Finite Group Databasebeta

← #10829287

Subgroups — #10829287

Order 768.

1120 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5635C211yesmaximal, characteristic
2C2×#5184C211yesmaximal, characteristic, complemented
3#82777C211yesmaximal, characteristic
4C2×#4791C211yesmaximal, characteristic, complemented
5C3×#2001C211yesmaximal, characteristic, complemented
6#72071C211yesmaximal, characteristic, complemented
7#71694C211yesmaximal, characteristic, complemented
8#71692C211yesmaximal, characteristic, complemented
9#70268C211yesmaximal, characteristic, complemented
10#70243C211yesmaximal, characteristic, complemented
11#70222C211yesmaximal, characteristic, complemented
12#69928C211yesmaximal, characteristic, complemented
13#69917C211yesmaximal, characteristic
14#68875C211yesmaximal, characteristic, complemented
15#68806C211yesmaximal, characteristic, complemented
16#24134—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C22×C4⋊Dic3C2211yescharacteristic
26#5635—24no—
27#5635—24no—
28C2×#897—21no—
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×#889—21no—
31C2×#888C2211yescharacteristic
32C2×#67⋊C4—21no—
33C2×#878—21no—
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5184—24no—
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#817C2211yescharacteristic
47C2×#817C2211yescharacteristic
48C2×#815C2211yescharacteristic
49C2×Dic3⋊C8C2211yescharacteristic
50#4990—21no—
51#4987C2211yescharacteristic
52#4982—21no—
53#4977C2211yescharacteristic
54C2×#808C2211yescharacteristic
55#4961—21no—
56#4945—21no—
57#4791—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#554—31no—
65C2×#475—31no—
66C2×#441—31no—
67#2536—31no—
68#2035—31no—
69#2035—31no—
70#2001—31no—
71#2001D311yescharacteristic, complemented
72#1993—31no—
73#1955—31no—
74#1872—31no—
75#1872—31no—
76#1853—31no—
77#1853—31no—
78#1805—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C22×#67D411yescharacteristic
83C23×Dic3—21no—
84C22×C4×D3—21no—
85C22×C4×D3C2311yescharacteristic
86C22×Dic6—21no—
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—41no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×#217—21no—
103C2×#217D411yescharacteristic
104#946—22no—
105#946—22no—
106#946—22no—
107#946—41no—
108Q8×Dic3—22no—
109Q8×Dic3—22no—
110Q8×Dic3—22no—
111Q8×Dic3D414yes—
112C4×#67—22no—
113C4×#67—22no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—22no—
121C2×C4⋊Dic3—22no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4D411yescharacteristic
132C2×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#897—28no—
138D3×C4⋊C4—22no—
139D3×C4⋊C4—22no—
140#889—28no—
141#888—22no—
142#888D414yes—
143#67⋊C4—28no—
144#878—28no—
145C3×#103—22no—
146C3×#103—41no—
147C3×C22⋊C8—22no—
148#835—22no—
149#835—22no—
150#835—22no—
151#835—41no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—41no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—41no—
159#817—22no—
160#817—22no—
161#815—22no—
162Dic3⋊C8—22no—
163#808—22no—
164C22×Q16C2×D311yescharacteristic
165#554—64no—
166#554—64no—
167C2×C4⋊Q8—31no—
168C2×#125—61no—
169C2×C22⋊Q8—31no—
170C2×C22⋊Q8—31no—
171C2×C22⋊Q8—61no—
172C2×C22⋊Q8—61no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C22×C4⋊C4—31no—
180C22×C4⋊C4—31no—
181#475—64no—
182#441—64no—
183C2×#106—31no—
184C2×#106—31no—
185C2×#106—31no—
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103C2×D311yescharacteristic
192C2×#103C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×#97—31no—
198#398—61no—
199#394—61no—
200#388—61no—
201#388—61no—
202#382—31no—
203#380—31no—
204#380—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340C2×D311yescharacteristic
211C24×C3C2×D411yescharacteristic
212C23×D3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×Q8#4112yes—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C2×#67—22no—
238C2×#67—22no—
239C2×#67—22no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—24no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—81no—
246C22×Dic3—81no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—24no—
257C2×C4×D3—81no—
258C2×C4×D3—81no—
259C2×Dic6—24no—
260C2×Dic6—81no—
261C2×Dic6—81no—
262C3×Q16—28no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8#4112yes—
269C3×C4⋊C4—24no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4C2×D412yes—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—42no—
277#217—22no—
278#217—42no—
279(C2×D3)⋊C4—24no—
280(C2×D3)⋊C4—22no—
281(C2×D3)⋊C4—42no—
282(C2×D3)⋊C4—42no—
283C4⋊Dic3—24no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—24no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—42no—
292C4⋊Dic3C2×D412yes—
293C4⋊Dic3C2×D412yes—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297Dic3⋊C4—22no—
298Dic3⋊C4—42no—
299C4×Dic3—24no—
300C4×Dic3—42no—
301C4×Dic3C2×D412yes—
302C4×Dic3C2×D412yes—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C22×Q8—61no—
310C22×Q8C22×D311yescharacteristic
311C22×Q8C22×D311yescharacteristic
312C22×D4—31no—
313C23×C4—31no—
314C23×C4—61no—
315C23×C4—61no—
316C23×C4C22×D311yescharacteristic
317C2×Q16—22no—
318C2×Q16—22no—
319C2×Q16—22no—
320C22×C8—31no—
321C22×C8—31no—
322C22×C8C22×D311yescharacteristic
323C22×C8C22×D311yescharacteristic
324C4⋊Q8—34no—
325C4⋊Q8—62no—
326#125—68no—
327C22⋊Q8—22no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8—41no—
331C22⋊Q8—68no—
332C22⋊Q8—68no—
333C22⋊Q8—62no—
334C22⋊Q8—62no—
335C22⋊Q8—62no—
336C22⋊Q8—121no—
337C4×Q8—34no—
338C4×Q8—62no—
339C4×Q8—62no—
340C4×Q8—62no—
341C4×D4—62no—
342C4×D4—62no—
343C4×D4—68no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—62no—
352C2×C4⋊C4—62no—
353C2×C4⋊C4—62no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—62no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C42—31no—
373C2×C42—61no—
374C2×C42—61no—
375#106—62no—
376#106—62no—
377#106—62no—
378C4⋊C8—62no—
379#103—22no—
380#103—41no—
381#103—62no—
382#103—62no—
383#103—62no—
384#103—121no—
385C22⋊C8—22no—
386C22⋊C8—62no—
387C22⋊C8—121no—
388C22⋊C8—121no—
389#97—62no—
390#95—61no—
391#95—61no—
392#95—61no—
393#95—61no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3#13712yes—
401C23×C3C22×D411yescharacteristic
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3#13712yes—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
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—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4H(5,𝔽2)11yescharacteristic
441C2×C3×C42−1+411yescharacteristic
442#67—28no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—22no—
448C2×Dic3—21no—
449C2×Dic3—22no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—84no—
463C2×Dic3#12012yes—
464C2×Dic3#12012yes—
465C4×D3—41no—
466C4×D3—41no—
467C4×D3—41no—
468C4×D3—41no—
469C4×D3—84no—
470Dic6—84no—
471C3×C8—22no—
472C3×C8—41no—
473C3⋊C8—41no—
474C3⋊C8—41no—
475C24—31no—
476C24D3×D411yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—64no—
488C2×Q8—241no—
489C2×Q8—241no—
490C2×Q8D3×D412yes—
491C2×Q8#23712yes—
492C2×D4—62no—
493C2×D4—62no—
494C2×D4—62no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—31no—
508C22×C4—64no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—64no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—241no—
521C22×C4—241no—
522C22×C4—241no—
523C22×C4—241no—
524C22×C4D3×D411yescharacteristic
525C22×C4C23×D311yescharacteristic
526Q16—28no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8#23712yes—
539C4⋊C4—24no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—32no—
544C4⋊C4—32no—
545C4⋊C4—42no—
546C4⋊C4—62no—
547C4⋊C4—64no—
548C4⋊C4—64no—
549C4⋊C4—64no—
550C4⋊C4—64no—
551C4⋊C4—64no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—122no—
559C4⋊C4—122no—
560C4⋊C4D3×D412yes—
561C22⋊C4—24no—
562C22⋊C4—42no—
563C22⋊C4—62no—
564C22⋊C4—64no—
565C22⋊C4—62no—
566C22⋊C4—122no—
567C22⋊C4—122no—
568C22⋊C4—122no—
569C42—32no—
570C42—32no—
571C42—64no—
572C42—122no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3C2×#12011yescharacteristic
581C22×C3#54611yescharacteristic
582C22×C3#54711yescharacteristic
583C22×C3C2×#13711yescharacteristic
584C22×C3C2×#13711yescharacteristic
585C22×C3#57711yescharacteristic
586C22×C3#57711yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—41no—
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—81no—
599C3×C4#52511yescharacteristic
600C3×C4#53711yescharacteristic
601C3×C4#54811yescharacteristic
602C3×C4#55011yescharacteristic
603Dic3—22no—
604Dic3—22no—
605Dic3—41no—
606Dic3—42no—
607Dic3—42no—
608Dic3—81no—
609Dic3—81no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—32no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23#91812yes—
624C23C2×D3×D411yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—244no—
634D4—68no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—62no—
661C2×C4—62no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—244no—
680C2×C4—244no—
681C2×C4C2×D3×D411yescharacteristic
682C2×C4C2×D3×D411yescharacteristic
683C2×C4C2×#23711yescharacteristic
684C2×C4C2×#23711yescharacteristic
685C2×C4#100411yescharacteristic
686C2×C4#101011yescharacteristic
687C8—22no—
688C8—41no—
689C8—121no—
690C8—121no—
691C2×C3—42no—
692C2×C3#240711yescharacteristic
693C2×C3#300411yescharacteristic
694C2×C3#300911yescharacteristic
695C2×C3#331611yescharacteristic
696C2×C3#331611yescharacteristic
697C2×C3#334411yescharacteristic
698C2×C3#334411yescharacteristic
699D3—42no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—62no—
708C22—62no—
709C22—62no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22D3×#12011yescharacteristic
715C22#559111yescharacteristic
716C22#561111yescharacteristic
717C22C2×#91811yescharacteristic
718C22#577011yescharacteristic
719C22D3×#13711yescharacteristic
720C22#577811yescharacteristic
721C4—42no—
722C4—41no—
723C4—42no—
724C4—42no—
725C4—62no—
726C4—62no—
727C4—81no—
728C4—122no—
729C4—122no—
730C4—121no—
731C4—241no—
732C4—241no—
733C4#558611yescharacteristic
734C4#559711yescharacteristic
735C4#559811yescharacteristic
736C4#571811yescharacteristic
737C3#2413411yescharacteristic, complemented, Sylow
738C2—42no—
739C2—122no—
740C2#7666811yescharacteristic
741C2#8018311yescharacteristic
742C2#8019811yescharacteristic
743C2#8022911yescharacteristic
744C2#8025511yescharacteristic
745C2#8075511yescharacteristic
746C2#8091911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC22×#67D4
hypercenter#2001D3
hypocenterC3#24134
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#5184C2semidirect
4. C2×#4791C2semidirect
5. C3×#2001C2semidirect
6. #72071C2semidirect
7. #71694C2semidirect
8. #71692C2semidirect
9. #70268C2semidirect
10. #70243C2semidirect
11. #70222C2semidirect
12. #69928C2semidirect
14. #68875C2semidirect
15. #68806C2semidirect
71. #2001D3semidirect
737. C3#24134semidirect

Maximal subgroups

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

subgroupindex
C2×#56352
C2×#51842
#827772
C2×#47912
C3×#20012
#720712
#716942
#716922
#702682
#702432
#702222
#699282
#699172
#688752
#688062
#241343