Finite Group Databasebeta

← #10846099

Subgroups — #10846099

Order 768.

1034 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4886C211yesmaximal, characteristic, complemented
2C2×#4887C211yesmaximal, characteristic, complemented
3C2×#4845C211yesmaximal, characteristic, complemented
4C2×#4836C211yesmaximal, characteristic, complemented
5#74369C211yesmaximal, characteristic, complemented
6#73798C211yesmaximal, characteristic
7C3×#1947C211yesmaximal, characteristic, complemented
8#70635C211yesmaximal, characteristic, complemented
9#70634C211yesmaximal, characteristic, complemented
10#69581C211yesmaximal, characteristic, complemented
11#69475C211yesmaximal, characteristic, complemented
12#68888C211yesmaximal, characteristic, complemented
13#68887C211yesmaximal, characteristic, complemented
14#68884C211yesmaximal, characteristic, complemented
15#68883C211yesmaximal, characteristic, complemented
16#25399—31nomaximal, Sylow
17C22×Dic12C2211yescharacteristic
18C22×#204C2211yescharacteristic
19C22×ΓL(1,𝔽25)C2211yescharacteristic
20C22×D3×C8C2211yescharacteristic
21C2×#897C2211yescharacteristic
22C2×#897C2211yescharacteristic
23C2×#897C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#875C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×C4×Dic6C2211yescharacteristic
30C2×C3×#107C2211yescharacteristic
31C2×C3×#107C2211yescharacteristic
32C2×C3×C4⋊C8C2211yescharacteristic
33C3×#384C2211yescharacteristic
34C3×C4×C4⋊C4C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39#4994—21no—
40#4994—21no—
41#4988—21no—
42#4987C2211yescharacteristic
43#4987C2211yescharacteristic
44#4984—21no—
45C2×#810C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4939—21no—
52#4939—21no—
53C2×#803C2211yescharacteristic
54#4887—24no—
55#4886—24no—
56#4845—24no—
57#4836—24no—
58#4677—21no—
59#4671—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#467—31no—
66C2×#464—31no—
67C2×#435—31no—
68#2540—31no—
69#2538—31no—
70#2036—31no—
71#2033—31no—
72#2001—31no—
73#2000—31no—
74#1959—31no—
75#1947D311yescharacteristic, complemented
76#1894—31no—
77#1893—31no—
78#1763—31no—
79C22×D12—21no—
80C22×D12—21no—
81C22×D12D411yescharacteristic
82C22×D12C2311yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×Dic6C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C42—21no—
96C2×C3×C42C2311yescharacteristic
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4D411yescharacteristic
108C2×(C2×D3)⋊C4D411yescharacteristic
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3—21no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3D411yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×Dic3⋊C4—21no—
116C2×C4×Dic3—21no—
117C22×C3⋊C8C2311yescharacteristic
118C22×C3⋊C8C2311yescharacteristic
119C2×Dic12—22no—
120C2×Dic12—22no—
121C2×Dic12—41no—
122C2×#204—22no—
123C2×#204—22no—
124C2×#204—41no—
125C2×ΓL(1,𝔽25)—22no—
126C2×ΓL(1,𝔽25)—22no—
127C2×ΓL(1,𝔽25)—41no—
128C2×D3×C8—22no—
129C2×D3×C8—22no—
130C2×D3×C8—41no—
131#897—22no—
132#897—22no—
133#897—22no—
134#897—22no—
135#897—41no—
136#897—41no—
137#897—41no—
138#897—41no—
139#895—22no—
140#895—22no—
141#895—41no—
142#895—41no—
143#875—22no—
144#875—22no—
145C4×D12—22no—
146C4×D12—22no—
147C4×Dic6—22no—
148C4×Dic6—22no—
149C3×#107—22no—
150C3×#107—22no—
151C3×C4⋊C8D414yescomplemented
152C3×#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#821—22no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—22no—
158#816—22no—
159#810—22no—
160#810—22no—
161#810—41no—
162#810D414yescomplemented
163#809—22no—
164#809—41no—
165#803—22no—
166C22×Q16—31no—
167C22×SD16—31no—
168C22×M16—31no—
169C23×C8—31no—
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179#468—64no—
180#467—64no—
181#464—64no—
182#435—64no—
183C2×#107C2×D311yescharacteristic
184C2×#107C2×D311yescharacteristic
185C2×C4⋊C8C2×D311yescharacteristic
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97—31no—
197#399—61no—
198#396—61no—
199#396—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#390—61no—
204#389—61no—
205#384C2×D311yescharacteristic
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C23×D3C2×D411yescharacteristic
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2411yescharacteristic
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3C2×D411yescharacteristic
227C22×Dic3C2×D411yescharacteristic
228C2×D12—22no—
229C2×D12—22no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—41no—
237C2×D12—42no—
238C2×D12—42no—
239C2×D12—42no—
240C2×D12—42no—
241C2×D12—81no—
242C2×D12—81no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
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×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—21no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6C2×D412yes—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8C2×D412yes—
272C2×C3×C8C2×D412yes—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—42no—
280C3×C4⋊C4—81no—
281C3×C4⋊C4C2×D412yes—
282C3×C4⋊C4#4112yes—
283C3×C42—81no—
284C3×C42C2×D412yes—
285C3×C42#4112yes—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—42no—
293(C2×D3)⋊C4—42no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—42no—
296(C2×D3)⋊C4—81no—
297(C2×D3)⋊C4—81no—
298C4⋊Dic3—22no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—42no—
302C4⋊Dic3—42no—
303C4⋊Dic3—42no—
304C4⋊Dic3—42no—
305Dic3⋊C4—42no—
306C4×Dic3—42no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8C2×D412yes—
313Dic12—44no—
314#204—44no—
315ΓL(1,𝔽25)—44no—
316D3×C8—44no—
317C22×Q8—31no—
318C22×Q8—31no—
319C22×D4—31no—
320C22×D4—31no—
321C22×D4—61no—
322C22×D4—61no—
323C23×C4—31no—
324C23×C4—31no—
325C2×Q16—62no—
326C2×Q16—62no—
327C2×Q16—121no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—121no—
331C2×M16—62no—
332C2×M16—62no—
333C2×M16—121no—
334C22×C8—31no—
335C22×C8—31no—
336C22×C8—62no—
337C22×C8—62no—
338C22×C8—121no—
339C22×C8C22×D311yescharacteristic
340C22×C8C22×D311yescharacteristic
341#124—62no—
342#124—62no—
343C22⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—121no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350C22⋊Q8—121no—
351#121—62no—
352#121—62no—
353#121—121no—
354#121—121no—
355C4×Q8—62no—
356C4×Q8—62no—
357C4×D4—62no—
358C4×D4—62no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—31no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C42—21no—
385C2×C42—61no—
386C2×C42C22×D311yescharacteristic
387#107—22no—
388#107—22no—
389C4⋊C8D1214yescomplemented
390#103—34no—
391#103—62no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—62no—
396#102—62no—
397#102—121no—
398C22⋊C8—62no—
399C22⋊C8—62no—
400#97—62no—
401#95—21no—
402#95—61no—
403#95—61no—
404C23×C3C22×D411yescharacteristic
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—41no—
419C22×D3—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3#13712yes—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
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—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4#12112yes—
443C2×C3×C4#12112yes—
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4H(5,𝔽2)11yescharacteristic
449C2×C3×C4H(5,𝔽2)11yescharacteristic
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465D12—44no—
466D12—41no—
467D12—41no—
468D12—41no—
469D12—41no—
470D12—84no—
471D12—84no—
472C4×D3—41no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—41no—
480Dic6—22no—
481Dic6—22no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486Dic6—41no—
487Dic6—41no—
488C3×C8—22no—
489C3×C8—22no—
490C3⋊C8—22no—
491C3⋊C8—41no—
492C24—31no—
493C24—31no—
494C24—61no—
495C2×Q8—32no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—61no—
499C2×Q8—61no—
500C2×Q8—61no—
501C2×Q8—61no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—61no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—121no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—241no—
521C2×D4—241no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4D3×D411yescharacteristic
544C22×C4D3×D411yescharacteristic
545C22×C4C23×D311yescharacteristic
546Q16—124no—
547SD16—124no—
548M16—124no—
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—124no—
560C2×C8C2×D1212yes—
561C2×C8C2×D1212yes—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—62no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—81no—
573C4⋊C4—122no—
574C4⋊C4—122no—
575C4⋊C4—122no—
576C4⋊C4—122no—
577C4⋊C4—122no—
578C4⋊C4D3×D412yes—
579C4⋊C4#23912yes—
580C22⋊C4—62no—
581C22⋊C4—62no—
582C22⋊C4—122no—
583C22⋊C4—122no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C22⋊C4—122no—
589C22⋊C4—122no—
590C22⋊C4—241no—
591C22⋊C4—241no—
592C42—81no—
593C42—122no—
594C42C2×D1212yes—
595C42#23912yes—
596C22×C3C2×#12111yescharacteristic
597C22×C3D4211yescharacteristic
598C22×C3#54611yescharacteristic
599C22×C3C2×#13711yescharacteristic
600C22×C3#57511yescharacteristic
601C22×C3#57611yescharacteristic
602C22×C3#57811yescharacteristic
603C2×D3—22no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—41no—
607C2×D3—41no—
608C2×D3—41no—
609C2×D3—41no—
610C2×D3—41no—
611C2×D3—41no—
612C2×D3—41no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—81no—
618C2×D3—81no—
619C2×D3—81no—
620C2×D3—81no—
621C2×D3—81no—
622C2×D3—81no—
623C2×D3—81no—
624C3×C4—22no—
625C3×C4—22no—
626C3×C4—42no—
627C3×C4—42no—
628C3×C4—81no—
629C3×C4—81no—
630C3×C4#53211yescharacteristic
631C3×C4#54011yescharacteristic
632C3×C4D4211yescharacteristic
633C3×C4#55011yescharacteristic
634Dic3—42no—
635Dic3—41no—
636Dic3—41no—
637Dic3—81no—
638Dic3—81no—
639C23—32no—
640C23—61no—
641C23—61no—
642C23—61no—
643C23—61no—
644C23—61no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23—121no—
660C23C2×D3×D411yescharacteristic
661Q8—62no—
662Q8—62no—
663Q8—121no—
664Q8—121no—
665Q8—121no—
666Q8—121no—
667Q8—121no—
668Q8—121no—
669D4—124no—
670D4—121no—
671D4—121no—
672D4—121no—
673D4—121no—
674D4—244no—
675D4—244no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—22no—
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—41no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—62no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
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—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4#89512yes—
716C2×C4#89512yes—
717C2×C4C22×D1211yescharacteristic
718C2×C4C2×D3×D411yescharacteristic
719C2×C4C2×#23911yescharacteristic
720C2×C4C2×#23911yescharacteristic
721C2×C4#100911yescharacteristic
722C2×C4#100911yescharacteristic
723C8—22no—
724C8—22no—
725C8—62no—
726C8—121no—
727C2×C3#242811yescharacteristic
728C2×C3#305611yescharacteristic
729C2×C3#306111yescharacteristic
730C2×C3#326811yescharacteristic
731C2×C3#327011yescharacteristic
732C2×C3#331311yescharacteristic
733C2×C3#331411yescharacteristic
734D3—42no—
735D3—81no—
736D3—161no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—241no—
752C22—241no—
753C22—241no—
754C22—241no—
755C22—241no—
756C22—241no—
757C22—241no—
758C22C2×#89511yescharacteristic
759C22#560911yescharacteristic
760C22#563011yescharacteristic
761C22#575711yescharacteristic
762C22#576611yescharacteristic
763C22#577311yescharacteristic
764C22D3×#13711yescharacteristic
765C4—22no—
766C4—22no—
767C4—42no—
768C4—42no—
769C4—81no—
770C4—81no—
771C4—121no—
772C4—121no—
773C4—122no—
774C4—241no—
775C4—241no—
776C4D4×D1211yescharacteristic
777C4#557711yescharacteristic
778C4#569711yescharacteristic
779C4#572511yescharacteristic
780C3#2539911yescharacteristic, complemented, Sylow
781C2—122no—
782C2—241no—
783C2—481no—
784C2#7622011yescharacteristic
785C2#7915011yescharacteristic
786C2#7921211yescharacteristic
787C2#8034811yescharacteristic
788C2#8048911yescharacteristic
789C2#8098211yescharacteristic
790C2#8112211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1947C2
socleC23×C3C22×D4
prime radical#73798C2
hypercenter#1947D3
hypocenterC3#25399
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. C2×#4886C2semidirect
2. C2×#4887C2semidirect
3. C2×#4845C2semidirect
4. C2×#4836C2semidirect
5. #74369C2semidirect
7. C3×#1947C2semidirect
8. #70635C2semidirect
9. #70634C2semidirect
10. #69581C2semidirect
11. #69475C2semidirect
12. #68888C2semidirect
13. #68887C2semidirect
14. #68884C2semidirect
15. #68883C2semidirect
75. #1947D3semidirect
151. C3×C4⋊C8D4semidirect
162. #810D4semidirect
389. C4⋊C8D12semidirect
780. C3#25399semidirect

Maximal subgroups

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

subgroupindex
C2×#48862
C2×#48872
C2×#48452
C2×#48362
#743692
#737982
C3×#19472
#706352
#706342
#695812
#694752
#688882
#688872
#688842
#688832
#253993