Finite Group Databasebeta

← C3×#24640 #10643247

Subgroups — C3×#24640 #10643247

Order 768.

918 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#463C211yesmaximal, characteristic
2C2×C3×#440C211yesmaximal, characteristic, complemented
3C3×#2545C211yesmaximal, characteristic, complemented
4C3×#2354C211yesmaximal, characteristic, complemented
5C3×#2055C211yesmaximal, characteristic, complemented
6C3×#2054C211yesmaximal, characteristic
7C3×#2013C211yesmaximal, characteristic, complemented
8C3×#2012C211yesmaximal, characteristic
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1981C211yesmaximal, characteristic, complemented
11C3×#1959C211yesmaximal, characteristic, complemented
12C3×#1940C211yesmaximal, characteristic, complemented
13C3×#1928C211yesmaximal, characteristic, complemented
14C3×#1925C211yesmaximal, characteristic, complemented
15C3×#1803C211yesmaximal, characteristic, complemented
16#24640C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×D4C2211yescharacteristic
25C2×C3×#117—21no—
26C3×#463—24no—
27C3×#440—24no—
28C2×C3×#107C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#97C2211yescharacteristic
43C3×#396—21no—
44C3×#396—21no—
45C3×#391C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#388—21no—
50C3×#388—21no—
51C3×#388—21no—
52C3×#388—21no—
53C3×#384C2211yescharacteristic
54C3×#380—21no—
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×C4×C4⋊C4C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#463C2×C311yescharacteristic
63C2×#440C2×C311yescharacteristic, complemented
64#2545C2×C311yescharacteristic, complemented
65#2354C2×C311yescharacteristic, complemented
66#2055C2×C311yescharacteristic, complemented
67#2054C2×C311yescharacteristic
68#2013C2×C311yescharacteristic, complemented
69#2012C2×C311yescharacteristic
70#1983C2×C311yescharacteristic, complemented
71#1981C2×C311yescharacteristic, complemented
72#1959C2×C311yescharacteristic, complemented
73#1940C2×C311yescharacteristic, complemented
74#1928C2×C311yescharacteristic, complemented
75#1925C2×C311yescharacteristic, complemented
76#1803C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C2×C3×SD16—22no—
83C2×C3×SD16—22no—
84C2×C3×SD16—22no—
85C2×C3×SD16—22no—
86C2×C3×SD16—41no—
87C2×C3×SD16—41no—
88C2×C3×D8—22no—
89C2×C3×D8—41no—
90C2×C3×D8—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×C4⋊Q8—22no—
96C3×C4⋊Q8—41no—
97C3×#124—22no—
98C3×#124—22no—
99C3×#124—22no—
100C3×#124—41no—
101C3×C4×Q8—22no—
102C3×C4×Q8—22no—
103C3×C4×D4—22no—
104C3×C4×D4D414yes—
105C3×#117—44no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4D411yescharacteristic
112C2×C3×C4⋊C4D411yescharacteristic
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×C42—21no—
129C2×C3×C42—21no—
130C2×C3×C42—21no—
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C2×C3×C42C2311yescharacteristic
134C3×#107—22no—
135C3×C4⋊C8—22no—
136C3×C4⋊C8—41no—
137C3×C4⋊C8—41no—
138C3×#103—22no—
139C3×#103—22no—
140C3×#103—22no—
141C3×#103—41no—
142C3×#103—41no—
143C3×#103—41no—
144C3×#102—22no—
145C3×#102—22no—
146C3×#102—22no—
147C3×#102—41no—
148C3×#97—22no—
149C3×#95—21no—
150C3×#95—21no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95D411yescharacteristic
154C3×#95D411yescharacteristic
155C22×SD16C22×C311yescharacteristic
156C22×SD16C22×C311yescharacteristic
157C22×D8C22×C311yescharacteristic
158C2×C4⋊Q8C22×C311yescharacteristic
159C2×#124C22×C311yescharacteristic
160C2×#124C22×C311yescharacteristic
161C2×C4×Q8C22×C311yescharacteristic
162C2×C4×D4C22×C311yescharacteristic
163C2×#117—21no—
164#463—24no—
165#440—24no—
166C2×#107C22×C311yescharacteristic
167C2×C4⋊C8C22×C311yescharacteristic
168C2×C4⋊C8C22×C311yescharacteristic
169C2×C4⋊C8C22×C311yescharacteristic
170C2×#103C22×C311yescharacteristic
171C2×#103C22×C311yescharacteristic
172C2×#103C22×C311yescharacteristic
173C2×#103C22×C311yescharacteristic
174C2×#103C22×C311yescharacteristic
175C2×#103C22×C311yescharacteristic
176C2×#102C22×C311yescharacteristic
177C2×#102C22×C311yescharacteristic
178C2×#102C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#97C22×C311yescharacteristic
181#396—21no—
182#396—21no—
183#391C22×C311yescharacteristic
184#390C22×C311yescharacteristic
185#390C22×C311yescharacteristic
186#390C22×C311yescharacteristic
187#388—21no—
188#388—21no—
189#388—21no—
190#388—21no—
191#384C22×C311yescharacteristic
192#380—21no—
193C4×C4⋊C4C22×C311yescharacteristic
194C4×C4⋊C4C22×C311yescharacteristic
195C4×C4⋊C4C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#336C22×C311yescharacteristic
199#336C22×C311yescharacteristic
200C24×C3—21no—
201C24×C3—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—21no—
213C2×C3×Q8#4112yes—
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—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4C2×D412yes—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C3×SD16—28no—
243C3×SD16—44no—
244C3×D8—44no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
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#4112yes—
257C3×C4⋊C4—22no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—42no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4—42no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4—81no—
271C3×C4⋊C4C2×D412yes—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—42no—
279C3×C22⋊C4—42no—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—81no—
282C3×C22⋊C4—81no—
283C3×C42—21no—
284C3×C42—21no—
285C3×C42—21no—
286C3×C42—21no—
287C3×C42—42no—
288C3×C42—42no—
289C3×C42—42no—
290C3×C42C2×D412yes—
291C3×C42#4112yes—
292C22×Q8C23×C311yescharacteristic
293C22×Q8C23×C311yescharacteristic
294C22×D4C23×C311yescharacteristic
295C22×D4C23×C311yescharacteristic
296C23×C4—21no—
297C2×SD16—22no—
298C2×SD16—22no—
299C2×SD16—22no—
300C2×SD16—22no—
301C2×SD16—41no—
302C2×SD16—41no—
303C2×D8—22no—
304C2×D8—41no—
305C2×D8—41no—
306C22×C8C23×C311yescharacteristic
307C22×C8C23×C311yescharacteristic
308C22×C8C23×C311yescharacteristic
309C22×C8C23×C311yescharacteristic
310C4⋊Q8—22no—
311C4⋊Q8—41no—
312#124—22no—
313#124—22no—
314#124—22no—
315#124—41no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×D4—22no—
319C4×D4C3×D414yes—
320#117—44no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4C3×D411yescharacteristic
327C2×C4⋊C4C3×D411yescharacteristic
328C2×C4⋊C4C23×C311yescharacteristic
329C2×C4⋊C4C23×C311yescharacteristic
330C2×C4⋊C4C23×C311yescharacteristic
331C2×C4⋊C4C23×C311yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
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×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42C23×C311yescharacteristic
347C2×C42C23×C311yescharacteristic
348C2×C42C23×C311yescharacteristic
349#107—22no—
350C4⋊C8—22no—
351C4⋊C8—41no—
352C4⋊C8—41no—
353#103—22no—
354#103—22no—
355#103—22no—
356#103—41no—
357#103—41no—
358#103—41no—
359#102—22no—
360#102—22no—
361#102—22no—
362#102—41no—
363#97—22no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95C3×D411yescharacteristic
369#95C3×D411yescharacteristic
370C23×C3—22no—
371C23×C3—41no—
372C23×C3—41no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3C22×D411yescharacteristic
385C3×Q8—22no—
386C3×Q8—22no—
387C3×Q8—41no—
388C3×Q8—41no—
389C3×Q8—41no—
390C3×Q8—41no—
391C3×Q8—41no—
392C3×Q8—41no—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—41no—
396C3×D4—41no—
397C3×D4—41no—
398C3×D4—41no—
399C3×D4—41no—
400C3×D4—41no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—48no—
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#12112yes—
436C2×C3×C4#12112yes—
437C2×C3×C4AGL(1,ℤ/8)12yes—
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—41no—
446C3×C8—41no—
447C3×C8—41no—
448C24—21no—
449C24—21no—
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—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4C2×C3×D412yes—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4C2×C3×D411yescharacteristic
484C22×C4C2×C3×D411yescharacteristic
485C22×C4C2×C3×D411yescharacteristic
486C22×C4C2×C3×D411yescharacteristic
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C24×C311yescharacteristic
490SD16—28no—
491SD16—44no—
492D8—44no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8C3×#4112yes—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—42no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—81no—
519C4⋊C4C2×C3×D412yes—
520C22⋊C4—24no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—42no—
536C42—42no—
537C42—42no—
538C42C2×C3×D412yes—
539C42C3×#4112yes—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—81no—
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#54611yescharacteristic
556C22×C3#55011yescharacteristic
557C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
558C22×C3#57511yescharacteristic
559C22×C3#57711yescharacteristic
560C22×C3#57811yescharacteristic
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—22no—
564C3×C4—42no—
565C3×C4—42no—
566C3×C4—41no—
567C3×C4—41no—
568C3×C4—41no—
569C3×C4—81no—
570C3×C4—81no—
571C3×C4—81no—
572C3×C4—81no—
573C3×C4#52511yescharacteristic
574C3×C4#53511yescharacteristic
575C3×C4#55311yescharacteristic
576C3×C4#55511yescharacteristic
577C23—22no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23C22×C3×D411yescharacteristic
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—41no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
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—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—48no—
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×C4C3×#12112yes—
643C2×C4C3×#12112yes—
644C2×C4C3×AGL(1,ℤ/8)12yes—
645C2×C4C22×C3×D411yescharacteristic
646C2×C4C2×C3×#4111yescharacteristic
647C2×C4C2×C3×#4111yescharacteristic
648C2×C4C2×C3×#4111yescharacteristic
649C2×C4C3×H(5,𝔽2)11yescharacteristic
650C2×C4C3×H(5,𝔽2)11yescharacteristic
651C8—22no—
652C8—41no—
653C8—41no—
654C8—41no—
655C2×C3—82no—
656C2×C3—161no—
657C2×C3#241411yescharacteristic
658C2×C3#303611yescharacteristic
659C2×C3#304611yescharacteristic
660C2×C3#330811yescharacteristic
661C2×C3#332111yescharacteristic
662C2×C3#339711yescharacteristic
663C2×C3#340211yescharacteristic
664C22—42no—
665C22—42no—
666C22—42no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22C2×C3×#12111yescharacteristic
679C22C3×#54611yescharacteristic
680C22C3×#55011yescharacteristic
681C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
682C22C3×#57511yescharacteristic
683C22C3×#57711yescharacteristic
684C22C3×#57811yescharacteristic
685C4—22no—
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C3×#52511yescharacteristic
698C4C3×#53511yescharacteristic
699C4C3×#55311yescharacteristic
700C4C3×#55511yescharacteristic
701C3#2464011yescharacteristic, direct product factor, Sylow
702C2—82no—
703C2—161no—
704C2C3×#241411yescharacteristic
705C2C3×#303611yescharacteristic
706C2C3×#304611yescharacteristic
707C2C3×#330811yescharacteristic
708C2C3×#332111yescharacteristic
709C2C3×#339711yescharacteristic
710C2C3×#340211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#440C2semidirect
3. C3×#2545C2semidirect
4. C3×#2354C2semidirect
5. C3×#2055C2semidirect
7. C3×#2013C2semidirect
9. C3×#1983C2semidirect
10. C3×#1981C2semidirect
11. C3×#1959C2semidirect
12. C3×#1940C2semidirect
13. C3×#1928C2semidirect
14. C3×#1925C2semidirect
15. C3×#1803C2semidirect
16. #24640C3direct (N × H)
63. C2×#440C2×C3semidirect
64. #2545C2×C3semidirect
65. #2354C2×C3semidirect
66. #2055C2×C3semidirect
68. #2013C2×C3semidirect
70. #1983C2×C3semidirect
71. #1981C2×C3semidirect
72. #1959C2×C3semidirect
73. #1940C2×C3semidirect
74. #1928C2×C3semidirect
75. #1925C2×C3semidirect
76. #1803C2×C3semidirect
701. C3#24640direct (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×#4402
C3×#25452
C3×#23542
C3×#20552
C3×#20542
C3×#20132
C3×#20122
C3×#19832
C3×#19812
C3×#19592
C3×#19402
C3×#19282
C3×#19252
C3×#18032
#246403