Finite Group Databasebeta

← #11786394

Subgroups — #11786394

Order 1152.

582 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 92 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×#3792C211yesmaximal, characteristic
2C2×C22⋊#622C211yesmaximal, characteristic
3C2×#63779C211yesmaximal, characteristic, complemented
4C2×C4⋊#622C211yesmaximal, characteristic, complemented
5C22⋊C4×C3⋊Dic3C211yesmaximal, characteristic
6#10590207C211yesmaximal, characteristic, complemented
7#10590207C211yesmaximal, characteristic, complemented
8C23×C3⋊Dic3C2211yescharacteristic
9C2×#3792—22no—
10C2×#3792—22no—
11C2×#3792—22no—
12C22×#622C2211yescharacteristic
13C22×#622C2211yescharacteristic
14C22×#622C2211yescharacteristic
15C22×#622C2211yescharacteristic
16C2×C32×C22⋊C4C411yescharacteristic
17C2×#3757C411yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22⋊#622—22no—
21#63779—22no—
22C4⋊#622—22no—
23#63658C411yescharacteristic
24#63658C411yescharacteristic
25Dic3×C22⋊C4—62no—
26C24×C32C2×C411yescharacteristic
27C22×C32×C4C2×C411yescharacteristic
28C22×C32×C4C2×C411yescharacteristic
29C22×C3⋊Dic3—21no—
30C22×C3⋊Dic3—21no—
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3C2×C411yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3⋊Dic3D412yes—
37C22×C3⋊Dic3Q812yes—
38C22×C3⋊Dic3C2311yescharacteristic
39#3792—28no—
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×#622—21no—
50C2×#622D412yes—
51C2×#622D412yes—
52C32×C22⋊C4—22no—
53#3757—22no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58#1851—91nomaximal, Sylow
59C23×Dic3—62no—
60C2×C3×C22⋊C4—22no—
61C2×#217—62no—
62C2×C4×Dic3—62no—
63C2×C4×Dic3—62no—
64C3⋊#95—62no—
65C3⋊#95—62no—
66C23×C32—21no—
67C23×C32—21no—
68C23×C32—21no—
69C23×C32—21no—
70C23×C32—21no—
71C23×C32—21no—
72C23×C32C4⋊C412yes—
73C23×C32C22×C411yescharacteristic
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4M1612yescomplemented
80C2×C3⋊Dic3—21no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3—21no—
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—22no—
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3C4⋊C412yes—
92C2×C3⋊Dic3M1612yescomplemented
93C2×C3⋊Dic3C2×D411yescharacteristic
94C2×C3⋊Dic3C2×D411yescharacteristic
95C2×C3⋊Dic3C2×D411yescharacteristic
96C2×C3⋊Dic3C2×Q811yescharacteristic
97C2×C3⋊Dic3#4111yescharacteristic
98C2×C3⋊Dic3#4111yescharacteristic
99#622—22no—
100#622—22no—
101#622—41no—
102#622—41no—
103C22×M16—91no—
104C2×C4⋊C8—91no—
105C2×C4⋊C8—91no—
106C2×C22⋊C8—91no—
107C4×C22⋊C4—91no—
108#336—91no—
109#336—91no—
110C24×C3—22no—
111C22×C3×C4—22no—
112C22×C3×C4—22no—
113C22×Dic3—62no—
114C22×Dic3—62no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117C22×Dic3—64no—
118C22×Dic3—64no—
119C22×Dic3—122no—
120C22×Dic3—122no—
121C22×Dic3—122no—
122C22×Dic3—122no—
123C3×C22⋊C4—28no—
124#217—68no—
125C4×Dic3—122no—
126C4×Dic3—122no—
127C4×Dic3—122no—
128C4×Dic3—122no—
129C22×C32—22no—
130C22×C32—22no—
131C22×C32—22no—
132C22×C32—41no—
133C22×C32—41no—
134C22×C32—41no—
135C22×C32—41no—
136C22×C32C2×C4⋊C411yescharacteristic
137C22×C32C4×D411yescharacteristic
138C22×C32C4×D411yescharacteristic
139C22×C32C2×M1611yescharacteristic
140C22×C32C2×M1611yescharacteristic
141C22×C32#13111yescharacteristic
142C22×C32#13111yescharacteristic
143C32×C4—22no—
144C32×C4—41no—
145C3⋊Dic3—22no—
146C3⋊Dic3—22no—
147C3⋊Dic3—41no—
148C3⋊Dic3#12011yescharacteristic
149C3⋊Dic3C22⋊Q811yescharacteristic
150C3⋊Dic3C22⋊Q811yescharacteristic
151C3⋊Dic3#12311yescharacteristic
152C23×C4—91no—
153C2×M16—182no—
154C2×M16—182no—
155C2×M16—182no—
156C22×C8—91no—
157C22×C8—91no—
158C22×C8—91no—
159C22×C8—91no—
160C2×C22⋊C4—91no—
161C2×C22⋊C4#15711yescharacteristic
162C2×C42—91no—
163C2×C42—91no—
164C4⋊C8—182no—
165C4⋊C8—182no—
166C22⋊C8—182no—
167#95—91no—
168#95—91no—
169C23×C3—24no—
170C23×C3—24no—
171C23×C3—22no—
172C23×C3—24no—
173C23×C3—42no—
174C23×C3—42no—
175C23×C3—42no—
176C23×C3—42no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—42no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×Dic3—62no—
184C2×Dic3—62no—
185C2×Dic3—62no—
186C2×Dic3—62no—
187C2×Dic3—62no—
188C2×Dic3—62no—
189C2×Dic3—64no—
190C2×Dic3—64no—
191C2×Dic3—64no—
192C2×Dic3—124no—
193C2×Dic3—124no—
194C2×Dic3—124no—
195C2×Dic3—124no—
196C2×Dic3—122no—
197C2×Dic3—122no—
198C2×Dic3—122no—
199C2×Dic3—122no—
200C2×Dic3—122no—
201C2×Dic3—122no—
202C2×C32—42no—
203C2×C32#38511yescharacteristic
204C2×C32#42311yescharacteristic
205C2×C32#42411yescharacteristic
206C2×C32#43511yescharacteristic
207C2×C32#43511yescharacteristic
208C2×C32#43611yescharacteristic
209C2×C32#43611yescharacteristic
210C24C2×#15711yescharacteristic
211C22×C4—91no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—92no—
215C22×C4—92no—
216C22×C4—91no—
217C22×C4—181no—
218C22×C4—181no—
219C22×C4—181no—
220C22×C4—181no—
221C22×C4C2×#15711yescharacteristic
222C22×C4C2×#15711yescharacteristic
223M16—188no—
224C2×C8—92no—
225C2×C8—92no—
226C2×C8—181no—
227C2×C8—181no—
228C2×C8—181no—
229C2×C8—181no—
230C2×C8—181no—
231C2×C8—181no—
232C2×C8—181no—
233C2×C8—181no—
234C2×C8—181no—
235C2×C8—181no—
236C22⋊C4—22no—
237C22⋊C4—182no—
238C42—181no—
239C42—181no—
240C42—181no—
241C42—181no—
242C22×C3—28no—
243C22×C3—22no—
244C22×C3—22no—
245C22×C3—22no—
246C22×C3—22no—
247C22×C3—22no—
248C22×C3—22no—
249C22×C3—22no—
250C22×C3—44no—
251C22×C3—44no—
252C22×C3—44no—
253C22×C3—44no—
254C22×C3—44no—
255C22×C3—44no—
256C3×C4—44no—
257C3×C4—44no—
258Dic3—62no—
259Dic3—62no—
260Dic3—62no—
261Dic3—62no—
262Dic3—124no—
263Dic3—124no—
264Dic3—124no—
265C32#185111yescharacteristic, complemented, Sylow
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23C4⋊#15712yes—
273C23C22×#15711yescharacteristic
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—91no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—91no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—92no—
286C2×C4—92no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—181no—
292C2×C4—181no—
293C2×C4—181no—
294C2×C4—181no—
295C2×C4—181no—
296C2×C4—181no—
297C2×C4—181no—
298C2×C4#379212yescomplemented
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—
310C2×C3—48no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#6428311yescharacteristic
319C22C2×C4⋊#15711yescharacteristic
320C22#6428711yescharacteristic
321C22#6428711yescharacteristic
322C22D4×#15711yescharacteristic
323C22D4×#15711yescharacteristic
324C22C2×#379211yescharacteristic
325C4—22no—
326C4—41no—
327C4—91no—
328C4—91no—
329C4—91no—
330C4—91no—
331C4—182no—
332C4—182no—
333C4—361no—
334C3—22no—
335C2—42no—
336C2#1059374111yescharacteristic
337C2#1059374211yescharacteristic
338C2#1059374311yescharacteristic
339C2#1059374611yescharacteristic
340C2#1059380511yescharacteristic
341C2#1059382011yescharacteristic
342C2#1059382111yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
FittingC2×C32×C22⋊C4C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1851
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63779C2semidirect
4. C2×C4⋊#622C2semidirect
6. #10590207C2semidirect
7. #10590207C2semidirect
79. C2×C32×C4M16semidirect
92. C2×C3⋊Dic3M16semidirect
265. C32#1851semidirect
298. C2×C4#3792semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C2×C22⋊#6222
C2×#637792
C2×C4⋊#6222
C22⋊C4×C3⋊Dic32
#105902072
#18519