Finite Group Databasebeta

← C3×#25635 #10644242

Subgroups — C3×#25635 #10644242

Order 768.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#559C211yesmaximal, characteristic, complemented
2C2×C3×#495C211yesmaximal, characteristic, complemented
3C2×C3×#463C211yesmaximal, characteristic, complemented
4C3×#2592C211yesmaximal, characteristic, complemented
5C3×#2015C211yesmaximal, characteristic, complemented
6C3×#2014C211yesmaximal, characteristic, complemented
7C3×#2012C211yesmaximal, characteristic, complemented
8C3×#2011C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1983C211yesmaximal, characteristic, complemented
11C3×#1880C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1877C211yesmaximal, characteristic, complemented
15C3×C4×#102C211yesmaximal, characteristic, complemented
16#25635C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C3×#559—24no—
24C3×#559—24no—
25C2×C3×#127C2211yescharacteristic
26C2×C3×#124—21no—
27C2×C3×#124C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic
29C2×C3×#124C2211yescharacteristic
30C2×C3×#123—21no—
31C2×C3×#123—21no—
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C2×C3×C4×D4—21no—
35C2×C3×C4×D4C2211yescharacteristic
36C2×C3×C4×D4C2211yescharacteristic
37C3×#495—24no—
38C3×#463—24no—
39C2×C3×C4⋊C8C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49C3×#397—21no—
50C3×#393—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#390C2211yescharacteristic
55C3×#388—21no—
56C3×#388—21no—
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#559C2×C311yescharacteristic, complemented
65C2×#495C2×C311yescharacteristic, complemented
66C2×#463C2×C311yescharacteristic, complemented
67#2592C2×C311yescharacteristic, complemented
68#2015C2×C311yescharacteristic, complemented
69#2014C2×C311yescharacteristic, complemented
70#2012C2×C311yescharacteristic, complemented
71#2011C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1983C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1879C2×C311yescharacteristic, complemented
76#1878C2×C311yescharacteristic, complemented
77#1877C2×C311yescharacteristic, complemented
78C4×#102C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4—21no—
83C22×C3×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C22×C3×D4C2311yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C23×C3×C4—21no—
88C23×C3×C4—21no—
89C2×C3×Q16—22no—
90C2×C3×Q16—22no—
91C2×C3×Q16—41no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—22no—
97C2×C3×SD16—41no—
98C2×C3×SD16—41no—
99C2×C3×SD16—41no—
100C2×C3×SD16—41no—
101C2×C3×D8—22no—
102C2×C3×D8—22no—
103C2×C3×D8—22no—
104C2×C3×D8—41no—
105C2×C3×D8—41no—
106C2×C3×D8—41no—
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×#127—22no—
112C3×#127—22no—
113C3×#124—28no—
114C3×#124—22no—
115C3×#124—22no—
116C3×#124—22no—
117C3×#124—22no—
118C3×#124—22no—
119C3×#124D414yes—
120C3×#123—28no—
121C3×#123—28no—
122C3×C4×Q8—22no—
123C3×C4×Q8—22no—
124C3×C4×Q8—22no—
125C3×C4×Q8—22no—
126C3×C4×D4—28no—
127C3×C4×D4—22no—
128C3×C4×D4—22no—
129C3×C4×D4—22no—
130C3×C4×D4D414yes—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4D411yescharacteristic
133C2×C3×C4⋊C4D411yescharacteristic
134C2×C3×C4⋊C4D411yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C42—21no—
151C2×C3×C42—21no—
152C2×C3×C42C2311yescharacteristic
153C2×C3×C42C2311yescharacteristic
154C2×C3×C42C2311yescharacteristic
155C3×C4⋊C8—22no—
156C3×#103—22no—
157C3×#103—41no—
158C3×#103—41no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—41no—
163C3×#102—41no—
164C3×C4×C8—22no—
165C3×#95—21no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C22×Q16C22×C311yescharacteristic
171C22×SD16C22×C311yescharacteristic
172C22×SD16C22×C311yescharacteristic
173C22×SD16C22×C311yescharacteristic
174C22×D8C22×C311yescharacteristic
175C22×D8C22×C311yescharacteristic
176#559—24no—
177#559—24no—
178C2×#127C22×C311yescharacteristic
179C2×#124—21no—
180C2×#124C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic
182C2×#124C22×C311yescharacteristic
183C2×#123—21no—
184C2×#123—21no—
185C2×C4×Q8C22×C311yescharacteristic
186C2×C4×Q8C22×C311yescharacteristic
187C2×C4×D4—21no—
188C2×C4×D4C22×C311yescharacteristic
189C2×C4×D4C22×C311yescharacteristic
190#495—24no—
191#463—24no—
192C2×C4⋊C8C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×C4×C8C22×C311yescharacteristic
202#397—21no—
203#393—21no—
204#391C22×C311yescharacteristic
205#391C22×C311yescharacteristic
206#390C22×C311yescharacteristic
207#390C22×C311yescharacteristic
208#388—21no—
209#388—21no—
210C4×C4⋊C4C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212#340C22×C311yescharacteristic
213#336C22×C311yescharacteristic
214#336C22×C311yescharacteristic
215#336C22×C311yescharacteristic
216#336C22×C311yescharacteristic
217C24×C3—21no—
218C24×C3—21no—
219C24×C3—21no—
220C2×C3×Q8—22no—
221C2×C3×Q8—22no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—41no—
234C2×C3×Q8C2×D412yes—
235C2×C3×D4—24no—
236C2×C3×D4—24no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—42no—
254C2×C3×D4—42no—
255C2×C3×D4—81no—
256C2×C3×D4—81no—
257C2×C3×D4C2×D412yes—
258C2×C3×D4C2×D412yes—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—24no—
262C22×C3×C4—24no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—81no—
267C22×C3×C4—81no—
268C22×C3×C4—81no—
269C22×C3×C4—81no—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D411yescharacteristic
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C3×Q16—44no—
278C3×SD16—44no—
279C3×SD16—44no—
280C3×SD16—44no—
281C3×D8—44no—
282C3×D8—44no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8#4112yes—
294C2×C3×C8#4112yes—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—22no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4C2×D412yes—
305C3×C22⋊C4—24no—
306C3×C22⋊C4—24no—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—24no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—81no—
316C3×C22⋊C4—81no—
317C3×C42—24no—
318C3×C42—21no—
319C3×C42—21no—
320C3×C42—21no—
321C3×C42—21no—
322C3×C42—81no—
323C3×C42C2×D412yes—
324C3×C42C2×D412yes—
325C22×Q8C3×D411yescharacteristic
326C22×Q8C23×C311yescharacteristic
327C22×Q8C23×C311yescharacteristic
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C23×C311yescharacteristic
331C22×D4C23×C311yescharacteristic
332C22×D4C23×C311yescharacteristic
333C23×C4—21no—
334C23×C4—21no—
335C2×Q16—22no—
336C2×Q16—22no—
337C2×Q16—41no—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—22no—
343C2×SD16—41no—
344C2×SD16—41no—
345C2×SD16—41no—
346C2×SD16—41no—
347C2×D8—22no—
348C2×D8—22no—
349C2×D8—22no—
350C2×D8—41no—
351C2×D8—41no—
352C2×D8—41no—
353C22×C8C23×C311yescharacteristic
354C22×C8C23×C311yescharacteristic
355C22×C8C23×C311yescharacteristic
356C22×C8C23×C311yescharacteristic
357#127—22no—
358#127—22no—
359#124—28no—
360#124—22no—
361#124—22no—
362#124—22no—
363#124—22no—
364#124—22no—
365#124C3×D414yes—
366#123—28no—
367#123—28no—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×D4—28no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4C3×D414yes—
377C2×C4⋊C4—21no—
378C2×C4⋊C4C3×D411yescharacteristic
379C2×C4⋊C4C3×D411yescharacteristic
380C2×C4⋊C4C3×D411yescharacteristic
381C2×C4⋊C4C23×C311yescharacteristic
382C2×C4⋊C4C23×C311yescharacteristic
383C2×C4⋊C4C23×C311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C23×C311yescharacteristic
399C2×C42C23×C311yescharacteristic
400C2×C42C23×C311yescharacteristic
401C4⋊C8—22no—
402#103—22no—
403#103—41no—
404#103—41no—
405#102—22no—
406#102—22no—
407#102—22no—
408#102—41no—
409#102—41no—
410C4×C8—22no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3C22×D411yescharacteristic
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—44no—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×D4—22no—
448C3×D4—22no—
449C3×D4—22no—
450C3×D4—22no—
451C3×D4—48no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—41no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4—41no—
459C3×D4—41no—
460C3×D4—84no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—22no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—41no—
482C2×C3×C4—41no—
483C2×C3×C4—41no—
484C2×C3×C4—41no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—84no—
492C2×C3×C4—84no—
493C2×C3×C4#12012yes—
494C2×C3×C4#12012yes—
495C2×C3×C4#13512yes—
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4C22×D411yescharacteristic
498C2×C3×C4C2×#4111yescharacteristic
499C2×C3×C4C2×#4111yescharacteristic
500C2×C3×C4H(5,𝔽2)11yescharacteristic
501C2×C3×C4H(5,𝔽2)11yescharacteristic
502C3×C8—22no—
503C3×C8—22no—
504C3×C8—41no—
505C3×C8—41no—
506C24—21no—
507C24—21no—
508C24—21no—
509C2×Q8—22no—
510C2×Q8—22no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—41no—
523C2×Q8C2×C3×D412yes—
524C2×D4—24no—
525C2×D4—24no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—81no—
545C2×D4—81no—
546C2×D4C2×C3×D412yes—
547C2×D4C2×C3×D412yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C2×C3×D411yescharacteristic
562C22×C4C2×C3×D411yescharacteristic
563C22×C4C2×C3×D411yescharacteristic
564C22×C4C2×C3×D411yescharacteristic
565C22×C4C24×C311yescharacteristic
566Q16—44no—
567SD16—44no—
568SD16—44no—
569SD16—44no—
570D8—44no—
571D8—44no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8C3×#4112yes—
583C2×C8C3×#4112yes—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4C2×C3×D412yes—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42—21no—
610C42—21no—
611C42—81no—
612C42C2×C3×D412yes—
613C42C2×C3×D412yes—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3C2×#12011yescharacteristic
636C22×C3#55011yescharacteristic
637C22×C3#55011yescharacteristic
638C22×C3C2×#13511yescharacteristic
639C22×C3#57511yescharacteristic
640C22×C3#57611yescharacteristic
641C22×C3#57711yescharacteristic
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—42no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4#53211yescharacteristic
654C3×C4#53511yescharacteristic
655C3×C4#54611yescharacteristic
656C3×C4#54611yescharacteristic
657C23—22no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23C22×C3×D411yescharacteristic
679Q8—22no—
680Q8—22no—
681Q8—44no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4C3×#12012yes—
735C2×C4C3×#12012yes—
736C2×C4C3×#13512yes—
737C2×C4C22×C3×D411yescharacteristic
738C2×C4C22×C3×D411yescharacteristic
739C2×C4C2×C3×#4111yescharacteristic
740C2×C4C2×C3×#4111yescharacteristic
741C2×C4C3×H(5,𝔽2)11yescharacteristic
742C2×C4C3×H(5,𝔽2)11yescharacteristic
743C8—22no—
744C8—22no—
745C8—41no—
746C8—41no—
747C2×C3—82no—
748C2×C3—82no—
749C2×C3—161no—
750C2×C3#243111yescharacteristic
751C2×C3#300211yescharacteristic
752C2×C3#301211yescharacteristic
753C2×C3#339411yescharacteristic
754C2×C3#339611yescharacteristic
755C2×C3#340111yescharacteristic
756C2×C3#340311yescharacteristic
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22C2×C3×#12011yescharacteristic
779C22C3×#55011yescharacteristic
780C22C3×#55011yescharacteristic
781C22C2×C3×#13511yescharacteristic
782C22C3×#57511yescharacteristic
783C22C3×#57611yescharacteristic
784C22C3×#57711yescharacteristic
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C3×#53211yescharacteristic
797C4C3×#53511yescharacteristic
798C4C3×#54611yescharacteristic
799C4C3×#54611yescharacteristic
800C3#2563511yescharacteristic, direct product factor, Sylow
801C2—82no—
802C2—82no—
803C2—161no—
804C2C3×#243111yescharacteristic
805C2C3×#300211yescharacteristic
806C2C3×#301211yescharacteristic
807C2C3×#339411yescharacteristic
808C2C3×#339611yescharacteristic
809C2C3×#340111yescharacteristic
810C2C3×#340311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#559C2semidirect
2. C2×C3×#495C2semidirect
3. C2×C3×#463C2semidirect
4. C3×#2592C2semidirect
5. C3×#2015C2semidirect
6. C3×#2014C2semidirect
7. C3×#2012C2semidirect
9. C3×#1984C2semidirect
10. C3×#1983C2semidirect
11. C3×#1880C2semidirect
12. C3×#1879C2semidirect
13. C3×#1878C2semidirect
14. C3×#1877C2semidirect
15. C3×C4×#102C2semidirect
16. #25635C3direct (N × H)
64. C2×#559C2×C3semidirect
65. C2×#495C2×C3semidirect
66. C2×#463C2×C3semidirect
67. #2592C2×C3semidirect
68. #2015C2×C3semidirect
69. #2014C2×C3semidirect
70. #2012C2×C3semidirect
72. #1984C2×C3semidirect
73. #1983C2×C3semidirect
74. #1880C2×C3semidirect
75. #1879C2×C3semidirect
76. #1878C2×C3semidirect
77. #1877C2×C3semidirect
78. C4×#102C2×C3semidirect
800. C3#25635direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5592
C2×C3×#4952
C2×C3×#4632
C3×#25922
C3×#20152
C3×#20142
C3×#20122
C3×#20112
C3×#19842
C3×#19832
C3×#18802
C3×#18792
C3×#18782
C3×#18772
C3×C4×#1022
#256353