Finite Group Databasebeta

← C4×#63728 #11783819

Subgroups — C4×#63728 #11783819

Order 1152.

516 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#3797C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic
3C2×#63728C212yesmaximal
4C4×#3712C211yesmaximal, characteristic
5#10590052C212yesmaximal
6C2×#3797C2211yescharacteristic
7C2×#3788C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×Dic6—21no—
10C4×#627—21no—
11#63900C2211yescharacteristic
12#63883C412yes—
13C4×#624C412yes—
14#63843—21no—
15#63838—21no—
16C2×#3712C2212yes—
17#63777—21no—
18C4×#622—21no—
19#63728C418yesdirect product factor
20C3×C4×C3⋊C8—21no—
21#63555—21no—
22C4×D3×Q8—61no—
23C4×ΓL(1,𝔽25)—61no—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×Dic6—21no—
28C2×#627—21no—
29C2×#624C2×C412yes—
30C2×#624C2×C412yes—
31#3797—22no—
32#3797C2×C414yes—
33C2×#622—22no—
34#3788—22no—
35#3788C2×C414yes—
36C32×C42D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3D411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C3×C4⋊Dic3—21no—
41C3×Dic3⋊C4—22no—
42C3×C4×Dic3—22no—
43C2×C3×C3⋊C8—22no—
44#3724—21no—
45Dic3⋊Dic3—22no—
46Dic32—22no—
47#3712—22no—
48#3712C2×C414yes—
49C4×#101—91nomaximal, Sylow
50C2×D3×Q8—61no—
51C3×C4×Q8—61no—
52Q8×Dic3—61no—
53C2×ΓL(1,𝔽25)—62no—
54D3×C4⋊C4—62no—
55D3×C4⋊C4—61no—
56#887—62no—
57#887—61no—
58C42×D3—62no—
59C42×D3—61no—
60C42×D3—61no—
61C4×Dic6—21no—
62C4×Dic6—62no—
63C3×C4×C8—61no—
64#815—62no—
65C4×C3⋊C8—21no—
66C22×C3⋊D3C22×C411yescharacteristic
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C2×D411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—41no—
75C4×C3⋊D3C22×C412yes—
76C4×C3⋊D3#4112yes—
77C2×C3×Dic3—22no—
78C2×C3×Dic3—22no—
79C3×Dic6—24no—
80#627—24no—
81#624—22no—
82#624—42no—
83#624C4214yes—
84#622—24no—
85C3×C3⋊C8—24no—
86C2×C4×Q8—91no—
87C2×#101—92no—
88C4×M16—91no—
89C4×M16—91no—
90#343—92no—
91C2×C3×Q8—61no—
92D3×Q8—64no—
93D3×Q8—64no—
94C2×C4×D3—62no—
95C2×C4×D3—61no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—62no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×Dic6—21no—
103C2×Dic6—62no—
104C2×C3×C8—62no—
105C3×C4⋊C4—62no—
106C3×C4⋊C4—61no—
107C3×C42—21no—
108C3×C42—21no—
109C3×C42—62no—
110C4⋊Dic3—21no—
111C4⋊Dic3—62no—
112Dic3⋊C4—22no—
113Dic3⋊C4—62no—
114Dic3⋊C4—62no—
115C4×Dic3—22no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C4×Dic3—62no—
123C4×Dic3—62no—
124C2×C3⋊C8—22no—
125ΓL(1,𝔽25)—64no—
126ΓL(1,𝔽25)—64no—
127C22×C32C2×C22⋊C411yescharacteristic
128C2×C3⋊D3—21no—
129C2×C3⋊D3—21no—
130C2×C3⋊D3C2×C4211yescharacteristic
131C2×C3⋊D3#11711yescharacteristic
132C32×C4—21no—
133C32×C4#10112yescomplemented
134C32×C4C4×D412yes—
135C3⋊Dic3—21no—
136C3⋊Dic3—21no—
137C3⋊Dic3C4×D412yes—
138C3×Dic3—24no—
139C3×Dic3—42no—
140C22×Q8—91no—
141C2×M16—92no—
142C2×M16—92no—
143C4×Q8—61no—
144C4×Q8—181no—
145C4×Q8—181no—
146C4×Q8—181no—
147C2×C4⋊C4—91no—
148C2×C4⋊C4—92no—
149C2×C42—92no—
150C2×C42—91no—
151#101—98no—
152#97—181no—
153#97—181no—
154C4×C8—61no—
155C4×C8—181no—
156C22×D3—61no—
157C22×D3—61no—
158C3×Q8—64no—
159C2×C3×C4—21no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—62no—
166C2×C3×C4—62no—
167C2×Dic3—22no—
168C2×Dic3—22no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C4×D3—64no—
176C4×D3—62no—
177C4×D3—62no—
178C4×D3—62no—
179C4×D3—62no—
180C4×D3—64no—
181C4×D3—64no—
182C4×D3—122no—
183C4×D3—124no—
184C4×D3—122no—
185C4×D3—122no—
186Dic6—24no—
187Dic6—68no—
188C3×C8—64no—
189C3⋊C8—24no—
190C2×C32C4×C22⋊C411yescharacteristic
191C2×C32C2×#10111yescharacteristic
192C2×C32#41311yescharacteristic
193C3⋊D3—21no—
194C3⋊D3—21no—
195C2×Q8—61no—
196C2×Q8—94no—
197C2×Q8—181no—
198C2×Q8—182no—
199C22×C4—92no—
200C22×C4—92no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—91no—
204M16—94no—
205M16—94no—
206M16—182no—
207M16—182no—
208C2×C8—62no—
209C2×C8—182no—
210C4⋊C4—61no—
211C4⋊C4—62no—
212C4⋊C4—181no—
213C4⋊C4—182no—
214C42—62no—
215C42—91no—
216C42—91no—
217C42—91no—
218C42—182no—
219C42GO+(4,𝔽2)11yescharacteristic
220C22×C3—21no—
221C22×C3—21no—
222C2×D3—61no—
223C2×D3—61no—
224C2×D3—61no—
225C2×D3—61no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—121no—
229C2×D3—121no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—22no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—41no—
236C3×C4—64no—
237C3×C4—122no—
238Dic3—24no—
239Dic3—42no—
240Dic3—62no—
241Dic3—62no—
242Dic3—62no—
243Dic3—121no—
244Dic3—121no—
245Dic3—121no—
246C32C4×#10111yescharacteristic, complemented, Sylow
247C23—91no—
248Q8—64no—
249Q8—184no—
250C2×C4—62no—
251C2×C4—62no—
252C2×C4—94no—
253C2×C4—91no—
254C2×C4—92no—
255C2×C4—92no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—182no—
259C2×C4—182no—
260C2×C4—361no—
261C2×C4—362no—
262C2×C4D32⋊C411yescharacteristic
263C2×C4D32⋊C411yescharacteristic
264C2×C4C2×GO+(4,𝔽2)11yescharacteristic
265C8—64no—
266C8—184no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273D3—62no—
274D3—62no—
275D3—121no—
276D3—121no—
277C22—91no—
278C22—91no—
279C22—181no—
280C22—181no—
281C22C2×D32⋊C411yescharacteristic
282C4—21no—
283C4—64no—
284C4—92no—
285C4—122no—
286C4—181no—
287C4—181no—
288C4#6372812yesdirect product factor
289C4C4×GO+(4,𝔽2)12yes—
290C3—21no—
291C3—21no—
292C2—181no—
293C2—181no—
294C2#1059331111yescharacteristic
295C2C2×#6372811yescharacteristic
296C2C4×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊D3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32C4×#101
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
19. #63728C4direct (N × H)
133. C32×C4#101semidirect
246. C32C4×#101semidirect
288. C4#63728direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#37972
C4×#37882
C2×#637282
C4×#37122
#105900522
C4×#1019