C4C2×C8semidirect
88. C2×C3⋊Dic3C2×C8semidirect
142. C2×C3⋊D3C4⋊C8semidirect
265. C32#1850semidirect
297. C2×C4#3787semidirect

Maximal subgroups

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

subgroupindex
C22×#37872
C2×#637792
C2×#637782
C2×C4⋊#6222
#105923652
#105902072
#18509