Finite Group Databasebeta

← C3×#33745 #10652352

Subgroups — C3×#33745 #10652352

Order 768.

496 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3177C211yesmaximal, characteristic, complemented
2C3×#3175C211yesmaximal, characteristic
3C3×#2255C211yesmaximal, characteristic, complemented
4C3×#2251C211yesmaximal, characteristic, complemented
5C3×#2242C211yesmaximal, characteristic, complemented
6C3×#2241C211yesmaximal, characteristic, complemented
7C3×#2220C211yesmaximal, characteristic
8C3×#2219C211yesmaximal, characteristic, complemented
9C3×#2217C211yesmaximal, characteristic
10C3×#2216C211yesmaximal, characteristic, complemented
11C3×#2176C211yesmaximal, characteristic, complemented
12C3×#2175C211yesmaximal, characteristic, complemented
13C3×C4×Q32C211yesmaximal, characteristic, complemented
14C3×C4×SD32C211yesmaximal, characteristic, complemented
15C3×#2108C211yesmaximal, characteristic, complemented
16#33745C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#542—21no—
18C3×#541—21no—
19C2×C3×Q32C2211yescharacteristic
20C2×C3×Q32C2211yescharacteristic
21C2×C3×SD32C2211yescharacteristic
22C2×C3×SD32C2211yescharacteristic
23C2×C3×M32C2211yescharacteristic
24C22×C3×C16C2211yescharacteristic
25C3×#500C2211yescharacteristic
26C3×#499C2211yescharacteristic
27C3×#495C2211yescharacteristic
28C3×#494C2211yescharacteristic
29C3×#491—21no—
30C3×#489—21no—
31C3×#470—21no—
32C3×#468—21no—
33C3×#467C2211yescharacteristic
34C3×#467C2211yescharacteristic
35C3×#467C2211yescharacteristic
36C3×#466C2211yescharacteristic
37C3×#441—21no—
38C3×#440—21no—
39C3×C4×Q16C2211yescharacteristic
40C3×C4×Q16C2211yescharacteristic
41C3×C4×Q16C2211yescharacteristic
42C3×C4×D8C2211yescharacteristic
43C3×#405C2211yescharacteristic
44C3×#367C2211yescharacteristic
45C3×#367C2211yescharacteristic
46C3×#366C2211yescharacteristic
47C3×#366C2211yescharacteristic
48C3×#358C2211yescharacteristic
49C3×#358C2211yescharacteristic
50C3×#358C2211yescharacteristic
51C3×#358C2211yescharacteristic
52C3×#358C2211yescharacteristic
53C3×#358C2211yescharacteristic
54C3×#357C2211yescharacteristic
55C3×#357C2211yescharacteristic
56C3×#346C2211yescharacteristic
57C3×#346C2211yescharacteristic
58C3×C4×C16C2211yescharacteristic
59C3×C4×C16C2211yescharacteristic
60#3177C2×C311yescharacteristic, complemented
61#3175C2×C311yescharacteristic
62#2255C2×C311yescharacteristic, complemented
63#2251C2×C311yescharacteristic, complemented
64#2242C2×C311yescharacteristic, complemented
65#2241C2×C311yescharacteristic, complemented
66#2220C2×C311yescharacteristic
67#2219C2×C311yescharacteristic, complemented
68#2217C2×C311yescharacteristic
69#2216C2×C311yescharacteristic, complemented
70#2176C2×C311yescharacteristic, complemented
71#2175C2×C311yescharacteristic, complemented
72C4×Q32C2×C311yescharacteristic, complemented
73C4×SD32C2×C311yescharacteristic, complemented
74#2108C2×C311yescharacteristic, complemented
75C2×C3×Q16—21no—
76C2×C3×Q16C2311yescharacteristic
77C2×C3×Q16C2311yescharacteristic
78C2×C3×Q16C2311yescharacteristic
79C2×C3×SD16—21no—
80C2×C3×D8C2311yescharacteristic
81C2×C3×M16D411yescharacteristic
82C22×C3×C8C2311yescharacteristic
83C3×C4⋊Q8—21no—
84C3×C4⋊Q8—21no—
85C3×#126—41no—
86C3×#126—41no—
87C3×#126—41no—
88C3×#125—21no—
89C3×#125—41no—
90C3×#125—41no—
91C3×#124—21no—
92C3×#124—41no—
93C3×#123—41no—
94C3×C22⋊Q8—21no—
95C3×C22⋊Q8—21no—
96C3×C22⋊Q8—21no—
97C3×C22⋊Q8—41no—
98C3×#121—21no—
99C3×C4×Q8—21no—
100C3×C4×Q8—21no—
101C3×C4×Q8—21no—
102C3×C4×D4—21no—
103C3×#117D411yescharacteristic
104C3×Q32—22no—
105C3×Q32—22no—
106C3×SD32—22no—
107C3×SD32—22no—
108C3×M32—22no—
109C2×C3×C16—22no—
110C2×C3×C16C2311yescharacteristic
111C2×C3×C16C2311yescharacteristic
112C2×C3×C16C2311yescharacteristic
113C2×C3×C16C2311yescharacteristic
114C3×#107—21no—
115C3×#107C2311yescharacteristic
116C3×#107C2311yescharacteristic
117C3×#107C2311yescharacteristic
118C3×#107C2311yescharacteristic
119C3×#106—21no—
120C3×#103—21no—
121C3×#103—21no—
122C3×#103—21no—
123C3×#103—21no—
124C3×#103—21no—
125C3×#103—21no—
126C3×#102—21no—
127C3×#102—21no—
128C3×#97D411yescharacteristic
129C3×#97D411yescharacteristic
130C3×C4×C8C2311yescharacteristic
131C3×C4×C8C2311yescharacteristic
132#542—21no—
133#541—21no—
134C2×Q32C22×C311yescharacteristic
135C2×Q32C22×C311yescharacteristic
136C2×SD32C22×C311yescharacteristic
137C2×SD32C22×C311yescharacteristic
138C2×M32C22×C311yescharacteristic
139C22×C16C22×C311yescharacteristic
140#500C22×C311yescharacteristic
141#499C22×C311yescharacteristic
142#495C22×C311yescharacteristic
143#494C22×C311yescharacteristic
144#491—21no—
145#489—21no—
146#470—21no—
147#468—21no—
148#467C22×C311yescharacteristic
149#467C22×C311yescharacteristic
150#467C22×C311yescharacteristic
151#466C22×C311yescharacteristic
152#441—21no—
153#440—21no—
154C4×Q16C22×C311yescharacteristic
155C4×Q16C22×C311yescharacteristic
156C4×Q16C22×C311yescharacteristic
157C4×D8C22×C311yescharacteristic
158#405C22×C311yescharacteristic
159#367C22×C311yescharacteristic
160#367C22×C311yescharacteristic
161#366C22×C311yescharacteristic
162#366C22×C311yescharacteristic
163#358C22×C311yescharacteristic
164#358C22×C311yescharacteristic
165#358C22×C311yescharacteristic
166#358C22×C311yescharacteristic
167#358C22×C311yescharacteristic
168#358C22×C311yescharacteristic
169#357C22×C311yescharacteristic
170#357C22×C311yescharacteristic
171#346C22×C311yescharacteristic
172#346C22×C311yescharacteristic
173C4×C16C22×C311yescharacteristic
174C4×C16C22×C311yescharacteristic
175C2×C3×Q8—21no—
176C2×C3×Q8—21no—
177C2×C3×Q8—21no—
178C2×C3×Q8—41no—
179C2×C3×D4—21no—
180C2×C3×D4—41no—
181C22×C3×C4—41no—
182C22×C3×C4C2×D411yescharacteristic
183C3×Q16—21no—
184C3×Q16—21no—
185C3×Q16—21no—
186C3×Q16—21no—
187C3×Q16—21no—
188C3×Q16—21no—
189C3×Q16—42no—
190C3×SD16—42no—
191C3×D8—21no—
192C3×D8—21no—
193C3×M16—22no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8C2×D411yescharacteristic
197C2×C3×C8C2×D411yescharacteristic
198C2×C3×C8C2×D411yescharacteristic
199C2×C3×C8C2411yescharacteristic
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—41no—
206C3×C4⋊C4—41no—
207C3×C4⋊C4—41no—
208C3×C4⋊C4—41no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—41no—
212C3×C4⋊C4—41no—
213C3×C4⋊C4—41no—
214C3×C4⋊C4—41no—
215C3×C4⋊C4D811yescharacteristic
216C3×C4⋊C4D811yescharacteristic
217C3×C22⋊C4—41no—
218C3×C22⋊C4—41no—
219C3×C22⋊C4—41no—
220C3×C22⋊C4—41no—
221C3×C22⋊C4—41no—
222C3×C22⋊C4—41no—
223C3×C22⋊C4—41no—
224C3×C22⋊C4D811yescharacteristic
225C3×C22⋊C4D811yescharacteristic
226C3×C42—41no—
227C3×C42—41no—
228C3×C42—41no—
229C3×C42C2×D411yescharacteristic
230C3×C42C2×D411yescharacteristic
231C3×C16—21no—
232C3×C16—21no—
233C3×C16#4112yes—
234C3×C16#4112yes—
235C2×Q16—21no—
236C2×Q16C23×C311yescharacteristic
237C2×Q16C23×C311yescharacteristic
238C2×Q16C23×C311yescharacteristic
239C2×SD16—21no—
240C2×D8C23×C311yescharacteristic
241C2×M16C3×D411yescharacteristic
242C22×C8C23×C311yescharacteristic
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245#126—41no—
246#126—41no—
247#126—41no—
248#125—21no—
249#125—41no—
250#125—41no—
251#124—21no—
252#124—41no—
253#123—41no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256C22⋊Q8—21no—
257C22⋊Q8—41no—
258#121—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×Q8—21no—
262C4×D4—21no—
263#117C3×D411yescharacteristic
264Q32—22no—
265Q32—22no—
266SD32—22no—
267SD32—22no—
268M32—22no—
269C2×C16—22no—
270C2×C16C23×C311yescharacteristic
271C2×C16C23×C311yescharacteristic
272C2×C16C23×C311yescharacteristic
273C2×C16C23×C311yescharacteristic
274#107—21no—
275#107C23×C311yescharacteristic
276#107C23×C311yescharacteristic
277#107C23×C311yescharacteristic
278#107C23×C311yescharacteristic
279#106—21no—
280#103—21no—
281#103—21no—
282#103—21no—
283#103—21no—
284#103—21no—
285#103—21no—
286#102—21no—
287#102—21no—
288#97C3×D411yescharacteristic
289#97C3×D411yescharacteristic
290C4×C8C23×C311yescharacteristic
291C4×C8C23×C311yescharacteristic
292C23×C3—41no—
293C23×C3C2×D811yescharacteristic
294C3×Q8—41no—
295C3×Q8—41no—
296C3×Q8—41no—
297C3×Q8—41no—
298C3×Q8—41no—
299C3×Q8—41no—
300C3×Q8—161no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—161no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—161no—
314C2×C3×C4C2×D811yescharacteristic
315C2×C3×C4C2×D811yescharacteristic
316C2×C3×C4C2×D811yescharacteristic
317C2×C3×C4C2×D811yescharacteristic
318C2×C3×C4C2×D811yescharacteristic
319C2×C3×C4C22×D411yescharacteristic
320C3×C8—21no—
321C3×C8—21no—
322C3×C8#13512yes—
323C3×C8C2×#4111yescharacteristic
324C3×C8C2×#4111yescharacteristic
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8—41no—
329C2×D4—21no—
330C2×D4—41no—
331C22×C4—41no—
332C22×C4C2×C3×D411yescharacteristic
333Q16—21no—
334Q16—21no—
335Q16—21no—
336Q16—21no—
337Q16—21no—
338Q16—21no—
339Q16—42no—
340SD16—42no—
341D8—21no—
342D8—21no—
343M16—22no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8C2×C3×D411yescharacteristic
347C2×C8C2×C3×D411yescharacteristic
348C2×C8C2×C3×D411yescharacteristic
349C2×C8C24×C311yescharacteristic
350C4⋊C4—21no—
351C4⋊C4—21no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—41no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4C3×D811yescharacteristic
366C4⋊C4C3×D811yescharacteristic
367C22⋊C4—41no—
368C22⋊C4—41no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4C3×D811yescharacteristic
375C22⋊C4C3×D811yescharacteristic
376C42—41no—
377C42—41no—
378C42—41no—
379C42C2×C3×D411yescharacteristic
380C42C2×C3×D411yescharacteristic
381C16—21no—
382C16—21no—
383C16C3×#4112yes—
384C16C3×#4112yes—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—81no—
389C22×C3—81no—
390C22×C3—81no—
391C22×C3C22×D811yescharacteristic
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—81no—
398C3×C4—81no—
399C3×C4—81no—
400C3×C4—81no—
401C3×C4—81no—
402C3×C4—81no—
403C3×C4—81no—
404C3×C4#53211yescharacteristic
405C3×C4C2×#13511yescharacteristic
406C23—41no—
407C23C2×C3×D811yescharacteristic
408Q8—41no—
409Q8—41no—
410Q8—41no—
411Q8—41no—
412Q8—41no—
413Q8—41no—
414Q8—161no—
415D4—41no—
416D4—41no—
417D4—161no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—161no—
428C2×C4C2×C3×D811yescharacteristic
429C2×C4C2×C3×D811yescharacteristic
430C2×C4C2×C3×D811yescharacteristic
431C2×C4C2×C3×D811yescharacteristic
432C2×C4C2×C3×D811yescharacteristic
433C2×C4C22×C3×D411yescharacteristic
434C8—21no—
435C8—21no—
436C8C3×#13512yes—
437C8C2×C3×#4111yescharacteristic
438C8C2×C3×#4111yescharacteristic
439C2×C3—41no—
440C2×C3—161no—
441C2×C3#316911yescharacteristic
442C2×C3#341611yescharacteristic
443C2×C3#341711yescharacteristic
444C22—21no—
445C22—21no—
446C22—21no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C22×C3×D811yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4C3×#53211yescharacteristic
464C4C2×C3×#13511yescharacteristic
465C3#3374511yescharacteristic, direct product factor, Sylow
466C2—41no—
467C2—161no—
468C2C3×#316911yescharacteristic
469C2C3×#341611yescharacteristic
470C2C3×#341711yescharacteristic
subgroupG/H
center, socleC22×C3C22×D8
commutator, Frattini, cosocleC2×C8C24×C3
prime radicalC3×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C3×#117 ◁ C3×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3177C2semidirect
3. C3×#2255C2semidirect
4. C3×#2251C2semidirect
5. C3×#2242C2semidirect
6. C3×#2241C2semidirect
8. C3×#2219C2semidirect
10. C3×#2216C2semidirect
11. C3×#2176C2semidirect
12. C3×#2175C2semidirect
13. C3×C4×Q32C2semidirect
14. C3×C4×SD32C2semidirect
15. C3×#2108C2semidirect
16. #33745C3direct (N × H)
60. #3177C2×C3semidirect
62. #2255C2×C3semidirect
63. #2251C2×C3semidirect
64. #2242C2×C3semidirect
65. #2241C2×C3semidirect
67. #2219C2×C3semidirect
69. #2216C2×C3semidirect
70. #2176C2×C3semidirect
71. #2175C2×C3semidirect
72. C4×Q32C2×C3semidirect
73. C4×SD32C2×C3semidirect
74. #2108C2×C3semidirect
465. C3#33745direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#31772
C3×#31752
C3×#22552
C3×#22512
C3×#22422
C3×#22412
C3×#22202
C3×#22192
C3×#22172
C3×#22162
C3×#21762
C3×#21752
C3×C4×Q322
C3×C4×SD322
C3×#21082
#337453