Finite Group Databasebeta

← #10701034

Subgroups — #10701034

Order 768.

998 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Dic3⋊C8C211yesmaximal, characteristic
2C2×#4977C211yesmaximal, characteristic
3C2×Dic3×C4⋊C4C211yesmaximal, characteristic
4C2×C3×#340C211yesmaximal, characteristic
5C2×#4551C211yesmaximal, characteristic
6C2×#4529C211yesmaximal, characteristic
7C2×#4529C211yesmaximal, characteristic
8#10850—31nomaximal, Sylow
9C23×C3×C8C2211yescharacteristic
10C22×C3×C4⋊C4C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic3C2211yescharacteristic
13C22×C4⋊Dic3C2211yescharacteristic
14C22×C4×Dic3—21no—
15C22×C4×Dic3C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
17C2×C3⋊#95—21no—
18C2×C3⋊#95—21no—
19C2×C3⋊#95—21no—
20C2×Dic3⋊C8—22no—
21C2×Dic3⋊C8—22no—
22C2×Dic3⋊C8C414yescomplemented
23#4977—22no—
24#4977C414yescomplemented
25Dic3×C4⋊C4—22no—
26Dic3×C4⋊C4C414yescomplemented
27C3×#340—22no—
28#4551—22no—
29#4529—22no—
30#4529—22no—
31C22×C4⋊C8—31no—
32C2×#382—31no—
33C2×C4×C4⋊C4—31no—
34C2×#340—31no—
35C2×#340—31no—
36C2×#340—31no—
37C2×#340D311yescharacteristic
38C23×C3×C4—21no—
39C23×C3×C4—21no—
40C23×C3×C4C2311yescharacteristic
41C23×Dic3—21no—
42C23×Dic3—21no—
43C23×Dic3D411yescharacteristic
44C23×Dic3D411yescharacteristic
45C22×C3×C8—21no—
46C22×C3×C8—21no—
47C22×C3×C8—21no—
48C22×C3×C8—21no—
49C22×C3×C8—21no—
50C22×C3×C8—21no—
51C22×C3×C8C2×C412yes—
52C2×C3×C4⋊C4—21no—
53C2×C3×C4⋊C4—21no—
54C2×C3×C4⋊C4—21no—
55C2×C3×C4⋊C4—21no—
56C2×C3×C4⋊C4—21no—
57C2×C3×C4⋊C4—21no—
58C2×C3×C4⋊C4—21no—
59C2×C3×C4⋊C4—21no—
60C2×C3×C4⋊C4C2×C412yes—
61C2×C3×C4⋊C4C2×C412yes—
62C2×C3×C4⋊C4D412yes—
63C2×C3×C4⋊C4Q812yes—
64C2×C4⋊Dic3—21no—
65C2×C4⋊Dic3—21no—
66C2×C4⋊Dic3—21no—
67C2×C4⋊Dic3—21no—
68C2×C4⋊Dic3—21no—
69C2×C4⋊Dic3—21no—
70C2×C4⋊Dic3—21no—
71C2×C4⋊Dic3—21no—
72C2×C4⋊Dic3C2×C412yes—
73C2×C4⋊Dic3C2×C412yes—
74C2×C4⋊Dic3D412yes—
75C2×C4⋊Dic3Q812yes—
76C2×C4×Dic3—24no—
77C2×C4×Dic3—42no—
78C2×C4×Dic3—42no—
79C2×C4×Dic3C2×C412yes—
80C2×C4×Dic3C2×C412yes—
81C2×C4×Dic3C2×C412yes—
82C2×C4×Dic3D412yes—
83C2×C4×Dic3D412yes—
84C2×C4×Dic3Q812yes—
85C22×C3⋊C8—21no—
86C22×C3⋊C8—21no—
87C22×C3⋊C8—21no—
88C22×C3⋊C8—21no—
89C22×C3⋊C8—21no—
90C22×C3⋊C8—21no—
91C22×C3⋊C8C2×C412yes—
92C3⋊#95—24no—
93C3⋊#95—24no—
94C3⋊#95—24no—
95Dic3⋊C8—28no—
96C23×C8—31no—
97C23×C8C2×D311yescharacteristic
98C22×C4⋊C4—31no—
99C22×C4⋊C4—31no—
100C22×C4⋊C4C2×D311yescharacteristic
101C22×C4⋊C4C2×D311yescharacteristic
102C22×C42—31no—
103C22×C42—61no—
104C2×C4⋊C8—34no—
105C2×C4⋊C8—62no—
106C2×C4⋊C8—62no—
107#382—34no—
108#382—62no—
109C4×C4⋊C4—34no—
110C4×C4⋊C4—62no—
111C2×#95—61no—
112C2×#95—61no—
113C2×#95—61no—
114#340—22no—
115#340—62no—
116#340—62no—
117#340—62no—
118C24×C3C2×D411yescharacteristic
119C22×C3×C4—22no—
120C22×C3×C4—22no—
121C22×C3×C4—22no—
122C22×C3×C4—22no—
123C22×C3×C4—41no—
124C22×C3×C4—41no—
125C22×C3×C4—41no—
126C22×C3×C4—41no—
127C22×C3×C4—41no—
128C22×C3×C4—41no—
129C22×C3×C4—41no—
130C22×C3×C4—41no—
131C22×C3×C4—41no—
132C22×C3×C4—41no—
133C22×C3×C4C22×C411yescharacteristic
134C22×C3×C4C22×C411yescharacteristic
135C22×C3×C4C22×C411yescharacteristic
136C22×C3×C4C2×D411yescharacteristic
137C22×C3×C4C2×D411yescharacteristic
138C22×C3×C4C2×D411yescharacteristic
139C22×C3×C4C2×D411yescharacteristic
140C22×C3×C4C2×Q811yescharacteristic
141C22×C3×C4C2×Q811yescharacteristic
142C22×C3×C4C2×Q811yescharacteristic
143C22×C3×C4#4111yescharacteristic
144C22×C3×C4#4111yescharacteristic
145C22×C3×C4#4111yescharacteristic
146C22×C3×C4#4111yescharacteristic
147C22×Dic3—21no—
148C22×Dic3—21no—
149C22×Dic3—21no—
150C22×Dic3—21no—
151C22×Dic3—21no—
152C22×Dic3—21no—
153C22×Dic3—21no—
154C22×Dic3—21no—
155C22×Dic3—22no—
156C22×Dic3—22no—
157C22×Dic3—22no—
158C22×Dic3—22no—
159C22×Dic3—41no—
160C22×Dic3—41no—
161C22×Dic3—41no—
162C22×Dic3—41no—
163C22×Dic3—41no—
164C22×Dic3—41no—
165C22×Dic3—41no—
166C22×Dic3—41no—
167C22×Dic3—41no—
168C22×Dic3—41no—
169C22×Dic3C22⋊C412yes—
170C22×Dic3C22⋊C412yes—
171C22×Dic3C22⋊C412yes—
172C22×Dic3C22⋊C412yes—
173C22×Dic3C4⋊C412yes—
174C22×Dic3C4⋊C412yes—
175C2×C3×C8—22no—
176C2×C3×C8—22no—
177C2×C3×C8—22no—
178C2×C3×C8—41no—
179C2×C3×C8—41no—
180C2×C3×C8—41no—
181C2×C3×C8—41no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—22no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—22no—
187C3×C4⋊C4—41no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4C4⋊C414yes—
190C4⋊Dic3—22no—
191C4⋊Dic3—22no—
192C4⋊Dic3—22no—
193C4⋊Dic3—22no—
194C4⋊Dic3—22no—
195C4⋊Dic3—41no—
196C4⋊Dic3—41no—
197C4⋊Dic3C4⋊C414yes—
198C4×Dic3—48no—
199C4×Dic3C4214yes—
200C4×Dic3C22⋊C414yes—
201C4×Dic3C4⋊C414yes—
202C4×Dic3C4⋊C414yes—
203C2×C3⋊C8—22no—
204C2×C3⋊C8—22no—
205C2×C3⋊C8—22no—
206C2×C3⋊C8—41no—
207C2×C3⋊C8—41no—
208C2×C3⋊C8—41no—
209C2×C3⋊C8—41no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—31no—
213C23×C4—31no—
214C23×C4—61no—
215C23×C4—61no—
216C23×C4C22×D311yescharacteristic
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—32no—
224C22×C8—61no—
225C22×C8—61no—
226C22×C8—61no—
227C22×C8—61no—
228C22×C8—61no—
229C22×C8—61no—
230C22×C8C4×D312yes—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—32no—
240C2×C4⋊C4—32no—
241C2×C4⋊C4—32no—
242C2×C4⋊C4—32no—
243C2×C4⋊C4—61no—
244C2×C4⋊C4—61no—
245C2×C4⋊C4—61no—
246C2×C4⋊C4—61no—
247C2×C4⋊C4—61no—
248C2×C4⋊C4—61no—
249C2×C4⋊C4—61no—
250C2×C4⋊C4—61no—
251C2×C4⋊C4Dic612yes—
252C2×C4⋊C4C4×D312yes—
253C2×C4⋊C4C4×D312yes—
254C2×C4⋊C4#6712yes—
255C2×C42—32no—
256C2×C42—32no—
257C2×C42—32no—
258C2×C42—32no—
259C2×C42—32no—
260C2×C42—32no—
261C2×C42—64no—
262C2×C42—122no—
263C2×C42—122no—
264C4⋊C8—68no—
265#95—64no—
266#95—64no—
267#95—64no—
268C23×C3C2×C22⋊C411yescharacteristic
269C23×C3C2×C22⋊C411yescharacteristic
270C23×C3C2×C4⋊C411yescharacteristic
271C23×C3#12111yescharacteristic
272C23×C3#12111yescharacteristic
273C23×C3C22⋊Q811yescharacteristic
274C23×C3C22⋊Q811yescharacteristic
275C23×C3#13511yescharacteristic
276C23×C3#13511yescharacteristic
277C23×C3#13511yescharacteristic
278C23×C3#13511yescharacteristic
279C23×C3AGL(1,ℤ/8)11yescharacteristic
280C23×C3AGL(1,ℤ/8)11yescharacteristic
281C23×C3#13711yescharacteristic
282C23×C3#13711yescharacteristic
283C2×C3×C4—24no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—81no—
294C2×C3×C4—81no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4C2×C4211yescharacteristic
298C2×C3×C4C2×C22⋊C411yescharacteristic
299C2×C3×C4C2×C4⋊C411yescharacteristic
300C2×C3×C4C2×C4⋊C411yescharacteristic
301C2×C3×C4C2×C4⋊C411yescharacteristic
302C2×C3×C4C2×C4⋊C411yescharacteristic
303C2×C3×C4#11711yescharacteristic
304C2×C3×C4#11711yescharacteristic
305C2×C3×C4C4×D411yescharacteristic
306C2×C3×C4C4×D411yescharacteristic
307C2×C3×C4C4×D411yescharacteristic
308C2×C3×C4C4×D411yescharacteristic
309C2×C3×C4C4×Q811yescharacteristic
310C2×C3×C4C4×Q811yescharacteristic
311C2×C3×C4C4×Q811yescharacteristic
312C2×C3×C4C4×Q811yescharacteristic
313C2×C3×C4#12111yescharacteristic
314C2×C3×C4#12111yescharacteristic
315C2×C3×C4C22⋊Q811yescharacteristic
316C2×C3×C4C22⋊Q811yescharacteristic
317C2×C3×C4#12411yescharacteristic
318C2×C3×C4#12411yescharacteristic
319C2×C3×C4#12511yescharacteristic
320C2×C3×C4#12511yescharacteristic
321C2×C3×C4#12711yescharacteristic
322C2×C3×C4C4⋊Q811yescharacteristic
323C2×C3×C4C4⋊Q811yescharacteristic
324C2×C3×C4C4⋊Q811yescharacteristic
325C2×Dic3—22no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—22no—
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—22no—
337C2×Dic3—24no—
338C2×Dic3—42no—
339C2×Dic3—42no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3—42no—
343C2×Dic3—42no—
344C2×Dic3—42no—
345C2×Dic3—42no—
346C2×Dic3—42no—
347C2×Dic3—81no—
348C2×Dic3—81no—
349C2×Dic3—81no—
350C2×Dic3—81no—
351C2×Dic3#9514yes—
352C2×Dic3#9514yes—
353C3×C8—42no—
354C3⋊C8—42no—
355C24D3×D411yescharacteristic
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—32no—
361C22×C4—32no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—32no—
365C22×C4—32no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4—61no—
380C22×C4—61no—
381C22×C4—61no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—62no—
385C22×C4—62no—
386C22×C4—62no—
387C22×C4—62no—
388C22×C4—121no—
389C22×C4—121no—
390C22×C4—121no—
391C22×C4—121no—
392C22×C4—121no—
393C22×C4—121no—
394C22×C4—121no—
395C22×C4—121no—
396C22×C4—121no—
397C22×C4—121no—
398C22×C4C2×Dic611yescharacteristic
399C22×C4C2×C4×D311yescharacteristic
400C22×C4C2×C4×D311yescharacteristic
401C22×C4C2×C4×D311yescharacteristic
402C22×C4#23511yescharacteristic
403C22×C4#23511yescharacteristic
404C22×C4D3×D411yescharacteristic
405C22×C4D3×D411yescharacteristic
406C22×C4D3×D411yescharacteristic
407C22×C4#23711yescharacteristic
408C22×C4#23711yescharacteristic
409C22×C4D3×Q811yescharacteristic
410C22×C4D3×Q811yescharacteristic
411C22×C4C2×#6711yescharacteristic
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—41no—
416C2×C8—41no—
417C2×C8—41no—
418C2×C8—41no—
419C2×C8—62no—
420C2×C8—62no—
421C2×C8—62no—
422C2×C8—121no—
423C2×C8—121no—
424C2×C8—121no—
425C2×C8—121no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—34no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—62no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C4⋊C4—62no—
438C4⋊C4—62no—
439C4⋊C4—121no—
440C4⋊C4—121no—
441C4⋊C4Dic3⋊C414yes—
442C42—34no—
443C42—34no—
444C42—34no—
445C42—34no—
446C42—128no—
447C22×C3C2×#9511yescharacteristic
448C22×C3#38011yescharacteristic
449C22×C3#38011yescharacteristic
450C22×C3#38911yescharacteristic
451C22×C3#38911yescharacteristic
452C22×C3#39011yescharacteristic
453C22×C3#39111yescharacteristic
454C22×C3#41611yescharacteristic
455C22×C3#41611yescharacteristic
456C22×C3#41611yescharacteristic
457C22×C3#41611yescharacteristic
458C22×C3#41711yescharacteristic
459C22×C3#41711yescharacteristic
460C22×C3#41811yescharacteristic
461C22×C3#41911yescharacteristic
462C22×C3#42711yescharacteristic
463C22×C3#42711yescharacteristic
464C22×C3#42811yescharacteristic
465C22×C3#42811yescharacteristic
466C22×C3#46311yescharacteristic
467C22×C3#46311yescharacteristic
468C22×C3#46311yescharacteristic
469C22×C3#46311yescharacteristic
470C22×C3#46411yescharacteristic
471C22×C3#46411yescharacteristic
472C22×C3#46411yescharacteristic
473C22×C3#46411yescharacteristic
474C22×C3#47811yescharacteristic
475C22×C3#47811yescharacteristic
476C22×C3#47811yescharacteristic
477C22×C3#47811yescharacteristic
478C22×C3#47911yescharacteristic
479C22×C3#47911yescharacteristic
480C22×C3#47911yescharacteristic
481C22×C3#47911yescharacteristic
482C3×C4—44no—
483C3×C4—82no—
484C3×C4C4×C4⋊C411yescharacteristic
485C3×C4C4×C4⋊C411yescharacteristic
486C3×C4#38211yescharacteristic
487C3×C4#38411yescharacteristic
488C3×C4#38911yescharacteristic
489C3×C4#38911yescharacteristic
490C3×C4#39011yescharacteristic
491C3×C4#39111yescharacteristic
492Dic3—24no—
493Dic3—24no—
494Dic3—44no—
495Dic3—82no—
496C23#87811yescharacteristic
497C23D3×C22⋊C411yescharacteristic
498C23D3×C22⋊C411yescharacteristic
499C23#88411yescharacteristic
500C23D3×C4⋊C411yescharacteristic
501C23#89611yescharacteristic
502C23#91111yescharacteristic
503C23#91211yescharacteristic
504C23#91411yescharacteristic
505C23#91511yescharacteristic
506C23#91611yescharacteristic
507C23#91611yescharacteristic
508C23#91811yescharacteristic
509C23#91911yescharacteristic
510C23#93911yescharacteristic
511C2×C4—24no—
512C2×C4—34no—
513C2×C4—34no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—64no—
536C2×C4—81no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—122no—
541C2×C4—122no—
542C2×C4—122no—
543C2×C4—122no—
544C2×C4—122no—
545C2×C4—122no—
546C2×C4—122no—
547C2×C4—122no—
548C2×C4—122no—
549C2×C4—241no—
550C2×C4—241no—
551C2×C4—241no—
552C2×C4—241no—
553C2×C4C4×Dic611yescharacteristic
554C2×C4C4×Dic611yescharacteristic
555C2×C4C42×D311yescharacteristic
556C2×C4#87211yescharacteristic
557C2×C4#87711yescharacteristic
558C2×C4#87811yescharacteristic
559C2×C4D3×C22⋊C411yescharacteristic
560C2×C4#67⋊C411yescharacteristic
561C2×C4#67⋊C411yescharacteristic
562C2×C4#88411yescharacteristic
563C2×C4#88511yescharacteristic
564C2×C4#88511yescharacteristic
565C2×C4#88711yescharacteristic
566C2×C4#88711yescharacteristic
567C2×C4#88811yescharacteristic
568C2×C4#88811yescharacteristic
569C2×C4#88911yescharacteristic
570C2×C4#88911yescharacteristic
571C2×C4D3×C4⋊C411yescharacteristic
572C2×C4D3×C4⋊C411yescharacteristic
573C2×C4D3×C4⋊C411yescharacteristic
574C2×C4#89611yescharacteristic
575C2×C4C2×Dic3⋊C411yescharacteristic
576C2×C4C4×#6711yescharacteristic
577C2×C4C4×#6711yescharacteristic
578C2×C4#93911yescharacteristic
579C2×C4#94011yescharacteristic
580C2×C4#94411yescharacteristic
581C8—42no—
582C8—122no—
583C2×C3C4⋊#9511yescharacteristic
584C2×C3#173511yescharacteristic
585C2×C3#173611yescharacteristic
586C2×C3#180411yescharacteristic
587C2×C3#180411yescharacteristic
588C2×C3#180511yescharacteristic
589C2×C3#180511yescharacteristic
590C2×C3#194911yescharacteristic
591C2×C3#194911yescharacteristic
592C2×C3#194911yescharacteristic
593C2×C3#194911yescharacteristic
594C2×C3#198311yescharacteristic
595C2×C3#198311yescharacteristic
596C2×C3#198911yescharacteristic
597C2×C3#198911yescharacteristic
598C22#464611yescharacteristic
599C22#464711yescharacteristic
600C22D3×#9511yescharacteristic
601C22#466711yescharacteristic
602C22#476311yescharacteristic
603C22#476611yescharacteristic
604C22#476711yescharacteristic
605C22#477011yescharacteristic
606C22#477111yescharacteristic
607C22#477211yescharacteristic
608C22#477211yescharacteristic
609C22#478711yescharacteristic
610C22#479611yescharacteristic
611C22#479811yescharacteristic
612C22#479911yescharacteristic
613C22#480211yescharacteristic
614C22#480311yescharacteristic
615C22#480411yescharacteristic
616C22#480411yescharacteristic
617C22#481911yescharacteristic
618C22#485711yescharacteristic
619C22#486011yescharacteristic
620C22#486111yescharacteristic
621C22#487111yescharacteristic
622C22#487711yescharacteristic
623C22#488011yescharacteristic
624C22#488111yescharacteristic
625C22#489111yescharacteristic
626C22#494211yescharacteristic
627C22#495711yescharacteristic
628C22#497611yescharacteristic
629C22#515311yescharacteristic
630C22#516511yescharacteristic
631C22#516611yescharacteristic
632C22#518511yescharacteristic
633C4—44no—
634C4—64no—
635C4—64no—
636C4—82no—
637C4—124no—
638C4—242no—
639C4#464611yescharacteristic
640C4#464711yescharacteristic
641C4#464911yescharacteristic
642C4#465011yescharacteristic
643C4C4×Dic3⋊C411yescharacteristic
644C4#495711yescharacteristic
645C4#497511yescharacteristic
646C4#497611yescharacteristic
647C3#1085011yescharacteristic, complemented, Sylow
648C2#6879711yescharacteristic
649C2#6879811yescharacteristic
650C2#6880111yescharacteristic
651C2#6880211yescharacteristic
652C2#6886611yescharacteristic
653C2#6886711yescharacteristic
654C2#6889311yescharacteristic
655C2#6890511yescharacteristic
656C2Dic3⋊#9511yescharacteristic
657C2#7015411yescharacteristic
658C2#7016211yescharacteristic
659C2#7022211yescharacteristic
660C2#7023011yescharacteristic
661C2#7056411yescharacteristic
662C2#7061611yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC2×C3×C4C2×C42
FrattiniC23×C4C22×D3
FittingC2×C3×#340C2
socle, prime radicalC24×C3C2×D4
cosocleC23×C3×C4C23
hypercenterC2×#340D3
hypocenterC3#10850
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
22. C2×Dic3⋊C8C4semidirect
24. #4977C4semidirect
26. Dic3×C4⋊C4C4semidirect
647. C3#10850semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3⋊C82
C2×#49772
C2×Dic3×C4⋊C42
C2×C3×#3402
C2×#45512
C2×#45292
#108503