Finite Group Databasebeta

← #10823495

Subgroups — #10823495

Order 768.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#540C211yesmaximal, characteristic, complemented
2C2×#5014C211yesmaximal, characteristic, complemented
3C2×C4×#213C211yesmaximal, characteristic, complemented
4#82236C211yesmaximal, characteristic, complemented
5#71767C211yesmaximal, characteristic, complemented
6#71762C211yesmaximal, characteristic, complemented
7#71743C211yesmaximal, characteristic, complemented
8#71739C211yesmaximal, characteristic, complemented
9#71684C211yesmaximal, characteristic, complemented
10#71684C211yesmaximal, characteristic, complemented
11#71680C211yesmaximal, characteristic, complemented
12#71679C211yesmaximal, characteristic, complemented
13#71609C211yesmaximal, characteristic, complemented
14C4×#832C211yesmaximal, characteristic, complemented
15#71582C211yesmaximal, characteristic, complemented
16#23580—31nomaximal, Sylow
17C3×#540—24no—
18C3×#540—24no—
19C2×C3×#127C2211yescharacteristic
20C2×C3×#125C2211yescharacteristic
21C2×C3×#123—21no—
22C2×C3×#123—21no—
23C2×C3×#121—21no—
24C2×C3×#121—21no—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×#213C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C2×#832C2211yescharacteristic
35C2×#832C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5014—24no—
44C4×#213—24no—
45#4990—21no—
46#4989—21no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4957—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54C4×C4⋊Dic3C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#540D311yescharacteristic, complemented
65C2×#442—31no—
66C2×C4×D8—31no—
67#2324—31no—
68#2059—31no—
69#2041—31no—
70#2034—31no—
71#2033—31no—
72#2025—31no—
73#2011—31no—
74#1999—31no—
75#1999—31no—
76#1762—31no—
77C4×#102—31no—
78#1750—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C23×C3×C4C2311yescharacteristic
88C22×#67—21no—
89C22×D12C2311yescharacteristic
90C22×C4×D3—21no—
91C3×#127—22no—
92C3×#127—22no—
93C3×#125—22no—
94C3×#125—22no—
95C3×#123—28no—
96C3×#123—28no—
97C3×#121—28no—
98C3×#121—28no—
99C3×#121—22no—
100C3×#121—22no—
101C3×#121—22no—
102C3×#121—22no—
103C3×C4×D4—22no—
104C3×C4×D4—22no—
105C3×C4×D4D414yescomplemented
106C3×C4×D4D414yescomplemented
107C3×#117—22no—
108C3×#117—22no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4D411yescharacteristic
112C2×C3×C4⋊C4D411yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#213—22no—
125C2×#213—22no—
126C2×#213—22no—
127C2×#213—22no—
128C2×#213—22no—
129C2×#213—22no—
130#930—22no—
131#930—22no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C4×D12—22no—
146C4×D12—22no—
147#832—22no—
148#832—22no—
149#832—22no—
150#832—22no—
151#832—22no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#830—22no—
158#809—22no—
159#809—22no—
160#808—22no—
161#807—22no—
162#803—22no—
163C4×C3⋊C8—22no—
164C22×D8—31no—
165C22×D8—31no—
166#540—24no—
167#540—24no—
168C2×#127C2×D311yescharacteristic
169C2×#125C2×D311yescharacteristic
170C2×#123—21no—
171C2×#123—21no—
172C2×#121—21no—
173C2×#121—21no—
174C2×#121—31no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4C2×D311yescharacteristic
179C2×C4×D4C2×D311yescharacteristic
180C2×#117C2×D311yescharacteristic
181#442—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#102—31no—
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C23×D3—21no—
215C2×C3×D4—24no—
216C2×C3×D4—24no—
217C2×C3×D4—24no—
218C2×C3×D4—24no—
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×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—81no—
230C2×C3×D4—81no—
231C2×C3×D4—81no—
232C2×C3×D4—81no—
233C2×C3×D4—81no—
234C2×C3×D4—81no—
235C2×C3×D4—81no—
236C2×C3×D4—81no—
237C2×C3×D4C2×D412yes—
238C2×C3×D4C2×D412yes—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—24no—
248C22×C3×C4—24no—
249C22×C3×C4—81no—
250C22×C3×C4—81no—
251C22×C3×C4—81no—
252C22×C3×C4—81no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—24no—
260C2×#67—81no—
261C2×#67—81no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12#4112yes—
271C2×C4×D3—42no—
272C2×C4×D3—81no—
273C2×C4×D3—81no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4C2×D412yes—
281C3×C4⋊C4C2×D412yes—
282C3×C22⋊C4—24no—
283C3×C22⋊C4—24no—
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—22no—
287C3×C22⋊C4—22no—
288C3×C42—21no—
289C3×C42—21no—
290C3×C42C2×D412yes—
291C3×C42C2×D412yes—
292#217—81no—
293#213—28no—
294#213—28no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4—81no—
298(C2×D3)⋊C4—81no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3#4112yes—
305Dic3⋊C4—81no—
306C4×Dic3—81no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8#4112yes—
318C2×C3⋊C8#4112yes—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—21no—
323C22×D4—31no—
324C22×D4—61no—
325C22×D4C22×D311yescharacteristic
326C22×D4C22×D311yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—61no—
330C23×C4C22×D311yescharacteristic
331C2×D8—62no—
332C2×D8—62no—
333C2×D8—62no—
334C2×D8—62no—
335C2×D8—62no—
336C2×D8—62no—
337C22×C8—31no—
338C22×C8—31no—
339C22×C8—31no—
340C22×C8—31no—
341#127—22no—
342#127—22no—
343#125—22no—
344#125—22no—
345#123—28no—
346#123—28no—
347#121—28no—
348#121—28no—
349#121—22no—
350#121—22no—
351#121—22no—
352#121—22no—
353#121—62no—
354#121—62no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4#6714yescomplemented
360C4×D4#6714yescomplemented
361#117—22no—
362#117—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—61no—
369C2×C4⋊C4#6711yescharacteristic
370C2×C4⋊C4#6711yescharacteristic
371C2×C4⋊C4C22×D311yescharacteristic
372C2×C4⋊C4C22×D311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—61no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4#6711yescharacteristic
383C2×C22⋊C4#6711yescharacteristic
384C2×C42—61no—
385C2×C42C22×D311yescharacteristic
386C2×C42C22×D311yescharacteristic
387#107—62no—
388#106—62no—
389#102—62no—
390#102—62no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397C22⋊C8—62no—
398C22⋊C8—62no—
399#97—62no—
400C4×C8—62no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—21no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—41no—
414C23×C3—41no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3C22×D411yescharacteristic
426C22×D3—22no—
427C22×D3—41no—
428C22×D3—41no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C3×D4—22no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—41no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—84no—
442C3×D4—84no—
443C3×D4—84no—
444C3×D4—84no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—84no—
469C2×C3×C4—84no—
470C2×C3×C4#12012yes—
471C2×C3×C4#12012yes—
472C2×C3×C4C22×D411yescharacteristic
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C2×#4111yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4C2×#4111yescharacteristic
478#67—84no—
479C2×Dic3—22no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488D12—22no—
489D12—22no—
490D12—41no—
491D12—41no—
492C4×D3—84no—
493C3⋊C8—22no—
494C3⋊C8—22no—
495C3⋊C8—41no—
496C3⋊C8—41no—
497C24—21no—
498C24—21no—
499C24—61no—
500C24C2×#6711yescharacteristic
501C2×D4—24no—
502C2×D4—24no—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—32no—
516C2×D4—64no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—61no—
522C2×D4—81no—
523C2×D4—81no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4—81no—
527C2×D4—81no—
528C2×D4—81no—
529C2×D4—81no—
530C2×D4—241no—
531C2×D4—241no—
532C2×D4C2×#6712yes—
533C2×D4C2×#6712yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—122no—
552C22×C4—241no—
553C22×C4—241no—
554C22×C4C2×#6711yescharacteristic
555C22×C4C2×#6711yescharacteristic
556C22×C4C2×#6711yescharacteristic
557C22×C4C2×#6711yescharacteristic
558C22×C4C2×#6711yescharacteristic
559C22×C4C23×D311yescharacteristic
560D8—68no—
561D8—68no—
562C2×C8—32no—
563C2×C8—32no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—32no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—241no—
587C4⋊C4C2×#6712yes—
588C4⋊C4C2×#6712yes—
589C22⋊C4—24no—
590C22⋊C4—24no—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—64no—
596C22⋊C4—122no—
597C22⋊C4—241no—
598C22⋊C4—241no—
599C22⋊C4—241no—
600C42—21no—
601C42—21no—
602C42—241no—
603C42C2×#6712yes—
604C42C2×#6712yes—
605C22×C3—41no—
606C22×C3—41no—
607C22×C3—41no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—42no—
613C22×C3—41no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3—81no—
621C22×C3—81no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3C2×#12011yescharacteristic
627C22×C3#52511yescharacteristic
628C22×C3#53211yescharacteristic
629C22×C3#57611yescharacteristic
630C22×C3#57611yescharacteristic
631C22×C3#57611yescharacteristic
632C22×C3#57711yescharacteristic
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—42no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—42no—
645C3×C4—41no—
646C3×C4—42no—
647C3×C4#52511yescharacteristic
648C3×C4#52511yescharacteristic
649C3×C4#53211yescharacteristic
650C3×C4#53211yescharacteristic
651Dic3—42no—
652Dic3—81no—
653Dic3—81no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—62no—
676C23—121no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23C22×#6711yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—62no—
692D4—62no—
693D4—84no—
694D4—84no—
695D4—84no—
696D4—84no—
697D4—121no—
698D4—121no—
699D4—244no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—62no—
724C2×C4—84no—
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—244no—
735C2×C4#95312yes—
736C2×C4#95312yes—
737C2×C4D3×#4111yescharacteristic
738C2×C4D3×#4111yescharacteristic
739C2×C4D3×#4111yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C2×C4C22×#6711yescharacteristic
742C2×C4C22×#6711yescharacteristic
743C8—62no—
744C8—62no—
745C8—121no—
746C8—121no—
747C2×C3—81no—
748C2×C3—82no—
749C2×C3—82no—
750C2×C3#238811yescharacteristic
751C2×C3#300811yescharacteristic
752C2×C3#301211yescharacteristic
753C2×C3#311911yescharacteristic
754C2×C3#312211yescharacteristic
755C2×C3#317611yescharacteristic
756C2×C3#317911yescharacteristic
757D3—82no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—122no—
780C22—122no—
781C22—122no—
782C22—241no—
783C22—241no—
784C22—241no—
785C22—241no—
786C22#582811yescharacteristic
787C22#583211yescharacteristic
788C22#583511yescharacteristic
789C22#583511yescharacteristic
790C22#583511yescharacteristic
791C22#583611yescharacteristic
792C22C2×#95311yescharacteristic
793C4—22no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—42no—
798C4—41no—
799C4—42no—
800C4—122no—
801C4—241no—
802C4—241no—
803C4#582811yescharacteristic
804C4#582811yescharacteristic
805C4#583211yescharacteristic
806C4#583211yescharacteristic
807C3#2358011yescharacteristic, complemented, Sylow
808C2—81no—
809C2—82no—
810C2—82no—
811C2—242no—
812C2#8343211yescharacteristic
813C2#8343311yescharacteristic
814C2#8343411yescharacteristic
815C2#8343511yescharacteristic
816C2#8409511yescharacteristic
817C2#8410111yescharacteristic
818C2#8410211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#540C2
socleC23×C3C22×D4
hypercenterC2×#540D3
hypocenterC3#23580
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×C3×#540C2semidirect
2. C2×#5014C2semidirect
3. C2×C4×#213C2semidirect
4. #82236C2semidirect
5. #71767C2semidirect
6. #71762C2semidirect
7. #71743C2semidirect
8. #71739C2semidirect
9. #71684C2semidirect
10. #71684C2semidirect
11. #71680C2semidirect
12. #71679C2semidirect
13. #71609C2semidirect
14. C4×#832C2semidirect
15. #71582C2semidirect
64. C2×#540D3semidirect
105. C3×C4×D4D4semidirect
106. C3×C4×D4D4semidirect
359. C4×D4#67semidirect
360. C4×D4#67semidirect
807. C3#23580semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5402
C2×#50142
C2×C4×#2132
#822362
#717672
#717622
#717432
#717392
#716842
#716802
#716792
#716092
C4×#8322
#715822
#235803