Finite Group Databasebeta

← C3×#13387 #10631994

Subgroups — C3×#13387 #10631994

Order 768.

428 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3058C211yesmaximal, characteristic
2C3×#2159C211yesmaximal, characteristic, complemented
3C2×C3×#361C211yesmaximal, characteristic, complemented
4C2×C3×#357C211yesmaximal, characteristic, complemented
5C2×C3×#350C211yesmaximal, characteristic, complemented
6C3×#1816C211yesmaximal, characteristic, complemented
7C3×#1382C211yesmaximal, characteristic, complemented
8#13387C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×D8C2211yescharacteristic
10C2×C3×#131C2211yescharacteristic
11C3×#535—21no—
12C2×C3×M32C2211yescharacteristic
13C22×C3×C16C2211yescharacteristic
14C3×#469—22no—
15C3×#466—21no—
16C3×#466—21no—
17C2×C3×#108C2211yescharacteristic
18C3×#427C2211yescharacteristic
19C2×C3×#107C2211yescharacteristic
20C3×#418—21no—
21C3×#417—21no—
22C3×#367—21no—
23C3×#366—21no—
24C3×#361—22no—
25C3×#357—22no—
26C3×#350—22no—
27C3×#343—21no—
28#3058C2×C311yescharacteristic
29#2159C2×C311yescharacteristic, complemented
30C2×#361C2×C311yescharacteristic, complemented
31C2×#357C2×C311yescharacteristic, complemented
32C2×#350C2×C311yescharacteristic, complemented
33#1816C2×C311yescharacteristic, complemented
34#1382C2×C311yescharacteristic, complemented
35C2×C3×#41D411yescharacteristic
36C22×C3×D4—21no—
37C2×C3×D8—21no—
38C2×C3×D8—21no—
39C2×C3×D8—21no—
40C2×C3×D8—21no—
41C2×C3×D8—21no—
42C2×C3×D8D412yes—
43C3×#131—21no—
44C3×#131—21no—
45C3×#131—21no—
46C3×#131—21no—
47C2×C3×M16—21no—
48C2×C3×M16—21no—
49C2×C3×M16D411yescharacteristic
50C22×C3×C8—21no—
51C22×C3×C8C2311yescharacteristic
52C3×#127—41no—
53C3×#124—41no—
54C3×#121—22no—
55C3×#121—22no—
56C3×#120—42no—
57C3×#117—21no—
58C2×C3×C4⋊C4—21no—
59C3×M32—21no—
60C3×M32D412yescomplemented
61C2×C3×C16—21no—
62C2×C3×C16—21no—
63C2×C3×C16—21no—
64C2×C3×C16—21no—
65C3×#108—21no—
66C3×#108—21no—
67C3×#107—21no—
68C3×#107—21no—
69C3×#107D411yescharacteristic
70C3×#107D411yescharacteristic
71C3×#106—21no—
72C3×#103—41no—
73C3×#102—22no—
74C3×#102—22no—
75C3×#102—41no—
76C22×D8C22×C311yescharacteristic
77C2×#131C22×C311yescharacteristic
78#535—21no—
79C2×M32C22×C311yescharacteristic
80C22×C16C22×C311yescharacteristic
81#469—22no—
82#466—21no—
83#466—21no—
84C2×#108C22×C311yescharacteristic
85#427C22×C311yescharacteristic
86C2×#107C22×C311yescharacteristic
87#418—21no—
88#417—21no—
89#367—21no—
90#366—21no—
91#361—22no—
92#357—22no—
93#350—22no—
94#343—21no—
95C24×C3—41no—
96C3×#41—21no—
97C3×#41—21no—
98C3×#41—21no—
99C3×#41—21no—
100C2×C3×Q8D811yescharacteristic
101C2×C3×D4—21no—
102C2×C3×D4—22no—
103C2×C3×D4—42no—
104C2×C3×D4—42no—
105C2×C3×D4—41no—
106C2×C3×D4—41no—
107C2×C3×D4—41no—
108C2×C3×D4—41no—
109C2×C3×D4—41no—
110C2×C3×D4D811yescharacteristic
111C22×C3×C4—21no—
112C22×C3×C4—41no—
113C22×C3×C4C2×D411yescharacteristic
114C3×D8—22no—
115C3×D8—22no—
116C3×D8—41no—
117C3×D8—41no—
118C3×M16—21no—
119C3×M16—21no—
120C3×M16—41no—
121C3×M16—41no—
122C3×M16—41no—
123C3×M16—41no—
124C2×C3×C8—21no—
125C2×C3×C8—41no—
126C2×C3×C8—41no—
127C2×C3×C8—41no—
128C2×C3×C8C2×D411yescharacteristic
129C2×C3×C8C2×D411yescharacteristic
130C2×C3×C8C2×D411yescharacteristic
131C2×C3×C8#4111yescharacteristic
132C2×C3×C8#4111yescharacteristic
133C2×C3×C8#4111yescharacteristic
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136C3×C4⋊C4—41no—
137C3×C4⋊C4—41no—
138C3×C22⋊C4—42no—
139C3×C22⋊C4—42no—
140C3×C22⋊C4—41no—
141C3×C42—41no—
142C3×C16—22no—
143C3×C16—41no—
144C2×#41C3×D411yescharacteristic
145C22×D4—21no—
146C2×D8—21no—
147C2×D8—21no—
148C2×D8—21no—
149C2×D8—21no—
150C2×D8—21no—
151C2×D8C3×D412yes—
152#131—21no—
153#131—21no—
154#131—21no—
155#131—21no—
156C2×M16—21no—
157C2×M16—21no—
158C2×M16C3×D411yescharacteristic
159C22×C8—21no—
160C22×C8C23×C311yescharacteristic
161#127—41no—
162#124—41no—
163#121—22no—
164#121—22no—
165#120—42no—
166#117—21no—
167C2×C4⋊C4—21no—
168M32—21no—
169M32C3×D412yescomplemented
170C2×C16—21no—
171C2×C16—21no—
172C2×C16—21no—
173C2×C16—21no—
174#108—21no—
175#108—21no—
176#107—21no—
177#107—21no—
178#107C3×D411yescharacteristic
179#107C3×D411yescharacteristic
180#106—21no—
181#103—41no—
182#102—22no—
183#102—22no—
184#102—41no—
185C23×C3—21no—
186C23×C3—42no—
187C23×C3—81no—
188C23×C3—81no—
189C23×C3—161no—
190C23×C3—161no—
191C23×C3AGL(1,ℤ/8)11yescharacteristic
192C3×Q8—21no—
193C3×Q8—21no—
194C3×D4—21no—
195C3×D4—21no—
196C3×D4—41no—
197C3×D4—41no—
198C3×D4—42no—
199C3×D4—42no—
200C3×D4—81no—
201C3×D4—81no—
202C3×D4—162no—
203C3×D4—162no—
204C2×C3×C4—21no—
205C2×C3×C4—41no—
206C2×C3×C4—41no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4—81no—
210C2×C3×C4—161no—
211C2×C3×C4#12011yescharacteristic
212C2×C3×C4#12111yescharacteristic
213C2×C3×C4#12311yescharacteristic
214C2×C3×C4C2×D811yescharacteristic
215C2×C3×C4#13511yescharacteristic
216C2×C3×C4#13711yescharacteristic
217C3×C8—41no—
218C3×C8—81no—
219C3×C8#12111yescharacteristic
220C3×C8#12111yescharacteristic
221C3×C8#12311yescharacteristic
222C3×C8#12411yescharacteristic
223C24—41no—
224#41—21no—
225#41—21no—
226#41—21no—
227#41—21no—
228C2×Q8C3×D811yescharacteristic
229C2×D4—21no—
230C2×D4—22no—
231C2×D4—42no—
232C2×D4—42no—
233C2×D4—41no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4C3×D811yescharacteristic
239C22×C4—21no—
240C22×C4—41no—
241C22×C4C2×C3×D411yescharacteristic
242D8—22no—
243D8—22no—
244D8—41no—
245D8—41no—
246M16—21no—
247M16—21no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252C2×C8—21no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8C2×C3×D411yescharacteristic
257C2×C8C2×C3×D411yescharacteristic
258C2×C8C2×C3×D411yescharacteristic
259C2×C8C3×#4111yescharacteristic
260C2×C8C3×#4111yescharacteristic
261C2×C8C3×#4111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—41no—
269C42—41no—
270C16—22no—
271C16—41no—
272C22×C3—21no—
273C22×C3—21no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3—82no—
278C22×C3—82no—
279C22×C3—82no—
280C22×C3—162no—
281C22×C3—162no—
282C22×C3#44711yescharacteristic
283C22×C3#46811yescharacteristic
284C22×C3#48211yescharacteristic
285C3×C4—41no—
286C3×C4—81no—
287C3×C4—81no—
288C3×C4—161no—
289C3×C4#39411yescharacteristic
290C3×C4#45211yescharacteristic
291C3×C4#46611yescharacteristic
292C3×C4#48011yescharacteristic
293C23—21no—
294C23—42no—
295C23—81no—
296C23—81no—
297C23—161no—
298C23—161no—
299C23C3×AGL(1,ℤ/8)11yescharacteristic
300Q8—21no—
301Q8—21no—
302D4—21no—
303D4—21no—
304D4—41no—
305D4—41no—
306D4—42no—
307D4—42no—
308D4—81no—
309D4—81no—
310D4—162no—
311D4—162no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—161no—
319C2×C4C3×#12011yescharacteristic
320C2×C4C3×#12111yescharacteristic
321C2×C4C3×#12311yescharacteristic
322C2×C4C2×C3×D811yescharacteristic
323C2×C4C3×#13511yescharacteristic
324C2×C4C3×#13711yescharacteristic
325C8—41no—
326C8—81no—
327C8C3×#12111yescharacteristic
328C8C3×#12111yescharacteristic
329C8C3×#12311yescharacteristic
330C8C3×#12411yescharacteristic
331C2×C3—21no—
332C2×C3—21no—
333C2×C3—81no—
334C2×C3—162no—
335C2×C3#203311yescharacteristic
336C2×C3#219211yescharacteristic
337C2×C3#219411yescharacteristic
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—162no—
347C22—162no—
348C22C3×#44711yescharacteristic
349C22C3×#46811yescharacteristic
350C22C3×#48211yescharacteristic
351C4—41no—
352C4—81no—
353C4—81no—
354C4—161no—
355C4C3×#39411yescharacteristic
356C4C3×#45211yescharacteristic
357C4C3×#46611yescharacteristic
358C4C3×#48011yescharacteristic
359C3#1338711yescharacteristic, direct product factor, Sylow
360C2—21no—
361C2—21no—
362C2—81no—
363C2—162no—
364C2C3×#203311yescharacteristic
365C2C3×#219211yescharacteristic
366C2C3×#219411yescharacteristic
subgroupG/H
center, socleC22×C3#447
commutator, Frattini, cosocleC22×C8C23×C3
prime radicalC3×#3058C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#2159C2semidirect
3. C2×C3×#361C2semidirect
4. C2×C3×#357C2semidirect
5. C2×C3×#350C2semidirect
6. C3×#1816C2semidirect
7. C3×#1382C2semidirect
8. #13387C3direct (N × H)
29. #2159C2×C3semidirect
30. C2×#361C2×C3semidirect
31. C2×#357C2×C3semidirect
32. C2×#350C2×C3semidirect
33. #1816C2×C3semidirect
34. #1382C2×C3semidirect
60. C3×M32D4semidirect
169. M32C3×D4semidirect
359. C3#13387direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#30582
C3×#21592
C2×C3×#3612
C2×C3×#3572
C2×C3×#3502
C3×#18162
C3×#13822
#133873