Finite Group Databasebeta

← #25144000

Subgroups — #25144000

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583114C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14583044C211yesmaximal, characteristic
4C2×C4×#10621882C211yesmaximal, characteristic, complemented
5#19138172C211yesmaximal, characteristic, complemented
6#19135990C211yesmaximal, characteristic, complemented
7#19135798C211yesmaximal, characteristic, complemented
8#19135777C211yesmaximal, characteristic, complemented
9#19135688C211yesmaximal, characteristic, complemented
10#19135455C211yesmaximal, characteristic, complemented
11#19135203C211yesmaximal, characteristic, complemented
12#19134932C211yesmaximal, characteristic, complemented
13#19134929C211yesmaximal, characteristic, complemented
14#19134842C211yesmaximal, characteristic, complemented
15C43×#2339C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C2×#13063313C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063299C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24#14583114—24no—
25#14583061—24no—
26#14583044—24no—
27C4×#10621882—24no—
28C2×#13063258C2211yescharacteristic
29C2×#13063258C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C4×C43⋊C8C2211yescharacteristic
42#14582828—21no—
43#14582814—21no—
44#14582805C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582775—21no—
47#14582758—21no—
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#391C2211yescharacteristic
57C43×#386—21no—
58C43×#386—21no—
59C43×#381—21no—
60C43×#380C2211yescharacteristic
61C4×C22⋊C4×C43C2211yescharacteristic
62C2×#95×C43—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—41no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621884—22no—
74C2×#10621884—22no—
75C2×#10621884—41no—
76C2×#10621882—22no—
77C2×#10621882—22no—
78C2×#10621882D414yes—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063313—22no—
84#13063313—41no—
85#13063304—22no—
86#13063304—41no—
87#13063299—22no—
88#13063299—41no—
89C4×D172—22no—
90C4×D172—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100#13063258—22no—
101#13063258—41no—
102C4⋊(C43⋊C8)—22no—
103#13063249—22no—
104#13063249—22no—
105#13063248—22no—
106#13063248—41no—
107#13063246—22no—
108#13063246D414yescomplemented
109#13063245—22no—
110#13063245—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—22no—
113C4×C43⋊C8—22no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C2×#41×C43—22no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—41no—
122C2×#41×C43—41no—
123C22×Q8×C43C2311yescharacteristic
124C22×D4×C43—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C23×C4×C43—21no—
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C4×D4×C43—22no—
131C4×D4×C43—22no—
132C4×D4×C43—41no—
133C4×D4×C43—41no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43D411yescharacteristic
140C2×C22⋊C4×C43D411yescharacteristic
141C2×C42×C43C2311yescharacteristic
142C2×C42×C43C2311yescharacteristic
143#95×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146#95×C43—21no—
147#95×C43—21no—
148#95×C43D411yescharacteristic
149#95×C43D411yescharacteristic
150C24×C43—21no—
151C24×C43C2×D411yescharacteristic
152C23×D43—21no—
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×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43#4112yes—
163C2×D4×C43—24no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43C2×D412yes—
170C2×D4×C43C2×D412yes—
171C2×D4×C43#4112yes—
172C22×C4×C43—24no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—42no—
186C22×C4×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—81no—
189C22×C4×C43—81no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—81no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172C2×D412yes—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—81no—
211C2×Dic86—21no—
212C2×Dic86—21no—
213C2×Dic86—21no—
214C2×Dic86—21no—
215C2×Dic86—21no—
216C2×Dic86—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—41no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—81no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—21no—
229C42×C43—21no—
230C22⋊Dic43—42no—
231#10621885—44no—
232#10621884—44no—
233#10621883—44no—
234#10621882—28no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237(C2×D43)⋊C4—42no—
238(C2×D43)⋊C4—42no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43C2×D412yes—
243Dic43⋊C4—42no—
244Dic43⋊C4—81no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C2×D412yes—
256C2×C43⋊C8C2×D412yes—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43C22×D411yescharacteristic
272C22×D43—22no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—41no—
278C22×D43—41no—
279Q8×C43—22no—
280Q8×C43—22no—
281Q8×C43—41no—
282Q8×C43—41no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—48no—
287D4×C43#12114yes—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—48no—
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—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—84no—
317C2×C4×C43—84no—
318C2×C4×C43#13512yes—
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C2×C4×C43H(5,𝔽2)11yescharacteristic
325C22⋊D43—84no—
326C2×Dic43—22no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335D172—22no—
336D172—22no—
337D172—41no—
338D172—41no—
339C4×D43—84no—
340Dic86—41no—
341Dic86—41no—
342Dic86—41no—
343Dic86—41no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346C43⋊C8—41no—
347C43⋊C8—41no—
348#25150—431nomaximal, Sylow
349C22×C43—24no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43#52511yescharacteristic
364C22×C43D4211yescharacteristic
365C22×C43D4211yescharacteristic
366C22×C43C2×#13511yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57611yescharacteristic
369C22×C43#57811yescharacteristic
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—81no—
374C2×D43—81no—
375C2×D43—81no—
376C2×D43—81no—
377C4×C43—22no—
378C4×C43—41no—
379C4×C43—42no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43—41no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43C2×#12111yescharacteristic
386C4×C43#53811yescharacteristic
387C4×C43#54611yescharacteristic
388C4×C43#54611yescharacteristic
389Dic43—42no—
390Dic43—81no—
391Dic43—81no—
392C2×#463—431no—
393C2×#452—431no—
394C2×#449—431no—
395C2×C4×D8—431no—
396#2427—431no—
397#2339D4311yescharacteristic, complemented
398#2068—431no—
399#2036—431no—
400#2033—431no—
401#2015—431no—
402#1969—431no—
403#1923—431no—
404#1877—431no—
405#1877—431no—
406#1862—431no—
407C2×C43—44no—
408C2×C43—81no—
409C2×C43#242411yescharacteristic
410C2×C43#310211yescharacteristic
411C2×C43#312411yescharacteristic
412C2×C43#326911yescharacteristic
413C2×C43#327311yescharacteristic
414C2×C43#328011yescharacteristic
415C2×C43#328311yescharacteristic
416D43—82no—
417C22×#41C2×D4311yescharacteristic
418C22×Q16—431no—
419C22×SD16—431no—
420C22×SD16—431no—
421C22×D8—431no—
422C2×#124—431no—
423C2×C22⋊Q8—431no—
424C2×#121—431no—
425C2×C4×D4—431no—
426C2×C4×D4C2×D4311yescharacteristic
427C2×C4×D4C2×D4311yescharacteristic
428#463—864no—
429#452—864no—
430#449—864no—
431C4×D8—864no—
432C2×#107—431no—
433C2×#107—431no—
434C2×C4⋊C8—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#103—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102—431no—
442C2×#102—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C4×C8—431no—
446#397—861no—
447#394—861no—
448#391—431no—
449#391C2×D4311yescharacteristic
450#391C2×D4311yescharacteristic
451#389—431no—
452#386—21no—
453#386—21no—
454#386—861no—
455#381—21no—
456#380—861no—
457#380C2×D4311yescharacteristic
458C4×C22⋊C4C2×D4311yescharacteristic
459C2×#95—21no—
460#340—431no—
461#340—431no—
462#336—431no—
463#336—431no—
464C43#2515011yescharacteristic, complemented, Sylow
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—22no—
469C2×#41—41no—
470C2×#41—41no—
471C22×Q8—431no—
472C22×Q8C22×D4311yescharacteristic
473C22×D4—21no—
474C22×D4—431no—
475C22×D4—861no—
476C22×D4C22×D4311yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—861no—
481C23×C4C22×D4311yescharacteristic
482C2×Q16—862no—
483C2×Q16—862no—
484C2×Q16—1721no—
485C2×SD16—862no—
486C2×SD16—862no—
487C2×SD16—862no—
488C2×SD16—862no—
489C2×SD16—862no—
490C2×SD16—1721no—
491C2×D8—434no—
492C2×D8—862no—
493C2×D8—862no—
494C22×C8—431no—
495C22×C8—431no—
496C22×C8—431no—
497C22×C8—431no—
498#124—862no—
499#124—1721no—
500C22⋊Q8—862no—
501C22⋊Q8—1721no—
502#121—862no—
503#121—1721no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—41no—
507C4×D4—41no—
508C4×D4—862no—
509C4×D4—1721no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C4⋊C4C22×D4311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4C22⋊D4311yescharacteristic
525C2×C22⋊C4C22⋊D4311yescharacteristic
526C2×C42C22×D4311yescharacteristic
527C2×C42C22×D4311yescharacteristic
528#107—862no—
529#107—1721no—
530C4⋊C8—862no—
531#103—862no—
532#103—862no—
533#103—862no—
534#103—1721no—
535#102—434no—
536#102—862no—
537#102—862no—
538#102—862no—
539C22⋊C8—862no—
540C22⋊C8—862no—
541C4×C8—862no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—861no—
548#95—861no—
549#95—861no—
550#95C22⋊D4311yescharacteristic
551#95C22⋊D4311yescharacteristic
552C24—21no—
553C24—861no—
554C24C2×C22⋊D4311yescharacteristic
555#41—44no—
556#41—44no—
557#41—44no—
558#41—44no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—861no—
565C2×Q8—861no—
566C2×Q8—861no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8#1062189812yes—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—432no—
578C2×D4—861no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—3441no—
584C2×D4—1722no—
585C2×D4—1722no—
586C2×D4#1062189812yes—
587C2×D4D4×D4312yes—
588C2×D4D4×D4312yes—
589C22×C4—24no—
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—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—3441no—
611C22×C4—1722no—
612C22×C4—1722no—
613C22×C4C2×C22⋊D4311yescharacteristic
614C22×C4C2×C22⋊D4311yescharacteristic
615C22×C4C2×C22⋊D4311yescharacteristic
616C22×C4C2×C22⋊D4311yescharacteristic
617C22×C4C2×C22⋊D4311yescharacteristic
618C22×C4C23×D4311yescharacteristic
619Q16—1724no—
620SD16—1724no—
621SD16—1724no—
622D8—868no—
623C2×C8—432no—
624C2×C8—432no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—432no—
640C4⋊C4—861no—
641C4⋊C4—861no—
642C4⋊C4—861no—
643C4⋊C4—3441no—
644C4⋊C4—1722no—
645C22⋊C4—22no—
646C22⋊C4—41no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—81no—
650C22⋊C4—1722no—
651C22⋊C4—1722no—
652C22⋊C4—1722no—
653C22⋊C4—1722no—
654C22⋊C4—1722no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—862no—
674C23—1721no—
675C23—1721no—
676C23—1721no—
677C23—1721no—
678C23—1721no—
679C23—1721no—
680C23C22×C22⋊D4311yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—1721no—
686Q8—1721no—
687Q8—1721no—
688Q8—1721no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—48no—
693D4—862no—
694D4—862no—
695D4—3444no—
696D4—1721no—
697D4—1721no—
698D4#1306329814yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
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—21no—
714C2×C4—48no—
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—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—84no—
728C2×C4—84no—
729C2×C4—862no—
730C2×C4—3444no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4#1306334512yes—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×D4×D4311yescharacteristic
742C2×C4C2×#1062189811yescharacteristic
743C2×C4C2×#1062189811yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337011yescharacteristic
746C8—862no—
747C8—862no—
748C8—1721no—
749C8—1721no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—3441no—
765C22—3441no—
766C22—3441no—
767C22—3441no—
768C22—1722no—
769C22—1722no—
770C22—1722no—
771C22#1458341011yescharacteristic
772C22D4×C22⋊D4311yescharacteristic
773C22D4×C22⋊D4311yescharacteristic
774C22C2×#1306334511yescharacteristic
775C22#1458369711yescharacteristic
776C22#1458370211yescharacteristic
777C22#1458371411yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—42no—
782C4—41no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—3441no—
787C4—3441no—
788C4—1722no—
789C4C2×#1306329811yescharacteristic
790C4#1458348711yescharacteristic
791C4#1458353911yescharacteristic
792C4#1458353911yescharacteristic
793C2—44no—
794C2—81no—
795C2—3442no—
796C2#1913813111yescharacteristic
797C2#1914461311yescharacteristic
798C2#1914485711yescharacteristic
799C2#1914614611yescharacteristic
800C2#1914620211yescharacteristic
801C2#1914627611yescharacteristic
802C2#1914631311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2339C2
socleC23×C43C22×D4
prime radicalC2×#14583044C2
hypercenter#2339D43
hypocenterC43#25150
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
1. C2×#14583114C2semidirect
2. C2×#14583061C2semidirect
4. C2×C4×#10621882C2semidirect
5. #19138172C2semidirect
6. #19135990C2semidirect
7. #19135798C2semidirect
8. #19135777C2semidirect
9. #19135688C2semidirect
10. #19135455C2semidirect
11. #19135203C2semidirect
12. #19134932C2semidirect
13. #19134929C2semidirect
14. #19134842C2semidirect
15. C43×#2339C2semidirect
108. #13063246D4semidirect
397. #2339D43semidirect
464. C43#25150semidirect

Maximal subgroups

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

subgroupindex
C2×#145831142
C2×#145830612
C2×#145830442
C2×C4×#106218822
#191381722
#191359902
#191357982
#191357772
#191356882
#191354552
#191352032
#191349322
#191349292
#191348422
C43×#23392
#2515043