Finite Group Databasebeta

← C3×#71899 #11778808

Subgroups — C3×#71899 #11778808

Order 1152.

507 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 114 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×#544C211yesmaximal, characteristic
2C3×#5044C212yesmaximal
3C3×#4986C211yesmaximal, characteristic
4C3×#4538C212yesmaximal
5C3×#4528C211yesmaximal, characteristic
6C3×#1617—31nomaximal
7#71899C311yesmaximal, characteristic, direct product factor
8C32×C4⋊Q8—22no—
9C32×#125—22no—
10C32×C22⋊Q8—21no—
11C32×C22⋊Q8C2212yes—
12C32×#117—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C3×#835—22no—
16C3×C3⋊#95—21no—
17C3×C3⋊#95—21no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20C3×#807—22no—
21C3×#544—21no—
22C3×#544D311yescharacteristic
23C3×#544C2×C311yescharacteristic
24C3×#484—32no—
25C3×#400—31no—
26#5044C2×C312yes—
27#4986C2×C311yescharacteristic
28C3×#328—32no—
29C3×#324—31no—
30#4538C2×C312yes—
31#4528C2×C311yescharacteristic
32C2×C32×Q8—21no—
33C2×C32×Q8D412yes—
34C22×C32×C4D411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4C2311yescharacteristic
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—22no—
43C32×C4⋊C4—22no—
44C32×C4⋊C4—22no—
45C32×C4⋊C4D412yes—
46C32×C22⋊C4—22no—
47C32×C42—22no—
48C3×C4⋊Dic3—22no—
49C2×C3×C3⋊C8—22no—
50#1617—31noSylow
51C3×C4⋊Q8—24no—
52C3×C4⋊Q8—22no—
53C3×C4⋊Q8—22no—
54C3×#125—24no—
55C3×#125—22no—
56C3×#125—22no—
57C3×C22⋊Q8—22no—
58C3×C22⋊Q8—21no—
59C3×C22⋊Q8—21no—
60C3×C22⋊Q8—22no—
61C3×C22⋊Q8C2×D312yes—
62C3×C22⋊Q8C22×C312yes—
63C3×#117—22no—
64C3×#117—21no—
65C3×#117—21no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—31no—
68C2×C3×C4⋊C4C2×D311yescharacteristic
69C2×C3×C4⋊C4C22×C311yescharacteristic
70C2×C4⋊Dic3C22×C311yescharacteristic
71C3×#107—62no—
72C3×#103—62no—
73C3×C22⋊C8—32no—
74C3×#95—31no—
75C3×#95—61no—
76C3×#95—61no—
77#835—22no—
78C3⋊#95—21no—
79C3⋊#95—21no—
80C3⋊#95C22×C311yescharacteristic
81#830C22×C312yes—
82#807—22no—
83C23×C32C2×D411yescharacteristic
84C32×Q8—42no—
85C32×Q8—81no—
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—22no—
89C2×C32×C4—22no—
90C2×C32×C4—21no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4Q1612yes—
94C2×C32×C4C2×D412yes—
95C2×C3×Dic3—41no—
96C2×C3×Dic3—41no—
97C2×C3×Dic3—42no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C3×C3⋊C8—42no—
101#544C3×D311yescharacteristic
102#484—32no—
103#400—31no—
104#328—32no—
105#324—31no—
106C2×C3×Q8—22no—
107C2×C3×Q8—21no—
108C2×C3×Q8—21no—
109C2×C3×Q8—22no—
110C2×C3×Q8#6712yes—
111C2×C3×Q8C3×D412yes—
112C22×C3×C4—21no—
113C22×C3×C4—21no—
114C22×C3×C4—21no—
115C22×C3×C4—61no—
116C22×C3×C4—61no—
117C22×C3×C4#6711yescharacteristic
118C22×C3×C4#6711yescharacteristic
119C22×C3×C4C3×D411yescharacteristic
120C22×C3×C4C3×D411yescharacteristic
121C22×C3×C4C22×D311yescharacteristic
122C22×C3×C4C23×C311yescharacteristic
123C22×Dic3—21no—
124C22×Dic3—21no—
125C2×C3×C8—62no—
126C3×C4⋊C4—24no—
127C3×C4⋊C4—22no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—22no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—24no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—24no—
140C3×C4⋊C4—22no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4—62no—
146C3×C4⋊C4#6712yes—
147C3×C4⋊C4C3×D412yes—
148C3×C22⋊C4—24no—
149C3×C22⋊C4—22no—
150C3×C22⋊C4—22no—
151C3×C42—24no—
152C3×C42—22no—
153C3×C42—22no—
154C4⋊Dic3—22no—
155C2×C3⋊C8—22no—
156C22×C32—21no—
157C22×C32—21no—
158C22×C32#12011yescharacteristic
159C22×C32C2×Q1611yescharacteristic
160C22×C32#13711yescharacteristic
161C32×C4—22no—
162C32×C4—22no—
163C32×C4—42no—
164C32×C4—41no—
165C32×C4—42no—
166C3×Dic3—81no—
167C3×Dic3—81no—
168C4⋊Q8—22no—
169#125—22no—
170C22⋊Q8—21no—
171C22⋊Q8C2×C3×D312yes—
172#117—21no—
173C2×C4⋊C4—31no—
174C2×C4⋊C4C2×C3×D311yescharacteristic
175#107—62no—
176#103—62no—
177C22⋊C8—32no—
178#95—31no—
179#95—61no—
180#95—61no—
181C23×C3—21no—
182C23×C3C2×#6711yescharacteristic
183C23×C3C2×C3×D411yescharacteristic
184C3×Q8—42no—
185C3×Q8—42no—
186C3×Q8—82no—
187C3×Q8—82no—
188C3×Q8—81no—
189C3×Q8—81no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—21no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—81no—
212C2×C3×C4—81no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4—122no—
216C2×C3×C4—121no—
217C2×C3×C4—121no—
218C2×C3×C4#21612yes—
219C2×C3×C4C3×Q1612yes—
220C2×C3×C4C2×#6712yes—
221C2×C3×C4C2×C3×D412yes—
222C2×Dic3—41no—
223C2×Dic3—41no—
224C2×Dic3—42no—
225C2×Dic3—41no—
226C2×Dic3—41no—
227C3×C8—122no—
228C3⋊C8—42no—
229C2×C32—21no—
230C2×C32—21no—
231C2×C32#45111yescharacteristic
232C2×C32#45411yescharacteristic
233C2×C32#45811yescharacteristic
234C2×Q8—21no—
235C2×Q8C3×#6712yes—
236C22×C4—61no—
237C22×C4—61no—
238C22×C4C3×#6711yescharacteristic
239C22×C4C3×#6711yescharacteristic
240C22×C4C22×C3×D311yescharacteristic
241C2×C8—62no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—62no—
249C4⋊C4C3×#6712yes—
250C22⋊C4—22no—
251C42—22no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3—21no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—21no—
259C22×C3—41no—
260C22×C3—41no—
261C22×C3#94211yescharacteristic
262C22×C3C2×#21611yescharacteristic
263C22×C3#95311yescharacteristic
264C22×C3C3×#12011yescharacteristic
265C22×C3C2×C3×Q1611yescharacteristic
266C22×C3C3×#13711yescharacteristic
267C3×C4—24no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—22no—
271C3×C4—22no—
272C3×C4—42no—
273C3×C4—42no—
274C3×C4—44no—
275C3×C4—44no—
276C3×C4—41no—
277C3×C4—42no—
278C3×C4—42no—
279C3×C4—42no—
280C3×C4—41no—
281C3×C4—42no—
282C3×C4—241no—
283C3×C4—241no—
284Dic3—81no—
285Dic3—81no—
286C32#161711yescharacteristic, complemented, Sylow
287C23C2×C3×#6711yescharacteristic
288Q8—42no—
289Q8—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—121no—
298C2×C4—121no—
299C2×C4—122no—
300C2×C4—121no—
301C2×C4—121no—
302C2×C4C3×#21612yes—
303C2×C4C2×C3×#6712yes—
304C8—122no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—21no—
309C2×C3—21no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—41no—
313C2×C3—41no—
314C2×C3#522811yescharacteristic
315C2×C3#524311yescharacteristic
316C2×C3#524511yescharacteristic
317C2×C3C3×#45111yescharacteristic
318C2×C3C3×#45411yescharacteristic
319C2×C3C3×#45811yescharacteristic
320C22—21no—
321C22—21no—
322C22C3×#94211yescharacteristic
323C22C2×C3×#21611yescharacteristic
324C22C3×#95311yescharacteristic
325C4—22no—
326C4—22no—
327C4—41no—
328C4—42no—
329C4—42no—
330C4—241no—
331C4—241no—
332C3—21no—
333C3#7189911yescharacteristic, direct product factor
334C3C3×#161711yescharacteristic, complemented
335C2—21no—
336C2—21no—
337C2C3×#522811yescharacteristic
338C2C3×#524311yescharacteristic
339C2C3×#524511yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#544C2
socleC22×C32#120
prime radicalC23×C32C2×D4
hypercenterC3×#544D3
hypocenterC3C3×#1617
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#544

Complements

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

NH ≅ G/Ntype
7. #71899C3direct (N × H)
286. C32#1617semidirect
333. C3#71899direct (N × H)
334. C3C3×#1617semidirect

Maximal subgroups

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

subgroupindex
C32×#5442
C3×#50442
C3×#49862
C3×#45382
C3×#45282
C3×#16173
#718993