Finite Group Databasebeta

← C3×#10907 #10629514

Subgroups — C3×#10907 #10629514

Order 768.

958 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#107C211yesmaximal, characteristic
2C2×C3×C4×C4⋊C4C211yesmaximal, characteristic
3C2×C3×#340C211yesmaximal, characteristic
4C2×C3×#340C211yesmaximal, characteristic
5C2×C3×#340C211yesmaximal, characteristic
6C2×C3×#336C211yesmaximal, characteristic
7C3×C4⋊#95C211yesmaximal, characteristic
8#10907C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×C8C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×C3×C4⋊C4C2211yescharacteristic
14C22×C3×C4⋊C4C2211yescharacteristic
15C22×C3×C42—21no—
16C22×C3×C42C2211yescharacteristic
17C2×C3×#107—22no—
18C2×C3×#107—22no—
19C2×C3×#107C414yescomplemented
20C3×C4×C4⋊C4—22no—
21C3×C4×C4⋊C4—22no—
22C2×C3×#95—21no—
23C2×C3×#95—21no—
24C2×C3×#95—21no—
25C3×#340—22no—
26C3×#340—22no—
27C3×#340C414yescomplemented
28C3×#336C414yescomplemented
29C22×#107C2×C311yescharacteristic
30C2×C4×C4⋊C4C2×C311yescharacteristic
31C2×#340C2×C311yescharacteristic
32C2×#340C2×C311yescharacteristic
33C2×#340C2×C311yescharacteristic
34C2×#336C2×C311yescharacteristic
35C4⋊#95C2×C311yescharacteristic
36C23×C3×C4—21no—
37C23×C3×C4—21no—
38C23×C3×C4—21no—
39C23×C3×C4—21no—
40C23×C3×C4D411yescharacteristic
41C23×C3×C4D411yescharacteristic
42C23×C3×C4C2311yescharacteristic
43C22×C3×C8—21no—
44C22×C3×C8—21no—
45C22×C3×C8—21no—
46C22×C3×C8—21no—
47C22×C3×C8—21no—
48C22×C3×C8—21no—
49C22×C3×C8—21no—
50C22×C3×C8—21no—
51C22×C3×C8—21no—
52C22×C3×C8—21no—
53C22×C3×C8C2×C412yes—
54C22×C3×C8C2×C412yes—
55C22×C3×C8C2×C412yes—
56C22×C3×C8C2×C412yes—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4—21no—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4C2×C412yes—
74C2×C3×C4⋊C4C2×C412yes—
75C2×C3×C4⋊C4C2×C412yes—
76C2×C3×C4⋊C4C2×C412yes—
77C2×C3×C4⋊C4D412yes—
78C2×C3×C4⋊C4D412yes—
79C2×C3×C4⋊C4D412yes—
80C2×C3×C4⋊C4Q812yes—
81C2×C3×C42—21no—
82C2×C3×C42—21no—
83C2×C3×C42—21no—
84C2×C3×C42—21no—
85C2×C3×C42—24no—
86C2×C3×C42—42no—
87C2×C3×C42—42no—
88C2×C3×C42C2×C412yes—
89C2×C3×C42Q812yes—
90C3×#107—28no—
91C3×#95—24no—
92C3×#95—42no—
93C3×#95—42no—
94C23×C8C22×C311yescharacteristic
95C23×C8C22×C311yescharacteristic
96C22×C4⋊C4C22×C311yescharacteristic
97C22×C4⋊C4C22×C311yescharacteristic
98C22×C4⋊C4C22×C311yescharacteristic
99C22×C4⋊C4C22×C311yescharacteristic
100C22×C42—21no—
101C22×C42C22×C311yescharacteristic
102C2×#107—22no—
103C2×#107—22no—
104C2×#107C3×C414yescomplemented
105C4×C4⋊C4—22no—
106C4×C4⋊C4—22no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110#340—22no—
111#340—22no—
112#340C3×C414yescomplemented
113#336C3×C414yescomplemented
114C24×C3C2×D411yescharacteristic
115C22×C3×C4—21no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—21no—
122C22×C3×C4—22no—
123C22×C3×C4—22no—
124C22×C3×C4—22no—
125C22×C3×C4—22no—
126C22×C3×C4—21no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—22no—
132C22×C3×C4—22no—
133C22×C3×C4—41no—
134C22×C3×C4—41no—
135C22×C3×C4—41no—
136C22×C3×C4—41no—
137C22×C3×C4—41no—
138C22×C3×C4—41no—
139C22×C3×C4—41no—
140C22×C3×C4—41no—
141C22×C3×C4—41no—
142C22×C3×C4—41no—
143C22×C3×C4—41no—
144C22×C3×C4—41no—
145C22×C3×C4—41no—
146C22×C3×C4—41no—
147C22×C3×C4—41no—
148C22×C3×C4—41no—
149C22×C3×C4—41no—
150C22×C3×C4—41no—
151C22×C3×C4—41no—
152C22×C3×C4—41no—
153C22×C3×C4C4⋊C412yes—
154C22×C3×C4C4⋊C412yes—
155C22×C3×C4D812yes—
156C22×C3×C4Q1612yes—
157C22×C3×C4C22×C411yescharacteristic
158C22×C3×C4C22×C411yescharacteristic
159C22×C3×C4C22×C411yescharacteristic
160C22×C3×C4C2×D411yescharacteristic
161C22×C3×C4C2×D411yescharacteristic
162C22×C3×C4C2×D411yescharacteristic
163C22×C3×C4C2×Q811yescharacteristic
164C22×C3×C4C2×Q811yescharacteristic
165C22×C3×C4#4111yescharacteristic
166C22×C3×C4#4111yescharacteristic
167C22×C3×C4#4111yescharacteristic
168C22×C3×C4#4111yescharacteristic
169C22×C3×C4#4111yescharacteristic
170C22×C3×C4#4111yescharacteristic
171C2×C3×C8—22no—
172C2×C3×C8—22no—
173C2×C3×C8—22no—
174C2×C3×C8—22no—
175C2×C3×C8—22no—
176C2×C3×C8—22no—
177C2×C3×C8—22no—
178C2×C3×C8—22no—
179C2×C3×C8—22no—
180C2×C3×C8—41no—
181C2×C3×C8—41no—
182C2×C3×C8—41no—
183C2×C3×C8—41no—
184C2×C3×C8C4214yescomplemented
185C3×C4⋊C4—22no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—22no—
189C3×C4⋊C4—22no—
190C3×C4⋊C4—22no—
191C3×C4⋊C4—22no—
192C3×C4⋊C4—22no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—41no—
197C3×C4⋊C4—41no—
198C3×C4⋊C4—41no—
199C3×C4⋊C4C22⋊C414yes—
200C3×C4⋊C4C4⋊C414yes—
201C3×C42—22no—
202C3×C42—22no—
203C3×C42—22no—
204C3×C42—22no—
205C3×C42—48no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4C3×D411yescharacteristic
211C23×C4C3×D411yescharacteristic
212C23×C4C23×C311yescharacteristic
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8C2×C3×C412yes—
224C22×C8C2×C3×C412yes—
225C22×C8C2×C3×C412yes—
226C22×C8C2×C3×C412yes—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C2×C3×C412yes—
244C2×C4⋊C4C2×C3×C412yes—
245C2×C4⋊C4C2×C3×C412yes—
246C2×C4⋊C4C2×C3×C412yes—
247C2×C4⋊C4C3×D412yes—
248C2×C4⋊C4C3×D412yes—
249C2×C4⋊C4C3×D412yes—
250C2×C4⋊C4C3×Q812yes—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42—24no—
256C2×C42—42no—
257C2×C42—42no—
258C2×C42C2×C3×C412yes—
259C2×C42C3×Q812yes—
260#107—28no—
261#95—24no—
262#95—42no—
263#95—42no—
264C23×C3C2×C4⋊C411yescharacteristic
265C23×C3C4×D411yescharacteristic
266C23×C3C4×D411yescharacteristic
267C23×C3#12011yescharacteristic
268C23×C3#12111yescharacteristic
269C23×C3C22⋊Q811yescharacteristic
270C23×C3#12311yescharacteristic
271C23×C3C2×D811yescharacteristic
272C23×C3C2×Q1611yescharacteristic
273C23×C3#13511yescharacteristic
274C23×C3#13511yescharacteristic
275C23×C3AGL(1,ℤ/8)11yescharacteristic
276C23×C3AGL(1,ℤ/8)11yescharacteristic
277C23×C3#13711yescharacteristic
278C23×C3#13711yescharacteristic
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—24no—
287C2×C3×C4—24no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—42no—
295C2×C3×C4—42no—
296C2×C3×C4—41no—
297C2×C3×C4—42no—
298C2×C3×C4—41no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—42no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—42no—
311C2×C3×C4—42no—
312C2×C3×C4—81no—
313C2×C3×C4—81no—
314C2×C3×C4—81no—
315C2×C3×C4—81no—
316C2×C3×C4—81no—
317C2×C3×C4—81no—
318C2×C3×C4—81no—
319C2×C3×C4—81no—
320C2×C3×C4#10714yescomplemented
321C2×C3×C4C2×C4211yescharacteristic
322C2×C3×C4C2×C22⋊C411yescharacteristic
323C2×C3×C4C2×C4⋊C411yescharacteristic
324C2×C3×C4#11711yescharacteristic
325C2×C3×C4#11711yescharacteristic
326C2×C3×C4#11711yescharacteristic
327C2×C3×C4C4×D411yescharacteristic
328C2×C3×C4C4×D411yescharacteristic
329C2×C3×C4C4×D411yescharacteristic
330C2×C3×C4C4×D411yescharacteristic
331C2×C3×C4C4×D411yescharacteristic
332C2×C3×C4C4×D411yescharacteristic
333C2×C3×C4C4×Q811yescharacteristic
334C2×C3×C4C4×Q811yescharacteristic
335C2×C3×C4C4×Q811yescharacteristic
336C2×C3×C4C4×Q811yescharacteristic
337C2×C3×C4#12111yescharacteristic
338C2×C3×C4C22⋊Q811yescharacteristic
339C2×C3×C4C22⋊Q811yescharacteristic
340C2×C3×C4C22⋊Q811yescharacteristic
341C2×C3×C4#12311yescharacteristic
342C2×C3×C4#12311yescharacteristic
343C2×C3×C4#12411yescharacteristic
344C2×C3×C4#12511yescharacteristic
345C2×C3×C4#12511yescharacteristic
346C2×C3×C4#12611yescharacteristic
347C2×C3×C4#12611yescharacteristic
348C2×C3×C4C4⋊Q811yescharacteristic
349C3×C8—24no—
350C3×C8—42no—
351C24C2×C3×D411yescharacteristic
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4C3×C4⋊C412yes—
391C22×C4C3×C4⋊C412yes—
392C22×C4C3×D812yes—
393C22×C4C3×Q1612yes—
394C22×C4C22×C3×C411yescharacteristic
395C22×C4C22×C3×C411yescharacteristic
396C22×C4C22×C3×C411yescharacteristic
397C22×C4C2×C3×D411yescharacteristic
398C22×C4C2×C3×D411yescharacteristic
399C22×C4C2×C3×D411yescharacteristic
400C22×C4C2×C3×Q811yescharacteristic
401C22×C4C2×C3×Q811yescharacteristic
402C22×C4C3×#4111yescharacteristic
403C22×C4C3×#4111yescharacteristic
404C22×C4C3×#4111yescharacteristic
405C22×C4C3×#4111yescharacteristic
406C22×C4C3×#4111yescharacteristic
407C22×C4C3×#4111yescharacteristic
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—41no—
420C2×C8—41no—
421C2×C8C3×C4214yescomplemented
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4C3×C22⋊C414yes—
437C4⋊C4C3×C4⋊C414yes—
438C42—22no—
439C42—22no—
440C42—22no—
441C42—22no—
442C42—48no—
443C22×C3C4×C4⋊C411yescharacteristic
444C22×C3#38511yescharacteristic
445C22×C3#38511yescharacteristic
446C22×C3#38611yescharacteristic
447C22×C3#38711yescharacteristic
448C22×C3#38811yescharacteristic
449C22×C3#38911yescharacteristic
450C22×C3C2×#10711yescharacteristic
451C22×C3#42711yescharacteristic
452C22×C3#42811yescharacteristic
453C22×C3#42811yescharacteristic
454C22×C3C4×D811yescharacteristic
455C22×C3C4×D811yescharacteristic
456C22×C3C4×Q1611yescharacteristic
457C22×C3C4×Q1611yescharacteristic
458C22×C3#44011yescharacteristic
459C22×C3#44011yescharacteristic
460C22×C3#44111yescharacteristic
461C22×C3#44211yescharacteristic
462C22×C3#44711yescharacteristic
463C22×C3#44911yescharacteristic
464C22×C3#45111yescharacteristic
465C22×C3#45211yescharacteristic
466C22×C3#45911yescharacteristic
467C22×C3#46211yescharacteristic
468C22×C3#46311yescharacteristic
469C22×C3#46411yescharacteristic
470C22×C3#47411yescharacteristic
471C22×C3#47711yescharacteristic
472C22×C3#47811yescharacteristic
473C22×C3#47911yescharacteristic
474C22×C3#48011yescharacteristic
475C22×C3#48211yescharacteristic
476C22×C3#48411yescharacteristic
477C22×C3#48511yescharacteristic
478C3×C4—24no—
479C3×C4—42no—
480C3×C4—44no—
481C3×C4—44no—
482C3×C4—82no—
483C3×C4—82no—
484C3×C4C4×C22⋊C411yescharacteristic
485C3×C4C4×C4⋊C411yescharacteristic
486C3×C4#38711yescharacteristic
487C3×C4#38711yescharacteristic
488C3×C4#38711yescharacteristic
489C3×C4#38811yescharacteristic
490C3×C4#38911yescharacteristic
491C3×C4#39111yescharacteristic
492C23C2×C3×C4⋊C411yescharacteristic
493C23C3×C4×D411yescharacteristic
494C23C3×C4×D411yescharacteristic
495C23C3×#12011yescharacteristic
496C23C3×#12111yescharacteristic
497C23C3×C22⋊Q811yescharacteristic
498C23C3×#12311yescharacteristic
499C23C2×C3×D811yescharacteristic
500C23C2×C3×Q1611yescharacteristic
501C23C3×#13511yescharacteristic
502C23C3×#13511yescharacteristic
503C23C3×AGL(1,ℤ/8)11yescharacteristic
504C23C3×AGL(1,ℤ/8)11yescharacteristic
505C23C3×#13711yescharacteristic
506C23C3×#13711yescharacteristic
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—81no—
541C2×C4—81no—
542C2×C4—81no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4C3×#10714yescomplemented
549C2×C4C2×C3×C4211yescharacteristic
550C2×C4C2×C3×C22⋊C411yescharacteristic
551C2×C4C2×C3×C4⋊C411yescharacteristic
552C2×C4C3×#11711yescharacteristic
553C2×C4C3×#11711yescharacteristic
554C2×C4C3×#11711yescharacteristic
555C2×C4C3×C4×D411yescharacteristic
556C2×C4C3×C4×D411yescharacteristic
557C2×C4C3×C4×D411yescharacteristic
558C2×C4C3×C4×D411yescharacteristic
559C2×C4C3×C4×D411yescharacteristic
560C2×C4C3×C4×D411yescharacteristic
561C2×C4C3×C4×Q811yescharacteristic
562C2×C4C3×C4×Q811yescharacteristic
563C2×C4C3×C4×Q811yescharacteristic
564C2×C4C3×C4×Q811yescharacteristic
565C2×C4C3×#12111yescharacteristic
566C2×C4C3×C22⋊Q811yescharacteristic
567C2×C4C3×C22⋊Q811yescharacteristic
568C2×C4C3×C22⋊Q811yescharacteristic
569C2×C4C3×#12311yescharacteristic
570C2×C4C3×#12311yescharacteristic
571C2×C4C3×#12411yescharacteristic
572C2×C4C3×#12511yescharacteristic
573C2×C4C3×#12511yescharacteristic
574C2×C4C3×#12611yescharacteristic
575C2×C4C3×#12611yescharacteristic
576C2×C4C3×C4⋊Q811yescharacteristic
577C8—24no—
578C8—42no—
579C2×C3#143611yescharacteristic
580C2×C3C4×#10711yescharacteristic
581C2×C3#177611yescharacteristic
582C2×C3#185211yescharacteristic
583C2×C3#185411yescharacteristic
584C2×C3#186211yescharacteristic
585C2×C3#186311yescharacteristic
586C2×C3#187811yescharacteristic
587C2×C3#187911yescharacteristic
588C2×C3#191811yescharacteristic
589C2×C3#192111yescharacteristic
590C2×C3#192511yescharacteristic
591C2×C3#192811yescharacteristic
592C2×C3#194711yescharacteristic
593C2×C3#194911yescharacteristic
594C22C3×C4×C4⋊C411yescharacteristic
595C22C3×#38511yescharacteristic
596C22C3×#38511yescharacteristic
597C22C3×#38611yescharacteristic
598C22C3×#38711yescharacteristic
599C22C3×#38811yescharacteristic
600C22C3×#38911yescharacteristic
601C22C2×C3×#10711yescharacteristic
602C22C3×#42711yescharacteristic
603C22C3×#42811yescharacteristic
604C22C3×#42811yescharacteristic
605C22C3×C4×D811yescharacteristic
606C22C3×C4×D811yescharacteristic
607C22C3×C4×Q1611yescharacteristic
608C22C3×C4×Q1611yescharacteristic
609C22C3×#44011yescharacteristic
610C22C3×#44011yescharacteristic
611C22C3×#44111yescharacteristic
612C22C3×#44211yescharacteristic
613C22C3×#44711yescharacteristic
614C22C3×#44911yescharacteristic
615C22C3×#45111yescharacteristic
616C22C3×#45211yescharacteristic
617C22C3×#45911yescharacteristic
618C22C3×#46211yescharacteristic
619C22C3×#46311yescharacteristic
620C22C3×#46411yescharacteristic
621C22C3×#47411yescharacteristic
622C22C3×#47711yescharacteristic
623C22C3×#47811yescharacteristic
624C22C3×#47911yescharacteristic
625C22C3×#48011yescharacteristic
626C22C3×#48211yescharacteristic
627C22C3×#48411yescharacteristic
628C22C3×#48511yescharacteristic
629C4—24no—
630C4—42no—
631C4—44no—
632C4—44no—
633C4—82no—
634C4—82no—
635C4C3×C4×C22⋊C411yescharacteristic
636C4C3×C4×C4⋊C411yescharacteristic
637C4C3×#38711yescharacteristic
638C4C3×#38711yescharacteristic
639C4C3×#38711yescharacteristic
640C4C3×#38811yescharacteristic
641C4C3×#38911yescharacteristic
642C4C3×#39111yescharacteristic
643C3#1090711yescharacteristic, direct product factor, Sylow
644C2C3×#143611yescharacteristic
645C2C3×C4×#10711yescharacteristic
646C2C3×#177611yescharacteristic
647C2C3×#185211yescharacteristic
648C2C3×#185411yescharacteristic
649C2C3×#186211yescharacteristic
650C2C3×#186311yescharacteristic
651C2C3×#187811yescharacteristic
652C2C3×#187911yescharacteristic
653C2C3×#191811yescharacteristic
654C2C3×#192111yescharacteristic
655C2C3×#192511yescharacteristic
656C2C3×#192811yescharacteristic
657C2C3×#194711yescharacteristic
658C2C3×#194911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C3C2×D4
commutatorC2×C4C2×C3×C42
Frattini, cosocleC23×C4C23×C3
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
8. #10907C3direct (N × H)
19. C2×C3×#107C4semidirect
27. C3×#340C4semidirect
28. C3×#336C4semidirect
104. C2×#107C3×C4semidirect
112. #340C3×C4semidirect
113. #336C3×C4semidirect
184. C2×C3×C8C42semidirect
320. C2×C3×C4#107semidirect
421. C2×C8C3×C42semidirect
548. C2×C4C3×#107semidirect
643. C3#10907direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1072
C2×C3×C4×C4⋊C42
C2×C3×#3402
C2×C3×#3362
C3×C4⋊#952
#109073