Finite Group Databasebeta

← C3×#26816 #10645423

Subgroups — C3×#26816 #10645423

Order 768.

904 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#486C211yesmaximal, characteristic
2C2×C3×C4×SD16C211yesmaximal, characteristic, complemented
3C3×#2451C211yesmaximal, characteristic, complemented
4C3×#2445C211yesmaximal, characteristic
5C3×#2065C211yesmaximal, characteristic, complemented
6C3×#2058C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2014C211yesmaximal, characteristic
9C3×#1968C211yesmaximal, characteristic, complemented
10C3×#1934C211yesmaximal, characteristic, complemented
11C3×#1934C211yesmaximal, characteristic, complemented
12C3×#1933C211yesmaximal, characteristic, complemented
13C3×#1880C211yesmaximal, characteristic, complemented
14C3×#1864C211yesmaximal, characteristic, complemented
15C3×C8×C4⋊C4C211yesmaximal, characteristic, complemented
16#26816C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#127C2211yescharacteristic
21C2×C3×#123—21no—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C3×#486—24no—
25C3×C4×SD16—24no—
26C2×C3×#106C2211yescharacteristic
27C2×C3×#106C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×#103C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C4×C8C2211yescharacteristic
38C2×C3×C4×C8C2211yescharacteristic
39C2×C3×C4×C8C2211yescharacteristic
40C3×#398—21no—
41C3×#395—21no—
42C3×#394—21no—
43C3×#394—21no—
44C3×#391—21no—
45C3×#391C2211yescharacteristic
46C3×#391C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#389C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#387—21no—
54C3×#386—21no—
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#486C2×C311yescharacteristic
63C2×C4×SD16C2×C311yescharacteristic, complemented
64#2451C2×C311yescharacteristic, complemented
65#2445C2×C311yescharacteristic
66#2065C2×C311yescharacteristic, complemented
67#2058C2×C311yescharacteristic, complemented
68#2055C2×C311yescharacteristic, complemented
69#2014C2×C311yescharacteristic
70#1968C2×C311yescharacteristic, complemented
71#1934C2×C311yescharacteristic, complemented
72#1934C2×C311yescharacteristic, complemented
73#1933C2×C311yescharacteristic, complemented
74#1880C2×C311yescharacteristic, complemented
75#1864C2×C311yescharacteristic, complemented
76C8×C4⋊C4C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C2×C3×SD16—22no—
85C2×C3×SD16—22no—
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C2×C3×SD16—22no—
89C2×C3×SD16—41no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C4⋊Q8—22no—
95C3×C4⋊Q8—41no—
96C3×#127—22no—
97C3×#127—41no—
98C3×#123—44no—
99C3×C4×Q8—22no—
100C3×C4×Q8—41no—
101C3×C4×D4—22no—
102C3×C4×D4—41no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4D411yescharacteristic
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
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⋊C4—21no—
122C2×C3×C42—21no—
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C3×#106—22no—
127C3×#106—41no—
128C3×C4⋊C8—22no—
129C3×#103—22no—
130C3×#103—22no—
131C3×#102—22no—
132C3×#102—22no—
133C3×#102—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102D414yes—
137C3×C4×C8—22no—
138C3×C4×C8—22no—
139C3×C4×C8—22no—
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
150C22×SD16C22×C311yescharacteristic
151C2×C4⋊Q8C22×C311yescharacteristic
152C2×#127C22×C311yescharacteristic
153C2×#123—21no—
154C2×C4×Q8C22×C311yescharacteristic
155C2×C4×D4C22×C311yescharacteristic
156#486—24no—
157C4×SD16—24no—
158C2×#106C22×C311yescharacteristic
159C2×#106C22×C311yescharacteristic
160C2×C4⋊C8C22×C311yescharacteristic
161C2×#103C22×C311yescharacteristic
162C2×#103C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×C4×C8C22×C311yescharacteristic
170C2×C4×C8C22×C311yescharacteristic
171C2×C4×C8C22×C311yescharacteristic
172#398—21no—
173#395—21no—
174#394—21no—
175#394—21no—
176#391—21no—
177#391C22×C311yescharacteristic
178#391C22×C311yescharacteristic
179#390C22×C311yescharacteristic
180#390C22×C311yescharacteristic
181#390C22×C311yescharacteristic
182#389C22×C311yescharacteristic
183#389C22×C311yescharacteristic
184#389C22×C311yescharacteristic
185#387—21no—
186#386—21no—
187C4×C4⋊C4C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193#336C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—42no—
202C2×C3×Q8—42no—
203C2×C3×Q8—81no—
204C2×C3×Q8#4112yes—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4—81no—
221C2×C3×D4—81no—
222C2×C3×D4C2×D412yes—
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—42no—
230C22×C3×C4—42no—
231C22×C3×C4—81no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C3×SD16—28no—
240C3×SD16—44no—
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×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8C2×D412yes—
251C2×C3×C8#4112yes—
252C2×C3×C8#4112yes—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—42no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—42no—
266C3×C4⋊C4—81no—
267C3×C4⋊C4—81no—
268C3×C4⋊C4SD1614yescomplemented
269C3×C4⋊C4C2×D412yes—
270C3×C22⋊C4—42no—
271C3×C22⋊C4—42no—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—81no—
275C3×C22⋊C4—81no—
276C3×C22⋊C4—81no—
277C3×C42—21no—
278C3×C42—21no—
279C3×C42—21no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—42no—
284C22×Q8—21no—
285C22×Q8C23×C311yescharacteristic
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C23×C311yescharacteristic
289C22×D4C23×C311yescharacteristic
290C23×C4—21no—
291C2×SD16—22no—
292C2×SD16—22no—
293C2×SD16—22no—
294C2×SD16—22no—
295C2×SD16—22no—
296C2×SD16—41no—
297C22×C8C23×C311yescharacteristic
298C22×C8C23×C311yescharacteristic
299C22×C8C23×C311yescharacteristic
300C22×C8C23×C311yescharacteristic
301C4⋊Q8—22no—
302C4⋊Q8—41no—
303#127—22no—
304#127—41no—
305#123—44no—
306C4×Q8—22no—
307C4×Q8—41no—
308C4×D4—22no—
309C4×D4—41no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4C3×D411yescharacteristic
316C2×C4⋊C4C3×D411yescharacteristic
317C2×C4⋊C4C23×C311yescharacteristic
318C2×C4⋊C4C23×C311yescharacteristic
319C2×C4⋊C4C23×C311yescharacteristic
320C2×C4⋊C4C23×C311yescharacteristic
321C2×C4⋊C4C23×C311yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C42—21no—
330C2×C42C23×C311yescharacteristic
331C2×C42C23×C311yescharacteristic
332C2×C42C23×C311yescharacteristic
333#106—22no—
334#106—41no—
335C4⋊C8—22no—
336#103—22no—
337#103—22no—
338#102—22no—
339#102—22no—
340#102—22no—
341#102—22no—
342#102—22no—
343#102C3×D414yes—
344C4×C8—22no—
345C4×C8—22no—
346C4×C8—22no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95C3×D411yescharacteristic
355#95C3×D411yescharacteristic
356C23×C3—22no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3C22×D411yescharacteristic
371C3×Q8—22no—
372C3×Q8—22no—
373C3×Q8—41no—
374C3×Q8—41no—
375C3×Q8—84no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—41no—
379C3×D4—41no—
380C3×D4—41no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—84no—
385C3×D4—84no—
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—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
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—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—84no—
419C2×C3×C4C2×SD1612yes—
420C2×C3×C4C2×SD1612yes—
421C2×C3×C4C2×SD1612yes—
422C2×C3×C4#13512yes—
423C2×C3×C4C22×D411yescharacteristic
424C2×C3×C4C2×#4111yescharacteristic
425C2×C3×C4C2×#4111yescharacteristic
426C2×C3×C4C2×#4111yescharacteristic
427C2×C3×C4H(5,𝔽2)11yescharacteristic
428C2×C3×C42−1+411yescharacteristic
429C3×C8—22no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—41no—
433C24—21no—
434C24—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—81no—
443C2×Q8C3×#4112yes—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—42no—
456C2×D4—42no—
457C2×D4—42no—
458C2×D4—42no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4C2×C3×D412yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—81no—
471C22×C4C2×C3×D411yescharacteristic
472C22×C4C2×C3×D411yescharacteristic
473C22×C4C2×C3×D411yescharacteristic
474C22×C4C2×C3×D411yescharacteristic
475C22×C4C2×C3×D411yescharacteristic
476C22×C4C2×C3×D411yescharacteristic
477C22×C4C24×C311yescharacteristic
478SD16—28no—
479SD16—44no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×C3×D412yes—
490C2×C8C3×#4112yes—
491C2×C8C3×#4112yes—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4C3×SD1614yescomplemented
508C4⋊C4C2×C3×D412yes—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—42no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—42no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3—81no—
529C22×C3—81no—
530C22×C3—81no—
531C22×C3—81no—
532C22×C3—81no—
533C22×C3—81no—
534C22×C3—81no—
535C22×C3—81no—
536C22×C3—81no—
537C22×C3#53211yescharacteristic
538C22×C3D4211yescharacteristic
539C22×C3#54811yescharacteristic
540C22×C3C22×SD1611yescharacteristic
541C22×C3C2×#13511yescharacteristic
542C22×C3#57611yescharacteristic
543C22×C3#57711yescharacteristic
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—22no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—41no—
551C3×C4—42no—
552C3×C4—81no—
553C3×C4—81no—
554C3×C4—81no—
555C3×C4—81no—
556C3×C4#52511yescharacteristic
557C3×C4#54211yescharacteristic
558C3×C4#54711yescharacteristic
559C3×C4#55111yescharacteristic
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23C22×C3×D411yescharacteristic
575Q8—22no—
576Q8—22no—
577Q8—41no—
578Q8—41no—
579Q8—84no—
580D4—22no—
581D4—22no—
582D4—41no—
583D4—41no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588D4—84no—
589D4—84no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
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×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4C2×C3×SD1612yes—
624C2×C4C2×C3×SD1612yes—
625C2×C4C2×C3×SD1612yes—
626C2×C4C3×#13512yes—
627C2×C4C22×C3×D411yescharacteristic
628C2×C4C2×C3×#4111yescharacteristic
629C2×C4C2×C3×#4111yescharacteristic
630C2×C4C2×C3×#4111yescharacteristic
631C2×C4C3×H(5,𝔽2)11yescharacteristic
632C2×C4C3×2−1+411yescharacteristic
633C8—22no—
634C8—22no—
635C8—22no—
636C8—41no—
637C2×C3—82no—
638C2×C3—161no—
639C2×C3#246111yescharacteristic
640C2×C3#316711yescharacteristic
641C2×C3#317911yescharacteristic
642C2×C3#328011yescharacteristic
643C2×C3D4×SD1611yescharacteristic
644C2×C3#336211yescharacteristic
645C2×C3#336511yescharacteristic
646C22—42no—
647C22—42no—
648C22—42no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22C3×#53211yescharacteristic
661C22C3×D4211yescharacteristic
662C22C3×#54811yescharacteristic
663C22C22×C3×SD1611yescharacteristic
664C22C2×C3×#13511yescharacteristic
665C22C3×#57611yescharacteristic
666C22C3×#57711yescharacteristic
667C4—22no—
668C4—22no—
669C4—22no—
670C4—22no—
671C4—41no—
672C4—42no—
673C4—41no—
674C4—42no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4C3×#52511yescharacteristic
680C4C3×#54211yescharacteristic
681C4C3×#54711yescharacteristic
682C4C3×#55111yescharacteristic
683C3#2681611yescharacteristic, direct product factor, Sylow
684C2—82no—
685C2—161no—
686C2C3×#246111yescharacteristic
687C2C3×#316711yescharacteristic
688C2C3×#317911yescharacteristic
689C2C3×#328011yescharacteristic
690C2C3×D4×SD1611yescharacteristic
691C2C3×#336211yescharacteristic
692C2C3×#336511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×SD16C2semidirect
3. C3×#2451C2semidirect
5. C3×#2065C2semidirect
6. C3×#2058C2semidirect
7. C3×#2055C2semidirect
9. C3×#1968C2semidirect
10. C3×#1934C2semidirect
11. C3×#1934C2semidirect
12. C3×#1933C2semidirect
13. C3×#1880C2semidirect
14. C3×#1864C2semidirect
15. C3×C8×C4⋊C4C2semidirect
16. #26816C3direct (N × H)
63. C2×C4×SD16C2×C3semidirect
64. #2451C2×C3semidirect
66. #2065C2×C3semidirect
67. #2058C2×C3semidirect
68. #2055C2×C3semidirect
70. #1968C2×C3semidirect
71. #1934C2×C3semidirect
72. #1934C2×C3semidirect
73. #1933C2×C3semidirect
74. #1880C2×C3semidirect
75. #1864C2×C3semidirect
76. C8×C4⋊C4C2×C3semidirect
268. C3×C4⋊C4SD16semidirect
507. C4⋊C4C3×SD16semidirect
683. C3#26816direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4862
C2×C3×C4×SD162
C3×#24512
C3×#24452
C3×#20652
C3×#20582
C3×#20552
C3×#20142
C3×#19682
C3×#19342
C3×#19332
C3×#18802
C3×#18642
C3×C8×C4⋊C42
#268163