Finite Group Databasebeta

← C3×#25708 #10644315

Subgroups — C3×#25708 #10644315

Order 768.

1028 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#552C211yesmaximal, characteristic
2C2×C3×#499C211yesmaximal, characteristic, complemented
3C2×C3×#479C211yesmaximal, characteristic, complemented
4C3×#2562C211yesmaximal, characteristic
5C3×#2036C211yesmaximal, characteristic, complemented
6C3×#2036C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8C3×#2035C211yesmaximal, characteristic, complemented
9C3×#1989C211yesmaximal, characteristic, complemented
10C3×#1954C211yesmaximal, characteristic
11C3×#1854C211yesmaximal, characteristic, complemented
12C3×#1854C211yesmaximal, characteristic, complemented
13C3×#1853C211yesmaximal, characteristic, complemented
14C3×#1852C211yesmaximal, characteristic, complemented
15C3×C4×#103C211yesmaximal, characteristic, complemented
16#25708C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#552—24no—
18C3×#552—24no—
19C2×C3×#126—21no—
20C2×C3×#125—21no—
21C2×C3×#125C2211yescharacteristic
22C2×C3×#125C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117—21no—
29C2×C3×#117C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C3×#499—24no—
32C3×#479—24no—
33C2×C3×#107C2211yescharacteristic
34C2×C3×#107C2211yescharacteristic
35C2×C3×#107C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×#106C2211yescharacteristic
38C2×C3×#106C2211yescharacteristic
39C2×C3×C4⋊C8C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49C3×#400—21no—
50C3×#394—21no—
51C3×#388—21no—
52C3×#388—21no—
53C3×#380C2211yescharacteristic
54C3×#380C2211yescharacteristic
55C3×#380C2211yescharacteristic
56C3×#380C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C2×#552C2×C311yescharacteristic
65C2×#499C2×C311yescharacteristic, complemented
66C2×#479C2×C311yescharacteristic, complemented
67#2562C2×C311yescharacteristic
68#2036C2×C311yescharacteristic, complemented
69#2036C2×C311yescharacteristic, complemented
70#2035C2×C311yescharacteristic, complemented
71#2035C2×C311yescharacteristic, complemented
72#1989C2×C311yescharacteristic, complemented
73#1954C2×C311yescharacteristic
74#1854C2×C311yescharacteristic, complemented
75#1854C2×C311yescharacteristic, complemented
76#1853C2×C311yescharacteristic, complemented
77#1852C2×C311yescharacteristic, complemented
78C4×#103C2×C311yescharacteristic, complemented
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4D411yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C3×#126—28no—
89C3×#125—28no—
90C3×#125—22no—
91C3×#125—22no—
92C3×#125—22no—
93C3×#125D414yes—
94C3×#123—28no—
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—22no—
98C3×C22⋊Q8—22no—
99C3×C4×Q8—22no—
100C3×C4×Q8D414yes—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C3×#117—28no—
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⋊C4—21no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—22no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4D411yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—21no—
128C2×C3×C22⋊C4—21no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4D411yescharacteristic
132C2×C3×C22⋊C4D411yescharacteristic
133C2×C3×C42—21no—
134C2×C3×C42—21no—
135C2×C3×C42—21no—
136C2×C3×C42C2311yescharacteristic
137C3×#107—22no—
138C3×#107—22no—
139C3×#107—22no—
140C3×#106—22no—
141C3×#106—22no—
142C3×#106—22no—
143C3×C4⋊C8—22no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×C22⋊C8—22no—
149C3×C22⋊C8—22no—
150C3×C22⋊C8—22no—
151C3×C22⋊C8—22no—
152C3×C4×C8—22no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158#552—24no—
159#552—24no—
160C2×#126—21no—
161C2×#125—21no—
162C2×#125C22×C311yescharacteristic
163C2×#125C22×C311yescharacteristic
164C2×#123—21no—
165C2×C22⋊Q8C22×C311yescharacteristic
166C2×C22⋊Q8C22×C311yescharacteristic
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×D4C22×C311yescharacteristic
169C2×#117—21no—
170C2×#117C22×C311yescharacteristic
171C22×C4⋊C4C22×C311yescharacteristic
172#499—24no—
173#479—24no—
174C2×#107C22×C311yescharacteristic
175C2×#107C22×C311yescharacteristic
176C2×#107C22×C311yescharacteristic
177C2×#106C22×C311yescharacteristic
178C2×#106C22×C311yescharacteristic
179C2×#106C22×C311yescharacteristic
180C2×C4⋊C8C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×#103C22×C311yescharacteristic
183C2×#103C22×C311yescharacteristic
184C2×#103C22×C311yescharacteristic
185C2×C22⋊C8C22×C311yescharacteristic
186C2×C22⋊C8C22×C311yescharacteristic
187C2×C22⋊C8C22×C311yescharacteristic
188C2×C22⋊C8C22×C311yescharacteristic
189C2×C4×C8C22×C311yescharacteristic
190#400—21no—
191#394—21no—
192#388—21no—
193#388—21no—
194#380C22×C311yescharacteristic
195#380C22×C311yescharacteristic
196#380C22×C311yescharacteristic
197#380C22×C311yescharacteristic
198C4×C4⋊C4C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203#340C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205C24×C3C2×D411yescharacteristic
206C24×C3C2×D411yescharacteristic
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8C2×D412yes—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—41no—
216C22×C3×C4—24no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
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—42no—
238C22×C3×C4—42no—
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C2×C3×C8—21no—
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#4112yes—
255C2×C3×C8#4112yes—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
261C3×C4⋊C4—24no—
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—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—42no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4C2×D412yes—
277C3×C4⋊C4C2×D412yes—
278C3×C4⋊C4C2×D412yes—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—22no—
283C3×C22⋊C4—22no—
284C3×C22⋊C4—42no—
285C3×C22⋊C4—42no—
286C3×C22⋊C4—81no—
287C3×C22⋊C4—81no—
288C3×C42—24no—
289C3×C42—24no—
290C3×C42—81no—
291C3×C42C2×D412yes—
292C3×C42C2×D412yes—
293C22×Q8C23×C311yescharacteristic
294C22×D4C3×D411yescharacteristic
295C23×C4—21no—
296C23×C4C23×C311yescharacteristic
297C23×C4C23×C311yescharacteristic
298C22×C8C23×C311yescharacteristic
299C22×C8C23×C311yescharacteristic
300C22×C8C23×C311yescharacteristic
301C22×C8C23×C311yescharacteristic
302#126—28no—
303#125—28no—
304#125—22no—
305#125—22no—
306#125—22no—
307#125C3×D414yes—
308#123—28no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C4×Q8—22no—
314C4×Q8C3×D414yes—
315C4×D4—22no—
316C4×D4—22no—
317#117—28no—
318#117—22no—
319#117—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4C3×D411yescharacteristic
331C2×C4⋊C4C23×C311yescharacteristic
332C2×C4⋊C4C23×C311yescharacteristic
333C2×C4⋊C4C23×C311yescharacteristic
334C2×C4⋊C4C23×C311yescharacteristic
335C2×C4⋊C4C23×C311yescharacteristic
336C2×C4⋊C4C23×C311yescharacteristic
337C2×C4⋊C4C23×C311yescharacteristic
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⋊C4C3×D411yescharacteristic
346C2×C22⋊C4C3×D411yescharacteristic
347C2×C42—21no—
348C2×C42—21no—
349C2×C42—21no—
350C2×C42C23×C311yescharacteristic
351#107—22no—
352#107—22no—
353#107—22no—
354#106—22no—
355#106—22no—
356#106—22no—
357C4⋊C8—22no—
358#103—22no—
359#103—22no—
360#103—22no—
361#103—22no—
362C22⋊C8—22no—
363C22⋊C8—22no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366C4×C8—22no—
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—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3#13512yes—
386C23×C3C22×D411yescharacteristic
387C3×Q8—22no—
388C3×Q8—22no—
389C3×Q8—41no—
390C3×Q8—41no—
391C3×D4—44no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—48no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
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#12012yes—
436C2×C3×C4#12012yes—
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C42−1+411yescharacteristic
442C2×C3×C42−1+411yescharacteristic
443C3×C8—22no—
444C3×C8—22no—
445C3×C8—41no—
446C3×C8—41no—
447C24C2×C3×D411yescharacteristic
448C24C2×C3×D411yescharacteristic
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×C3×D412yes—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—41no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4C2×C3×D411yescharacteristic
482C22×C4C2×C3×D411yescharacteristic
483C22×C4C2×C3×D411yescharacteristic
484C22×C4C2×C3×D411yescharacteristic
485C22×C4C24×C311yescharacteristic
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8C3×#4112yes—
497C2×C8C3×#4112yes—
498C4⋊C4—24no—
499C4⋊C4—24no—
500C4⋊C4—24no—
501C4⋊C4—24no—
502C4⋊C4—24no—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4C2×C3×D412yes—
519C4⋊C4C2×C3×D412yes—
520C4⋊C4C2×C3×D412yes—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—81no—
529C22⋊C4—81no—
530C42—24no—
531C42—24no—
532C42—81no—
533C42C2×C3×D412yes—
534C42C2×C3×D412yes—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3C2×#12011yescharacteristic
550C22×C3#54711yescharacteristic
551C22×C3#54711yescharacteristic
552C22×C3C2×#13511yescharacteristic
553C22×C3#57511yescharacteristic
554C22×C3#57711yescharacteristic
555C22×C3#57811yescharacteristic
556C3×C4—22no—
557C3×C4—22no—
558C3×C4—41no—
559C3×C4—41no—
560C3×C4—42no—
561C3×C4—42no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—81no—
565C3×C4—81no—
566C3×C4—81no—
567C3×C4—81no—
568C3×C4#53211yescharacteristic
569C3×C4#53611yescharacteristic
570C3×C4#54811yescharacteristic
571C3×C4#54811yescharacteristic
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23C3×#13512yes—
586C23C22×C3×D411yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—44no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—48no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
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×C4C3×#12012yes—
636C2×C4C3×#12012yes—
637C2×C4C22×C3×D411yescharacteristic
638C2×C4C22×C3×D411yescharacteristic
639C2×C4C2×C3×#4111yescharacteristic
640C2×C4C2×C3×#4111yescharacteristic
641C2×C4C3×2−1+411yescharacteristic
642C2×C4C3×2−1+411yescharacteristic
643C8—22no—
644C8—22no—
645C8—41no—
646C8—41no—
647C2×C3—42no—
648C2×C3—81no—
649C2×C3#243211yescharacteristic
650C2×C3#300211yescharacteristic
651C2×C3#301311yescharacteristic
652C2×C3#333611yescharacteristic
653C2×C3#333711yescharacteristic
654C2×C3#335111yescharacteristic
655C2×C3#335211yescharacteristic
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22C2×C3×#12011yescharacteristic
671C22C3×#54711yescharacteristic
672C22C3×#54711yescharacteristic
673C22C2×C3×#13511yescharacteristic
674C22C3×#57511yescharacteristic
675C22C3×#57711yescharacteristic
676C22C3×#57811yescharacteristic
677C4—22no—
678C4—22no—
679C4—41no—
680C4—41no—
681C4—42no—
682C4—42no—
683C4—42no—
684C4—42no—
685C4—81no—
686C4—81no—
687C4—81no—
688C4—81no—
689C4C3×#53211yescharacteristic
690C4C3×#53611yescharacteristic
691C4C3×#54811yescharacteristic
692C4C3×#54811yescharacteristic
693C3#2570811yescharacteristic, direct product factor, Sylow
694C2—42no—
695C2—81no—
696C2C3×#243211yescharacteristic
697C2C3×#300211yescharacteristic
698C2C3×#301311yescharacteristic
699C2C3×#333611yescharacteristic
700C2C3×#333711yescharacteristic
701C2C3×#335111yescharacteristic
702C2C3×#335211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#499C2semidirect
3. C2×C3×#479C2semidirect
5. C3×#2036C2semidirect
6. C3×#2036C2semidirect
7. C3×#2035C2semidirect
8. C3×#2035C2semidirect
9. C3×#1989C2semidirect
11. C3×#1854C2semidirect
12. C3×#1854C2semidirect
13. C3×#1853C2semidirect
14. C3×#1852C2semidirect
15. C3×C4×#103C2semidirect
16. #25708C3direct (N × H)
65. C2×#499C2×C3semidirect
66. C2×#479C2×C3semidirect
68. #2036C2×C3semidirect
69. #2036C2×C3semidirect
70. #2035C2×C3semidirect
71. #2035C2×C3semidirect
72. #1989C2×C3semidirect
74. #1854C2×C3semidirect
75. #1854C2×C3semidirect
76. #1853C2×C3semidirect
77. #1852C2×C3semidirect
78. C4×#103C2×C3semidirect
693. C3#25708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5522
C2×C3×#4992
C2×C3×#4792
C3×#25622
C3×#20362
C3×#20352
C3×#19892
C3×#19542
C3×#18542
C3×#18532
C3×#18522
C3×C4×#1032
#257083