Finite Group Databasebeta

← C3×#26410 #10645017

Subgroups — C3×#26410 #10645017

Order 768.

902 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2440C211yesmaximal, characteristic, complemented
2C3×#2361C211yesmaximal, characteristic
3C3×#2100C211yesmaximal, characteristic, complemented
4C3×#2088C211yesmaximal, characteristic, complemented
5C3×#2065C211yesmaximal, characteristic, complemented
6C3×#2023C211yesmaximal, characteristic, complemented
7C3×#1987C211yesmaximal, characteristic, complemented
8C3×#1920C211yesmaximal, characteristic, complemented
9C3×#1893C211yesmaximal, characteristic
10C3×#1874C211yesmaximal, characteristic
11C3×#1864C211yesmaximal, characteristic, complemented
12C3×#1853C211yesmaximal, characteristic, complemented
13C3×#1850C211yesmaximal, characteristic, complemented
14C3×#1802C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#26410C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8—21no—
20C2×C3×#121C2211yescharacteristic
21C2×C3×C4×D4—21no—
22C2×C3×C4×D4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C22×C3×C4⋊C4C2211yescharacteristic
25C2×C3×#106C2211yescharacteristic
26C2×C3×#106C2211yescharacteristic
27C2×C3×C4⋊C8C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C3×#398—21no—
35C3×#395—21no—
36C3×#390C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C3×#388—21no—
41C3×#386—21no—
42C3×#385—21no—
43C3×#385—21no—
44C3×#384C2211yescharacteristic
45C3×#380C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C22⋊C4C2211yescharacteristic
48C3×#340C2211yescharacteristic
49C3×#340C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2440C2×C311yescharacteristic, complemented
61#2361C2×C311yescharacteristic
62#2100C2×C311yescharacteristic, complemented
63#2088C2×C311yescharacteristic, complemented
64#2065C2×C311yescharacteristic, complemented
65#2023C2×C311yescharacteristic, complemented
66#1987C2×C311yescharacteristic, complemented
67#1920C2×C311yescharacteristic, complemented
68#1893C2×C311yescharacteristic
69#1874C2×C311yescharacteristic
70#1864C2×C311yescharacteristic, complemented
71#1853C2×C311yescharacteristic, complemented
72#1850C2×C311yescharacteristic, complemented
73#1802C2×C311yescharacteristic, complemented
74C2×#340C2×C311yescharacteristic, complemented
75C22×C3×Q8—21no—
76C22×C3×D4—21no—
77C22×C3×D4C2311yescharacteristic
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C23×C3×C4—21no—
81C23×C3×C4C2311yescharacteristic
82C22×C3×C8—22no—
83C22×C3×C8—41no—
84C22×C3×C8—41no—
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C4⋊Q8—22no—
90C3×C4⋊Q8—41no—
91C3×C22⋊Q8—44no—
92C3×#121—22no—
93C3×#121Q814yescomplemented
94C3×C4×D4—22no—
95C3×C4×D4—41no—
96C3×C4×D4—44no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—21no—
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—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—41no—
108C2×C3×C4⋊C4—41no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4D411yescharacteristic
122C2×C3×C22⋊C4D411yescharacteristic
123C2×C3×C42—21no—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C3×#106—22no—
127C3×#106—41no—
128C3×C4⋊C8—41no—
129C3×C4⋊C8—41no—
130C3×#102—22no—
131C3×#102—41no—
132C3×#102—41no—
133C3×#102—41no—
134C3×C22⋊C8—22no—
135C3×#95—21no—
136C3×#95—21no—
137C3×#95—21no—
138C3×#95—21no—
139C3×#95—21no—
140C3×#95D411yescharacteristic
141C3×#95D411yescharacteristic
142C23×C8C22×C311yescharacteristic
143C2×C4⋊Q8C22×C311yescharacteristic
144C2×C22⋊Q8—21no—
145C2×#121C22×C311yescharacteristic
146C2×C4×D4—21no—
147C2×C4×D4C22×C311yescharacteristic
148C22×C4⋊C4C22×C311yescharacteristic
149C22×C4⋊C4C22×C311yescharacteristic
150C2×#106C22×C311yescharacteristic
151C2×#106C22×C311yescharacteristic
152C2×C4⋊C8C22×C311yescharacteristic
153C2×C4⋊C8C22×C311yescharacteristic
154C2×#102C22×C311yescharacteristic
155C2×#102C22×C311yescharacteristic
156C2×#102C22×C311yescharacteristic
157C2×#102C22×C311yescharacteristic
158C2×C22⋊C8C22×C311yescharacteristic
159#398—21no—
160#395—21no—
161#390C22×C311yescharacteristic
162#389C22×C311yescharacteristic
163#389C22×C311yescharacteristic
164#389C22×C311yescharacteristic
165#388—21no—
166#386—21no—
167#385—21no—
168#385—21no—
169#384C22×C311yescharacteristic
170#380C22×C311yescharacteristic
171C4×C4⋊C4C22×C311yescharacteristic
172C4×C22⋊C4C22×C311yescharacteristic
173#340C22×C311yescharacteristic
174#340C22×C311yescharacteristic
175#340C22×C311yescharacteristic
176#340C22×C311yescharacteristic
177#340C22×C311yescharacteristic
178#340C22×C311yescharacteristic
179#340C22×C311yescharacteristic
180#340C22×C311yescharacteristic
181#340C22×C311yescharacteristic
182#340C22×C311yescharacteristic
183#336C22×C311yescharacteristic
184#336C22×C311yescharacteristic
185C24×C3—21no—
186C24×C3C2×D411yescharacteristic
187C2×C3×Q8—42no—
188C2×C3×Q8—42no—
189C2×C3×Q8—81no—
190C2×C3×D4—24no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—42no—
197C2×C3×D4—42no—
198C2×C3×D4C2×Q812yes—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—42no—
211C22×C3×C4—42no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4—81no—
217C22×C3×C4—81no—
218C22×C3×C4—81no—
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×Q812yes—
225C22×C3×C4#4112yes—
226C22×C3×C4C2411yescharacteristic
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—44no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—42no—
252C3×C4⋊C4—42no—
253C3×C4⋊C4—42no—
254C3×C4⋊C4—42no—
255C3×C4⋊C4—42no—
256C3×C4⋊C4—42no—
257C3×C4⋊C4—42no—
258C3×C4⋊C4—81no—
259C3×C4⋊C4C2×Q812yes—
260C3×C4⋊C4#4112yes—
261C3×C4⋊C4#4112yes—
262C3×C22⋊C4—22no—
263C3×C22⋊C4—24no—
264C3×C22⋊C4—42no—
265C3×C22⋊C4—42no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—81no—
268C3×C22⋊C4SD1614yes—
269C3×C42—21no—
270C3×C42—21no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—42no—
274C22×Q8—21no—
275C22×D4—21no—
276C22×D4C23×C311yescharacteristic
277C23×C4—21no—
278C23×C4—21no—
279C23×C4—21no—
280C23×C4C23×C311yescharacteristic
281C22×C8—22no—
282C22×C8—41no—
283C22×C8—41no—
284C22×C8C23×C311yescharacteristic
285C22×C8C23×C311yescharacteristic
286C22×C8C23×C311yescharacteristic
287C22×C8C23×C311yescharacteristic
288C4⋊Q8—22no—
289C4⋊Q8—41no—
290C22⋊Q8—44no—
291#121—22no—
292#121C3×Q814yescomplemented
293C4×D4—22no—
294C4×D4—41no—
295C4×D4—44no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4C23×C311yescharacteristic
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⋊C4C3×D411yescharacteristic
321C2×C22⋊C4C3×D411yescharacteristic
322C2×C42—21no—
323C2×C42C23×C311yescharacteristic
324C2×C42C23×C311yescharacteristic
325#106—22no—
326#106—41no—
327C4⋊C8—41no—
328C4⋊C8—41no—
329#102—22no—
330#102—41no—
331#102—41no—
332#102—41no—
333C22⋊C8—22no—
334#95—21no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95C3×D411yescharacteristic
340#95C3×D411yescharacteristic
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—22no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3C22⋊Q812yes—
353C23×C3C2×SD1612yes—
354C23×C3AGL(1,ℤ/8)12yes—
355C23×C3C22×D411yescharacteristic
356C3×Q8—84no—
357C3×D4—22no—
358C3×D4—22no—
359C3×D4—48no—
360C3×D4—41no—
361C3×D4—41no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
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—84no—
400C2×C3×C4—84no—
401C2×C3×C4—84no—
402C2×C3×C4C22⋊Q812yes—
403C2×C3×C4C2×SD1612yes—
404C2×C3×C4C2×SD1612yes—
405C2×C3×C4C22×Q811yescharacteristic
406C2×C3×C4C2×#4111yescharacteristic
407C2×C3×C4C2×#4111yescharacteristic
408C2×C3×C4C2×#4111yescharacteristic
409C2×C3×C4H(5,𝔽2)11yescharacteristic
410C2×C3×C4H(5,𝔽2)11yescharacteristic
411C3×C8—41no—
412C3×C8—41no—
413C3×C8—41no—
414C3×C8—41no—
415C24—21no—
416C24C2×C3×D411yescharacteristic
417C2×Q8—42no—
418C2×Q8—42no—
419C2×Q8—81no—
420C2×D4—24no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4C2×C3×Q812yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4C2×C3×D411yescharacteristic
450C22×C4C2×C3×D411yescharacteristic
451C22×C4C2×C3×D411yescharacteristic
452C22×C4C2×C3×D411yescharacteristic
453C22×C4C2×C3×D411yescharacteristic
454C22×C4C2×C3×Q812yes—
455C22×C4C3×#4112yes—
456C22×C4C24×C311yescharacteristic
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—44no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—81no—
489C4⋊C4C2×C3×Q812yes—
490C4⋊C4C3×#4112yes—
491C4⋊C4C3×#4112yes—
492C22⋊C4—22no—
493C22⋊C4—24no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—81no—
498C22⋊C4C3×SD1614yes—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—42no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—42no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—81no—
514C22×C3—81no—
515C22×C3—81no—
516C22×C3—81no—
517C22×C3#47614yes—
518C22×C3C2×C22⋊Q811yescharacteristic
519C22×C3#54611yescharacteristic
520C22×C3#54611yescharacteristic
521C22×C3C22×SD1611yescharacteristic
522C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
523C22×C3#57611yescharacteristic
524C22×C3#57811yescharacteristic
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—22no—
528C3×C4—42no—
529C3×C4—41no—
530C3×C4—41no—
531C3×C4—42no—
532C3×C4—42no—
533C3×C4—81no—
534C3×C4—81no—
535C3×C4—81no—
536C3×C4—81no—
537C3×C4#52911yescharacteristic
538C3×C4#53811yescharacteristic
539C3×C4#55411yescharacteristic
540C3×C4#55411yescharacteristic
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—22no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C3×C22⋊Q812yes—
553C23C2×C3×SD1612yes—
554C23C3×AGL(1,ℤ/8)12yes—
555C23C22×C3×D411yescharacteristic
556Q8—84no—
557D4—22no—
558D4—22no—
559D4—48no—
560D4—41no—
561D4—41no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4C3×C22⋊Q812yes—
603C2×C4C2×C3×SD1612yes—
604C2×C4C2×C3×SD1612yes—
605C2×C4C22×C3×Q811yescharacteristic
606C2×C4C2×C3×#4111yescharacteristic
607C2×C4C2×C3×#4111yescharacteristic
608C2×C4C2×C3×#4111yescharacteristic
609C2×C4C3×H(5,𝔽2)11yescharacteristic
610C2×C4C3×H(5,𝔽2)11yescharacteristic
611C8—41no—
612C8—41no—
613C8—41no—
614C8—41no—
615C2×C3—24no—
616C2×C3—82no—
617C2×C3#245011yescharacteristic
618C2×C3C2×#47611yescharacteristic
619C2×C3#308311yescharacteristic
620C2×C3#329511yescharacteristic
621C2×C3#329811yescharacteristic
622C2×C3#330811yescharacteristic
623C2×C3#331811yescharacteristic
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C3×#47614yes—
638C22C2×C3×C22⋊Q811yescharacteristic
639C22C3×#54611yescharacteristic
640C22C3×#54611yescharacteristic
641C22C22×C3×SD1611yescharacteristic
642C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
643C22C3×#57611yescharacteristic
644C22C3×#57811yescharacteristic
645C4—22no—
646C4—22no—
647C4—22no—
648C4—42no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—81no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4C3×#52911yescharacteristic
658C4C3×#53811yescharacteristic
659C4C3×#55411yescharacteristic
660C4C3×#55411yescharacteristic
661C3#2641011yescharacteristic, direct product factor, Sylow
662C2—24no—
663C2—82no—
664C2C3×#245011yescharacteristic
665C2C2×C3×#47611yescharacteristic
666C2C3×#308311yescharacteristic
667C2C3×#329511yescharacteristic
668C2C3×#329811yescharacteristic
669C2C3×#330811yescharacteristic
670C2C3×#331811yescharacteristic
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. C3×#2440C2semidirect
3. C3×#2100C2semidirect
4. C3×#2088C2semidirect
5. C3×#2065C2semidirect
6. C3×#2023C2semidirect
7. C3×#1987C2semidirect
8. C3×#1920C2semidirect
11. C3×#1864C2semidirect
12. C3×#1853C2semidirect
13. C3×#1850C2semidirect
14. C3×#1802C2semidirect
15. C2×C3×#340C2semidirect
16. #26410C3direct (N × H)
60. #2440C2×C3semidirect
62. #2100C2×C3semidirect
63. #2088C2×C3semidirect
64. #2065C2×C3semidirect
65. #2023C2×C3semidirect
66. #1987C2×C3semidirect
67. #1920C2×C3semidirect
70. #1864C2×C3semidirect
71. #1853C2×C3semidirect
72. #1850C2×C3semidirect
73. #1802C2×C3semidirect
74. C2×#340C2×C3semidirect
93. C3×#121Q8semidirect
292. #121C3×Q8semidirect
661. C3#26410direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#24402
C3×#23612
C3×#21002
C3×#20882
C3×#20652
C3×#20232
C3×#19872
C3×#19202
C3×#18932
C3×#18742
C3×#18642
C3×#18532
C3×#18502
C3×#18022
C2×C3×#3402
#264103