Finite Group Databasebeta

← C3×D3×#356 #11796469

Subgroups — C3×D3×#356 #11796469

Order 1152.

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

normal subgroups only

This group has 510 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
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2C3×D3×#101C212yesmaximal
3C32×#356C211yesmaximal, characteristic, complemented
4C3×#4548C211yesmaximal, characteristic, complemented
5C3×#4478C212yesmaximal, complemented
6C2×C3×#356—31nomaximal
7D3×#356C311yesmaximal, characteristic, direct product factor
8C2×C3×D3×Q8C411yescharacteristic
9C2×C3×D3×Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C3×#944C411yescharacteristic
12C3×#944C2211yescharacteristic
13C3×D3×M16—22no—
14C3×D3×C4⋊C4—22no—
15C3×#888—22no—
16C3×C42×D3C411yescharacteristic
17C3×#869C411yescharacteristic
18C32×#101C2212yes—
19C3×#836C2212yes—
20C3×#824—22no—
21C2×C3×C4⋊Q8—31no—
22D3×C4⋊Q8C2×C311yescharacteristic
23C2×C3×#101—32no—
24D3×#101C2×C312yes—
25C3×#356—21no—
26C3×#356—31no—
27C3×#356—32no—
28C3×#356D311yescharacteristic, direct product factor
29C3×#356C2×C311yescharacteristic, complemented
30#4548C2×C311yescharacteristic, complemented
31#4478C2×C312yescomplemented
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×Q8C2311yescharacteristic
34C3×D3×Q8—41no—
35C3×D3×Q8—41no—
36C3×D3×Q8—41no—
37C3×D3×Q8—41no—
38C2×C3×C4×D3—21no—
39C2×C3×C4×D3—21no—
40C2×C3×C4×D3C2×C411yescharacteristic
41C2×C3×C4×D3D412yes—
42C2×C3×Dic6—21no—
43C2×C3×Dic6C2×C411yescharacteristic
44C2×C3×Dic6C2×C411yescharacteristic
45C2×C3×Dic6D412yes—
46C32×M16—22no—
47C32×C4⋊C4—22no—
48C32×C42C2×C411yescharacteristic
49C3×C4⋊Dic3—22no—
50C3×Dic3⋊C4—22no—
51C3×Dic3⋊C4—22no—
52C3×C4×Dic3—21no—
53C3×C4×Dic3C2×C411yescharacteristic
54C3×#208—22no—
55C3×ΓL(1,𝔽25)—42no—
56C3×D3×C8—42no—
57C2×#356—31noSylow
58C22×C3×Q8—31no—
59C22×C3×Q8—31no—
60C2×D3×Q8C3×C411yescharacteristic
61C2×D3×Q8C22×C311yescharacteristic
62C2×C3×M16—62no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8—31no—
65C3×C4⋊Q8—31no—
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8—62no—
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×C4⋊Q8C22×C311yescharacteristic
70C2×C3×C4⋊C4—62no—
71C2×C3×C42—31no—
72#944C3×C411yescharacteristic
73#944C22×C311yescharacteristic
74D3×M16—22no—
75D3×C4⋊C4—22no—
76#888—22no—
77C42×D3C3×C411yescharacteristic
78#869C3×C411yescharacteristic
79C3×#101—22no—
80C3×#101—32no—
81C3×#101—62no—
82C3×#101C2×D312yes—
83C3×#101C22×C312yes—
84#836C22×C312yes—
85#824—22no—
86C22×C3×D3C22⋊C411yescharacteristic
87C32×Q8—41no—
88C32×Q8—41no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4C22×C411yescharacteristic
92C2×C32×C4C2×D412yes—
93C2×C3×Dic3—21no—
94C2×C3×Dic3—21no—
95C2×C3×Dic3C22⋊C411yescharacteristic
96C2×C3×Dic3C22⋊C412yes—
97C3×C4×D3—24no—
98C3×C4×D3—22no—
99C3×C4×D3—22no—
100C3×C4×D3—21no—
101C3×C4×D3—21no—
102C3×C4×D3—41no—
103C3×C4×D3—41no—
104C3×Dic6—41no—
105C3×Dic6—42no—
106C3×Dic6—42no—
107C3×Dic6—41no—
108C32×C8—42no—
109C3×C3⋊C8—42no—
110C2×C4⋊Q8—31no—
111C2×#101—32no—
112#356—31no—
113#356—32no—
114#356C3×D311yescharacteristic, direct product factor
115C2×C3×Q8—21no—
116C2×C3×Q8—21no—
117C2×C3×Q8—31no—
118C2×C3×Q8—32no—
119C2×C3×Q8—31no—
120C2×C3×Q8—61no—
121C2×C3×Q8—121no—
122C2×C3×Q8—121no—
123C2×C3×Q8—121no—
124C2×C3×Q8—121no—
125C2×C3×Q8C4×D311yescharacteristic
126C2×C3×Q8C2×C3×C411yescharacteristic
127C2×C3×Q8C22×D311yescharacteristic
128C2×C3×Q8C23×C311yescharacteristic
129C22×C3×C4—31no—
130C22×C3×C4—32no—
131C22×C3×C4—61no—
132C22×C3×C4—61no—
133D3×Q8—41no—
134D3×Q8—41no—
135D3×Q8—41no—
136D3×Q8—41no—
137C2×C4×D3—21no—
138C2×C4×D3—21no—
139C2×C4×D3C2×C3×C411yescharacteristic
140C2×C4×D3C3×D412yes—
141C2×Dic6—21no—
142C2×Dic6C2×C3×C411yescharacteristic
143C2×Dic6C2×C3×C411yescharacteristic
144C2×Dic6C3×D412yes—
145C3×M16—22no—
146C3×M16—22no—
147C3×M16—42no—
148C3×M16—62no—
149C3×M16—122no—
150C2×C3×C8—122no—
151C3×C4⋊C4—22no—
152C3×C4⋊C4—22no—
153C3×C4⋊C4—42no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4—62no—
156C3×C4⋊C4—62no—
157C3×C42—21no—
158C3×C42—31no—
159C3×C42—61no—
160C3×C42C4×D311yescharacteristic
161C3×C42C2×C3×C411yescharacteristic
162C4⋊Dic3—22no—
163Dic3⋊C4—22no—
164Dic3⋊C4—22no—
165C4×Dic3—21no—
166C4×Dic3C2×C3×C411yescharacteristic
167#208—22no—
168ΓL(1,𝔽25)—42no—
169D3×C8—42no—
170C22×C32C2×C22⋊C411yescharacteristic
171C2×C3×D3—22no—
172C2×C3×D3#9911yescharacteristic
173C2×C3×D3#9911yescharacteristic
174C32×C4—22no—
175C32×C4—22no—
176C32×C4—21no—
177C32×C4—41no—
178C3×Dic3—22no—
179C3×Dic3—21no—
180C3×Dic3—22no—
181C3×Dic3—41no—
182C22×Q8—31no—
183C22×Q8—31no—
184C2×M16—62no—
185C4⋊Q8—31no—
186C4⋊Q8—31no—
187C4⋊Q8—31no—
188C4⋊Q8—62no—
189C4⋊Q8C2×C3×D311yescharacteristic
190C2×C4⋊C4—62no—
191C2×C42—31no—
192#101—32no—
193#101—62no—
194#101C2×C3×D312yes—
195C23×C3—31no—
196C22×D3C3×C22⋊C411yescharacteristic
197C3×Q8—41no—
198C3×Q8—41no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×Q8—81no—
202C3×Q8—81no—
203C3×Q8—122no—
204C3×Q8—121no—
205C3×Q8—121no—
206C3×Q8—122no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—31no—
214C2×C3×C4—32no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—62no—
218C2×C3×C4—62no—
219C2×C3×C4—61no—
220C2×C3×C4—61no—
221C2×C3×C4—64no—
222C2×C3×C4—61no—
223C2×C3×C4—61no—
224C2×C3×C4—121no—
225C2×C3×C4—121no—
226C2×C3×C4C2×C4×D311yescharacteristic
227C2×C3×C4D3×D412yes—
228C2×C3×C4C22×C3×C411yescharacteristic
229C2×C3×C4C2×C3×D412yes—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3C3×C22⋊C411yescharacteristic
233C2×Dic3C3×C22⋊C412yes—
234C4×D3—24no—
235C4×D3—22no—
236C4×D3—22no—
237C4×D3—21no—
238C4×D3—21no—
239C4×D3—41no—
240C4×D3—41no—
241Dic6—41no—
242Dic6—42no—
243Dic6—42no—
244Dic6—41no—
245C3×C8—42no—
246C3×C8—42no—
247C3×C8—82no—
248C3×C8—122no—
249C3⋊C8—42no—
250C2×C32—21no—
251C2×C32C2×#9911yescharacteristic
252C3×D3—21no—
253C3×D3#35612yesdirect product factor
254C2×Q8—31no—
255C2×Q8—32no—
256C2×Q8—31no—
257C2×Q8—61no—
258C2×Q8—121no—
259C2×Q8—121no—
260C2×Q8—121no—
261C2×Q8—121no—
262C2×Q8C3×C4×D311yescharacteristic
263C2×Q8C22×C3×D311yescharacteristic
264C22×C4—31no—
265C22×C4—32no—
266C22×C4—61no—
267C22×C4—61no—
268M16—22no—
269M16—62no—
270M16—122no—
271C2×C8—122no—
272C4⋊C4—22no—
273C4⋊C4—62no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C42—31no—
277C42—61no—
278C42C3×C4×D311yescharacteristic
279C22×C3—21no—
280C22×C3—31no—
281C22×C3—31no—
282C22×C3—62no—
283C22×C3D3×C22⋊C411yescharacteristic
284C22×C3C2×C3×C22⋊C411yescharacteristic
285C2×D3—22no—
286C2×D3C3×#9911yescharacteristic
287C2×D3C3×#9911yescharacteristic
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—22no—
291C3×C4—21no—
292C3×C4—22no—
293C3×C4—21no—
294C3×C4—42no—
295C3×C4—41no—
296C3×C4—42no—
297C3×C4—41no—
298C3×C4—41no—
299C3×C4—62no—
300C3×C4—61no—
301C3×C4—62no—
302C3×C4—81no—
303C3×C4—121no—
304Dic3—22no—
305Dic3—21no—
306Dic3—22no—
307Dic3—41no—
308C32C2×#35611yescharacteristic, complemented, Sylow
309C23—31no—
310Q8—41no—
311Q8—41no—
312Q8—122no—
313Q8—121no—
314Q8—121no—
315Q8—122no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—31no—
319C2×C4—32no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—64no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—121no—
328C2×C4—121no—
329C2×C4C2×C3×C4×D311yescharacteristic
330C2×C4C3×D3×D412yes—
331C8—42no—
332C8—122no—
333C2×C3—21no—
334C2×C3—21no—
335C2×C3—21no—
336C2×C3—32no—
337C2×C3—41no—
338C2×C3—61no—
339C2×C3D3×#9911yescharacteristic
340C2×C3C2×C3×#9911yescharacteristic
341D3—21no—
342D3C3×#35612yesdirect product factor
343C22—31no—
344C22—31no—
345C22—62no—
346C22C3×D3×C22⋊C411yescharacteristic
347C4—22no—
348C4—22no—
349C4—21no—
350C4—41no—
351C4—62no—
352C4—61no—
353C4—62no—
354C4—121no—
355C3—21no—
356C3D3×#35611yescharacteristic, direct product factor
357C3C2×C3×#35611yescharacteristic, complemented
358C2—21no—
359C2—32no—
360C2—61no—
361C2C3×D3×#9911yescharacteristic
subgroupG/H
centerC2×C3D3×#99
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×Q8C22×C3×D3
FittingC32×#356C2
socleC2×C32C2×#99
prime radicalC22×C3×D3C22⋊C4
cosocleC2×C3×Q8C23×C3
hypercenterC3×#356D3
hypocenterC3C2×C3×#356
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×Q8 ◁ C3×#356

Complements

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

NH ≅ G/Ntype
3. C32×#356C2semidirect
4. C3×#4548C2semidirect
5. C3×#4478C2semidirect
7. D3×#356C3direct (N × H)
28. C3×#356D3direct (N × H)
29. C3×#356C2×C3semidirect
30. #4548C2×C3semidirect
31. #4478C2×C3semidirect
114. #356C3×D3direct (N × H)
253. C3×D3#356direct (N × H)
308. C32C2×#356semidirect
342. D3C3×#356direct (N × H)
356. C3D3×#356direct (N × H)
357. C3C2×C3×#356semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
C3×D3×#1012
C32×#3562
C3×#45482
C3×#44782
C2×C3×#3563
D3×#3563