Finite Group Databasebeta

← C3×#24668 #10643275

Subgroups — C3×#24668 #10643275

Order 768.

914 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#460C211yesmaximal, characteristic, complemented
2C2×C3×#433C211yesmaximal, characteristic, complemented
3C3×#2619C211yesmaximal, characteristic
4C3×#2323C211yesmaximal, characteristic, complemented
5C3×#2034C211yesmaximal, characteristic, complemented
6C3×#2033C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1982C211yesmaximal, characteristic, complemented
10C3×#1973C211yesmaximal, characteristic, complemented
11C3×#1968C211yesmaximal, characteristic, complemented
12C3×#1949C211yesmaximal, characteristic, complemented
13C3×#1936C211yesmaximal, characteristic, complemented
14C3×#1934C211yesmaximal, characteristic, complemented
15C3×#1805C211yesmaximal, characteristic, complemented
16#24668C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×#127C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×#117C2211yescharacteristic
25C3×#460—24no—
26C3×#433—24no—
27C2×C3×#107C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
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×#394—21no—
44C3×#394—21no—
45C3×#392—21no—
46C3×#392—21no—
47C3×#391C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389—21no—
51C3×#389C2211yescharacteristic
52C3×#388—21no—
53C3×#388—21no—
54C3×#387—21no—
55C3×#382C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C2×#460C2×C311yescharacteristic, complemented
63C2×#433C2×C311yescharacteristic, complemented
64#2619C2×C311yescharacteristic
65#2323C2×C311yescharacteristic, complemented
66#2034C2×C311yescharacteristic, complemented
67#2033C2×C311yescharacteristic, complemented
68#2000C2×C311yescharacteristic, complemented
69#2000C2×C311yescharacteristic, complemented
70#1982C2×C311yescharacteristic, complemented
71#1973C2×C311yescharacteristic, complemented
72#1968C2×C311yescharacteristic, complemented
73#1949C2×C311yescharacteristic, complemented
74#1936C2×C311yescharacteristic, complemented
75#1934C2×C311yescharacteristic, complemented
76#1805C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C2×C3×SD16—22no—
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C2×C3×SD16—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×#127—22no—
96C3×#127—22no—
97C3×C22⋊Q8—22no—
98C3×C22⋊Q8—22no—
99C3×#121—41no—
100C3×#121—41no—
101C3×#121—41no—
102C3×#121—41no—
103C3×C4×Q8—22no—
104C3×C4×Q8—22no—
105C3×#117—22no—
106C3×#117—22no—
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⋊C4D411yescharacteristic
126C2×C3×C22⋊C4D411yescharacteristic
127C2×C3×C42—21no—
128C2×C3×C42—21no—
129C2×C3×C42C2311yescharacteristic
130C2×C3×C42C2311yescharacteristic
131C3×#107—41no—
132C3×#106—41no—
133C3×C4⋊C8—22no—
134C3×C4⋊C8D414yescomplemented
135C3×#103—41no—
136C3×#103—41no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—22no—
140C3×#102—22no—
141C3×#102—41no—
142C3×#102—41no—
143C3×C22⋊C8—22no—
144C3×C22⋊C8—22no—
145C3×#97—22no—
146C3×C4×C8—22no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C22×SD16C22×C311yescharacteristic
155C22×SD16C22×C311yescharacteristic
156C2×#127C22×C311yescharacteristic
157C2×C22⋊Q8C22×C311yescharacteristic
158C2×#121C22×C311yescharacteristic
159C2×#121C22×C311yescharacteristic
160C2×C4×Q8C22×C311yescharacteristic
161C2×#117C22×C311yescharacteristic
162#460—24no—
163#433—24no—
164C2×#107C22×C311yescharacteristic
165C2×#106C22×C311yescharacteristic
166C2×C4⋊C8C22×C311yescharacteristic
167C2×C4⋊C8C22×C311yescharacteristic
168C2×#103C22×C311yescharacteristic
169C2×#103C22×C311yescharacteristic
170C2×#102C22×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#394—21no—
181#394—21no—
182#392—21no—
183#392—21no—
184#391C22×C311yescharacteristic
185#390C22×C311yescharacteristic
186#390C22×C311yescharacteristic
187#389—21no—
188#389C22×C311yescharacteristic
189#388—21no—
190#388—21no—
191#387—21no—
192#382C22×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#4112yes—
208C2×C3×D4—21no—
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—42no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4—81no—
225C2×C3×D4—81no—
226C2×C3×D4—81no—
227C2×C3×D4—81no—
228C2×C3×D4—81no—
229C2×C3×D4—81no—
230C2×C3×D4—81no—
231C2×C3×D4—81no—
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—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2411yescharacteristic
250C3×SD16—44no—
251C3×SD16—44no—
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×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8C2×D412yes—
263C2×C3×C8C2×D412yes—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—42no—
277C3×C4⋊C4—81no—
278C3×C4⋊C4#4112yes—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—22no—
281C3×C22⋊C4—22no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—42no—
284C3×C22⋊C4—81no—
285C3×C22⋊C4—81no—
286C3×C22⋊C4—81no—
287C3×C22⋊C4—81no—
288C3×C22⋊C4—81no—
289C3×C42—21no—
290C3×C42—21no—
291C3×C42—42no—
292C3×C42—81no—
293C3×C42C2×D412yes—
294C3×C42#4112yes—
295C22×Q8C23×C311yescharacteristic
296C22×D4—21no—
297C22×D4—21no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C23×C311yescharacteristic
301C22×D4C23×C311yescharacteristic
302C23×C4C23×C311yescharacteristic
303C2×SD16—22no—
304C2×SD16—22no—
305C2×SD16—22no—
306C2×SD16—22no—
307C2×SD16—41no—
308C2×SD16—41no—
309C22×C8C23×C311yescharacteristic
310C22×C8C23×C311yescharacteristic
311C22×C8C23×C311yescharacteristic
312C22×C8C23×C311yescharacteristic
313#127—22no—
314#127—22no—
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317#121—41no—
318#121—41no—
319#121—41no—
320#121—41no—
321C4×Q8—22no—
322C4×Q8—22no—
323#117—22no—
324#117—22no—
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⋊C4C3×D411yescharacteristic
344C2×C22⋊C4C3×D411yescharacteristic
345C2×C42—21no—
346C2×C42—21no—
347C2×C42C23×C311yescharacteristic
348C2×C42C23×C311yescharacteristic
349#107—41no—
350#106—41no—
351C4⋊C8—22no—
352C4⋊C8C3×D414yescomplemented
353#103—41no—
354#103—41no—
355#102—22no—
356#102—22no—
357#102—22no—
358#102—22no—
359#102—41no—
360#102—41no—
361C22⋊C8—22no—
362C22⋊C8—22no—
363#97—22no—
364C4×C8—22no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—41no—
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—22no—
395C3×Q8—22no—
396C3×Q8—41no—
397C3×Q8—41no—
398C3×D4—41no—
399C3×D4—41no—
400C3×D4—41no—
401C3×D4—41no—
402C3×D4—41no—
403C3×D4—41no—
404C3×D4—41no—
405C3×D4—41no—
406C3×D4—84no—
407C3×D4—84no—
408C3×D4—84no—
409C3×D4—84no—
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—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
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—41no—
444C2×C3×C4—41no—
445C2×C3×C4#12112yes—
446C2×C3×C4#12112yes—
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452C2×C3×C4H(5,𝔽2)11yescharacteristic
453C3×C8—22no—
454C3×C8—22no—
455C3×C8—41no—
456C3×C8—41no—
457C24—21no—
458C24—21no—
459C24C2×C3×D411yescharacteristic
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8C3×#4112yes—
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—21no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—81no—
483C2×D4—81no—
484C2×D4—81no—
485C2×D4—81no—
486C2×D4—81no—
487C2×D4—81no—
488C2×D4—81no—
489C2×D4—81no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4C2×C3×D411yescharacteristic
503C22×C4C2×C3×D411yescharacteristic
504C22×C4C2×C3×D411yescharacteristic
505C22×C4C2×C3×D411yescharacteristic
506C22×C4C2×C3×D411yescharacteristic
507C22×C4C24×C311yescharacteristic
508SD16—44no—
509SD16—44no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×C3×D412yes—
521C2×C8C2×C3×D412yes—
522C4⋊C4—24no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—81no—
536C4⋊C4C3×#4112yes—
537C22⋊C4—24no—
538C22⋊C4—22no—
539C22⋊C4—22no—
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—42no—
550C42—81no—
551C42C2×C3×D412yes—
552C42C3×#4112yes—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—81no—
561C22×C3—81no—
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×C3—81no—
574C22×C3C2×#12111yescharacteristic
575C22×C3#52511yescharacteristic
576C22×C3#53511yescharacteristic
577C22×C3#57611yescharacteristic
578C22×C3#57711yescharacteristic
579C22×C3#57711yescharacteristic
580C22×C3#57711yescharacteristic
581C3×C4—22no—
582C3×C4—22no—
583C3×C4—42no—
584C3×C4—41no—
585C3×C4—42no—
586C3×C4—41no—
587C3×C4—41no—
588C3×C4—81no—
589C3×C4—81no—
590C3×C4—81no—
591C3×C4—81no—
592C3×C4#54611yescharacteristic
593C3×C4#55011yescharacteristic
594C3×C4#55311yescharacteristic
595C3×C4#55511yescharacteristic
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
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—
616C23—41no—
617C23C22×C3×D411yescharacteristic
618Q8—22no—
619Q8—22no—
620Q8—41no—
621Q8—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—84no—
631D4—84no—
632D4—84no—
633D4—84no—
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—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
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—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4C3×#12112yes—
670C2×C4C3×#12112yes—
671C2×C4C22×C3×D411yescharacteristic
672C2×C4C2×C3×#4111yescharacteristic
673C2×C4C2×C3×#4111yescharacteristic
674C2×C4C2×C3×#4111yescharacteristic
675C2×C4C3×H(5,𝔽2)11yescharacteristic
676C2×C4C3×H(5,𝔽2)11yescharacteristic
677C8—22no—
678C8—22no—
679C8—41no—
680C8—41no—
681C2×C3—81no—
682C2×C3—161no—
683C2×C3—161no—
684C2×C3#241411yescharacteristic
685C2×C3#305711yescharacteristic
686C2×C3#306211yescharacteristic
687C2×C3#311911yescharacteristic
688C2×C3#312611yescharacteristic
689C2×C3#322211yescharacteristic
690C2×C3#322411yescharacteristic
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22C2×C3×#12111yescharacteristic
713C22C3×#52511yescharacteristic
714C22C3×#53511yescharacteristic
715C22C3×#57611yescharacteristic
716C22C3×#57711yescharacteristic
717C22C3×#57711yescharacteristic
718C22C3×#57711yescharacteristic
719C4—22no—
720C4—22no—
721C4—41no—
722C4—42no—
723C4—41no—
724C4—41no—
725C4—42no—
726C4—81no—
727C4—81no—
728C4—81no—
729C4—81no—
730C4C3×#54611yescharacteristic
731C4C3×#55011yescharacteristic
732C4C3×#55311yescharacteristic
733C4C3×#55511yescharacteristic
734C3#2466811yescharacteristic, direct product factor, Sylow
735C2—81no—
736C2—161no—
737C2—161no—
738C2C3×#241411yescharacteristic
739C2C3×#305711yescharacteristic
740C2C3×#306211yescharacteristic
741C2C3×#311911yescharacteristic
742C2C3×#312611yescharacteristic
743C2C3×#322211yescharacteristic
744C2C3×#322411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2619C2
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×#460C2semidirect
2. C2×C3×#433C2semidirect
4. C3×#2323C2semidirect
5. C3×#2034C2semidirect
6. C3×#2033C2semidirect
7. C3×#2000C2semidirect
8. C3×#2000C2semidirect
9. C3×#1982C2semidirect
10. C3×#1973C2semidirect
11. C3×#1968C2semidirect
12. C3×#1949C2semidirect
13. C3×#1936C2semidirect
14. C3×#1934C2semidirect
15. C3×#1805C2semidirect
16. #24668C3direct (N × H)
62. C2×#460C2×C3semidirect
63. C2×#433C2×C3semidirect
65. #2323C2×C3semidirect
66. #2034C2×C3semidirect
67. #2033C2×C3semidirect
68. #2000C2×C3semidirect
69. #2000C2×C3semidirect
70. #1982C2×C3semidirect
71. #1973C2×C3semidirect
72. #1968C2×C3semidirect
73. #1949C2×C3semidirect
74. #1936C2×C3semidirect
75. #1934C2×C3semidirect
76. #1805C2×C3semidirect
134. C3×C4⋊C8D4semidirect
352. C4⋊C8C3×D4semidirect
734. C3#24668direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4602
C2×C3×#4332
C3×#26192
C3×#23232
C3×#20342
C3×#20332
C3×#20002
C3×#19822
C3×#19732
C3×#19682
C3×#19492
C3×#19362
C3×#19342
C3×#18052
#246683