Finite Group Databasebeta

← C3×#70025 #11793130

Subgroups — C3×#70025 #11793130

Order 1152.

661 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5483C211yesmaximal, characteristic, complemented
2C2×C32×#99C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4C2×C3×#834C211yesmaximal, characteristic
5C3×#4527C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7C3×#4526C211yesmaximal, characteristic, complemented
8C3×#2032—31nomaximal
9#70025C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×C3×#217C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C3×#924—22no—
18C3×#878—22no—
19C3×#878—22no—
20C32×#99—22no—
21C3×#834—22no—
22C3×#834—22no—
23C3×#543—31no—
24#5483C2×C311yescharacteristic, complemented
25C2×C3×#99—21no—
26C2×C3×#99—31no—
27C2×C3×#99—31no—
28C2×C3×#99D311yescharacteristic
29C2×C3×#99C2×C311yescharacteristic
30C2×#834C2×C311yescharacteristic
31C2×#834C2×C311yescharacteristic
32C3×#342—31no—
33C3×#342—31no—
34C3×#342—31no—
35#4527C2×C311yescharacteristic, complemented
36#4527C2×C311yescharacteristic, complemented
37#4526C2×C311yescharacteristic, complemented
38C24×C32Q811yescharacteristic, complemented
39C24×C32C2311yescharacteristic
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4Q811yescharacteristic, complemented
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C2×C3×Dic6—22no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4—21no—
56C32×C22⋊C4—21no—
57C32×C22⋊C4D412yes—
58C3×#217—21no—
59C3×#217—21no—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217D412yes—
65C3×#217D412yes—
66C3×C4⋊Dic3—22no—
67C3×Dic3⋊C4—24no—
68#2032—31noSylow
69C22×C3×D4—21no—
70C22×C3×D4C2×D311yescharacteristic
71C22×C3×D4C22×C311yescharacteristic
72C3×C22⋊Q8—62no—
73C3×C22⋊Q8—62no—
74C3×C22⋊Q8—62no—
75C2×C3×C22⋊C4—21no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4—31no—
81C2×C3×C22⋊C4C2×D311yescharacteristic
82C2×C3×C22⋊C4C2×D311yescharacteristic
83C2×C3×C22⋊C4C22×C311yescharacteristic
84C2×C3×C22⋊C4C22×C311yescharacteristic
85C2×#217C22×C311yescharacteristic
86C2×#217C22×C311yescharacteristic
87C2×#217C22×C311yescharacteristic
88C2×#217C22×C311yescharacteristic
89#924—22no—
90#878—22no—
91#878—22no—
92C3×#99—24no—
93C3×#99—22no—
94C3×#99—22no—
95C3×#99—62no—
96C3×#99—62no—
97#834—22no—
98#834—22no—
99C23×C32—21no—
100C23×C32—21no—
101C23×C32—21no—
102C23×C32—81no—
103C23×C32—81no—
104C23×C32C2×D411yescharacteristic
105C23×C32C2×D411yescharacteristic
106C23×C32C2×D411yescharacteristic
107C23×C32C2×Q811yescharacteristic
108C23×C32#4111yescharacteristic
109C23×C32#4111yescharacteristic
110C23×C32#4111yescharacteristic
111C32×D4—41no—
112C32×D4—41no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4—21no—
116C2×C32×C4—22no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4—81no—
121C2×C32×C4—81no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—81no—
127C2×C3×Dic3—81no—
128C2×C3×Dic3—81no—
129C2×C3×Dic3—81no—
130C3×Dic6—82no—
131#543—31no—
132C2×#99—31no—
133C2×#99—31no—
134C2×#99C3×D311yescharacteristic
135#342—31no—
136#342—31no—
137#342—31no—
138C24×C3—21no—
139C24×C3—21no—
140C24×C3Dic611yescharacteristic, complemented
141C24×C3C3×Q811yescharacteristic, complemented
142C24×C3C22×D311yescharacteristic
143C24×C3C23×C311yescharacteristic
144C2×C3×Q8—62no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—21no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—41no—
160C2×C3×D4—41no—
161C2×C3×D4—41no—
162C2×C3×D4—41no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4Dic611yescharacteristic, complemented
175C22×C3×C4C3×Q811yescharacteristic, complemented
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—21no—
179C22×Dic3—21no—
180C2×Dic6—22no—
181C3×C4⋊C4—64no—
182C3×C4⋊C4—62no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—22no—
186C3×C22⋊C4—21no—
187C3×C22⋊C4—21no—
188C3×C22⋊C4—21no—
189C3×C22⋊C4—21no—
190C3×C22⋊C4—22no—
191C3×C22⋊C4—32no—
192C3×C22⋊C4—32no—
193C3×C22⋊C4—41no—
194C3×C22⋊C4—41no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4#6712yes—
202C3×C22⋊C4C3×D412yes—
203#217—21no—
204#217—21no—
205#217—21no—
206#217—21no—
207#217—21no—
208#217—21no—
209#217C3×D412yes—
210#217C3×D412yes—
211C4⋊Dic3—22no—
212Dic3⋊C4—24no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32—41no—
218C22×C32—41no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32—81no—
222C22×C32—81no—
223C22×C32—81no—
224C22×C32#12011yescharacteristic
225C22×C32C22⋊Q811yescharacteristic
226C22×C32C22⋊Q811yescharacteristic
227C22×C32C22⋊Q811yescharacteristic
228C22×C32#12411yescharacteristic
229C22×C32#12411yescharacteristic
230C22×C32#12411yescharacteristic
231C32×C4—41no—
232C32×C4—42no—
233C32×C4—81no—
234C3×Dic3—42no—
235C3×Dic3—42no—
236C3×Dic3—81no—
237C3×Dic3—81no—
238C22×D4C2×C3×D311yescharacteristic
239C22⋊Q8—62no—
240C22⋊Q8—62no—
241C22⋊Q8—62no—
242C2×C22⋊C4—31no—
243C2×C22⋊C4—31no—
244C2×C22⋊C4—31no—
245C2×C22⋊C4—31no—
246C2×C22⋊C4C2×C3×D311yescharacteristic
247C2×C22⋊C4C2×C3×D311yescharacteristic
248#99—22no—
249#99—62no—
250#99—62no—
251C23×C3—22no—
252C23×C3—21no—
253C23×C3—21no—
254C23×C3—21no—
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—21no—
258C23×C3—21no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—21no—
263C23×C3—21no—
264C23×C3—21no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3—81no—
268C23×C3—81no—
269C23×C3—82no—
270C23×C3—81no—
271C23×C3—81no—
272C23×C3—82no—
273C23×C3C2×Dic611yescharacteristic
274C23×C3#23511yescharacteristic
275C23×C3D3×D411yescharacteristic
276C23×C3D3×D411yescharacteristic
277C23×C3#23711yescharacteristic
278C23×C3#23711yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C23×C3C2×C3×D411yescharacteristic
281C23×C3C2×C3×D411yescharacteristic
282C23×C3C2×C3×D411yescharacteristic
283C23×C3C2×C3×Q811yescharacteristic
284C23×C3C3×#4111yescharacteristic
285C23×C3C3×#4111yescharacteristic
286C23×C3C3×#4111yescharacteristic
287C3×Q8—242no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—42no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C3×D4—41no—
296C3×D4—41no—
297C3×D4—41no—
298C3×D4—41no—
299C3×D4—41no—
300C2×C3×C4—22no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—42no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—81no—
318C2×C3×C4—81no—
319C2×C3×C4—82no—
320C2×C3×C4—82no—
321C2×C3×C4—81no—
322C2×C3×C4—81no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—241no—
326C2×C3×C4—241no—
327C2×C3×C4—241no—
328C2×C3×C4—241no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—81no—
334C2×Dic3—81no—
335C2×Dic3—81no—
336C2×Dic3—81no—
337Dic6—82no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32—81no—
346C2×C32#39311yescharacteristic
347C24C3×Dic611yescharacteristic, complemented
348C24C22×C3×D311yescharacteristic
349C2×Q8—62no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4C3×Dic611yescharacteristic, complemented
363C4⋊C4—64no—
364C4⋊C4—62no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—32no—
369C22⋊C4—32no—
370C22⋊C4—61no—
371C22⋊C4—61no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4C3×#6712yes—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—42no—
401C22×C3—42no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—81no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3—81no—
408C22×C3—81no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—82no—
415C22×C3—82no—
416C22×C3—82no—
417C22×C3#87811yescharacteristic
418C22×C3#87811yescharacteristic
419C22×C3#88511yescharacteristic
420C22×C3#88511yescharacteristic
421C22×C3#92411yescharacteristic
422C22×C3#93611yescharacteristic
423C22×C3#93711yescharacteristic
424C22×C3C3×#12011yescharacteristic
425C22×C3C3×C22⋊Q811yescharacteristic
426C22×C3C3×C22⋊Q811yescharacteristic
427C22×C3C3×C22⋊Q811yescharacteristic
428C22×C3C3×#12411yescharacteristic
429C22×C3C3×#12411yescharacteristic
430C22×C3C3×#12411yescharacteristic
431C3×C4—42no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—41no—
435C3×C4—41no—
436C3×C4—82no—
437C3×C4—81no—
438C3×C4—81no—
439C3×C4—82no—
440C3×C4—122no—
441C3×C4—122no—
442C3×C4—241no—
443C3×C4—241no—
444Dic3—42no—
445Dic3—42no—
446Dic3—81no—
447Dic3—81no—
448C32#203211yescharacteristic, complemented, Sylow
449C23—21no—
450C23—21no—
451C23—21no—
452C23—81no—
453C23—81no—
454C23C2×C3×Dic611yescharacteristic
455C23C3×#23511yescharacteristic
456C23C3×D3×D411yescharacteristic
457C23C3×D3×D411yescharacteristic
458C23C3×#23711yescharacteristic
459C23C3×#23711yescharacteristic
460C23C2×C3×#6711yescharacteristic
461Q8—242no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—41no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—22no—
470C2×C4—41no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—241no—
478C2×C4—241no—
479C2×C4—241no—
480C2×C4—241no—
481C2×C3—22no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—41no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3—82no—
504C2×C3—81no—
505C2×C3—81no—
506C2×C3#494711yescharacteristic
507C2×C3C3×#39311yescharacteristic
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22C3×#87811yescharacteristic
520C22C3×#87811yescharacteristic
521C22C3×#88511yescharacteristic
522C22C3×#88511yescharacteristic
523C22C3×#92411yescharacteristic
524C22C3×#93611yescharacteristic
525C22C3×#93711yescharacteristic
526C4—42no—
527C4—41no—
528C4—81no—
529C4—122no—
530C4—122no—
531C4—241no—
532C4—241no—
533C3—21no—
534C3#7002511yescharacteristic, direct product factor
535C3C3×#203211yescharacteristic, complemented
536C2—21no—
537C2—21no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—81no—
544C2C3×#494711yescharacteristic
subgroupG/H
centerC2×C3#4947
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC2×C32×#99C2
socleC2×C32#393
prime radicalC22×C32×D4C22
hypercenterC2×C3×#99D3
hypocenterC3C3×#2032
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C24×C3 ◁ C2×C3×#99

Complements

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

NH ≅ G/Ntype
1. C3×#5483C2semidirect
5. C3×#4527C2semidirect
6. C3×#4527C2semidirect
7. C3×#4526C2semidirect
9. #70025C3direct (N × H)
24. #5483C2×C3semidirect
35. #4527C2×C3semidirect
36. #4527C2×C3semidirect
37. #4526C2×C3semidirect
38. C24×C32Q8semidirect
48. C22×C32×C4Q8semidirect
140. C24×C3Dic6semidirect
141. C24×C3C3×Q8semidirect
174. C22×C3×C4Dic6semidirect
175. C22×C3×C4C3×Q8semidirect
347. C24C3×Dic6semidirect
362. C22×C4C3×Dic6semidirect
448. C32#2032semidirect
534. C3#70025direct (N × H)
535. C3C3×#2032semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
C2×C32×#992
C2×C3×#8342
C3×#45272
C3×#45262
C3×#20323
#700253