Finite Group Databasebeta

← #10829202

Subgroups — #10829202

Order 768.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5695C211yesmaximal, characteristic
2C2×C3×#479C211yesmaximal, characteristic, complemented
3#82499C211yesmaximal, characteristic, complemented
4C2×C4×#215C211yesmaximal, characteristic, complemented
5#71740C211yesmaximal, characteristic, complemented
6#70634C211yesmaximal, characteristic, complemented
7#70633C211yesmaximal, characteristic, complemented
8#70581C211yesmaximal, characteristic, complemented
9#70579C211yesmaximal, characteristic, complemented
10#70480C211yesmaximal, characteristic, complemented
11#70470C211yesmaximal, characteristic, complemented
12#70272C211yesmaximal, characteristic, complemented
13#70272C211yesmaximal, characteristic, complemented
14#70269C211yesmaximal, characteristic, complemented
15#70268C211yesmaximal, characteristic, complemented
16#24126—31nomaximal, Sylow
17C2×C3×#125C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C22×#215C2211yescharacteristic
22#5695—24no—
23#5695—24no—
24C2×#898—21no—
25C2×#895—21no—
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#894—21no—
29C2×#893—21no—
30C2×#892C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C3×#479—24no—
35C2×C3×#107C2211yescharacteristic
36C2×C3×#106C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C4×#215—24no—
48#4991—21no—
49#4987C2211yescharacteristic
50#4987C2211yescharacteristic
51#4981—21no—
52C2×#809C2211yescharacteristic
53C2×#808C2211yescharacteristic
54#4940—21no—
55#4940—21no—
56#4936C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#479D311yescharacteristic, complemented
66C2×C4×SD16—31no—
67#2536—31no—
68#2034—31no—
69#2033—31no—
70#2000—31no—
71#2000—31no—
72#1991—31no—
73#1954—31no—
74#1873—31no—
75#1872—31no—
76#1854—31no—
77#1853—31no—
78#1804—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×D12—21no—
81C22×D12—21no—
82C22×D12D411yescharacteristic
83C22×D12C2311yescharacteristic
84C22×C4×D3—21no—
85C22×C4×D3—21no—
86C22×C4×D3C2311yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×#125—22no—
91C3×#125D414yes—
92C3×C4×Q8—22no—
93C3×C4×Q8—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—21no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C42—21no—
101C2×C3×C42C2311yescharacteristic
102#946—22no—
103#946—22no—
104#946—41no—
105#946—41no—
106C2×#215—22no—
107C2×#215—22no—
108C2×#215—22no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×(C2×D3)⋊C4D411yescharacteristic
119C2×C4⋊Dic3D411yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×C4×Dic3—21no—
127C22×C3⋊C8C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129#898—28no—
130#895—28no—
131#895—22no—
132#895—22no—
133#895—22no—
134#895—22no—
135#894—28no—
136#893—28no—
137#892—22no—
138#892—22no—
139D3×C4⋊C4—22no—
140D3×C4⋊C4—22no—
141C4×D12—22no—
142C4×D12—22no—
143C4×D12—22no—
144C4×D12D414yes—
145C3×#107—22no—
146C3×#106—22no—
147C3×C4⋊C8—22no—
148C3×#103—22no—
149C3×#103—22no—
150#835—22no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#821—41no—
156#821—41no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—41no—
160(C2×D3)⋊C8—41no—
161#809—22no—
162#808—22no—
163C4×C3⋊C8—22no—
164C22×SD16—31no—
165#553—64no—
166#553—64no—
167C2×#126—61no—
168C2×#125C2×D311yescharacteristic
169C2×#123—61no—
170C2×C22⋊Q8—31no—
171C2×C22⋊Q8—31no—
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—61no—
175C2×C4×Q8C2×D311yescharacteristic
176C2×C4×D4—31no—
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C2×#117—31no—
180C22×C4⋊C4—31no—
181#479—24no—
182C4×SD16—64no—
183C2×#107C2×D311yescharacteristic
184C2×#106—31no—
185C2×#106C2×D311yescharacteristic
186C2×C4⋊C8C2×D311yescharacteristic
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C4×C8—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#340—31no—
211C23×D3—21no—
212C23×D3C2×D411yescharacteristic
213C23×D3C2×D411yescharacteristic
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8#4112yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2411yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3C2×D411yescharacteristic
231C22×Dic3C2×D411yescharacteristic
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—24no—
237C2×D12—22no—
238C2×D12—22no—
239C2×D12—21no—
240C2×D12—24no—
241C2×D12—41no—
242C2×D12—42no—
243C2×D12—42no—
244C2×D12—81no—
245C2×D12—81no—
246C2×D12C2×D412yes—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
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—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—24no—
260C2×C4×D3—24no—
261C2×C4×D3—81no—
262C2×C4×D3—81no—
263C2×C4×D3—81no—
264C2×C4×D3—81no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—24no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—42no—
278C3×C4⋊C4C2×D412yes—
279C3×C4⋊C4C2×D412yes—
280C3×C42—42no—
281C3×C42C2×D412yes—
282C3×C42C2×D412yes—
283#215—28no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294C4⋊Dic3—22no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300C4⋊Dic3C2×D412yes—
301Dic3⋊C4—24no—
302Dic3⋊C4—42no—
303Dic3⋊C4—42no—
304C4×Dic3—24no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8#4112yes—
311C22×Q8C22×D311yescharacteristic
312C22×D4—31no—
313C22×D4—31no—
314C22×D4—61no—
315C22×D4—61no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—61no—
319C23×C4—61no—
320C2×SD16—62no—
321C2×SD16—62no—
322C2×SD16—62no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8C22×D311yescharacteristic
326C22×C8C22×D311yescharacteristic
327#126—68no—
328#125—22no—
329#125#6714yes—
330#123—68no—
331C22⋊Q8—62no—
332C22⋊Q8—62no—
333C22⋊Q8—121no—
334C22⋊Q8—121no—
335#121—62no—
336#121—62no—
337#121—68no—
338#121—62no—
339#121—62no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×D4—34no—
343C4×D4—68no—
344C4×D4—62no—
345C4×D4—62no—
346C4×D4—62no—
347#117—62no—
348#117—62no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—62no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4C22×D311yescharacteristic
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C42—21no—
375C2×C42—61no—
376C2×C42C22×D311yescharacteristic
377#107—22no—
378#106—22no—
379#106—62no—
380C4⋊C8—22no—
381#103—22no—
382#103—22no—
383#103—62no—
384#102—62no—
385#102—121no—
386#102—121no—
387C22⋊C8—62no—
388C22⋊C8—62no—
389C22⋊C8—121no—
390C22⋊C8—121no—
391C4×C8—62no—
392#95—61no—
393#95—61no—
394#95—61no—
395#95—61no—
396C23×C3C22×D411yescharacteristic
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—22no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3#13512yes—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—41no—
421C3×Q8—41no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
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×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4#12012yes—
439C2×C3×C4#12012yes—
440C2×C3×C4C22×D411yescharacteristic
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C4H(5,𝔽2)11yescharacteristic
445C2×C3×C42−1+411yescharacteristic
446C2×Dic3—21no—
447C2×Dic3—22no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461D12—22no—
462D12—22no—
463D12—44no—
464D12—48no—
465D12—41no—
466D12—41no—
467D12—84no—
468C4×D3—41no—
469C4×D3—41no—
470C4×D3—41no—
471C4×D3—41no—
472C4×D3—41no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—84no—
477C4×D3—84no—
478C3×C8—41no—
479C3×C8—41no—
480C3⋊C8—22no—
481C3⋊C8—41no—
482C24—31no—
483C24—31no—
484C24—61no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8#23912yes—
491C2×D4—32no—
492C2×D4—62no—
493C2×D4—64no—
494C2×D4—64no—
495C2×D4—62no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—121no—
502C2×D4—122no—
503C2×D4—122no—
504C2×D4—241no—
505C2×D4—241no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—31no—
511C22×C4—31no—
512C22×C4—64no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—64no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—241no—
530C22×C4—241no—
531C22×C4—241no—
532C22×C4—241no—
533C22×C4D3×D411yescharacteristic
534C22×C4D3×D411yescharacteristic
535C22×C4C23×D311yescharacteristic
536SD16—68no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—32no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—32no—
556C4⋊C4—42no—
557C4⋊C4—64no—
558C4⋊C4—62no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—122no—
565C4⋊C4—122no—
566C4⋊C4C2×#6712yes—
567C4⋊C4C2×#6712yes—
568C22⋊C4—64no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—62no—
572C22⋊C4—62no—
573C22⋊C4—64no—
574C22⋊C4—122no—
575C22⋊C4—122no—
576C22⋊C4—122no—
577C22⋊C4—122no—
578C42—42no—
579C42—64no—
580C42D3×D412yes—
581C42C2×#6712yes—
582C22×C3C2×#12011yescharacteristic
583C22×C3#54611yescharacteristic
584C22×C3#54711yescharacteristic
585C22×C3C2×#13511yescharacteristic
586C22×C3#57511yescharacteristic
587C22×C3#57711yescharacteristic
588C22×C3#57711yescharacteristic
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—41no—
595C2×D3—41no—
596C2×D3—41no—
597C2×D3—41no—
598C2×D3—41no—
599C2×D3—42no—
600C2×D3—41no—
601C2×D3—42no—
602C2×D3—42no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—42no—
615C3×C4—81no—
616C3×C4#52511yescharacteristic
617C3×C4#53711yescharacteristic
618C3×C4#54811yescharacteristic
619C3×C4#55011yescharacteristic
620Dic3—41no—
621Dic3—41no—
622Dic3—42no—
623Dic3—81no—
624Dic3—81no—
625C23—32no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—62no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23C2×D3×D411yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—62no—
652D4—62no—
653D4—124no—
654D4—128no—
655D4—121no—
656D4—121no—
657D4—244no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—61no—
675C2×C4—62no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—244no—
698C2×C4—244no—
699C2×C4#93712yes—
700C2×C4#93712yes—
701C2×C4C2×D3×D411yescharacteristic
702C2×C4C2×#23911yescharacteristic
703C2×C4#100711yescharacteristic
704C2×C4D3×#4111yescharacteristic
705C2×C4#100911yescharacteristic
706C2×C4C22×#6711yescharacteristic
707C8—41no—
708C8—41no—
709C8—62no—
710C8—121no—
711C2×C3#240711yescharacteristic
712C2×C3#300211yescharacteristic
713C2×C3#300911yescharacteristic
714C2×C3#330111yescharacteristic
715C2×C3#332611yescharacteristic
716C2×C3#333711yescharacteristic
717C2×C3#335111yescharacteristic
718D3—42no—
719D3—81no—
720D3—82no—
721C22—62no—
722C22—62no—
723C22—62no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22—121no—
728C22—122no—
729C22—121no—
730C22—121no—
731C22—121no—
732C22—121no—
733C22—121no—
734C22—121no—
735C22—122no—
736C22—121no—
737C22—122no—
738C22—241no—
739C22—241no—
740C22—241no—
741C22—241no—
742C22#563011yescharacteristic
743C22#563111yescharacteristic
744C22D3×#13511yescharacteristic
745C22#576811yescharacteristic
746C22#577811yescharacteristic
747C22#577811yescharacteristic
748C22C2×#93711yescharacteristic
749C4—22no—
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—81no—
755C4—122no—
756C4—121no—
757C4—121no—
758C4—241no—
759C4—241no—
760C4#562711yescharacteristic
761C4#562911yescharacteristic
762C4#581711yescharacteristic
763C4#583411yescharacteristic
764C3#2412611yescharacteristic, complemented, Sylow
765C2—122no—
766C2—241no—
767C2—242no—
768C2#8124611yescharacteristic
769C2#8125111yescharacteristic
770C2#8125411yescharacteristic
771C2#8125911yescharacteristic
772C2#8281211yescharacteristic
773C2#8391111yescharacteristic
774C2#8398211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#479C2
socleC23×C3C22×D4
prime radicalC2×#5695C2
hypercenterC2×#479D3
hypocenterC3#24126
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. C2×C3×#479C2semidirect
3. #82499C2semidirect
4. C2×C4×#215C2semidirect
5. #71740C2semidirect
6. #70634C2semidirect
7. #70633C2semidirect
8. #70581C2semidirect
9. #70579C2semidirect
10. #70480C2semidirect
11. #70470C2semidirect
12. #70272C2semidirect
13. #70272C2semidirect
14. #70269C2semidirect
15. #70268C2semidirect
65. C2×#479D3semidirect
764. C3#24126semidirect

Maximal subgroups

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

subgroupindex
C2×#56952
C2×C3×#4792
#824992
C2×C4×#2152
#717402
#706342
#706332
#705812
#705792
#704802
#704702
#702722
#702692
#702682
#241263