Finite Group Databasebeta

← C3×#69158 #11796361

Subgroups — C3×#69158 #11796361

Order 1152.

551 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 551 conjugacy classes of subgroups — too many to draw. Only its 110 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×#5668C211yesmaximal, characteristic
2C3×#4740C212yesmaximal, complemented
3C32×#354C211yesmaximal, characteristic, complemented
4C3×#4541C211yesmaximal, characteristic, complemented
5C3×#4474C212yesmaximal, complemented
6C3×#2126—31nomaximal
7#69158C311yesmaximal, characteristic, direct product factor
8C2×C3×#239C411yescharacteristic, complemented
9C2×C3×#237C2211yescharacteristic
10C32×#124C2211yescharacteristic
11C3×#944C411yescharacteristic, complemented
12C3×#940C2211yescharacteristic
13C3×#884—22no—
14C3×#67⋊C4—22no—
15C3×#877—22no—
16C3×#875C411yescharacteristic, complemented
17C3×C42×D3C411yescharacteristic, complemented
18C32×#99C2212yes—
19C3×#834C2212yes—
20C3×#806—22no—
21C3×#532—31no—
22#5668C2×C311yescharacteristic
23C3×#410—32no—
24#4740C2×C312yescomplemented
25C3×#354—21no—
26C3×#354—31no—
27C3×#354D311yescharacteristic, complemented
28C3×#354C2×C311yescharacteristic, complemented
29C3×#353—32no—
30#4541C2×C311yescharacteristic, complemented
31#4474C2×C312yescomplemented
32C2×C32×Q8C2×C411yescharacteristic
33C2×C32×D4C2311yescharacteristic
34C2×C3×#67—22no—
35C2×C3×#67D412yes—
36C22×C3×Dic3D412yes—
37C3×#239—41no—
38C3×#239—41no—
39C3×#237—41no—
40C3×#237—41no—
41C2×C3×D12—21no—
42C2×C3×D12C2×C411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×Dic6C2×C411yescharacteristic
47C32×C22⋊C4—22no—
48C32×C22⋊C4—22no—
49C32×C42C2×C411yescharacteristic
50C3×#217—22no—
51C3×(C2×D3)⋊C4—22no—
52C3×Dic3⋊C4—22no—
53C3×Dic3⋊C4—42no—
54C3×C4×Dic3—21no—
55C3×C4×Dic3—42no—
56C3×C4×Dic3C2×C411yescharacteristic
57#2126—31noSylow
58C2×C3×#41—31no—
59C2×C3×#41—31no—
60C2×#239C3×C411yescharacteristic, complemented
61C2×#237C22×C311yescharacteristic
62C3×C4⋊Q8—31no—
63C3×#127—31no—
64C3×#124—21no—
65C3×#124—31no—
66C3×#124C2×D311yescharacteristic
67C3×#124C22×C311yescharacteristic
68C3×#121—62no—
69C3×C4×D4—62no—
70C3×#117—62no—
71C2×C3×C42—31no—
72#944C3×C411yescharacteristic, complemented
73#940C22×C311yescharacteristic
74#884—22no—
75#67⋊C4—22no—
76#877—22no—
77#875C3×C411yescharacteristic, complemented
78C42×D3C3×C411yescharacteristic, complemented
79C3×#99—22no—
80C3×#99—32no—
81C3×#99—62no—
82C3×#99C2×D312yes—
83C3×#99C22×C312yes—
84#834C22×C312yes—
85#806—22no—
86C23×C32C2×D412yes—
87C22×C3×D3—21no—
88C22×C3×D3C22⋊C411yescharacteristic
89C32×Q8—41no—
90C32×D4—41no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—42no—
94C2×C32×C4C22×C411yescharacteristic
95C3×#67—42no—
96C3×#67—44no—
97C2×C3×Dic3—21no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—22no—
100C2×C3×Dic3—42no—
101C2×C3×Dic3C22⋊C412yes—
102C2×C3×Dic3C22⋊C411yescharacteristic
103C3×D12—41no—
104C3×D12—42no—
105C3×C4×D3—21no—
106C3×C4×D3—21no—
107C3×C4×D3—42no—
108C3×C4×D3—41no—
109C3×C4×D3—41no—
110C3×Dic6—41no—
111#532—31no—
112#410—32no—
113#354—31no—
114#354C3×D311yescharacteristic, complemented
115#353—32no—
116C3×#41—121no—
117C3×#41—121no—
118C3×#41—121no—
119C3×#41—121no—
120C2×C3×Q8—21no—
121C2×C3×Q8—31no—
122C2×C3×Q8C4×D311yescharacteristic
123C2×C3×Q8C2×C3×C411yescharacteristic
124C2×C3×D4—21no—
125C2×C3×D4—32no—
126C2×C3×D4—31no—
127C2×C3×D4—61no—
128C2×C3×D4—62no—
129C2×C3×D4C22×D311yescharacteristic
130C2×C3×D4C23×C311yescharacteristic
131C22×C3×C4—32no—
132C22×C3×C4—31no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C2×#67—22no—
136C2×#67C3×D412yes—
137C22×Dic3C3×D412yes—
138#239—41no—
139#239—41no—
140#237—41no—
141#237—41no—
142C2×D12—21no—
143C2×D12C2×C3×C411yescharacteristic
144C2×C4×D3—21no—
145C2×C4×D3—21no—
146C2×C4×D3C2×C3×C411yescharacteristic
147C2×Dic6C2×C3×C411yescharacteristic
148C3×C4⋊C4—62no—
149C3×C4⋊C4—122no—
150C3×C22⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—22no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—42no—
155C3×C22⋊C4—42no—
156C3×C22⋊C4—62no—
157C3×C22⋊C4—62no—
158C3×C42—21no—
159C3×C42—31no—
160C3×C42—61no—
161C3×C42—122no—
162C3×C42C4×D311yescharacteristic
163C3×C42C2×C3×C411yescharacteristic
164#217—22no—
165(C2×D3)⋊C4—22no—
166Dic3⋊C4—22no—
167Dic3⋊C4—42no—
168C4×Dic3—21no—
169C4×Dic3—42no—
170C4×Dic3C2×C3×C411yescharacteristic
171C22×C32—22no—
172C22×C32—42no—
173C22×C32C2×C22⋊C411yescharacteristic
174C2×C3×D3—21no—
175C2×C3×D3—41no—
176C2×C3×D3—42no—
177C2×C3×D3—41no—
178C32×C4—21no—
179C32×C4—41no—
180C32×C4—41no—
181C32×C4—82no—
182C3×Dic3—22no—
183C3×Dic3—22no—
184C3×Dic3—82no—
185C3×Dic3#9911yescharacteristic
186C3×Dic3#9911yescharacteristic
187C2×#41—31no—
188C2×#41—31no—
189C4⋊Q8—31no—
190#127—31no—
191#124—31no—
192#124C2×C3×D311yescharacteristic
193#121—62no—
194C4×D4—62no—
195#117—62no—
196C2×C42—31no—
197#99—32no—
198#99—62no—
199#99C2×C3×D312yes—
200C23×C3—22no—
201C23×C3—31no—
202C23×C3—61no—
203C23×C3D3×D412yes—
204C23×C3C2×C3×D412yes—
205C22×D3—21no—
206C22×D3C3×C22⋊C411yescharacteristic
207C3×Q8—41no—
208C3×Q8—41no—
209C3×Q8—81no—
210C3×Q8—121no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—81no—
214C3×D4—121no—
215C3×D4—122no—
216C3×D4—122no—
217C3×D4—124no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—31no—
224C2×C3×C4—32no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—42no—
228C2×C3×C4—42no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—62no—
232C2×C3×C4—62no—
233C2×C3×C4—61no—
234C2×C3×C4—82no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4—122no—
238C2×C3×C4—122no—
239C2×C3×C4C2×C4×D311yescharacteristic
240C2×C3×C4C22×C3×C411yescharacteristic
241#67—42no—
242#67—44no—
243C2×Dic3—21no—
244C2×Dic3—22no—
245C2×Dic3—22no—
246C2×Dic3—42no—
247C2×Dic3C3×C22⋊C412yes—
248C2×Dic3C3×C22⋊C411yescharacteristic
249D12—41no—
250D12—42no—
251C4×D3—21no—
252C4×D3—21no—
253C4×D3—42no—
254C4×D3—41no—
255C4×D3—41no—
256Dic6—41no—
257C2×C32—21no—
258C2×C32—42no—
259C2×C32C2×#9911yescharacteristic
260C3×D3—41no—
261C3×D3—81no—
262#41—121no—
263#41—121no—
264#41—121no—
265#41—121no—
266C2×Q8—31no—
267C2×Q8C3×C4×D311yescharacteristic
268C2×D4—32no—
269C2×D4—31no—
270C2×D4—61no—
271C2×D4—62no—
272C2×D4C22×C3×D311yescharacteristic
273C22×C4—32no—
274C22×C4—31no—
275C22×C4—61no—
276C22×C4—61no—
277C4⋊C4—62no—
278C4⋊C4—122no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—62no—
282C22⋊C4—62no—
283C42—31no—
284C42—61no—
285C42—122no—
286C42C3×C4×D311yescharacteristic
287C22×C3—22no—
288C22×C3—22no—
289C22×C3—21no—
290C22×C3—42no—
291C22×C3—42no—
292C22×C3—42no—
293C22×C3—61no—
294C22×C3—82no—
295C22×C3—121no—
296C22×C3—122no—
297C22×C3—121no—
298C22×C3D3×C22⋊C411yescharacteristic
299C22×C3C2×C3×C22⋊C411yescharacteristic
300C2×D3—21no—
301C2×D3—41no—
302C2×D3—42no—
303C2×D3—41no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—31no—
307C3×C4—31no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—41no—
313C3×C4—62no—
314C3×C4—62no—
315C3×C4—81no—
316C3×C4—81no—
317C3×C4—82no—
318C3×C4—82no—
319C3×C4—162no—
320C3×C4—242no—
321Dic3—22no—
322Dic3—22no—
323Dic3—82no—
324Dic3C3×#9911yescharacteristic
325Dic3C3×#9911yescharacteristic
326C32#212611yescharacteristic, complemented, Sylow
327C23—31no—
328C23—61no—
329C23C3×D3×D412yes—
330Q8—41no—
331Q8—121no—
332D4—41no—
333D4—121no—
334D4—122no—
335D4—122no—
336D4—124no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—31no—
340C2×C4—32no—
341C2×C4—42no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—62no—
345C2×C4—62no—
346C2×C4—61no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4—122no—
350C2×C4—122no—
351C2×C4C2×C3×C4×D311yescharacteristic
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—41no—
356C2×C3—42no—
357C2×C3—42no—
358C2×C3—82no—
359C2×C3—121no—
360C2×C3—241no—
361C2×C3D3×#9911yescharacteristic
362C2×C3C2×C3×#9911yescharacteristic
363D3—41no—
364D3—81no—
365C22—22no—
366C22—42no—
367C22—61no—
368C22—121no—
369C22—122no—
370C22—121no—
371C22C3×D3×C22⋊C411yescharacteristic
372C4—21no—
373C4—31no—
374C4—31no—
375C4—41no—
376C4—41no—
377C4—62no—
378C4—62no—
379C4—82no—
380C4—242no—
381C3—21no—
382C3#6915811yescharacteristic, direct product factor
383C3C3×#212611yescharacteristic, complemented
384C2—21no—
385C2—42no—
386C2—121no—
387C2—241no—
388C2C3×D3×#9911yescharacteristic
subgroupG/H
centerC2×C3D3×#99
commutatorC2×C3×C4C22×C3×C4
FrattiniC2×D4C22×C3×D3
FittingC32×#354C2
socleC2×C32C2×#99
prime radicalC3×#5668C2
cosocleC2×C3×D4C23×C3
hypercenterC3×#354D3
hypocenterC3C3×#2126
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3 ◁ C2×C3×D4 ◁ C3×#354

Complements

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

NH ≅ G/Ntype
2. C3×#4740C2semidirect
3. C32×#354C2semidirect
4. C3×#4541C2semidirect
5. C3×#4474C2semidirect
7. #69158C3direct (N × H)
8. C2×C3×#239C4semidirect
11. C3×#944C4semidirect
16. C3×#875C4semidirect
17. C3×C42×D3C4semidirect
24. #4740C2×C3semidirect
27. C3×#354D3semidirect
28. C3×#354C2×C3semidirect
30. #4541C2×C3semidirect
31. #4474C2×C3semidirect
60. C2×#239C3×C4semidirect
72. #944C3×C4semidirect
77. #875C3×C4semidirect
78. C42×D3C3×C4semidirect
114. #354C3×D3semidirect
326. C32#2126semidirect
382. C3#69158direct (N × H)
383. C3C3×#2126semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
C3×#47402
C32×#3542
C3×#45412
C3×#44742
C3×#21263
#691583