Finite Group Databasebeta

← #25129801

Subgroups — #25129801

Order 11008.

1284 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic86C211yesmaximal, characteristic
2C2×#14583240C211yesmaximal, characteristic, complemented
3C2×#14582907C211yesmaximal, characteristic, complemented
4#19135841C211yesmaximal, characteristic, complemented
5#19135841C211yesmaximal, characteristic, complemented
6#19135798C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic, complemented
8#19135026C211yesmaximal, characteristic, complemented
9#19134893C211yesmaximal, characteristic
10#19134862C211yesmaximal, characteristic, complemented
11#19134848C211yesmaximal, characteristic, complemented
12#19134529C211yesmaximal, characteristic, complemented
13#19134529C211yesmaximal, characteristic, complemented
14#19134529C211yesmaximal, characteristic, complemented
15C43×#2485C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19D4×Dic86—24no—
20D4×Dic86—24no—
21C2×#13063325C2211yescharacteristic
22C2×#13063324—21no—
23C2×#13063304C2211yescharacteristic
24C2×#13063304C2211yescharacteristic
25C2×#13063302—21no—
26C2×#13063302—21no—
27C2×C4×Dic86C2211yescharacteristic
28C2×D4×Dic43—21no—
29#14583240—24no—
30C2×#13063258C2211yescharacteristic
31C2×#13063256C2211yescharacteristic
32#14582907—24no—
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42C2×#13063248C2211yescharacteristic
43C2×#13063248C2211yescharacteristic
44C2×#13063248C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C43×#397—21no—
55C43×#394—21no—
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#388—21no—
59C43×#387—21no—
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C22×Dic86—22no—
64C22×Dic86—22no—
65C22×Dic86—22no—
66C22×Dic86—21no—
67C22×Dic86—21no—
68C22×Dic86—22no—
69C22×Dic86—22no—
70C22×Dic86—22no—
71C22×Dic86—22no—
72C22×Dic86—41no—
73C22×Dic86—41no—
74C22×Dic86—41no—
75C22×Dic86—41no—
76C22×Dic86D414yes—
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C23×Dic43—21no—
81C23×Dic43—21no—
82C2×#10621877—22no—
83C2×#10621877—41no—
84C2×#10621877—41no—
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89#13063325—22no—
90#13063325—22no—
91#13063324—28no—
92#13063304—22no—
93#13063304—22no—
94#13063304—22no—
95#13063304D414yes—
96#13063302—28no—
97#13063302—28no—
98C4×Dic86—22no—
99C4×Dic86—22no—
100D4×Dic43—28no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C4×Dic43—21no—
110#13063258—22no—
111#13063256—22no—
112#13063248—22no—
113#13063248—22no—
114#13063248—22no—
115#13063248—22no—
116#13063248—22no—
117#13063248—22no—
118#13063248—22no—
119#13063248—22no—
120#13063248—41no—
121#13063248—41no—
122#13063248—41no—
123#13063248—41no—
124C22⋊(C43⋊C8)—22no—
125C22⋊(C43⋊C8)—41no—
126C22⋊(C43⋊C8)—41no—
127C22×D4×C43D411yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C23×C4×C43C2311yescharacteristic
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132#117×C43—22no—
133#117×C43—22no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149#95×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2411yescharacteristic
180C22×Dic43—24no—
181C22×Dic43—24no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—42no—
187C22×Dic43—42no—
188C22×Dic43—42no—
189C22×Dic43—42no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86—21no—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—28no—
202C2×Dic86—24no—
203C2×Dic86—24no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—44no—
207C2×Dic86—44no—
208C2×Dic86—44no—
209C2×Dic86—44no—
210C2×Dic86—44no—
211C2×Dic86—44no—
212C2×Dic86—42no—
213C2×Dic86—42no—
214C2×Dic86—42no—
215C2×Dic86—42no—
216C2×Dic86—44no—
217C2×Dic86C2×D412yes—
218C2×Dic86C2×D412yes—
219C2×Dic86C2×D412yes—
220C2×Dic86#4112yes—
221C2×Dic86#4112yes—
222C4⋊C4×C43—22no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—42no—
232C4⋊C4×C43—81no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—22no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—81no—
238C22⋊C4×C43—81no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—42no—
242C22⋊Dic43—24no—
243C22⋊Dic43—24no—
244C4⋊Dic43—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43—21no—
247C4⋊Dic43C2×D412yes—
248Dic43⋊C4—24no—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251C4×Dic43—24no—
252#10621877—44no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8—21no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43#12012yes—
278C23×C43#13712yes—
279C23×C43C22×D411yescharacteristic
280D4×C43—28no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43#12012yes—
312C2×C4×C43#13712yes—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—48no—
326C2×Dic43—48no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333Dic86—22no—
334Dic86—22no—
335Dic86—22no—
336Dic86—22no—
337Dic86—22no—
338Dic86—22no—
339Dic86—22no—
340Dic86—48no—
341Dic86—48no—
342Dic86—41no—
343Dic86—41no—
344Dic86—41no—
345Dic86—41no—
346Dic86#12314yes—
347C43⋊C8—41no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350C43⋊C8—41no—
351#24053—431nomaximal, Sylow
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—22no—
356C22×C43—22no—
357C22×C43—22no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43C2×#12011yescharacteristic
367C22×C43#54611yescharacteristic
368C22×C43#54611yescharacteristic
369C22×C43C2×#13711yescharacteristic
370C22×C43C2×#13711yescharacteristic
371C22×C43#57711yescharacteristic
372C22×C43#57811yescharacteristic
373C4×C43—22no—
374C4×C43—22no—
375C4×C43—41no—
376C4×C43—41no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43C2×#12311yescharacteristic
382C4×C43#53411yescharacteristic
383C4×C43#54611yescharacteristic
384C4×C43#54611yescharacteristic
385Dic43—24no—
386Dic43—42no—
387Dic43—42no—
388Dic43—42no—
389C2×D4×Q8—431no—
390C2×#485—431no—
391C2×#419—431no—
392#2485D4311yescharacteristic
393#2043—431no—
394#2043—431no—
395#2036—431no—
396#2035—431no—
397#1894—431no—
398#1870—431no—
399#1865—431no—
400#1863—431no—
401#1787—431no—
402#1787—431no—
403#1787—431no—
404C2×C43—42no—
405C2×C43—42no—
406C2×C43#240511yescharacteristic
407C2×C43#300411yescharacteristic
408C2×C43#301311yescharacteristic
409C2×C43#331211yescharacteristic
410C2×C43#332011yescharacteristic
411C2×C43#332811yescharacteristic
412C2×C43#332911yescharacteristic
413C23×Q8—431no—
414C23×Q8—431no—
415C22×M16—431no—
416D4×Q8—864no—
417D4×Q8—864no—
418C2×C4⋊Q8—431no—
419C2×C4⋊Q8—861no—
420C2×C22⋊Q8—431no—
421C2×C22⋊Q8—431no—
422C2×C22⋊Q8—861no—
423C2×C22⋊Q8—861no—
424C2×C4×Q8—431no—
425C2×C4×D4—861no—
426C2×C4×D4C2×D4311yescharacteristic
427C2×#117C2×D4311yescharacteristic
428#485—864no—
429C2×#107—431no—
430C2×#106—431no—
431#419—864no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447#397—21no—
448#394—21no—
449#389C2×D4311yescharacteristic
450#389C2×D4311yescharacteristic
451#388—21no—
452#387—21no—
453#380C2×D4311yescharacteristic
454#380C2×D4311yescharacteristic
455#380C2×D4311yescharacteristic
456#340—431no—
457#340—431no—
458#336—431no—
459#336—431no—
460C43#2405311yescharacteristic, complemented, Sylow
461C22×Q8—434no—
462C22×Q8—431no—
463C22×Q8—431no—
464C22×Q8—431no—
465C22×Q8—862no—
466C22×Q8—862no—
467C22×Q8—862no—
468C22×Q8—862no—
469C22×Q8—862no—
470C22×Q8—862no—
471C22×Q8—862no—
472C22×Q8—861no—
473C22×Q8—861no—
474C22×Q8—1721no—
475C22×Q8—1721no—
476C22×Q8—1721no—
477C22×Q8—1721no—
478C22×D4C22⋊D4311yescharacteristic
479C23×C4—861no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483C2×M16—862no—
484C2×M16—1721no—
485C2×M16—1721no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8—431no—
489C22×C8—431no—
490C4⋊Q8—862no—
491C4⋊Q8—862no—
492C4⋊Q8—868no—
493C22⋊Q8—434no—
494C22⋊Q8—868no—
495C22⋊Q8—868no—
496C22⋊Q8—862no—
497C22⋊Q8—862no—
498C22⋊Q8—862no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×D4—22no—
502C4×D4—22no—
503C4×D4—868no—
504#117—22no—
505#117—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4C22⋊D4311yescharacteristic
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C4⋊C4C22×D4311yescharacteristic
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4C22⋊D4311yescharacteristic
526C2×C22⋊C4C22⋊D4311yescharacteristic
527C2×C42—21no—
528C2×C42—861no—
529C2×C42C22×D4311yescharacteristic
530#107—862no—
531#106—862no—
532#103—862no—
533#103—862no—
534#103—862no—
535#103—862no—
536#103—862no—
537#103—862no—
538#103—862no—
539#103—862no—
540#103—1721no—
541#103—1721no—
542#103—1721no—
543#103—1721no—
544C22⋊C8—862no—
545C22⋊C8—1721no—
546C22⋊C8—1721no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552C24C2×C22⋊D4311yescharacteristic
553C24C2×C22⋊D4311yescharacteristic
554C2×Q8—432no—
555C2×Q8—432no—
556C2×Q8—432no—
557C2×Q8—432no—
558C2×Q8—432no—
559C2×Q8—864no—
560C2×Q8—868no—
561C2×Q8—864no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8—1722no—
576C2×Q8—1722no—
577C2×Q8—1722no—
578C2×Q8—1722no—
579C2×Q8—1724no—
580C2×Q8—1724no—
581C2×Q8—1724no—
582C2×Q8—1724no—
583C2×Q8—1724no—
584C2×Q8—1724no—
585C2×Q8—1724no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—861no—
604C22×C4—864no—
605C22×C4—864no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—1722no—
610C22×C4—1722no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4D4×D4312yes—
614C22×C4D4×D4312yes—
615C22×C4C2×C22⋊D4311yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C2×C22⋊D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620M16—1724no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C4⋊C4—22no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—81no—
644C4⋊C4—432no—
645C4⋊C4—864no—
646C4⋊C4—864no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—861no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—81no—
656C22⋊C4—81no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C42—21no—
660C42—21no—
661C42—42no—
662C42—864no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23#1306329312yes—
676C23#1306335512yes—
677C23C22×C22⋊D4311yescharacteristic
678Q8—434no—
679Q8—862no—
680Q8—862no—
681Q8—862no—
682Q8—862no—
683Q8—862no—
684Q8—862no—
685Q8—862no—
686Q8—1728no—
687Q8—1728no—
688Q8—1721no—
689Q8—1721no—
690Q8—1721no—
691Q8—1721no—
692D4—28no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
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—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—1728no—
730C2×C4—1728no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4#1306329312yes—
738C2×C4#1306335512yes—
739C2×C4C2×D4×D4311yescharacteristic
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4#41×D4311yescharacteristic
742C2×C4#41×D4311yescharacteristic
743C2×C4#1306337111yescharacteristic
744C2×C4#1306337111yescharacteristic
745C8—1721no—
746C8—1721no—
747C8—1721no—
748C8—1721no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22C2×#1306329311yescharacteristic
764C22#1458353711yescharacteristic
765C22#1458353711yescharacteristic
766C22C2×#1306335511yescharacteristic
767C22C2×#1306335511yescharacteristic
768C22#1458371011yescharacteristic
769C22#1458371411yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—81no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4—864no—
779C4—1722no—
780C4—1722no—
781C4—1722no—
782C4#123×D4311yescharacteristic
783C4#1458346011yescharacteristic
784C4#1458354111yescharacteristic
785C4#1458354111yescharacteristic
786C2—42no—
787C2—42no—
788C2#1913791911yescharacteristic
789C2#1914382811yescharacteristic
790C2#1914390711yescharacteristic
791C2#1914664011yescharacteristic
792C2#1914676011yescharacteristic
793C2#1914687211yescharacteristic
794C2#1914688311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2485C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenter#2485D43
hypocenterC43#24053
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2485

Complements

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

NH ≅ G/Ntype
2. C2×#14583240C2semidirect
3. C2×#14582907C2semidirect
4. #19135841C2semidirect
5. #19135841C2semidirect
6. #19135798C2semidirect
7. #19135791C2semidirect
8. #19135026C2semidirect
10. #19134862C2semidirect
11. #19134848C2semidirect
12. #19134529C2semidirect
13. #19134529C2semidirect
14. #19134529C2semidirect
460. C43#24053semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic862
C2×#145832402
C2×#145829072
#191358412
#191357982
#191357912
#191350262
#191348932
#191348622
#191348482
#191345292
C43×#24852
#2405343