Finite Group Databasebeta

← C3×#71023 #11781467

Subgroups — C3×#71023 #11781467

Order 1152.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#460C211yesmaximal, characteristic
2C3×#5070C211yesmaximal, characteristic
3C3×#5031C211yesmaximal, characteristic, complemented
4C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic
6C3×#4482C211yesmaximal, characteristic, complemented
7C3×#4479C211yesmaximal, characteristic, complemented
8C3×#1682—31nomaximal
9#71023C311yesmaximal, characteristic, direct product factor
10C2×C32×SD16—21no—
11C32×#127C2211yescharacteristic
12C32×C4×Q8C2211yescharacteristic
13C2×C3×#216—21no—
14C3×#869C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16C32×#102—21no—
17C3×#832—21no—
18C3×#832—21no—
19C3×#810—21no—
20C3×C4⋊(C3⋊C8)—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#486—31no—
26C3×#462—31no—
27C3×#460—21no—
28C3×#460D311yescharacteristic
29C3×#460C2×C311yescharacteristic
30C3×C8×Q8—31no—
31#5070C2×C311yescharacteristic
32#5031C2×C311yescharacteristic, complemented
33Q8×C3⋊C8C2×C311yescharacteristic, complemented
34C3×#335—31no—
35C3×#332—31no—
36C3×#331—31no—
37#4544C2×C311yescharacteristic
38#4482C2×C311yescharacteristic, complemented
39#4479C2×C311yescharacteristic, complemented
40C2×C32×Q8D411yescharacteristic
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C3×Dic6—21no—
45C32×SD16—42no—
46C2×C32×C8—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C3×#216—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1682—31noSylow
59C2×C3×Q16—61no—
60C2×C3×SD16—22no—
61C2×C3×SD16—21no—
62C2×C3×SD16—21no—
63C3×C4⋊Q8—31no—
64C3×#127—21no—
65C3×#127C2×D311yescharacteristic
66C3×#127C22×C311yescharacteristic
67C3×C4×Q8—21no—
68C3×C4×Q8C2×D311yescharacteristic
69C3×C4×Q8C22×C311yescharacteristic
70C2×#216—21no—
71#869C22×C311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—61no—
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4⋊C8C22×C311yescharacteristic
78C3×#103—61no—
79C3×#102—22no—
80C3×#102—21no—
81C3×#102—21no—
82C3×#102—61no—
83C3×#102—61no—
84C3×C4×C8—31no—
85C3×C4×C8—61no—
86#832—21no—
87#832—21no—
88#810—21no—
89C4⋊(C3⋊C8)—21no—
90C4⋊(C3⋊C8)C22×C311yescharacteristic
91C4⋊(C3⋊C8)C22×C311yescharacteristic
92C4×C3⋊C8—21no—
93C4×C3⋊C8C22×C311yescharacteristic
94C23×C32—41no—
95C32×Q8—21no—
96C32×Q8D812yes—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—81no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C3×Dic3—41no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C32×C8—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#486—31no—
116#462—31no—
117#460C3×D311yescharacteristic
118C8×Q8—31no—
119#335—31no—
120#332—31no—
121#331—31no—
122C2×C3×Q8—21no—
123C2×C3×Q8—61no—
124C2×C3×Q8#6711yescharacteristic
125C2×C3×Q8C3×D411yescharacteristic
126C2×C3×D4—22no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—41no—
134C2×C3×D4—41no—
135C2×Dic6—21no—
136C3×Q16—122no—
137C3×SD16—44no—
138C3×SD16—42no—
139C3×SD16—42no—
140C2×C3×C8—22no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—31no—
144C2×C3×C8—31no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4#6711yescharacteristic
154C3×C4⋊C4C3×D411yescharacteristic
155C3×C42—21no—
156C3×C42—21no—
157C3×C42—21no—
158C3×C42—41no—
159C3×C42C22×D311yescharacteristic
160C3×C42C23×C311yescharacteristic
161#216—42no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8C3×D411yescharacteristic
167C2×C3⋊C8C3×D411yescharacteristic
168C22×C32—81no—
169C22×C32—81no—
170C22×C32—81no—
171C22×C32#12111yescharacteristic
172C32×C4—22no—
173C32×C4—21no—
174C32×C4—41no—
175C32×C4C2×D811yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4#13511yescharacteristic
178C32×C4#13711yescharacteristic
179C3×Dic3—81no—
180C2×Q16—61no—
181C2×SD16—21no—
182C4⋊Q8—31no—
183#127C2×C3×D311yescharacteristic
184C4×Q8C2×C3×D311yescharacteristic
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—61no—
188C4⋊C8C2×C3×D311yescharacteristic
189#103—61no—
190#102—21no—
191#102—61no—
192#102—61no—
193C4×C8—31no—
194C4×C8—61no—
195C23×C3—42no—
196C23×C3—41no—
197C23×C3—41no—
198C3×Q8—21no—
199C3×Q8—21no—
200C3×Q8—22no—
201C3×Q8—41no—
202C3×Q8—121no—
203C3×Q8—121no—
204C3×Q8#21312yes—
205C3×Q8C3×D812yes—
206C3×D4—42no—
207C3×D4—42no—
208C3×D4—41no—
209C3×D4—41no—
210C3×D4—41no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—81no—
217C3×D4—81no—
218C3×D4—81no—
219C3×D4—81no—
220C3×D4—82no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—121no—
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4#23711yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×C3×C4C2×C3×D411yescharacteristic
235C2×C3×C4C2×C3×D411yescharacteristic
236C2×C3×C4C3×#4111yescharacteristic
237C2×Dic3—41no—
238Dic6—41no—
239Dic6—41no—
240C3×C8—42no—
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—61no—
244C3×C8—61no—
245C3×C8—121no—
246C3×C8—121no—
247C3⋊C8—21no—
248C3⋊C8—21no—
249C3⋊C8—41no—
250C3⋊C8—41no—
251C2×C32—161no—
252C2×C32#46411yescharacteristic
253C2×C32#46611yescharacteristic
254C2×C32#47111yescharacteristic
255C2×Q8—61no—
256C2×Q8C3×#6711yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260Q16—122no—
261SD16—42no—
262C2×C8—21no—
263C2×C8—31no—
264C2×C8—31no—
265C2×C8—61no—
266C2×C8—61no—
267C4⋊C4—21no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C4⋊C4C3×#6711yescharacteristic
271C42—21no—
272C42C22×C3×D311yescharacteristic
273C22×C3—21no—
274C22×C3—82no—
275C22×C3—82no—
276C22×C3—82no—
277C22×C3—81no—
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3—81no—
282C22×C3—81no—
283C22×C3#93911yescharacteristic
284C22×C3C3×#12111yescharacteristic
285C3×C4—21no—
286C3×C4—22no—
287C3×C4—22no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—42no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—81no—
298C3×C4—241no—
299C3×C4#91511yescharacteristic
300C3×C4#91611yescharacteristic
301C3×C4C2×#21311yescharacteristic
302C3×C4#95011yescharacteristic
303C3×C4C2×C3×D811yescharacteristic
304C3×C4C3×#13511yescharacteristic
305C3×C4C3×#13511yescharacteristic
306C3×C4C3×#13711yescharacteristic
307Dic3—81no—
308C32#168211yescharacteristic, complemented, Sylow
309C23—41no—
310Q8—21no—
311Q8—121no—
312Q8—121no—
313Q8C3×#21312yes—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—41no—
318D4—81no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—121no—
322C2×C4C3×D3×D411yescharacteristic
323C2×C4C3×#23711yescharacteristic
324C2×C4C2×C3×#6711yescharacteristic
325C8—41no—
326C8—61no—
327C8—61no—
328C8—121no—
329C8—121no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—162no—
334C2×C3—161no—
335C2×C3—161no—
336C2×C3#503811yescharacteristic
337C2×C3#516611yescharacteristic
338C2×C3#520011yescharacteristic
339C2×C3C3×#46411yescharacteristic
340C2×C3C3×#46611yescharacteristic
341C2×C3C3×#47111yescharacteristic
342C22—81no—
343C22—81no—
344C22—81no—
345C22C3×#93911yescharacteristic
346C4—21no—
347C4—22no—
348C4—41no—
349C4—241no—
350C4C3×#91511yescharacteristic
351C4C3×#91611yescharacteristic
352C4C2×C3×#21311yescharacteristic
353C4C3×#95011yescharacteristic
354C3—21no—
355C3#7102311yescharacteristic, direct product factor
356C3C3×#168211yescharacteristic, complemented
357C2—161no—
358C2C3×#503811yescharacteristic
359C2C3×#516611yescharacteristic
360C2C3×#520011yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#460C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenterC3×#460D3
hypocenterC3C3×#1682
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#460

Complements

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

NH ≅ G/Ntype
3. C3×#5031C2semidirect
4. C3×Q8×C3⋊C8C2semidirect
6. C3×#4482C2semidirect
7. C3×#4479C2semidirect
9. #71023C3direct (N × H)
32. #5031C2×C3semidirect
33. Q8×C3⋊C8C2×C3semidirect
38. #4482C2×C3semidirect
39. #4479C2×C3semidirect
308. C32#1682semidirect
355. C3#71023direct (N × H)
356. C3C3×#1682semidirect

Maximal subgroups

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

subgroupindex
C32×#4602
C3×#50702
C3×#50312
C3×Q8×C3⋊C82
C3×#45442
C3×#44822
C3×#44792
C3×#16823
#710233