Finite Group Databasebeta

← C3×#71105 #11781763

Subgroups — C3×#71105 #11781763

Order 1152.

386 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#474C211yesmaximal, characteristic
2C3×#5092C211yesmaximal, characteristic, complemented
3C3×#5012C211yesmaximal, characteristic
4C3×#5007C211yesmaximal, characteristic
5C3×#4547C211yesmaximal, characteristic, complemented
6C3×#4486C211yesmaximal, characteristic, complemented
7C3×#4480C211yesmaximal, characteristic, complemented
8C3×#1689—31nomaximal
9#71105C311yesmaximal, characteristic, direct product factor
10C32×C4⋊Q8C2211yescharacteristic
11C32×C4×D4C2211yescharacteristic
12C2×C3×#216—21no—
13C2×C3×#216—21no—
14C2×C3×#208—21no—
15C3×#869C2211yescharacteristic
16C32×#107—21no—
17C32×C4⋊C8C2211yescharacteristic
18C32×#102—21no—
19C3×#832—21no—
20C3×#830—21no—
21C3×#807—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#494—31no—
26C3×#474—21no—
27C3×#474—31no—
28C3×#474D311yescharacteristic
29C3×#474C2×C311yescharacteristic
30C3×#436—31no—
31#5092C2×C311yescharacteristic, complemented
32#5012C2×C311yescharacteristic
33#5007C2×C311yescharacteristic
34C3×#334—31no—
35C3×#332—31no—
36C3×#332—31no—
37#4547C2×C311yescharacteristic, complemented
38#4486C2×C311yescharacteristic, complemented
39#4480C2×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×#216—42no—
51C3×#216—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×#208—42no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#1689—31noSylow
60C2×C3×Q16—61no—
61C2×C3×Q16—61no—
62C2×C3×M16—61no—
63C3×C4⋊Q8—21no—
64C3×C4⋊Q8—31no—
65C3×C4⋊Q8C2×D311yescharacteristic
66C3×C4⋊Q8C22×C311yescharacteristic
67C3×C4×D4—21no—
68C3×C4×D4C2×D311yescharacteristic
69C3×C4×D4C22×C311yescharacteristic
70C2×#216—21no—
71C2×#216—21no—
72C2×#208—21no—
73#869C22×C311yescharacteristic
74C3×#107—22no—
75C3×#107—21no—
76C3×#107—21no—
77C3×#107—61no—
78C3×C4⋊C8—21no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8C2×D311yescharacteristic
82C3×C4⋊C8C22×C311yescharacteristic
83C3×#102—22no—
84C3×#102—21no—
85C3×#102—21no—
86C3×#102—61no—
87C3×C22⋊C8—61no—
88C3×C4×C8—31no—
89#832—21no—
90#830—21no—
91#807—21no—
92C4⋊(C3⋊C8)C22×C311yescharacteristic
93C4⋊(C3⋊C8)C22×C311yescharacteristic
94C4×C3⋊C8C22×C311yescharacteristic
95C23×C32—21no—
96C32×Q8—41no—
97C32×Q8—41no—
98C32×D4—21no—
99C32×D4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
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—41no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8D812yes—
115#494—31no—
116#474—31no—
117#474C3×D311yescharacteristic
118#436—31no—
119#334—31no—
120#332—31no—
121#332—31no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—41no—
125C2×C3×Q8—61no—
126C2×C3×D4—21no—
127C2×C3×D4#6711yescharacteristic
128C2×C3×D4C3×D411yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—41no—
132C2×Dic6—21no—
133C3×Q16—122no—
134C3×Q16—122no—
135C3×M16—122no—
136C2×C3×C8—22no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—61no—
142C2×C3×C8—61no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4#6711yescharacteristic
153C3×C4⋊C4C3×D411yescharacteristic
154C3×C22⋊C4—21no—
155C3×C22⋊C4—21no—
156C3×C22⋊C4—41no—
157C3×C42—21no—
158C3×C42C22×D311yescharacteristic
159C3×C42C23×C311yescharacteristic
160#216—42no—
161#216—42no—
162C4⋊Dic3—21no—
163C4⋊Dic3—21no—
164#208—42no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167C2×C3⋊C8C3×D411yescharacteristic
168C2×C3⋊C8C3×D411yescharacteristic
169C22×C32—41no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32#12111yescharacteristic
173C32×C4—21no—
174C32×C4—41no—
175C32×C4—81no—
176C32×C4C2×D811yescharacteristic
177C32×C4AGL(1,ℤ/8)11yescharacteristic
178C32×C4#13711yescharacteristic
179C32×C4#13711yescharacteristic
180C3×Dic3—81no—
181C2×Q16—61no—
182C2×Q16—61no—
183C2×M16—61no—
184C4⋊Q8—31no—
185C4⋊Q8C2×C3×D311yescharacteristic
186C4×D4C2×C3×D311yescharacteristic
187#107—21no—
188#107—61no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191C4⋊C8C2×C3×D311yescharacteristic
192#102—21no—
193#102—61no—
194C22⋊C8—61no—
195C4×C8—31no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—41no—
199C3×Q8—41no—
200C3×Q8—41no—
201C3×Q8—41no—
202C3×Q8—41no—
203C3×Q8—81no—
204C3×Q8—81no—
205C3×Q8—121no—
206C3×Q8—121no—
207C3×D4—22no—
208C3×D4—21no—
209C3×D4—21no—
210C3×D4—21no—
211C3×D4—21no—
212C3×D4—41no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—42no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—81no—
227C2×C3×C4—81no—
228C2×C3×C4—121no—
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4#23711yescharacteristic
231C2×C3×C4C2×#6711yescharacteristic
232C2×C3×C4C2×C3×D411yescharacteristic
233C2×C3×C4C2×C3×D411yescharacteristic
234C2×C3×C4C3×#4111yescharacteristic
235C2×Dic3—41no—
236Dic6—41no—
237Dic6—41no—
238C3×C8—32no—
239C3×C8—42no—
240C3×C8—41no—
241C3×C8—41no—
242C3×C8—61no—
243C3×C8—121no—
244C3×C8—121no—
245C3⋊C8—21no—
246C3⋊C8—41no—
247C3⋊C8—41no—
248C3⋊C8C3×D812yes—
249C2×C32—81no—
250C2×C32#45911yescharacteristic
251C2×C32#47011yescharacteristic
252C2×C32#47311yescharacteristic
253C2×Q8—21no—
254C2×Q8—61no—
255C2×D4C3×#6711yescharacteristic
256C22×C4—21no—
257Q16—122no—
258Q16—122no—
259M16—122no—
260C2×C8—21no—
261C2×C8—31no—
262C2×C8—31no—
263C2×C8—61no—
264C2×C8—61no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4C3×#6711yescharacteristic
270C22⋊C4—21no—
271C42C22×C3×D311yescharacteristic
272C22×C3—21no—
273C22×C3—42no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—41no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3—81no—
281C22×C3—81no—
282C22×C3#93911yescharacteristic
283C22×C3C3×#12111yescharacteristic
284C3×C4—21no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—41no—
293C3×C4—81no—
294C3×C4—82no—
295C3×C4—81no—
296C3×C4—81no—
297C3×C4—241no—
298C3×C4D3×D811yescharacteristic
299C3×C4#91111yescharacteristic
300C3×C4#94211yescharacteristic
301C3×C4#95111yescharacteristic
302C3×C4C2×C3×D811yescharacteristic
303C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
304C3×C4C3×#13711yescharacteristic
305C3×C4C3×#13711yescharacteristic
306Dic3—81no—
307C32#168911yescharacteristic, complemented, Sylow
308C23—21no—
309Q8—41no—
310Q8—41no—
311Q8—121no—
312Q8—121no—
313D4—21no—
314D4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—121no—
320C2×C4C3×D3×D411yescharacteristic
321C2×C4C3×#23711yescharacteristic
322C2×C4C2×C3×#6711yescharacteristic
323C8—32no—
324C8—41no—
325C8—61no—
326C8—121no—
327C8—121no—
328C2×C3—21no—
329C2×C3—21no—
330C2×C3—21no—
331C2×C3—82no—
332C2×C3—81no—
333C2×C3—81no—
334C2×C3#505211yescharacteristic
335C2×C3#515011yescharacteristic
336C2×C3#520411yescharacteristic
337C2×C3C3×#45911yescharacteristic
338C2×C3C3×#47011yescharacteristic
339C2×C3C3×#47311yescharacteristic
340C22—41no—
341C22—41no—
342C22—41no—
343C22C3×#93911yescharacteristic
344C4—21no—
345C4—41no—
346C4—81no—
347C4—241no—
348C4C3×D3×D811yescharacteristic
349C4C3×#91111yescharacteristic
350C4C3×#94211yescharacteristic
351C4C3×#95111yescharacteristic
352C3—21no—
353C3#7110511yescharacteristic, direct product factor
354C3C3×#168911yescharacteristic, complemented
355C2—81no—
356C2C3×#505211yescharacteristic
357C2C3×#515011yescharacteristic
358C2C3×#520411yescharacteristic
subgroupG/H
centerC22×C3#939
commutator, cosocleC3×C42C23×C3
FrattiniC42C22×C3×D3
FittingC32×#474C2
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC3×#474D3
hypocenterC3C3×#1689
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×#5092C2semidirect
5. C3×#4547C2semidirect
6. C3×#4486C2semidirect
7. C3×#4480C2semidirect
9. #71105C3direct (N × H)
31. #5092C2×C3semidirect
37. #4547C2×C3semidirect
38. #4486C2×C3semidirect
39. #4480C2×C3semidirect
307. C32#1689semidirect
353. C3#71105direct (N × H)
354. C3C3×#1689semidirect

Maximal subgroups

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

subgroupindex
C32×#4742
C3×#50922
C3×#50122
C3×#50072
C3×#45472
C3×#44862
C3×#44802
C3×#16893
#711053