Finite Group Databasebeta

← #10823430

Subgroups — #10823430

Order 768.

1260 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5557C211yesmaximal, characteristic, complemented
2C2×C3×#442C211yesmaximal, characteristic, complemented
3C4×#938C211yesmaximal, characteristic, complemented
4C2×#5018C211yesmaximal, characteristic, complemented
5#72045C211yesmaximal, characteristic, complemented
6#72043C211yesmaximal, characteristic
7#71609C211yesmaximal, characteristic, complemented
8#70582C211yesmaximal, characteristic, complemented
9#70566C211yesmaximal, characteristic, complemented
10#70216C211yesmaximal, characteristic, complemented
11#70206C211yesmaximal, characteristic, complemented
12#70205C211yesmaximal, characteristic, complemented
13#70164C211yesmaximal, characteristic, complemented
14#69813C211yesmaximal, characteristic, complemented
15#69807C211yesmaximal, characteristic, complemented
16#23575—31nomaximal, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×#938C2211yescharacteristic
22C2×#936C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C2×C4×#67—21no—
25C2×C4×#67—21no—
26C2×#926—21no—
27#5557—24no—
28#5557—24no—
29C2×#897C2211yescharacteristic
30C2×#890C2211yescharacteristic
31C2×#883—21no—
32C2×#879—21no—
33C2×C42×D3C2211yescharacteristic
34C2×C4×Dic6C2211yescharacteristic
35C3×#442—24no—
36C2×C3×#106C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#97C2211yescharacteristic
40#5221C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C4×#217—21no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49#5018—24no—
50#4987C2211yescharacteristic
51#4972C2211yescharacteristic
52C2×#810C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4956—21no—
55#4944—21no—
56C4×C4⋊Dic3C2211yescharacteristic
57C2×#803C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#529—31no—
65C2×#442D311yescharacteristic, complemented
66C2×#440—31no—
67C4×#121—31no—
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2025—31no—
73#2012—31no—
74#2000—31no—
75#1999—31no—
76#1763—31no—
77#1762—31no—
78#1749—31no—
79C22×C3×D4C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C2×C3×D8—22no—
90C2×C3×D8—22no—
91C2×C3×D8—22no—
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C3×C4×D4—22no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×C4×D4D414yescomplemented
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C42C2311yescharacteristic
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109#938—22no—
110#938—22no—
111#938—22no—
112#938—22no—
113#936—22no—
114#936—22no—
115C2×#214—22no—
116C2×#214—22no—
117C2×#214—22no—
118C4×#67—28no—
119C4×#67—44no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122#926—28no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3—21no—
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×C4×Dic3—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3D411yescharacteristic
135C2×C4×Dic3C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138#897—22no—
139#897—22no—
140#890—22no—
141#890—22no—
142#883—28no—
143#879—28no—
144C42×D3—22no—
145C42×D3—22no—
146C4×Dic6—22no—
147C4×Dic6D414yescomplemented
148C3×#106—22no—
149C3×#102—22no—
150C3×#102—22no—
151C3×#97—22no—
152#832—22no—
153#832—22no—
154#832—22no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—22no—
160#816—22no—
161#816—22no—
162#810—22no—
163#807—22no—
164#803—22no—
165C22×SD16—31no—
166C22×D8C2×D311yescharacteristic
167#529—64no—
168#529—64no—
169C2×#126—61no—
170C2×#125—31no—
171C2×#124—31no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—61no—
178C2×C4×D4—61no—
179C2×C4×D4C2×D311yescharacteristic
180C2×C4×D4C2×D311yescharacteristic
181C2×#117—61no—
182C22×C42—31no—
183#442—24no—
184#440—64no—
185C2×#107—31no—
186C2×#106C2×D311yescharacteristic
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102C2×D311yescharacteristic
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×#97—31no—
198C2×#97C2×D311yescharacteristic
199#390—31no—
200#389—31no—
201#388—61no—
202#386—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205C4×C22⋊C4—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4C2×D412yes—
226C2×C3×D4#4112yes—
227C22×C3×C4—21no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—42no—
231C22×C3×C4—42no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2411yescharacteristic
238C2×#67—24no—
239C2×#67—24no—
240C2×#67—42no—
241C2×#67—42no—
242C2×#67—42no—
243C2×#67—42no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C22×Dic3C2×D411yescharacteristic
251C2×C4×D3—22no—
252C2×C4×D3—22no—
253C2×C4×D3—22no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—41no—
261C2×C4×D3—41no—
262C2×C4×D3—41no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6C2×D412yes—
269C3×D8—28no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8#4112yes—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4C2×D412yes—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—42no—
282C3×C42C2×D412yes—
283C3×C42C2×D412yes—
284#217—24no—
285#217—24no—
286#217—24no—
287#217—24no—
288#217—42no—
289#217—42no—
290#214—28no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—42no—
293C4⋊Dic3—24no—
294C4⋊Dic3—24no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3C2×D412yes—
300C4⋊Dic3#4112yes—
301Dic3⋊C4—24no—
302Dic3⋊C4—24no—
303Dic3⋊C4—42no—
304C4×Dic3—24no—
305C4×Dic3—22no—
306C4×Dic3—22no—
307C4×Dic3—21no—
308C4×Dic3—21no—
309C4×Dic3—42no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8#4112yes—
316C22×Q8—31no—
317C22×D4—61no—
318C22×D4—61no—
319C22×D4C22×D311yescharacteristic
320C22×D4C22×D311yescharacteristic
321C23×C4—21no—
322C23×C4—21no—
323C23×C4—31no—
324C23×C4—31no—
325C23×C4—31no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×D8—22no—
330C2×D8—22no—
331C2×D8—22no—
332C22×C8—31no—
333C22×C8—31no—
334C22×C8C22×D311yescharacteristic
335C22×C8C22×D311yescharacteristic
336#126—68no—
337#125—62no—
338#125—62no—
339#124—62no—
340#124—62no—
341#123—68no—
342C22⋊Q8—62no—
343C22⋊Q8—62no—
344#121—62no—
345#121—62no—
346#121—62no—
347#121—62no—
348C4×Q8—34no—
349C4×Q8—62no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—68no—
354C4×D4—124no—
355C4×D4#6714yescomplemented
356#117—68no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C42—31no—
378C2×C42—31no—
379C2×C42—31no—
380C2×C42—61no—
381C2×C42—62no—
382C2×C42—62no—
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—22no—
387#103—62no—
388#103—62no—
389#103—62no—
390#102—22no—
391#102—22no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397#97—22no—
398#97—62no—
399#95—61no—
400#95—61no—
401#95—61no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3C22×D411yescharacteristic
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3AGL(1,ℤ/8)12yes—
424C3×D4—22no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—41no—
429C3×D4—41no—
430C3×D4—41no—
431C3×D4—41no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—48no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—84no—
444C2×C3×C4#12012yes—
445C2×C3×C4#12012yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452#67—48no—
453#67—48no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C4×D3—44no—
476C4×D3—44no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481Dic6—22no—
482Dic6—22no—
483Dic6—41no—
484Dic6—41no—
485C3×C8—22no—
486C3×C8—41no—
487C3⋊C8—22no—
488C3⋊C8—41no—
489C24—21no—
490C24—21no—
491C24—31no—
492C2×Q8—32no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—64no—
509C2×D4—64no—
510C2×D4—122no—
511C2×D4—122no—
512C2×D4—122no—
513C2×D4—122no—
514C2×D4#23512yes—
515C2×D4C2×#6712yes—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—21no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—31no—
522C22×C4—42no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—62no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—62no—
532C22×C4—62no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—121no—
541C22×C4—121no—
542C22×C4—121no—
543C22×C4D3×D411yescharacteristic
544C22×C4D3×D411yescharacteristic
545C22×C4C23×D311yescharacteristic
546SD16—68no—
547D8—28no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—32no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8#23512yes—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—32no—
564C4⋊C4—32no—
565C4⋊C4—64no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—64no—
569C4⋊C4—61no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—122no—
574C4⋊C4C2×#6712yes—
575C22⋊C4—24no—
576C22⋊C4—42no—
577C22⋊C4—64no—
578C22⋊C4—64no—
579C22⋊C4—64no—
580C22⋊C4—64no—
581C22⋊C4—64no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C42—62no—
586C42—62no—
587C42—64no—
588C42—61no—
589C42—61no—
590C42—122no—
591C42D3×D412yes—
592C42C2×#6712yes—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—81no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—81no—
606C22×C3—81no—
607C22×C3C2×#12011yescharacteristic
608C22×C3#52511yescharacteristic
609C22×C3#53211yescharacteristic
610C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
611C22×C3#57511yescharacteristic
612C22×C3#57511yescharacteristic
613C22×C3#57511yescharacteristic
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—22no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—42no—
624C3×C4—81no—
625C3×C4#52511yescharacteristic
626C3×C4#52511yescharacteristic
627C3×C4#53211yescharacteristic
628C3×C4#53211yescharacteristic
629Dic3—42no—
630Dic3—42no—
631Dic3—41no—
632Dic3—41no—
633Dic3—41no—
634Dic3—42no—
635Dic3—81no—
636C23—22no—
637C23—22no—
638C23—32no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23C2×D3×D411yescharacteristic
658Q8—62no—
659Q8—62no—
660Q8—121no—
661Q8—121no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—128no—
671D4—128no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—48no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—62no—
691C2×C4—62no—
692C2×C4—61no—
693C2×C4—62no—
694C2×C4—61no—
695C2×C4—84no—
696C2×C4—124no—
697C2×C4—124no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—121no—
704C2×C4—121no—
705C2×C4—121no—
706C2×C4—121no—
707C2×C4—121no—
708C2×C4—121no—
709C2×C4—121no—
710C2×C4—121no—
711C2×C4#93712yes—
712C2×C4#93712yes—
713C2×C4C2×#23511yescharacteristic
714C2×C4C2×#23511yescharacteristic
715C2×C4C2×D3×D411yescharacteristic
716C2×C4D3×#4111yescharacteristic
717C2×C4D3×#4111yescharacteristic
718C2×C4C22×#6711yescharacteristic
719C8—22no—
720C8—41no—
721C8—62no—
722C8—121no—
723C2×C3—82no—
724C2×C3—82no—
725C2×C3#238811yescharacteristic
726C2×C3#300511yescharacteristic
727C2×C3#300611yescharacteristic
728C2×C3#311111yescharacteristic
729C2×C3#311411yescharacteristic
730C2×C3#318011yescharacteristic
731C2×C3#318311yescharacteristic
732D3—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—62no—
740C22—62no—
741C22—62no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22#554711yescharacteristic
755C22#554811yescharacteristic
756C22D3×AGL(1,ℤ/8)11yescharacteristic
757C22#577311yescharacteristic
758C22#577311yescharacteristic
759C22#577311yescharacteristic
760C22C2×#93711yescharacteristic
761C4—22no—
762C4—22no—
763C4—42no—
764C4—81no—
765C4—121no—
766C4—122no—
767C4—121no—
768C4—121no—
769C4—122no—
770C4—122no—
771C4—241no—
772C4#554711yescharacteristic
773C4#554811yescharacteristic
774C4#579111yescharacteristic
775C4#583211yescharacteristic
776C3#2357511yescharacteristic, complemented, Sylow
777C2—82no—
778C2—82no—
779C2—122no—
780C2#7986211yescharacteristic
781C2#7987011yescharacteristic
782C2#7987111yescharacteristic
783C2#7987611yescharacteristic
784C2#8240011yescharacteristic
785C2#8394511yescharacteristic
786C2#8394611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#442C2
socleC23×C3C22×D4
prime radical#72043C2
hypercenterC2×#442D3
hypocenterC3#23575
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#5557C2semidirect
2. C2×C3×#442C2semidirect
3. C4×#938C2semidirect
4. C2×#5018C2semidirect
5. #72045C2semidirect
7. #71609C2semidirect
8. #70582C2semidirect
9. #70566C2semidirect
10. #70216C2semidirect
11. #70206C2semidirect
12. #70205C2semidirect
13. #70164C2semidirect
14. #69813C2semidirect
15. #69807C2semidirect
65. C2×#442D3semidirect
97. C3×C4×D4D4semidirect
147. C4×Dic6D4semidirect
355. C4×D4#67semidirect
776. C3#23575semidirect

Maximal subgroups

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

subgroupindex
C2×#55572
C2×C3×#4422
C4×#9382
C2×#50182
#720452
#720432
#716092
#705822
#705662
#702162
#702062
#702052
#701642
#698132
#698072
#235753