Finite Group Databasebeta

← C3×#29666 #10648273

Subgroups — C3×#29666 #10648273

Order 768.

1190 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#463C211yesmaximal, characteristic, complemented
4C3×#2850C211yesmaximal, characteristic, complemented
5C3×#2026C211yesmaximal, characteristic, complemented
6C3×#2025C211yesmaximal, characteristic, complemented
7C3×#2015C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic, complemented
9C3×#2001C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic
13C3×#1805C211yesmaximal, characteristic, complemented
14C3×#1804C211yesmaximal, characteristic, complemented
15C3×#1797C211yesmaximal, characteristic, complemented
16#29666C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C3×#529—24no—
22C3×#529—24no—
23C2×C3×#126—21no—
24C2×C3×#125C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×#123—21no—
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×D4—21no—
34C2×C3×C4×D4C2211yescharacteristic
35C2×C3×#117—21no—
36C22×C3×C42C2211yescharacteristic
37C3×#464—24no—
38C3×#463—24no—
39C2×C3×C4⋊C8C2211yescharacteristic
40C2×C3×C4⋊C8C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C3×#391C2211yescharacteristic
52C3×#390C2211yescharacteristic
53C3×#388—21no—
54C3×#388—21no—
55C3×#386—21no—
56C3×#386—21no—
57C3×#382C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#529C2×C311yescharacteristic, complemented
65C2×#464C2×C311yescharacteristic, complemented
66C2×#463C2×C311yescharacteristic, complemented
67#2850C2×C311yescharacteristic, complemented
68#2026C2×C311yescharacteristic, complemented
69#2025C2×C311yescharacteristic, complemented
70#2015C2×C311yescharacteristic, complemented
71#2012C2×C311yescharacteristic, complemented
72#2001C2×C311yescharacteristic, complemented
73#2000C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic
76#1805C2×C311yescharacteristic, complemented
77#1804C2×C311yescharacteristic, complemented
78#1797C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4D411yescharacteristic
87C23×C3×C4D411yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C2×C3×Q16—22no—
90C2×C3×Q16—41no—
91C2×C3×Q16—41no—
92C2×C3×SD16—22no—
93C2×C3×SD16—22no—
94C2×C3×SD16—41no—
95C2×C3×SD16—41no—
96C2×C3×SD16—41no—
97C2×C3×SD16—41no—
98C2×C3×D8—22no—
99C2×C3×D8—41no—
100C2×C3×D8—41no—
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×#126—28no—
106C3×#125—22no—
107C3×#125—22no—
108C3×#124—22no—
109C3×#124—22no—
110C3×#124—22no—
111C3×#124—22no—
112C3×#123—28no—
113C3×C22⋊Q8—22no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—41no—
116C3×C22⋊Q8—41no—
117C3×#121—22no—
118C3×#121—22no—
119C3×#121—41no—
120C3×#121—41no—
121C3×C4×Q8—22no—
122C3×C4×Q8D414yescomplemented
123C3×C4×D4—28no—
124C3×C4×D4—22no—
125C3×C4×D4D414yescomplemented
126C3×#117—28no—
127C2×C3×C4⋊C4—21no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
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×C42—21no—
148C2×C3×C42—22no—
149C2×C3×C42—22no—
150C2×C3×C42D411yescharacteristic
151C2×C3×C42D411yescharacteristic
152C2×C3×C42C2311yescharacteristic
153C2×C3×C42C2311yescharacteristic
154C3×C4⋊C8—22no—
155C3×C4⋊C8—22no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#103—41no—
159C3×#103—41no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—41no—
163C3×#102—41no—
164C3×C22⋊C8—41no—
165C3×C22⋊C8—41no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C22×Q16C22×C311yescharacteristic
171C22×SD16C22×C311yescharacteristic
172C22×SD16C22×C311yescharacteristic
173C22×D8C22×C311yescharacteristic
174#529—24no—
175#529—24no—
176C2×#126—21no—
177C2×#125C22×C311yescharacteristic
178C2×#124C22×C311yescharacteristic
179C2×#124C22×C311yescharacteristic
180C2×#123—21no—
181C2×C22⋊Q8C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×#121C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×Q8C22×C311yescharacteristic
186C2×C4×D4—21no—
187C2×C4×D4C22×C311yescharacteristic
188C2×#117—21no—
189C22×C42C22×C311yescharacteristic
190#464—24no—
191#463—24no—
192C2×C4⋊C8C22×C311yescharacteristic
193C2×C4⋊C8C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#103C22×C311yescharacteristic
196C2×#103C22×C311yescharacteristic
197C2×#103C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×#102C22×C311yescharacteristic
202C2×C22⋊C8C22×C311yescharacteristic
203C2×C22⋊C8C22×C311yescharacteristic
204#391C22×C311yescharacteristic
205#390C22×C311yescharacteristic
206#388—21no—
207#388—21no—
208#386—21no—
209#386—21no—
210#382C22×C311yescharacteristic
211#340C22×C311yescharacteristic
212#340C22×C311yescharacteristic
213#340C22×C311yescharacteristic
214#340C22×C311yescharacteristic
215#336C22×C311yescharacteristic
216#336C22×C311yescharacteristic
217C24×C3—21no—
218C24×C3—21no—
219C24×C3C2×D411yescharacteristic
220C2×C3×Q8—21no—
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×Q8C2×D412yes—
232C2×C3×D4—24no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
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—42no—
245C2×C3×D4—42no—
246C2×C3×D4—42no—
247C2×C3×D4—42no—
248C2×C3×D4—42no—
249C2×C3×D4C2×D412yes—
250C22×C3×C4—22no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—22no—
256C22×C3×C4—24no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—41no—
267C22×C3×C4—41no—
268C22×C3×C4—41no—
269C22×C3×C4—42no—
270C22×C3×C4—42no—
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×D8—44no—
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×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C3×C4⋊C4—24no—
294C3×C4⋊C4—24no—
295C3×C4⋊C4—24no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—42no—
304C3×C4⋊C4C2×D412yes—
305C3×C4⋊C4C2×D412yes—
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—42no—
316C3×C22⋊C4—42no—
317C3×C42—22no—
318C3×C42—22no—
319C3×C42—24no—
320C3×C42—21no—
321C3×C42—21no—
322C3×C42C2×D412yes—
323C3×C42C2×D412yes—
324C22×Q8C23×C311yescharacteristic
325C22×Q8C23×C311yescharacteristic
326C22×D4—21no—
327C22×D4—21no—
328C22×D4C23×C311yescharacteristic
329C22×D4C23×C311yescharacteristic
330C23×C4—21no—
331C23×C4C3×D411yescharacteristic
332C23×C4C3×D411yescharacteristic
333C23×C4C23×C311yescharacteristic
334C2×Q16—22no—
335C2×Q16—41no—
336C2×Q16—41no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—41no—
340C2×SD16—41no—
341C2×SD16—41no—
342C2×SD16—41no—
343C2×D8—22no—
344C2×D8—41no—
345C2×D8—41no—
346C22×C8C23×C311yescharacteristic
347C22×C8C23×C311yescharacteristic
348C22×C8C23×C311yescharacteristic
349C22×C8C23×C311yescharacteristic
350#126—28no—
351#125—22no—
352#125—22no—
353#124—22no—
354#124—22no—
355#124—22no—
356#124—22no—
357#123—28no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—41no—
361C22⋊Q8—41no—
362#121—22no—
363#121—22no—
364#121—41no—
365#121—41no—
366C4×Q8—22no—
367C4×Q8C3×D414yescomplemented
368C4×D4—28no—
369C4×D4—22no—
370C4×D4C3×D414yescomplemented
371#117—28no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4C23×C311yescharacteristic
378C2×C4⋊C4C23×C311yescharacteristic
379C2×C4⋊C4C23×C311yescharacteristic
380C2×C4⋊C4C23×C311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
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×C42—21no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42C3×D411yescharacteristic
396C2×C42C3×D411yescharacteristic
397C2×C42C23×C311yescharacteristic
398C2×C42C23×C311yescharacteristic
399C4⋊C8—22no—
400C4⋊C8—22no—
401#103—22no—
402#103—22no—
403#103—41no—
404#103—41no—
405#102—22no—
406#102—22no—
407#102—41no—
408#102—41no—
409C22⋊C8—41no—
410C22⋊C8—41no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—22no—
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#13512yes—
436C23×C3C22×D411yescharacteristic
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×Q8—41no—
442C3×Q8—41no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—22no—
446C3×D4—22no—
447C3×D4—48no—
448C3×D4—41no—
449C3×D4—41no—
450C3×D4—41no—
451C3×D4—41no—
452C3×D4—41no—
453C3×D4—41no—
454C3×D4—84no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—44no—
472C2×C3×C4—44no—
473C2×C3×C4—48no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
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#12012yes—
494C2×C3×C4#12012yes—
495C2×C3×C4C22×D411yescharacteristic
496C2×C3×C4C22×D411yescharacteristic
497C2×C3×C4H(5,𝔽2)11yescharacteristic
498C2×C3×C4H(5,𝔽2)11yescharacteristic
499C2×C3×C4H(5,𝔽2)11yescharacteristic
500C2×C3×C42−1+411yescharacteristic
501C3×C8—41no—
502C3×C8—41no—
503C3×C8—41no—
504C3×C8—41no—
505C24—21no—
506C24—21no—
507C24C2×C3×D411yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
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×Q8C2×C3×D412yes—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4C2×C3×D412yes—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4C2×C3×D411yescharacteristic
560C22×C4C2×C3×D411yescharacteristic
561C22×C4C2×C3×D411yescharacteristic
562C22×C4C2×C3×D411yescharacteristic
563C22×C4C2×C3×D411yescharacteristic
564C22×C4C24×C311yescharacteristic
565Q16—44no—
566SD16—44no—
567SD16—44no—
568D8—44no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
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—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—42no—
592C4⋊C4C2×C3×D412yes—
593C4⋊C4C2×C3×D412yes—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C42—22no—
606C42—22no—
607C42—24no—
608C42—21no—
609C42—21no—
610C42C2×C3×D412yes—
611C42C2×C3×D412yes—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
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×C3C2×#12011yescharacteristic
634C22×C3#53511yescharacteristic
635C22×C3#53711yescharacteristic
636C22×C3C2×#13511yescharacteristic
637C22×C3#57511yescharacteristic
638C22×C3#57511yescharacteristic
639C22×C3#57511yescharacteristic
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—41no—
643C3×C4—42no—
644C3×C4—41no—
645C3×C4—42no—
646C3×C4—41no—
647C3×C4—42no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4#53511yescharacteristic
652C3×C4#53511yescharacteristic
653C3×C4#53711yescharacteristic
654C3×C4#53711yescharacteristic
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—22no—
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—
675C23C3×#13512yes—
676C23C22×C3×D411yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681Q8—41no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
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—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—48no—
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×C4C3×#12012yes—
734C2×C4C3×#12012yes—
735C2×C4C22×C3×D411yescharacteristic
736C2×C4C22×C3×D411yescharacteristic
737C2×C4C3×H(5,𝔽2)11yescharacteristic
738C2×C4C3×H(5,𝔽2)11yescharacteristic
739C2×C4C3×H(5,𝔽2)11yescharacteristic
740C2×C4C3×2−1+411yescharacteristic
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C2×C3—42no—
746C2×C3—82no—
747C2×C3—161no—
748C2×C3#261511yescharacteristic
749C2×C3#300211yescharacteristic
750C2×C3#300511yescharacteristic
751C2×C3#321111yescharacteristic
752C2×C3#321911yescharacteristic
753C2×C3#325011yescharacteristic
754C2×C3#325611yescharacteristic
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22C2×C3×#12011yescharacteristic
777C22C3×#53511yescharacteristic
778C22C3×#53711yescharacteristic
779C22C2×C3×#13511yescharacteristic
780C22C3×#57511yescharacteristic
781C22C3×#57511yescharacteristic
782C22C3×#57511yescharacteristic
783C4—22no—
784C4—22no—
785C4—41no—
786C4—42no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4C3×#53511yescharacteristic
795C4C3×#53511yescharacteristic
796C4C3×#53711yescharacteristic
797C4C3×#53711yescharacteristic
798C3#2966611yescharacteristic, direct product factor, Sylow
799C2—42no—
800C2—82no—
801C2—161no—
802C2C3×#261511yescharacteristic
803C2C3×#300211yescharacteristic
804C2C3×#300511yescharacteristic
805C2C3×#321111yescharacteristic
806C2C3×#321911yescharacteristic
807C2C3×#325011yescharacteristic
808C2C3×#325611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C2×C3×#464C2semidirect
3. C2×C3×#463C2semidirect
4. C3×#2850C2semidirect
5. C3×#2026C2semidirect
6. C3×#2025C2semidirect
7. C3×#2015C2semidirect
8. C3×#2012C2semidirect
9. C3×#2001C2semidirect
10. C3×#2000C2semidirect
11. C3×#2000C2semidirect
13. C3×#1805C2semidirect
14. C3×#1804C2semidirect
15. C3×#1797C2semidirect
16. #29666C3direct (N × H)
64. C2×#529C2×C3semidirect
65. C2×#464C2×C3semidirect
66. C2×#463C2×C3semidirect
67. #2850C2×C3semidirect
68. #2026C2×C3semidirect
69. #2025C2×C3semidirect
70. #2015C2×C3semidirect
71. #2012C2×C3semidirect
72. #2001C2×C3semidirect
73. #2000C2×C3semidirect
74. #2000C2×C3semidirect
76. #1805C2×C3semidirect
77. #1804C2×C3semidirect
78. #1797C2×C3semidirect
122. C3×C4×Q8D4semidirect
125. C3×C4×D4D4semidirect
367. C4×Q8C3×D4semidirect
370. C4×D4C3×D4semidirect
798. C3#29666direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C3×#4642
C2×C3×#4632
C3×#28502
C3×#20262
C3×#20252
C3×#20152
C3×#20122
C3×#20012
C3×#20002
C3×#19992
C3×#18052
C3×#18042
C3×#17972
#296663