Finite Group Databasebeta

← C3×#35883 #10654490

Subgroups — C3×#35883 #10654490

Order 768.

1622 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2645C213yesmaximal, complemented
2C3×#2514C213yesmaximal, complemented
3C3×#2514C213yesmaximal, complemented
4C3×#2511C213yesmaximal, complemented
5C3×#2497C213yesmaximal
6C3×#2495C213yesmaximal
7C3×#2494C213yesmaximal
8C3×#2401C213yesmaximal
9C3×#2351C211yesmaximal, characteristic, complemented
10C3×#2351C211yesmaximal, characteristic, complemented
11C3×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
12C3×Q8×C22⋊C4C211yesmaximal, characteristic
13C3×Q8×C22⋊C4C211yesmaximal, characteristic
14C3×Q8×C22⋊C4C211yesmaximal, characteristic
15C3×#2276C211yesmaximal, characteristic, complemented
16#35883C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×C3×C4×Q8C2211yescharacteristic
21C2×C3×C4×Q8C2211yescharacteristic
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C3×#401C2216yes—
25C3×#401C2213yes—
26C3×#400C2213yes—
27C3×#400C2216yes—
28C3×#400C2216yes—
29C3×#400C2213yes—
30C3×#400C2213yes—
31C3×#397C2211yescharacteristic
32C3×#397C2213yes—
33C3×#397C2213yes—
34C3×#396C2213yes—
35C3×#391C2213yes—
36C3×#391C2213yes—
37C3×#391C2213yes—
38C3×#391C2213yes—
39C3×#391C2213yes—
40C3×#391C2213yes—
41C3×#389C2213yes—
42C3×#389C2213yes—
43C3×#389C2213yes—
44C3×#389C2213yes—
45C3×#389C2213yes—
46C3×#389C2213yes—
47C3×#388C2216yes—
48C3×#387C2216yes—
49C3×#387C2216yes—
50C3×#384C2213yes—
51C3×#383C2216yes—
52C3×#382C2213yes—
53C3×#382C2213yes—
54C3×#380C2213yes—
55C3×#380C2213yes—
56C3×#380C2213yes—
57C3×C4×C4⋊C4C2213yes—
58C3×C4×C4⋊C4C2213yes—
59C3×C4×C4⋊C4C2213yes—
60C3×C4×C4⋊C4C2213yes—
61C3×C4×C4⋊C4C2213yes—
62C3×C4×C4⋊C4C2213yes—
63C3×C4×C22⋊C4C2213yes—
64C3×C4×C22⋊C4C2213yes—
65C3×C4×C22⋊C4C2213yes—
66C3×#376C2213yes—
67#2645C2×C313yescomplemented
68#2514C2×C313yescomplemented
69#2514C2×C313yescomplemented
70#2511C2×C313yescomplemented
71#2497C2×C313yes—
72#2495C2×C313yes—
73#2494C2×C313yes—
74#2401C2×C313yes—
75#2351C2×C311yescharacteristic, complemented
76#2351C2×C311yescharacteristic, complemented
77Q8×C4⋊C4C2×C311yescharacteristic, complemented
78Q8×C22⋊C4C2×C311yescharacteristic
79Q8×C22⋊C4C2×C311yescharacteristic
80Q8×C22⋊C4C2×C311yescharacteristic
81#2276C2×C311yescharacteristic, complemented
82C22×C3×Q8—24no—
83C22×C3×Q8—24no—
84C22×C3×Q8—24no—
85C22×C3×Q8C2313yes—
86C22×C3×Q8C2311yescharacteristic
87C23×C3×C4C2313yes—
88C3×C4×Q8—24no—
89C3×C4×Q8—24no—
90C3×C4×Q8—24no—
91C3×C4×Q8—24no—
92C3×C4×Q8—24no—
93C3×C4×Q8—24no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2313yes—
96C2×C3×C4⋊C4C2313yes—
97C2×C3×C4⋊C4C2313yes—
98C2×C3×C4⋊C4C2313yes—
99C2×C3×C4⋊C4C2313yes—
100C2×C3×C4⋊C4C2313yes—
101C2×C3×C4⋊C4C2313yes—
102C2×C3×C4⋊C4C2313yes—
103C2×C3×C4⋊C4C2313yes—
104C2×C3×C4⋊C4C2313yes—
105C2×C3×C4⋊C4C2313yes—
106C2×C3×C4⋊C4C2316yes—
107C2×C3×C22⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4C2311yescharacteristic
110C2×C3×C22⋊C4C2313yes—
111C2×C3×C22⋊C4C2313yes—
112C2×C3×C22⋊C4C2313yes—
113C2×C3×C42C2313yes—
114C2×C3×C42C2313yes—
115C2×C3×C42C2313yes—
116C2×C3×C42C2313yes—
117C2×C3×C42C2313yes—
118C2×C3×C42C2313yes—
119C2×C3×C42C2316yes—
120C3×#95C2311yescharacteristic
121C3×#95C2313yes—
122C3×#95C2313yes—
123C3×#95C2313yes—
124C3×#95C2313yes—
125C3×#95C2313yes—
126C3×#95C2313yes—
127C3×#95C2313yes—
128C3×#95C2313yes—
129C3×#95C2313yes—
130C3×#95C2311yescharacteristic
131C3×#95C2311yescharacteristic
132C3×#95C2313yes—
133C3×#95C2313yes—
134C3×#95C2313yes—
135C3×#95C2313yes—
136C3×#95C2316yes—
137C3×#95C2316yes—
138C3×#95C2316yes—
139C3×#95C2316yes—
140C3×#95C2316yes—
141C23×Q8C22×C311yescharacteristic
142C2×C4×Q8C22×C311yescharacteristic
143C2×C4×Q8C22×C311yescharacteristic
144C2×C4×Q8C22×C311yescharacteristic
145C2×C4×Q8C22×C311yescharacteristic
146C2×C4×Q8C22×C311yescharacteristic
147C2×C4×Q8C22×C311yescharacteristic
148#401C22×C316yes—
149#401C22×C313yes—
150#400C22×C313yes—
151#400C22×C316yes—
152#400C22×C316yes—
153#400C22×C313yes—
154#400C22×C313yes—
155#397C22×C311yescharacteristic
156#397C22×C313yes—
157#397C22×C313yes—
158#396C22×C313yes—
159#391C22×C313yes—
160#391C22×C313yes—
161#391C22×C313yes—
162#391C22×C313yes—
163#391C22×C313yes—
164#391C22×C313yes—
165#389C22×C313yes—
166#389C22×C313yes—
167#389C22×C313yes—
168#389C22×C313yes—
169#389C22×C313yes—
170#389C22×C313yes—
171#388C22×C316yes—
172#387C22×C316yes—
173#387C22×C316yes—
174#384C22×C313yes—
175#383C22×C316yes—
176#382C22×C313yes—
177#382C22×C313yes—
178#380C22×C313yes—
179#380C22×C313yes—
180#380C22×C313yes—
181C4×C4⋊C4C22×C313yes—
182C4×C4⋊C4C22×C313yes—
183C4×C4⋊C4C22×C313yes—
184C4×C4⋊C4C22×C313yes—
185C4×C4⋊C4C22×C313yes—
186C4×C4⋊C4C22×C313yes—
187C4×C22⋊C4C22×C313yes—
188C4×C22⋊C4C22×C313yes—
189C4×C22⋊C4C22×C313yes—
190#376C22×C313yes—
191C24×C3C2411yescharacteristic
192C2×C3×Q8—26no—
193C2×C3×Q8—26no—
194C2×C3×Q8—26no—
195C2×C3×Q8—416no—
196C2×C3×Q8#4114yes—
197C2×C3×Q8#4114yes—
198C2×C3×Q8#4114yes—
199C22×C3×C4—26no—
200C22×C3×C4—26no—
201C22×C3×C4—26no—
202C22×C3×C4C2413yes—
203C22×C3×C4C2411yescharacteristic
204C22×C3×C4C2411yescharacteristic
205C22×C3×C4C2411yescharacteristic
206C22×C3×C4C2411yescharacteristic
207C22×C3×C4C2411yescharacteristic
208C22×C3×C4C2413yes—
209C22×C3×C4C2413yes—
210C22×C3×C4C2413yes—
211C22×C3×C4C2413yes—
212C22×C3×C4C2413yes—
213C22×C3×C4C2413yes—
214C22×C3×C4C2411yescharacteristic
215C22×C3×C4C2413yes—
216C3×C4⋊C4—26no—
217C3×C4⋊C4—26no—
218C3×C4⋊C4—26no—
219C3×C4⋊C4—26no—
220C3×C4⋊C4—26no—
221C3×C4⋊C4—26no—
222C3×C4⋊C4—22no—
223C3×C4⋊C4—26no—
224C3×C4⋊C4—43no—
225C3×C4⋊C4—43no—
226C3×C4⋊C4—43no—
227C3×C4⋊C4—43no—
228C3×C4⋊C4—46no—
229C3×C22⋊C4—22no—
230C3×C22⋊C4—22no—
231C3×C22⋊C4—26no—
232C3×C22⋊C4—22no—
233C3×C22⋊C4—43no—
234C3×C22⋊C4—43no—
235C3×C42—26no—
236C3×C42—26no—
237C3×C42—26no—
238C3×C42—26no—
239C3×C42—26no—
240C3×C42—26no—
241C3×C42—46no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—24no—
245C22×Q8C23×C313yes—
246C22×Q8C23×C311yescharacteristic
247C23×C4C23×C313yes—
248C4×Q8—24no—
249C4×Q8—24no—
250C4×Q8—24no—
251C4×Q8—24no—
252C4×Q8—24no—
253C4×Q8—24no—
254C2×C4⋊C4C23×C313yes—
255C2×C4⋊C4C23×C313yes—
256C2×C4⋊C4C23×C313yes—
257C2×C4⋊C4C23×C313yes—
258C2×C4⋊C4C23×C313yes—
259C2×C4⋊C4C23×C313yes—
260C2×C4⋊C4C23×C311yescharacteristic
261C2×C4⋊C4C23×C313yes—
262C2×C4⋊C4C23×C313yes—
263C2×C4⋊C4C23×C313yes—
264C2×C4⋊C4C23×C313yes—
265C2×C4⋊C4C23×C313yes—
266C2×C4⋊C4C23×C316yes—
267C2×C22⋊C4C23×C311yescharacteristic
268C2×C22⋊C4C23×C311yescharacteristic
269C2×C22⋊C4C23×C311yescharacteristic
270C2×C22⋊C4C23×C313yes—
271C2×C22⋊C4C23×C313yes—
272C2×C22⋊C4C23×C313yes—
273C2×C42C23×C313yes—
274C2×C42C23×C313yes—
275C2×C42C23×C313yes—
276C2×C42C23×C313yes—
277C2×C42C23×C313yes—
278C2×C42C23×C313yes—
279C2×C42C23×C316yes—
280#95C23×C311yescharacteristic
281#95C23×C313yes—
282#95C23×C313yes—
283#95C23×C313yes—
284#95C23×C313yes—
285#95C23×C313yes—
286#95C23×C313yes—
287#95C23×C313yes—
288#95C23×C313yes—
289#95C23×C313yes—
290#95C23×C311yescharacteristic
291#95C23×C311yescharacteristic
292#95C23×C313yes—
293#95C23×C313yes—
294#95C23×C313yes—
295#95C23×C313yes—
296#95C23×C316yes—
297#95C23×C316yes—
298#95C23×C316yes—
299#95C23×C316yes—
300#95C23×C316yes—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C32−1+412yes—
308C23×C3C2511yescharacteristic
309C3×Q8—412no—
310C3×Q8#126116yes—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—23no—
319C2×C3×C4—23no—
320C2×C3×C4—23no—
321C2×C3×C4—23no—
322C2×C3×C4—23no—
323C2×C3×C4—23no—
324C2×C3×C4—23no—
325C2×C3×C4—23no—
326C2×C3×C4—23no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—23no—
330C2×C3×C4—23no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—23no—
335C2×C3×C4—23no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—23no—
339C2×C3×C4—23no—
340C2×C3×C4—23no—
341C2×C3×C4—23no—
342C2×C3×C4—23no—
343C2×C3×C4—23no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—23no—
347C2×C3×C4—21no—
348C2×C3×C4—23no—
349C2×C3×C4—412no—
350C2×C3×C4C2×#4116yes—
351C2×C3×C4C2×#4116yes—
352C2×C3×C4C2×#4116yes—
353C2×C3×C42−1+412yes—
354C24C24×C311yescharacteristic
355C2×Q8—26no—
356C2×Q8—26no—
357C2×Q8—26no—
358C2×Q8—416no—
359C2×Q8C3×#4114yes—
360C2×Q8C3×#4114yes—
361C2×Q8C3×#4114yes—
362C22×C4—26no—
363C22×C4—26no—
364C22×C4—26no—
365C22×C4C24×C313yes—
366C22×C4C24×C311yescharacteristic
367C22×C4C24×C311yescharacteristic
368C22×C4C24×C311yescharacteristic
369C22×C4C24×C311yescharacteristic
370C22×C4C24×C311yescharacteristic
371C22×C4C24×C313yes—
372C22×C4C24×C313yes—
373C22×C4C24×C313yes—
374C22×C4C24×C313yes—
375C22×C4C24×C313yes—
376C22×C4C24×C313yes—
377C22×C4C24×C311yescharacteristic
378C22×C4C24×C313yes—
379C4⋊C4—26no—
380C4⋊C4—26no—
381C4⋊C4—26no—
382C4⋊C4—26no—
383C4⋊C4—26no—
384C4⋊C4—26no—
385C4⋊C4—22no—
386C4⋊C4—26no—
387C4⋊C4—43no—
388C4⋊C4—43no—
389C4⋊C4—43no—
390C4⋊C4—43no—
391C4⋊C4—46no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—26no—
395C22⋊C4—22no—
396C22⋊C4—43no—
397C22⋊C4—43no—
398C42—26no—
399C42—26no—
400C42—26no—
401C42—26no—
402C42—26no—
403C42—26no—
404C42—46no—
405C22×C3—22no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3C22×#4111yescharacteristic
413C22×C3C22×#4111yescharacteristic
414C22×C3C22×#4111yescharacteristic
415C22×C3C2×2−1+411yescharacteristic
416C22×C3C2×2−1+411yescharacteristic
417C22×C3#58511yescharacteristic
418C22×C3#58511yescharacteristic
419C3×C4—22no—
420C3×C4—43no—
421C3×C4—43no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—43no—
425C3×C4—43no—
426C3×C4—41no—
427C3×C4—43no—
428C3×C4—41no—
429C3×C4—41no—
430C3×C4—43no—
431C3×C4—43no—
432C3×C4C2×#126112yes—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23C3×2−1+412yes—
440C23C25×C311yescharacteristic
441Q8—412no—
442Q8C3×#126116yes—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—23no—
451C2×C4—23no—
452C2×C4—23no—
453C2×C4—23no—
454C2×C4—23no—
455C2×C4—23no—
456C2×C4—23no—
457C2×C4—23no—
458C2×C4—23no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—23no—
462C2×C4—23no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—23no—
467C2×C4—23no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—23no—
471C2×C4—23no—
472C2×C4—23no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—23no—
479C2×C4—21no—
480C2×C4—23no—
481C2×C4—412no—
482C2×C4C2×C3×#4116yes—
483C2×C4C2×C3×#4116yes—
484C2×C4C2×C3×#4116yes—
485C2×C4C3×2−1+412yes—
486C2×C3—42no—
487C2×C3C22×#12611yescharacteristic
488C2×C3#351611yescharacteristic
489C2×C3#351611yescharacteristic
490C2×C3#351611yescharacteristic
491C2×C3#351811yescharacteristic
492C2×C3#352311yescharacteristic
493C2×C3#352411yescharacteristic
494C22—22no—
495C22—22no—
496C22—22no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22C22×C3×#4111yescharacteristic
502C22C22×C3×#4111yescharacteristic
503C22C22×C3×#4111yescharacteristic
504C22C2×C3×2−1+411yescharacteristic
505C22C2×C3×2−1+411yescharacteristic
506C22C3×#58511yescharacteristic
507C22C3×#58511yescharacteristic
508C4—22no—
509C4—43no—
510C4—43no—
511C4—41no—
512C4—41no—
513C4—43no—
514C4—43no—
515C4—41no—
516C4—43no—
517C4—41no—
518C4—41no—
519C4—43no—
520C4—43no—
521C4C2×C3×#126112yes—
522C3#3588311yescharacteristic, direct product factor, Sylow
523C2—42no—
524C2C22×C3×#12611yescharacteristic
525C2C3×#351611yescharacteristic
526C2C3×#351611yescharacteristic
527C2C3×#351611yescharacteristic
528C2C3×#351811yescharacteristic
529C2C3×#352311yescharacteristic
530C2C3×#352411yescharacteristic
subgroupG/H
center, socleC23×C3C25
commutator, Frattini, cosocleC23C25×C3
prime radicalC24×C3C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2645C2semidirect
2. C3×#2514C2semidirect
3. C3×#2514C2semidirect
4. C3×#2511C2semidirect
9. C3×#2351C2semidirect
10. C3×#2351C2semidirect
11. C3×Q8×C4⋊C4C2semidirect
15. C3×#2276C2semidirect
16. #35883C3direct (N × H)
67. #2645C2×C3semidirect
68. #2514C2×C3semidirect
69. #2514C2×C3semidirect
70. #2511C2×C3semidirect
75. #2351C2×C3semidirect
76. #2351C2×C3semidirect
77. Q8×C4⋊C4C2×C3semidirect
81. #2276C2×C3semidirect
522. C3#35883direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#26452
C3×#25142
C3×#25112
C3×#24972
C3×#24952
C3×#24942
C3×#24012
C3×#23512
C3×Q8×C4⋊C42
C3×Q8×C22⋊C42
C3×#22762
#358833