Finite Group Databasebeta

← C3×#79261 #11868090

Subgroups — C3×#79261 #11868090

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5748C211yesmaximal, characteristic, complemented
2C2×C3×#908C211yesmaximal, characteristic, complemented
3C2×C3×#908C211yesmaximal, characteristic, complemented
4C3×#5745C211yesmaximal, characteristic, complemented
5C32×#430C211yesmaximal, characteristic, complemented
6C3×#5132C211yesmaximal, characteristic, complemented
7C2×C3×#823C211yesmaximal, characteristic, complemented
8C3×#4898C214yesmaximal, complemented
9C3×#4897C214yesmaximal, complemented
10C3×#3068—31nomaximal
11#79261C311yesmaximal, characteristic, direct product factor
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#909—21no—
20C3×#909C2212yescomplemented
21C3×#908—22no—
22C3×#908—21no—
23C3×#908—22no—
24C3×#908—22no—
25C3×#908C2214yes—
26C3×#908C2212yescomplemented
27C3×#907—22no—
28C3×D3×M16—22no—
29C3×#904—22no—
30C2×C3×D24—21no—
31C2×C3×D24C2212yescomplemented
32C2×C3×#204—21no—
33C2×C3×#204C2212yescomplemented
34C3×#901C2214yescomplemented
35C32×#108C2214yescomplemented
36C3×#824C2212yescomplemented
37C3×#823C2214yescomplemented
38C3×#823C2212yescomplemented
39C3×#575—31no—
40C2×C3×AGL(1,ℤ/8)—31no—
41C2×C3×AGL(1,ℤ/8)—31no—
42C3×#568—31no—
43#5748C2×C311yescharacteristic, complemented
44C2×#908C2×C311yescharacteristic, complemented
45C2×#908C2×C311yescharacteristic, complemented
46#5745C2×C311yescharacteristic, complemented
47C3×#472—34no—
48C3×#471—34no—
49C3×#430—21no—
50C3×#430D311yescharacteristic, complemented
51C3×#430C2×C311yescharacteristic, complemented
52C3×#413—31no—
53C2×C3×#100—31no—
54#5132C2×C311yescharacteristic, complemented
55C2×#823C2×C311yescharacteristic, complemented
56#4898C2×C314yescomplemented
57#4897C2×C314yescomplemented
58C23×C3×D3—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235—21no—
68C3×#235D412yes—
69C3×#235C2312yes—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12D411yescharacteristic
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C32×M16—21no—
83C32×M16—21no—
84C32×M16D412yes—
85C32×M16D412yes—
86C32×M16C2312yes—
87C32×M16C2312yes—
88C2×C32×C8—21no—
89C2×C32×C8—21no—
90C2×C32×C8C2312yes—
91C3×#208—21no—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C3×Dic12—22no—
95C3×D24—24no—
96C3×D24—22no—
97C3×D24—24no—
98C3×#204—22no—
99C3×#204—24no—
100C3×#204—22no—
101C3×#204—24no—
102C3×ΓL(1,𝔽25)—24no—
103C3×D3×C8—24no—
104#3068—31noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×D4—31no—
108C2×#235C22×C311yescharacteristic
109C2×#235C22×C311yescharacteristic
110C22×D12C22×C311yescharacteristic
111C3×#137—32no—
112C3×#137—61no—
113C3×AGL(1,ℤ/8)—34no—
114C3×AGL(1,ℤ/8)—32no—
115C3×AGL(1,ℤ/8)—61no—
116C3×AGL(1,ℤ/8)—62no—
117C3×AGL(1,ℤ/8)—62no—
118C3×AGL(1,ℤ/8)—62no—
119C3×#135—62no—
120C2×C3×SD16—32no—
121C2×C3×SD16—61no—
122C2×C3×D8—32no—
123C2×C3×D8—61no—
124C3×#131—34no—
125C3×#131—62no—
126C2×C3×M16—21no—
127C2×C3×M16—21no—
128C2×C3×M16—21no—
129C2×C3×M16—31no—
130C2×C3×M16—62no—
131C2×C3×M16C2×D311yescharacteristic
132C2×C3×M16C2×D311yescharacteristic
133C2×C3×M16C2×D311yescharacteristic
134C2×C3×M16C22×C311yescharacteristic
135C2×C3×M16C22×C311yescharacteristic
136C2×C3×M16C22×C311yescharacteristic
137C2×#208C22×C311yescharacteristic
138#909—21no—
139#909C22×C312yescomplemented
140#908—22no—
141#908—21no—
142#908—22no—
143#908—22no—
144#908C22×C314yes—
145#908C22×C312yescomplemented
146#907—22no—
147D3×M16—22no—
148#904—22no—
149C2×D24—21no—
150C2×D24C22×C312yescomplemented
151C2×#204—21no—
152C2×#204C22×C312yescomplemented
153#901C22×C314yescomplemented
154C3×#108—24no—
155C3×#108C2×D314yescomplemented
156C3×#108C22×C314yescomplemented
157C3×#101—32no—
158C3×#100—34no—
159C3×#100—32no—
160#824C22×C312yescomplemented
161#823C22×C314yescomplemented
162#823C22×C312yescomplemented
163C23×C32#4111yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C22×C3×D3—21no—
167C22×C3×D3—41no—
168C22×C3×D3—41no—
169C22×C3×D3—82no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4#4111yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C3×#67—22no—
177C3×#67—22no—
178C3×#67—41no—
179C3×#67—41no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12—22no—
184C3×D12—22no—
185C3×D12—21no—
186C3×D12—21no—
187C3×D12—41no—
188C3×D12—41no—
189C3×D12C2×D412yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×C4×D3—41no—
193C3×C4×D3—41no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196C3×Dic6—21no—
197C3×Dic6C2×D412yes—
198C32×C8—22no—
199C32×C8—22no—
200C32×C8C2×D414yes—
201C3×C3⋊C8—22no—
202#575—31no—
203C2×AGL(1,ℤ/8)—31no—
204C2×AGL(1,ℤ/8)—31no—
205#568—31no—
206#472—34no—
207#471—34no—
208#430C3×D311yescharacteristic, complemented
209#413—31no—
210C2×#100—31no—
211C24×C3—61no—
212C23×D3—21no—
213C3×#41—32no—
214C3×#41—32no—
215C3×#41—61no—
216C3×#41—61no—
217C3×#41—61no—
218C3×#41—61no—
219C3×#41—61no—
220C3×#41—61no—
221C2×C3×Q8—31no—
222C2×C3×Q8—31no—
223C2×C3×D4—31no—
224C2×C3×D4—31no—
225C2×C3×D4—32no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C22×C3×C4—21no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C23×C311yescharacteristic
238C2×#67—21no—
239C2×#67—21no—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—21no—
244#235—21no—
245#235—21no—
246#235C3×D412yes—
247#235C23×C312yes—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12C3×D411yescharacteristic
254C2×D12C23×C312yes—
255C2×D12C23×C311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×Dic6C3×D411yescharacteristic
259C2×Dic6C23×C311yescharacteristic
260C3×Q16—62no—
261C3×SD16—62no—
262C3×SD16—64no—
263C3×SD16—62no—
264C3×SD16—64no—
265C3×D8—64no—
266C3×D8—62no—
267C3×D8—64no—
268C3×M16—21no—
269C3×M16—21no—
270C3×M16—21no—
271C3×M16—21no—
272C3×M16—22no—
273C3×M16—22no—
274C3×M16—22no—
275C3×M16—22no—
276C3×M16—32no—
277C3×M16—41no—
278C3×M16—41no—
279C3×M16—61no—
280C3×M16—64no—
281C3×M16D1212yes—
282C3×M16D1212yes—
283C3×M16C3×D412yes—
284C3×M16C3×D412yes—
285C3×M16C22×D312yes—
286C3×M16C22×D312yes—
287C3×M16C23×C312yes—
288C3×M16C23×C312yes—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—22no—
294C2×C3×C8—41no—
295C2×C3×C8—41no—
296C2×C3×C8—61no—
297C2×C3×C8—64no—
298C2×C3×C8C22×D312yes—
299C2×C3×C8C23×C312yes—
300#208—21no—
301#208C23×C312yes—
302C2×C3⋊C8—21no—
303Dic12—22no—
304D24—24no—
305D24—22no—
306D24—24no—
307#204—22no—
308#204—24no—
309#204—22no—
310#204—24no—
311ΓL(1,𝔽25)—24no—
312D3×C8—24no—
313C22×C32—41no—
314C22×C32#12111yescharacteristic
315C22×C32#12111yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C2×C3×D3—22no—
318C2×C3×D3—41no—
319C2×C3×D3—42no—
320C2×C3×D3—81no—
321C2×C3×D3—82no—
322C2×C3×D3—82no—
323C2×C3×D3—81no—
324C2×C3×D3—82no—
325C32×C4#12111yescharacteristic
326C32×C4#12111yescharacteristic
327C32×C4C22×D411yescharacteristic
328C32×C4C22×D411yescharacteristic
329C3×Dic3—22no—
330C3×Dic3—41no—
331C2×#41—31no—
332C2×#41—31no—
333C22×D4—31no—
334#137—32no—
335#137—61no—
336AGL(1,ℤ/8)—34no—
337AGL(1,ℤ/8)—32no—
338AGL(1,ℤ/8)—61no—
339AGL(1,ℤ/8)—62no—
340AGL(1,ℤ/8)—62no—
341AGL(1,ℤ/8)—62no—
342#135—62no—
343C2×SD16—32no—
344C2×SD16—61no—
345C2×D8—32no—
346C2×D8—61no—
347#131—34no—
348#131—62no—
349C2×M16—31no—
350C2×M16—62no—
351C2×M16C2×C3×D311yescharacteristic
352C2×M16C2×C3×D311yescharacteristic
353C2×M16C2×C3×D311yescharacteristic
354#108C2×C3×D314yescomplemented
355#101—32no—
356#100—34no—
357#100—32no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3—62no—
362C23×C3—121no—
363C23×C3—121no—
364C23×C3—242no—
365C23×C3#23911yescharacteristic
366C23×C3C3×#4111yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—82no—
373C3×Q8—32no—
374C3×Q8—61no—
375C3×Q8—61no—
376C3×Q8—61no—
377C3×D4—32no—
378C3×D4—62no—
379C3×D4—62no—
380C3×D4—61no—
381C3×D4—61no—
382C3×D4—62no—
383C3×D4—62no—
384C3×D4—61no—
385C3×D4—121no—
386C3×D4—121no—
387C3×D4—121no—
388C3×D4—121no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4C2×D1211yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4#23911yescharacteristic
406C2×C3×C4C2×C3×D411yescharacteristic
407C2×C3×C4C2×C3×D411yescharacteristic
408C2×C3×C4C2×C3×D411yescharacteristic
409C2×C3×C4C2×C3×D411yescharacteristic
410C2×C3×C4C3×#4111yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C24×C311yescharacteristic
413#67—22no—
414#67—22no—
415#67—41no—
416#67—41no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419D12—21no—
420D12—22no—
421D12—22no—
422D12—21no—
423D12—21no—
424D12—41no—
425D12—41no—
426D12C2×C3×D412yes—
427C4×D3—22no—
428C4×D3—22no—
429C4×D3—41no—
430C4×D3—41no—
431Dic6—21no—
432Dic6—21no—
433Dic6—21no—
434Dic6C2×C3×D412yes—
435C3×C8—22no—
436C3×C8—22no—
437C3×C8—22no—
438C3×C8—22no—
439C3×C8—24no—
440C3×C8—42no—
441C3×C8—42no—
442C3×C8—62no—
443C3×C8C2×D1214yes—
444C3×C8C2×C3×D414yes—
445C3⋊C8—22no—
446C2×C32—21no—
447C2×C32—21no—
448C2×C32—21no—
449C2×C32C2×#12111yescharacteristic
450C3×D3—42no—
451C3×D3—81no—
452C3×D3—82no—
453C24—61no—
454#41—32no—
455#41—32no—
456#41—61no—
457#41—61no—
458#41—61no—
459#41—61no—
460#41—61no—
461#41—61no—
462C2×Q8—31no—
463C2×Q8—31no—
464C2×D4—31no—
465C2×D4—32no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—61no—
473C2×D4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4C22×C3×D311yescharacteristic
477Q16—62no—
478SD16—62no—
479SD16—64no—
480SD16—62no—
481SD16—64no—
482D8—64no—
483D8—62no—
484D8—64no—
485M16—21no—
486M16—21no—
487M16—32no—
488M16—61no—
489M16—64no—
490M16C3×D1212yes—
491M16C3×D1212yes—
492M16C22×C3×D312yes—
493M16C22×C3×D312yes—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—61no—
497C2×C8—64no—
498C2×C8C22×C3×D312yes—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—62no—
505C22×C3—81no—
506C22×C3—121no—
507C22×C3—122no—
508C22×C3—241no—
509C22×C3—242no—
510C22×C3—241no—
511C22×C3—242no—
512C22×C3—242no—
513C22×C3#89511yescharacteristic
514C22×C3#89511yescharacteristic
515C22×C3C3×#12111yescharacteristic
516C22×C3C3×#12111yescharacteristic
517C22×C3C2×#23911yescharacteristic
518C22×C3C2×C3×#4111yescharacteristic
519C2×D3—22no—
520C2×D3—41no—
521C2×D3—42no—
522C2×D3—81no—
523C2×D3—82no—
524C2×D3—82no—
525C2×D3—82no—
526C2×D3—81no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—62no—
532C3×C4—121no—
533C3×C4#89511yescharacteristic
534C3×C4#89511yescharacteristic
535C3×C4C3×#12111yescharacteristic
536C3×C4C3×#12111yescharacteristic
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×C3×D411yescharacteristic
540C3×C4C22×C3×D411yescharacteristic
541Dic3—22no—
542Dic3—41no—
543C32#306811yescharacteristic, complemented, Sylow
544C23—61no—
545C23—61no—
546C23—62no—
547C23—121no—
548C23—121no—
549C23—242no—
550C23C3×#23911yescharacteristic
551Q8—32no—
552Q8—61no—
553Q8—61no—
554Q8—61no—
555D4—32no—
556D4—62no—
557D4—62no—
558D4—61no—
559D4—61no—
560D4—62no—
561D4—62no—
562D4—61no—
563D4—121no—
564D4—121no—
565D4—121no—
566D4—121no—
567C2×C4—61no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—61no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4C2×C3×D1211yescharacteristic
574C2×C4C2×C3×D1211yescharacteristic
575C2×C4C3×D3×D411yescharacteristic
576C2×C4C3×D3×D411yescharacteristic
577C2×C4C3×#23911yescharacteristic
578C2×C4C23×C3×D311yescharacteristic
579C8—22no—
580C8—22no—
581C8—62no—
582C8C2×C3×D1214yes—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—41no—
591C2×C3—41no—
592C2×C3—41no—
593C2×C3—122no—
594C2×C3—242no—
595C2×C3—241no—
596C2×C3C2×#89511yescharacteristic
597C2×C3C2×C3×#12111yescharacteristic
598D3—42no—
599D3—82no—
600D3—81no—
601C22—41no—
602C22—62no—
603C22—121no—
604C22—122no—
605C22—241no—
606C22—242no—
607C22—241no—
608C22—242no—
609C22—242no—
610C22C3×#89511yescharacteristic
611C22C3×#89511yescharacteristic
612C22C2×C3×#23911yescharacteristic
613C4—62no—
614C4—121no—
615C4C3×#89511yescharacteristic
616C4C3×#89511yescharacteristic
617C4C22×C3×D1211yescharacteristic
618C4C2×C3×D3×D411yescharacteristic
619C3—21no—
620C3#7926111yescharacteristic, direct product factor
621C3C3×#306811yescharacteristic, complemented
622C2—21no—
623C2—21no—
624C2—21no—
625C2—122no—
626C2—242no—
627C2—241no—
628C2C2×C3×#89511yescharacteristic
subgroupG/H
centerC2×C3C2×#895
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#430C2
socleC2×C32C2×#121
hypercenterC3×#430D3
hypocenterC3C3×#3068
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#430

Complements

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

NH ≅ G/Ntype
1. C3×#5748C2semidirect
2. C2×C3×#908C2semidirect
3. C2×C3×#908C2semidirect
4. C3×#5745C2semidirect
5. C32×#430C2semidirect
6. C3×#5132C2semidirect
7. C2×C3×#823C2semidirect
8. C3×#4898C2semidirect
9. C3×#4897C2semidirect
11. #79261C3direct (N × H)
20. C3×#909C22semidirect
26. C3×#908C22semidirect
31. C2×C3×D24C22semidirect
33. C2×C3×#204C22semidirect
34. C3×#901C22semidirect
35. C32×#108C22semidirect
36. C3×#824C22semidirect
37. C3×#823C22semidirect
38. C3×#823C22semidirect
43. #5748C2×C3semidirect
44. C2×#908C2×C3semidirect
45. C2×#908C2×C3semidirect
46. #5745C2×C3semidirect
50. C3×#430D3semidirect
51. C3×#430C2×C3semidirect
54. #5132C2×C3semidirect
55. C2×#823C2×C3semidirect
56. #4898C2×C3semidirect
57. #4897C2×C3semidirect
139. #909C22×C3semidirect
145. #908C22×C3semidirect
150. C2×D24C22×C3semidirect
152. C2×#204C22×C3semidirect
153. #901C22×C3semidirect
155. C3×#108C2×D3semidirect
156. C3×#108C22×C3semidirect
160. #824C22×C3semidirect
161. #823C22×C3semidirect
162. #823C22×C3semidirect
208. #430C3×D3semidirect
354. #108C2×C3×D3semidirect
543. C32#3068semidirect
620. C3#79261direct (N × H)
621. C3C3×#3068semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
C2×C3×#9082
C3×#57452
C32×#4302
C3×#51322
C2×C3×#8232
C3×#48982
C3×#48972
C3×#30683
#792613