Finite Group Databasebeta

← C3×#25654 #10644261

Subgroups — C3×#25654 #10644261

Order 768.

1018 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#556C211yesmaximal, characteristic
2C2×C3×#488C211yesmaximal, characteristic
3C2×C3×#479C211yesmaximal, characteristic, complemented
4C3×#2584C211yesmaximal, characteristic, complemented
5C3×#2043C211yesmaximal, characteristic, complemented
6C3×#2043C211yesmaximal, characteristic, complemented
7C3×#2042C211yesmaximal, characteristic
8C3×#2042C211yesmaximal, characteristic
9C3×#1984C211yesmaximal, characteristic, complemented
10C3×#1983C211yesmaximal, characteristic
11C3×#1865C211yesmaximal, characteristic, complemented
12C3×#1864C211yesmaximal, characteristic
13C3×#1863C211yesmaximal, characteristic, complemented
14C3×#1862C211yesmaximal, characteristic
15C3×C4×#103C211yesmaximal, characteristic, complemented
16#25654C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#556—24no—
18C3×#556—24no—
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#126—21no—
21C2×C3×#126—21no—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#124C2211yescharacteristic
24C2×C3×#124C2211yescharacteristic
25C2×C3×C22⋊Q8—21no—
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117—21no—
31C3×#488—24no—
32C3×#479—24no—
33C2×C3×#107C2211yescharacteristic
34C2×C3×#106C2211yescharacteristic
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×C4×C8C2211yescharacteristic
49C3×#398—21no—
50C3×#395—21no—
51C3×#389—21no—
52C3×#389—21no—
53C3×#389C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#389C2211yescharacteristic
57C3×C4×C4⋊C4C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#556C2×C311yescharacteristic
65C2×#488C2×C311yescharacteristic
66C2×#479C2×C311yescharacteristic, complemented
67#2584C2×C311yescharacteristic, complemented
68#2043C2×C311yescharacteristic, complemented
69#2043C2×C311yescharacteristic, complemented
70#2042C2×C311yescharacteristic
71#2042C2×C311yescharacteristic
72#1984C2×C311yescharacteristic, complemented
73#1983C2×C311yescharacteristic
74#1865C2×C311yescharacteristic, complemented
75#1864C2×C311yescharacteristic
76#1863C2×C311yescharacteristic, complemented
77#1862C2×C311yescharacteristic
78C4×#103C2×C311yescharacteristic, complemented
79C22×C3×Q8D411yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C3×C4⋊Q8—22no—
89C3×C4⋊Q8—22no—
90C3×#126—28no—
91C3×#126—28no—
92C3×#125—22no—
93C3×#125—22no—
94C3×#124—22no—
95C3×#124—22no—
96C3×#124—22no—
97C3×#124D414yes—
98C3×C22⋊Q8—28no—
99C3×C4×Q8—22no—
100C3×C4×Q8—22no—
101C3×C4×Q8—22no—
102C3×C4×Q8—22no—
103C3×C4×Q8—22no—
104C3×C4×Q8D414yes—
105C3×C4×D4—22no—
106C3×C4×D4—22no—
107C3×#117—28no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4—21no—
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⋊C4—21no—
118C2×C3×C4⋊C4D411yescharacteristic
119C2×C3×C4⋊C4D411yescharacteristic
120C2×C3×C4⋊C4D411yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C4⋊C4C2311yescharacteristic
125C2×C3×C4⋊C4C2311yescharacteristic
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×C42—21no—
132C2×C3×C42—21no—
133C2×C3×C42—21no—
134C2×C3×C42C2311yescharacteristic
135C2×C3×C42C2311yescharacteristic
136C2×C3×C42C2311yescharacteristic
137C3×#107—22no—
138C3×#106—22no—
139C3×C4⋊C8—22no—
140C3×#103—22no—
141C3×#103—22no—
142C3×#103—22no—
143C3×#103—22no—
144C3×#103—22no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×#102—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#102—22no—
152C3×C4×C8—22no—
153C3×#95—21no—
154C3×#95—21no—
155C3×#95—21no—
156C3×#95—21no—
157C3×#95—21no—
158#556—24no—
159#556—24no—
160C2×C4⋊Q8C22×C311yescharacteristic
161C2×#126—21no—
162C2×#126—21no—
163C2×#125C22×C311yescharacteristic
164C2×#124C22×C311yescharacteristic
165C2×#124C22×C311yescharacteristic
166C2×C22⋊Q8—21no—
167C2×C4×Q8C22×C311yescharacteristic
168C2×C4×Q8C22×C311yescharacteristic
169C2×C4×Q8C22×C311yescharacteristic
170C2×C4×D4C22×C311yescharacteristic
171C2×#117—21no—
172#488—24no—
173#479—24no—
174C2×#107C22×C311yescharacteristic
175C2×#106C22×C311yescharacteristic
176C2×C4⋊C8C22×C311yescharacteristic
177C2×#103C22×C311yescharacteristic
178C2×#103C22×C311yescharacteristic
179C2×#103C22×C311yescharacteristic
180C2×#103C22×C311yescharacteristic
181C2×#103C22×C311yescharacteristic
182C2×#103C22×C311yescharacteristic
183C2×#103C22×C311yescharacteristic
184C2×#103C22×C311yescharacteristic
185C2×#102C22×C311yescharacteristic
186C2×#102C22×C311yescharacteristic
187C2×#102C22×C311yescharacteristic
188C2×#102C22×C311yescharacteristic
189C2×C4×C8C22×C311yescharacteristic
190#398—21no—
191#395—21no—
192#389—21no—
193#389—21no—
194#389C22×C311yescharacteristic
195#389C22×C311yescharacteristic
196#389C22×C311yescharacteristic
197#389C22×C311yescharacteristic
198C4×C4⋊C4C22×C311yescharacteristic
199#340C22×C311yescharacteristic
200#340C22×C311yescharacteristic
201#336C22×C311yescharacteristic
202#336C22×C311yescharacteristic
203#336C22×C311yescharacteristic
204#336C22×C311yescharacteristic
205C24×C3—21no—
206C2×C3×Q8—22no—
207C2×C3×Q8—22no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—41no—
219C2×C3×Q8C2×D412yes—
220C2×C3×Q8C2×D412yes—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4C2×D412yes—
227C22×C3×C4—24no—
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—42no—
236C22×C3×C4—42no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
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—21no—
255C2×C3×C8—21no—
256C3×C4⋊C4—24no—
257C3×C4⋊C4—24no—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—22no—
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—42no—
271C3×C4⋊C4—42no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—81no—
275C3×C4⋊C4—81no—
276C3×C4⋊C4C2×D412yes—
277C3×C4⋊C4#4112yes—
278C3×C4⋊C4#4112yes—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C42—24no—
285C3×C42—24no—
286C3×C42—21no—
287C3×C42—21no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42—81no—
291C3×C42C2×D412yes—
292C3×C42C2×D412yes—
293C22×Q8C3×D411yescharacteristic
294C22×Q8C23×C311yescharacteristic
295C22×Q8C23×C311yescharacteristic
296C22×D4C23×C311yescharacteristic
297C23×C4—21no—
298C22×C8C23×C311yescharacteristic
299C22×C8C23×C311yescharacteristic
300C22×C8C23×C311yescharacteristic
301C22×C8C23×C311yescharacteristic
302C4⋊Q8—22no—
303C4⋊Q8—22no—
304#126—28no—
305#126—28no—
306#125—22no—
307#125—22no—
308#124—22no—
309#124—22no—
310#124—22no—
311#124C3×D414yes—
312C22⋊Q8—28no—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8C3×D414yes—
319C4×D4—22no—
320C4×D4—22no—
321#117—28no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4C3×D411yescharacteristic
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×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—21no—
348C2×C42C23×C311yescharacteristic
349C2×C42C23×C311yescharacteristic
350C2×C42C23×C311yescharacteristic
351#107—22no—
352#106—22no—
353C4⋊C8—22no—
354#103—22no—
355#103—22no—
356#103—22no—
357#103—22no—
358#103—22no—
359#103—22no—
360#103—22no—
361#103—22no—
362#102—22no—
363#102—22no—
364#102—22no—
365#102—22no—
366C4×C8—22no—
367#95—21no—
368#95—21no—
369#95—21no—
370#95—21no—
371#95—21no—
372C23×C3—22no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3C22×D411yescharacteristic
380C3×Q8—22no—
381C3×Q8—22no—
382C3×Q8—22no—
383C3×Q8—22no—
384C3×Q8—44no—
385C3×Q8—41no—
386C3×Q8—41no—
387C3×Q8—41no—
388C3×Q8—41no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—41no—
392C3×D4—41no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—48no—
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#12012yes—
431C2×C3×C4#12012yes—
432C2×C3×C4#13512yes—
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C22×D411yescharacteristic
435C2×C3×C4C2×#4111yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C42−1+411yescharacteristic
438C2×C3×C42−1+411yescharacteristic
439C3×C8—41no—
440C3×C8—41no—
441C3×C8—41no—
442C3×C8—41no—
443C24—21no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—41no—
457C2×Q8C2×C3×D412yes—
458C2×Q8C2×C3×D412yes—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4C2×C3×D412yes—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—42no—
474C22×C4—42no—
475C22×C4C2×C3×D411yescharacteristic
476C22×C4C2×C3×D411yescharacteristic
477C22×C4C2×C3×D411yescharacteristic
478C22×C4C2×C3×D411yescharacteristic
479C22×C4C2×C3×D411yescharacteristic
480C22×C4C2×C3×D411yescharacteristic
481C22×C4C24×C311yescharacteristic
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—81no—
513C4⋊C4—81no—
514C4⋊C4C2×C3×D412yes—
515C4⋊C4C3×#4112yes—
516C4⋊C4C3×#4112yes—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C42—24no—
523C42—24no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—81no—
529C42C2×C3×D412yes—
530C42C2×C3×D412yes—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—81no—
535C22×C3—81no—
536C22×C3—81no—
537C22×C3—81no—
538C22×C3C2×#12011yescharacteristic
539C22×C3#54811yescharacteristic
540C22×C3#54811yescharacteristic
541C22×C3C2×#13511yescharacteristic
542C22×C3#57511yescharacteristic
543C22×C3#57711yescharacteristic
544C22×C3#57811yescharacteristic
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—42no—
549C3×C4—42no—
550C3×C4—42no—
551C3×C4—42no—
552C3×C4—41no—
553C3×C4—42no—
554C3×C4—41no—
555C3×C4—41no—
556C3×C4—81no—
557C3×C4—81no—
558C3×C4#53211yescharacteristic
559C3×C4#53611yescharacteristic
560C3×C4#54711yescharacteristic
561C3×C4#54711yescharacteristic
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23C22×C3×D411yescharacteristic
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—22no—
574Q8—44no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—22no—
580D4—22no—
581D4—41no—
582D4—41no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—48no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
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×C4C3×#12012yes—
621C2×C4C3×#12012yes—
622C2×C4C3×#13512yes—
623C2×C4C22×C3×D411yescharacteristic
624C2×C4C22×C3×D411yescharacteristic
625C2×C4C2×C3×#4111yescharacteristic
626C2×C4C2×C3×#4111yescharacteristic
627C2×C4C3×2−1+411yescharacteristic
628C2×C4C3×2−1+411yescharacteristic
629C8—41no—
630C8—41no—
631C8—41no—
632C8—41no—
633C2×C3—82no—
634C2×C3#243211yescharacteristic
635C2×C3#300211yescharacteristic
636C2×C3#301311yescharacteristic
637C2×C3#336011yescharacteristic
638C2×C3#336411yescharacteristic
639C2×C3#337611yescharacteristic
640C2×C3#337711yescharacteristic
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22C2×C3×#12011yescharacteristic
649C22C3×#54811yescharacteristic
650C22C3×#54811yescharacteristic
651C22C2×C3×#13511yescharacteristic
652C22C3×#57511yescharacteristic
653C22C3×#57711yescharacteristic
654C22C3×#57811yescharacteristic
655C4—22no—
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—42no—
665C4—42no—
666C4—81no—
667C4—81no—
668C4C3×#53211yescharacteristic
669C4C3×#53611yescharacteristic
670C4C3×#54711yescharacteristic
671C4C3×#54711yescharacteristic
672C3#2565411yescharacteristic, direct product factor, Sylow
673C2—82no—
674C2C3×#243211yescharacteristic
675C2C3×#300211yescharacteristic
676C2C3×#301311yescharacteristic
677C2C3×#336011yescharacteristic
678C2C3×#336411yescharacteristic
679C2C3×#337611yescharacteristic
680C2C3×#337711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
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
3. C2×C3×#479C2semidirect
4. C3×#2584C2semidirect
5. C3×#2043C2semidirect
6. C3×#2043C2semidirect
9. C3×#1984C2semidirect
11. C3×#1865C2semidirect
13. C3×#1863C2semidirect
15. C3×C4×#103C2semidirect
16. #25654C3direct (N × H)
66. C2×#479C2×C3semidirect
67. #2584C2×C3semidirect
68. #2043C2×C3semidirect
69. #2043C2×C3semidirect
72. #1984C2×C3semidirect
74. #1865C2×C3semidirect
76. #1863C2×C3semidirect
78. C4×#103C2×C3semidirect
672. C3#25654direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5562
C2×C3×#4882
C2×C3×#4792
C3×#25842
C3×#20432
C3×#20422
C3×#19842
C3×#19832
C3×#18652
C3×#18642
C3×#18632
C3×#18622
C3×C4×#1032
#256543