Finite Group Databasebeta

← C3×#69220 #11796641

Subgroups — C3×#69220 #11796641

Order 1152.

485 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#919C211yesmaximal, characteristic
2C2×C3×D3×C16C211yesmaximal, characteristic, complemented
3C3×#4880C211yesmaximal, characteristic, complemented
4C32×#358C211yesmaximal, characteristic, complemented
5C3×#4564C211yesmaximal, characteristic, complemented
6C3×#4509C211yesmaximal, characteristic, complemented
7C3×#4491C211yesmaximal, characteristic, complemented
8C3×#2138—31nomaximal
9#69220C311yesmaximal, characteristic, direct product factor
10C2×C3×#239—21no—
11C2×C32×Q16C2211yescharacteristic
12C2×C3×#215—21no—
13C3×#919—22no—
14C3×#919C414yescomplemented
15C2×C3×D24C2211yescharacteristic
16C2×C3×D3×C8C2211yescharacteristic
17C3×#892—21no—
18C2×C32×C16C2211yescharacteristic
19C32×#107C2211yescharacteristic
20C3×#818C2211yescharacteristic
21C2×C3×C3⋊C16C2211yescharacteristic
22C3×#808—21no—
23C3×D3×C16—22no—
24C2×C3×#135—31no—
25C2×#919C2×C311yescharacteristic
26C22×C3×C16—31no—
27C3×#427—31no—
28C2×D3×C16C2×C311yescharacteristic, complemented
29#4880C2×C311yescharacteristic, complemented
30C3×#358—21no—
31C3×#358—31no—
32C3×#358D311yescharacteristic, complemented
33C3×#358C2×C311yescharacteristic, complemented
34C3×#357—31no—
35C3×#357—31no—
36#4564C2×C311yescharacteristic, complemented
37#4509C2×C311yescharacteristic, complemented
38#4491C2×C311yescharacteristic, complemented
39C2×C32×Q8—21no—
40C3×#239—24no—
41C3×#239—42no—
42C2×C3×D12—21no—
43C2×C3×D12—41no—
44C2×C3×C4×D3—41no—
45C2×C3×C4×D3D411yescharacteristic
46C32×Q16—21no—
47C32×Q16C2×C412yes—
48C2×C32×C8C2311yescharacteristic
49C32×C4⋊C4—21no—
50C3×#215—24no—
51C3×(C2×D3)⋊C4—41no—
52C3×C4⋊Dic3—21no—
53C3×C4×Dic3—41no—
54C2×C3×C3⋊C8D411yescharacteristic
55C3×D24—21no—
56C3×D24C2×C412yes—
57C3×D3×C8C2×C412yes—
58C3×D3×C8D412yes—
59C32×C16—21no—
60C3×C3⋊C16—21no—
61#2138—31noSylow
62C2×C3×#41—61no—
63C2×#239—21no—
64C3×#135—34no—
65C3×#135—62no—
66C2×C3×Q16—21no—
67C2×C3×Q16C2×D311yescharacteristic
68C2×C3×Q16C22×C311yescharacteristic
69C2×C3×SD16—61no—
70C2×C3×D8—31no—
71C22×C3×C8—31no—
72C3×#117—61no—
73C2×#215—21no—
74#919—22no—
75#919C3×C414yescomplemented
76C2×D24C22×C311yescharacteristic
77C2×D3×C8C22×C311yescharacteristic
78#892—21no—
79C2×C3×C16—21no—
80C2×C3×C16—31no—
81C2×C3×C16—62no—
82C2×C3×C16C2×D311yescharacteristic
83C2×C3×C16C22×C311yescharacteristic
84C3×#107—21no—
85C3×#107—31no—
86C3×#107C2×D311yescharacteristic
87C3×#107C22×C311yescharacteristic
88C3×#106—61no—
89#818C22×C311yescharacteristic
90C2×C3⋊C16C22×C311yescharacteristic
91#808—21no—
92D3×C16—22no—
93C22×C3×D3—41no—
94C22×C3×D3D811yescharacteristic
95C32×Q8—22no—
96C32×Q8—41no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C3×Dic3—41no—
101C2×C3×Dic3D811yescharacteristic
102C3×D12—22no—
103C3×D12—44no—
104C3×D12—41no—
105C3×C4×D3—44no—
106C3×C4×D3C22⋊C412yes—
107C3×C4×D3SD1612yes—
108C32×C8C22×C411yescharacteristic
109C32×C8C2×D411yescharacteristic
110C3×C3⋊C8C22⋊C412yes—
111C2×#135—31no—
112C22×C16—31no—
113#427—31no—
114#358—31no—
115#358C3×D311yescharacteristic, complemented
116#357—31no—
117#357—31no—
118C3×#41—64no—
119C3×#41—122no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—41no—
123C2×C3×D4—61no—
124C2×C3×D4—121no—
125C22×C3×C4—31no—
126C22×C3×C4—121no—
127#239—24no—
128#239—42no—
129C2×D12—21no—
130C2×D12—41no—
131C2×C4×D3—41no—
132C2×C4×D3C3×D411yescharacteristic
133C3×Q16—21no—
134C3×Q16—21no—
135C3×Q16—22no—
136C3×Q16—41no—
137C3×Q16C4×D312yes—
138C3×Q16C2×C3×C412yes—
139C3×SD16—64no—
140C3×D8—32no—
141C3×D8—61no—
142C2×C3×C8—21no—
143C2×C3×C8—31no—
144C2×C3×C8—32no—
145C2×C3×C8—32no—
146C2×C3×C8C22×D311yescharacteristic
147C2×C3×C8C23×C311yescharacteristic
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—61no—
152C3×C22⋊C4—121no—
153C3×C42—121no—
154#215—24no—
155(C2×D3)⋊C4—41no—
156C4⋊Dic3—21no—
157C4×Dic3—41no—
158C2×C3⋊C8C3×D411yescharacteristic
159D24—21no—
160D24C2×C3×C412yes—
161D3×C8C2×C3×C412yes—
162D3×C8C3×D412yes—
163C3×C16—21no—
164C3×C16—21no—
165C3×C16—41no—
166C3×C16—61no—
167C3⋊C16—21no—
168C22×C32C2×D811yescharacteristic
169C2×C3×D3—21no—
170C2×C3×D3—21no—
171C2×C3×D3—42no—
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C2×C3×D3#10212yes—
175C32×C4—42no—
176C32×C4—81no—
177C32×C4C2×C22⋊C411yescharacteristic
178C32×C4C2×SD1611yescharacteristic
179C3×Dic3—81no—
180C3×Dic3#10212yes—
181C2×#41—61no—
182#135—34no—
183#135—62no—
184C2×Q16C2×C3×D311yescharacteristic
185C2×SD16—61no—
186C2×D8—31no—
187C22×C8—31no—
188#117—61no—
189C2×C16—31no—
190C2×C16—62no—
191C2×C16C2×C3×D311yescharacteristic
192#107—31no—
193#107C2×C3×D311yescharacteristic
194#106—61no—
195C23×C3—31no—
196C23×C3—121no—
197C22×D3—41no—
198C22×D3C3×D811yescharacteristic
199C3×Q8—22no—
200C3×Q8—22no—
201C3×Q8—42no—
202C3×Q8—41no—
203C3×Q8—41no—
204C3×Q8—81no—
205C3×D4—62no—
206C3×D4—124no—
207C3×D4—121no—
208C2×C3×C4—21no—
209C2×C3×C4—31no—
210C2×C3×C4—32no—
211C2×C3×C4—32no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—81no—
217C2×C3×C4—81no—
218C2×C3×C4—124no—
219C2×C3×C4—121no—
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4C2×C3×D411yescharacteristic
222C2×Dic3—41no—
223C2×Dic3C3×D811yescharacteristic
224D12—22no—
225D12—44no—
226D12—41no—
227C4×D3—44no—
228C4×D3C3×C22⋊C412yes—
229C4×D3C3×SD1612yes—
230C3×C8—21no—
231C3×C8—21no—
232C3×C8—32no—
233C3×C8C2×C4×D311yescharacteristic
234C3×C8D3×D411yescharacteristic
235C3×C8C22×C3×C411yescharacteristic
236C3×C8C2×C3×D411yescharacteristic
237C3⋊C8C3×C22⋊C412yes—
238C2×C32C2×#10211yescharacteristic
239C2×C32#50811yescharacteristic
240C2×C32#50811yescharacteristic
241C3×D3—22no—
242C3×D3—82no—
243#41—64no—
244#41—122no—
245C2×Q8—21no—
246C2×D4—61no—
247C2×D4—121no—
248C22×C4—31no—
249C22×C4—121no—
250Q16—21no—
251Q16C3×C4×D312yes—
252SD16—64no—
253D8—32no—
254D8—61no—
255C2×C8—31no—
256C2×C8—32no—
257C2×C8—32no—
258C2×C8C22×C3×D311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—61no—
261C22⋊C4—121no—
262C42—121no—
263C16—21no—
264C16—61no—
265C22×C3—21no—
266C22×C3—32no—
267C22×C3—61no—
268C22×C3—61no—
269C22×C3—122no—
270C22×C3—241no—
271C22×C3—241no—
272C22×C3D3×D811yescharacteristic
273C22×C3C2×C3×D811yescharacteristic
274C2×D3—21no—
275C2×D3—21no—
276C2×D3—42no—
277C2×D3—81no—
278C2×D3—81no—
279C2×D3C3×#10212yes—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—32no—
283C3×C4—42no—
284C3×C4—42no—
285C3×C4—82no—
286C3×C4—81no—
287C3×C4—81no—
288C3×C4—161no—
289C3×C4—241no—
290C3×C4D3×C22⋊C411yescharacteristic
291C3×C4D3×SD1611yescharacteristic
292C3×C4C2×C3×C22⋊C411yescharacteristic
293C3×C4C2×C3×SD1611yescharacteristic
294Dic3—81no—
295Dic3C3×#10212yes—
296C32#213811yescharacteristic, complemented, Sylow
297C23—31no—
298C23—121no—
299Q8—22no—
300Q8—41no—
301D4—62no—
302D4—124no—
303D4—121no—
304C2×C4—31no—
305C2×C4—32no—
306C2×C4—32no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—124no—
310C2×C4—121no—
311C2×C4C3×D3×D411yescharacteristic
312C8—32no—
313C8C2×C3×C4×D311yescharacteristic
314C8C3×D3×D411yescharacteristic
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—62no—
319C2×C3—242no—
320C2×C3D3×#10211yescharacteristic
321C2×C3#491611yescharacteristic
322C2×C3#491911yescharacteristic
323C2×C3C2×C3×#10211yescharacteristic
324C2×C3C3×#50811yescharacteristic
325C2×C3C3×#50811yescharacteristic
326D3—22no—
327D3—82no—
328C22—32no—
329C22—61no—
330C22—61no—
331C22—122no—
332C22—241no—
333C22—241no—
334C22C3×D3×D811yescharacteristic
335C4—32no—
336C4—42no—
337C4—81no—
338C4—241no—
339C4C3×D3×C22⋊C411yescharacteristic
340C4C3×D3×SD1611yescharacteristic
341C3—21no—
342C3#6922011yescharacteristic, direct product factor
343C3C3×#213811yescharacteristic, complemented
344C2—62no—
345C2—242no—
346C2C3×D3×#10211yescharacteristic
347C2C3×#491611yescharacteristic
348C2C3×#491911yescharacteristic
subgroupG/H
centerC22×C3D3×D8
commutatorC3×C8C22×C3×C4
FrattiniC2×C8C22×C3×D3
FittingC32×#358C2
socleC22×C32C2×D8
prime radicalC2×C3×#919C2
cosocleC2×C3×C8C23×C3
hypercenterC3×#358D3
hypocenterC3C3×#2138
LCSG ▷ C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C3×#358

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C16C2semidirect
3. C3×#4880C2semidirect
4. C32×#358C2semidirect
5. C3×#4564C2semidirect
6. C3×#4509C2semidirect
7. C3×#4491C2semidirect
9. #69220C3direct (N × H)
14. C3×#919C4semidirect
28. C2×D3×C16C2×C3semidirect
29. #4880C2×C3semidirect
32. C3×#358D3semidirect
33. C3×#358C2×C3semidirect
36. #4564C2×C3semidirect
37. #4509C2×C3semidirect
38. #4491C2×C3semidirect
75. #919C3×C4semidirect
115. #358C3×D3semidirect
296. C32#2138semidirect
342. C3#69220direct (N × H)
343. C3C3×#2138semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9192
C2×C3×D3×C162
C3×#48802
C32×#3582
C3×#45642
C3×#45092
C3×#44912
C3×#21383
#692203