Finite Group Databasebeta

← C3×#71147 #11779658

Subgroups — C3×#71147 #11779658

Order 1152.

442 conjugacy classes of subgroups.

The subgroup lattice has 391 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5542C211yesmaximal, characteristic
2C32×#476C211yesmaximal, characteristic
3C3×#5091C211yesmaximal, characteristic, complemented
4C3×#5079C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4482C211yesmaximal, characteristic, complemented
8C3×#1638—31nomaximal
9#71147C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C3×#936—21no—
13C3×#926—21no—
14C3×#924—21no—
15C3×#887—21no—
16C3×#879—22no—
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C32×#106—21no—
20C32×C4⋊C8C2211yescharacteristic
21C32×#102—21no—
22C3×#835—22no—
23C3×#810—21no—
24C3×#807—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27C3×#556—31no—
28#5542C2×C311yescharacteristic
29C3×#487—31no—
30C3×#477—31no—
31C3×#476—21no—
32C3×#476D311yescharacteristic
33C3×#476C2×C311yescharacteristic
34#5091C2×C311yescharacteristic, complemented
35#5079C2×C311yescharacteristic, complemented
36C3×#332—31no—
37C3×Q8⋊C8—31no—
38C3×D4⋊C8—31no—
39D4⋊(C3⋊C8)C2×C311yescharacteristic
40#4484C2×C311yescharacteristic, complemented
41#4482C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×D4D411yescharacteristic
44C22×C32×C4—21no—
45C2×C3×Dic6—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C32×C8—21no—
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C4⋊C4D411yescharacteristic
51C32×C22⋊C4—21no—
52C32×C42C2311yescharacteristic
53C3×#217—22no—
54C3×#217—22no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3D412yes—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—22no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—22no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#1638—31noSylow
65C3×C4⋊Q8—21no—
66C3×C4⋊Q8—31no—
67C3×C4⋊Q8C2×D311yescharacteristic
68C3×C4⋊Q8C22×C311yescharacteristic
69C3×#126—62no—
70C3×#124—61no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—31no—
73C3×C4×Q8—61no—
74C3×C4×D4—21no—
75C3×C4×D4C2×D311yescharacteristic
76C3×C4×D4C22×C311yescharacteristic
77C3×#117—61no—
78#936—21no—
79#926—21no—
80#924—21no—
81#887—21no—
82#879—22no—
83#869C22×C311yescharacteristic
84C4×Dic6C22×C311yescharacteristic
85C3×#107—61no—
86C3×#106—22no—
87C3×#106—21no—
88C3×#106—21no—
89C3×C4⋊C8—21no—
90C3×C4⋊C8—31no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C22×C311yescharacteristic
93C3×#103—61no—
94C3×#103—62no—
95C3×#102—22no—
96C3×#102—21no—
97C3×#102—21no—
98C3×C4×C8—31no—
99#835—22no—
100#810—21no—
101#807—21no—
102C4⋊(C3⋊C8)C22×C311yescharacteristic
103C4×C3⋊C8C22×C311yescharacteristic
104C23×C32—21no—
105C32×Q8—42no—
106C32×D4—21no—
107C32×D4—21no—
108C2×C32×C4—21no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C32×C8—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125#556—31no—
126#487—31no—
127#477—31no—
128#476C3×D311yescharacteristic
129#332—31no—
130Q8⋊C8—31no—
131D4⋊C8—31no—
132C2×C3×Q8—21no—
133C2×C3×Q8—21no—
134C2×C3×Q8—31no—
135C2×C3×Q8—41no—
136C2×C3×Q8—61no—
137C2×C3×D4—21no—
138C2×C3×D4#6711yescharacteristic
139C2×C3×D4C3×D411yescharacteristic
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—41no—
143C2×Dic6—21no—
144C2×Dic6C3×D411yescharacteristic
145C2×C3×C8—22no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150C3×C4⋊C4—22no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—32no—
157C3×C4⋊C4—31no—
158C3×C4⋊C4—41no—
159C3×C4⋊C4—62no—
160C3×C4⋊C4—61no—
161C3×C4⋊C4—61no—
162C3×C4⋊C4#6711yescharacteristic
163C3×C4⋊C4C3×D411yescharacteristic
164C3×C22⋊C4—21no—
165C3×C22⋊C4—21no—
166C3×C22⋊C4—41no—
167C3×C22⋊C4—62no—
168C3×C22⋊C4—62no—
169C3×C42—21no—
170C3×C42—62no—
171C3×C42—61no—
172C3×C42C22×D311yescharacteristic
173C3×C42C23×C311yescharacteristic
174#217—22no—
175#217—22no—
176C4⋊Dic3—21no—
177C4⋊Dic3C3×D411yescharacteristic
178C4⋊Dic3C3×D412yes—
179Dic3⋊C4—22no—
180Dic3⋊C4—21no—
181C4×Dic3—22no—
182C4×Dic3—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C22×C32—41no—
186C22×C32—41no—
187C22×C32—41no—
188C22×C32#12011yescharacteristic
189C32×C4—21no—
190C32×C4—41no—
191C32×C4—81no—
192C32×C4#13511yescharacteristic
193C32×C4#13511yescharacteristic
194C32×C4#13711yescharacteristic
195C32×C4#13711yescharacteristic
196C3×Dic3—41no—
197C3×Dic3—42no—
198C3×Dic3—41no—
199C4⋊Q8—31no—
200C4⋊Q8C2×C3×D311yescharacteristic
201#126—62no—
202#124—61no—
203C22⋊Q8—61no—
204C4×Q8—31no—
205C4×Q8—61no—
206C4×D4C2×C3×D311yescharacteristic
207#117—61no—
208#107—61no—
209#106—21no—
210C4⋊C8—31no—
211C4⋊C8C2×C3×D311yescharacteristic
212#103—61no—
213#103—62no—
214#102—21no—
215C4×C8—31no—
216C23×C3—21no—
217C23×C3—21no—
218C23×C3—41no—
219C3×Q8—42no—
220C3×Q8—42no—
221C3×Q8—61no—
222C3×Q8—61no—
223C3×Q8—82no—
224C3×Q8—121no—
225C3×Q8—121no—
226C3×D4—22no—
227C3×D4—21no—
228C3×D4—21no—
229C3×D4—21no—
230C3×D4—21no—
231C3×D4—41no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—41no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4—42no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—61no—
246C2×C3×C4—62no—
247C2×C3×C4—61no—
248C2×C3×C4—81no—
249C2×C3×C4—81no—
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4C2×#6711yescharacteristic
253C2×C3×C4C2×C3×D411yescharacteristic
254C2×C3×C4C2×C3×D411yescharacteristic
255C2×C3×C4C2×C3×D411yescharacteristic
256C2×Dic3—21no—
257C2×Dic3—21no—
258C2×Dic3—22no—
259Dic6—21no—
260Dic6—21no—
261Dic6—41no—
262Dic6—41no—
263C3×C8—42no—
264C3×C8—41no—
265C3×C8—41no—
266C3×C8—121no—
267C3×C8—121no—
268C3⋊C8—41no—
269C3⋊C8—41no—
270C2×C32—81no—
271C2×C32#45211yescharacteristic
272C2×C32#45211yescharacteristic
273C2×C32#45411yescharacteristic
274C2×Q8—21no—
275C2×Q8—31no—
276C2×Q8—61no—
277C2×D4C3×#6711yescharacteristic
278C22×C4—21no—
279C2×C8—21no—
280C2×C8—61no—
281C2×C8—61no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—32no—
285C4⋊C4—31no—
286C4⋊C4—62no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4C3×#6711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—62no—
292C22⋊C4—62no—
293C42—62no—
294C42—61no—
295C42C22×C3×D311yescharacteristic
296C22×C3—21no—
297C22×C3—42no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—81no—
305C22×C3—81no—
306C22×C3#93711yescharacteristic
307C22×C3C3×#12011yescharacteristic
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—81no—
318C3×C4—82no—
319C3×C4—81no—
320C3×C4—81no—
321C3×C4—121no—
322C3×C4—121no—
323C3×C4—122no—
324C3×C4#91511yescharacteristic
325C3×C4#91611yescharacteristic
326C3×C4#94211yescharacteristic
327C3×C4#95011yescharacteristic
328C3×C4C3×#13511yescharacteristic
329C3×C4C3×#13511yescharacteristic
330C3×C4C3×#13711yescharacteristic
331C3×C4C3×#13711yescharacteristic
332Dic3—41no—
333Dic3—42no—
334Dic3—41no—
335C32#163811yescharacteristic, complemented, Sylow
336C23—21no—
337Q8—42no—
338Q8—61no—
339Q8—61no—
340Q8—121no—
341Q8—121no—
342D4—21no—
343D4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—61no—
349C2×C4—62no—
350C2×C4—61no—
351C2×C4C3×D3×D411yescharacteristic
352C2×C4C3×D3×D411yescharacteristic
353C2×C4C2×C3×#6711yescharacteristic
354C8—41no—
355C8—121no—
356C8—121no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—82no—
361C2×C3—81no—
362C2×C3—81no—
363C2×C3#504711yescharacteristic
364C2×C3#517311yescharacteristic
365C2×C3#520111yescharacteristic
366C2×C3C3×#45211yescharacteristic
367C2×C3C3×#45211yescharacteristic
368C2×C3C3×#45411yescharacteristic
369C22—41no—
370C22—41no—
371C22—41no—
372C22C3×#93711yescharacteristic
373C4—21no—
374C4—41no—
375C4—81no—
376C4—121no—
377C4—121no—
378C4—122no—
379C4C3×#91511yescharacteristic
380C4C3×#91611yescharacteristic
381C4C3×#94211yescharacteristic
382C4C3×#95011yescharacteristic
383C3—21no—
384C3#7114711yescharacteristic, direct product factor
385C3C3×#163811yescharacteristic, complemented
386C2—81no—
387C2C3×#504711yescharacteristic
388C2C3×#517311yescharacteristic
389C2C3×#520111yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#476C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC3×#476D3
hypocenterC3C3×#1638
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#476

Complements

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

NH ≅ G/Ntype
3. C3×#5091C2semidirect
4. C3×#5079C2semidirect
6. C3×#4484C2semidirect
7. C3×#4482C2semidirect
9. #71147C3direct (N × H)
34. #5091C2×C3semidirect
35. #5079C2×C3semidirect
40. #4484C2×C3semidirect
41. #4482C2×C3semidirect
335. C32#1638semidirect
384. C3#71147direct (N × H)
385. C3C3×#1638semidirect

Maximal subgroups

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

subgroupindex
C3×#55422
C32×#4762
C3×#50912
C3×#50792
C3×D4⋊(C3⋊C8)2
C3×#44842
C3×#44822
C3×#16383
#711473