Finite Group Databasebeta

← C3×#30469 #10649076

Subgroups — C3×#30469 #10649076

Order 768.

1100 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#497C211yesmaximal, characteristic, complemented
2C2×C3×#461C211yesmaximal, characteristic, complemented
3C2×C3×#451C211yesmaximal, characteristic, complemented
4C2×C3×#448C211yesmaximal, characteristic
5C3×#2434C211yesmaximal, characteristic, complemented
6C3×#2427C211yesmaximal, characteristic
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2043C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#2001C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic
13C3×#1935C211yesmaximal, characteristic, complemented
14C3×#1924C211yesmaximal, characteristic, complemented
15C3×#1877C211yesmaximal, characteristic, complemented
16#30469C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×Q8C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C3×#497—24no—
32C3×#461—24no—
33C3×#451—24no—
34C3×#448—24no—
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×#97C2211yescharacteristic
47C3×#397—21no—
48C3×#395—21no—
49C3×#395—21no—
50C3×#394—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#386—21no—
56C3×#385—21no—
57C3×#385—21no—
58C3×#380—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#497C2×C311yescharacteristic, complemented
65C2×#461C2×C311yescharacteristic, complemented
66C2×#451C2×C311yescharacteristic, complemented
67C2×#448C2×C311yescharacteristic
68#2434C2×C311yescharacteristic, complemented
69#2427C2×C311yescharacteristic
70#2056C2×C311yescharacteristic, complemented
71#2043C2×C311yescharacteristic, complemented
72#2016C2×C311yescharacteristic, complemented
73#2015C2×C311yescharacteristic, complemented
74#2001C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic
76#1935C2×C311yescharacteristic, complemented
77#1924C2×C311yescharacteristic, complemented
78#1877C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C22×C3×Q8—41no—
85C22×C3×Q8—41no—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×Q8C2311yescharacteristic
90C22×C3×D4—21no—
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—21no—
93C23×C3×C4—21no—
94C23×C3×C4C2311yescharacteristic
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×Q16—22no—
99C2×C3×Q16—41no—
100C2×C3×Q16—41no—
101C2×C3×Q16—41no—
102C2×C3×Q16—41no—
103C2×C3×Q16—41no—
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16—41no—
109C2×C3×SD16—41no—
110C2×C3×SD16—41no—
111C2×C3×SD16—41no—
112C2×C3×SD16D414yes—
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C3×C4⋊Q8—22no—
118C3×C4⋊Q8—22no—
119C3×C4⋊Q8—41no—
120C3×C4⋊Q8—41no—
121C3×#124—22no—
122C3×#124—41no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—41no—
125C3×C22⋊Q8—41no—
126C3×C22⋊Q8—41no—
127C3×#121—22no—
128C3×#121—41no—
129C3×C4×D4—22no—
130C3×C4×D4—41no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
148C2×C3×C22⋊C4D411yescharacteristic
149C2×C3×C42C2311yescharacteristic
150C2×C3×C42C2311yescharacteristic
151C3×C4⋊C8—22no—
152C3×#103—22no—
153C3×#103—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—41no—
157C3×#103—41no—
158C3×#103D414yescomplemented
159C3×#102—41no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—22no—
162C3×#97—22no—
163C3×#95—21no—
164C3×#95—21no—
165C3×#95—21no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C3×#95D411yescharacteristic
171C3×#95D411yescharacteristic
172C23×Q8C22×C311yescharacteristic
173C22×Q16C22×C311yescharacteristic
174C22×Q16C22×C311yescharacteristic
175C22×Q16C22×C311yescharacteristic
176C22×SD16C22×C311yescharacteristic
177C22×SD16C22×C311yescharacteristic
178C22×SD16C22×C311yescharacteristic
179C2×C4⋊Q8C22×C311yescharacteristic
180C2×C4⋊Q8C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×D4C22×C311yescharacteristic
186#497—24no—
187#461—24no—
188#451—24no—
189#448—24no—
190C2×C4⋊C8C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#103C22×C311yescharacteristic
197C2×#103C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×C22⋊C8C22×C311yescharacteristic
200C2×C22⋊C8C22×C311yescharacteristic
201C2×#97C22×C311yescharacteristic
202#397—21no—
203#395—21no—
204#395—21no—
205#394—21no—
206#391C22×C311yescharacteristic
207#391C22×C311yescharacteristic
208#391C22×C311yescharacteristic
209#389C22×C311yescharacteristic
210#386—21no—
211#385—21no—
212#385—21no—
213#380—21no—
214C4×C22⋊C4C22×C311yescharacteristic
215#340C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217#336C22×C311yescharacteristic
218#336C22×C311yescharacteristic
219C24×C3—21no—
220C24×C3C2×D411yescharacteristic
221C2×C3×Q8—21no—
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—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—42no—
244C2×C3×Q8—42no—
245C2×C3×Q8—42no—
246C2×C3×Q8—44no—
247C2×C3×Q8—44no—
248C2×C3×Q8—44no—
249C2×C3×Q8—44no—
250C2×C3×Q8C2×D412yes—
251C2×C3×Q8C2×D412yes—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4—81no—
260C2×C3×D4C2×D412yes—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—42no—
275C22×C3×C4—42no—
276C22×C3×C4—42no—
277C22×C3×C4—42no—
278C22×C3×C4—42no—
279C22×C3×C4—81no—
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C3×Q16—44no—
287C3×Q16—44no—
288C3×Q16—44no—
289C3×SD16—44no—
290C3×SD16—44no—
291C3×SD16—44no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8C2×D412yes—
303C2×C3×C8C2×D412yes—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—42no—
310C3×C4⋊C4—42no—
311C3×C4⋊C4—42no—
312C3×C4⋊C4—42no—
313C3×C4⋊C4—42no—
314C3×C4⋊C4—42no—
315C3×C4⋊C4—81no—
316C3×C4⋊C4C2×D412yes—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42—21no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—41no—
333C22×Q8—41no—
334C22×Q8—41no—
335C22×Q8—41no—
336C22×Q8C23×C311yescharacteristic
337C22×Q8C23×C311yescharacteristic
338C22×Q8C23×C311yescharacteristic
339C22×Q8C23×C311yescharacteristic
340C22×D4—21no—
341C22×D4C23×C311yescharacteristic
342C23×C4—21no—
343C23×C4—21no—
344C23×C4C23×C311yescharacteristic
345C2×Q16—22no—
346C2×Q16—22no—
347C2×Q16—22no—
348C2×Q16—22no—
349C2×Q16—41no—
350C2×Q16—41no—
351C2×Q16—41no—
352C2×Q16—41no—
353C2×Q16—41no—
354C2×SD16—22no—
355C2×SD16—22no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—41no—
359C2×SD16—41no—
360C2×SD16—41no—
361C2×SD16—41no—
362C2×SD16C3×D414yes—
363C22×C8C23×C311yescharacteristic
364C22×C8C23×C311yescharacteristic
365C22×C8C23×C311yescharacteristic
366C22×C8C23×C311yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369C4⋊Q8—41no—
370C4⋊Q8—41no—
371#124—22no—
372#124—41no—
373C22⋊Q8—22no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C22⋊Q8—41no—
377#121—22no—
378#121—41no—
379C4×D4—22no—
380C4×D4—41no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4C23×C311yescharacteristic
389C2×C4⋊C4C23×C311yescharacteristic
390C2×C4⋊C4C23×C311yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4C3×D411yescharacteristic
398C2×C22⋊C4C3×D411yescharacteristic
399C2×C42C23×C311yescharacteristic
400C2×C42C23×C311yescharacteristic
401C4⋊C8—22no—
402#103—22no—
403#103—22no—
404#103—22no—
405#103—22no—
406#103—41no—
407#103—41no—
408#103C3×D414yescomplemented
409#102—41no—
410C22⋊C8—22no—
411C22⋊C8—22no—
412#97—22no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95C3×D411yescharacteristic
421#95C3×D411yescharacteristic
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—41no—
430C23×C3—41no—
431C23×C3—41no—
432C23×C3—41no—
433C23×C3—41no—
434C23×C3—41no—
435C23×C3#13712yes—
436C23×C3C22×D411yescharacteristic
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8—48no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×Q8—41no—
446C3×Q8—41no—
447C3×Q8—41no—
448C3×Q8—41no—
449C3×Q8—41no—
450C3×Q8—41no—
451C3×Q8—41no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×D4—22no—
455C3×D4—22no—
456C3×D4—41no—
457C3×D4—41no—
458C3×D4—84no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—48no—
477C2×C3×C4—41no—
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—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—84no—
500C2×C3×C4#13712yes—
501C2×C3×C4C22×D411yescharacteristic
502C2×C3×C4C22×D411yescharacteristic
503C2×C3×C4H(5,𝔽2)11yescharacteristic
504C2×C3×C4H(5,𝔽2)11yescharacteristic
505C2×C3×C4H(5,𝔽2)11yescharacteristic
506C2×C3×C4H(5,𝔽2)11yescharacteristic
507C3×C8—22no—
508C3×C8—22no—
509C3×C8—41no—
510C3×C8—41no—
511C24—21no—
512C24C2×C3×D411yescharacteristic
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—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—42no—
536C2×Q8—42no—
537C2×Q8—42no—
538C2×Q8—44no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8—44no—
542C2×Q8C2×C3×D412yes—
543C2×Q8C2×C3×D412yes—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4—81no—
552C2×D4C2×C3×D412yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—81no—
572C22×C4C2×C3×D411yescharacteristic
573C22×C4C2×C3×D411yescharacteristic
574C22×C4C2×C3×D411yescharacteristic
575C22×C4C2×C3×D411yescharacteristic
576C22×C4C2×C3×D411yescharacteristic
577C22×C4C24×C311yescharacteristic
578Q16—44no—
579Q16—44no—
580Q16—44no—
581SD16—44no—
582SD16—44no—
583SD16—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8C2×C3×D412yes—
595C2×C8C2×C3×D412yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—42no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—81no—
608C4⋊C4C2×C3×D412yes—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—22no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3#53511yescharacteristic
636C22×C3D4211yescharacteristic
637C22×C3D4211yescharacteristic
638C22×C3C2×#13711yescharacteristic
639C22×C3C2×#13711yescharacteristic
640C22×C3#57711yescharacteristic
641C22×C3#57811yescharacteristic
642C3×C4—22no—
643C3×C4—41no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4—81no—
653C3×C4—81no—
654C3×C4#53411yescharacteristic
655C3×C4#53511yescharacteristic
656C3×C4D4211yescharacteristic
657C3×C4#56011yescharacteristic
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C3×#13712yes—
672C23C22×C3×D411yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—48no—
678Q8—41no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689Q8—41no—
690D4—22no—
691D4—22no—
692D4—41no—
693D4—41no—
694D4—84no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—48no—
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—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—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—84no—
736C2×C4C3×#13712yes—
737C2×C4C22×C3×D411yescharacteristic
738C2×C4C22×C3×D411yescharacteristic
739C2×C4C3×H(5,𝔽2)11yescharacteristic
740C2×C4C3×H(5,𝔽2)11yescharacteristic
741C2×C4C3×H(5,𝔽2)11yescharacteristic
742C2×C4C3×H(5,𝔽2)11yescharacteristic
743C8—22no—
744C8—22no—
745C8—41no—
746C8—41no—
747C2×C3—42no—
748C2×C3—82no—
749C2×C3#266911yescharacteristic
750C2×C3#321811yescharacteristic
751C2×C3#322511yescharacteristic
752C2×C3#326611yescharacteristic
753C2×C3#326611yescharacteristic
754C2×C3#327011yescharacteristic
755C2×C3#327611yescharacteristic
756C22—22no—
757C22—22no—
758C22—22no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22C3×#53511yescharacteristic
771C22C3×D4211yescharacteristic
772C22C3×D4211yescharacteristic
773C22C2×C3×#13711yescharacteristic
774C22C2×C3×#13711yescharacteristic
775C22C3×#57711yescharacteristic
776C22C3×#57811yescharacteristic
777C4—22no—
778C4—41no—
779C4—42no—
780C4—42no—
781C4—41no—
782C4—42no—
783C4—41no—
784C4—41no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4—81no—
789C4C3×#53411yescharacteristic
790C4C3×#53511yescharacteristic
791C4C3×D4211yescharacteristic
792C4C3×#56011yescharacteristic
793C3#3046911yescharacteristic, direct product factor, Sylow
794C2—42no—
795C2—82no—
796C2C3×#266911yescharacteristic
797C2C3×#321811yescharacteristic
798C2C3×#322511yescharacteristic
799C2C3×#326611yescharacteristic
800C2C3×#326611yescharacteristic
801C2C3×#327011yescharacteristic
802C2C3×#327611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#497C2semidirect
2. C2×C3×#461C2semidirect
3. C2×C3×#451C2semidirect
5. C3×#2434C2semidirect
7. C3×#2056C2semidirect
8. C3×#2043C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
11. C3×#2001C2semidirect
13. C3×#1935C2semidirect
14. C3×#1924C2semidirect
15. C3×#1877C2semidirect
16. #30469C3direct (N × H)
64. C2×#497C2×C3semidirect
65. C2×#461C2×C3semidirect
66. C2×#451C2×C3semidirect
68. #2434C2×C3semidirect
70. #2056C2×C3semidirect
71. #2043C2×C3semidirect
72. #2016C2×C3semidirect
73. #2015C2×C3semidirect
74. #2001C2×C3semidirect
76. #1935C2×C3semidirect
77. #1924C2×C3semidirect
78. #1877C2×C3semidirect
158. C3×#103D4semidirect
408. #103C3×D4semidirect
793. C3#30469direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4972
C2×C3×#4612
C2×C3×#4512
C2×C3×#4482
C3×#24342
C3×#24272
C3×#20562
C3×#20432
C3×#20162
C3×#20152
C3×#20012
C3×#20002
C3×#19352
C3×#19242
C3×#18772
#304693