Finite Group Databasebeta

← C3×#24657 #10643264

Subgroups — C3×#24657 #10643264

Order 768.

902 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#464C211yesmaximal, characteristic, complemented
2C2×C3×#432C211yesmaximal, characteristic, complemented
3C3×#2850C211yesmaximal, characteristic
4C3×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
5C3×#2036C211yesmaximal, characteristic, complemented
6C3×#2034C211yesmaximal, characteristic
7C3×#2001C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1973C211yesmaximal, characteristic, complemented
11C3×#1971C211yesmaximal, characteristic, complemented
12C3×#1949C211yesmaximal, characteristic, complemented
13C3×#1936C211yesmaximal, characteristic, complemented
14C3×#1935C211yesmaximal, characteristic, complemented
15C3×#1805C211yesmaximal, characteristic, complemented
16#24657C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C22×C3×C42C2211yescharacteristic
25C3×#464—24no—
26C3×#432—24no—
27C2×C3×#107C2211yescharacteristic
28C2×C3×#106C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic
41C2×C3×#97C2211yescharacteristic
42C2×C3×#97C2211yescharacteristic
43C3×#391C2211yescharacteristic
44C3×#391C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#389C2211yescharacteristic
47C3×#388—21no—
48C3×#388—21no—
49C3×#387—21no—
50C3×#386—21no—
51C3×#386—21no—
52C3×#385—21no—
53C3×#382C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×C4×C4⋊C4—21no—
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×C4×C22⋊C4—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C2×#464C2×C311yescharacteristic, complemented
63C2×#432C2×C311yescharacteristic, complemented
64#2850C2×C311yescharacteristic
65C4×C22⋊Q8C2×C311yescharacteristic, complemented
66#2036C2×C311yescharacteristic, complemented
67#2034C2×C311yescharacteristic
68#2001C2×C311yescharacteristic, complemented
69#2000C2×C311yescharacteristic
70#1983C2×C311yescharacteristic, complemented
71#1973C2×C311yescharacteristic, complemented
72#1971C2×C311yescharacteristic, complemented
73#1949C2×C311yescharacteristic, complemented
74#1936C2×C311yescharacteristic, complemented
75#1935C2×C311yescharacteristic, complemented
76#1805C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4D411yescharacteristic
82C23×C3×C4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C2×C3×Q16—22no—
85C2×C3×Q16—22no—
86C2×C3×Q16—41no—
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×#124—22no—
95C3×#124—22no—
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—22no—
98C3×C22⋊Q8—41no—
99C3×C22⋊Q8—41no—
100C3×#121—41no—
101C3×#121—41no—
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C42—22no—
122C2×C3×C42—22no—
123C2×C3×C42—21no—
124C2×C3×C42—21no—
125C2×C3×C42D411yescharacteristic
126C2×C3×C42D411yescharacteristic
127C2×C3×C42C2311yescharacteristic
128C2×C3×C42C2311yescharacteristic
129C3×#107—41no—
130C3×#106—41no—
131C3×C4⋊C8—22no—
132C3×C4⋊C8D414yescomplemented
133C3×#103—22no—
134C3×#103—22no—
135C3×#103—41no—
136C3×#103—41no—
137C3×#103—41no—
138C3×#102—22no—
139C3×#102—22no—
140C3×#102—41no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×#97—22no—
144C3×#97—22no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C22×Q16C22×C311yescharacteristic
155C22×SD16C22×C311yescharacteristic
156C2×#124C22×C311yescharacteristic
157C2×C22⋊Q8C22×C311yescharacteristic
158C2×C22⋊Q8C22×C311yescharacteristic
159C2×#121C22×C311yescharacteristic
160C2×C4×Q8C22×C311yescharacteristic
161C22×C42C22×C311yescharacteristic
162#464—24no—
163#432—24no—
164C2×#107C22×C311yescharacteristic
165C2×#106C22×C311yescharacteristic
166C2×C4⋊C8C22×C311yescharacteristic
167C2×C4⋊C8C22×C311yescharacteristic
168C2×#103C22×C311yescharacteristic
169C2×#103C22×C311yescharacteristic
170C2×#103C22×C311yescharacteristic
171C2×#103C22×C311yescharacteristic
172C2×#103C22×C311yescharacteristic
173C2×#102C22×C311yescharacteristic
174C2×#102C22×C311yescharacteristic
175C2×#102C22×C311yescharacteristic
176C2×C22⋊C8C22×C311yescharacteristic
177C2×C22⋊C8C22×C311yescharacteristic
178C2×#97C22×C311yescharacteristic
179C2×#97C22×C311yescharacteristic
180#391C22×C311yescharacteristic
181#391C22×C311yescharacteristic
182#390C22×C311yescharacteristic
183#389C22×C311yescharacteristic
184#388—21no—
185#388—21no—
186#387—21no—
187#386—21no—
188#386—21no—
189#385—21no—
190#382C22×C311yescharacteristic
191#380C22×C311yescharacteristic
192C4×C4⋊C4—21no—
193C4×C4⋊C4C22×C311yescharacteristic
194C4×C22⋊C4—21no—
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199C24×C3—21no—
200C24×C3C2×D411yescharacteristic
201C2×C3×Q8—21no—
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×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8#4112yes—
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—42no—
220C2×C3×D4—42no—
221C2×C3×D4—42no—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
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—41no—
239C22×C3×C4—41no—
240C22×C3×C4—41no—
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2411yescharacteristic
247C3×Q16—44no—
248C3×SD16—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—24no—
262C3×C4⋊C4—21no—
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—42no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4#4112yes—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C42—22no—
284C3×C42—22no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—42no—
288C3×C42—42no—
289C3×C42C2×D412yes—
290C3×C42#4112yes—
291C22×Q8C23×C311yescharacteristic
292C22×Q8C23×C311yescharacteristic
293C22×D4—21no—
294C22×D4C23×C311yescharacteristic
295C23×C4C3×D411yescharacteristic
296C23×C4C3×D411yescharacteristic
297C23×C4C23×C311yescharacteristic
298C2×Q16—22no—
299C2×Q16—22no—
300C2×Q16—41no—
301C2×SD16—22no—
302C2×SD16—22no—
303C2×SD16—41no—
304C22×C8C23×C311yescharacteristic
305C22×C8C23×C311yescharacteristic
306C22×C8C23×C311yescharacteristic
307C22×C8C23×C311yescharacteristic
308#124—22no—
309#124—22no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—41no—
313C22⋊Q8—41no—
314#121—41no—
315#121—41no—
316C4×Q8—22no—
317C4×Q8—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4C23×C311yescharacteristic
323C2×C4⋊C4C23×C311yescharacteristic
324C2×C4⋊C4C23×C311yescharacteristic
325C2×C4⋊C4C23×C311yescharacteristic
326C2×C4⋊C4C23×C311yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42C3×D411yescharacteristic
340C2×C42C3×D411yescharacteristic
341C2×C42C23×C311yescharacteristic
342C2×C42C23×C311yescharacteristic
343#107—41no—
344#106—41no—
345C4⋊C8—22no—
346C4⋊C8C3×D414yescomplemented
347#103—22no—
348#103—22no—
349#103—41no—
350#103—41no—
351#103—41no—
352#102—22no—
353#102—22no—
354#102—41no—
355C22⋊C8—22no—
356C22⋊C8—22no—
357#97—22no—
358#97—22no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3#13712yes—
382C23×C3C22×D411yescharacteristic
383C3×Q8—22no—
384C3×Q8—22no—
385C3×Q8—41no—
386C3×Q8—41no—
387C3×Q8—41no—
388C3×Q8—41no—
389C3×Q8—41no—
390C3×Q8—41no—
391C3×D4—41no—
392C3×D4—41no—
393C3×D4—41no—
394C3×D4—41no—
395C3×D4—84no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—44no—
412C2×C3×C4—44no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
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#12112yes—
437C2×C3×C4#12112yes—
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4C2×#4111yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443C2×C3×C4H(5,𝔽2)11yescharacteristic
444C3×C8—22no—
445C3×C8—22no—
446C3×C8—41no—
447C3×C8—41no—
448C24—21no—
449C24C2×C3×D411yescharacteristic
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C3×#4112yes—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C2×C3×D411yescharacteristic
495C22×C4C24×C311yescharacteristic
496Q16—44no—
497SD16—44no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8C2×C3×D412yes—
509C2×C8C2×C3×D412yes—
510C4⋊C4—24no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4C3×#4112yes—
524C22⋊C4—24no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C42—22no—
533C42—22no—
534C42—21no—
535C42—21no—
536C42—42no—
537C42—42no—
538C42C2×C3×D412yes—
539C42C3×#4112yes—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—81no—
548C22×C3—81no—
549C22×C3—81no—
550C22×C3—81no—
551C22×C3—81no—
552C22×C3—81no—
553C22×C3—81no—
554C22×C3C2×#12111yescharacteristic
555C22×C3#52511yescharacteristic
556C22×C3#53511yescharacteristic
557C22×C3C2×#13711yescharacteristic
558C22×C3#57511yescharacteristic
559C22×C3#57511yescharacteristic
560C22×C3#57511yescharacteristic
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—42no—
564C3×C4—41no—
565C3×C4—42no—
566C3×C4—41no—
567C3×C4—41no—
568C3×C4—81no—
569C3×C4—81no—
570C3×C4—81no—
571C3×C4—81no—
572C3×C4—81no—
573C3×C4#54611yescharacteristic
574C3×C4#55011yescharacteristic
575C3×C4#55311yescharacteristic
576C3×C4#55511yescharacteristic
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23C3×#13712yes—
591C23C22×C3×D411yescharacteristic
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4C3×#12112yes—
646C2×C4C3×#12112yes—
647C2×C4C22×C3×D411yescharacteristic
648C2×C4C2×C3×#4111yescharacteristic
649C2×C4C2×C3×#4111yescharacteristic
650C2×C4C2×C3×#4111yescharacteristic
651C2×C4C3×H(5,𝔽2)11yescharacteristic
652C2×C4C3×H(5,𝔽2)11yescharacteristic
653C8—22no—
654C8—22no—
655C8—41no—
656C8—41no—
657C2×C3—42no—
658C2×C3—161no—
659C2×C3#241411yescharacteristic
660C2×C3#305411yescharacteristic
661C2×C3#305611yescharacteristic
662C2×C3#311111yescharacteristic
663C2×C3#311711yescharacteristic
664C2×C3#321511yescharacteristic
665C2×C3#321911yescharacteristic
666C22—22no—
667C22—22no—
668C22—22no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22C2×C3×#12111yescharacteristic
681C22C3×#52511yescharacteristic
682C22C3×#53511yescharacteristic
683C22C2×C3×#13711yescharacteristic
684C22C3×#57511yescharacteristic
685C22C3×#57511yescharacteristic
686C22C3×#57511yescharacteristic
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4—81no—
699C4C3×#54611yescharacteristic
700C4C3×#55011yescharacteristic
701C4C3×#55311yescharacteristic
702C4C3×#55511yescharacteristic
703C3#2465711yescharacteristic, direct product factor, Sylow
704C2—42no—
705C2—161no—
706C2C3×#241411yescharacteristic
707C2C3×#305411yescharacteristic
708C2C3×#305611yescharacteristic
709C2C3×#311111yescharacteristic
710C2C3×#311711yescharacteristic
711C2C3×#321511yescharacteristic
712C2C3×#321911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
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×#464C2semidirect
2. C2×C3×#432C2semidirect
4. C3×C4×C22⋊Q8C2semidirect
5. C3×#2036C2semidirect
7. C3×#2001C2semidirect
9. C3×#1983C2semidirect
10. C3×#1973C2semidirect
11. C3×#1971C2semidirect
12. C3×#1949C2semidirect
13. C3×#1936C2semidirect
14. C3×#1935C2semidirect
15. C3×#1805C2semidirect
16. #24657C3direct (N × H)
62. C2×#464C2×C3semidirect
63. C2×#432C2×C3semidirect
65. C4×C22⋊Q8C2×C3semidirect
66. #2036C2×C3semidirect
68. #2001C2×C3semidirect
70. #1983C2×C3semidirect
71. #1973C2×C3semidirect
72. #1971C2×C3semidirect
73. #1949C2×C3semidirect
74. #1936C2×C3semidirect
75. #1935C2×C3semidirect
76. #1805C2×C3semidirect
132. C3×C4⋊C8D4semidirect
346. C4⋊C8C3×D4semidirect
703. C3#24657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4642
C2×C3×#4322
C3×#28502
C3×C4×C22⋊Q82
C3×#20362
C3×#20342
C3×#20012
C3×#20002
C3×#19832
C3×#19732
C3×#19712
C3×#19492
C3×#19362
C3×#19352
C3×#18052
#246573