Finite Group Databasebeta

← C3×#24175 #10642782

Subgroups — C3×#24175 #10642782

Order 768.

1030 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3512C211yesmaximal, characteristic
2C3×#3037C211yesmaximal, characteristic, complemented
3C3×C4×#137C211yesmaximal, characteristic, complemented
4C3×#2565C211yesmaximal, characteristic, complemented
5C3×#2040C211yesmaximal, characteristic, complemented
6C3×#2039C211yesmaximal, characteristic, complemented
7C3×#2007C211yesmaximal, characteristic, complemented
8C3×#2007C211yesmaximal, characteristic, complemented
9C3×#1998C211yesmaximal, characteristic, complemented
10C3×#1980C211yesmaximal, characteristic, complemented
11C3×#1882C211yesmaximal, characteristic, complemented
12C3×#1882C211yesmaximal, characteristic, complemented
13C3×#1860C211yesmaximal, characteristic, complemented
14C3×#1859C211yesmaximal, characteristic, complemented
15C3×#1806C211yesmaximal, characteristic, complemented
16#24175C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#137C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic
20C3×#553—21no—
21C3×#553—21no—
22C3×#553—22no—
23C3×#553—22no—
24C3×#552—21no—
25C3×#552—21no—
26C3×#541—21no—
27C3×#540—21no—
28C3×#537C2211yescharacteristic
29C3×#537C2211yescharacteristic
30C3×#532C2211yescharacteristic
31C3×#529—21no—
32C3×#529—21no—
33C2×C3×#125C2211yescharacteristic
34C3×#520C2211yescharacteristic
35C3×#520C2211yescharacteristic
36C3×C4×#41C2211yescharacteristic
37C2×C3×C4×Q8C2211yescharacteristic
38C3×#464—21no—
39C3×#464—21no—
40C3×#462—21no—
41C3×#460—21no—
42C3×#441—21no—
43C3×#440—21no—
44C3×C4×Q16—21no—
45C3×C4×SD16—21no—
46C3×#428C2211yescharacteristic
47C3×#423C2211yescharacteristic
48C2×C3×#104C2211yescharacteristic
49C2×C3×#104C2211yescharacteristic
50C2×C3×#104C2211yescharacteristic
51C2×C3×#104C2211yescharacteristic
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic
54C3×#419C2211yescharacteristic
55C3×#417C2211yescharacteristic
56C3×#417C2211yescharacteristic
57C3×#417C2211yescharacteristic
58C3×C4×M16C2211yescharacteristic
59C3×#398—22no—
60C3×#391C2211yescharacteristic
61C3×#391C2211yescharacteristic
62C3×#387—22no—
63C3×#384C2211yescharacteristic
64C3×#382C2211yescharacteristic
65C3×C4×C4⋊C4C2211yescharacteristic
66C3×#343C2211yescharacteristic
67C3×#343C2211yescharacteristic
68C3×#343C2211yescharacteristic
69C3×#343C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3512C2×C311yescharacteristic
73#3037C2×C311yescharacteristic, complemented
74C4×#137C2×C311yescharacteristic, complemented
75#2565C2×C311yescharacteristic, complemented
76#2040C2×C311yescharacteristic, complemented
77#2039C2×C311yescharacteristic, complemented
78#2007C2×C311yescharacteristic, complemented
79#2007C2×C311yescharacteristic, complemented
80#1998C2×C311yescharacteristic, complemented
81#1980C2×C311yescharacteristic, complemented
82#1882C2×C311yescharacteristic, complemented
83#1882C2×C311yescharacteristic, complemented
84#1860C2×C311yescharacteristic, complemented
85#1859C2×C311yescharacteristic, complemented
86#1806C2×C311yescharacteristic, complemented
87C2×C3×#41C2311yescharacteristic
88C2×C3×#41C2311yescharacteristic
89C2×C3×#41C2311yescharacteristic
90C22×C3×Q8C2311yescharacteristic
91C3×#137—22no—
92C3×#137—22no—
93C3×#137—22no—
94C3×#137—22no—
95C3×#137—41no—
96C3×#137—41no—
97C2×C3×Q16—21no—
98C2×C3×Q16—21no—
99C2×C3×Q16—21no—
100C2×C3×SD16—21no—
101C2×C3×SD16—21no—
102C2×C3×SD16—21no—
103C2×C3×M16C2311yescharacteristic
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C2×C3×M16C2311yescharacteristic
107C3×C4⋊Q8D411yescharacteristic
108C3×#127D411yescharacteristic
109C3×#126—22no—
110C3×#126—22no—
111C3×#126—22no—
112C3×#126—22no—
113C3×#125—22no—
114C3×#125—22no—
115C3×#125—21no—
116C3×#125—21no—
117C3×#125—21no—
118C3×#125—21no—
119C3×#124D411yescharacteristic
120C3×#124D411yescharacteristic
121C3×#123—22no—
122C3×#123—22no—
123C3×#123—22no—
124C3×#123—22no—
125C3×C22⋊Q8—21no—
126C3×C22⋊Q8—21no—
127C3×C22⋊Q8—21no—
128C3×C22⋊Q8—21no—
129C3×#121—22no—
130C3×#121—22no—
131C3×#121—21no—
132C3×#121—21no—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121—21no—
136C3×#121—21no—
137C3×#121—22no—
138C3×#121—22no—
139C3×C4×Q8—21no—
140C3×C4×Q8—21no—
141C3×C4×Q8—21no—
142C3×C4×Q8—21no—
143C3×C4×Q8—21no—
144C3×C4×Q8—21no—
145C3×C4×Q8D411yescharacteristic
146C3×C4×Q8D411yescharacteristic
147C3×C4×D4—22no—
148C3×C4×D4—22no—
149C3×C4×D4—21no—
150C3×C4×D4—21no—
151C3×C4×D4—21no—
152C3×C4×D4—21no—
153C3×C4×D4—22no—
154C3×C4×D4—22no—
155C3×C4×D4—21no—
156C3×C4×D4—21no—
157C3×C4×D4D411yescharacteristic
158C3×C4×D4D411yescharacteristic
159C3×#117—22no—
160C3×#117—22no—
161C3×#117—21no—
162C3×#117—21no—
163C3×#117—21no—
164C3×#117C2311yescharacteristic
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4—21no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—22no—
169C2×C3×C4⋊C4—21no—
170C2×C3×C4⋊C4D412yes—
171C2×C3×C4⋊C4D412yes—
172C2×C3×C4⋊C4C2311yescharacteristic
173C2×C3×C4⋊C4C2311yescharacteristic
174C2×C3×C4⋊C4C2311yescharacteristic
175C2×C3×C42—21no—
176C2×C3×C42—21no—
177C2×C3×C42C2311yescharacteristic
178C2×C3×C42C2311yescharacteristic
179C2×C3×C42C2311yescharacteristic
180C3×#107—21no—
181C3×#106—21no—
182C3×C4⋊C8—21no—
183C3×C4⋊C8—21no—
184C3×#104—22no—
185C3×#104—22no—
186C3×#104—41no—
187C3×#104—41no—
188C3×#104—41no—
189C3×#104—41no—
190C3×#103—21no—
191C3×#103—21no—
192C3×#103—21no—
193C3×#103—21no—
194C3×#103—21no—
195C3×#102—21no—
196C3×#102—21no—
197C3×#102—21no—
198C3×#97—21no—
199C3×C4×C8—21no—
200C3×#95—21no—
201C3×#95—22no—
202C3×#95—22no—
203C3×#95—22no—
204C2×#137C22×C311yescharacteristic
205C2×#137C22×C311yescharacteristic
206C2×#137C22×C311yescharacteristic
207#553—21no—
208#553—21no—
209#553—22no—
210#553—22no—
211#552—21no—
212#552—21no—
213#541—21no—
214#540—21no—
215#537C22×C311yescharacteristic
216#537C22×C311yescharacteristic
217#532C22×C311yescharacteristic
218#529—21no—
219#529—21no—
220C2×#125C22×C311yescharacteristic
221#520C22×C311yescharacteristic
222#520C22×C311yescharacteristic
223C4×#41C22×C311yescharacteristic
224C2×C4×Q8C22×C311yescharacteristic
225#464—21no—
226#464—21no—
227#462—21no—
228#460—21no—
229#441—21no—
230#440—21no—
231C4×Q16—21no—
232C4×SD16—21no—
233#428C22×C311yescharacteristic
234#423C22×C311yescharacteristic
235C2×#104C22×C311yescharacteristic
236C2×#104C22×C311yescharacteristic
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239C2×#104C22×C311yescharacteristic
240C2×#104C22×C311yescharacteristic
241#419C22×C311yescharacteristic
242#417C22×C311yescharacteristic
243#417C22×C311yescharacteristic
244#417C22×C311yescharacteristic
245C4×M16C22×C311yescharacteristic
246#398—22no—
247#391C22×C311yescharacteristic
248#391C22×C311yescharacteristic
249#387—22no—
250#384C22×C311yescharacteristic
251#382C22×C311yescharacteristic
252C4×C4⋊C4C22×C311yescharacteristic
253#343C22×C311yescharacteristic
254#343C22×C311yescharacteristic
255#343C22×C311yescharacteristic
256#343C22×C311yescharacteristic
257#339C22×C311yescharacteristic
258#339C22×C311yescharacteristic
259C3×#41—21no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—21no—
271C2×C3×Q8—21no—
272C2×C3×Q8—21no—
273C2×C3×Q8—21no—
274C2×C3×Q8—21no—
275C2×C3×Q8—21no—
276C2×C3×Q8C2×D411yescharacteristic
277C2×C3×Q8C2×D411yescharacteristic
278C2×C3×Q8C2×D411yescharacteristic
279C2×C3×Q8#4112yes—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4—21no—
283C2×C3×D4—22no—
284C2×C3×D4—22no—
285C2×C3×D4—21no—
286C2×C3×D4—21no—
287C2×C3×D4C2×D411yescharacteristic
288C2×C3×D4C2×D411yescharacteristic
289C2×C3×D4C2×D411yescharacteristic
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—21no—
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×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2411yescharacteristic
306C3×Q16—24no—
307C3×Q16—42no—
308C3×Q16—42no—
309C3×SD16—24no—
310C3×SD16—42no—
311C3×SD16—42no—
312C3×M16—21no—
313C3×M16—21no—
314C3×M16—21no—
315C3×M16—21no—
316C3×M16—21no—
317C3×M16—21no—
318C3×M16—21no—
319C3×M16#4112yes—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—22no—
328C3×C4⋊C4—22no—
329C3×C4⋊C4—22no—
330C3×C4⋊C4—22no—
331C3×C4⋊C4—22no—
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—42no—
343C3×C4⋊C4—44no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—41no—
346C3×C4⋊C4C2×D411yescharacteristic
347C3×C4⋊C4C2×D411yescharacteristic
348C3×C22⋊C4—22no—
349C3×C22⋊C4—22no—
350C3×C22⋊C4—22no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—22no—
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×C42—22no—
362C3×C42—22no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—21no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—41no—
371C3×C42—41no—
372C3×C42C2×D411yescharacteristic
373C3×C42C2×D411yescharacteristic
374C3×C42C2×D411yescharacteristic
375C3×C42C2×D411yescharacteristic
376C2×#41C23×C311yescharacteristic
377C2×#41C23×C311yescharacteristic
378C2×#41C23×C311yescharacteristic
379C22×Q8C23×C311yescharacteristic
380#137—22no—
381#137—22no—
382#137—22no—
383#137—22no—
384#137—41no—
385#137—41no—
386C2×Q16—21no—
387C2×Q16—21no—
388C2×Q16—21no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16—21no—
392C2×M16C23×C311yescharacteristic
393C2×M16C23×C311yescharacteristic
394C2×M16C23×C311yescharacteristic
395C2×M16C23×C311yescharacteristic
396C4⋊Q8C3×D411yescharacteristic
397#127C3×D411yescharacteristic
398#126—22no—
399#126—22no—
400#126—22no—
401#126—22no—
402#125—22no—
403#125—22no—
404#125—21no—
405#125—21no—
406#125—21no—
407#125—21no—
408#124C3×D411yescharacteristic
409#124C3×D411yescharacteristic
410#123—22no—
411#123—22no—
412#123—22no—
413#123—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418#121—22no—
419#121—22no—
420#121—21no—
421#121—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—21no—
426#121—22no—
427#121—22no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8C3×D411yescharacteristic
435C4×Q8C3×D411yescharacteristic
436C4×D4—22no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4C3×D411yescharacteristic
447C4×D4C3×D411yescharacteristic
448#117—22no—
449#117—22no—
450#117—21no—
451#117—21no—
452#117—21no—
453#117C23×C311yescharacteristic
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4C3×D412yes—
460C2×C4⋊C4C3×D412yes—
461C2×C4⋊C4C23×C311yescharacteristic
462C2×C4⋊C4C23×C311yescharacteristic
463C2×C4⋊C4C23×C311yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42C23×C311yescharacteristic
467C2×C42C23×C311yescharacteristic
468C2×C42C23×C311yescharacteristic
469#107—21no—
470#106—21no—
471C4⋊C8—21no—
472C4⋊C8—21no—
473#104—22no—
474#104—22no—
475#104—41no—
476#104—41no—
477#104—41no—
478#104—41no—
479#103—21no—
480#103—21no—
481#103—21no—
482#103—21no—
483#103—21no—
484#102—21no—
485#102—21no—
486#102—21no—
487#97—21no—
488C4×C8—21no—
489#95—21no—
490#95—22no—
491#95—22no—
492#95—22no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3C22×D411yescharacteristic
497C3×Q8—22no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—22no—
501C3×Q8—21no—
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—41no—
506C3×Q8—41no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—81no—
520C3×D4—81no—
521C3×D4—82no—
522C3×D4—82no—
523C2×C3×C4—22no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—22no—
530C2×C3×C4—22no—
531C2×C3×C4—22no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—42no—
545C2×C3×C4—42no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—81no—
552C2×C3×C4—81no—
553C2×C3×C4—82no—
554C2×C3×C4—82no—
555C2×C3×C4#12011yescharacteristic
556C2×C3×C4#12011yescharacteristic
557C2×C3×C4#12011yescharacteristic
558C2×C3×C4#12011yescharacteristic
559C2×C3×C4C22×D411yescharacteristic
560C2×C3×C4C22×D411yescharacteristic
561C2×C3×C4C2×#4111yescharacteristic
562C2×C3×C4C2×#4111yescharacteristic
563C2×C3×C4H(5,𝔽2)11yescharacteristic
564C2×C3×C42−1+411yescharacteristic
565C3×C8—22no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—41no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580#41—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×C3×D411yescharacteristic
587C2×Q8C2×C3×D411yescharacteristic
588C2×Q8C2×C3×D411yescharacteristic
589C2×Q8C3×#4112yes—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4C2×C3×D411yescharacteristic
598C2×D4C2×C3×D411yescharacteristic
599C2×D4C2×C3×D411yescharacteristic
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4C2×C3×D412yes—
612C22×C4C2×C3×D412yes—
613C22×C4C2×C3×D411yescharacteristic
614C22×C4C2×C3×D411yescharacteristic
615C22×C4C24×C311yescharacteristic
616Q16—24no—
617Q16—42no—
618Q16—42no—
619SD16—24no—
620SD16—42no—
621SD16—42no—
622M16—21no—
623M16—21no—
624M16—21no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16C3×#4112yes—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—44no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C4⋊C4C2×C3×D411yescharacteristic
657C4⋊C4C2×C3×D411yescharacteristic
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C42—22no—
672C42—22no—
673C42—21no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—41no—
681C42—41no—
682C42C2×C3×D411yescharacteristic
683C42C2×C3×D411yescharacteristic
684C42C2×C3×D411yescharacteristic
685C42C2×C3×D411yescharacteristic
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3C2×#12011yescharacteristic
698C22×C3#54811yescharacteristic
699C22×C3#55011yescharacteristic
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—21no—
704C3×C4—42no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4—42no—
709C3×C4—42no—
710C3×C4—41no—
711C3×C4—42no—
712C3×C4—41no—
713C3×C4—81no—
714C3×C4—81no—
715C3×C4#52511yescharacteristic
716C3×C4#53711yescharacteristic
717C3×C4#54611yescharacteristic
718C3×C4#54711yescharacteristic
719C23—21no—
720C23—21no—
721C23—21no—
722C23C22×C3×D411yescharacteristic
723Q8—22no—
724Q8—21no—
725Q8—21no—
726Q8—22no—
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—41no—
732Q8—41no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—81no—
746D4—81no—
747D4—82no—
748D4—82no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4—81no—
779C2×C4—82no—
780C2×C4—82no—
781C2×C4C3×#12011yescharacteristic
782C2×C4C3×#12011yescharacteristic
783C2×C4C3×#12011yescharacteristic
784C2×C4C3×#12011yescharacteristic
785C2×C4C22×C3×D411yescharacteristic
786C2×C4C22×C3×D411yescharacteristic
787C2×C4C2×C3×#4111yescharacteristic
788C2×C4C2×C3×#4111yescharacteristic
789C2×C4C3×H(5,𝔽2)11yescharacteristic
790C2×C4C3×2−1+411yescharacteristic
791C8—22no—
792C8—41no—
793C8—41no—
794C8—41no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—81no—
798C2×C3—81no—
799C2×C3—81no—
800C2×C3#240711yescharacteristic
801C2×C3#301811yescharacteristic
802C2×C3#302211yescharacteristic
803C22—21no—
804C22—21no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22C2×C3×#12011yescharacteristic
815C22C3×#54811yescharacteristic
816C22C3×#55011yescharacteristic
817C4—21no—
818C4—21no—
819C4—21no—
820C4—21no—
821C4—42no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—42no—
827C4—41no—
828C4—42no—
829C4—41no—
830C4—81no—
831C4—81no—
832C4C3×#52511yescharacteristic
833C4C3×#53711yescharacteristic
834C4C3×#54611yescharacteristic
835C4C3×#54711yescharacteristic
836C3#2417511yescharacteristic, direct product factor, Sylow
837C2—21no—
838C2—21no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C3×#240711yescharacteristic
843C2C3×#301811yescharacteristic
844C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3512C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3037C2semidirect
3. C3×C4×#137C2semidirect
4. C3×#2565C2semidirect
5. C3×#2040C2semidirect
6. C3×#2039C2semidirect
7. C3×#2007C2semidirect
8. C3×#2007C2semidirect
9. C3×#1998C2semidirect
10. C3×#1980C2semidirect
11. C3×#1882C2semidirect
12. C3×#1882C2semidirect
13. C3×#1860C2semidirect
14. C3×#1859C2semidirect
15. C3×#1806C2semidirect
16. #24175C3direct (N × H)
73. #3037C2×C3semidirect
74. C4×#137C2×C3semidirect
75. #2565C2×C3semidirect
76. #2040C2×C3semidirect
77. #2039C2×C3semidirect
78. #2007C2×C3semidirect
79. #2007C2×C3semidirect
80. #1998C2×C3semidirect
81. #1980C2×C3semidirect
82. #1882C2×C3semidirect
83. #1882C2×C3semidirect
84. #1860C2×C3semidirect
85. #1859C2×C3semidirect
86. #1806C2×C3semidirect
836. C3#24175direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35122
C3×#30372
C3×C4×#1372
C3×#25652
C3×#20402
C3×#20392
C3×#20072
C3×#19982
C3×#19802
C3×#18822
C3×#18602
C3×#18592
C3×#18062
#241753