Finite Group Databasebeta

← C3×#71873 #11796569

Subgroups — C3×#71873 #11796569

Order 1152.

595 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 595 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C32×#536C211yesmaximal, characteristic
2C3×#5237C212yesmaximal
3C3×#4548C214yesmaximal, complemented
4C3×#2135—31nomaximal
5#71873C311yesmaximal, characteristic, direct product factor
6C2×C32×#41C2211yescharacteristic
7C22×C32×Q8C411yescharacteristic
8C32×C4⋊Q8C2212yes—
9C32×#124C412yes—
10C32×#123—22no—
11C32×C22⋊Q8—22no—
12C32×#117C411yescharacteristic
13C2×C3×#208—22no—
14C3×#836C2214yes—
15C3×#833—22no—
16C3×#536—21no—
17C3×#536D311yescharacteristic
18C3×#536C2×C311yescharacteristic
19C3×#413—32no—
20#5237C2×C312yes—
21C3×#356—34no—
22#4548C2×C314yescomplemented
23C32×#41—42no—
24C2×C32×Q8—21no—
25C2×C32×Q8—42no—
26C2×C32×Q8C2×C412yes—
27C2×C32×Q8C2311yescharacteristic
28C2×C32×D4C2×C411yescharacteristic
29C2×C32×D4D412yes—
30C22×C32×C4—21no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D412yes—
33C32×C4⋊C4—21no—
34C32×C4⋊C4—24no—
35C32×C22⋊C4—21no—
36C32×C22⋊C4—24no—
37C32×C42C2×C412yes—
38C3×#208—24no—
39C3×#208—42no—
40C2×C3×C3⋊C8—42no—
41#2135—31noSylow
42C2×C3×#41—21no—
43C2×C3×#41C2×D311yescharacteristic
44C2×C3×#41C22×C311yescharacteristic
45C22×C3×Q8—21no—
46C22×C3×Q8Dic311yescharacteristic
47C22×C3×Q8C3×C411yescharacteristic
48C2×C3×M16—62no—
49C3×C4⋊Q8—22no—
50C3×C4⋊Q8C2×D312yes—
51C3×C4⋊Q8C22×C312yes—
52C3×#124—22no—
53C3×#124Dic312yes—
54C3×#124C3×C412yes—
55C3×#123—24no—
56C3×#123—22no—
57C3×#123—22no—
58C3×C22⋊Q8—24no—
59C3×C22⋊Q8—22no—
60C3×C22⋊Q8—22no—
61C3×#117—21no—
62C3×#117Dic311yescharacteristic
63C3×#117C3×C411yescharacteristic
64C2×#208—22no—
65C3×#101—34no—
66C3×#100—62no—
67#836C22×C314yes—
68#833—22no—
69C23×C32C22⋊C412yes—
70C23×C32C22⋊C411yescharacteristic
71C32×Q8—41no—
72C32×Q8—42no—
73C32×Q8—42no—
74C32×D4—41no—
75C32×D4—42no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4—22no—
81C2×C32×C4—42no—
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C22×C411yescharacteristic
84C2×C32×C4C2×D412yes—
85C3×C3⋊C8—44no—
86#536C3×D311yescharacteristic
87#413—32no—
88#356—34no—
89C3×#41—42no—
90C3×#41—42no—
91C3×#41—44no—
92C2×C3×Q8—22no—
93C2×C3×Q8—21no—
94C2×C3×Q8—21no—
95C2×C3×Q8—22no—
96C2×C3×Q8—21no—
97C2×C3×Q8—42no—
98C2×C3×Q8—42no—
99C2×C3×Q8—44no—
100C2×C3×Q8C2×Dic312yes—
101C2×C3×Q8C2×C3×C412yes—
102C2×C3×Q8C22×D311yescharacteristic
103C2×C3×Q8C23×C311yescharacteristic
104C2×C3×D4—21no—
105C2×C3×D4—22no—
106C2×C3×D4C2×Dic311yescharacteristic
107C2×C3×D4#6712yes—
108C2×C3×D4C2×C3×C411yescharacteristic
109C2×C3×D4C3×D412yes—
110C22×C3×C4—22no—
111C22×C3×C4—21no—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—22no—
115C22×C3×C4C2×Dic311yescharacteristic
116C22×C3×C4#6712yes—
117C22×C3×C4C2×C3×C411yescharacteristic
118C22×C3×C4C3×D412yes—
119C3×M16—64no—
120C3×M16—122no—
121C2×C3×C8—122no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—28no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4—24no—
127C3×C4⋊C4—24no—
128C3×C22⋊C4—22no—
129C3×C22⋊C4—28no—
130C3×C22⋊C4—21no—
131C3×C22⋊C4—24no—
132C3×C22⋊C4—21no—
133C3×C22⋊C4—24no—
134C3×C42—22no—
135C3×C42C2×Dic312yes—
136C3×C42C2×C3×C412yes—
137#208—24no—
138#208—42no—
139C2×C3⋊C8—42no—
140C22×C32—21no—
141C22×C32—22no—
142C22×C32—41no—
143C22×C32—42no—
144C22×C32C2×C22⋊C411yescharacteristic
145C32×C4—21no—
146C32×C4—22no—
147C32×C4—42no—
148C32×C4—42no—
149C32×C4#9912yes—
150C2×#41C2×C3×D311yescharacteristic
151C22×Q8C3×Dic311yescharacteristic
152C2×M16—62no—
153C4⋊Q8C2×C3×D312yes—
154#124C3×Dic312yes—
155#123—22no—
156C22⋊Q8—22no—
157#117C3×Dic311yescharacteristic
158#101—34no—
159#100—62no—
160C23×C3—21no—
161C23×C3—22no—
162C23×C3#21712yes—
163C23×C3#21711yescharacteristic
164C23×C3C3×C22⋊C412yes—
165C23×C3C3×C22⋊C411yescharacteristic
166C3×Q8—41no—
167C3×Q8—41no—
168C3×Q8—42no—
169C3×Q8—42no—
170C3×Q8—44no—
171C3×Q8—44no—
172C3×Q8—42no—
173C3×Q8—42no—
174C3×Q8—42no—
175C3×D4—41no—
176C3×D4—42no—
177C3×D4—41no—
178C3×D4—42no—
179C3×D4—42no—
180C3×D4—44no—
181C2×C3×C4—24no—
182C2×C3×C4—22no—
183C2×C3×C4—22no—
184C2×C3×C4—22no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—22no—
188C2×C3×C4—24no—
189C2×C3×C4—24no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—22no—
193C2×C3×C4—22no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—22no—
197C2×C3×C4—42no—
198C2×C3×C4—42no—
199C2×C3×C4—44no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4#21711yescharacteristic
203C2×C3×C4C3×C22⋊C411yescharacteristic
204C2×C3×C4C22×Dic311yescharacteristic
205C2×C3×C4C2×#6712yes—
206C2×C3×C4C22×C3×C411yescharacteristic
207C2×C3×C4C2×C3×D412yes—
208C3×C8—124no—
209C3⋊C8—44no—
210C2×C32—21no—
211C2×C32—41no—
212C2×C32—42no—
213C2×C32C2×#9911yescharacteristic
214#41—42no—
215C2×Q8—21no—
216C2×Q8—42no—
217C2×Q8C2×C3×Dic312yes—
218C2×Q8C22×C3×D311yescharacteristic
219C2×D4C2×C3×Dic311yescharacteristic
220C2×D4C3×#6712yes—
221C22×C4—21no—
222C22×C4C2×C3×Dic311yescharacteristic
223C22×C4C3×#6712yes—
224M16—64no—
225M16—122no—
226C2×C8—122no—
227C4⋊C4—21no—
228C4⋊C4—24no—
229C22⋊C4—21no—
230C22⋊C4—24no—
231C42C2×C3×Dic312yes—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—22no—
237C22×C3—21no—
238C22×C3—42no—
239C22×C3—42no—
240C22×C3—41no—
241C22×C3—42no—
242C22×C3—41no—
243C22×C3—42no—
244C22×C3—44no—
245C22×C3C2×#21711yescharacteristic
246C22×C3C2×C3×C22⋊C411yescharacteristic
247C3×C4—22no—
248C3×C4—22no—
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—21no—
252C3×C4—22no—
253C3×C4—42no—
254C3×C4—44no—
255C3×C4—44no—
256C3×C4—42no—
257C3×C4—42no—
258C3×C4—42no—
259C3×C4—42no—
260C3×C4#83412yes—
261C3×C4C3×#9912yes—
262C32#213511yescharacteristic, complemented, Sylow
263C23C3×#21712yes—
264C23C3×#21711yescharacteristic
265Q8—41no—
266Q8—42no—
267Q8—42no—
268D4—41no—
269D4—42no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4C3×#21711yescharacteristic
277C2×C4C22×C3×Dic311yescharacteristic
278C2×C4C2×C3×#6712yes—
279C8—124no—
280C2×C3—22no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—42no—
285C2×C3—41no—
286C2×C3—42no—
287C2×C3—41no—
288C2×C3—42no—
289C2×C3—82no—
290C2×C3C2×#83411yescharacteristic
291C2×C3C2×C3×#9911yescharacteristic
292C22—21no—
293C22—22no—
294C22—41no—
295C22—42no—
296C22C2×C3×#21711yescharacteristic
297C4—22no—
298C4—21no—
299C4—42no—
300C4—42no—
301C4C3×#83412yes—
302C3—21no—
303C3#7187311yescharacteristic, direct product factor
304C3C3×#213511yescharacteristic, complemented
305C2—21no—
306C2—41no—
307C2—42no—
308C2C2×C3×#83411yescharacteristic
subgroupG/H
centerC2×C3C2×#834
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×Q8C22×C3×D3
FittingC32×#536C2
socleC2×C32C2×#99
prime radicalC2×C32×#41C22
cosocleC2×C3×Q8C23×C3
hypercenterC3×#536D3
hypocenterC3C3×#2135
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×#41 ◁ C3×#536

Complements

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

NH ≅ G/Ntype
3. C3×#4548C2semidirect
5. #71873C3direct (N × H)
22. #4548C2×C3semidirect
262. C32#2135semidirect
303. C3#71873direct (N × H)
304. C3C3×#2135semidirect

Maximal subgroups

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

subgroupindex
C32×#5362
C3×#52372
C3×#45482
C3×#21353
#718733