Finite Group Databasebeta

← #10846116

Subgroups — #10846116

Order 768.

1048 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82416C211yesmaximal, characteristic
2C2×#5019C211yesmaximal, characteristic, complemented
3C2×#4780C211yesmaximal, characteristic, complemented
4C2×#4778C211yesmaximal, characteristic, complemented
5C2×#4706C211yesmaximal, characteristic, complemented
6#73800C211yesmaximal, characteristic, complemented
7C3×#1762C211yesmaximal, characteristic, complemented
8#70205C211yesmaximal, characteristic, complemented
9#70205C211yesmaximal, characteristic, complemented
10#69822C211yesmaximal, characteristic, complemented
11#69468C211yesmaximal, characteristic, complemented
12#68884C211yesmaximal, characteristic, complemented
13#68882C211yesmaximal, characteristic, complemented
14#68825C211yesmaximal, characteristic, complemented
15#68824C211yesmaximal, characteristic, complemented
16#25400—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#938C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×#214C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23C22×D3×C8C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#897C2211yescharacteristic
26C2×#897C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×C4×D12C2211yescharacteristic
29C2×#869C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#97C2211yescharacteristic
33C3×C4×C4⋊C4C2211yescharacteristic
34#5213—21no—
35#5213—21no—
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39C2×#816C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#5019—24no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#808C2211yescharacteristic
48C2×#807C2211yescharacteristic
49#4960—21no—
50#4953—21no—
51#4939—21no—
52#4936C2211yescharacteristic
53#4935—21no—
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4780—24no—
56#4778—24no—
57#4706—24no—
58#4677—21no—
59#4677—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#465—31no—
66C2×#461—31no—
67C2×#435—31no—
68#2542—31no—
69#2535—31no—
70#2036—31no—
71#2035—31no—
72#2000—31no—
73#2000—31no—
74#1960—31no—
75#1949—31no—
76#1894—31no—
77#1892—31no—
78#1762D311yescharacteristic, complemented
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×D12D411yescharacteristic
84C22×C4×D3C2311yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×Dic6C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4×D4—22no—
91C3×C4×D4—22no—
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C22⋊C4—21no—
96C2×C3×C42—21no—
97C2×C3×C42C2311yescharacteristic
98C2×#217—21no—
99C2×#217—21no—
100#938—22no—
101#938—22no—
102#938—41no—
103#938—41no—
104C2×#214—22no—
105C2×#214—22no—
106C2×#214—22no—
107C2×#214—22no—
108C2×#214—41no—
109C2×#214—41no—
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)⋊C4D411yescharacteristic
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3D411yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C2×ΓL(1,𝔽25)—22no—
130C2×ΓL(1,𝔽25)—22no—
131C2×ΓL(1,𝔽25)—41no—
132C2×D3×C8—22no—
133C2×D3×C8—22no—
134C2×D3×C8—41no—
135#897—22no—
136#897—22no—
137#897—22no—
138#897—22no—
139#897—41no—
140#897—41no—
141#897—41no—
142#897—41no—
143C4×D12—22no—
144C4×D12—22no—
145#869—22no—
146#869—22no—
147C3×#102—22no—
148C3×#102D414yescomplemented
149C3×#97—22no—
150C3×#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155(C2×D3)⋊C8—22no—
156(C2×D3)⋊C8—22no—
157#816—22no—
158#816—22no—
159#816—41no—
160#816—41no—
161#810—22no—
162#810—22no—
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166C22×SD16—31no—
167C22×SD16—31no—
168C22×M16—31no—
169C23×C8—31no—
170C2×C4⋊Q8—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×D4—31no—
178C2×C4×D4C2×D311yescharacteristic
179#468—64no—
180#465—64no—
181#461—64no—
182#435—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#102C2×D311yescharacteristic
193C2×#102C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×#97C2×D311yescharacteristic
197#399—61no—
198#399—61no—
199#397—61no—
200#392—61no—
201#390—61no—
202#386—61no—
203#386—61no—
204#384—61no—
205#382—31no—
206#380—31no—
207#380—31no—
208C4×C4⋊C4C2×D311yescharacteristic
209#340—31no—
210#340—31no—
211#340C2×D311yescharacteristic
212#340C2×D311yescharacteristic
213C24×C3—21no—
214C23×D3C2×D411yescharacteristic
215C23×D3C2×D411yescharacteristic
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4C2×D412yes—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—42no—
226C22×C3×C4—81no—
227C22×C3×C4—81no—
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2411yescharacteristic
231C2×#67—42no—
232C2×#67—42no—
233C2×#67—42no—
234C2×#67—42no—
235C2×#67—81no—
236C2×#67—81no—
237C22×Dic3—21no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C2×D12—22no—
244C2×D12—22no—
245C2×D12—41no—
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×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—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×Dic6—21no—
267C2×Dic6—21no—
268C2×Dic6—21no—
269C2×Dic6—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8C2×D412yes—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4C2×D412yes—
281C3×C4⋊C4#4112yes—
282C3×C22⋊C4—42no—
283C3×C42—42no—
284C3×C42C2×D412yes—
285C3×C42#4112yes—
286#217—42no—
287#217—42no—
288#214—44no—
289#214—44no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—22no—
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—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—42no—
304C4⋊Dic3—42no—
305C4⋊Dic3—42no—
306C4⋊Dic3—42no—
307C4⋊Dic3—42no—
308C4⋊Dic3—42no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8C2×D412yes—
314C2×C3⋊C8C2×D412yes—
315ΓL(1,𝔽25)—44no—
316D3×C8—44no—
317C22×Q8—31no—
318C22×Q8—31no—
319C22×D4—31no—
320C22×D4—61no—
321C22×D4—61no—
322C22×D4C22×D311yescharacteristic
323C23×C4—21no—
324C23×C4—31no—
325C23×C4—31no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C2×SD16—62no—
330C2×SD16—121no—
331C2×SD16—121no—
332C2×M16—62no—
333C2×M16—62no—
334C2×M16—121no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—62no—
338C22×C8—62no—
339C22×C8—121no—
340C22×C8C22×D311yescharacteristic
341C22×C8C22×D311yescharacteristic
342C4⋊Q8—62no—
343C4⋊Q8—62no—
344C22⋊Q8—62no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
348C22⋊Q8—121no—
349C22⋊Q8—121no—
350C22⋊Q8—121no—
351C22⋊Q8—121no—
352#121—62no—
353#121—62no—
354#121—121no—
355#121—121no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—62no—
359C4×D4—62no—
360C2×C4⋊C4—31no—
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⋊C4—61no—
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—31no—
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×C42—21no—
384C2×C42C22×D311yescharacteristic
385#107—62no—
386#106—62no—
387C4⋊C8—34no—
388#103—62no—
389#103—62no—
390#103—62no—
391#103—62no—
392#103—121no—
393#103—121no—
394#102—22no—
395#102D1214yescomplemented
396C22⋊C8—62no—
397C22⋊C8—62no—
398#97—22no—
399#95—21no—
400#95—61no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—22no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3C22×D411yescharacteristic
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—21no—
422C22×D3—21no—
423C22×D3—21no—
424C22×D3—21no—
425C22×D3#13712yes—
426C3×D4—22no—
427C3×D4—22no—
428C3×D4—41no—
429C3×D4—41no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
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—41no—
443C2×C3×C4—84no—
444C2×C3×C4#12112yes—
445C2×C3×C4#12112yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4H(5,𝔽2)11yescharacteristic
451C2×C3×C4H(5,𝔽2)11yescharacteristic
452#67—84no—
453#67—84no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472D12—44no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478C4×D3—41no—
479C4×D3—41no—
480C4×D3—41no—
481Dic6—41no—
482Dic6—41no—
483Dic6—41no—
484Dic6—41no—
485Dic6—41no—
486Dic6—41no—
487Dic6—41no—
488Dic6—41no—
489C3×C8—22no—
490C3×C8—41no—
491C3⋊C8—22no—
492C3⋊C8—22no—
493C24—21no—
494C24—31no—
495C24—31no—
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×Q8—61no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—62no—
514C2×D4—62no—
515C2×D4—121no—
516C2×D4—122no—
517C2×D4—122no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4—241no—
521C2×D4—241no—
522C2×D4C2×D1212yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—31no—
527C22×C4—31no—
528C22×C4—42no—
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×C4—61no—
544C22×C4—61no—
545C22×C4—81no—
546C22×C4—81no—
547C22×C4D3×D411yescharacteristic
548C22×C4D3×D411yescharacteristic
549C22×C4C23×D311yescharacteristic
550SD16—124no—
551SD16—124no—
552M16—124no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—32no—
559C2×C8—32no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C2×C8—124no—
565C2×C8C2×D1212yes—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—62no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—122no—
576C4⋊C4—122no—
577C4⋊C4—122no—
578C4⋊C4—122no—
579C4⋊C4—122no—
580C4⋊C4—122no—
581C4⋊C4C2×D1212yes—
582C4⋊C4#23512yes—
583C22⋊C4—42no—
584C22⋊C4—62no—
585C22⋊C4—62no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C22⋊C4—122no—
589C22⋊C4—122no—
590C22⋊C4—122no—
591C22⋊C4—122no—
592C22⋊C4—241no—
593C22⋊C4—241no—
594C42—42no—
595C42#23512yes—
596C42D3×D412yes—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—42no—
600C22×C3—81no—
601C22×C3—81no—
602C22×C3—81no—
603C22×C3—81no—
604C22×C3C2×#12111yescharacteristic
605C22×C3D4211yescharacteristic
606C22×C3#54611yescharacteristic
607C22×C3C2×#13711yescharacteristic
608C22×C3#57511yescharacteristic
609C22×C3#57711yescharacteristic
610C22×C3#57711yescharacteristic
611C2×D3—22no—
612C2×D3—22no—
613C2×D3—22no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C2×D3—41no—
624C2×D3—41no—
625C3×C4—22no—
626C3×C4—22no—
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—81no—
630C3×C4#53211yescharacteristic
631C3×C4#54011yescharacteristic
632C3×C4D4211yescharacteristic
633C3×C4#55011yescharacteristic
634Dic3—41no—
635Dic3—41no—
636Dic3—81no—
637Dic3—81no—
638Dic3—81no—
639Dic3—81no—
640C23—22no—
641C23—32no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—61no—
653C23—61no—
654C23—61no—
655C23—61no—
656C23—61no—
657C23—61no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23C2×D3×D411yescharacteristic
662Q8—121no—
663Q8—121no—
664Q8—121no—
665Q8—121no—
666Q8—121no—
667Q8—121no—
668Q8—121no—
669Q8—121no—
670D4—22no—
671D4—22no—
672D4—41no—
673D4—41no—
674D4—124no—
675D4—244no—
676D4—244no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—84no—
697C2×C4—121no—
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—121no—
712C2×C4—121no—
713C2×C4—121no—
714C2×C4—121no—
715C2×C4—121no—
716C2×C4—121no—
717C2×C4#88412yes—
718C2×C4#88412yes—
719C2×C4C22×D1211yescharacteristic
720C2×C4C2×#23511yescharacteristic
721C2×C4C2×#23511yescharacteristic
722C2×C4C2×D3×D411yescharacteristic
723C2×C4#100911yescharacteristic
724C2×C4#100911yescharacteristic
725C8—22no—
726C8—41no—
727C8—62no—
728C8—62no—
729C2×C3—82no—
730C2×C3#242811yescharacteristic
731C2×C3#305611yescharacteristic
732C2×C3#305711yescharacteristic
733C2×C3#326611yescharacteristic
734C2×C3#326711yescharacteristic
735C2×C3#330711yescharacteristic
736C2×C3#332011yescharacteristic
737D3—42no—
738D3—81no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—62no—
743C22—62no—
744C22—62no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22C2×#88411yescharacteristic
761C22D4×D1211yescharacteristic
762C22#555011yescharacteristic
763C22#577311yescharacteristic
764C22#577511yescharacteristic
765C22#577511yescharacteristic
766C22D3×#13711yescharacteristic
767C4—22no—
768C4—22no—
769C4—42no—
770C4—42no—
771C4—81no—
772C4—121no—
773C4—121no—
774C4—241no—
775C4—241no—
776C4—241no—
777C4—241no—
778C4#547711yescharacteristic
779C4#553511yescharacteristic
780C4D4×D1211yescharacteristic
781C4#555311yescharacteristic
782C3#2540011yescharacteristic, complemented, Sylow
783C2—82no—
784C2—122no—
785C2—241no—
786C2#7348711yescharacteristic
787C2#7888911yescharacteristic
788C2#7893111yescharacteristic
789C2#7979511yescharacteristic
790C2#7980411yescharacteristic
791C2#7987911yescharacteristic
792C2#7988111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1762C2
socleC23×C3C22×D4
prime radical#82416C2
hypercenter#1762D3
hypocenterC3#25400
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
2. C2×#5019C2semidirect
3. C2×#4780C2semidirect
4. C2×#4778C2semidirect
5. C2×#4706C2semidirect
6. #73800C2semidirect
7. C3×#1762C2semidirect
8. #70205C2semidirect
9. #70205C2semidirect
10. #69822C2semidirect
11. #69468C2semidirect
12. #68884C2semidirect
13. #68882C2semidirect
14. #68825C2semidirect
15. #68824C2semidirect
78. #1762D3semidirect
148. C3×#102D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
395. #102D12semidirect
782. C3#25400semidirect

Maximal subgroups

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

subgroupindex
#824162
C2×#50192
C2×#47802
C2×#47782
C2×#47062
#738002
C3×#17622
#702052
#698222
#694682
#688842
#688822
#688252
#688242
#254003