Finite Group Databasebeta

← #10848753

Subgroups — #10848753

Order 768.

1178 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5600C211yesmaximal, characteristic
2C2×#5167C211yesmaximal, characteristic, complemented
3#82811C211yesmaximal, characteristic, complemented
4C2×#4797C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic
6#72047C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic
9#70281C211yesmaximal, characteristic, complemented
10#70171C211yesmaximal, characteristic, complemented
11#70159C211yesmaximal, characteristic, complemented
12#69964C211yesmaximal, characteristic, complemented
13#69906C211yesmaximal, characteristic, complemented
14#68908C211yesmaximal, characteristic, complemented
15#68805C211yesmaximal, characteristic, complemented
16#25604—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#944C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C2×#936C2211yescharacteristic
23C2×#935—21no—
24C2×D4×Dic3—21no—
25C2×D4×Dic3C2211yescharacteristic
26C22×#214C2211yescharacteristic
27C2×#924C2211yescharacteristic
28C2×#924C2211yescharacteristic
29C22×C4×Dic3C2211yescharacteristic
30C22×Dic12C2211yescharacteristic
31#5600—24no—
32#5600—24no—
33C2×#890C2211yescharacteristic
34C2×#887C2211yescharacteristic
35C2×#879—21no—
36C2×#877—21no—
37C2×C3×#103C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40#5229C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5167—24no—
45C2×#816C2211yescharacteristic
46C2×#816C2211yescharacteristic
47C2×#815C2211yescharacteristic
48C2×#815C2211yescharacteristic
49#4976—21no—
50#4976—21no—
51#4975C2211yescharacteristic
52#4973C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#810C2211yescharacteristic
55#4942—21no—
56#4942—21no—
57#4797—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#497—31no—
66C2×#491—31no—
67#2857—31no—
68#2001—31no—
69#2001—31no—
70#2000—31no—
71#2000D311yescharacteristic
72#1992—31no—
73#1959—31no—
74#1878—31no—
75#1878—31no—
76#1877—31no—
77#1877—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3—21no—
84C23×Dic3D411yescharacteristic
85C23×Dic3D411yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—41no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C22⋊Q8—41no—
94C3×C22⋊Q8—41no—
95C3×#121—22no—
96C3×#121—22no—
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×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107#944—22no—
108#944—22no—
109C2×#216—22no—
110C2×#216—22no—
111C2×#216—41no—
112#936—22no—
113#936D414yes—
114#935—28no—
115D4×Dic3—28no—
116D4×Dic3—22no—
117D4×Dic3—22no—
118C2×#214—22no—
119C2×#214—22no—
120C2×#214—41no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124#924—22no—
125#924—22no—
126#924—41no—
127#924—41no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×C4×Dic3—21no—
137C2×C4×Dic3—22no—
138C2×C4×Dic3—22no—
139C2×C4×Dic3D411yescharacteristic
140C2×C4×Dic3D411yescharacteristic
141C2×C4×Dic3C2311yescharacteristic
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×Dic12—22no—
146C2×Dic12—22no—
147C2×Dic12—41no—
148#890—22no—
149#890D414yes—
150#887—22no—
151#887—22no—
152#879—28no—
153#877—28no—
154C3×#103—22no—
155C3×#102—41no—
156C3×C22⋊C8—22no—
157#835—22no—
158#832—41no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163#830—22no—
164#816—22no—
165#816—41no—
166#815—22no—
167#815—22no—
168#810—22no—
169#810—41no—
170C22×Q16—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×SD16C2×D311yescharacteristic
174C2×C4⋊Q8—31no—
175#529—64no—
176#529—64no—
177C2×#126—61no—
178C2×#125—31no—
179C2×#124—31no—
180C2×#123—61no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8—31no—
183C2×C22⋊Q8C2×D311yescharacteristic
184C2×#121C2×D311yescharacteristic
185C2×C4×Q8—31no—
186C2×C4×D4—31no—
187C2×C4×D4—61no—
188C2×#117—61no—
189C22×C42—31no—
190#497—64no—
191#491—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#103—31no—
197C2×#103C2×D311yescharacteristic
198C2×#102—31no—
199C2×#102C2×D311yescharacteristic
200C2×C22⋊C8—31no—
201C2×C22⋊C8C2×D311yescharacteristic
202C2×#97—31no—
203C2×#97—31no—
204#391—31no—
205#391—31no—
206#389—61no—
207#389—61no—
208#384—31no—
209#380—61no—
210#380—61no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340C2×D311yescharacteristic
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×D4—24no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—42no—
232C2×C3×D4—42no—
233C2×C3×D4C2×D412yes—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2411yescharacteristic
245C22×Dic3—24no—
246C22×Dic3—22no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—41no—
255C22×Dic3—41no—
256C22×Dic3—42no—
257C22×Dic3—42no—
258C22×Dic3C2×D411yescharacteristic
259C22×Dic3C2×D411yescharacteristic
260C22×Dic3C2×D411yescharacteristic
261C22×Dic3C2×D411yescharacteristic
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6C2×D412yes—
274C3×SD16—44no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8#4112yes—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—42no—
285C3×C4⋊C4C2×D412yes—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—42no—
288#217—24no—
289#217—24no—
290#217—24no—
291#217—24no—
292#217—42no—
293#216—44no—
294#214—44no—
295C4⋊Dic3—21no—
296C4⋊Dic3—24no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305Dic3⋊C4—42no—
306Dic3⋊C4—42no—
307Dic3⋊C4—42no—
308C4×Dic3—24no—
309C4×Dic3—21no—
310C4×Dic3—21no—
311C4×Dic3—22no—
312C4×Dic3—22no—
313C4×Dic3C2×D412yes—
314C4×Dic3C2×D412yes—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8#4112yes—
321Dic12—44no—
322C22×Q8—31no—
323C22×Q8—31no—
324C22×Q8C22×D311yescharacteristic
325C22×D4—21no—
326C22×D4C22×D311yescharacteristic
327C23×C4—31no—
328C23×C4—31no—
329C23×C4—61no—
330C23×C4C22×D311yescharacteristic
331C2×Q16—62no—
332C2×Q16—62no—
333C2×Q16—62no—
334C2×Q16—62no—
335C2×Q16—121no—
336C2×Q16—121no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—41no—
340C2×SD16—62no—
341C2×SD16—62no—
342C2×SD16—121no—
343C22×C8—31no—
344C22×C8—31no—
345C22×C8C22×D311yescharacteristic
346C22×C8C22×D311yescharacteristic
347C4⋊Q8—62no—
348C4⋊Q8—62no—
349#126—68no—
350#125—34no—
351#125—62no—
352#124—34no—
353#124—62no—
354#123—68no—
355C22⋊Q8—41no—
356C22⋊Q8—41no—
357C22⋊Q8—62no—
358C22⋊Q8—62no—
359C22⋊Q8—121no—
360C22⋊Q8—121no—
361#121—22no—
362#121—22no—
363C4×Q8—62no—
364C4×Q8—62no—
365C4×D4—62no—
366C4×D4—68no—
367C4×D4—62no—
368#117—68no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—31no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—61no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4—61no—
380C2×C4⋊C4—61no—
381C2×C4⋊C4C22×D311yescharacteristic
382C2×C4⋊C4C22×D311yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C42—31no—
391C2×C42—31no—
392C2×C42—31no—
393C2×C42—31no—
394C2×C42—62no—
395C2×C42—62no—
396C2×C42—61no—
397#103—22no—
398#103—62no—
399#103—62no—
400#103—62no—
401#103—121no—
402#103—121no—
403#102—41no—
404#102—121no—
405C22⋊C8—22no—
406C22⋊C8—62no—
407#97—62no—
408#97—62no—
409#95—61no—
410#95—61no—
411#95—61no—
412#95—61no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—22no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3#13712yes—
427C23×C3C22×D411yescharacteristic
428C3×Q8—41no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×D4—22no—
433C3×D4—22no—
434C3×D4—48no—
435C3×D4—41no—
436C3×D4—41no—
437C2×C3×C4—21no—
438C2×C3×C4—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4H(5,𝔽2)11yescharacteristic
458C2×C3×C4H(5,𝔽2)11yescharacteristic
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—44no—
471C2×Dic3—44no—
472C2×Dic3—48no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3#12012yes—
484C2×Dic3#12012yes—
485C2×Dic3#13712yes—
486Dic6—22no—
487Dic6—22no—
488Dic6—41no—
489Dic6—41no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493Dic6—41no—
494C3×C8—22no—
495C3×C8—41no—
496C3⋊C8—22no—
497C3⋊C8—41no—
498C24—21no—
499C24D3×D411yescharacteristic
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—32no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×D4—24no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—42no—
525C2×D4—42no—
526C2×D4D3×D412yes—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—64no—
544C22×C4—62no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—122no—
550C22×C4—121no—
551C22×C4—121no—
552C22×C4—122no—
553C22×C4D3×D411yescharacteristic
554C22×C4C23×D311yescharacteristic
555Q16—124no—
556Q16—124no—
557SD16—44no—
558SD16—124no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—32no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8#23712yes—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—32no—
575C4⋊C4—42no—
576C4⋊C4—64no—
577C4⋊C4—64no—
578C4⋊C4—64no—
579C4⋊C4—64no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—122no—
584C4⋊C4—122no—
585C4⋊C4—122no—
586C4⋊C4—122no—
587C4⋊C4—122no—
588C4⋊C4D3×D412yes—
589C22⋊C4—24no—
590C22⋊C4—42no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—122no—
596C42—32no—
597C42—32no—
598C42—62no—
599C42—62no—
600C42—64no—
601C42—61no—
602C42—61no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3C2×#12011yescharacteristic
618C22×C3#53211yescharacteristic
619C22×C3#53511yescharacteristic
620C22×C3C2×#13711yescharacteristic
621C22×C3C2×#13711yescharacteristic
622C22×C3#57511yescharacteristic
623C22×C3#57511yescharacteristic
624C3×C4—41no—
625C3×C4—42no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4#54611yescharacteristic
629C3×C4#54611yescharacteristic
630C3×C4#55011yescharacteristic
631C3×C4#55011yescharacteristic
632Dic3—22no—
633Dic3—22no—
634Dic3—22no—
635Dic3—42no—
636Dic3—41no—
637Dic3—42no—
638Dic3—81no—
639Dic3—81no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23#91512yes—
654C23C2×D3×D411yescharacteristic
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8—62no—
660Q8—62no—
661Q8—121no—
662Q8—121no—
663Q8—121no—
664Q8—121no—
665Q8—121no—
666Q8—121no—
667D4—22no—
668D4—22no—
669D4—48no—
670D4—41no—
671D4—41no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—62no—
701C2×C4—62no—
702C2×C4—124no—
703C2×C4—124no—
704C2×C4—128no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4C2×D3×D411yescharacteristic
716C2×C4C2×D3×D411yescharacteristic
717C2×C4C2×#23711yescharacteristic
718C2×C4#100411yescharacteristic
719C2×C4#100411yescharacteristic
720C2×C4D3×#4111yescharacteristic
721C8—22no—
722C8—41no—
723C8—62no—
724C8—121no—
725C2×C3—42no—
726C2×C3—82no—
727C2×C3#243111yescharacteristic
728C2×C3#300711yescharacteristic
729C2×C3#300711yescharacteristic
730C2×C3#317211yescharacteristic
731C2×C3#318111yescharacteristic
732C2×C3#321811yescharacteristic
733C2×C3#321911yescharacteristic
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22D3×#12011yescharacteristic
749C22#559211yescharacteristic
750C22#559611yescharacteristic
751C22C2×#91511yescharacteristic
752C22#576811yescharacteristic
753C22#577311yescharacteristic
754C22D3×#13711yescharacteristic
755C4—42no—
756C4—41no—
757C4—62no—
758C4—62no—
759C4—62no—
760C4—81no—
761C4—81no—
762C4—121no—
763C4—122no—
764C4—122no—
765C4—241no—
766C4—241no—
767C4#559111yescharacteristic
768C4#559911yescharacteristic
769C4#561011yescharacteristic
770C4#571811yescharacteristic
771C3#2560411yescharacteristic, complemented, Sylow
772C2—42no—
773C2—82no—
774C2#7667211yescharacteristic
775C2#8003511yescharacteristic
776C2#8007911yescharacteristic
777C2#8014711yescharacteristic
778C2#8022811yescharacteristic
779C2#8063911yescharacteristic
780C2#8078511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×C3×#121C22
hypercenter#2000D3
hypocenterC3#25604
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. C2×#5167C2semidirect
3. #82811C2semidirect
4. C2×#4797C2semidirect
6. #72047C2semidirect
7. #71700C2semidirect
9. #70281C2semidirect
10. #70171C2semidirect
11. #70159C2semidirect
12. #69964C2semidirect
13. #69906C2semidirect
14. #68908C2semidirect
15. #68805C2semidirect
771. C3#25604semidirect

Maximal subgroups

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

subgroupindex
C2×#56002
C2×#51672
#828112
C2×#47972
C3×#20002
#720472
#717002
#716852
#702812
#701712
#701592
#699642
#699062
#689082
#688052
#256043