Finite Group Databasebeta

← C3×#68336 #11775314

Subgroups — C3×#68336 #11775314

Order 1152.

588 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C22⋊Q8C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic
3C3×#4664C211yesmaximal, characteristic
4C32×#328C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7C3×#4452C211yesmaximal, characteristic, complemented
8C3×#1511—31nomaximal
9#68336C311yesmaximal, characteristic, direct product factor
10C2×C3×D3×Q8C411yescharacteristic, complemented
11C22×C3×C4×D3C2211yescharacteristic
12C32×C22⋊Q8C2211yescharacteristic
13C3×#946C411yescharacteristic, complemented
14C2×C3×(C2×D3)⋊C4—21no—
15C3×#924C2211yescharacteristic
16C2×C3×ΓL(1,𝔽25)—21no—
17C3×#897C411yescharacteristic, complemented
18C3×#896—21no—
19C3×D3×C4⋊C4—21no—
20C3×D3×C4⋊C4C411yescharacteristic, complemented
21C3×D3×C22⋊C4—21no—
22C3×#878—21no—
23C32×C22⋊C8C2211yescharacteristic
24C32×#95C2211yescharacteristic
25C3×C3⋊#95—21no—
26C3×C3⋊#95C2211yescharacteristic
27C3×#830C2211yescharacteristic
28C3×(C2×D3)⋊C8—21no—
29C2×C3×C22⋊Q8—31no—
30D3×C22⋊Q8C2×C311yescharacteristic
31C3×#407—31no—
32C3×#381—31no—
33#4726C2×C311yescharacteristic
34#4664C2×C311yescharacteristic
35C3×#328—21no—
36C3×#328—31no—
37C3×#328—31no—
38C3×#328—31no—
39C3×#328D311yescharacteristic, complemented
40C3×#328C2×C311yescharacteristic, complemented
41#4538C2×C311yescharacteristic, complemented
42#4467C2×C311yescharacteristic, complemented
43#4452C2×C311yescharacteristic, complemented
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8C2×C411yescharacteristic
46C22×C32×C4—21no—
47C22×C32×C4C2311yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C3×D3×Q8—42no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—42no—
54C2×C3×C4×D3C2×C411yescharacteristic
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×Dic6—21no—
59C2×C3×Dic6C2×C411yescharacteristic
60C2×C32×C8—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2×C411yescharacteristic
63C32×C22⋊C4—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—42no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2×C411yescharacteristic
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—21no—
73C2×C3×C3⋊C8—21no—
74C3×ΓL(1,𝔽25)—42no—
75#1511—31noSylow
76C22×C3×Q8—31no—
77C23×C3×C4—31no—
78C2×D3×Q8C3×C411yescharacteristic, complemented
79C22×C4×D3C22×C311yescharacteristic
80C2×C3×M16—61no—
81C3×C22⋊Q8—21no—
82C3×C22⋊Q8—31no—
83C3×C22⋊Q8—31no—
84C3×C22⋊Q8—31no—
85C3×C22⋊Q8—61no—
86C3×C22⋊Q8—61no—
87C3×C22⋊Q8C2×D311yescharacteristic
88C3×C22⋊Q8C22×C311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4—61no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C22⋊C4—61no—
93#946C3×C411yescharacteristic, complemented
94C2×(C2×D3)⋊C4—21no—
95#924C22×C311yescharacteristic
96C2×ΓL(1,𝔽25)—21no—
97#897C3×C411yescharacteristic, complemented
98#896—21no—
99D3×C4⋊C4—21no—
100D3×C4⋊C4C3×C411yescharacteristic, complemented
101D3×C22⋊C4—21no—
102#878—21no—
103C3×C22⋊C8—21no—
104C3×C22⋊C8—31no—
105C3×C22⋊C8—61no—
106C3×C22⋊C8C2×D311yescharacteristic
107C3×C22⋊C8C22×C311yescharacteristic
108C3×#95—21no—
109C3×#95—31no—
110C3×#95—61no—
111C3×#95C2×D311yescharacteristic
112C3×#95C22×C311yescharacteristic
113C3⋊#95—21no—
114C3⋊#95C22×C311yescharacteristic
115#830C22×C311yescharacteristic
116(C2×D3)⋊C8—21no—
117C23×C32C2×D411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3C22⋊C411yescharacteristic
123C22×C3×D3C22⋊C411yescharacteristic
124C32×Q8—41no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4—41no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3C22⋊C411yescharacteristic
140C2×C3×Dic3C22⋊C411yescharacteristic
141C3×C4×D3—22no—
142C3×C4×D3—22no—
143C3×C4×D3—41no—
144C3×C4×D3—41no—
145C3×C4×D3—42no—
146C3×C4×D3—42no—
147C3×Dic6—42no—
148C3×Dic6—41no—
149C32×C8—41no—
150C3×C3⋊C8—41no—
151C2×C22⋊Q8—31no—
152#407—31no—
153#381—31no—
154#328—31no—
155#328—31no—
156#328—31no—
157#328C3×D311yescharacteristic, complemented
158C24×C3—31no—
159C23×D3C3×D411yescharacteristic
160C2×C3×Q8—21no—
161C2×C3×Q8—31no—
162C2×C3×Q8—61no—
163C2×C3×Q8—122no—
164C2×C3×Q8C4×D311yescharacteristic
165C2×C3×Q8C2×C3×C411yescharacteristic
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—31no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—41no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—122no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C23×C311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3C3×D411yescharacteristic
183D3×Q8—42no—
184C2×C4×D3—21no—
185C2×C4×D3—21no—
186C2×C4×D3—42no—
187C2×C4×D3C2×C3×C411yescharacteristic
188C2×C4×D3C2×C3×C411yescharacteristic
189C2×C4×D3C3×D411yescharacteristic
190C2×C4×D3C3×D411yescharacteristic
191C2×Dic6—21no—
192C2×Dic6C2×C3×C411yescharacteristic
193C3×M16—122no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—41no—
197C2×C3×C8—61no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—31no—
202C3×C4⋊C4—41no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4C4×D311yescharacteristic
208C3×C4⋊C4C2×C3×C411yescharacteristic
209C3×C22⋊C4—21no—
210C3×C22⋊C4—21no—
211C3×C22⋊C4—41no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—61no—
215C3×C22⋊C4—122no—
216#217—21no—
217(C2×D3)⋊C4—21no—
218(C2×D3)⋊C4—21no—
219(C2×D3)⋊C4—42no—
220C4⋊Dic3—21no—
221C4⋊Dic3C2×C3×C411yescharacteristic
222Dic3⋊C4—21no—
223Dic3⋊C4—21no—
224Dic3⋊C4—21no—
225C2×C3⋊C8—21no—
226ΓL(1,𝔽25)—42no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32C2×C22⋊C411yescharacteristic
230C22×C32#13711yescharacteristic
231C22×C32#13711yescharacteristic
232C2×C3×D3—21no—
233C2×C3×D3—21no—
234C2×C3×D3—21no—
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3#9912yes—
240C32×C4—21no—
241C32×C4—21no—
242C32×C4—41no—
243C32×C4—41no—
244C32×C4—81no—
245C3×Dic3—21no—
246C3×Dic3—21no—
247C3×Dic3—41no—
248C3×Dic3—41no—
249C3×Dic3—81no—
250C22×Q8—31no—
251C23×C4—31no—
252C2×M16—61no—
253C22⋊Q8—31no—
254C22⋊Q8—31no—
255C22⋊Q8—31no—
256C22⋊Q8—61no—
257C22⋊Q8—61no—
258C22⋊Q8C2×C3×D311yescharacteristic
259C2×C4⋊C4—31no—
260C2×C4⋊C4—61no—
261C2×C22⋊C4—61no—
262C2×C22⋊C4—61no—
263C22⋊C8—31no—
264C22⋊C8—61no—
265C22⋊C8C2×C3×D311yescharacteristic
266#95—31no—
267#95—61no—
268#95C2×C3×D311yescharacteristic
269C23×C3—21no—
270C23×C3—31no—
271C23×C3—31no—
272C23×C3—62no—
273C23×C3—61no—
274C23×C3—61no—
275C23×C3—121no—
276C23×C3D3×D411yescharacteristic
277C23×C3C2×C3×D411yescharacteristic
278C22×D3—21no—
279C22×D3—21no—
280C22×D3—22no—
281C22×D3—41no—
282C22×D3C3×C22⋊C411yescharacteristic
283C22×D3C3×C22⋊C411yescharacteristic
284C3×Q8—41no—
285C3×Q8—41no—
286C3×Q8—81no—
287C3×Q8—121no—
288C3×Q8—122no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—31no—
296C2×C3×C4—31no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—42no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—81no—
313C2×C3×C4—81no—
314C2×C3×C4—81no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—122no—
318C2×C3×C4—122no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4C2×C4×D311yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4C22×C3×C411yescharacteristic
326C2×C3×C4C2×C3×D411yescharacteristic
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3C3×C22⋊C411yescharacteristic
334C2×Dic3C3×C22⋊C411yescharacteristic
335C4×D3—22no—
336C4×D3—22no—
337C4×D3—41no—
338C4×D3—41no—
339C4×D3—42no—
340C4×D3—42no—
341Dic6—42no—
342Dic6—41no—
343C3×C8—41no—
344C3×C8—41no—
345C3×C8—81no—
346C3×C8—121no—
347C3⋊C8—41no—
348C2×C32—21no—
349C2×C32—21no—
350C2×C32C2×#9911yescharacteristic
351C2×C32#41911yescharacteristic
352C2×C32#42111yescharacteristic
353C3×D3—22no—
354C3×D3—41no—
355C24—31no—
356C2×Q8—31no—
357C2×Q8—61no—
358C2×Q8—122no—
359C2×Q8C3×C4×D311yescharacteristic
360C22×C4—21no—
361C22×C4—31no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—31no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—122no—
370C22×C4C22×C3×D311yescharacteristic
371M16—122no—
372C2×C8—21no—
373C2×C8—61no—
374C4⋊C4—21no—
375C4⋊C4—31no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4C3×C4×D311yescharacteristic
381C22⋊C4—21no—
382C22⋊C4—61no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—122no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—32no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—61no—
397C22×C3—61no—
398C22×C3—61no—
399C22×C3—61no—
400C22×C3—61no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3D3×C22⋊C411yescharacteristic
404C22×C3#91511yescharacteristic
405C22×C3#91811yescharacteristic
406C22×C3C2×C3×C22⋊C411yescharacteristic
407C22×C3C3×#13711yescharacteristic
408C22×C3C3×#13711yescharacteristic
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—21no—
412C2×D3—21no—
413C2×D3—21no—
414C2×D3—42no—
415C2×D3—42no—
416C2×D3C3×#9912yes—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—41no—
422C3×C4—41no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—41no—
427C3×C4—61no—
428C3×C4—61no—
429C3×C4—81no—
430C3×C4—81no—
431C3×C4—81no—
432C3×C4—81no—
433C3×C4—82no—
434C3×C4—121no—
435C3×C4—121no—
436C3×C4—241no—
437Dic3—21no—
438Dic3—21no—
439Dic3—41no—
440Dic3—41no—
441Dic3—81no—
442C32#151111yescharacteristic, complemented, Sylow
443C23—31no—
444C23—31no—
445C23—62no—
446C23—61no—
447C23—61no—
448C23—121no—
449C23C3×D3×D411yescharacteristic
450Q8—41no—
451Q8—121no—
452Q8—122no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4—122no—
468C2×C4—122no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4C2×C3×C4×D311yescharacteristic
474C2×C4C3×D3×D411yescharacteristic
475C8—41no—
476C8—121no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—62no—
487C2×C3—121no—
488C2×C3D3×#9911yescharacteristic
489C2×C3#480211yescharacteristic
490C2×C3#482111yescharacteristic
491C2×C3C2×C3×#9911yescharacteristic
492C2×C3C3×#41911yescharacteristic
493C2×C3C3×#42111yescharacteristic
494D3—22no—
495D3—41no—
496C22—21no—
497C22—21no—
498C22—32no—
499C22—61no—
500C22—61no—
501C22—61no—
502C22—61no—
503C22—61no—
504C22—122no—
505C22—122no—
506C22C3×D3×C22⋊C411yescharacteristic
507C22C3×#91511yescharacteristic
508C22C3×#91811yescharacteristic
509C4—21no—
510C4—21no—
511C4—41no—
512C4—41no—
513C4—61no—
514C4—61no—
515C4—81no—
516C4—121no—
517C4—121no—
518C4—241no—
519C3—21no—
520C3#6833611yescharacteristic, direct product factor
521C3C3×#151111yescharacteristic, complemented
522C2—21no—
523C2—21no—
524C2—62no—
525C2—121no—
526C2C3×D3×#9911yescharacteristic
527C2C3×#480211yescharacteristic
528C2C3×#482111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#328C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3D4
cosocleC22×C3×C4C23×C3
hypercenterC3×#328D3
hypocenterC3C3×#1511
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#328

Complements

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

NH ≅ G/Ntype
4. C32×#328C2semidirect
5. C3×#4538C2semidirect
6. C3×#4467C2semidirect
7. C3×#4452C2semidirect
9. #68336C3direct (N × H)
10. C2×C3×D3×Q8C4semidirect
13. C3×#946C4semidirect
17. C3×#897C4semidirect
20. C3×D3×C4⋊C4C4semidirect
39. C3×#328D3semidirect
40. C3×#328C2×C3semidirect
41. #4538C2×C3semidirect
42. #4467C2×C3semidirect
43. #4452C2×C3semidirect
78. C2×D3×Q8C3×C4semidirect
93. #946C3×C4semidirect
97. #897C3×C4semidirect
100. D3×C4⋊C4C3×C4semidirect
157. #328C3×D3semidirect
442. C32#1511semidirect
520. C3#68336direct (N × H)
521. C3C3×#1511semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C22⋊Q82
C3×#47262
C3×#46642
C32×#3282
C3×#45382
C3×#44672
C3×#44522
C3×#15113
#683363