Finite Group Databasebeta

← C3×#71793 #11792628

Subgroups — C3×#71793 #11792628

Order 1152.

885 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4⋊Q8C211yesmaximal, characteristic
2C22×C3×#216C212yesmaximal
3C2×C3×#835C212yesmaximal
4C3×#4929C211yesmaximal, characteristic
5C3×#4524C211yesmaximal, characteristic
6C3×#2016—31nomaximal
7#71793C311yesmaximal, characteristic, direct product factor
8C22×C32×Q8C2212yes—
9C22×C3×Dic6C2211yescharacteristic
10C32×C4⋊Q8—24no—
11C2×C32×C4⋊C4—22no—
12C2×C32×C42C2211yescharacteristic
13C2×C3×#216—24no—
14C2×C3×#216—24no—
15C2×C3×#216—24no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2212yes—
18C3×#835—24no—
19C3×C3⋊#95—22no—
20C22×C3×Q16—32no—
21C2×C3×C4⋊Q8—21no—
22C2×C3×C4⋊Q8D311yescharacteristic
23C2×C3×C4⋊Q8C2×C311yescharacteristic
24C22×#216C2×C312yes—
25C2×C3×#103—32no—
26C3×#391—31no—
27C2×#835C2×C312yes—
28#4929C2×C311yescharacteristic
29C3×#336—31no—
30#4524C2×C311yescharacteristic
31C2×C32×Q8—22no—
32C2×C32×Q8—22no—
33C2×C32×Q8—22no—
34C2×C32×Q8—22no—
35C2×C32×Q8—22no—
36C2×C32×Q8D414yes—
37C22×C32×C4—22no—
38C22×C32×C4D412yes—
39C22×C32×C4C2311yescharacteristic
40C22×C3×Dic3—21no—
41C22×C3×Dic3—21no—
42C2×C3×Dic6—22no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6—21no—
45C2×C3×Dic6D412yes—
46C32×C4⋊C4—28no—
47C32×C42—22no—
48C3×#216—216no—
49C3×C4⋊Dic3—22no—
50C2×C3×C3⋊C8—22no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8D414yes—
53#2016—31noSylow
54C22×C3×Q8—22no—
55C22×C3×Q8—31no—
56C22×C3×Q8C2×D312yes—
57C22×C3×Q8C22×C312yes—
58C22×Dic6C22×C311yescharacteristic
59C2×C3×Q16—64no—
60C2×C3×Q16—64no—
61C2×C3×Q16—64no—
62C22×C3×C8—32no—
63C3×C4⋊Q8—28no—
64C3×C4⋊Q8—24no—
65C3×C4⋊Q8—24no—
66C2×C3×C4⋊C4—24no—
67C2×C3×C4⋊C4—22no—
68C2×C3×C4⋊C4—22no—
69C2×C3×C4⋊C4—31no—
70C2×C3×C42—21no—
71C2×C3×C42C2×D311yescharacteristic
72C2×C3×C42C22×C311yescharacteristic
73C2×#216—24no—
74C2×#216—24no—
75C2×#216—24no—
76C2×C4⋊Dic3C22×C311yescharacteristic
77C22×C3⋊C8C22×C312yes—
78C3×#103—64no—
79C3×#95—62no—
80#835—24no—
81C3⋊#95—22no—
82C23×C32C2×D411yescharacteristic
83C32×Q8—24no—
84C32×Q8—24no—
85C32×Q8—42no—
86C32×Q8—42no—
87C2×C32×C4—22no—
88C2×C32×C4—22no—
89C2×C32×C4—24no—
90C2×C32×C4—42no—
91C2×C32×C4—42no—
92C2×C32×C4Q1614yescomplemented
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4C2×D412yes—
95C2×C32×C4C2×D412yes—
96C2×C32×C4#4111yescharacteristic
97C2×C3×Dic3—22no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—41no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—42no—
102C3×Dic6—24no—
103C3×Dic6—42no—
104C3×C3⋊C8—24no—
105C22×Q16—32no—
106C2×C4⋊Q8C3×D311yescharacteristic
107C2×#103—32no—
108#391—31no—
109#336—31no—
110C2×C3×Q8—24no—
111C2×C3×Q8—22no—
112C2×C3×Q8—22no—
113C2×C3×Q8—22no—
114C2×C3×Q8—22no—
115C2×C3×Q8—22no—
116C2×C3×Q8—22no—
117C2×C3×Q8—22no—
118C2×C3×Q8—22no—
119C2×C3×Q8—22no—
120C2×C3×Q8—22no—
121C2×C3×Q8—24no—
122C2×C3×Q8—32no—
123C2×C3×Q8—42no—
124C2×C3×Q8—42no—
125C2×C3×Q8—42no—
126C2×C3×Q8—42no—
127C2×C3×Q8—61no—
128C2×C3×Q8—62no—
129C2×C3×Q8—62no—
130C2×C3×Q8#6714yes—
131C2×C3×Q8C3×D414yes—
132C22×C3×C4—24no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—22no—
136C22×C3×C4—21no—
137C22×C3×C4—61no—
138C22×C3×C4—61no—
139C22×C3×C4#6712yes—
140C22×C3×C4C3×D412yes—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C23×C311yescharacteristic
143C22×Dic3—21no—
144C22×Dic3—21no—
145C2×Dic6—22no—
146C2×Dic6—22no—
147C2×Dic6—21no—
148C2×Dic6C3×D412yes—
149C3×Q16—616no—
150C2×C3×C8—34no—
151C2×C3×C8—62no—
152C2×C3×C8—62no—
153C3×C4⋊C4—216no—
154C3×C4⋊C4—28no—
155C3×C4⋊C4—28no—
156C3×C4⋊C4—62no—
157C3×C42—24no—
158C3×C42—22no—
159C3×C42—22no—
160#216—216no—
161C4⋊Dic3—22no—
162C2×C3⋊C8—22no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8C3×D414yes—
165C22×C32#12011yescharacteristic
166C22×C32#12111yescharacteristic
167C22×C32#12711yescharacteristic
168C22×C32C2×Q1612yes—
169C22×C32#13712yes—
170C32×C4—24no—
171C32×C4—44no—
172C32×C4#12012yes—
173C32×C4#12112yes—
174C3×Dic3—42no—
175C3×Dic3—81no—
176C22×Q8—31no—
177C22×Q8C2×C3×D312yes—
178C2×Q16—64no—
179C2×Q16—64no—
180C2×Q16—64no—
181C22×C8—32no—
182C4⋊Q8—24no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—31no—
185C2×C42C2×C3×D311yescharacteristic
186#103—64no—
187#95—62no—
188C23×C3—21no—
189C23×C3C2×#6711yescharacteristic
190C23×C3C2×C3×D411yescharacteristic
191C3×Q8—24no—
192C3×Q8—24no—
193C3×Q8—24no—
194C3×Q8—24no—
195C3×Q8—44no—
196C3×Q8—44no—
197C3×Q8—44no—
198C3×Q8—44no—
199C3×Q8—42no—
200C3×Q8—42no—
201C3×Q8—42no—
202C3×Q8—42no—
203C3×Q8—64no—
204C3×Q8—122no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—22no—
210C2×C3×C4—22no—
211C2×C3×C4—28no—
212C2×C3×C4—24no—
213C2×C3×C4—24no—
214C2×C3×C4—24no—
215C2×C3×C4—21no—
216C2×C3×C4—22no—
217C2×C3×C4—21no—
218C2×C3×C4—22no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4—42no—
222C2×C3×C4—42no—
223C2×C3×C4—42no—
224C2×C3×C4—42no—
225C2×C3×C4—62no—
226C2×C3×C4—121no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4—122no—
230C2×C3×C4#21614yescomplemented
231C2×C3×C4C3×Q1614yescomplemented
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D412yes—
234C2×C3×C4#23711yescharacteristic
235C2×C3×C4C2×#6712yes—
236C2×C3×C4C2×C3×D411yescharacteristic
237C2×C3×C4C2×C3×D412yes—
238C2×C3×C4C2×C3×D412yes—
239C2×C3×C4C3×#4111yescharacteristic
240C2×Dic3—22no—
241C2×Dic3—41no—
242C2×Dic3—41no—
243C2×Dic3—41no—
244C2×Dic3—42no—
245Dic6—24no—
246Dic6—42no—
247C3×C8—64no—
248C3⋊C8—24no—
249C2×C32#39211yescharacteristic
250C2×C32#45112yes—
251C2×C32#46212yes—
252C2×C32#49411yescharacteristic
253C2×C32#49711yescharacteristic
254C2×Q8—22no—
255C2×Q8—22no—
256C2×Q8—22no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—32no—
260C2×Q8—61no—
261C2×Q8—62no—
262C2×Q8—62no—
263C2×Q8C3×#6714yes—
264C22×C4—22no—
265C22×C4—61no—
266C22×C4—61no—
267C22×C4C3×#6712yes—
268C22×C4C22×C3×D311yescharacteristic
269Q16—616no—
270C2×C8—34no—
271C2×C8—62no—
272C2×C8—62no—
273C4⋊C4—28no—
274C4⋊C4—62no—
275C42—22no—
276C22×C3—21no—
277C22×C3—21no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—21no—
281C22×C3#93811yescharacteristic
282C22×C3#94011yescharacteristic
283C22×C3#94212yes—
284C22×C3C2×#21612yes—
285C22×C3#95311yescharacteristic
286C22×C3C3×#12011yescharacteristic
287C22×C3C3×#12111yescharacteristic
288C22×C3C3×#12711yescharacteristic
289C22×C3C2×C3×Q1612yes—
290C22×C3C3×#13712yes—
291C3×C4—28no—
292C3×C4—24no—
293C3×C4—24no—
294C3×C4—22no—
295C3×C4—22no—
296C3×C4—48no—
297C3×C4—44no—
298C3×C4—44no—
299C3×C4—122no—
300C3×C4—241no—
301C3×C4#93712yes—
302C3×C4#93912yes—
303C3×C4C3×#12012yes—
304C3×C4C3×#12112yes—
305Dic3—42no—
306Dic3—81no—
307C32#201611yescharacteristic, complemented, Sylow
308C23C2×C3×#6711yescharacteristic
309Q8—24no—
310Q8—24no—
311Q8—42no—
312Q8—42no—
313Q8—64no—
314Q8—122no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—62no—
321C2×C4—121no—
322C2×C4—121no—
323C2×C4—121no—
324C2×C4—122no—
325C2×C4C3×#21614yescomplemented
326C2×C4C3×D3×D411yescharacteristic
327C2×C4C3×D3×D412yes—
328C2×C4C3×#23711yescharacteristic
329C2×C4C2×C3×#6712yes—
330C8—64no—
331C2×C3—21no—
332C2×C3—22no—
333C2×C3—21no—
334C2×C3—22no—
335C2×C3—21no—
336C2×C3#508611yescharacteristic
337C2×C3#509012yes—
338C2×C3#509211yescharacteristic
339C2×C3#522311yescharacteristic
340C2×C3#522812yes—
341C2×C3C3×#39211yescharacteristic
342C2×C3C3×#45112yes—
343C2×C3C3×#46212yes—
344C2×C3C3×#49411yescharacteristic
345C2×C3C3×#49711yescharacteristic
346C22C3×#93811yescharacteristic
347C22C3×#94011yescharacteristic
348C22C3×#94212yes—
349C22C2×C3×#21612yes—
350C22C3×#95311yescharacteristic
351C4—24no—
352C4—44no—
353C4—122no—
354C4—241no—
355C4C3×#93712yes—
356C4C3×#93912yes—
357C3—21no—
358C3#7179311yescharacteristic, direct product factor
359C3C3×#201611yescharacteristic, complemented
360C2C3×#508611yescharacteristic
361C2C3×#509012yes—
362C2C3×#509211yescharacteristic
363C2C3×#522311yescharacteristic
364C2C3×#522812yes—
subgroupG/H
centerC23×C3C2×#67
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C4⋊Q8C2
socle, prime radicalC23×C32C2×D4
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C3×#2016
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
7. #71793C3direct (N × H)
92. C2×C32×C4Q16semidirect
230. C2×C3×C4#216semidirect
231. C2×C3×C4C3×Q16semidirect
307. C32#2016semidirect
325. C2×C4C3×#216semidirect
358. C3#71793direct (N × H)
359. C3C3×#2016semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4⋊Q82
C22×C3×#2162
C2×C3×#8352
C3×#49292
C3×#45242
C3×#20163
#717933