Finite Group Databasebeta

← C3×#24347 #10642954

Subgroups — C3×#24347 #10642954

Order 768.

1140 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic, complemented
3C2×C3×#442C211yesmaximal, characteristic
4C3×#2538C211yesmaximal, characteristic, complemented
5C3×#2059C211yesmaximal, characteristic, complemented
6C3×#2058C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2023C211yesmaximal, characteristic, complemented
9C3×#1992C211yesmaximal, characteristic, complemented
10C3×#1985C211yesmaximal, characteristic, complemented
11C3×#1879C211yesmaximal, characteristic
12C3×#1879C211yesmaximal, characteristic
13C3×#1864C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic, complemented
15C3×#1802C211yesmaximal, characteristic, complemented
16#24347C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C3×#554—24no—
19C3×#554—24no—
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#125C2211yescharacteristic
22C2×C3×#125C2211yescharacteristic
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8—21no—
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C22×C3×C4⋊C4—21no—
33C3×#478—24no—
34C3×#442—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×#106C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#97C2211yescharacteristic
46C3×#396—21no—
47C3×#396—21no—
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#384C2211yescharacteristic
53C3×#380—21no—
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#554C2×C311yescharacteristic, complemented
65C2×#478C2×C311yescharacteristic, complemented
66C2×#442C2×C311yescharacteristic
67#2538C2×C311yescharacteristic, complemented
68#2059C2×C311yescharacteristic, complemented
69#2058C2×C311yescharacteristic, complemented
70#2025C2×C311yescharacteristic, complemented
71#2023C2×C311yescharacteristic, complemented
72#1992C2×C311yescharacteristic, complemented
73#1985C2×C311yescharacteristic, complemented
74#1879C2×C311yescharacteristic
75#1879C2×C311yescharacteristic
76#1864C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic, complemented
78#1802C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8D411yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C2×C3×D8—22no—
88C2×C3×D8—22no—
89C2×C3×D8Q814yescomplemented
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C4⋊Q8—22no—
95C3×C4⋊Q8—22no—
96C3×#125—22no—
97C3×#125—22no—
98C3×#125—22no—
99C3×#125D414yes—
100C3×C22⋊Q8—28no—
101C3×C22⋊Q8—28no—
102C3×C22⋊Q8—28no—
103C3×C22⋊Q8—44no—
104C3×C4×Q8—22no—
105C3×C4×Q8—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C3×C4×D4—22no—
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C3×C4×D4—22no—
113C3×C4×D4D414yes—
114C2×C3×C4⋊C4—28no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4D411yescharacteristic
125C2×C3×C4⋊C4D411yescharacteristic
126C2×C3×C4⋊C4D411yescharacteristic
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—21no—
137C2×C3×C22⋊C4—21no—
138C2×C3×C22⋊C4—21no—
139C2×C3×C22⋊C4—21no—
140C2×C3×C22⋊C4—21no—
141C2×C3×C42C2311yescharacteristic
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C3×#107—22no—
145C3×#106—22no—
146C3×#106—22no—
147C3×C4⋊C8—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×#102—22no—
153C3×#102—22no—
154C3×#97—22no—
155C3×#95—21no—
156C3×#95—21no—
157C22×D8C22×C311yescharacteristic
158#554—24no—
159#554—24no—
160C2×C4⋊Q8C22×C311yescharacteristic
161C2×#125C22×C311yescharacteristic
162C2×#125C22×C311yescharacteristic
163C2×C22⋊Q8—21no—
164C2×C22⋊Q8—21no—
165C2×C22⋊Q8—21no—
166C2×C22⋊Q8—21no—
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×D4C22×C311yescharacteristic
169C2×C4×D4C22×C311yescharacteristic
170C2×C4×D4C22×C311yescharacteristic
171C2×C4×D4C22×C311yescharacteristic
172C22×C4⋊C4—21no—
173#478—24no—
174#442—24no—
175C2×#107C22×C311yescharacteristic
176C2×#106C22×C311yescharacteristic
177C2×#106C22×C311yescharacteristic
178C2×C4⋊C8C22×C311yescharacteristic
179C2×#102C22×C311yescharacteristic
180C2×#102C22×C311yescharacteristic
181C2×#102C22×C311yescharacteristic
182C2×#102C22×C311yescharacteristic
183C2×#102C22×C311yescharacteristic
184C2×#102C22×C311yescharacteristic
185C2×#97C22×C311yescharacteristic
186#396—21no—
187#396—21no—
188#390C22×C311yescharacteristic
189#390C22×C311yescharacteristic
190#389C22×C311yescharacteristic
191#389C22×C311yescharacteristic
192#384C22×C311yescharacteristic
193#380—21no—
194#340C22×C311yescharacteristic
195#340C22×C311yescharacteristic
196#340C22×C311yescharacteristic
197#340C22×C311yescharacteristic
198#340C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#336C22×C311yescharacteristic
201#336C22×C311yescharacteristic
202#336C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204C24×C3—21no—
205C24×C3—21no—
206C2×C3×Q8—24no—
207C2×C3×Q8—22no—
208C2×C3×Q8—22no—
209C2×C3×Q8—41no—
210C2×C3×Q8—81no—
211C2×C3×Q8—81no—
212C2×C3×D4—21no—
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—21no—
220C2×C3×D4C2×D412yes—
221C2×C3×D4C2×Q812yes—
222C2×C3×D4C2×Q812yes—
223C2×C3×D4#4112yes—
224C22×C3×C4—24no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—24no—
229C22×C3×C4—24no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4—42no—
236C22×C3×C4—42no—
237C22×C3×C4—42no—
238C22×C3×C4—81no—
239C22×C3×C4—81no—
240C22×C3×C4—81no—
241C22×C3×C4—81no—
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2411yescharacteristic
249C3×D8—28no—
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×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8C2×Q812yes—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—42no—
280C3×C4⋊C4—42no—
281C3×C4⋊C4—42no—
282C3×C4⋊C4—81no—
283C3×C4⋊C4C2×D412yes—
284C3×C4⋊C4C2×D412yes—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—42no—
291C3×C22⋊C4—42no—
292C3×C22⋊C4—81no—
293C3×C22⋊C4—81no—
294C3×C42—21no—
295C3×C42—21no—
296C3×C42—21no—
297C3×C42—21no—
298C3×C42C2×D412yes—
299C3×C42C2×D412yes—
300C22×Q8—21no—
301C22×Q8C3×D411yescharacteristic
302C22×D4C23×C311yescharacteristic
303C22×D4C23×C311yescharacteristic
304C23×C4—21no—
305C23×C4—21no—
306C23×C4—21no—
307C23×C4—21no—
308C2×D8—22no—
309C2×D8—22no—
310C2×D8C3×Q814yescomplemented
311C22×C8C23×C311yescharacteristic
312C22×C8C23×C311yescharacteristic
313C22×C8C23×C311yescharacteristic
314C22×C8C23×C311yescharacteristic
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317#125—22no—
318#125—22no—
319#125—22no—
320#125C3×D414yes—
321C22⋊Q8—28no—
322C22⋊Q8—28no—
323C22⋊Q8—28no—
324C22⋊Q8—44no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×D4—22no—
328C4×D4—22no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4C3×D414yes—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4C3×D411yescharacteristic
346C2×C4⋊C4C3×D411yescharacteristic
347C2×C4⋊C4C3×D411yescharacteristic
348C2×C4⋊C4C23×C311yescharacteristic
349C2×C4⋊C4C23×C311yescharacteristic
350C2×C4⋊C4C23×C311yescharacteristic
351C2×C4⋊C4C23×C311yescharacteristic
352C2×C4⋊C4C23×C311yescharacteristic
353C2×C4⋊C4C23×C311yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C42C23×C311yescharacteristic
363C2×C42C23×C311yescharacteristic
364C2×C42C23×C311yescharacteristic
365#107—22no—
366#106—22no—
367#106—22no—
368C4⋊C8—22no—
369#102—22no—
370#102—22no—
371#102—22no—
372#102—22no—
373#102—22no—
374#102—22no—
375#97—22no—
376#95—21no—
377#95—21no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3C22×D411yescharacteristic
393C3×Q8—44no—
394C3×Q8—84no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—22no—
399C3×D4—22no—
400C3×D4—41no—
401C3×D4—41no—
402C3×D4C22⋊Q814yescomplemented
403C2×C3×C4—21no—
404C2×C3×C4—21no—
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—21no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—48no—
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—41no—
437C2×C3×C4—84no—
438C2×C3×C4—84no—
439C2×C3×C4—84no—
440C2×C3×C4#12012yes—
441C2×C3×C4#12012yes—
442C2×C3×C4AGL(1,ℤ/8)12yes—
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C22×Q811yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C42−1+411yescharacteristic
448C2×C3×C42−1+411yescharacteristic
449C3×C8—22no—
450C3×C8—41no—
451C3×C8—41no—
452C3×C8—41no—
453C24—21no—
454C24—21no—
455C2×Q8—24no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—41no—
459C2×Q8—81no—
460C2×Q8—81no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4C2×C3×D412yes—
470C2×D4C2×C3×Q812yes—
471C2×D4C2×C3×Q812yes—
472C2×D4C3×#4112yes—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D411yescharacteristic
493C22×C4C2×C3×D411yescharacteristic
494C22×C4C2×C3×D411yescharacteristic
495C22×C4C2×C3×D411yescharacteristic
496C22×C4C2×C3×D411yescharacteristic
497C22×C4C24×C311yescharacteristic
498D8—28no—
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×C8—21no—
509C2×C8—21no—
510C2×C8C2×C3×Q812yes—
511C4⋊C4—24no—
512C4⋊C4—24no—
513C4⋊C4—24no—
514C4⋊C4—22no—
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4C2×C3×D412yes—
533C4⋊C4C2×C3×D412yes—
534C4⋊C4C2×C3×D412yes—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—81no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42C2×C3×D412yes—
548C42C2×C3×D412yes—
549C22×C3—24no—
550C22×C3—42no—
551C22×C3—42no—
552C22×C3—42no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—42no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—81no—
563C22×C3C2×#12011yescharacteristic
564C22×C3#54811yescharacteristic
565C22×C3D4×Q811yescharacteristic
566C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
567C22×C3#57511yescharacteristic
568C22×C3#57611yescharacteristic
569C22×C3#57711yescharacteristic
570C3×C4—22no—
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—41no—
574C3×C4—42no—
575C3×C4—41no—
576C3×C4—41no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—81no—
580C3×C4—81no—
581C3×C4—81no—
582C3×C4C2×C22⋊Q811yescharacteristic
583C3×C4#53611yescharacteristic
584C3×C4#54811yescharacteristic
585C3×C4D4×Q811yescharacteristic
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C22×C3×D411yescharacteristic
601Q8—44no—
602Q8—84no—
603D4—22no—
604D4—22no—
605D4—22no—
606D4—22no—
607D4—22no—
608D4—41no—
609D4—41no—
610D4C3×C22⋊Q814yescomplemented
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—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—48no—
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×C4—84no—
646C2×C4—84no—
647C2×C4—84no—
648C2×C4C3×#12012yes—
649C2×C4C3×#12012yes—
650C2×C4C3×AGL(1,ℤ/8)12yes—
651C2×C4C22×C3×D411yescharacteristic
652C2×C4C22×C3×D411yescharacteristic
653C2×C4C22×C3×Q811yescharacteristic
654C2×C4C2×C3×#4111yescharacteristic
655C2×C4C3×2−1+411yescharacteristic
656C2×C4C3×2−1+411yescharacteristic
657C8—22no—
658C8—41no—
659C8—41no—
660C8—41no—
661C2×C3—44no—
662C2×C3—82no—
663C2×C3#240911yescharacteristic
664C2×C3#300611yescharacteristic
665C2×C3#301211yescharacteristic
666C2×C3#336611yescharacteristic
667C2×C3#337611yescharacteristic
668C2×C3#338411yescharacteristic
669C2×C3#338911yescharacteristic
670C22—24no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22C2×C3×#12011yescharacteristic
685C22C3×#54811yescharacteristic
686C22C3×D4×Q811yescharacteristic
687C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
688C22C3×#57511yescharacteristic
689C22C3×#57611yescharacteristic
690C22C3×#57711yescharacteristic
691C4—22no—
692C4—22no—
693C4—22no—
694C4—41no—
695C4—42no—
696C4—41no—
697C4—41no—
698C4—42no—
699C4—42no—
700C4—81no—
701C4—81no—
702C4—81no—
703C4C2×C3×C22⋊Q811yescharacteristic
704C4C3×#53611yescharacteristic
705C4C3×#54811yescharacteristic
706C4C3×D4×Q811yescharacteristic
707C3#2434711yescharacteristic, direct product factor, Sylow
708C2—44no—
709C2—82no—
710C2C3×#240911yescharacteristic
711C2C3×#300611yescharacteristic
712C2C3×#301211yescharacteristic
713C2C3×#336611yescharacteristic
714C2C3×#337611yescharacteristic
715C2C3×#338411yescharacteristic
716C2C3×#338911yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#554C2semidirect
2. C2×C3×#478C2semidirect
4. C3×#2538C2semidirect
5. C3×#2059C2semidirect
6. C3×#2058C2semidirect
7. C3×#2025C2semidirect
8. C3×#2023C2semidirect
9. C3×#1992C2semidirect
10. C3×#1985C2semidirect
13. C3×#1864C2semidirect
14. C3×#1862C2semidirect
15. C3×#1802C2semidirect
16. #24347C3direct (N × H)
64. C2×#554C2×C3semidirect
65. C2×#478C2×C3semidirect
67. #2538C2×C3semidirect
68. #2059C2×C3semidirect
69. #2058C2×C3semidirect
70. #2025C2×C3semidirect
71. #2023C2×C3semidirect
72. #1992C2×C3semidirect
73. #1985C2×C3semidirect
76. #1864C2×C3semidirect
77. #1862C2×C3semidirect
78. #1802C2×C3semidirect
89. C2×C3×D8Q8semidirect
310. C2×D8C3×Q8semidirect
402. C3×D4C22⋊Q8semidirect
610. D4C3×C22⋊Q8semidirect
707. C3#24347direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5542
C2×C3×#4782
C2×C3×#4422
C3×#25382
C3×#20592
C3×#20582
C3×#20252
C3×#20232
C3×#19922
C3×#19852
C3×#18792
C3×#18642
C3×#18622
C3×#18022
#243473