Finite Group Databasebeta

← #10845982

Subgroups — #10845982

Order 768.

1084 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#82416C211yesmaximal, characteristic, complemented
2C2×#5016C211yesmaximal, characteristic, complemented
3C2×#4782C211yesmaximal, characteristic, complemented
4C2×#4780C211yesmaximal, characteristic, complemented
5C2×#4688C211yesmaximal, characteristic, complemented
6#73798C211yesmaximal, characteristic, complemented
7C3×C4×#102C211yesmaximal, characteristic, complemented
8#70205C211yesmaximal, characteristic, complemented
9#70204C211yesmaximal, characteristic, complemented
10#69773C211yesmaximal, characteristic, complemented
11#69468C211yesmaximal, characteristic, complemented
12#68885C211yesmaximal, characteristic, complemented
13#68884C211yesmaximal, characteristic, complemented
14#68824C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#25390—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#938C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C22×ΓL(1,𝔽25)C2211yescharacteristic
23C22×ΓL(1,𝔽25)C2211yescharacteristic
24C2×#897C2211yescharacteristic
25C2×#897C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#895C2211yescharacteristic
28C2×#875C2211yescharacteristic
29C2×C4×D12C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×C4×C8C2211yescharacteristic
33C3×C4×C4⋊C4C2211yescharacteristic
34#5213—21no—
35#5213—21no—
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×#816C2211yescharacteristic
42#5016—24no—
43#4987C2211yescharacteristic
44#4987C2211yescharacteristic
45C2×#810C2211yescharacteristic
46C2×#809C2211yescharacteristic
47C2×#808C2211yescharacteristic
48C2×#807C2211yescharacteristic
49#4960—21no—
50#4953—21no—
51#4939—21no—
52#4939—21no—
53#4936C2211yescharacteristic
54C2×C4⋊(C3⋊C8)C2211yescharacteristic
55#4782—24no—
56#4780—24no—
57#4688—24no—
58#4677—21no—
59#4671—21no—
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#469—31no—
65C2×#468—31no—
66C2×#463—31no—
67C2×#436—31no—
68#2540—31no—
69#2535—31no—
70#2035—31no—
71#2033—31no—
72#2000—31no—
73#1999—31no—
74#1958—31no—
75#1949—31no—
76#1895—31no—
77#1894—31no—
78C4×#102D311yescharacteristic, complemented
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×D12—21no—
84C22×D12—21no—
85C22×D12D411yescharacteristic
86C22×D12C2311yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C22×C4×D3C2311yescharacteristic
89C22×Dic6C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C3×C4×D4—22no—
93C3×C4×D4—22no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C22⋊C4—21no—
98C2×C3×C42—21no—
99C2×C3×C42C2311yescharacteristic
100C2×#217—21no—
101C2×#217—21no—
102#938—22no—
103#938—22no—
104#938—41no—
105#938—41no—
106C2×#214—22no—
107C2×#214—22no—
108C2×#214—41no—
109C2×#213—22no—
110C2×#213—22no—
111C2×#213—41no—
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)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4D411yescharacteristic
121C2×(C2×D3)⋊C4D411yescharacteristic
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)—22no—
132C2×ΓL(1,𝔽25)—22no—
133C2×ΓL(1,𝔽25)—41no—
134C2×ΓL(1,𝔽25)—41no—
135#897—22no—
136#897—22no—
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—
147C3×#102—22no—
148C3×#102D414yescomplemented
149C3×C4×C8—22no—
150C3×#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155#821—22no—
156#821—41no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—22no—
159#816—22no—
160#816—41no—
161#810—22no—
162#809—22no—
163#808—22no—
164#807—22no—
165C4⋊(C3⋊C8)D414yescomplemented
166C22×SD16—31no—
167C22×D8—31no—
168C22×M16—31no—
169C22×M16—31no—
170C2×#124—31no—
171C2×C22⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×#121—31no—
174C2×#121—31no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×D4—31no—
178C2×C4×D4C2×D311yescharacteristic
179#469—64no—
180#468—64no—
181#463—64no—
182#436—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×C4⋊C8—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
193C2×#102C2×D311yescharacteristic
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C4×C8C2×D311yescharacteristic
197#399—61no—
198#397—61no—
199#392—61no—
200#392—61no—
201#390—61no—
202#390—61no—
203#386—61no—
204#386—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×D3—21no—
215C23×D3C2×D411yescharacteristic
216C23×D3C2×D411yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4C2×D412yes—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—42no—
227C22×C3×C4—81no—
228C22×C3×C4—81no—
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C2×#67—42no—
233C2×#67—42no—
234C2×#67—42no—
235C2×#67—42no—
236C2×#67—81no—
237C2×#67—81no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C2×D12—22no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—41no—
251C2×D12—41no—
252C2×D12—42no—
253C2×D12—42no—
254C2×D12—42no—
255C2×D12—42no—
256C2×D12—81no—
257C2×D12—81no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×C4×D3—21no—
268C2×C4×D3—21no—
269C2×C4×D3—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8C2×D412yes—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4C2×D412yes—
287C3×C4⋊C4#4112yes—
288C3×C22⋊C4—42no—
289C3×C42—81no—
290C3×C42C2×D412yes—
291C3×C42#4112yes—
292#217—42no—
293#217—42no—
294#214—44no—
295#213—44no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—42no—
301(C2×D3)⋊C4—42no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—81no—
305(C2×D3)⋊C4—81no—
306C4⋊Dic3—22no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3—42no—
312C4⋊Dic3—42no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8C2×D412yes—
318C2×C3⋊C8C2×D412yes—
319ΓL(1,𝔽25)—44no—
320ΓL(1,𝔽25)—44no—
321C22×Q8—31no—
322C22×D4—31no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4—61no—
326C22×D4—61no—
327C22×D4—61no—
328C22×D4C22×D311yescharacteristic
329C23×C4—21no—
330C23×C4—31no—
331C23×C4—31no—
332C2×SD16—62no—
333C2×SD16—62no—
334C2×SD16—121no—
335C2×D8—62no—
336C2×D8—62no—
337C2×D8—121no—
338C2×M16—62no—
339C2×M16—62no—
340C2×M16—62no—
341C2×M16—62no—
342C2×M16—121no—
343C2×M16—121no—
344C22×C8—31no—
345C22×C8—31no—
346C22×C8C22×D311yescharacteristic
347C22×C8C22×D311yescharacteristic
348#124—62no—
349#124—62no—
350C22⋊Q8—62no—
351C22⋊Q8—62no—
352C22⋊Q8—121no—
353C22⋊Q8—121no—
354#121—62no—
355#121—62no—
356#121—62no—
357#121—62no—
358#121—121no—
359#121—121no—
360#121—121no—
361#121—121no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—62no—
365C4×D4—62no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—61no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—31no—
376C2×C22⋊C4—31no—
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×C22⋊C4—61no—
385C2×C22⋊C4—61no—
386C2×C22⋊C4—61no—
387C2×C42—21no—
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391C4⋊C8—34no—
392#103—62no—
393#103—62no—
394#103—121no—
395#102—22no—
396#102—62no—
397#102—62no—
398#102—121no—
399#102D1214yescomplemented
400C22⋊C8—62no—
401C22⋊C8—62no—
402C4×C8—22no—
403#95—21no—
404#95—61no—
405#95—61no—
406#95—61no—
407#95—61no—
408C23×C3—22no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3C22×D411yescharacteristic
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—21no—
426C22×D3—21no—
427C22×D3—21no—
428C22×D3—21no—
429C22×D3—21no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×D4—22no—
438C3×D4—22no—
439C3×D4—41no—
440C3×D4—41no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—84no—
455C2×C3×C4#12112yes—
456C2×C3×C4#12112yes—
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C22×D411yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×C3×C4H(5,𝔽2)11yescharacteristic
462C2×C3×C4H(5,𝔽2)11yescharacteristic
463#67—84no—
464#67—84no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480D12—44no—
481D12—41no—
482D12—41no—
483D12—41no—
484D12—41no—
485D12—84no—
486D12—84no—
487C4×D3—41no—
488C4×D3—41no—
489C4×D3—41no—
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—41no—
493C4×D3—41no—
494C4×D3—41no—
495Dic6—41no—
496Dic6—41no—
497Dic6—41no—
498Dic6—41no—
499C3×C8—22no—
500C3×C8—41no—
501C3⋊C8—22no—
502C3⋊C8—22no—
503C24—21no—
504C24—31no—
505C24—31no—
506C24—61no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—62no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—61no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—121no—
526C2×D4—121no—
527C2×D4—122no—
528C2×D4—122no—
529C2×D4—122no—
530C2×D4—122no—
531C2×D4—122no—
532C2×D4—122no—
533C2×D4—122no—
534C2×D4—122no—
535C2×D4—241no—
536C2×D4—241no—
537C2×D4—241no—
538C2×D4—241no—
539C2×D4C2×D1212yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—42no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—61no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4C23×D311yescharacteristic
566SD16—124no—
567D8—124no—
568M16—124no—
569M16—124no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—32no—
576C2×C8—32no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8C2×D1212yes—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—62no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4—122no—
593C4⋊C4C2×D1212yes—
594C4⋊C4#23512yes—
595C22⋊C4—42no—
596C22⋊C4—62no—
597C22⋊C4—62no—
598C22⋊C4—122no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C22⋊C4—122no—
606C22⋊C4—241no—
607C22⋊C4—241no—
608C42—81no—
609C42#23512yes—
610C42D3×D412yes—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3C2×#12111yescharacteristic
619C22×C3D4211yescharacteristic
620C22×C3#54611yescharacteristic
621C22×C3#57511yescharacteristic
622C22×C3#57511yescharacteristic
623C22×C3#57611yescharacteristic
624C22×C3#57711yescharacteristic
625C2×D3—41no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C2×D3—81no—
643C2×D3—81no—
644C2×D3—81no—
645C2×D3—81no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—81no—
651C3×C4#53211yescharacteristic
652C3×C4#54011yescharacteristic
653C3×C4D4211yescharacteristic
654C3×C4#55011yescharacteristic
655Dic3—41no—
656Dic3—41no—
657Dic3—81no—
658Dic3—81no—
659Dic3—81no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—61no—
668C23—61no—
669C23—61no—
670C23—61no—
671C23—61no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—121no—
682C23—121no—
683C23—121no—
684C23—121no—
685C23—121no—
686C23—121no—
687C23—121no—
688C23C2×D3×D411yescharacteristic
689Q8—121no—
690Q8—121no—
691Q8—121no—
692Q8—121no—
693D4—22no—
694D4—22no—
695D4—41no—
696D4—41no—
697D4—124no—
698D4—121no—
699D4—121no—
700D4—121no—
701D4—121no—
702D4—244no—
703D4—244no—
704D4—244no—
705D4—244no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—84no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4—121no—
743C2×C4#88412yes—
744C2×C4#88412yes—
745C2×C4C22×D1211yescharacteristic
746C2×C4C2×#23511yescharacteristic
747C2×C4C2×#23511yescharacteristic
748C2×C4C2×D3×D411yescharacteristic
749C2×C4#100911yescharacteristic
750C2×C4#100911yescharacteristic
751C8—22no—
752C8—41no—
753C8—62no—
754C8—62no—
755C2×C3—82no—
756C2×C3#242811yescharacteristic
757C2×C3#305411yescharacteristic
758C2×C3#306211yescharacteristic
759C2×C3#327311yescharacteristic
760C2×C3#327511yescharacteristic
761C2×C3#332211yescharacteristic
762C2×C3#332611yescharacteristic
763D3—81no—
764D3—81no—
765D3—161no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—241no—
788C22—241no—
789C22—241no—
790C22—241no—
791C22—241no—
792C22—241no—
793C22—241no—
794C22C2×#88411yescharacteristic
795C22D4×D1211yescharacteristic
796C22#555011yescharacteristic
797C22#575711yescharacteristic
798C22#576211yescharacteristic
799C22#576811yescharacteristic
800C22#576811yescharacteristic
801C4—22no—
802C4—22no—
803C4—42no—
804C4—42no—
805C4—81no—
806C4—121no—
807C4—121no—
808C4—241no—
809C4—241no—
810C4—241no—
811C4#547711yescharacteristic
812C4#553511yescharacteristic
813C4D4×D1211yescharacteristic
814C4#555311yescharacteristic
815C3#2539011yescharacteristic, complemented, Sylow
816C2—82no—
817C2—241no—
818C2—241no—
819C2—481no—
820C2#7348711yescharacteristic
821C2#7875211yescharacteristic
822C2#7883911yescharacteristic
823C2#7960411yescharacteristic
824C2#7961111yescharacteristic
825C2#7967111yescharacteristic
826C2#7968411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C4×#102C2
socleC23×C3C22×D4
hypercenterC4×#102D3
hypocenterC3#25390
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #82416C2semidirect
2. C2×#5016C2semidirect
3. C2×#4782C2semidirect
4. C2×#4780C2semidirect
5. C2×#4688C2semidirect
6. #73798C2semidirect
7. C3×C4×#102C2semidirect
8. #70205C2semidirect
9. #70204C2semidirect
10. #69773C2semidirect
11. #69468C2semidirect
12. #68885C2semidirect
13. #68884C2semidirect
14. #68824C2semidirect
15. #68822C2semidirect
78. C4×#102D3semidirect
148. C3×#102D4semidirect
165. C4⋊(C3⋊C8)D4semidirect
399. #102D12semidirect
815. C3#25390semidirect

Maximal subgroups

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

subgroupindex
#824162
C2×#50162
C2×#47822
C2×#47802
C2×#46882
#737982
C3×C4×#1022
#702052
#702042
#697732
#694682
#688852
#688842
#688242
#688222
#253903