Finite Group Databasebeta

← #10846104

Subgroups — #10846104

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
1#82779C211yesmaximal, characteristic
2C2×#5051C211yesmaximal, characteristic, complemented
3C2×#4886C211yesmaximal, characteristic, complemented
4C2×#4798C211yesmaximal, characteristic, complemented
5C2×#4730C211yesmaximal, characteristic, complemented
6#73936C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8#70615C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70271C211yesmaximal, characteristic, complemented
11#70227C211yesmaximal, characteristic, complemented
12#69962C211yesmaximal, characteristic, complemented
13#69515C211yesmaximal, characteristic, complemented
14#68822C211yesmaximal, characteristic, complemented
15#68783C211yesmaximal, characteristic, complemented
16#25399—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×#947C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C2×#930C2211yescharacteristic
22C2×C4×#67C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C23×C3⋊C8C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#895C2211yescharacteristic
29C2×#887C2211yescharacteristic
30C2×C3×#107C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C3×#380C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39C2×#815C2211yescharacteristic
40C2×Dic3⋊C8C2211yescharacteristic
41#5051—24no—
42#4993—21no—
43#4988—21no—
44#4987C2211yescharacteristic
45#4975C2211yescharacteristic
46Dic3×C4⋊C4C2211yescharacteristic
47C2×#810C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4960—21no—
52#4957—21no—
53#4957—21no—
54#4948—21no—
55#4886—24no—
56#4798—24no—
57#4730—24no—
58#4676—21no—
59#4647—21no—
60C3×#340C2211yescharacteristic
61#4551C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#468—31no—
65C2×#467—31no—
66C2×#464—31no—
67C2×#435—31no—
68#2540—31no—
69#2538—31no—
70#2036D311yescharacteristic, complemented
71#2033—31no—
72#2001—31no—
73#2000—31no—
74#1959—31no—
75#1947—31no—
76#1894—31no—
77#1893—31no—
78#1763—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C22⋊Q8—22no—
90C3×C22⋊Q8—41no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—21no—
97C2×#217—21no—
98C2×#217D411yescharacteristic
99#947—22no—
100#947—22no—
101#946—22no—
102#946—41no—
103C2×#216—22no—
104C2×#216—22no—
105C2×#216—41no—
106#930—22no—
107#930—41no—
108C4×#67—22no—
109C4×#67—22no—
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×C4⋊Dic3—21no—
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121#924—22no—
122#924—41no—
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4D411yescharacteristic
129C2×C4×Dic3—21no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3C2311yescharacteristic
132C22×C3⋊C8—22no—
133C22×C3⋊C8—22no—
134C22×C3⋊C8—41no—
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137C2×#204—22no—
138C2×#204—22no—
139C2×#204—41no—
140C2×ΓL(1,𝔽25)—22no—
141C2×ΓL(1,𝔽25)—22no—
142C2×ΓL(1,𝔽25)—41no—
143#897—22no—
144#897—41no—
145#895—22no—
146#895—41no—
147#887—22no—
148#887—22no—
149C3×#107—22no—
150C3×#103—22no—
151C3×#103—41no—
152C3×C22⋊C8—22no—
153C3×#95—21no—
154#835—22no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#821—41no—
158(C2×D3)⋊C8—22no—
159#816—22no—
160#815—22no—
161Dic3⋊C8D414yescomplemented
162#810D414yescomplemented
163#809—22no—
164#809—22no—
165#807—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⋊Q8C2×D311yescharacteristic
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×#107—31no—
184C2×#107C2×D311yescharacteristic
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8C2×D311yescharacteristic
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#384—31no—
206#380—31no—
207#380C2×D311yescharacteristic
208C4×C4⋊C4—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340C2×D311yescharacteristic
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C23×D3C2×D411yescharacteristic
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2411yescharacteristic
234C2×#67—22no—
235C2×#67—22no—
236C2×#67—41no—
237C2×#67—42no—
238C2×#67—42no—
239C2×#67—81no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3C2×D411yescharacteristic
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—81no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—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×C8—21no—
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—42no—
279C3×C4⋊C4C2×D412yes—
280C3×C22⋊C4—42no—
281C3×C22⋊C4—81no—
282#217—22no—
283#217—42no—
284#216—44no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—81no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—42no—
297C4⋊Dic3#4112yes—
298Dic3⋊C4—22no—
299Dic3⋊C4—42no—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302Dic3⋊C4—42no—
303Dic3⋊C4—81no—
304C4×Dic3—42no—
305C4×Dic3—81no—
306C4×Dic3C2×D412yes—
307C4×Dic3#4112yes—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—44no—
313C2×C3⋊C8C2×D412yes—
314C2×C3⋊C8C2×D412yes—
315#204—44no—
316ΓL(1,𝔽25)—44no—
317C22×Q8—31no—
318C22×Q8C22×D311yescharacteristic
319C22×D4—31no—
320C22×D4—31no—
321C22×D4—61no—
322C22×D4—61no—
323C23×C4—31no—
324C23×C4C22×D311yescharacteristic
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—22no—
344C22⋊Q8—41no—
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C22⋊Q8—62no—
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—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—21no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—31no—
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—31no—
385C2×C42—61no—
386C2×C42—61no—
387#107—22no—
388#107—62no—
389C4⋊C8—34no—
390#103—22no—
391#103—34no—
392#103—41no—
393#103—62no—
394#103—62no—
395#102—62no—
396#102—62no—
397#102—121no—
398C22⋊C8—22no—
399C22⋊C8—62no—
400#97—62no—
401#95—21no—
402#95—61no—
403#95—61no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3#13712yes—
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—41no—
420C22×D3—41no—
421C22×D3—41no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C3×Q8—41no—
427C3×Q8—41no—
428C3×Q8—41no—
429C3×Q8—41no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
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—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×C4C22×D411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4H(5,𝔽2)11yescharacteristic
454C2×C3×C4H(5,𝔽2)11yescharacteristic
455#67—44no—
456#67—84no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—22no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—22no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3#12112yes—
474C2×Dic3#12112yes—
475D12—41no—
476D12—41no—
477D12—41no—
478D12—41no—
479D12—84no—
480C4×D3—41no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484Dic6—22no—
485Dic6—22no—
486Dic6—41no—
487Dic6—41no—
488C3×C8—22no—
489C3×C8—41no—
490C3⋊C8—22no—
491C3⋊C8—22no—
492C24—31no—
493C24—61no—
494C24D3×D411yescharacteristic
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—32no—
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—122no—
516C2×D4—122no—
517C2×D4—121no—
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—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—31no—
533C22×C4—31no—
534C22×C4—31no—
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×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—21no—
554C2×C8—32no—
555C2×C8—32no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—124no—
561C2×C8D3×D412yes—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—32no—
568C4⋊C4—42no—
569C4⋊C4—62no—
570C4⋊C4—61no—
571C4⋊C4—61no—
572C4⋊C4—61no—
573C4⋊C4—122no—
574C4⋊C4—122no—
575C4⋊C4—122no—
576C4⋊C4—122no—
577C4⋊C4—122no—
578C4⋊C4—241no—
579C4⋊C4D3×D412yes—
580C22⋊C4—42no—
581C22⋊C4—62no—
582C22⋊C4—62no—
583C22⋊C4—81no—
584C22⋊C4—122no—
585C22⋊C4—122no—
586C22⋊C4—122no—
587C22⋊C4—122no—
588C22⋊C4—122no—
589C22⋊C4—122no—
590C22⋊C4—122no—
591C22⋊C4—241no—
592C42—32no—
593C42—32no—
594C42—122no—
595C42—241no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3C2×#12111yescharacteristic
604C22×C3D4211yescharacteristic
605C22×C3#54611yescharacteristic
606C22×C3C2×#13711yescharacteristic
607C22×C3#57511yescharacteristic
608C22×C3#57611yescharacteristic
609C22×C3#57811yescharacteristic
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—41no—
625C3×C4—42no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4—81no—
629C3×C4#53211yescharacteristic
630C3×C4#54011yescharacteristic
631C3×C4D4211yescharacteristic
632C3×C4#55011yescharacteristic
633Dic3—22no—
634Dic3—22no—
635Dic3—42no—
636Dic3—41no—
637Dic3—42no—
638Dic3—81no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—61no—
646C23—61no—
647C23—61no—
648C23—61no—
649C23—61no—
650C23—61no—
651C23—61no—
652C23—121no—
653C23—121no—
654C23—121no—
655C23—121no—
656C23—121no—
657C23—121no—
658C23—121no—
659C23#91812yes—
660C23C2×D3×D411yescharacteristic
661Q8—41no—
662Q8—41no—
663Q8—41no—
664Q8—41no—
665Q8—62no—
666Q8—62no—
667Q8—121no—
668Q8—121no—
669D4—124no—
670D4—121no—
671D4—121no—
672D4—121no—
673D4—121no—
674D4—244no—
675D4—244no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—32no—
681C2×C4—32no—
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—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—62no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—62no—
705C2×C4—61no—
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×C4C2×D3×D411yescharacteristic
718C2×C4C2×D3×D411yescharacteristic
719C2×C4#100411yescharacteristic
720C2×C4D3×#4111yescharacteristic
721C2×C4D3×#4111yescharacteristic
722C2×C4#100911yescharacteristic
723C8—22no—
724C8—41no—
725C8—62no—
726C8—62no—
727C2×C3—42no—
728C2×C3#242811yescharacteristic
729C2×C3#305611yescharacteristic
730C2×C3#306111yescharacteristic
731C2×C3#326811yescharacteristic
732C2×C3#327011yescharacteristic
733C2×C3#331311yescharacteristic
734C2×C3#331411yescharacteristic
735D3—81no—
736D3—161no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
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—
758C22#559011yescharacteristic
759C22D3×#12111yescharacteristic
760C22#565411yescharacteristic
761C22C2×#91811yescharacteristic
762C22#576811yescharacteristic
763C22#577411yescharacteristic
764C22#577911yescharacteristic
765C4—42no—
766C4—41no—
767C4—62no—
768C4—62no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4—122no—
773C4—121no—
774C4—122no—
775C4—241no—
776C4#559911yescharacteristic
777C4#560911yescharacteristic
778C4#566311yescharacteristic
779C4#566811yescharacteristic
780C3#2539911yescharacteristic, complemented, Sylow
781C2—42no—
782C2—241no—
783C2—481no—
784C2#7690311yescharacteristic
785C2#8012811yescharacteristic
786C2#8020811yescharacteristic
787C2#8075911yescharacteristic
788C2#8080811yescharacteristic
789C2#8148611yescharacteristic
790C2#8155211yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2036C2
socleC23×C3C22×D4
prime radical#82779C2
hypercenter#2036D3
hypocenterC3#25399
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#5051C2semidirect
3. C2×#4886C2semidirect
4. C2×#4798C2semidirect
5. C2×#4730C2semidirect
6. #73936C2semidirect
7. C3×#2036C2semidirect
8. #70615C2semidirect
9. #70273C2semidirect
10. #70271C2semidirect
11. #70227C2semidirect
12. #69962C2semidirect
13. #69515C2semidirect
14. #68822C2semidirect
15. #68783C2semidirect
70. #2036D3semidirect
161. Dic3⋊C8D4semidirect
162. #810D4semidirect
780. C3#25399semidirect

Maximal subgroups

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

subgroupindex
#827792
C2×#50512
C2×#48862
C2×#47982
C2×#47302
#739362
C3×#20362
#706152
#702732
#702712
#702272
#699622
#695152
#688222
#687832
#253993