Finite Group Databasebeta

← C3×#24667 #10643274

Subgroups — C3×#24667 #10643274

Order 768.

912 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#463C211yesmaximal, characteristic, complemented
2C2×C3×#433C211yesmaximal, characteristic, complemented
3C3×#2620C211yesmaximal, characteristic, complemented
4C3×#2324C211yesmaximal, characteristic, complemented
5C3×#2035C211yesmaximal, characteristic, complemented
6C3×#2034C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8C3×#1999C211yesmaximal, characteristic
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1972C211yesmaximal, characteristic, complemented
11C3×#1968C211yesmaximal, characteristic, complemented
12C3×#1948C211yesmaximal, characteristic, complemented
13C3×#1935C211yesmaximal, characteristic, complemented
14C3×#1934C211yesmaximal, characteristic, complemented
15C3×#1802C211yesmaximal, characteristic, complemented
16#24667C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C2×C3×#117C2211yescharacteristic
25C3×#463—24no—
26C3×#433—24no—
27C2×C3×#106C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×#97C2211yescharacteristic
42C2×C3×C4×C8C2211yescharacteristic
43C3×#396—21no—
44C3×#396—21no—
45C3×#394—21no—
46C3×#394—21no—
47C3×#391C2211yescharacteristic
48C3×#390—21no—
49C3×#390C2211yescharacteristic
50C3×#390C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#388—21no—
53C3×#386—21no—
54C3×#385—21no—
55C3×#384C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C2×#463C2×C311yescharacteristic, complemented
63C2×#433C2×C311yescharacteristic, complemented
64#2620C2×C311yescharacteristic, complemented
65#2324C2×C311yescharacteristic, complemented
66#2035C2×C311yescharacteristic, complemented
67#2034C2×C311yescharacteristic, complemented
68#2000C2×C311yescharacteristic, complemented
69#1999C2×C311yescharacteristic
70#1983C2×C311yescharacteristic, complemented
71#1972C2×C311yescharacteristic, complemented
72#1968C2×C311yescharacteristic, complemented
73#1948C2×C311yescharacteristic, complemented
74#1935C2×C311yescharacteristic, complemented
75#1934C2×C311yescharacteristic, complemented
76#1802C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C2×C3×SD16—22no—
85C2×C3×SD16—22no—
86C2×C3×SD16—41no—
87C2×C3×D8—22no—
88C2×C3×D8—22no—
89C2×C3×D8—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×#124—22no—
95C3×#124—22no—
96C3×C22⋊Q8—41no—
97C3×C22⋊Q8—41no—
98C3×#121—22no—
99C3×#121—22no—
100C3×#121—41no—
101C3×#121—41no—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×#117—22no—
105C3×#117—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4D411yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C22⋊C4D411yescharacteristic
130C2×C3×C42—21no—
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C3×#106—41no—
134C3×#106—41no—
135C3×C4⋊C8—22no—
136C3×C4⋊C8D414yescomplemented
137C3×#103—22no—
138C3×#103—22no—
139C3×#103—41no—
140C3×#102—22no—
141C3×#102—22no—
142C3×#102—41no—
143C3×#102—41no—
144C3×#102—41no—
145C3×C22⋊C8—22no—
146C3×C22⋊C8—22no—
147C3×#97—22no—
148C3×C4×C8—22no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C22×SD16C22×C311yescharacteristic
155C22×D8C22×C311yescharacteristic
156C2×#124C22×C311yescharacteristic
157C2×C22⋊Q8C22×C311yescharacteristic
158C2×#121C22×C311yescharacteristic
159C2×#121C22×C311yescharacteristic
160C2×C4×D4C22×C311yescharacteristic
161C2×#117C22×C311yescharacteristic
162#463—24no—
163#433—24no—
164C2×#106C22×C311yescharacteristic
165C2×#106C22×C311yescharacteristic
166C2×C4⋊C8C22×C311yescharacteristic
167C2×C4⋊C8C22×C311yescharacteristic
168C2×#103C22×C311yescharacteristic
169C2×#103C22×C311yescharacteristic
170C2×#103C22×C311yescharacteristic
171C2×#102C22×C311yescharacteristic
172C2×#102C22×C311yescharacteristic
173C2×#102C22×C311yescharacteristic
174C2×#102C22×C311yescharacteristic
175C2×#102C22×C311yescharacteristic
176C2×C22⋊C8C22×C311yescharacteristic
177C2×C22⋊C8C22×C311yescharacteristic
178C2×#97C22×C311yescharacteristic
179C2×C4×C8C22×C311yescharacteristic
180#396—21no—
181#396—21no—
182#394—21no—
183#394—21no—
184#391C22×C311yescharacteristic
185#390—21no—
186#390C22×C311yescharacteristic
187#390C22×C311yescharacteristic
188#389C22×C311yescharacteristic
189#388—21no—
190#386—21no—
191#385—21no—
192#384C22×C311yescharacteristic
193#380C22×C311yescharacteristic
194C4×C4⋊C4C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199C24×C3—21no—
200C24×C3—21no—
201C24×C3C2×D411yescharacteristic
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×D4—24no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—42no—
221C2×C3×D4—81no—
222C2×C3×D4—81no—
223C2×C3×D4—81no—
224C2×C3×D4—81no—
225C2×C3×D4#4112yes—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—42no—
239C22×C3×C4—81no—
240C22×C3×C4—81no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C3×SD16—44no—
248C3×D8—44no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8C2×D412yes—
260C2×C3×C8C2×D412yes—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—81no—
274C3×C4⋊C4—81no—
275C3×C4⋊C4—81no—
276C3×C4⋊C4#4112yes—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—22no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—42no—
285C3×C22⋊C4—81no—
286C3×C22⋊C4—81no—
287C3×C22⋊C4—81no—
288C3×C22⋊C4—81no—
289C3×C22⋊C4—81no—
290C3×C42—21no—
291C3×C42—21no—
292C3×C42—81no—
293C3×C42C2×D412yes—
294C3×C42#4112yes—
295C22×Q8C23×C311yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4C23×C311yescharacteristic
299C22×D4C23×C311yescharacteristic
300C23×C4—21no—
301C23×C4C23×C311yescharacteristic
302C2×SD16—22no—
303C2×SD16—22no—
304C2×SD16—41no—
305C2×D8—22no—
306C2×D8—22no—
307C2×D8—41no—
308C22×C8C23×C311yescharacteristic
309C22×C8C23×C311yescharacteristic
310C22×C8C23×C311yescharacteristic
311C22×C8C23×C311yescharacteristic
312#124—22no—
313#124—22no—
314C22⋊Q8—41no—
315C22⋊Q8—41no—
316#121—22no—
317#121—22no—
318#121—41no—
319#121—41no—
320C4×D4—22no—
321C4×D4—22no—
322#117—22no—
323#117—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C3×D411yescharacteristic
329C2×C4⋊C4C3×D411yescharacteristic
330C2×C4⋊C4C23×C311yescharacteristic
331C2×C4⋊C4C23×C311yescharacteristic
332C2×C4⋊C4C23×C311yescharacteristic
333C2×C4⋊C4C23×C311yescharacteristic
334C2×C4⋊C4C23×C311yescharacteristic
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4C3×D411yescharacteristic
347C2×C22⋊C4C3×D411yescharacteristic
348C2×C42—21no—
349C2×C42C23×C311yescharacteristic
350C2×C42C23×C311yescharacteristic
351#106—41no—
352#106—41no—
353C4⋊C8—22no—
354C4⋊C8C3×D414yescomplemented
355#103—22no—
356#103—22no—
357#103—41no—
358#102—22no—
359#102—22no—
360#102—41no—
361#102—41no—
362#102—41no—
363C22⋊C8—22no—
364C22⋊C8—22no—
365#97—22no—
366C4×C8—22no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—41no—
393C23×C3C22×D411yescharacteristic
394C3×Q8—41no—
395C3×Q8—41no—
396C3×Q8—41no—
397C3×Q8—41no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—41no—
401C3×D4—41no—
402C3×D4—41no—
403C3×D4—41no—
404C3×D4—41no—
405C3×D4—41no—
406C3×D4—84no—
407C3×D4—84no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—84no—
444C2×C3×C4#12112yes—
445C2×C3×C4#12112yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4H(5,𝔽2)11yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C3×C8—22no—
453C3×C8—22no—
454C3×C8—41no—
455C3×C8—41no—
456C24—21no—
457C24—21no—
458C24C2×C3×D411yescharacteristic
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×D4—24no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—42no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4C3×#4112yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4C2×C3×D411yescharacteristic
499C22×C4C2×C3×D411yescharacteristic
500C22×C4C2×C3×D411yescharacteristic
501C22×C4C2×C3×D411yescharacteristic
502C22×C4C2×C3×D411yescharacteristic
503C22×C4C24×C311yescharacteristic
504SD16—44no—
505D8—44no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8C2×C3×D412yes—
517C2×C8C2×C3×D412yes—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—81no—
531C4⋊C4—81no—
532C4⋊C4—81no—
533C4⋊C4C3×#4112yes—
534C22⋊C4—24no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C22⋊C4—81no—
546C22⋊C4—81no—
547C42—21no—
548C42—21no—
549C42—81no—
550C42C2×C3×D412yes—
551C42C3×#4112yes—
552C22×C3—41no—
553C22×C3—42no—
554C22×C3—41no—
555C22×C3—42no—
556C22×C3—41no—
557C22×C3—42no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—41no—
561C22×C3—41no—
562C22×C3—81no—
563C22×C3—81no—
564C22×C3—81no—
565C22×C3—81no—
566C22×C3—81no—
567C22×C3—81no—
568C22×C3—81no—
569C22×C3—81no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3—81no—
573C22×C3C2×#12111yescharacteristic
574C22×C3#52511yescharacteristic
575C22×C3#53511yescharacteristic
576C22×C3#57611yescharacteristic
577C22×C3#57711yescharacteristic
578C22×C3#57711yescharacteristic
579C22×C3#57711yescharacteristic
580C3×C4—22no—
581C3×C4—22no—
582C3×C4—42no—
583C3×C4—41no—
584C3×C4—41no—
585C3×C4—41no—
586C3×C4—81no—
587C3×C4—81no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4#54611yescharacteristic
592C3×C4#55011yescharacteristic
593C3×C4#55311yescharacteristic
594C3×C4#55511yescharacteristic
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—22no—
601C23—21no—
602C23—21no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23C22×C3×D411yescharacteristic
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—22no—
622D4—22no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—84no—
630D4—84no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—84no—
667C2×C4C3×#12112yes—
668C2×C4C3×#12112yes—
669C2×C4C22×C3×D411yescharacteristic
670C2×C4C2×C3×#4111yescharacteristic
671C2×C4C2×C3×#4111yescharacteristic
672C2×C4C2×C3×#4111yescharacteristic
673C2×C4C3×H(5,𝔽2)11yescharacteristic
674C2×C4C3×H(5,𝔽2)11yescharacteristic
675C8—22no—
676C8—22no—
677C8—41no—
678C8—41no—
679C2×C3—81no—
680C2×C3—82no—
681C2×C3—161no—
682C2×C3#241411yescharacteristic
683C2×C3#306011yescharacteristic
684C2×C3#306211yescharacteristic
685C2×C3#311811yescharacteristic
686C2×C3#312511yescharacteristic
687C2×C3#322111yescharacteristic
688C2×C3#322411yescharacteristic
689C22—41no—
690C22—42no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22C2×C3×#12111yescharacteristic
711C22C3×#52511yescharacteristic
712C22C3×#53511yescharacteristic
713C22C3×#57611yescharacteristic
714C22C3×#57711yescharacteristic
715C22C3×#57711yescharacteristic
716C22C3×#57711yescharacteristic
717C4—22no—
718C4—22no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—42no—
723C4—81no—
724C4—81no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4C3×#54611yescharacteristic
729C4C3×#55011yescharacteristic
730C4C3×#55311yescharacteristic
731C4C3×#55511yescharacteristic
732C3#2466711yescharacteristic, direct product factor, Sylow
733C2—81no—
734C2—82no—
735C2—161no—
736C2C3×#241411yescharacteristic
737C2C3×#306011yescharacteristic
738C2C3×#306211yescharacteristic
739C2C3×#311811yescharacteristic
740C2C3×#312511yescharacteristic
741C2C3×#322111yescharacteristic
742C2C3×#322411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#463C2semidirect
2. C2×C3×#433C2semidirect
3. C3×#2620C2semidirect
4. C3×#2324C2semidirect
5. C3×#2035C2semidirect
6. C3×#2034C2semidirect
7. C3×#2000C2semidirect
9. C3×#1983C2semidirect
10. C3×#1972C2semidirect
11. C3×#1968C2semidirect
12. C3×#1948C2semidirect
13. C3×#1935C2semidirect
14. C3×#1934C2semidirect
15. C3×#1802C2semidirect
16. #24667C3direct (N × H)
62. C2×#463C2×C3semidirect
63. C2×#433C2×C3semidirect
64. #2620C2×C3semidirect
65. #2324C2×C3semidirect
66. #2035C2×C3semidirect
67. #2034C2×C3semidirect
68. #2000C2×C3semidirect
70. #1983C2×C3semidirect
71. #1972C2×C3semidirect
72. #1968C2×C3semidirect
73. #1948C2×C3semidirect
74. #1935C2×C3semidirect
75. #1934C2×C3semidirect
76. #1802C2×C3semidirect
136. C3×C4⋊C8D4semidirect
354. C4⋊C8C3×D4semidirect
732. C3#24667direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4632
C2×C3×#4332
C3×#26202
C3×#23242
C3×#20352
C3×#20342
C3×#20002
C3×#19992
C3×#19832
C3×#19722
C3×#19682
C3×#19482
C3×#19352
C3×#19342
C3×#18022
#246673