Finite Group Databasebeta

← C3×#78995 #11865201

Subgroups — C3×#78995 #11865201

Order 1152.

1485 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2C2×C3×#951C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C32×#421C211yesmaximal, characteristic, complemented
6C3×#5132C211yesmaximal, characteristic, complemented
7C3×#5005C211yesmaximal, characteristic, complemented
8C3×#4826C214yesmaximal, complemented
9C3×#4825C214yesmaximal, complemented
10C3×#3022—31nomaximal
11#78995C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C3×#1010—21no—
14C3×#1010C2212yes—
15C3×#1009—21no—
16C3×#1009C2212yes—
17C3×D3×#41—22no—
18C3×D3×#41—22no—
19C3×#1007—21no—
20C3×#1004—21no—
21C3×#1004—22no—
22C2×C3×#235—22no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C22×C3×Dic6C2211yescharacteristic, complemented
26C2×C32×M16C2211yescharacteristic, complemented
27C32×#117C2211yescharacteristic, complemented
28C3×#951—22no—
29C3×#951C2214yescomplemented
30C2×C3×#216—21no—
31C2×C3×#214—21no—
32C2×C3×#208C2211yescharacteristic, complemented
33C3×#909—22no—
34C3×#909C2214yescomplemented
35C2×C3×Dic12—21no—
36C2×C3×#204—21no—
37C3×#897—22no—
38C3×#886—22no—
39C3×#875C2212yescomplemented
40C3×#869C2212yescomplemented
41C32×#104C2214yescomplemented
42C3×#824C2212yescomplemented
43C3×#823C2212yescomplemented
44C3×#805C2214yescomplemented
45C3×#585—31no—
46#5964C2×C311yescharacteristic
47C2×C3×#137—31no—
48C2×C3×#137—31no—
49C3×#536—31no—
50C2×#951C2×C311yescharacteristic, complemented
51C2×#909C2×C311yescharacteristic, complemented
52#5526C2×C311yescharacteristic, complemented
53C3×#456—34no—
54C3×#455—34no—
55C3×#421—21no—
56C3×#421—31no—
57C3×#421D311yescharacteristic, complemented
58C3×#421C2×C311yescharacteristic, complemented
59C3×#413—31no—
60#5132C2×C311yescharacteristic, complemented
61#5005C2×C311yescharacteristic, complemented
62#4826C2×C314yescomplemented
63#4825C2×C314yescomplemented
64C32×#41—21no—
65C32×#41—21no—
66C32×#41D412yes—
67C32×#41C2312yes—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—24no—
74C2×C3×#67—21no—
75C2×C3×#67D412yes—
76C22×C3×Dic3—21no—
77C3×#239—22no—
78C3×#239—22no—
79C3×D3×Q8—22no—
80C3×D3×Q8—22no—
81C3×#237—24no—
82C3×#237—22no—
83C3×#237—22no—
84C3×#237—24no—
85C3×D3×D4—24no—
86C3×D3×D4—22no—
87C3×D3×D4—24no—
88C3×D3×D4—22no—
89C3×#235—24no—
90C3×#235—24no—
91C3×#235—21no—
92C3×#235—21no—
93C3×#235—21no—
94C3×#235—21no—
95C3×#235—21no—
96C3×#235—21no—
97C3×#235—22no—
98C3×#235—22no—
99C3×#235D412yes—
100C3×#235C2312yes—
101C2×C3×D12—22no—
102C2×C3×D12D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—24no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3D412yes—
107C2×C3×Dic6—22no—
108C2×C3×Dic6—21no—
109C2×C3×Dic6—21no—
110C2×C3×Dic6—21no—
111C2×C3×Dic6—21no—
112C2×C3×Dic6—21no—
113C2×C3×Dic6D411yescharacteristic
114C2×C3×Dic6C2312yes—
115C2×C3×Dic6C2311yescharacteristic
116C32×M16—21no—
117C32×M16C2312yes—
118C2×C32×C8—21no—
119C32×C4⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C42C2312yes—
122C3×#216—24no—
123C3×#214—24no—
124C3×(C2×D3)⋊C4—24no—
125C3×C4⋊Dic3—24no—
126C3×#208—21no—
127C3×#208C2312yes—
128C2×C3×C3⋊C8—21no—
129C3×Dic12—24no—
130C3×#204—24no—
131#3022—31noSylow
132C3×2−1+4—32no—
133C3×2−1+4—61no—
134C3×2−1+4—61no—
135C3×H(5,𝔽2)—32no—
136C3×H(5,𝔽2)—62no—
137C3×H(5,𝔽2)—61no—
138C3×H(5,𝔽2)—61no—
139C2×C3×#41—21no—
140C2×C3×#41—31no—
141C2×C3×#41—31no—
142C2×C3×#41—62no—
143C2×C3×#41—62no—
144C2×C3×#41—62no—
145C2×C3×#41C2×D311yescharacteristic
146C2×C3×#41C22×C311yescharacteristic
147C22×C3×Q8—31no—
148#1010—21no—
149#1010C22×C312yes—
150#1009—21no—
151#1009C22×C312yes—
152D3×#41—22no—
153D3×#41—22no—
154#1007—21no—
155#1004—21no—
156#1004—22no—
157C2×#235—22no—
158C2×#235C22×C311yescharacteristic
159C2×#235C22×C311yescharacteristic
160C22×Dic6C22×C311yescharacteristic, complemented
161C3×#137—34no—
162C3×#137—34no—
163C3×#137—62no—
164C3×#137—62no—
165C2×C3×Q16—61no—
166C2×C3×Q16—61no—
167C2×C3×SD16—61no—
168C2×C3×SD16—61no—
169C2×C3×M16—21no—
170C2×C3×M16—31no—
171C2×C3×M16C2×D311yescharacteristic, complemented
172C2×C3×M16C22×C311yescharacteristic, complemented
173C3×C4⋊Q8—32no—
174C3×#124—32no—
175C3×#123—62no—
176C3×C22⋊Q8—62no—
177C3×#117—21no—
178C3×#117C2×D311yescharacteristic, complemented
179C3×#117C22×C311yescharacteristic, complemented
180#951—22no—
181#951C22×C314yescomplemented
182C2×#216—21no—
183C2×#214—21no—
184C2×#208C22×C311yescharacteristic, complemented
185#909—22no—
186#909C22×C314yescomplemented
187C2×Dic12—21no—
188C2×#204—21no—
189#897—22no—
190#886—22no—
191#875C22×C312yescomplemented
192#869C22×C312yescomplemented
193C3×#104—24no—
194C3×#104—34no—
195C3×#104C2×D314yescomplemented
196C3×#104C22×C314yescomplemented
197C3×#101—32no—
198C3×#100—32no—
199#824C22×C312yescomplemented
200#823C22×C312yescomplemented
201#805C22×C314yescomplemented
202C23×C32—21no—
203C23×C32C2×D411yescharacteristic
204C22×C3×D3—24no—
205C22×C3×D3—21no—
206C22×C3×D3C2×D412yes—
207C32×Q8—21no—
208C32×Q8C2×D412yes—
209C32×D4—22no—
210C32×D4—22no—
211C32×D4—21no—
212C32×D4C2×D412yes—
213C2×C32×C4—21no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4—22no—
217C2×C32×C4C2×D411yescharacteristic
218C2×C32×C4C2×D411yescharacteristic
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2411yescharacteristic
223C3×#67—24no—
224C3×#67—24no—
225C3×#67—22no—
226C3×#67—22no—
227C3×#67—22no—
228C3×#67—22no—
229C2×C3×Dic3—24no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—41no—
233C2×C3×Dic3—41no—
234C2×C3×Dic3C2×D412yes—
235C3×D12—24no—
236C3×D12—21no—
237C3×D12—21no—
238C3×D12—21no—
239C3×D12C2×D412yes—
240C3×C4×D3—24no—
241C3×C4×D3—24no—
242C3×C4×D3—22no—
243C3×C4×D3—22no—
244C3×C4×D3—22no—
245C3×C4×D3—22no—
246C3×Dic6—24no—
247C3×Dic6—21no—
248C3×Dic6—21no—
249C3×Dic6—21no—
250C3×Dic6—22no—
251C3×Dic6—22no—
252C3×Dic6—41no—
253C3×Dic6—41no—
254C3×Dic6C2×D412yes—
255C32×C8—22no—
256C3×C3⋊C8—22no—
257#585—31no—
258C2×#137—31no—
259C2×#137—31no—
260#536—31no—
261#456—34no—
262#455—34no—
263#421—31no—
264#421C3×D311yescharacteristic, complemented
265#413—31no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—22no—
271C3×#41—22no—
272C3×#41—32no—
273C3×#41—32no—
274C3×#41—41no—
275C3×#41—41no—
276C3×#41—62no—
277C3×#41—62no—
278C3×#41—64no—
279C3×#41—64no—
280C3×#41—64no—
281C3×#41—64no—
282C3×#41—62no—
283C3×#41—62no—
284C3×#41—62no—
285C3×#41—62no—
286C3×#41—61no—
287C3×#41—61no—
288C3×#41—61no—
289C3×#41—61no—
290C3×#41—61no—
291C3×#41—61no—
292C3×#41D1212yes—
293C3×#41C3×D412yes—
294C3×#41C22×D312yes—
295C3×#41C23×C312yes—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—32no—
300C2×C3×Q8—62no—
301C2×C3×Q8—62no—
302C2×C3×Q8—62no—
303C2×C3×Q8—61no—
304C2×C3×Q8—61no—
305C2×C3×Q8—61no—
306C2×C3×Q8—61no—
307C2×C3×Q8—61no—
308C2×C3×Q8D1211yescharacteristic
309C2×C3×Q8C3×D411yescharacteristic
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—32no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—41no—
317C2×C3×D4—62no—
318C2×C3×D4—64no—
319C2×C3×D4—64no—
320C2×C3×D4—62no—
321C2×C3×D4—64no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4D1211yescharacteristic
325C2×C3×D4C3×D411yescharacteristic
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—32no—
330C22×C3×C4—41no—
331C22×C3×C4—64no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C23×C311yescharacteristic
336C2×#67—24no—
337C2×#67—21no—
338C2×#67C3×D412yes—
339C22×Dic3—21no—
340#239—22no—
341#239—22no—
342D3×Q8—22no—
343D3×Q8—22no—
344#237—24no—
345#237—22no—
346#237—22no—
347#237—24no—
348D3×D4—24no—
349D3×D4—22no—
350D3×D4—24no—
351D3×D4—22no—
352#235—24no—
353#235—24no—
354#235—21no—
355#235—21no—
356#235—21no—
357#235—21no—
358#235—21no—
359#235—21no—
360#235—22no—
361#235—22no—
362#235C3×D412yes—
363#235C23×C312yes—
364C2×D12—22no—
365C2×D12C3×D411yescharacteristic
366C2×D12C23×C311yescharacteristic
367C2×C4×D3—24no—
368C2×C4×D3—21no—
369C2×C4×D3C3×D412yes—
370C2×Dic6—22no—
371C2×Dic6—21no—
372C2×Dic6—21no—
373C2×Dic6—21no—
374C2×Dic6—21no—
375C2×Dic6—21no—
376C2×Dic6C3×D411yescharacteristic
377C2×Dic6C23×C312yes—
378C2×Dic6C23×C311yescharacteristic
379C3×Q16—64no—
380C3×Q16—64no—
381C3×SD16—64no—
382C3×SD16—64no—
383C3×M16—21no—
384C3×M16—21no—
385C3×M16—22no—
386C3×M16—32no—
387C3×M16—41no—
388C3×M16—61no—
389C3×M16C22×D312yes—
390C3×M16C23×C312yes—
391C2×C3×C8—21no—
392C2×C3×C8—21no—
393C2×C3×C8—41no—
394C2×C3×C8—61no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—41no—
398C3×C4⋊C4—64no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—64no—
403C3×C42—22no—
404C3×C42C22×D312yes—
405C3×C42C23×C312yes—
406#216—24no—
407#214—24no—
408(C2×D3)⋊C4—24no—
409C4⋊Dic3—24no—
410#208—21no—
411#208C23×C312yes—
412C2×C3⋊C8—21no—
413Dic12—24no—
414#204—24no—
415C22×C32—22no—
416C22×C32—41no—
417C22×C32—81no—
418C22×C32#12011yescharacteristic
419C22×C32#12011yescharacteristic
420C22×C32C22×D411yescharacteristic
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—42no—
424C2×C3×D3—81no—
425C2×C3×D3—84no—
426C32×C4—22no—
427C32×C4—42no—
428C32×C4#12011yescharacteristic
429C32×C4#12011yescharacteristic
430C32×C4C22×D411yescharacteristic
431C32×C4C22×D411yescharacteristic
432C3×Dic3—22no—
433C3×Dic3—22no—
434C3×Dic3—42no—
4352−1+4—32no—
4362−1+4—61no—
4372−1+4—61no—
438H(5,𝔽2)—32no—
439H(5,𝔽2)—62no—
440H(5,𝔽2)—61no—
441H(5,𝔽2)—61no—
442C2×#41—31no—
443C2×#41—31no—
444C2×#41—62no—
445C2×#41—62no—
446C2×#41—62no—
447C2×#41C2×C3×D311yescharacteristic
448C22×Q8—31no—
449#137—34no—
450#137—34no—
451#137—62no—
452#137—62no—
453C2×Q16—61no—
454C2×Q16—61no—
455C2×SD16—61no—
456C2×SD16—61no—
457C2×M16—31no—
458C2×M16C2×C3×D311yescharacteristic, complemented
459C4⋊Q8—32no—
460#124—32no—
461#123—62no—
462C22⋊Q8—62no—
463#117C2×C3×D311yescharacteristic, complemented
464#104—34no—
465#104C2×C3×D314yescomplemented
466#101—32no—
467#100—32no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—32no—
472C23×C3—41no—
473C23×C3—64no—
474C23×C3—61no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×C3×D411yescharacteristic
477C22×D3—24no—
478C22×D3—21no—
479C22×D3C2×C3×D412yes—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—22no—
483C3×Q8—32no—
484C3×Q8—41no—
485C3×Q8—64no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—62no—
490C3×Q8—62no—
491C3×Q8—121no—
492C3×Q8—121no—
493C3×Q8C2×D1212yes—
494C3×Q8C2×C3×D412yes—
495C3×D4—22no—
496C3×D4—22no—
497C3×D4—22no—
498C3×D4—22no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—22no—
502C3×D4—32no—
503C3×D4—41no—
504C3×D4—42no—
505C3×D4—42no—
506C3×D4—64no—
507C3×D4—64no—
508C3×D4—64no—
509C3×D4—62no—
510C3×D4—62no—
511C3×D4—62no—
512C3×D4—62no—
513C3×D4—61no—
514C3×D4—61no—
515C3×D4—61no—
516C3×D4C2×D1212yes—
517C3×D4C2×C3×D412yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—22no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—22no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—32no—
533C2×C3×C4—42no—
534C2×C3×C4—42no—
535C2×C3×C4—41no—
536C2×C3×C4—42no—
537C2×C3×C4—64no—
538C2×C3×C4—64no—
539C2×C3×C4—64no—
540C2×C3×C4—61no—
541C2×C3×C4—62no—
542C2×C3×C4—62no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—62no—
546C2×C3×C4—121no—
547C2×C3×C4—121no—
548C2×C3×C4C2×D1211yescharacteristic
549C2×C3×C4C2×D1211yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4C2×C3×D411yescharacteristic
554C2×C3×C4C2×C3×D411yescharacteristic
555C2×C3×C4C2×C3×D411yescharacteristic
556C2×C3×C4C2×C3×D411yescharacteristic
557C2×C3×C4C2×C3×D411yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C24×C311yescharacteristic
560#67—24no—
561#67—24no—
562#67—22no—
563#67—22no—
564#67—22no—
565#67—22no—
566C2×Dic3—24no—
567C2×Dic3—21no—
568C2×Dic3—22no—
569C2×Dic3—41no—
570C2×Dic3—41no—
571C2×Dic3C2×C3×D412yes—
572D12—24no—
573D12—21no—
574D12—21no—
575D12—21no—
576D12C2×C3×D412yes—
577C4×D3—24no—
578C4×D3—24no—
579C4×D3—22no—
580C4×D3—22no—
581C4×D3—22no—
582C4×D3—22no—
583Dic6—24no—
584Dic6—21no—
585Dic6—21no—
586Dic6—21no—
587Dic6—22no—
588Dic6—22no—
589Dic6—41no—
590Dic6—41no—
591Dic6C2×C3×D412yes—
592C3×C8—22no—
593C3×C8—22no—
594C3×C8—42no—
595C3×C8—62no—
596C3⋊C8—22no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—42no—
601C2×C32C2×#12011yescharacteristic
602C3×D3—42no—
603C3×D3—42no—
604#41—21no—
605#41—21no—
606#41—32no—
607#41—32no—
608#41—62no—
609#41—62no—
610#41—64no—
611#41—64no—
612#41—64no—
613#41—64no—
614#41—62no—
615#41—62no—
616#41—62no—
617#41—62no—
618#41—61no—
619#41—61no—
620#41—61no—
621#41—61no—
622#41—61no—
623#41—61no—
624#41C3×D1212yes—
625#41C22×C3×D312yes—
626C2×Q8—31no—
627C2×Q8—32no—
628C2×Q8—31no—
629C2×Q8—62no—
630C2×Q8—62no—
631C2×Q8—62no—
632C2×Q8—61no—
633C2×Q8—61no—
634C2×Q8—61no—
635C2×Q8—61no—
636C2×Q8—61no—
637C2×Q8C3×D1211yescharacteristic
638C2×D4—21no—
639C2×D4—32no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—62no—
643C2×D4—64no—
644C2×D4—64no—
645C2×D4—62no—
646C2×D4—64no—
647C2×D4—61no—
648C2×D4—62no—
649C2×D4C3×D1211yescharacteristic
650C22×C4—21no—
651C22×C4—32no—
652C22×C4—64no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4C22×C3×D311yescharacteristic
656Q16—64no—
657Q16—64no—
658SD16—64no—
659SD16—64no—
660M16—21no—
661M16—32no—
662M16—61no—
663M16C22×C3×D312yes—
664C2×C8—21no—
665C2×C8—61no—
666C4⋊C4—21no—
667C4⋊C4—64no—
668C22⋊C4—21no—
669C22⋊C4—64no—
670C42C22×C3×D312yes—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—42no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—82no—
685C22×C3—122no—
686C22×C3—241no—
687C22×C3—244no—
688C22×C3#88211yescharacteristic
689C22×C3#88211yescharacteristic
690C22×C3C3×#12011yescharacteristic
691C22×C3C3×#12011yescharacteristic
692C22×C3C2×D3×D411yescharacteristic
693C22×C3C22×C3×D411yescharacteristic
694C2×D3—22no—
695C2×D3—22no—
696C2×D3—42no—
697C2×D3—81no—
698C2×D3—84no—
699C3×C4—22no—
700C3×C4—22no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—21no—
705C3×C4—42no—
706C3×C4—42no—
707C3×C4—42no—
708C3×C4—62no—
709C3×C4—62no—
710C3×C4—82no—
711C3×C4—122no—
712C3×C4#88211yescharacteristic
713C3×C4#88211yescharacteristic
714C3×C4C3×#12011yescharacteristic
715C3×C4C3×#12011yescharacteristic
716C3×C4C22×D1211yescharacteristic
717C3×C4C2×D3×D411yescharacteristic
718C3×C4C22×C3×D411yescharacteristic
719C3×C4C22×C3×D411yescharacteristic
720Dic3—22no—
721Dic3—22no—
722Dic3—42no—
723C32#302211yescharacteristic, complemented, Sylow
724C23—21no—
725C23—32no—
726C23—64no—
727C23—61no—
728C23C3×D3×D411yescharacteristic
729Q8—21no—
730Q8—32no—
731Q8—64no—
732Q8—61no—
733Q8—61no—
734Q8—61no—
735Q8—62no—
736Q8—62no—
737Q8—121no—
738Q8—121no—
739Q8C2×C3×D1212yes—
740D4—22no—
741D4—22no—
742D4—21no—
743D4—32no—
744D4—64no—
745D4—64no—
746D4—64no—
747D4—62no—
748D4—62no—
749D4—62no—
750D4—62no—
751D4—61no—
752D4—61no—
753D4—61no—
754D4C2×C3×D1212yes—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—32no—
760C2×C4—64no—
761C2×C4—64no—
762C2×C4—64no—
763C2×C4—61no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—62no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4C2×C3×D1211yescharacteristic
772C2×C4C2×C3×D1211yescharacteristic
773C2×C4C3×D3×D411yescharacteristic
774C2×C4C3×D3×D411yescharacteristic
775C2×C4C3×D3×D411yescharacteristic
776C2×C4C23×C3×D311yescharacteristic
777C8—22no—
778C8—62no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—41no—
787C2×C3—41no—
788C2×C3—41no—
789C2×C3—42no—
790C2×C3—42no—
791C2×C3—82no—
792C2×C3—122no—
793C2×C3—122no—
794C2×C3C2×#88211yescharacteristic
795C2×C3C2×C3×#12011yescharacteristic
796D3—42no—
797D3—42no—
798C22—22no—
799C22—41no—
800C22—62no—
801C22—62no—
802C22—81no—
803C22—122no—
804C22—241no—
805C22—244no—
806C22C3×#88211yescharacteristic
807C22C3×#88211yescharacteristic
808C22C2×C3×D3×D411yescharacteristic
809C4—22no—
810C4—42no—
811C4—62no—
812C4—62no—
813C4—122no—
814C4C3×#88211yescharacteristic
815C4C3×#88211yescharacteristic
816C4C22×C3×D1211yescharacteristic
817C4C2×C3×D3×D411yescharacteristic
818C3—21no—
819C3#7899511yescharacteristic, direct product factor
820C3C3×#302211yescharacteristic, complemented
821C2—21no—
822C2—21no—
823C2—21no—
824C2—42no—
825C2—122no—
826C2—122no—
827C2C2×C3×#88211yescharacteristic
subgroupG/H
centerC2×C3C2×#882
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#421C2
socleC2×C32C2×#120
prime radicalC3×#5964C2
hypercenterC3×#421D3
hypocenterC3C3×#3022
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#421

Complements

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

NH ≅ G/Ntype
2. C2×C3×#951C2semidirect
3. C2×C3×#909C2semidirect
4. C3×#5526C2semidirect
5. C32×#421C2semidirect
6. C3×#5132C2semidirect
7. C3×#5005C2semidirect
8. C3×#4826C2semidirect
9. C3×#4825C2semidirect
11. #78995C3direct (N × H)
25. C22×C3×Dic6C22semidirect
26. C2×C32×M16C22semidirect
27. C32×#117C22semidirect
29. C3×#951C22semidirect
32. C2×C3×#208C22semidirect
34. C3×#909C22semidirect
39. C3×#875C22semidirect
40. C3×#869C22semidirect
41. C32×#104C22semidirect
42. C3×#824C22semidirect
43. C3×#823C22semidirect
44. C3×#805C22semidirect
50. C2×#951C2×C3semidirect
51. C2×#909C2×C3semidirect
52. #5526C2×C3semidirect
57. C3×#421D3semidirect
58. C3×#421C2×C3semidirect
60. #5132C2×C3semidirect
61. #5005C2×C3semidirect
62. #4826C2×C3semidirect
63. #4825C2×C3semidirect
160. C22×Dic6C22×C3semidirect
171. C2×C3×M16C2×D3semidirect
172. C2×C3×M16C22×C3semidirect
178. C3×#117C2×D3semidirect
179. C3×#117C22×C3semidirect
181. #951C22×C3semidirect
184. C2×#208C22×C3semidirect
186. #909C22×C3semidirect
191. #875C22×C3semidirect
192. #869C22×C3semidirect
195. C3×#104C2×D3semidirect
196. C3×#104C22×C3semidirect
199. #824C22×C3semidirect
200. #823C22×C3semidirect
201. #805C22×C3semidirect
264. #421C3×D3semidirect
458. C2×M16C2×C3×D3semidirect
463. #117C2×C3×D3semidirect
465. #104C2×C3×D3semidirect
723. C32#3022semidirect
819. C3#78995direct (N × H)
820. C3C3×#3022semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C2×C3×#9512
C2×C3×#9092
C3×#55262
C32×#4212
C3×#51322
C3×#50052
C3×#48262
C3×#48252
C3×#30223
#789953