Finite Group Databasebeta

← #25144191

Subgroups — #25144191

Order 11008.

1112 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583119C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14582991C211yesmaximal, characteristic, complemented
4#19138157C211yesmaximal, characteristic, complemented
5#19137436C211yesmaximal, characteristic, complemented
6#19135979C211yesmaximal, characteristic, complemented
7#19135799C211yesmaximal, characteristic, complemented
8#19135774C211yesmaximal, characteristic, complemented
9#19135670C211yesmaximal, characteristic, complemented
10#19135462C211yesmaximal, characteristic, complemented
11#19135198C211yesmaximal, characteristic, complemented
12#19134952C211yesmaximal, characteristic, complemented
13#19134947C211yesmaximal, characteristic, complemented
14#19134851C211yesmaximal, characteristic, complemented
15C2×C43×#449C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063312C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23#14583119—24no—
24#14583061—24no—
25#14582991—24no—
26C2×#13063259C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×Dic43⋊C8C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582822—21no—
38#14582813—21no—
39#14582802—21no—
40#14582802—21no—
41#14582802—21no—
42#14582802C2211yescharacteristic
43#14582802C2211yescharacteristic
44#14582802C2211yescharacteristic
45#14582798C2211yescharacteristic
46#14582787—21no—
47#14582759—21no—
48#14582759C2211yescharacteristic
49C4×C22⋊Dic43—21no—
50C4×C22⋊Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C22×D8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C43×#449—24no—
60C2×#103×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885D414yescomplemented
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063312—22no—
73#13063312—41no—
74#13063304—22no—
75#13063304—41no—
76Q8×Dic43—22no—
77Q8×Dic43—22no—
78Q8×Dic43—41no—
79Q8×Dic43—41no—
80#13063290—22no—
81#13063290—41no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43D411yescharacteristic
101C2×C22⋊Dic43D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107#13063259—41no—
108#13063258—22no—
109Dic43⋊C8—22no—
110#13063250—22no—
111#13063250—22no—
112#13063249—22no—
113#13063246—22no—
114#13063246—22no—
115#13063246—41no—
116C22⋊(C43⋊C8)—22no—
117C8×Dic43—22no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95D411yescharacteristic
121C43⋊#95D411yescharacteristic
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—22no—
125C2×#41×C43—22no—
126C2×#41×C43—41no—
127C2×#41×C43—41no—
128C22×Q8×C43C2311yescharacteristic
129C22×D4×C43—21no—
130C22×D4×C43—21no—
131C22×D4×C43C2311yescharacteristic
132C22×D4×C43C2311yescharacteristic
133C23×C4×C43—21no—
134C23×C4×C43C2311yescharacteristic
135C2×SD16×C43—22no—
136C2×SD16×C43—22no—
137C2×SD16×C43—22no—
138C2×D8×C43—22no—
139C2×D8×C43—22no—
140C2×D8×C43—41no—
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143#121×C43—22no—
144#121×C43—41no—
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#103×C43D414yes—
148#102×C43—22no—
149C22⋊C8×C43—22no—
150C24×C43—21no—
151C24×C43—21no—
152C24×C43C2×D411yescharacteristic
153#41×C43—44no—
154#41×C43—44no—
155#41×C43—44no—
156#41×C43—44no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C2×D412yes—
161C2×Q8×C43C2×D412yes—
162C2×Q8×C43#4112yes—
163C2×D4×C43—24no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—42no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—81no—
180C2×D4×C43#4112yes—
181C22×C4×C43—24no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C2×Dic86—21no—
203C2×Dic86—21no—
204C2×Dic86—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86C2×D412yes—
208SD16×C43—44no—
209D8×C43—44no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43C2×D412yes—
216C4⋊C4×C43—21no—
217C4⋊C4×C43C2×D412yes—
218C22⋊C4×C43—42no—
219C22⋊Dic43—22no—
220C22⋊Dic43—41no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—42no—
224C22⋊Dic43—42no—
225C22⋊Dic43—42no—
226C22⋊Dic43—42no—
227C22⋊Dic43—81no—
228C22⋊Dic43—81no—
229C22⋊Dic43—81no—
230C22⋊Dic43—81no—
231#10621885—28no—
232#10621883—44no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—42no—
240C4⋊Dic43—42no—
241C4⋊Dic43—81no—
242Dic43⋊C4—42no—
243Dic43⋊C4—42no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—21no—
248C4×Dic43—42no—
249C4×Dic43—42no—
250C4×Dic43—42no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8C2×D412yes—
257C23×C43—21no—
258C23×C43—22no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43C22×D411yescharacteristic
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—22no—
282Q8×C43#12114yes—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—48no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—84no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—48no—
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×C43C22×D411yescharacteristic
308C2×C4×C43C22×D411yescharacteristic
309C2×C4×C43C2×#4111yescharacteristic
310C2×C4×C43C2×#4111yescharacteristic
311C2×C4×C43H(5,𝔽2)11yescharacteristic
312C2×C4×C43H(5,𝔽2)11yescharacteristic
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—22no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43#13512yes—
337Dic86—22no—
338Dic86—22no—
339Dic86—41no—
340Dic86—41no—
341C8×C43—22no—
342C8×C43—41no—
343C43⋊C8—22no—
344C43⋊C8—41no—
345#25163—431nomaximal, Sylow
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43#52511yescharacteristic
368C22×C43D4211yescharacteristic
369C22×C43D4211yescharacteristic
370C22×C43C2×#13511yescharacteristic
371C22×C43#57511yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57811yescharacteristic
374C4×C43—24no—
375C4×C43—41no—
376C4×C43—42no—
377C4×C43C2×#12111yescharacteristic
378C4×C43#53811yescharacteristic
379C4×C43#54611yescharacteristic
380C4×C43#54611yescharacteristic
381Dic43—22no—
382Dic43—42no—
383Dic43—41no—
384Dic43—41no—
385Dic43—41no—
386Dic43—81no—
387Dic43—81no—
388Dic43—81no—
389C2×#464—431no—
390C2×#452—431no—
391C2×#449D4311yescharacteristic
392C2×C4×Q16—431no—
393#2426—431no—
394#2341—431no—
395#2067—431no—
396#2036—431no—
397#2033—431no—
398#2012—431no—
399#1970—431no—
400#1923—431no—
401#1880—431no—
402#1880—431no—
403#1863—431no—
404C2×C43—81no—
405C2×C43—82no—
406C2×C43—161no—
407C2×C43#242411yescharacteristic
408C2×C43#310211yescharacteristic
409C2×C43#312411yescharacteristic
410C2×C43#326811yescharacteristic
411C2×C43#327711yescharacteristic
412C2×C43#328511yescharacteristic
413C2×C43#328711yescharacteristic
414C22×#41C2×D4311yescharacteristic
415C22×Q16—431no—
416C22×SD16—431no—
417C22×SD16C2×D4311yescharacteristic
418C22×D8C2×D4311yescharacteristic
419C2×#124—431no—
420C2×C22⋊Q8—431no—
421C2×#121C2×D4311yescharacteristic
422C2×C4×Q8—431no—
423C2×C4×Q8—431no—
424C2×C4×Q8—431no—
425#464—864no—
426#452—864no—
427#449—24no—
428C4×Q16—864no—
429C2×#107—431no—
430C2×#107—431no—
431C2×C4⋊C8—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103—431no—
435C2×#103C2×D4311yescharacteristic
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102C2×D4311yescharacteristic
440C2×C22⋊C8—431no—
441C2×C22⋊C8C2×D4311yescharacteristic
442C2×C4×C8—431no—
443#396—861no—
444#394—861no—
445#390—431no—
446#390—431no—
447#390—431no—
448#390—861no—
449#390—861no—
450#390—861no—
451#389—431no—
452#388—861no—
453#380—431no—
454#380—861no—
455C4×C22⋊C4—431no—
456C4×C22⋊C4—861no—
457#340—431no—
458#340—431no—
459#336—431no—
460#336—431no—
461C43#2516311yescharacteristic, complemented, Sylow
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C22×Q8—431no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—21no—
471C22×D4—21no—
472C22×D4C22×D4311yescharacteristic
473C22×D4C22×D4311yescharacteristic
474C23×C4—21no—
475C23×C4C22×D4311yescharacteristic
476C2×Q16—434no—
477C2×Q16—862no—
478C2×Q16—862no—
479C2×SD16—22no—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—862no—
483C2×SD16—862no—
484C2×SD16—1721no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C22×C8—431no—
489C22×C8—431no—
490C22×C8C22×D4311yescharacteristic
491C22×C8C22×D4311yescharacteristic
492#124—862no—
493#124—1721no—
494C22⋊Q8—862no—
495C22⋊Q8—1721no—
496#121—22no—
497#121—41no—
498C4×Q8—862no—
499C4×Q8—862no—
500C4×Q8—862no—
501C4×Q8—1721no—
502C4×Q8—1721no—
503C4×Q8—1721no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—431no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C42—431no—
527C2×C42—431no—
528C2×C42—861no—
529C2×C42—861no—
530C2×C42—861no—
531#107—862no—
532#107—1721no—
533C4⋊C8—862no—
534#103—862no—
535#103—862no—
536#103—862no—
537#103C22⋊D4314yes—
538#102—22no—
539#102—862no—
540#102—862no—
541#102—1721no—
542C22⋊C8—22no—
543C22⋊C8—862no—
544C4×C8—862no—
545#95—431no—
546#95—431no—
547#95—861no—
548#95—861no—
549C24—21no—
550C24—21no—
551C24D4×D4311yescharacteristic
552#41—44no—
553#41—44no—
554#41—44no—
555#41—44no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—432no—
560C2×Q8—861no—
561C2×Q8—861no—
562C2×Q8—861no—
563C2×Q8—861no—
564C2×Q8—861no—
565C2×Q8D4×D4312yes—
566C2×Q8#1062190012yes—
567C2×Q8C2×C22⋊D4312yes—
568C2×D4—24no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—81no—
585C2×D4#1062190012yes—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—431no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4D4×D4311yescharacteristic
606C22×C4C23×D4311yescharacteristic
607Q16—868no—
608SD16—44no—
609SD16—1724no—
610D8—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—432no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8C2×C22⋊D4312yes—
623C4⋊C4—21no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—3441no—
631C4⋊C4—1722no—
632C4⋊C4—1722no—
633C4⋊C4—1722no—
634C4⋊C4—1722no—
635C4⋊C4C2×C22⋊D4312yes—
636C22⋊C4—42no—
637C22⋊C4—862no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—3441no—
641C22⋊C4—3441no—
642C22⋊C4—1722no—
643C22⋊C4—1722no—
644C22⋊C4—1721no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—861no—
650C42—861no—
651C42—861no—
652C42—861no—
653C42—1722no—
654C42—1722no—
655C42—1722no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23C2×D4×D4311yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—862no—
682Q8—862no—
683Q8—1721no—
684Q8—1721no—
685Q8#1306329614yes—
686D4—22no—
687D4—22no—
688D4—48no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—84no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—48no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—432no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—862no—
722C2×C4—861no—
723C2×C4—1721no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4C22×C22⋊D4311yescharacteristic
736C2×C4C2×#1062190011yescharacteristic
737C2×C4C2×#1062190011yescharacteristic
738C2×C4#1306337011yescharacteristic
739C2×C4#1306337011yescharacteristic
740C8—22no—
741C8—41no—
742C8—862no—
743C8—1721no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22#1458340511yescharacteristic
766C22#1458353111yescharacteristic
767C22D4×C22⋊D4311yescharacteristic
768C22#135×D4311yescharacteristic
769C22#1458369511yescharacteristic
770C22#1458370311yescharacteristic
771C22#1458371311yescharacteristic
772C4—24no—
773C4—41no—
774C4—42no—
775C4—862no—
776C4—3441no—
777C4—3441no—
778C4—3441no—
779C4—1721no—
780C4—1722no—
781C4—1721no—
782C4—1721no—
783C4C2×#1306329611yescharacteristic
784C4#1458348411yescharacteristic
785C4#1458353611yescharacteristic
786C4#1458354311yescharacteristic
787C2—81no—
788C2—82no—
789C2—161no—
790C2#1913812711yescharacteristic
791C2#1914460611yescharacteristic
792C2#1914485011yescharacteristic
793C2#1914612911yescharacteristic
794C2#1914624511yescharacteristic
795C2#1914633011yescharacteristic
796C2#1914634811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43#25163
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#14583119C2semidirect
2. C2×#14583061C2semidirect
3. C2×#14582991C2semidirect
4. #19138157C2semidirect
5. #19137436C2semidirect
6. #19135979C2semidirect
7. #19135799C2semidirect
8. #19135774C2semidirect
9. #19135670C2semidirect
10. #19135462C2semidirect
11. #19135198C2semidirect
12. #19134952C2semidirect
13. #19134947C2semidirect
14. #19134851C2semidirect
66. C2×#10621885D4semidirect
461. C43#25163semidirect

Maximal subgroups

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

subgroupindex
C2×#145831192
C2×#145830612
C2×#145829912
#191381572
#191374362
#191359792
#191357992
#191357742
#191356702
#191354622
#191351982
#191349522
#191349472
#191348512
C2×C43×#4492
#2516343