Finite Group Databasebeta

← C3×#83993 #11865189

Subgroups — C3×#83993 #11865189

Order 1152.

1537 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2C2×C32×#137C211yesmaximal, characteristic, complemented
3C3×#5816C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C3×#5236C211yesmaximal, characteristic, complemented
6C3×#5205C214yesmaximal, complemented
7C3×#5202C214yesmaximal, complemented
8C3×#5139C211yesmaximal, characteristic, complemented
9C3×#5132C211yesmaximal, characteristic, complemented
10C3×#3022—31nomaximal
11#83993C311yesmaximal, characteristic, direct product factor
12C2×C32×#41C2211yescharacteristic
13C22×C32×Q8C2211yescharacteristic, complemented
14C3×#1010—21no—
15C3×#1010C2212yes—
16C3×#1009—21no—
17C3×#1009C2212yes—
18C3×D3×#41—22no—
19C3×D3×#41—22no—
20C3×#1007—21no—
21C3×#1004—21no—
22C3×#1004—22no—
23C2×C3×#235—22no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26C32×#137—22no—
27C32×#137C2214yescomplemented
28C2×C32×Q16—21no—
29C2×C32×SD16—21no—
30C2×C32×M16C2211yescharacteristic, complemented
31C3×#947C2212yescomplemented
32C3×#946—22no—
33C3×#944C2212yescomplemented
34C2×C3×#216—21no—
35C3×#942—22no—
36C3×#942C2214yescomplemented
37C2×C3×#215—21no—
38C3×#929—22no—
39C3×#926C2211yescharacteristic, complemented
40C2×C3×#208C2211yescharacteristic, complemented
41C3×#837C2214yescomplemented
42C3×#825C2214yescomplemented
43C3×#824C2212yescomplemented
44C3×#823C2212yescomplemented
45C3×#585—31no—
46#5964C2×C311yescharacteristic
47C2×C3×#137—21no—
48C2×C3×#137—31no—
49C2×C3×#137D311yescharacteristic, complemented
50C2×C3×#137C2×C311yescharacteristic, complemented
51C3×#536—31no—
52#5816C2×C311yescharacteristic, complemented
53C2×#942C2×C311yescharacteristic, complemented
54C3×#456—34no—
55C3×#455—34no—
56C3×#421—31no—
57C3×#421—31no—
58C3×#413—31no—
59#5236C2×C311yescharacteristic, complemented
60#5205C2×C314yescomplemented
61#5202C2×C314yescomplemented
62#5139C2×C311yescharacteristic, complemented
63#5132C2×C311yescharacteristic, complemented
64C32×#41—21no—
65C32×#41—21no—
66C32×#41D412yes—
67C32×#41C2312yes—
68C2×C32×Q8—21no—
69C2×C32×Q8—21no—
70C2×C32×Q8—21no—
71C2×C32×Q8—21no—
72C2×C32×Q8—21no—
73C2×C32×Q8D411yescharacteristic
74C2×C32×Q8C2312yes—
75C2×C32×D4—21no—
76C2×C32×D4D411yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4C2311yescharacteristic
80C2×C3×#67—24no—
81C2×C3×#67—21no—
82C2×C3×#67D412yes—
83C3×#239—22no—
84C3×#239—22no—
85C3×D3×Q8—22no—
86C3×D3×Q8—22no—
87C3×#237—24no—
88C3×#237—22no—
89C3×#237—22no—
90C3×#237—24no—
91C3×D3×D4—24no—
92C3×D3×D4—22no—
93C3×D3×D4—24no—
94C3×D3×D4—22no—
95C3×#235—24no—
96C3×#235—24no—
97C3×#235—21no—
98C3×#235—21no—
99C3×#235—21no—
100C3×#235—21no—
101C3×#235—21no—
102C3×#235—21no—
103C3×#235—22no—
104C3×#235—22no—
105C3×#235D412yes—
106C3×#235C2312yes—
107C2×C3×D12—22no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—24no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3D412yes—
113C2×C3×Dic6—22no—
114C2×C3×Dic6D411yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C32×Q16—24no—
117C32×SD16—24no—
118C32×M16—21no—
119C32×M16C2312yes—
120C2×C32×C8—21no—
121C3×#217—21no—
122C3×#216—24no—
123C3×#215—24no—
124C3×(C2×D3)⋊C4—24no—
125C3×C4⋊Dic3—21no—
126C3×Dic3⋊C4—24no—
127C3×C4×Dic3C2312yes—
128C3×#208—21no—
129C3×#208C2312yes—
130C2×C3×C3⋊C8—21no—
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—21no—
148C22×C3×Q8C2×D311yescharacteristic, complemented
149C22×C3×Q8C22×C311yescharacteristic, complemented
150#1010—21no—
151#1010C22×C312yes—
152#1009—21no—
153#1009C22×C312yes—
154D3×#41—22no—
155D3×#41—22no—
156#1007—21no—
157#1004—21no—
158#1004—22no—
159C2×#235—22no—
160C2×#235C22×C311yescharacteristic
161C2×#235C22×C311yescharacteristic
162C3×#137—24no—
163C3×#137—22no—
164C3×#137—22no—
165C3×#137—24no—
166C3×#137—34no—
167C3×#137—62no—
168C3×#137C2×D314yescomplemented
169C3×#137C22×C314yescomplemented
170C2×C3×Q16—22no—
171C2×C3×Q16—21no—
172C2×C3×Q16—21no—
173C2×C3×Q16—61no—
174C2×C3×SD16—22no—
175C2×C3×SD16—21no—
176C2×C3×SD16—21no—
177C2×C3×SD16—61no—
178C2×C3×M16—21no—
179C2×C3×M16—31no—
180C2×C3×M16C2×D311yescharacteristic, complemented
181C2×C3×M16C22×C311yescharacteristic, complemented
182C3×C4⋊Q8—32no—
183C3×#124—32no—
184C3×#123—62no—
185C3×C22⋊Q8—62no—
186C3×#117—31no—
187#947C22×C312yescomplemented
188#946—22no—
189#944C22×C312yescomplemented
190C2×#216—21no—
191#942—22no—
192#942C22×C314yescomplemented
193C2×#215—21no—
194#929—22no—
195#926C22×C311yescharacteristic, complemented
196C2×#208C22×C311yescharacteristic, complemented
197C3×#104—34no—
198C3×#104—34no—
199C3×#101—32no—
200C3×#100—32no—
201#837C22×C314yescomplemented
202#825C22×C314yescomplemented
203#824C22×C312yescomplemented
204#823C22×C312yescomplemented
205C23×C32—21no—
206C23×C32C2×D411yescharacteristic
207C22×C3×D3—24no—
208C22×C3×D3—21no—
209C22×C3×D3C2×D412yes—
210C32×Q8—22no—
211C32×Q8—21no—
212C32×Q8—22no—
213C32×Q8—41no—
214C32×Q8—41no—
215C32×Q8C2×D412yes—
216C32×D4—22no—
217C32×D4—22no—
218C32×D4—21no—
219C32×D4C2×D412yes—
220C2×C32×C4—21no—
221C2×C32×C4—22no—
222C2×C32×C4—22no—
223C2×C32×C4—22no—
224C2×C32×C4—41no—
225C2×C32×C4—41no—
226C2×C32×C4C2×D411yescharacteristic
227C2×C32×C4C2×D411yescharacteristic
228C2×C32×C4C2×D411yescharacteristic
229C2×C32×C4C2×D411yescharacteristic
230C2×C32×C4C2×D411yescharacteristic
231C2×C32×C4C2411yescharacteristic
232C3×#67—24no—
233C3×#67—24no—
234C3×#67—22no—
235C3×#67—22no—
236C3×#67—22no—
237C3×#67—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3C2×D412yes—
242C3×D12—24no—
243C3×D12—21no—
244C3×D12—21no—
245C3×D12—21no—
246C3×D12C2×D412yes—
247C3×C4×D3—24no—
248C3×C4×D3—24no—
249C3×C4×D3—22no—
250C3×C4×D3—22no—
251C3×C4×D3—22no—
252C3×C4×D3—22no—
253C3×Dic6—24no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6C2×D412yes—
258C32×C8—22no—
259C3×C3⋊C8—22no—
260#585—31no—
261C2×#137—31no—
262C2×#137C3×D311yescharacteristic, complemented
263#536—31no—
264#456—34no—
265#455—34no—
266#421—31no—
267#421—31no—
268#413—31no—
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—22no—
274C3×#41—22no—
275C3×#41—32no—
276C3×#41—32no—
277C3×#41—41no—
278C3×#41—41no—
279C3×#41—62no—
280C3×#41—62no—
281C3×#41—64no—
282C3×#41—64no—
283C3×#41—64no—
284C3×#41—64no—
285C3×#41—62no—
286C3×#41—62no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—61no—
290C3×#41—61no—
291C3×#41—61no—
292C3×#41—61no—
293C3×#41—61no—
294C3×#41—61no—
295C3×#41#6712yes—
296C3×#41C3×D412yes—
297C3×#41C22×D312yes—
298C3×#41C23×C312yes—
299C2×C3×Q8—21no—
300C2×C3×Q8—21no—
301C2×C3×Q8—22no—
302C2×C3×Q8—22no—
303C2×C3×Q8—21no—
304C2×C3×Q8—21no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—21no—
312C2×C3×Q8—22no—
313C2×C3×Q8—31no—
314C2×C3×Q8—31no—
315C2×C3×Q8—41no—
316C2×C3×Q8—41no—
317C2×C3×Q8—41no—
318C2×C3×Q8—62no—
319C2×C3×Q8—62no—
320C2×C3×Q8—62no—
321C2×C3×Q8#6711yescharacteristic
322C2×C3×Q8C3×D411yescharacteristic
323C2×C3×Q8C22×D312yes—
324C2×C3×Q8C23×C312yes—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—32no—
329C2×C3×D4—31no—
330C2×C3×D4—31no—
331C2×C3×D4—41no—
332C2×C3×D4—62no—
333C2×C3×D4—64no—
334C2×C3×D4—64no—
335C2×C3×D4—62no—
336C2×C3×D4—64no—
337C2×C3×D4—61no—
338C2×C3×D4—62no—
339C2×C3×D4#6711yescharacteristic
340C2×C3×D4C3×D411yescharacteristic
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—32no—
347C22×C3×C4—41no—
348C22×C3×C4—41no—
349C22×C3×C4—64no—
350C22×C3×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C23×C311yescharacteristic
353C2×#67—24no—
354C2×#67—21no—
355C2×#67C3×D412yes—
356#239—22no—
357#239—22no—
358D3×Q8—22no—
359D3×Q8—22no—
360#237—24no—
361#237—22no—
362#237—22no—
363#237—24no—
364D3×D4—24no—
365D3×D4—22no—
366D3×D4—24no—
367D3×D4—22no—
368#235—24no—
369#235—24no—
370#235—21no—
371#235—21no—
372#235—21no—
373#235—21no—
374#235—21no—
375#235—21no—
376#235—22no—
377#235—22no—
378#235C3×D412yes—
379#235C23×C312yes—
380C2×D12—22no—
381C2×D12C3×D411yescharacteristic
382C2×D12C23×C311yescharacteristic
383C2×C4×D3—24no—
384C2×C4×D3—21no—
385C2×C4×D3C3×D412yes—
386C2×Dic6—22no—
387C2×Dic6C3×D411yescharacteristic
388C2×Dic6C23×C311yescharacteristic
389C3×Q16—28no—
390C3×Q16—24no—
391C3×Q16—24no—
392C3×Q16—64no—
393C3×SD16—28no—
394C3×SD16—24no—
395C3×SD16—24no—
396C3×SD16—64no—
397C3×M16—22no—
398C3×M16—21no—
399C3×M16—21no—
400C3×M16—22no—
401C3×M16—32no—
402C3×M16—61no—
403C3×M16C22×D312yes—
404C3×M16C23×C312yes—
405C2×C3×C8—22no—
406C2×C3×C8—21no—
407C2×C3×C8—21no—
408C2×C3×C8—61no—
409C3×C4⋊C4—64no—
410C3×C4⋊C4—61no—
411C3×C22⋊C4—64no—
412C3×C22⋊C4—61no—
413C3×C42—32no—
414#217—21no—
415#216—24no—
416#215—24no—
417(C2×D3)⋊C4—24no—
418C4⋊Dic3—21no—
419Dic3⋊C4—24no—
420C4×Dic3C23×C312yes—
421#208—21no—
422#208C23×C312yes—
423C2×C3⋊C8—21no—
424C22×C32—22no—
425C22×C32—41no—
426C22×C32—81no—
427C22×C32#12011yescharacteristic
428C22×C32#12011yescharacteristic
429C22×C32C22×D411yescharacteristic
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—42no—
433C2×C3×D3—81no—
434C2×C3×D3—84no—
435C32×C4—22no—
436C32×C4—42no—
437C32×C4#12011yescharacteristic
438C32×C4#12011yescharacteristic
439C32×C4C22×D411yescharacteristic
440C32×C4C22×D411yescharacteristic
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—42no—
4442−1+4—32no—
4452−1+4—61no—
4462−1+4—61no—
447H(5,𝔽2)—32no—
448H(5,𝔽2)—62no—
449H(5,𝔽2)—61no—
450H(5,𝔽2)—61no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—62no—
454C2×#41—62no—
455C2×#41—62no—
456C2×#41C2×C3×D311yescharacteristic
457C22×Q8C2×C3×D311yescharacteristic, complemented
458#137—22no—
459#137—34no—
460#137—62no—
461#137C2×C3×D314yescomplemented
462C2×Q16—21no—
463C2×Q16—61no—
464C2×SD16—21no—
465C2×SD16—61no—
466C2×M16—31no—
467C2×M16C2×C3×D311yescharacteristic, complemented
468C4⋊Q8—32no—
469#124—32no—
470#123—62no—
471C22⋊Q8—62no—
472#117—31no—
473#104—34no—
474#104—34no—
475#101—32no—
476#100—32no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—32no—
481C23×C3—41no—
482C23×C3—64no—
483C23×C3—61no—
484C23×C3D3×D411yescharacteristic
485C23×C3C2×C3×D411yescharacteristic
486C22×D3—24no—
487C22×D3—21no—
488C22×D3C2×C3×D412yes—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—24no—
492C3×Q8—22no—
493C3×Q8—22no—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—22no—
497C3×Q8—32no—
498C3×Q8—42no—
499C3×Q8—41no—
500C3×Q8—42no—
501C3×Q8—42no—
502C3×Q8—41no—
503C3×Q8—41no—
504C3×Q8—41no—
505C3×Q8—41no—
506C3×Q8—64no—
507C3×Q8—61no—
508C3×Q8—61no—
509C3×Q8—61no—
510C3×Q8C2×#6712yes—
511C3×Q8C2×C3×D412yes—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—22no—
519C3×D4—32no—
520C3×D4—41no—
521C3×D4—42no—
522C3×D4—42no—
523C3×D4—64no—
524C3×D4—64no—
525C3×D4—64no—
526C3×D4—62no—
527C3×D4—62no—
528C3×D4—62no—
529C3×D4—62no—
530C3×D4—61no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4C2×#6712yes—
534C3×D4C2×C3×D412yes—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—32no—
550C2×C3×C4—42no—
551C2×C3×C4—42no—
552C2×C3×C4—41no—
553C2×C3×C4—42no—
554C2×C3×C4—42no—
555C2×C3×C4—42no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—64no—
561C2×C3×C4—64no—
562C2×C3×C4—64no—
563C2×C3×C4—61no—
564C2×C3×C4—62no—
565C2×C3×C4—62no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4C2×#6711yescharacteristic
573C2×C3×C4C2×#6711yescharacteristic
574C2×C3×C4C2×C3×D411yescharacteristic
575C2×C3×C4C2×C3×D411yescharacteristic
576C2×C3×C4C2×C3×D411yescharacteristic
577C2×C3×C4C2×C3×D411yescharacteristic
578C2×C3×C4C2×C3×D411yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580C2×C3×C4C24×C311yescharacteristic
581#67—24no—
582#67—24no—
583#67—22no—
584#67—22no—
585#67—22no—
586#67—22no—
587C2×Dic3—24no—
588C2×Dic3—21no—
589C2×Dic3—22no—
590C2×Dic3C2×C3×D412yes—
591D12—24no—
592D12—21no—
593D12—21no—
594D12—21no—
595D12C2×C3×D412yes—
596C4×D3—24no—
597C4×D3—24no—
598C4×D3—22no—
599C4×D3—22no—
600C4×D3—22no—
601C4×D3—22no—
602Dic6—24no—
603Dic6—21no—
604Dic6—21no—
605Dic6—21no—
606Dic6C2×C3×D412yes—
607C3×C8—24no—
608C3×C8—22no—
609C3×C8—22no—
610C3×C8—62no—
611C3⋊C8—22no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—42no—
616C2×C32C2×#12011yescharacteristic
617C3×D3—42no—
618C3×D3—42no—
619#41—21no—
620#41—21no—
621#41—32no—
622#41—32no—
623#41—62no—
624#41—62no—
625#41—64no—
626#41—64no—
627#41—64no—
628#41—64no—
629#41—62no—
630#41—62no—
631#41—62no—
632#41—62no—
633#41—61no—
634#41—61no—
635#41—61no—
636#41—61no—
637#41—61no—
638#41—61no—
639#41C3×#6712yes—
640#41C22×C3×D312yes—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—31no—
647C2×Q8—31no—
648C2×Q8—62no—
649C2×Q8—62no—
650C2×Q8—62no—
651C2×Q8C3×#6711yescharacteristic
652C2×Q8C22×C3×D312yes—
653C2×D4—21no—
654C2×D4—32no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—62no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—62no—
661C2×D4—64no—
662C2×D4—61no—
663C2×D4—62no—
664C2×D4C3×#6711yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—32no—
668C22×C4—64no—
669C22×C4—61no—
670C22×C4C22×C3×D311yescharacteristic
671Q16—24no—
672Q16—64no—
673SD16—24no—
674SD16—64no—
675M16—21no—
676M16—32no—
677M16—61no—
678M16C22×C3×D312yes—
679C2×C8—21no—
680C2×C8—61no—
681C4⋊C4—64no—
682C4⋊C4—61no—
683C22⋊C4—64no—
684C22⋊C4—61no—
685C42—32no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—82no—
700C22×C3—122no—
701C22×C3—241no—
702C22×C3—244no—
703C22×C3#93711yescharacteristic
704C22×C3#93711yescharacteristic
705C22×C3C3×#12011yescharacteristic
706C22×C3C3×#12011yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C22×C3C22×C3×D411yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—42no—
712C2×D3—81no—
713C2×D3—84no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—42no—
721C3×C4—44no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—62no—
725C3×C4—62no—
726C3×C4—122no—
727C3×C4#93711yescharacteristic
728C3×C4#93711yescharacteristic
729C3×C4C3×#12011yescharacteristic
730C3×C4C3×#12011yescharacteristic
731C3×C4C2×D3×D411yescharacteristic
732C3×C4C22×#6711yescharacteristic
733C3×C4C22×C3×D411yescharacteristic
734C3×C4C22×C3×D411yescharacteristic
735Dic3—22no—
736Dic3—22no—
737Dic3—42no—
738C32#302211yescharacteristic, complemented, Sylow
739C23—21no—
740C23—32no—
741C23—64no—
742C23—61no—
743C23C3×D3×D411yescharacteristic
744Q8—21no—
745Q8—22no—
746Q8—22no—
747Q8—32no—
748Q8—41no—
749Q8—41no—
750Q8—64no—
751Q8—61no—
752Q8—61no—
753Q8—61no—
754Q8C2×C3×#6712yes—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—32no—
759D4—64no—
760D4—64no—
761D4—64no—
762D4—62no—
763D4—62no—
764D4—62no—
765D4—62no—
766D4—61no—
767D4—61no—
768D4—61no—
769D4C2×C3×#6712yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—32no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—64no—
778C2×C4—64no—
779C2×C4—64no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—62no—
784C2×C4—62no—
785C2×C4—62no—
786C2×C4C3×D3×D411yescharacteristic
787C2×C4C3×D3×D411yescharacteristic
788C2×C4C3×D3×D411yescharacteristic
789C2×C4C2×C3×#6711yescharacteristic
790C2×C4C2×C3×#6711yescharacteristic
791C2×C4C23×C3×D311yescharacteristic
792C8—22no—
793C8—62no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—42no—
805C2×C3—42no—
806C2×C3—82no—
807C2×C3—122no—
808C2×C3—122no—
809C2×C3C2×#93711yescharacteristic
810C2×C3C2×C3×#12011yescharacteristic
811D3—42no—
812D3—42no—
813C22—22no—
814C22—41no—
815C22—62no—
816C22—62no—
817C22—81no—
818C22—122no—
819C22—241no—
820C22—244no—
821C22C3×#93711yescharacteristic
822C22C3×#93711yescharacteristic
823C22C2×C3×D3×D411yescharacteristic
824C4—22no—
825C4—42no—
826C4—62no—
827C4—62no—
828C4—122no—
829C4C3×#93711yescharacteristic
830C4C3×#93711yescharacteristic
831C4C2×C3×D3×D411yescharacteristic
832C4C22×C3×#6711yescharacteristic
833C3—21no—
834C3#8399311yescharacteristic, direct product factor
835C3C3×#302211yescharacteristic, complemented
836C2—21no—
837C2—21no—
838C2—21no—
839C2—42no—
840C2—122no—
841C2—122no—
842C2C2×C3×#93711yescharacteristic
subgroupG/H
centerC2×C3C2×#937
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC2×C32×#137C2
socleC2×C32C2×#120
prime radicalC3×#5964C2
hypercenterC2×C3×#137D3
hypocenterC3C3×#3022
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
2. C2×C32×#137C2semidirect
3. C3×#5816C2semidirect
4. C2×C3×#942C2semidirect
5. C3×#5236C2semidirect
6. C3×#5205C2semidirect
7. C3×#5202C2semidirect
8. C3×#5139C2semidirect
9. C3×#5132C2semidirect
11. #83993C3direct (N × H)
13. C22×C32×Q8C22semidirect
27. C32×#137C22semidirect
30. C2×C32×M16C22semidirect
31. C3×#947C22semidirect
33. C3×#944C22semidirect
36. C3×#942C22semidirect
39. C3×#926C22semidirect
40. C2×C3×#208C22semidirect
41. C3×#837C22semidirect
42. C3×#825C22semidirect
43. C3×#824C22semidirect
44. C3×#823C22semidirect
49. C2×C3×#137D3semidirect
50. C2×C3×#137C2×C3semidirect
52. #5816C2×C3semidirect
53. C2×#942C2×C3semidirect
59. #5236C2×C3semidirect
60. #5205C2×C3semidirect
61. #5202C2×C3semidirect
62. #5139C2×C3semidirect
63. #5132C2×C3semidirect
148. C22×C3×Q8C2×D3semidirect
149. C22×C3×Q8C22×C3semidirect
168. C3×#137C2×D3semidirect
169. C3×#137C22×C3semidirect
180. C2×C3×M16C2×D3semidirect
181. C2×C3×M16C22×C3semidirect
187. #947C22×C3semidirect
189. #944C22×C3semidirect
192. #942C22×C3semidirect
195. #926C22×C3semidirect
196. C2×#208C22×C3semidirect
201. #837C22×C3semidirect
202. #825C22×C3semidirect
203. #824C22×C3semidirect
204. #823C22×C3semidirect
262. C2×#137C3×D3semidirect
457. C22×Q8C2×C3×D3semidirect
461. #137C2×C3×D3semidirect
467. C2×M16C2×C3×D3semidirect
738. C32#3022semidirect
834. C3#83993direct (N × H)
835. 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×C32×#1372
C3×#58162
C2×C3×#9422
C3×#52362
C3×#52052
C3×#52022
C3×#51392
C3×#51322
C3×#30223
#839933