Finite Group Databasebeta

← C3×#21896 #10640503

Subgroups — C3×#21896 #10640503

Order 768.

1078 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic
2C2×C3×#424C211yesmaximal, characteristic, complemented
3C3×#2314C211yesmaximal, characteristic, complemented
4C3×#1988C211yesmaximal, characteristic, complemented
5C3×#1987C211yesmaximal, characteristic, complemented
6C3×#1983C211yesmaximal, characteristic, complemented
7C3×#1983C211yesmaximal, characteristic, complemented
8C3×#1895C211yesmaximal, characteristic
9C3×#1894C211yesmaximal, characteristic, complemented
10C3×#1893C211yesmaximal, characteristic
11C3×#1892C211yesmaximal, characteristic, complemented
12C3×#1805C211yesmaximal, characteristic, complemented
13C3×#1804C211yesmaximal, characteristic, complemented
14C3×#1803C211yesmaximal, characteristic, complemented
15C3×#1802C211yesmaximal, characteristic, complemented
16#21896C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×M16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C3×#542—24no—
20C3×#542C418yescomplemented
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#126—21no—
23C2×C3×#124—21no—
24C2×C3×#124C2211yescharacteristic
25C2×C3×#123—21no—
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×C4×Q8C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×#117C2211yescharacteristic
32C3×#424—24no—
33C2×C3×C4⋊C8C2211yescharacteristic
34C2×C3×C4⋊C8C2211yescharacteristic
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×C4⋊C8C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C3×#388—21no—
46C3×#388—21no—
47C3×#387—21no—
48C3×#387—21no—
49C3×#384C2211yescharacteristic
50C3×#382C2211yescharacteristic
51C3×#380C2211yescharacteristic
52C3×#380C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C2×#542C2×C311yescharacteristic
64C2×#424C2×C311yescharacteristic, complemented
65#2314C2×C311yescharacteristic, complemented
66#1988C2×C311yescharacteristic, complemented
67#1987C2×C311yescharacteristic, complemented
68#1983C2×C311yescharacteristic, complemented
69#1983C2×C311yescharacteristic, complemented
70#1895C2×C311yescharacteristic
71#1894C2×C311yescharacteristic, complemented
72#1893C2×C311yescharacteristic
73#1892C2×C311yescharacteristic, complemented
74#1805C2×C311yescharacteristic, complemented
75#1804C2×C311yescharacteristic, complemented
76#1803C2×C311yescharacteristic, complemented
77#1802C2×C311yescharacteristic, complemented
78C22×C3×Q8—21no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C2×C3×M16—22no—
85C2×C3×M16—41no—
86C2×C3×M16—41no—
87C22×C3×C8—22no—
88C22×C3×C8—41no—
89C22×C3×C8—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C4⋊Q8—22no—
95C3×C4⋊Q8C2×C414yes—
96C3×#126—28no—
97C3×#124—28no—
98C3×#124—22no—
99C3×#124C2×C414yes—
100C3×#123—28no—
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—28no—
103C3×C22⋊Q8C2×C414yes—
104C3×#121—22no—
105C3×#121C2×C414yes—
106C3×C4×Q8—22no—
107C3×C4×Q8C2×C414yes—
108C3×C4×D4—22no—
109C3×C4×D4C2×C414yes—
110C3×#117C2×C414yes—
111C3×#117D414yes—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4D411yescharacteristic
118C2×C3×C4⋊C4D411yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
132C2×C3×C22⋊C4D411yescharacteristic
133C2×C3×C22⋊C4D411yescharacteristic
134C2×C3×C42—21no—
135C2×C3×C42—21no—
136C2×C3×C42—21no—
137C2×C3×C42C2311yescharacteristic
138C2×C3×C42C2311yescharacteristic
139C3×C4⋊C8—22no—
140C3×C4⋊C8—22no—
141C3×C4⋊C8—22no—
142C3×C4⋊C8—22no—
143C3×#103—41no—
144C3×#103—41no—
145C3×#103—41no—
146C3×#103—41no—
147C3×#102—41no—
148C3×#102—41no—
149C3×#102—41no—
150C3×#102—41no—
151C3×#95—21no—
152C3×#95—21no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C22×M16C22×C311yescharacteristic
158C23×C8C22×C311yescharacteristic
159#542—24no—
160#542C3×C418yescomplemented
161C2×C4⋊Q8C22×C311yescharacteristic
162C2×#126—21no—
163C2×#124—21no—
164C2×#124C22×C311yescharacteristic
165C2×#123—21no—
166C2×C22⋊Q8—21no—
167C2×C22⋊Q8C22×C311yescharacteristic
168C2×#121C22×C311yescharacteristic
169C2×C4×Q8C22×C311yescharacteristic
170C2×C4×D4C22×C311yescharacteristic
171C2×#117C22×C311yescharacteristic
172#424—24no—
173C2×C4⋊C8C22×C311yescharacteristic
174C2×C4⋊C8C22×C311yescharacteristic
175C2×C4⋊C8C22×C311yescharacteristic
176C2×C4⋊C8C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×#102C22×C311yescharacteristic
185#388—21no—
186#388—21no—
187#387—21no—
188#387—21no—
189#384C22×C311yescharacteristic
190#382C22×C311yescharacteristic
191#380C22×C311yescharacteristic
192#380C22×C311yescharacteristic
193C4×C4⋊C4C22×C311yescharacteristic
194C4×C4⋊C4C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#340C22×C311yescharacteristic
202#340C22×C311yescharacteristic
203C24×C3—21no—
204C24×C3C2×D411yescharacteristic
205C2×C3×Q8—24no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—81no—
212C2×C3×Q8—81no—
213C2×C3×Q8C22×C412yes—
214C2×C3×D4—24no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—81no—
221C2×C3×D4—81no—
222C2×C3×D4C22×C412yes—
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—24no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—81no—
236C22×C3×C4—81no—
237C22×C3×C4C22×C412yes—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D412yes—
244C22×C3×C4C2411yescharacteristic
245C3×M16—44no—
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—21no—
257C2×C3×C8—21no—
258C2×C3×C8—44no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—24no—
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—21no—
272C3×C4⋊C4—81no—
273C3×C4⋊C4—81no—
274C3×C4⋊C4C22⋊C414yes—
275C3×C4⋊C4C22⋊C414yes—
276C3×C4⋊C4C22×C412yes—
277C3×C4⋊C4C22×C412yes—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—81no—
284C3×C22⋊C4—81no—
285C3×C22⋊C4C22⋊C414yes—
286C3×C22⋊C4C22⋊C414yes—
287C3×C42—24no—
288C3×C42—81no—
289C3×C42—81no—
290C3×C42C22×C412yes—
291C3×C42C22×C412yes—
292C3×C42C2×D412yes—
293C3×C42C2×D412yes—
294C22×Q8—21no—
295C22×Q8C23×C311yescharacteristic
296C22×D4—21no—
297C22×D4C23×C311yescharacteristic
298C23×C4—21no—
299C23×C4C23×C311yescharacteristic
300C2×M16—22no—
301C2×M16—41no—
302C2×M16—41no—
303C22×C8—22no—
304C22×C8—41no—
305C22×C8—41no—
306C22×C8C23×C311yescharacteristic
307C22×C8C23×C311yescharacteristic
308C22×C8C23×C311yescharacteristic
309C22×C8C23×C311yescharacteristic
310C4⋊Q8—22no—
311C4⋊Q8C2×C3×C414yes—
312#126—28no—
313#124—28no—
314#124—22no—
315#124C2×C3×C414yes—
316#123—28no—
317C22⋊Q8—22no—
318C22⋊Q8—28no—
319C22⋊Q8C2×C3×C414yes—
320#121—22no—
321#121C2×C3×C414yes—
322C4×Q8—22no—
323C4×Q8C2×C3×C414yes—
324C4×D4—22no—
325C4×D4C2×C3×C414yes—
326#117C2×C3×C414yes—
327#117C3×D414yes—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4C3×D411yescharacteristic
334C2×C4⋊C4C3×D411yescharacteristic
335C2×C4⋊C4C23×C311yescharacteristic
336C2×C4⋊C4C23×C311yescharacteristic
337C2×C4⋊C4C23×C311yescharacteristic
338C2×C4⋊C4C23×C311yescharacteristic
339C2×C4⋊C4C23×C311yescharacteristic
340C2×C4⋊C4C23×C311yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4C3×D411yescharacteristic
349C2×C22⋊C4C3×D411yescharacteristic
350C2×C42—21no—
351C2×C42—21no—
352C2×C42—21no—
353C2×C42C23×C311yescharacteristic
354C2×C42C23×C311yescharacteristic
355C4⋊C8—22no—
356C4⋊C8—22no—
357C4⋊C8—22no—
358C4⋊C8—22no—
359#103—41no—
360#103—41no—
361#103—41no—
362#103—41no—
363#102—41no—
364#102—41no—
365#102—41no—
366#102—41no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372#95—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—22no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3C2×C22⋊C412yes—
387C23×C3C22×D411yescharacteristic
388C3×Q8—22no—
389C3×Q8—22no—
390C3×Q8—41no—
391C3×Q8—41no—
392C3×Q8—84no—
393C3×D4—22no—
394C3×D4—22no—
395C3×D4—41no—
396C3×D4—41no—
397C3×D4—84no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
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—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
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—84no—
434C2×C3×C4C2×C22⋊C412yes—
435C2×C3×C4C2×C22⋊C412yes—
436C2×C3×C4C2×C22⋊C412yes—
437C2×C3×C4C2×C22⋊C412yes—
438C2×C3×C4C2×C22⋊C412yes—
439C2×C3×C4C23×C411yescharacteristic
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4H(5,𝔽2)11yescharacteristic
442C2×C3×C4H(5,𝔽2)11yescharacteristic
443C2×C3×C42−1+411yescharacteristic
444C2×C3×C42−1+411yescharacteristic
445C3×C8—41no—
446C3×C8—41no—
447C3×C8—41no—
448C3×C8—41no—
449C24—21no—
450C24C2×C3×D411yescharacteristic
451C2×Q8—24no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—81no—
458C2×Q8—81no—
459C2×Q8C22×C3×C412yes—
460C2×D4—24no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—81no—
467C2×D4—81no—
468C2×D4C22×C3×C412yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4C22×C3×C412yes—
484C22×C4C2×C3×D411yescharacteristic
485C22×C4C2×C3×D411yescharacteristic
486C22×C4C2×C3×D411yescharacteristic
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D412yes—
490C22×C4C24×C311yescharacteristic
491M16—44no—
492C2×C8—21no—
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×C8—44no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
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—21no—
517C4⋊C4—21no—
518C4⋊C4—81no—
519C4⋊C4—81no—
520C4⋊C4C3×C22⋊C414yes—
521C4⋊C4C3×C22⋊C414yes—
522C4⋊C4C22×C3×C412yes—
523C4⋊C4C22×C3×C412yes—
524C22⋊C4—24no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—81no—
530C22⋊C4—81no—
531C22⋊C4C3×C22⋊C414yes—
532C22⋊C4C3×C22⋊C414yes—
533C42—24no—
534C42—81no—
535C42—81no—
536C42C22×C3×C412yes—
537C42C22×C3×C412yes—
538C42C2×C3×D412yes—
539C42C2×C3×D412yes—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—42no—
550C22×C3—81no—
551C22×C3—81no—
552C22×C3—81no—
553C22×C3—81no—
554C22×C3C22×C22⋊C411yescharacteristic
555C22×C3#53711yescharacteristic
556C22×C3#53711yescharacteristic
557C22×C3#57611yescharacteristic
558C22×C3#57711yescharacteristic
559C22×C3#57711yescharacteristic
560C22×C3#57811yescharacteristic
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—42no—
567C3×C4—42no—
568C3×C4—42no—
569C3×C4—81no—
570C3×C4—81no—
571C3×C4—81no—
572C3×C4—81no—
573C3×C4#52011yescharacteristic
574C3×C4#52011yescharacteristic
575C3×C4#53511yescharacteristic
576C3×C4#53611yescharacteristic
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—22no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23C2×C3×C22⋊C412yes—
591C23C22×C3×D411yescharacteristic
592Q8—22no—
593Q8—22no—
594Q8—41no—
595Q8—41no—
596Q8—84no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—84no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
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×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4C2×C3×C22⋊C412yes—
639C2×C4C2×C3×C22⋊C412yes—
640C2×C4C2×C3×C22⋊C412yes—
641C2×C4C2×C3×C22⋊C412yes—
642C2×C4C2×C3×C22⋊C412yes—
643C2×C4C23×C3×C411yescharacteristic
644C2×C4C22×C3×D411yescharacteristic
645C2×C4C3×H(5,𝔽2)11yescharacteristic
646C2×C4C3×H(5,𝔽2)11yescharacteristic
647C2×C4C3×2−1+411yescharacteristic
648C2×C4C3×2−1+411yescharacteristic
649C8—41no—
650C8—41no—
651C8—41no—
652C8—41no—
653C2×C3—42no—
654C2×C3—82no—
655C2×C3#231111yescharacteristic
656C2×C3#289711yescharacteristic
657C2×C3#289811yescharacteristic
658C2×C3#325711yescharacteristic
659C2×C3#325811yescharacteristic
660C2×C3#326211yescharacteristic
661C2×C3#326311yescharacteristic
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22C22×C3×C22⋊C411yescharacteristic
677C22C3×#53711yescharacteristic
678C22C3×#53711yescharacteristic
679C22C3×#57611yescharacteristic
680C22C3×#57711yescharacteristic
681C22C3×#57711yescharacteristic
682C22C3×#57811yescharacteristic
683C4—22no—
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—42no—
689C4—42no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4C3×#52011yescharacteristic
696C4C3×#52011yescharacteristic
697C4C3×#53511yescharacteristic
698C4C3×#53611yescharacteristic
699C3#2189611yescharacteristic, direct product factor, Sylow
700C2—42no—
701C2—82no—
702C2C3×#231111yescharacteristic
703C2C3×#289711yescharacteristic
704C2C3×#289811yescharacteristic
705C2C3×#325711yescharacteristic
706C2C3×#325811yescharacteristic
707C2C3×#326211yescharacteristic
708C2C3×#326311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutatorC2×C4C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#424C2semidirect
3. C3×#2314C2semidirect
4. C3×#1988C2semidirect
5. C3×#1987C2semidirect
6. C3×#1983C2semidirect
7. C3×#1983C2semidirect
9. C3×#1894C2semidirect
11. C3×#1892C2semidirect
12. C3×#1805C2semidirect
13. C3×#1804C2semidirect
14. C3×#1803C2semidirect
15. C3×#1802C2semidirect
16. #21896C3direct (N × H)
20. C3×#542C4semidirect
64. C2×#424C2×C3semidirect
65. #2314C2×C3semidirect
66. #1988C2×C3semidirect
67. #1987C2×C3semidirect
68. #1983C2×C3semidirect
69. #1983C2×C3semidirect
71. #1894C2×C3semidirect
73. #1892C2×C3semidirect
74. #1805C2×C3semidirect
75. #1804C2×C3semidirect
76. #1803C2×C3semidirect
77. #1802C2×C3semidirect
160. #542C3×C4semidirect
699. C3#21896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×C3×#4242
C3×#23142
C3×#19882
C3×#19872
C3×#19832
C3×#18952
C3×#18942
C3×#18932
C3×#18922
C3×#18052
C3×#18042
C3×#18032
C3×#18022
#218963