Finite Group Databasebeta

← C3×#72082 #11798117

Subgroups — C3×#72082 #11798117

Order 1152.

593 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#135C211yesmaximal, characteristic, complemented
2C2×C3×#828C211yesmaximal, characteristic, complemented
3C2×C3×#826C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C3×#4564C211yesmaximal, characteristic, complemented
6C3×#4562C211yesmaximal, characteristic, complemented
7C3×#4549C211yesmaximal, characteristic, complemented
8C3×#2186—31nomaximal
9#72082C311yesmaximal, characteristic, direct product factor
10C2×C32×#41—21no—
11C32×#135—22no—
12C32×#135—22no—
13C2×C32×Q16C2211yescharacteristic
14C2×C32×SD16—21no—
15C2×C32×D8C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17C3×#930—21no—
18C2×C3×D24C2211yescharacteristic
19C3×#828—22no—
20C3×#826—22no—
21C3×#821—21no—
22C3×#818C2211yescharacteristic
23C2×C3×C3⋊C16C2211yescharacteristic
24C2×C3×C3⋊C16C2211yescharacteristic
25C2×C3×#135—21no—
26C2×C3×#135D311yescharacteristic, complemented
27C2×C3×#135C2×C311yescharacteristic, complemented
28C2×C3×SD32—31no—
29C2×C3×D16—31no—
30C3×#466—31no—
31C2×#828C2×C311yescharacteristic, complemented
32C2×#826C2×C311yescharacteristic, complemented
33#5115C2×C311yescharacteristic, complemented
34C3×#358—31no—
35C3×#357—31no—
36C3×C22⋊C16—31no—
37#4564C2×C311yescharacteristic, complemented
38#4562C2×C311yescharacteristic, complemented
39#4549C2×C311yescharacteristic, complemented
40C32×#41—24no—
41C32×#41—42no—
42C2×C32×Q8—21no—
43C2×C32×D4—21no—
44C2×C32×D4—41no—
45C22×C32×C4—41no—
46C22×C32×C4D411yescharacteristic
47C2×C3×#67—41no—
48C2×C3×D12—21no—
49C32×Q16—21no—
50C32×Q16D412yescomplemented
51C32×SD16—24no—
52C32×D8—21no—
53C32×D8D412yescomplemented
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8D411yescharacteristic
57C2×C32×C8C2311yescharacteristic
58C3×(C2×D3)⋊C4—41no—
59C3×C4⋊Dic3—21no—
60C3×D24—21no—
61C3×D24—21no—
62C3×C3⋊C16—21no—
63C3×C3⋊C16—21no—
64#2186—31noSylow
65C2×C3×#41—22no—
66C2×C3×#41—21no—
67C2×C3×#41—21no—
68C3×#135—24no—
69C3×#135—24no—
70C3×#135—22no—
71C3×#135—22no—
72C3×#135—22no—
73C3×#135—22no—
74C2×C3×Q16—21no—
75C2×C3×Q16C2×D311yescharacteristic
76C2×C3×Q16C22×C311yescharacteristic
77C2×C3×SD16—22no—
78C2×C3×SD16—21no—
79C2×C3×SD16—21no—
80C2×C3×D8—21no—
81C2×C3×D8—31no—
82C2×C3×D8C2×D311yescharacteristic
83C2×C3×D8C22×C311yescharacteristic
84C22×C3×C8—21no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C3×#121—61no—
88#930—21no—
89C2×D24C22×C311yescharacteristic
90C3×SD32—62no—
91C3×D16—62no—
92C2×C3×C16—31no—
93C2×C3×C16—31no—
94C3×#107—31no—
95C3×#102—61no—
96#828—22no—
97#826—22no—
98#821—21no—
99#818C22×C311yescharacteristic
100C2×C3⋊C16C22×C311yescharacteristic
101C2×C3⋊C16C22×C311yescharacteristic
102C23×C32—41no—
103C23×C32D811yescharacteristic
104C22×C3×D3—41no—
105C32×Q8—22no—
106C32×Q8—41no—
107C32×D4—22no—
108C32×D4—44no—
109C32×D4—41no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—44no—
113C2×C32×C4—41no—
114C2×C32×C4D811yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C3×#67—82no—
117C2×C3×Dic3—41no—
118C3×D12—41no—
119C3×D12—41no—
120C32×C8—21no—
121C32×C8C2×D411yescharacteristic
122C32×C8C2×D411yescharacteristic
123C2×#135C3×D311yescharacteristic, complemented
124C2×SD32—31no—
125C2×D16—31no—
126#466—31no—
127#358—31no—
128#357—31no—
129C22⋊C16—31no—
130C3×#41—28no—
131C3×#41—24no—
132C3×#41—24no—
133C3×#41—44no—
134C3×#41—42no—
135C3×#41—42no—
136C2×C3×Q8—22no—
137C2×C3×Q8—21no—
138C2×C3×Q8—21no—
139C2×C3×D4—22no—
140C2×C3×D4—21no—
141C2×C3×D4—21no—
142C2×C3×D4—42no—
143C2×C3×D4—41no—
144C2×C3×D4—41no—
145C2×C3×D4—61no—
146C2×C3×D4—121no—
147C22×C3×C4—21no—
148C22×C3×C4—42no—
149C22×C3×C4—41no—
150C22×C3×C4—41no—
151C22×C3×C4#6711yescharacteristic
152C22×C3×C4C3×D411yescharacteristic
153C2×#67—41no—
154C2×D12—21no—
155C3×Q16—22no—
156C3×Q16—21no—
157C3×Q16—21no—
158C3×Q16—22no—
159C3×Q16#6712yescomplemented
160C3×Q16C3×D412yescomplemented
161C3×SD16—28no—
162C3×SD16—24no—
163C3×SD16—24no—
164C3×D8—22no—
165C3×D8—21no—
166C3×D8—21no—
167C3×D8—22no—
168C3×D8—61no—
169C3×D8—61no—
170C3×D8#6712yescomplemented
171C3×D8C3×D412yescomplemented
172C2×C3×C8—22no—
173C2×C3×C8—22no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8#6711yescharacteristic
181C2×C3×C8C3×D411yescharacteristic
182C2×C3×C8C22×D311yescharacteristic
183C2×C3×C8C23×C311yescharacteristic
184C3×C4⋊C4—61no—
185C3×C22⋊C4—121no—
186(C2×D3)⋊C4—41no—
187C4⋊Dic3—21no—
188D24—21no—
189D24—21no—
190C3×C16—61no—
191C3×C16—61no—
192C3⋊C16—21no—
193C3⋊C16—21no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—42no—
198C22×C32—81no—
199C22×C32—81no—
200C22×C32C2×D811yescharacteristic
201C2×C3×D3—81no—
202C2×C3×D3—81no—
203C2×C3×D3—81no—
204C32×C4—21no—
205C32×C4—42no—
206C32×C4#12011yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C3×Dic3—81no—
209C2×#41—21no—
210#135—22no—
211#135—22no—
212C2×Q16C2×C3×D311yescharacteristic
213C2×SD16—21no—
214C2×D8—31no—
215C2×D8C2×C3×D311yescharacteristic
216C22×C8C2×C3×D311yescharacteristic
217#121—61no—
218SD32—62no—
219D16—62no—
220C2×C16—31no—
221C2×C16—31no—
222#107—31no—
223#102—61no—
224C23×C3—21no—
225C23×C3—42no—
226C23×C3—41no—
227C23×C3—41no—
228C23×C3—121no—
229C23×C3#21311yescharacteristic
230C23×C3C3×D811yescharacteristic
231C22×D3—41no—
232C3×Q8—24no—
233C3×Q8—22no—
234C3×Q8—22no—
235C3×Q8—42no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×D4—24no—
239C3×D4—22no—
240C3×D4—22no—
241C3×D4—42no—
242C3×D4—48no—
243C3×D4—44no—
244C3×D4—44no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—242no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—48no—
259C2×C3×C4—44no—
260C2×C3×C4—44no—
261C2×C3×C4—42no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—121no—
265C2×C3×C4#21311yescharacteristic
266C2×C3×C4C3×D811yescharacteristic
267C2×C3×C4C2×#6711yescharacteristic
268C2×C3×C4C2×C3×D411yescharacteristic
269#67—82no—
270C2×Dic3—41no—
271D12—41no—
272D12—41no—
273C3×C8—22no—
274C3×C8—21no—
275C3×C8—21no—
276C3×C8—21no—
277C3×C8—21no—
278C3×C8C2×#6711yescharacteristic
279C3×C8C2×#6711yescharacteristic
280C3×C8C2×C3×D411yescharacteristic
281C3×C8C2×C3×D411yescharacteristic
282C2×C32—41no—
283C2×C32—82no—
284C2×C32#44711yescharacteristic
285C2×C32#50811yescharacteristic
286C2×C32#50911yescharacteristic
287C3×D3—161no—
288#41—24no—
289#41—42no—
290C2×Q8—21no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—61no—
294C2×D4—121no—
295C22×C4—41no—
296C22×C4C3×#6711yescharacteristic
297Q16—21no—
298Q16C3×#6712yescomplemented
299SD16—24no—
300D8—21no—
301D8—61no—
302D8—61no—
303D8C3×#6712yescomplemented
304C2×C8—21no—
305C2×C8—21no—
306C2×C8C3×#6711yescharacteristic
307C2×C8C22×C3×D311yescharacteristic
308C4⋊C4—61no—
309C22⋊C4—121no—
310C16—61no—
311C16—61no—
312C22×C3—22no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—41no—
321C22×C3—41no—
322C22×C3—44no—
323C22×C3—42no—
324C22×C3—42no—
325C22×C3—82no—
326C22×C3—82no—
327C22×C3—81no—
328C22×C3—81no—
329C22×C3—81no—
330C22×C3—81no—
331C22×C3—241no—
332C22×C3—241no—
333C22×C3—241no—
334C22×C3C2×#21311yescharacteristic
335C22×C3C2×C3×D811yescharacteristic
336C2×D3—81no—
337C2×D3—81no—
338C2×D3—81no—
339C3×C4—22no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—21no—
343C3×C4—21no—
344C3×C4—44no—
345C3×C4—42no—
346C3×C4—42no—
347C3×C4—241no—
348C3×C4#93211yescharacteristic
349C3×C4#95311yescharacteristic
350C3×C4C3×#12011yescharacteristic
351C3×C4C3×AGL(1,ℤ/8)11yescharacteristic
352Dic3—81no—
353C32#218611yescharacteristic, complemented, Sylow
354C23—41no—
355C23—121no—
356C23C3×#21311yescharacteristic
357Q8—22no—
358Q8—41no—
359D4—22no—
360D4—44no—
361D4—41no—
362D4—121no—
363D4—121no—
364D4—242no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—44no—
368C2×C4—41no—
369C2×C4—121no—
370C2×C4C3×#21311yescharacteristic
371C2×C4C2×C3×#6711yescharacteristic
372C8—21no—
373C8C2×C3×#6711yescharacteristic
374C8C2×C3×#6711yescharacteristic
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—21no—
378C2×C3—42no—
379C2×C3—41no—
380C2×C3—41no—
381C2×C3—84no—
382C2×C3—82no—
383C2×C3—82no—
384C2×C3—481no—
385C2×C3#519311yescharacteristic
386C2×C3#519411yescharacteristic
387C2×C3#521711yescharacteristic
388C2×C3C3×#44711yescharacteristic
389C2×C3C3×#50811yescharacteristic
390C2×C3C3×#50911yescharacteristic
391D3—161no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—42no—
396C22—81no—
397C22—81no—
398C22—241no—
399C22—241no—
400C22—241no—
401C22C2×C3×#21311yescharacteristic
402C4—21no—
403C4—42no—
404C4—241no—
405C4C3×#93211yescharacteristic
406C4C3×#95311yescharacteristic
407C3—21no—
408C3#7208211yescharacteristic, direct product factor
409C3C3×#218611yescharacteristic, complemented
410C2—41no—
411C2—82no—
412C2—481no—
413C2C3×#519311yescharacteristic
414C2C3×#519411yescharacteristic
415C2C3×#521711yescharacteristic
subgroupG/H
centerC22×C3C2×#213
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC2×C32×#135C2
socleC22×C32C2×D8
hypercenterC2×C3×#135D3
hypocenterC3C3×#2186
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×C8 ◁ C2×C3×#135

Complements

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

NH ≅ G/Ntype
1. C2×C32×#135C2semidirect
2. C2×C3×#828C2semidirect
3. C2×C3×#826C2semidirect
4. C3×#5115C2semidirect
5. C3×#4564C2semidirect
6. C3×#4562C2semidirect
7. C3×#4549C2semidirect
9. #72082C3direct (N × H)
26. C2×C3×#135D3semidirect
27. C2×C3×#135C2×C3semidirect
31. C2×#828C2×C3semidirect
32. C2×#826C2×C3semidirect
33. #5115C2×C3semidirect
37. #4564C2×C3semidirect
38. #4562C2×C3semidirect
39. #4549C2×C3semidirect
50. C32×Q16D4semidirect
53. C32×D8D4semidirect
123. C2×#135C3×D3semidirect
159. C3×Q16#67semidirect
160. C3×Q16C3×D4semidirect
170. C3×D8#67semidirect
171. C3×D8C3×D4semidirect
298. Q16C3×#67semidirect
303. D8C3×#67semidirect
353. C32#2186semidirect
408. C3#72082direct (N × H)
409. C3C3×#2186semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1352
C2×C3×#8282
C2×C3×#8262
C3×#51152
C3×#45642
C3×#45622
C3×#45492
C3×#21863
#720823