Finite Group Databasebeta

← C3×#19013 #10637620

Subgroups — C3×#19013 #10637620

Order 768.

810 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3531C211yesmaximal, characteristic
2C3×#3240C211yesmaximal, characteristic, complemented
3C3×#3237C211yesmaximal, characteristic, complemented
4C3×#3181C211yesmaximal, characteristic, complemented
5C3×#1664C211yesmaximal, characteristic, complemented
6C3×#1664C211yesmaximal, characteristic, complemented
7C3×#1664C211yesmaximal, characteristic, complemented
8C3×#1663C211yesmaximal, characteristic, complemented
9C3×#1663C211yesmaximal, characteristic, complemented
10C3×#1662C211yesmaximal, characteristic, complemented
11C3×#1661C211yesmaximal, characteristic, complemented
12C3×#1660C211yesmaximal, characteristic, complemented
13C3×#1535C211yesmaximal, characteristic, complemented
14C3×#1532C211yesmaximal, characteristic, complemented
15C3×#1531C211yesmaximal, characteristic, complemented
16#19013C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#564C2211yescharacteristic
18C3×#563—21no—
19C3×#563—21no—
20C3×#563—21no—
21C3×#563—21no—
22C3×#563C2211yescharacteristic
23C3×#563C2211yescharacteristic
24C3×#562—21no—
25C3×#562—21no—
26C3×#562C2211yescharacteristic
27C3×#533—21no—
28C3×#533—21no—
29C3×#533C2211yescharacteristic
30C3×#533C2211yescharacteristic
31C3×#529—21no—
32C3×#529—21no—
33C3×#529—21no—
34C3×#529—21no—
35C3×#529C2211yescharacteristic
36C3×#529C2211yescharacteristic
37C3×#501C2211yescharacteristic
38C3×#501C2211yescharacteristic
39C3×#501C2211yescharacteristic
40C3×#501C2211yescharacteristic
41C3×#501C2211yescharacteristic
42C3×#497C2211yescharacteristic
43C3×#491C2211yescharacteristic
44C3×#491C2211yescharacteristic
45C3×#491C2211yescharacteristic
46C3×#489C2211yescharacteristic
47C3×#489C2211yescharacteristic
48C3×#489C2211yescharacteristic
49C3×#485—21no—
50C3×#485—21no—
51C3×#485—21no—
52C3×#482—21no—
53C3×#479—21no—
54C3×#478—21no—
55C3×#477—21no—
56C3×#475—21no—
57C3×#467—21no—
58C3×#465—21no—
59C3×#441—21no—
60C3×#440—21no—
61C3×#432C2211yescharacteristic
62C3×#432C2211yescharacteristic
63C2×C3×#97C2211yescharacteristic
64C3×#330C2211yescharacteristic
65C3×#330C2211yescharacteristic
66C3×#330C2211yescharacteristic
67C3×#330C2211yescharacteristic
68C3×#330C2211yescharacteristic
69C3×#330C2211yescharacteristic
70C3×#330C2211yescharacteristic
71C3×#330C2211yescharacteristic
72C3×#329C2211yescharacteristic
73C3×#329C2211yescharacteristic
74C3×#329C2211yescharacteristic
75C3×#329C2211yescharacteristic
76#3531C2×C311yescharacteristic
77#3240C2×C311yescharacteristic, complemented
78#3237C2×C311yescharacteristic, complemented
79#3181C2×C311yescharacteristic, complemented
80#1664C2×C311yescharacteristic, complemented
81#1664C2×C311yescharacteristic, complemented
82#1664C2×C311yescharacteristic, complemented
83#1663C2×C311yescharacteristic, complemented
84#1663C2×C311yescharacteristic, complemented
85#1662C2×C311yescharacteristic, complemented
86#1661C2×C311yescharacteristic, complemented
87#1660C2×C311yescharacteristic, complemented
88#1535C2×C311yescharacteristic, complemented
89#1532C2×C311yescharacteristic, complemented
90#1531C2×C311yescharacteristic, complemented
91C2×C3×Q16—21no—
92C2×C3×SD16—21no—
93C22×C3×C8—21no—
94C3×C4⋊Q8—21no—
95C3×C4⋊Q8—21no—
96C3×C4⋊Q8—21no—
97C3×C4⋊Q8—21no—
98C3×C4⋊Q8D411yescharacteristic
99C3×C4⋊Q8D411yescharacteristic
100C3×C4⋊Q8C2311yescharacteristic
101C3×C4⋊Q8C2311yescharacteristic
102C3×#126—21no—
103C3×#126—21no—
104C3×#126—21no—
105C3×#126—21no—
106C3×#126—21no—
107C3×#126—21no—
108C3×#126—21no—
109C3×#126—21no—
110C3×#126—21no—
111C3×#126—21no—
112C3×#125—21no—
113C3×#125—21no—
114C3×#125—21no—
115C3×#125—21no—
116C3×#125—21no—
117C3×#125—21no—
118C3×#125—21no—
119C3×#125—21no—
120C3×#125—21no—
121C3×#125C2311yescharacteristic
122C3×#125C2311yescharacteristic
123C3×#125C2311yescharacteristic
124C3×#125C2311yescharacteristic
125C3×#124—21no—
126C3×#124—21no—
127C3×#124—21no—
128C3×#124—21no—
129C3×#124C2311yescharacteristic
130C3×#124C2311yescharacteristic
131C3×#123—21no—
132C3×#123—21no—
133C3×#123—21no—
134C3×#123—21no—
135C3×#123—21no—
136C3×#123—21no—
137C3×#123—21no—
138C3×#123—21no—
139C3×#123—21no—
140C3×#123—21no—
141C3×C22⋊Q8—21no—
142C3×C22⋊Q8—21no—
143C3×C22⋊Q8—21no—
144C3×C22⋊Q8—21no—
145C3×C22⋊Q8—21no—
146C3×C22⋊Q8—21no—
147C3×C22⋊Q8—21no—
148C3×C22⋊Q8—21no—
149C3×C22⋊Q8—21no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8D411yescharacteristic
158C3×C22⋊Q8D411yescharacteristic
159C3×#121—21no—
160C3×#121—21no—
161C3×#121—21no—
162C3×#121—21no—
163C3×#121D411yescharacteristic
164C3×#121D411yescharacteristic
165C3×C4×Q8—21no—
166C3×C4×Q8—21no—
167C3×C4×Q8—21no—
168C3×C4×Q8—21no—
169C3×C4×Q8—21no—
170C3×C4×Q8—21no—
171C3×C4×Q8D411yescharacteristic
172C3×C4×Q8D411yescharacteristic
173C3×C4×D4—21no—
174C3×C4×D4—21no—
175C3×C4×D4—21no—
176C3×C4×D4—21no—
177C3×C4×D4D411yescharacteristic
178C3×C4×D4D411yescharacteristic
179C3×#117—21no—
180C3×#117—21no—
181C3×#117—21no—
182C3×#117—21no—
183C3×#117—21no—
184C3×#117D411yescharacteristic
185C3×#117D411yescharacteristic
186C2×C3×C42—21no—
187C2×C3×C42—21no—
188C2×C3×C42C2311yescharacteristic
189C3×#107—21no—
190C3×#107—21no—
191C3×#107—21no—
192C3×#107—21no—
193C3×#107—21no—
194C3×#106—21no—
195C3×#106—21no—
196C3×#106—21no—
197C3×#106—21no—
198C3×#106—21no—
199C3×C4⋊C8—21no—
200C3×C4⋊C8—21no—
201C3×#103—21no—
202C3×#103—21no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—21no—
210C3×#102—21no—
211C3×#102—21no—
212C3×#102—21no—
213C3×C22⋊C8—21no—
214C3×C22⋊C8—21no—
215C3×#97—21no—
216C3×#97C2311yescharacteristic
217C3×#97C2311yescharacteristic
218C3×#97C2311yescharacteristic
219C3×#97C2311yescharacteristic
220C3×#97C2311yescharacteristic
221C3×#97C2311yescharacteristic
222#564C22×C311yescharacteristic
223#563—21no—
224#563—21no—
225#563—21no—
226#563—21no—
227#563C22×C311yescharacteristic
228#563C22×C311yescharacteristic
229#562—21no—
230#562—21no—
231#562C22×C311yescharacteristic
232#533—21no—
233#533—21no—
234#533C22×C311yescharacteristic
235#533C22×C311yescharacteristic
236#529—21no—
237#529—21no—
238#529—21no—
239#529—21no—
240#529C22×C311yescharacteristic
241#529C22×C311yescharacteristic
242#501C22×C311yescharacteristic
243#501C22×C311yescharacteristic
244#501C22×C311yescharacteristic
245#501C22×C311yescharacteristic
246#501C22×C311yescharacteristic
247#497C22×C311yescharacteristic
248#491C22×C311yescharacteristic
249#491C22×C311yescharacteristic
250#491C22×C311yescharacteristic
251#489C22×C311yescharacteristic
252#489C22×C311yescharacteristic
253#489C22×C311yescharacteristic
254#485—21no—
255#485—21no—
256#485—21no—
257#482—21no—
258#479—21no—
259#478—21no—
260#477—21no—
261#475—21no—
262#467—21no—
263#465—21no—
264#441—21no—
265#440—21no—
266#432C22×C311yescharacteristic
267#432C22×C311yescharacteristic
268C2×#97C22×C311yescharacteristic
269#330C22×C311yescharacteristic
270#330C22×C311yescharacteristic
271#330C22×C311yescharacteristic
272#330C22×C311yescharacteristic
273#330C22×C311yescharacteristic
274#330C22×C311yescharacteristic
275#330C22×C311yescharacteristic
276#330C22×C311yescharacteristic
277#329C22×C311yescharacteristic
278#329C22×C311yescharacteristic
279#329C22×C311yescharacteristic
280#329C22×C311yescharacteristic
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—21no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8C2×D411yescharacteristic
288C2×C3×Q8C2×D411yescharacteristic
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4C2×D411yescharacteristic
294C2×C3×D4C2×D411yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C3×Q16—42no—
305C3×SD16—42no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—42no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—41no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4C2×D411yescharacteristic
346C3×C4⋊C4C2×D411yescharacteristic
347C3×C4⋊C4C2×D411yescharacteristic
348C3×C4⋊C4C2×D411yescharacteristic
349C3×C4⋊C4C2×D411yescharacteristic
350C3×C4⋊C4C2×D411yescharacteristic
351C3×C4⋊C4C2×D411yescharacteristic
352C3×C4⋊C4C2×D411yescharacteristic
353C3×C22⋊C4—21no—
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—41no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42—41no—
383C3×C42C2×D411yescharacteristic
384C3×C42C2×D411yescharacteristic
385C3×C42C2×D411yescharacteristic
386C3×C42C2411yescharacteristic
387C2×Q16—21no—
388C2×SD16—21no—
389C22×C8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8—21no—
393C4⋊Q8—21no—
394C4⋊Q8C3×D411yescharacteristic
395C4⋊Q8C3×D411yescharacteristic
396C4⋊Q8C23×C311yescharacteristic
397C4⋊Q8C23×C311yescharacteristic
398#126—21no—
399#126—21no—
400#126—21no—
401#126—21no—
402#126—21no—
403#126—21no—
404#126—21no—
405#126—21no—
406#126—21no—
407#126—21no—
408#125—21no—
409#125—21no—
410#125—21no—
411#125—21no—
412#125—21no—
413#125—21no—
414#125—21no—
415#125—21no—
416#125—21no—
417#125C23×C311yescharacteristic
418#125C23×C311yescharacteristic
419#125C23×C311yescharacteristic
420#125C23×C311yescharacteristic
421#124—21no—
422#124—21no—
423#124—21no—
424#124—21no—
425#124C23×C311yescharacteristic
426#124C23×C311yescharacteristic
427#123—21no—
428#123—21no—
429#123—21no—
430#123—21no—
431#123—21no—
432#123—21no—
433#123—21no—
434#123—21no—
435#123—21no—
436#123—21no—
437C22⋊Q8—21no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442C22⋊Q8—21no—
443C22⋊Q8—21no—
444C22⋊Q8—21no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8C3×D411yescharacteristic
454C22⋊Q8C3×D411yescharacteristic
455#121—21no—
456#121—21no—
457#121—21no—
458#121—21no—
459#121C3×D411yescharacteristic
460#121C3×D411yescharacteristic
461C4×Q8—21no—
462C4×Q8—21no—
463C4×Q8—21no—
464C4×Q8—21no—
465C4×Q8—21no—
466C4×Q8—21no—
467C4×Q8C3×D411yescharacteristic
468C4×Q8C3×D411yescharacteristic
469C4×D4—21no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4C3×D411yescharacteristic
474C4×D4C3×D411yescharacteristic
475#117—21no—
476#117—21no—
477#117—21no—
478#117—21no—
479#117—21no—
480#117C3×D411yescharacteristic
481#117C3×D411yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42C23×C311yescharacteristic
485#107—21no—
486#107—21no—
487#107—21no—
488#107—21no—
489#107—21no—
490#106—21no—
491#106—21no—
492#106—21no—
493#106—21no—
494#106—21no—
495C4⋊C8—21no—
496C4⋊C8—21no—
497#103—21no—
498#103—21no—
499#103—21no—
500#103—21no—
501#103—21no—
502#103—21no—
503#103—21no—
504#103—21no—
505#103—21no—
506#102—21no—
507#102—21no—
508#102—21no—
509C22⋊C8—21no—
510C22⋊C8—21no—
511#97—21no—
512#97C23×C311yescharacteristic
513#97C23×C311yescharacteristic
514#97C23×C311yescharacteristic
515#97C23×C311yescharacteristic
516#97C23×C311yescharacteristic
517#97C23×C311yescharacteristic
518C23×C3—21no—
519C23×C3—21no—
520C23×C3#12011yescharacteristic
521C3×Q8—41no—
522C3×Q8—41no—
523C3×Q8—41no—
524C3×Q8—41no—
525C3×Q8—42no—
526C3×Q8—81no—
527C3×Q8—81no—
528C3×Q8—81no—
529C3×Q8—81no—
530C3×D4—41no—
531C3×D4—41no—
532C3×D4—81no—
533C3×D4—81no—
534C3×D4—81no—
535C3×D4—81no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—42no—
550C2×C3×C4—42no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—81no—
554C2×C3×C4—81no—
555C2×C3×C4—81no—
556C2×C3×C4—81no—
557C2×C3×C4#12011yescharacteristic
558C2×C3×C4#12011yescharacteristic
559C2×C3×C4#12011yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C22×D411yescharacteristic
562C2×C3×C4C22×D411yescharacteristic
563C3×C8—22no—
564C3×C8—41no—
565C3×C8—41no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—41no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8C2×C3×D411yescharacteristic
576C2×Q8C2×C3×D411yescharacteristic
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4C2×C3×D411yescharacteristic
582C2×D4C2×C3×D411yescharacteristic
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4C2×C3×D411yescharacteristic
590C22×C4C2×C3×D411yescharacteristic
591C22×C4C2×C3×D411yescharacteristic
592Q16—42no—
593SD16—42no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—42no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×C3×D411yescharacteristic
634C4⋊C4C2×C3×D411yescharacteristic
635C4⋊C4C2×C3×D411yescharacteristic
636C4⋊C4C2×C3×D411yescharacteristic
637C4⋊C4C2×C3×D411yescharacteristic
638C4⋊C4C2×C3×D411yescharacteristic
639C4⋊C4C2×C3×D411yescharacteristic
640C4⋊C4C2×C3×D411yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—41no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—41no—
671C42C2×C3×D411yescharacteristic
672C42C2×C3×D411yescharacteristic
673C42C2×C3×D411yescharacteristic
674C42C24×C311yescharacteristic
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3C2×#12011yescharacteristic
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—81no—
702C3×C4—81no—
703C23—21no—
704C23—21no—
705C23C3×#12011yescharacteristic
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—42no—
711Q8—81no—
712Q8—81no—
713Q8—81no—
714Q8—81no—
715D4—41no—
716D4—41no—
717D4—81no—
718D4—81no—
719D4—81no—
720D4—81no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4C3×#12011yescharacteristic
743C2×C4C3×#12011yescharacteristic
744C2×C4C3×#12011yescharacteristic
745C2×C4C22×C3×D411yescharacteristic
746C2×C4C22×C3×D411yescharacteristic
747C2×C4C22×C3×D411yescharacteristic
748C8—22no—
749C8—41no—
750C8—41no—
751C8—41no—
752C8—41no—
753C8—41no—
754C2×C3—41no—
755C2×C3—81no—
756C2×C3—81no—
757C2×C3#301811yescharacteristic
758C2×C3#302011yescharacteristic
759C2×C3#302211yescharacteristic
760C22—21no—
761C22—21no—
762C22—21no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22C2×C3×#12011yescharacteristic
770C4—21no—
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—81no—
787C4—81no—
788C3#1901311yescharacteristic, direct product factor, Sylow
789C2—41no—
790C2—81no—
791C2—81no—
792C2C3×#301811yescharacteristic
793C2C3×#302011yescharacteristic
794C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
prime radicalC3×#3531C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3240C2semidirect
3. C3×#3237C2semidirect
4. C3×#3181C2semidirect
5. C3×#1664C2semidirect
6. C3×#1664C2semidirect
7. C3×#1664C2semidirect
8. C3×#1663C2semidirect
9. C3×#1663C2semidirect
10. C3×#1662C2semidirect
11. C3×#1661C2semidirect
12. C3×#1660C2semidirect
13. C3×#1535C2semidirect
14. C3×#1532C2semidirect
15. C3×#1531C2semidirect
16. #19013C3direct (N × H)
77. #3240C2×C3semidirect
78. #3237C2×C3semidirect
79. #3181C2×C3semidirect
80. #1664C2×C3semidirect
81. #1664C2×C3semidirect
82. #1664C2×C3semidirect
83. #1663C2×C3semidirect
84. #1663C2×C3semidirect
85. #1662C2×C3semidirect
86. #1661C2×C3semidirect
87. #1660C2×C3semidirect
88. #1535C2×C3semidirect
89. #1532C2×C3semidirect
90. #1531C2×C3semidirect
788. C3#19013direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35312
C3×#32402
C3×#32372
C3×#31812
C3×#16642
C3×#16632
C3×#16622
C3×#16612
C3×#16602
C3×#15352
C3×#15322
C3×#15312
#190133