Finite Group Databasebeta

← C3×#30415 #10649022

Subgroups — C3×#30415 #10649022

Order 768.

1052 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#468C211yesmaximal, characteristic, complemented
2C2×C3×#448C211yesmaximal, characteristic, complemented
3C3×#2537C211yesmaximal, characteristic
4C3×#2409C211yesmaximal, characteristic, complemented
5C3×#2095C211yesmaximal, characteristic, complemented
6C3×#2075C211yesmaximal, characteristic, complemented
7C3×#2072C211yesmaximal, characteristic, complemented
8C3×#2036C211yesmaximal, characteristic, complemented
9C3×#2033C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1877C211yesmaximal, characteristic, complemented
13C3×#1877C211yesmaximal, characteristic, complemented
14C3×#1870C211yesmaximal, characteristic, complemented
15C3×#1787C211yesmaximal, characteristic, complemented
16#30415C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×#121—21no—
24C2×C3×#121C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C3×#468—24no—
29C3×#448—24no—
30C2×C3×#107C2211yescharacteristic
31C2×C3×#107C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×C22⋊C8C2211yescharacteristic
42C2×C3×C22⋊C8C2211yescharacteristic
43C3×#395—21no—
44C3×#394—21no—
45C3×#394—21no—
46C3×#393—21no—
47C3×#391C2211yescharacteristic
48C3×#391C2211yescharacteristic
49C3×#386—21no—
50C3×#385—21no—
51C3×#384C2211yescharacteristic
52C3×#380—21no—
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#468C2×C311yescharacteristic, complemented
63C2×#448C2×C311yescharacteristic, complemented
64#2537C2×C311yescharacteristic
65#2409C2×C311yescharacteristic, complemented
66#2095C2×C311yescharacteristic, complemented
67#2075C2×C311yescharacteristic, complemented
68#2072C2×C311yescharacteristic, complemented
69#2036C2×C311yescharacteristic, complemented
70#2033C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1894C2×C311yescharacteristic, complemented
73#1877C2×C311yescharacteristic, complemented
74#1877C2×C311yescharacteristic, complemented
75#1870C2×C311yescharacteristic, complemented
76#1787C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—41no—
81C22×C3×Q8—41no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4D411yescharacteristic
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C2×C3×SD16—22no—
95C2×C3×SD16—22no—
96C2×C3×SD16—41no—
97C2×C3×SD16—41no—
98C2×C3×SD16—41no—
99C2×C3×SD16D414yescomplemented
100C2×C3×M16—22no—
101C2×C3×M16—41no—
102C2×C3×M16—41no—
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—41no—
110C3×C22⋊Q8—41no—
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—41no—
114C3×#121—41no—
115C3×#121—44no—
116C3×C4×D4—41no—
117C3×C4×D4—41no—
118C3×C4×D4—41no—
119C3×C4×D4—41no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
126C2×C3×C4⋊C4C2311yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4D411yescharacteristic
139C2×C3×C22⋊C4D411yescharacteristic
140C2×C3×C42C2311yescharacteristic
141C3×#107—22no—
142C3×#107—41no—
143C3×#103—22no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#103—41no—
147C3×#103—41no—
148C3×#103—41no—
149C3×#102—22no—
150C3×#102—41no—
151C3×C22⋊C8—22no—
152C3×C22⋊C8—41no—
153C3×C22⋊C8—41no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158C3×#95—21no—
159C3×#95—21no—
160C3×#95—21no—
161C23×Q8C22×C311yescharacteristic
162C22×SD16C22×C311yescharacteristic
163C22×SD16C22×C311yescharacteristic
164C22×M16C22×C311yescharacteristic
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×#121—21no—
168C2×#121C22×C311yescharacteristic
169C2×#121C22×C311yescharacteristic
170C2×C4×D4C22×C311yescharacteristic
171C2×C4×D4C22×C311yescharacteristic
172#468—24no—
173#448—24no—
174C2×#107C22×C311yescharacteristic
175C2×#107C22×C311yescharacteristic
176C2×#103C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×C22⋊C8C22×C311yescharacteristic
185C2×C22⋊C8C22×C311yescharacteristic
186C2×C22⋊C8C22×C311yescharacteristic
187#395—21no—
188#394—21no—
189#394—21no—
190#393—21no—
191#391C22×C311yescharacteristic
192#391C22×C311yescharacteristic
193#386—21no—
194#385—21no—
195#384C22×C311yescharacteristic
196#380—21no—
197#380C22×C311yescharacteristic
198#380C22×C311yescharacteristic
199#380C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205#336C22×C311yescharacteristic
206C24×C3—21no—
207C24×C3C2×D411yescharacteristic
208C24×C3C2×D411yescharacteristic
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—42no—
220C2×C3×Q8—42no—
221C2×C3×Q8—42no—
222C2×C3×Q8—44no—
223C2×C3×Q8—44no—
224C2×C3×Q8—44no—
225C2×C3×Q8—44no—
226C2×C3×Q8C2×D412yes—
227C2×C3×Q8#4112yes—
228C2×C3×D4—22no—
229C2×C3×D4—22no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—41no—
236C2×C3×D4—42no—
237C2×C3×D4—42no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—81no—
241C2×C3×D4—81no—
242C2×C3×D4C2×D412yes—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—42no—
263C22×C3×C4—42no—
264C22×C3×C4—42no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—42no—
268C22×C3×C4C2×D411yescharacteristic
269C22×C3×C4C2×D411yescharacteristic
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2411yescharacteristic
273C3×SD16—44no—
274C3×SD16—44no—
275C3×M16—44no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8—21no—
287C2×C3×C8C2×D412yes—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4—21no—
292C3×C4⋊C4—21no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—41no—
299C3×C4⋊C4—42no—
300C3×C4⋊C4—42no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4—81no—
303C3×C22⋊C4—41no—
304C3×C22⋊C4—41no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—42no—
307C3×C22⋊C4—42no—
308C3×C22⋊C4—42no—
309C3×C22⋊C4—42no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313C3×C42—21no—
314C3×C42—21no—
315C22×Q8—21no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—41no—
319C22×Q8—41no—
320C22×Q8—41no—
321C22×Q8—41no—
322C22×Q8C23×C311yescharacteristic
323C22×Q8C23×C311yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C3×D411yescharacteristic
327C22×D4C23×C311yescharacteristic
328C23×C4—21no—
329C23×C4—21no—
330C23×C4C23×C311yescharacteristic
331C23×C4C23×C311yescharacteristic
332C2×SD16—22no—
333C2×SD16—22no—
334C2×SD16—41no—
335C2×SD16—41no—
336C2×SD16—41no—
337C2×SD16C3×D414yescomplemented
338C2×M16—22no—
339C2×M16—41no—
340C2×M16—41no—
341C22×C8C23×C311yescharacteristic
342C22×C8C23×C311yescharacteristic
343C22×C8C23×C311yescharacteristic
344C22×C8C23×C311yescharacteristic
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—41no—
348C22⋊Q8—41no—
349#121—22no—
350#121—22no—
351#121—41no—
352#121—41no—
353#121—44no—
354C4×D4—41no—
355C4×D4—41no—
356C4×D4—41no—
357C4×D4—41no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4C3×D411yescharacteristic
363C2×C4⋊C4C23×C311yescharacteristic
364C2×C4⋊C4C23×C311yescharacteristic
365C2×C4⋊C4C23×C311yescharacteristic
366C2×C4⋊C4C23×C311yescharacteristic
367C2×C4⋊C4C23×C311yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4C3×D411yescharacteristic
377C2×C22⋊C4C3×D411yescharacteristic
378C2×C42C23×C311yescharacteristic
379#107—22no—
380#107—41no—
381#103—22no—
382#103—22no—
383#103—22no—
384#103—41no—
385#103—41no—
386#103—41no—
387#102—22no—
388#102—41no—
389C22⋊C8—22no—
390C22⋊C8—41no—
391C22⋊C8—41no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3AGL(1,ℤ/8)12yes—
420C23×C3C22×D411yescharacteristic
421C3×Q8—22no—
422C3×Q8—22no—
423C3×Q8—22no—
424C3×Q8—22no—
425C3×Q8—48no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×Q8—41no—
429C3×Q8—41no—
430C3×D4—22no—
431C3×D4—22no—
432C3×D4—44no—
433C3×D4—41no—
434C3×D4—41no—
435C3×D4—84no—
436C3×D4—84no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—48no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—84no—
479C2×C3×C4#13712yes—
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484C2×C3×C4H(5,𝔽2)11yescharacteristic
485C2×C3×C4H(5,𝔽2)11yescharacteristic
486C3×C8—22no—
487C3×C8—41no—
488C3×C8—41no—
489C3×C8—41no—
490C24—21no—
491C24C2×C3×D411yescharacteristic
492C24C2×C3×D411yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8C2×C3×D412yes—
511C2×Q8C3×#4112yes—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—41no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C2×C3×D412yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4C2×C3×D411yescharacteristic
553C22×C4C2×C3×D411yescharacteristic
554C22×C4C2×C3×D411yescharacteristic
555C22×C4C2×C3×D411yescharacteristic
556C22×C4C24×C311yescharacteristic
557SD16—44no—
558SD16—44no—
559M16—44no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8C2×C3×D412yes—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—41no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—81no—
587C22⋊C4—41no—
588C22⋊C4—41no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—42no—
597C42—21no—
598C42—21no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—42no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—42no—
613C22×C3—41no—
614C22×C3—42no—
615C22×C3—41no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3#53411yescharacteristic
621C22×C3D4211yescharacteristic
622C22×C3#54611yescharacteristic
623C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
624C22×C3C2×#13711yescharacteristic
625C22×C3#57711yescharacteristic
626C22×C3#57811yescharacteristic
627C3×C4—22no—
628C3×C4—41no—
629C3×C4—41no—
630C3×C4—42no—
631C3×C4—42no—
632C3×C4—41no—
633C3×C4—81no—
634C3×C4—81no—
635C3×C4—81no—
636C3×C4—81no—
637C3×C4—81no—
638C3×C4#53411yescharacteristic
639C3×C4#53811yescharacteristic
640C3×C4#54611yescharacteristic
641C3×C4#56011yescharacteristic
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23C3×AGL(1,ℤ/8)12yes—
663C23C22×C3×D411yescharacteristic
664Q8—22no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—48no—
669Q8—41no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673D4—22no—
674D4—22no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—84no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—48no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4C3×#13712yes—
723C2×C4C22×C3×D411yescharacteristic
724C2×C4C2×C3×#4111yescharacteristic
725C2×C4C3×H(5,𝔽2)11yescharacteristic
726C2×C4C3×H(5,𝔽2)11yescharacteristic
727C2×C4C3×H(5,𝔽2)11yescharacteristic
728C2×C4C3×H(5,𝔽2)11yescharacteristic
729C8—22no—
730C8—41no—
731C8—41no—
732C8—41no—
733C2×C3—42no—
734C2×C3—81no—
735C2×C3—82no—
736C2×C3#266811yescharacteristic
737C2×C3#319311yescharacteristic
738C2×C3#320111yescharacteristic
739C2×C3#326511yescharacteristic
740C2×C3#327611yescharacteristic
741C2×C3#330811yescharacteristic
742C2×C3#332911yescharacteristic
743C22—22no—
744C22—22no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22C3×#53411yescharacteristic
765C22C3×D4211yescharacteristic
766C22C3×#54611yescharacteristic
767C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
768C22C2×C3×#13711yescharacteristic
769C22C3×#57711yescharacteristic
770C22C3×#57811yescharacteristic
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—42no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4C3×#53411yescharacteristic
783C4C3×#53811yescharacteristic
784C4C3×#54611yescharacteristic
785C4C3×#56011yescharacteristic
786C3#3041511yescharacteristic, direct product factor, Sylow
787C2—42no—
788C2—81no—
789C2—82no—
790C2C3×#266811yescharacteristic
791C2C3×#319311yescharacteristic
792C2C3×#320111yescharacteristic
793C2C3×#326511yescharacteristic
794C2C3×#327611yescharacteristic
795C2C3×#330811yescharacteristic
796C2C3×#332911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#468C2semidirect
2. C2×C3×#448C2semidirect
4. C3×#2409C2semidirect
5. C3×#2095C2semidirect
6. C3×#2075C2semidirect
7. C3×#2072C2semidirect
8. C3×#2036C2semidirect
9. C3×#2033C2semidirect
10. C3×#2000C2semidirect
11. C3×#1894C2semidirect
12. C3×#1877C2semidirect
13. C3×#1877C2semidirect
14. C3×#1870C2semidirect
15. C3×#1787C2semidirect
16. #30415C3direct (N × H)
62. C2×#468C2×C3semidirect
63. C2×#448C2×C3semidirect
65. #2409C2×C3semidirect
66. #2095C2×C3semidirect
67. #2075C2×C3semidirect
68. #2072C2×C3semidirect
69. #2036C2×C3semidirect
70. #2033C2×C3semidirect
71. #2000C2×C3semidirect
72. #1894C2×C3semidirect
73. #1877C2×C3semidirect
74. #1877C2×C3semidirect
75. #1870C2×C3semidirect
76. #1787C2×C3semidirect
99. C2×C3×SD16D4semidirect
337. C2×SD16C3×D4semidirect
786. C3#30415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4682
C2×C3×#4482
C3×#25372
C3×#24092
C3×#20952
C3×#20752
C3×#20722
C3×#20362
C3×#20332
C3×#20002
C3×#18942
C3×#18772
C3×#18702
C3×#17872
#304153