Finite Group Databasebeta

← C3×#71103 #11781513

Subgroups — C3×#71103 #11781513

Order 1152.

374 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#474C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic
4C3×#5008C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4481C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1683—31nomaximal
9#71103C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C22×C3×C3⋊C8—21no—
13C3×#869C2211yescharacteristic
14C32×#107—21no—
15C32×C4⋊C8C2211yescharacteristic
16C32×#102—21no—
17C3×#835—21no—
18C3×#835—21no—
19C3×#832—21no—
20C3×#830—21no—
21C3×#808—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#487—31no—
26C3×#476—31no—
27C3×#474—21no—
28C3×#474D311yescharacteristic
29C3×#474C2×C311yescharacteristic
30C3×C8×D4—31no—
31#5079C2×C311yescharacteristic, complemented
32D4×C3⋊C8C2×C311yescharacteristic
33#5008C2×C311yescharacteristic
34C3×#335—31no—
35C3×#333—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic, complemented
38#4481C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×Q8—21no—
41C2×C32×D4D411yescharacteristic
42C22×C32×C4—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C22⋊C4—21no—
49C32×C42C2311yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—42no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#1683—31noSylow
58C22×C3×C8—61no—
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×C4⋊Q8C22×C311yescharacteristic
63C3×C4×D4—21no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C22×C311yescharacteristic
66C22×C3⋊C8—21no—
67#869C22×C311yescharacteristic
68C3×#107—22no—
69C3×#107—21no—
70C3×#107—21no—
71C3×#106—61no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C22×C311yescharacteristic
77C3×#103—61no—
78C3×#103—61no—
79C3×#102—22no—
80C3×#102—21no—
81C3×#102—21no—
82C3×#102—61no—
83C3×C22⋊C8—61no—
84C3×C4×C8—31no—
85#835—21no—
86#835—21no—
87#832—21no—
88#830—21no—
89#808—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8C22×C311yescharacteristic
93C23×C32—21no—
94C32×Q8—41no—
95C32×Q8—41no—
96C32×D4—21no—
97C32×D4Q1612yes—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3×Dic3—41no—
106C3×Dic6—81no—
107C32×C8—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—31no—
113#476—31no—
114#474C3×D311yescharacteristic
115C8×D4—31no—
116#335—31no—
117#333—31no—
118#332—31no—
119C2×C3×Q8—21no—
120C2×C3×Q8—21no—
121C2×C3×Q8—41no—
122C2×C3×Q8—61no—
123C2×C3×D4—21no—
124C2×C3×D4#6711yescharacteristic
125C2×C3×D4C3×D411yescharacteristic
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—41no—
129C2×Dic6—21no—
130C2×C3×C8—22no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C2×C3×C8—122no—
138C3×C4⋊C4—22no—
139C3×C4⋊C4—21no—
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—41no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4#6711yescharacteristic
148C3×C4⋊C4C3×D411yescharacteristic
149C3×C22⋊C4—21no—
150C3×C22⋊C4—21no—
151C3×C22⋊C4—41no—
152C3×C42—21no—
153C3×C42C22×D311yescharacteristic
154C3×C42C23×C311yescharacteristic
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—42no—
160C2×C3⋊C8C3×D411yescharacteristic
161C2×C3⋊C8C3×D411yescharacteristic
162C22×C32—22no—
163C22×C32—41no—
164C22×C32—41no—
165C22×C32#12111yescharacteristic
166C32×C4—21no—
167C32×C4—41no—
168C32×C4—81no—
169C32×C4C2×Q1611yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4#13511yescharacteristic
172C32×C4AGL(1,ℤ/8)11yescharacteristic
173C3×Dic3—81no—
174C22×C8—61no—
175C4⋊Q8—31no—
176C4⋊Q8C2×C3×D311yescharacteristic
177C4×D4C2×C3×D311yescharacteristic
178#107—21no—
179#106—61no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8C2×C3×D311yescharacteristic
183#103—61no—
184#103—61no—
185#102—21no—
186#102—61no—
187C22⋊C8—61no—
188C4×C8—31no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—41no—
192C3×Q8—41no—
193C3×Q8—41no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×Q8—81no—
197C3×Q8—81no—
198C3×Q8—241no—
199C3×D4—21no—
200C3×D4—21no—
201C3×D4—22no—
202C3×D4—41no—
203C3×D4#21612yes—
204C3×D4C3×Q1612yes—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—42no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—81no—
219C2×C3×C4—81no—
220C2×C3×C4—121no—
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4#23711yescharacteristic
223C2×C3×C4C2×#6711yescharacteristic
224C2×C3×C4C2×C3×D411yescharacteristic
225C2×C3×C4C2×C3×D411yescharacteristic
226C2×C3×C4C3×#4111yescharacteristic
227C2×Dic3—41no—
228Dic6—81no—
229C3×C8—42no—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—61no—
233C3×C8—61no—
234C3×C8—121no—
235C3×C8—121no—
236C3⋊C8—21no—
237C3⋊C8—21no—
238C3⋊C8—41no—
239C3⋊C8—41no—
240C2×C32—42no—
241C2×C32#46311yescharacteristic
242C2×C32#46711yescharacteristic
243C2×C32#47111yescharacteristic
244C2×Q8—21no—
245C2×Q8—61no—
246C2×D4C3×#6711yescharacteristic
247C22×C4—21no—
248C2×C8—21no—
249C2×C8—31no—
250C2×C8—31no—
251C2×C8—61no—
252C2×C8—61no—
253C2×C8—122no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—61no—
257C4⋊C4—61no—
258C4⋊C4C3×#6711yescharacteristic
259C22⋊C4—21no—
260C42C22×C3×D311yescharacteristic
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—42no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—81no—
270C22×C3—81no—
271C22×C3#93911yescharacteristic
272C22×C3C3×#12111yescharacteristic
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—81no—
283C3×C4—82no—
284C3×C4—81no—
285C3×C4—81no—
286C3×C4—241no—
287C3×C4#91111yescharacteristic
288C3×C4#91211yescharacteristic
289C3×C4C2×#21611yescharacteristic
290C3×C4#95011yescharacteristic
291C3×C4C2×C3×Q1611yescharacteristic
292C3×C4C3×#13511yescharacteristic
293C3×C4C3×#13511yescharacteristic
294C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
295Dic3—81no—
296C32#168311yescharacteristic, complemented, Sylow
297C23—21no—
298Q8—41no—
299Q8—41no—
300Q8—241no—
301D4—21no—
302D4C3×#21612yes—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—121no—
308C2×C4C3×D3×D411yescharacteristic
309C2×C4C3×#23711yescharacteristic
310C2×C4C2×C3×#6711yescharacteristic
311C8—41no—
312C8—61no—
313C8—61no—
314C8—121no—
315C8—121no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3—42no—
320C2×C3—42no—
321C2×C3—82no—
322C2×C3#505111yescharacteristic
323C2×C3#515311yescharacteristic
324C2×C3#520311yescharacteristic
325C2×C3C3×#46311yescharacteristic
326C2×C3C3×#46711yescharacteristic
327C2×C3C3×#47111yescharacteristic
328C22—22no—
329C22—41no—
330C22—41no—
331C22C3×#93911yescharacteristic
332C4—21no—
333C4—41no—
334C4—81no—
335C4—241no—
336C4C3×#91111yescharacteristic
337C4C3×#91211yescharacteristic
338C4C2×C3×#21611yescharacteristic
339C4C3×#95011yescharacteristic
340C3—21no—
341C3#7110311yescharacteristic, direct product factor
342C3C3×#168311yescharacteristic, complemented
343C2—42no—
344C2C3×#505111yescharacteristic
345C2C3×#515311yescharacteristic
346C2C3×#520311yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#474C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×#474D3
hypocenterC3C3×#1683
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#474

Complements

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

NH ≅ G/Ntype
2. C3×#5079C2semidirect
5. C3×#4547C2semidirect
6. C3×#4481C2semidirect
7. C3×#4479C2semidirect
9. #71103C3direct (N × H)
31. #5079C2×C3semidirect
37. #4547C2×C3semidirect
38. #4481C2×C3semidirect
39. #4479C2×C3semidirect
296. C32#1683semidirect
341. C3#71103direct (N × H)
342. C3C3×#1683semidirect

Maximal subgroups

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

subgroupindex
C32×#4742
C3×#50792
C3×D4×C3⋊C82
C3×#50082
C3×#45472
C3×#44812
C3×#44792
C3×#16833
#711033