Finite Group Databasebeta

← C3×#26785 #10645392

Subgroups — C3×#26785 #10645392

Order 768.

888 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#484C211yesmaximal, characteristic, complemented
2C2×C3×#478C211yesmaximal, characteristic, complemented
3C3×#2489C211yesmaximal, characteristic, complemented
4C3×#2361C211yesmaximal, characteristic
5C3×#2068C211yesmaximal, characteristic, complemented
6C3×#2059C211yesmaximal, characteristic, complemented
7C3×#2033C211yesmaximal, characteristic
8C3×#2000C211yesmaximal, characteristic
9C3×#1968C211yesmaximal, characteristic, complemented
10C3×#1927C211yesmaximal, characteristic, complemented
11C3×#1925C211yesmaximal, characteristic, complemented
12C3×#1923C211yesmaximal, characteristic, complemented
13C3×#1877C211yesmaximal, characteristic, complemented
14C3×#1853C211yesmaximal, characteristic, complemented
15C3×C4×#107C211yesmaximal, characteristic, complemented
16#26785C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4—21no—
22C2×C3×C4×D4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C3×#484—24no—
25C3×#478—24no—
26C2×C3×#107C2211yescharacteristic
27C2×C3×#107C2211yescharacteristic
28C2×C3×#107C2211yescharacteristic
29C2×C3×#106C2211yescharacteristic
30C2×C3×#106C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic
41C3×#400—21no—
42C3×#397—21no—
43C3×#391C2211yescharacteristic
44C3×#391C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#389C2211yescharacteristic
47C3×#388—21no—
48C3×#388—21no—
49C3×#386—21no—
50C3×#385—21no—
51C3×#382—21no—
52C3×#380C2211yescharacteristic
53C3×C4×C4⋊C4C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×C4×C22⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#484C2×C311yescharacteristic, complemented
63C2×#478C2×C311yescharacteristic, complemented
64#2489C2×C311yescharacteristic, complemented
65#2361C2×C311yescharacteristic
66#2068C2×C311yescharacteristic, complemented
67#2059C2×C311yescharacteristic, complemented
68#2033C2×C311yescharacteristic
69#2000C2×C311yescharacteristic
70#1968C2×C311yescharacteristic, complemented
71#1927C2×C311yescharacteristic, complemented
72#1925C2×C311yescharacteristic, complemented
73#1923C2×C311yescharacteristic, complemented
74#1877C2×C311yescharacteristic, complemented
75#1853C2×C311yescharacteristic, complemented
76C4×#107C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×D4—21no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C2×C3×SD16—22no—
84C2×C3×SD16—22no—
85C2×C3×SD16—41no—
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×#125—22no—
91C3×#125—41no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—41no—
94C3×#121—22no—
95C3×#121—22no—
96C3×C4×D4—22no—
97C3×C4×D4—41no—
98C3×C4×D4—44no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—41no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4D411yescharacteristic
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C42—21no—
121C2×C3×C42—21no—
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C3×#107—22no—
125C3×#107—22no—
126C3×#107D414yescomplemented
127C3×#106—22no—
128C3×#106—41no—
129C3×C4⋊C8—22no—
130C3×#103—22no—
131C3×#103—22no—
132C3×#103—22no—
133C3×#102—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×C22⋊C8—22no—
137C3×C22⋊C8—22no—
138C3×C4×C8—22no—
139C3×#95—21no—
140C3×#95—21no—
141C3×#95—21no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95D411yescharacteristic
148C3×#95D411yescharacteristic
149C22×SD16C22×C311yescharacteristic
150C2×#125C22×C311yescharacteristic
151C2×C22⋊Q8C22×C311yescharacteristic
152C2×#121C22×C311yescharacteristic
153C2×C4×D4—21no—
154C2×C4×D4C22×C311yescharacteristic
155C22×C4⋊C4C22×C311yescharacteristic
156#484—24no—
157#478—24no—
158C2×#107C22×C311yescharacteristic
159C2×#107C22×C311yescharacteristic
160C2×#107C22×C311yescharacteristic
161C2×#106C22×C311yescharacteristic
162C2×#106C22×C311yescharacteristic
163C2×C4⋊C8C22×C311yescharacteristic
164C2×#103C22×C311yescharacteristic
165C2×#103C22×C311yescharacteristic
166C2×#103C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×C22⋊C8C22×C311yescharacteristic
171C2×C22⋊C8C22×C311yescharacteristic
172C2×C4×C8C22×C311yescharacteristic
173#400—21no—
174#397—21no—
175#391C22×C311yescharacteristic
176#391C22×C311yescharacteristic
177#390C22×C311yescharacteristic
178#389C22×C311yescharacteristic
179#388—21no—
180#388—21no—
181#386—21no—
182#385—21no—
183#382—21no—
184#380C22×C311yescharacteristic
185C4×C4⋊C4C22×C311yescharacteristic
186C4×C4⋊C4C22×C311yescharacteristic
187C4×C22⋊C4C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193#336C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3C2×D411yescharacteristic
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×D4—24no—
203C2×C3×D4—21no—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—42no—
209C2×C3×D4—42no—
210C2×C3×D4#4112yes—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
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—42no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—42no—
228C22×C3×C4—81no—
229C22×C3×C4—81no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C3×SD16—44no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8C2×D412yes—
248C2×C3×C8#4112yes—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—42no—
259C3×C4⋊C4—42no—
260C3×C4⋊C4—42no—
261C3×C4⋊C4—42no—
262C3×C4⋊C4—42no—
263C3×C4⋊C4C2×D412yes—
264C3×C4⋊C4C2×D412yes—
265C3×C4⋊C4#4112yes—
266C3×C22⋊C4—24no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—42no—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—81no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—42no—
279C3×C42—42no—
280C22×Q8C23×C311yescharacteristic
281C22×D4—21no—
282C22×D4C23×C311yescharacteristic
283C23×C4—21no—
284C23×C4—21no—
285C23×C4C23×C311yescharacteristic
286C2×SD16—22no—
287C2×SD16—22no—
288C2×SD16—41no—
289C22×C8C23×C311yescharacteristic
290C22×C8C23×C311yescharacteristic
291C22×C8C23×C311yescharacteristic
292C22×C8C23×C311yescharacteristic
293#125—22no—
294#125—41no—
295C22⋊Q8—22no—
296C22⋊Q8—41no—
297#121—22no—
298#121—22no—
299C4×D4—22no—
300C4×D4—41no—
301C4×D4—44no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4C23×C311yescharacteristic
310C2×C4⋊C4C23×C311yescharacteristic
311C2×C4⋊C4C23×C311yescharacteristic
312C2×C4⋊C4C23×C311yescharacteristic
313C2×C4⋊C4C23×C311yescharacteristic
314C2×C4⋊C4C23×C311yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4C3×D411yescharacteristic
322C2×C22⋊C4C3×D411yescharacteristic
323C2×C42—21no—
324C2×C42—21no—
325C2×C42C23×C311yescharacteristic
326C2×C42C23×C311yescharacteristic
327#107—22no—
328#107—22no—
329#107C3×D414yescomplemented
330#106—22no—
331#106—41no—
332C4⋊C8—22no—
333#103—22no—
334#103—22no—
335#103—22no—
336#102—22no—
337#102—22no—
338#102—22no—
339C22⋊C8—22no—
340C22⋊C8—22no—
341C4×C8—22no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95C3×D411yescharacteristic
351#95C3×D411yescharacteristic
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—22no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3#13512yes—
366C23×C3C22×D411yescharacteristic
367C3×Q8—41no—
368C3×Q8—41no—
369C3×Q8—41no—
370C3×Q8—41no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—48no—
374C3×D4—41no—
375C3×D4—41no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
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—84no—
416C2×C3×C4—84no—
417C2×C3×C4AGL(1,ℤ/8)12yes—
418C2×C3×C4C22×D411yescharacteristic
419C2×C3×C4C2×#4111yescharacteristic
420C2×C3×C4C2×#4111yescharacteristic
421C2×C3×C4C2×#4111yescharacteristic
422C2×C3×C4H(5,𝔽2)11yescharacteristic
423C2×C3×C42−1+411yescharacteristic
424C3×C8—22no—
425C3×C8—22no—
426C3×C8—41no—
427C3×C8—41no—
428C24—21no—
429C24C2×C3×D411yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×D4—24no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—42no—
443C2×D4—42no—
444C2×D4C3×#4112yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4C2×C3×D411yescharacteristic
465C22×C4C2×C3×D411yescharacteristic
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D411yescharacteristic
468C22×C4C2×C3×D411yescharacteristic
469C22×C4C24×C311yescharacteristic
470SD16—44no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8C2×C3×D412yes—
482C2×C8C3×#4112yes—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4C2×C3×D412yes—
498C4⋊C4C2×C3×D412yes—
499C4⋊C4C3×#4112yes—
500C22⋊C4—24no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—81no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—42no—
513C42—42no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—81no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3#52511yescharacteristic
529C22×C3D4211yescharacteristic
530C22×C3#54711yescharacteristic
531C22×C3C2×#13511yescharacteristic
532C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
533C22×C3#57711yescharacteristic
534C22×C3#57811yescharacteristic
535C3×C4—22no—
536C3×C4—41no—
537C3×C4—42no—
538C3×C4—41no—
539C3×C4—41no—
540C3×C4—42no—
541C3×C4—42no—
542C3×C4—41no—
543C3×C4—81no—
544C3×C4—81no—
545C3×C4—81no—
546C3×C4—81no—
547C3×C4#53211yescharacteristic
548C3×C4#54211yescharacteristic
549C3×C4#54811yescharacteristic
550C3×C4#55111yescharacteristic
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23C3×#13512yes—
565C23C22×C3×D411yescharacteristic
566Q8—41no—
567Q8—41no—
568Q8—41no—
569Q8—41no—
570D4—22no—
571D4—22no—
572D4—48no—
573D4—41no—
574D4—41no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
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—84no—
615C2×C4—84no—
616C2×C4C3×AGL(1,ℤ/8)12yes—
617C2×C4C22×C3×D411yescharacteristic
618C2×C4C2×C3×#4111yescharacteristic
619C2×C4C2×C3×#4111yescharacteristic
620C2×C4C2×C3×#4111yescharacteristic
621C2×C4C3×H(5,𝔽2)11yescharacteristic
622C2×C4C3×2−1+411yescharacteristic
623C8—22no—
624C8—22no—
625C8—41no—
626C8—41no—
627C2×C3—42no—
628C2×C3—82no—
629C2×C3#246111yescharacteristic
630C2×C3#310511yescharacteristic
631C2×C3#312011yescharacteristic
632C2×C3#327211yescharacteristic
633C2×C3#328511yescharacteristic
634C2×C3#333711yescharacteristic
635C2×C3#334311yescharacteristic
636C22—22no—
637C22—22no—
638C22—22no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22C3×#52511yescharacteristic
651C22C3×D4211yescharacteristic
652C22C3×#54711yescharacteristic
653C22C2×C3×#13511yescharacteristic
654C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
655C22C3×#57711yescharacteristic
656C22C3×#57811yescharacteristic
657C4—22no—
658C4—41no—
659C4—41no—
660C4—42no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—42no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4C3×#53211yescharacteristic
670C4C3×#54211yescharacteristic
671C4C3×#54811yescharacteristic
672C4C3×#55111yescharacteristic
673C3#2678511yescharacteristic, direct product factor, Sylow
674C2—42no—
675C2—82no—
676C2C3×#246111yescharacteristic
677C2C3×#310511yescharacteristic
678C2C3×#312011yescharacteristic
679C2C3×#327211yescharacteristic
680C2C3×#328511yescharacteristic
681C2C3×#333711yescharacteristic
682C2C3×#334311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#484C2semidirect
2. C2×C3×#478C2semidirect
3. C3×#2489C2semidirect
5. C3×#2068C2semidirect
6. C3×#2059C2semidirect
9. C3×#1968C2semidirect
10. C3×#1927C2semidirect
11. C3×#1925C2semidirect
12. C3×#1923C2semidirect
13. C3×#1877C2semidirect
14. C3×#1853C2semidirect
15. C3×C4×#107C2semidirect
16. #26785C3direct (N × H)
62. C2×#484C2×C3semidirect
63. C2×#478C2×C3semidirect
64. #2489C2×C3semidirect
66. #2068C2×C3semidirect
67. #2059C2×C3semidirect
70. #1968C2×C3semidirect
71. #1927C2×C3semidirect
72. #1925C2×C3semidirect
73. #1923C2×C3semidirect
74. #1877C2×C3semidirect
75. #1853C2×C3semidirect
76. C4×#107C2×C3semidirect
126. C3×#107D4semidirect
329. #107C3×D4semidirect
673. C3#26785direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4842
C2×C3×#4782
C3×#24892
C3×#23612
C3×#20682
C3×#20592
C3×#20332
C3×#20002
C3×#19682
C3×#19272
C3×#19252
C3×#19232
C3×#18772
C3×#18532
C3×C4×#1072
#267853