Finite Group Databasebeta

← C3×#13339 #10631946

Subgroups — C3×#13339 #10631946

Order 768.

534 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#510C211yesmaximal, characteristic
2C22×C3×Q32C211yesmaximal, characteristic, complemented
3C3×#3156C211yesmaximal, characteristic
4C2×C3×#362C211yesmaximal, characteristic, complemented
5C2×C3×#359C211yesmaximal, characteristic
6C3×#1979C211yesmaximal, characteristic, complemented
7C3×#1379C211yesmaximal, characteristic, complemented
8#13339C311yesmaximal, characteristic, direct product factor, Sylow
9C2×C3×#137—21no—
10C2×C3×#135C2211yescharacteristic
11C22×C3×Q16C2211yescharacteristic
12C22×C3×Q16C2211yescharacteristic
13C3×#536—21no—
14C3×#510—22no—
15C3×#510—22no—
16C2×C3×Q32—22no—
17C2×C3×Q32—22no—
18C2×C3×Q32—21no—
19C2×C3×Q32—22no—
20C2×C3×SD32—21no—
21C2×C3×M32C2211yescharacteristic
22C22×C3×C16C2211yescharacteristic
23C3×#497—22no—
24C3×#495—21no—
25C3×#494—21no—
26C2×C3×#108C2211yescharacteristic
27C3×#419—21no—
28C2×C3×#101—21no—
29C3×#405C2211yescharacteristic
30C3×#362—22no—
31C3×#359—22no—
32C2×#510C2×C311yescharacteristic
33C22×Q32C2×C311yescharacteristic, complemented
34#3156C2×C311yescharacteristic
35C2×#362C2×C311yescharacteristic, complemented
36C2×#359C2×C311yescharacteristic
37#1979C2×C311yescharacteristic, complemented
38#1379C2×C311yescharacteristic, complemented
39C2×C3×#41—21no—
40C22×C3×Q8—21no—
41C22×C3×Q8—21no—
42C3×#137—42no—
43C3×#137—42no—
44C3×#135—21no—
45C3×#135—21no—
46C3×#135—21no—
47C3×#135—21no—
48C2×C3×Q16—22no—
49C2×C3×Q16—21no—
50C2×C3×Q16—21no—
51C2×C3×Q16—21no—
52C2×C3×Q16—21no—
53C2×C3×Q16—21no—
54C2×C3×Q16—21no—
55C2×C3×Q16—21no—
56C2×C3×Q16—21no—
57C2×C3×Q16—21no—
58C2×C3×Q16—21no—
59C2×C3×Q16D412yes—
60C2×C3×Q16D412yes—
61C2×C3×Q16D411yescharacteristic
62C2×C3×SD16—22no—
63C2×C3×SD16—21no—
64C2×C3×D8D411yescharacteristic
65C2×C3×M16—21no—
66C2×C3×M16D411yescharacteristic
67C22×C3×C8C2311yescharacteristic
68C3×C4⋊Q8—22no—
69C3×#124—22no—
70C3×#123—42no—
71C3×C22⋊Q8—42no—
72C3×#117D411yescharacteristic
73C3×Q32—28no—
74C3×Q32—24no—
75C3×SD32—24no—
76C3×M32—21no—
77C3×M32D412yes—
78C2×C3×C16—21no—
79C2×C3×C16—21no—
80C2×C3×C16—21no—
81C2×C3×C16D412yes—
82C3×#108—21no—
83C3×#108—21no—
84C3×#103—42no—
85C3×#101—42no—
86C3×#97—21no—
87C3×C4×C8—21no—
88C2×#137—21no—
89C2×#135C22×C311yescharacteristic
90C22×Q16C22×C311yescharacteristic
91C22×Q16C22×C311yescharacteristic
92#536—21no—
93#510—22no—
94#510—22no—
95C2×Q32—22no—
96C2×Q32—22no—
97C2×Q32—21no—
98C2×Q32—22no—
99C2×SD32—21no—
100C2×M32C22×C311yescharacteristic
101C22×C16C22×C311yescharacteristic
102#497—22no—
103#495—21no—
104#494—21no—
105C2×#108C22×C311yescharacteristic
106#419—21no—
107C2×#101—21no—
108#405C22×C311yescharacteristic
109#362—22no—
110#359—22no—
111C3×#41—41no—
112C3×#41—41no—
113C3×#41—41no—
114C3×#41—41no—
115C2×C3×Q8—22no—
116C2×C3×Q8—21no—
117C2×C3×Q8—22no—
118C2×C3×Q8—41no—
119C2×C3×Q8—41no—
120C2×C3×Q8—41no—
121C2×C3×Q8—41no—
122C2×C3×Q8—41no—
123C2×C3×Q8—41no—
124C2×C3×Q8—41no—
125C2×C3×Q8—41no—
126C2×C3×Q8—41no—
127C2×C3×Q8—41no—
128C2×C3×D4—21no—
129C2×C3×D4—41no—
130C22×C3×C4—41no—
131C22×C3×C4—41no—
132C22×C3×C4—41no—
133C22×C3×C4C2×D411yescharacteristic
134C3×Q16—22no—
135C3×Q16—22no—
136C3×Q16—22no—
137C3×Q16—21no—
138C3×Q16—22no—
139C3×Q16—21no—
140C3×Q16—44no—
141C3×Q16—41no—
142C3×Q16—41no—
143C3×Q16—41no—
144C3×Q16—41no—
145C3×SD16—44no—
146C3×SD16—41no—
147C3×SD16—41no—
148C3×D8—21no—
149C3×D8—21no—
150C3×M16—21no—
151C3×M16—41no—
152C3×M16—41no—
153C3×M16D812yes—
154C2×C3×C8—21no—
155C2×C3×C8—41no—
156C2×C3×C8C2×D411yescharacteristic
157C2×C3×C8C2×D411yescharacteristic
158C2×C3×C8C2×D411yescharacteristic
159C2×C3×C8C2×D411yescharacteristic
160C2×C3×C8C2×D411yescharacteristic
161C2×C3×C8#4111yescharacteristic
162C3×C4⋊C4—44no—
163C3×C4⋊C4D812yes—
164C3×C22⋊C4—21no—
165C3×C22⋊C4—44no—
166C3×C42—21no—
167C3×C16—22no—
168C3×C16—22no—
169C2×#41—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172#137—42no—
173#137—42no—
174#135—21no—
175#135—21no—
176#135—21no—
177#135—21no—
178C2×Q16—22no—
179C2×Q16—21no—
180C2×Q16—21no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—21no—
184C2×Q16—21no—
185C2×Q16—21no—
186C2×Q16—21no—
187C2×Q16—21no—
188C2×Q16—21no—
189C2×Q16C3×D412yes—
190C2×Q16C3×D412yes—
191C2×Q16C3×D411yescharacteristic
192C2×SD16—22no—
193C2×SD16—21no—
194C2×D8C3×D411yescharacteristic
195C2×M16—21no—
196C2×M16C3×D411yescharacteristic
197C22×C8C23×C311yescharacteristic
198C4⋊Q8—22no—
199#124—22no—
200#123—42no—
201C22⋊Q8—42no—
202#117C3×D411yescharacteristic
203Q32—28no—
204Q32—24no—
205SD32—24no—
206M32—21no—
207M32C3×D412yes—
208C2×C16—21no—
209C2×C16—21no—
210C2×C16—21no—
211C2×C16C3×D412yes—
212#108—21no—
213#108—21no—
214#103—42no—
215#101—42no—
216#97—21no—
217C4×C8—21no—
218C23×C3—41no—
219C23×C3AGL(1,ℤ/8)11yescharacteristic
220C3×Q8—41no—
221C3×Q8—42no—
222C3×Q8—42no—
223C3×Q8—42no—
224C3×Q8—41no—
225C3×Q8—42no—
226C3×Q8—81no—
227C3×Q8—81no—
228C3×Q8—81no—
229C3×Q8—81no—
230C3×D4—41no—
231C3×D4—41no—
232C3×D4—81no—
233C3×D4—81no—
234C2×C3×C4—22no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—42no—
238C2×C3×C4—81no—
239C2×C3×C4—81no—
240C2×C3×C4—81no—
241C2×C3×C4—81no—
242C2×C3×C4—81no—
243C2×C3×C4—81no—
244C2×C3×C4#12011yescharacteristic
245C2×C3×C4#12111yescharacteristic
246C2×C3×C4#12711yescharacteristic
247C2×C3×C4C2×D811yescharacteristic
248C2×C3×C4C2×D811yescharacteristic
249C2×C3×C4AGL(1,ℤ/8)11yescharacteristic
250C3×C8—22no—
251C3×C8—81no—
252C3×C8#12011yescharacteristic
253C3×C8#12011yescharacteristic
254C3×C8#12111yescharacteristic
255C3×C8#12111yescharacteristic
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×D4—21no—
274C2×D4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4C2×C3×D411yescharacteristic
279Q16—22no—
280Q16—22no—
281Q16—22no—
282Q16—21no—
283Q16—22no—
284Q16—21no—
285Q16—44no—
286Q16—41no—
287Q16—41no—
288Q16—41no—
289Q16—41no—
290SD16—44no—
291SD16—41no—
292SD16—41no—
293D8—21no—
294D8—21no—
295M16—21no—
296M16—41no—
297M16—41no—
298M16C3×D812yes—
299C2×C8—21no—
300C2×C8—41no—
301C2×C8C2×C3×D411yescharacteristic
302C2×C8C2×C3×D411yescharacteristic
303C2×C8C2×C3×D411yescharacteristic
304C2×C8C2×C3×D411yescharacteristic
305C2×C8C2×C3×D411yescharacteristic
306C2×C8C3×#4111yescharacteristic
307C4⋊C4—44no—
308C4⋊C4C3×D812yes—
309C22⋊C4—21no—
310C22⋊C4—44no—
311C42—21no—
312C16—22no—
313C16—22no—
314C22×C3—22no—
315C22×C3—82no—
316C22×C3—81no—
317C22×C3#44711yescharacteristic
318C22×C3#45911yescharacteristic
319C22×C3#49611yescharacteristic
320C3×C4—42no—
321C3×C4—81no—
322C3×C4—82no—
323C3×C4—82no—
324C3×C4#39211yescharacteristic
325C3×C4#44711yescharacteristic
326C3×C4#45911yescharacteristic
327C3×C4#49311yescharacteristic
328C23—41no—
329C23C3×AGL(1,ℤ/8)11yescharacteristic
330Q8—41no—
331Q8—42no—
332Q8—42no—
333Q8—42no—
334Q8—41no—
335Q8—42no—
336Q8—81no—
337Q8—81no—
338Q8—81no—
339Q8—81no—
340D4—41no—
341D4—41no—
342D4—81no—
343D4—81no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4C3×#12011yescharacteristic
355C2×C4C3×#12111yescharacteristic
356C2×C4C3×#12711yescharacteristic
357C2×C4C2×C3×D811yescharacteristic
358C2×C4C2×C3×D811yescharacteristic
359C2×C4C3×AGL(1,ℤ/8)11yescharacteristic
360C8—22no—
361C8—81no—
362C8C3×#12011yescharacteristic
363C8C3×#12011yescharacteristic
364C8C3×#12111yescharacteristic
365C8C3×#12111yescharacteristic
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—161no—
369C2×C3#201111yescharacteristic
370C2×C3#219512yes—
371C22—22no—
372C22—81no—
373C22—82no—
374C22C3×#44711yescharacteristic
375C22C3×#45911yescharacteristic
376C22C3×#49611yescharacteristic
377C4—42no—
378C4—81no—
379C4—82no—
380C4—82no—
381C4C3×#39211yescharacteristic
382C4C3×#44711yescharacteristic
383C4C3×#45911yescharacteristic
384C4C3×#49311yescharacteristic
385C3#1333911yescharacteristic, direct product factor, Sylow
386C2—21no—
387C2—21no—
388C2—161no—
389C2C3×#201111yescharacteristic
390C2C3×#219512yes—
subgroupG/H
center, socleC22×C3#447
commutator, Frattini, cosocleC22×C8C23×C3
prime radicalC2×C3×#135C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×Q32C2semidirect
4. C2×C3×#362C2semidirect
6. C3×#1979C2semidirect
7. C3×#1379C2semidirect
8. #13339C3direct (N × H)
33. C22×Q32C2×C3semidirect
35. C2×#362C2×C3semidirect
37. #1979C2×C3semidirect
38. #1379C2×C3semidirect
385. C3#13339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5102
C22×C3×Q322
C3×#31562
C2×C3×#3622
C2×C3×#3592
C3×#19792
C3×#13792
#133393