Finite Group Databasebeta

← #25107942

Subgroups — #25107942

Order 11008.

1136 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
1#19137290C211yesmaximal, characteristic, complemented
2#19137177C211yesmaximal, characteristic, complemented
3#19135472C211yesmaximal, characteristic, complemented
4#19135462C211yesmaximal, characteristic, complemented
5#19135294C211yesmaximal, characteristic, complemented
6#19135280C211yesmaximal, characteristic, complemented
7#19135224C211yesmaximal, characteristic, complemented
8#19135217C211yesmaximal, characteristic, complemented
9#19134945C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134918C211yesmaximal, characteristic, complemented
12#19134796C211yesmaximal, characteristic, complemented
13#19134526C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic, complemented
15C2×C43×#447C211yesmaximal, characteristic
16C2×D4×Dic43C2211yescharacteristic, complemented
17C2×#13063284C2211yescharacteristic
18C2×#13063284C2211yescharacteristic
19C2×#13063259C2211yescharacteristic, complemented
20C2×#13063257C2211yescharacteristic, complemented
21C2×#13063246C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic, complemented
26C2×#13063246C2211yescharacteristic, complemented
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063235C2211yescharacteristic, complemented
29C2×C8×Dic43C2211yescharacteristic, complemented
30#14582802—21no—
31#14582802—21no—
32#14582802—21no—
33#14582802C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic, complemented
38#14582798C2211yescharacteristic, complemented
39#14582792—21no—
40#14582779—21no—
41#14582774—21no—
42#14582759C2211yescharacteristic
43#14582755—21no—
44#14582755—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46#14582662C2211yescharacteristic, complemented
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52C23×D4×C43C2211yescharacteristic
53C22×D8×C43C2211yescharacteristic
54C22×D8×C43C2211yescharacteristic
55C2×#121×C43C2211yescharacteristic
56C43×#447C418yescomplemented
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C23×Dic43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63D4×Dic43—41no—
64D4×Dic43—41no—
65#13063284—41no—
66#13063284—41no—
67#13063284—41no—
68#13063284—41no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43D411yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43D411yescharacteristic
90C2×C22⋊Dic43D411yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95#13063259—41no—
96#13063257—41no—
97#13063246—41no—
98#13063246—41no—
99#13063246—41no—
100#13063246—41no—
101#13063246—41no—
102#13063246—41no—
103C22⋊(C43⋊C8)—22no—
104#13063235—41no—
105C8×Dic43—41no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C25×C43—21no—
110C22×D4×C43—21no—
111C22×D4×C43—21no—
112C22×D4×C43—22no—
113C22×D4×C43—41no—
114C22×D4×C43—41no—
115C22×D4×C43—41no—
116C22×D4×C43—41no—
117C22×D4×C43C2×C414yescomplemented
118C22×D4×C43C2311yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C2×D8×C43—41no—
123C2×D8×C43—41no—
124C2×D8×C43—41no—
125C2×D8×C43—41no—
126C2×D8×C43C2×C414yes—
127C2×D8×C43C2×C414yes—
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#121×C43—22no—
131#121×C43C2×C414yes—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134#102×C43C2×C414yescomplemented
135#102×C43C2×C414yescomplemented
136C22⋊C8×C43C2×C414yescomplemented
137C24×C43—21no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—24no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—81no—
144C24×C43—81no—
145C24×C43—81no—
146C24×C43—81no—
147C24×C43C2×D411yescharacteristic
148C2×D4×C43—24no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—24no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—44no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43—42no—
170C2×D4×C43—42no—
171C2×D4×C43—81no—
172C2×D4×C43—81no—
173C2×D4×C43C22×C412yes—
174C2×D4×C43C22×C412yes—
175C2×D4×C43C22×C412yes—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43C22×C412yes—
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43#4112yes—
184C22×C4×C43C2411yescharacteristic
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—42no—
190C22×Dic43—81no—
191C22×Dic43—81no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196D8×C43—44no—
197D8×C43—44no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43C22×C412yes—
203C2×C8×C43C22×C412yes—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C22×C412yes—
206C22⋊C4×C43—24no—
207C22⋊Dic43—41no—
208C22⋊Dic43—41no—
209C22⋊Dic43—42no—
210C22⋊Dic43—42no—
211C22⋊Dic43—81no—
212C22⋊Dic43—81no—
213C22⋊Dic43—81no—
214C22⋊Dic43—81no—
215C22⋊Dic43—81no—
216C22⋊Dic43—81no—
217C22⋊Dic43—81no—
218C22⋊Dic43—81no—
219C22⋊Dic43—81no—
220C22⋊Dic43—81no—
221C22⋊Dic43—81no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—41no—
231C4⋊Dic43—41no—
232C4⋊Dic43—81no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—21no—
237C4×Dic43—42no—
238C4×Dic43—81no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—22no—
254C23×C43—48no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
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—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43—84no—
277C23×C43—84no—
278C23×C43—84no—
279C23×C43C4×D412yes—
280C23×C43C22×D411yescharacteristic
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—48no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—41no—
293D4×C43—41no—
294D4×C43—84no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43C4×D412yes—
305C2×C4×C43C23×C411yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43H(5,𝔽2)11yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—41no—
324C2×Dic43—41no—
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—84no—
336C8×C43—22no—
337C8×C43—22no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340#22056—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—816no—
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—81no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43C2×C4×D411yescharacteristic
371C22×C43#53411yescharacteristic
372C22×C43#53511yescharacteristic
373C22×C43#57611yescharacteristic
374C22×C43#57611yescharacteristic
375C22×C43#57611yescharacteristic
376C22×C43#57711yescharacteristic
377C4×C43—22no—
378C4×C43—42no—
379C4×C43#51811yescharacteristic
380C4×C43#51811yescharacteristic
381C4×C43#53811yescharacteristic
382C4×C43#53811yescharacteristic
383Dic43—41no—
384Dic43—41no—
385Dic43—41no—
386Dic43—41no—
387Dic43—81no—
388Dic43—81no—
389Dic43—81no—
390Dic43—81no—
391C2×#447D4311yescharacteristic
392#2324—431no—
393#2309—431no—
394#1972—431no—
395#1970—431no—
396#1936—431no—
397#1934—431no—
398#1926—431no—
399#1925—431no—
400#1879—431no—
401#1879—431no—
402#1875—431no—
403#1854—431no—
404#1786—431no—
405#1750—431no—
406C2×C43—42no—
407C2×C43—82no—
408C2×C43—82no—
409C2×C43—82no—
410C2×C43#232111yescharacteristic
411C2×C43#294611yescharacteristic
412C2×C43#294811yescharacteristic
413C2×C43#319811yescharacteristic
414C2×C43#319911yescharacteristic
415C2×C43#322011yescharacteristic
416C2×C43#322411yescharacteristic
417C23×D4C2×D4311yescharacteristic
418C22×D8C2×D4311yescharacteristic
419C22×D8C2×D4311yescharacteristic
420C2×#121C2×D4311yescharacteristic
421C2×C4×D4—431no—
422C2×#117—431no—
423C2×#117—431no—
424#447Dic4318yescomplemented
425C2×#107—431no—
426C2×#106—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102—431no—
432C2×#102—431no—
433C2×#102C2×D4311yescharacteristic
434C2×#102C2×D4311yescharacteristic
435C2×C22⋊C8—431no—
436C2×C22⋊C8C2×D4311yescharacteristic
437C2×#97—431no—
438C2×C4×C8—431no—
439#390—431no—
440#390—431no—
441#390—431no—
442#390—431no—
443#390—431no—
444#390—861no—
445#390—861no—
446#390—861no—
447#389—431no—
448#388—861no—
449#386—861no—
450#385—861no—
451#380—431no—
452#379—861no—
453#379—861no—
454C4×C4⋊C4—431no—
455#340—431no—
456#340—431no—
457#340—431no—
458#340—431no—
459#336—431no—
460#336—431no—
461C43#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—21no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×Dic4314yescomplemented
471C22×D4C22×D4311yescharacteristic
472C22×D4C22×D4311yescharacteristic
473C22×D4C22×D4311yescharacteristic
474C23×C4—861no—
475C23×C4C22×D4311yescharacteristic
476C2×D8—41no—
477C2×D8—41no—
478C2×D8—41no—
479C2×D8—41no—
480C2×D8C2×Dic4314yes—
481C2×D8C2×Dic4314yes—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8C22×D4311yescharacteristic
485C22×C8C22×D4311yescharacteristic
486#121—22no—
487#121C2×Dic4314yes—
488C4×D4—1721no—
489C4×D4—1721no—
490#117—1721no—
491#117—1721no—
492#117—1721no—
493#117—1721no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C42—431no—
519C2×C42—431no—
520C2×C42—861no—
521C2×C42—861no—
522#107—1721no—
523#106—1721no—
524#102—1721no—
525#102—1721no—
526#102—1721no—
527#102—1721no—
528#102—1721no—
529#102—1721no—
530#102C2×Dic4314yescomplemented
531#102C2×Dic4314yescomplemented
532C22⋊C8—862no—
533C22⋊C8C2×Dic4314yescomplemented
534#97—1721no—
535C4×C8—1721no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—24no—
543C24—42no—
544C24—42no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—81no—
549C24D4×D4311yescharacteristic
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—81no—
574C2×D4—81no—
575C2×D4C22×Dic4312yes—
576C2×D4C22×Dic4312yes—
577C2×D4C22×Dic4312yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—3441no—
592C22×C4—3441no—
593C22×C4—1722no—
594C22×C4D4×D4311yescharacteristic
595C22×C4#1062190012yes—
596C22×C4C22×Dic4312yes—
597C22×C4C23×D4311yescharacteristic
598D8—44no—
599D8—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8C22×Dic4312yes—
611C2×C8C22×Dic4312yes—
612C4⋊C4—21no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—861no—
621C4⋊C4—3441no—
622C4⋊C4—1721no—
623C4⋊C4—1721no—
624C4⋊C4C22×Dic4312yes—
625C22⋊C4—24no—
626C22⋊C4—3441no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—3441no—
631C22⋊C4—3441no—
632C22⋊C4—3441no—
633C22⋊C4—3441no—
634C22⋊C4—3441no—
635C22⋊C4—3441no—
636C22⋊C4—3441no—
637C22⋊C4—1721no—
638C22⋊C4—1721no—
639C22⋊C4—1722no—
640C22⋊C4—1722no—
641C42—861no—
642C42—861no—
643C42—861no—
644C42—861no—
645C42—3441no—
646C42—1722no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—48no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
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—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—84no—
681C23D4×Dic4312yes—
682C23C2×D4×D4311yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—48no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—3444no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
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×C4D4×Dic4312yes—
732C2×C4C23×Dic4311yescharacteristic
733C2×C4C2×#1062190011yescharacteristic
734C2×C4#1306337011yescharacteristic
735C2×C4#1306337011yescharacteristic
736C2×C4#1306337011yescharacteristic
737C2×C4#1306337011yescharacteristic
738C8—22no—
739C8—22no—
740C8—1721no—
741C8—1721no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—816no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22C2×D4×Dic4311yescharacteristic
772C22#1458345911yescharacteristic
773C22#1458346411yescharacteristic
774C22#1458370011yescharacteristic
775C22#1458370011yescharacteristic
776C22#1458370311yescharacteristic
777C22#1458370911yescharacteristic
778C4—22no—
779C4—42no—
780C4—3441no—
781C4—3441no—
782C4—3441no—
783C4—3441no—
784C4—1721no—
785C4—1721no—
786C4—1721no—
787C4—1721no—
788C4#1458337411yescharacteristic
789C4#1458337411yescharacteristic
790C4#1458348411yescharacteristic
791C4#1458348411yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—82no—
796C2#1913725611yescharacteristic
797C2#1914342811yescharacteristic
798C2#1914344711yescharacteristic
799C2#1914544311yescharacteristic
800C2#1914545811yescharacteristic
801C2#1914564111yescharacteristic
802C2#1914568511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#447C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#447D43
hypocenterC43#22056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. #19137290C2semidirect
2. #19137177C2semidirect
3. #19135472C2semidirect
4. #19135462C2semidirect
5. #19135294C2semidirect
6. #19135280C2semidirect
7. #19135224C2semidirect
8. #19135217C2semidirect
9. #19134945C2semidirect
10. #19134945C2semidirect
11. #19134918C2semidirect
12. #19134796C2semidirect
13. #19134526C2semidirect
14. #19134363C2semidirect
16. C2×D4×Dic43C22semidirect
19. C2×#13063259C22semidirect
20. C2×#13063257C22semidirect
25. C2×#13063246C22semidirect
26. C2×#13063246C22semidirect
28. C2×#13063235C22semidirect
29. C2×C8×Dic43C22semidirect
37. #14582802C22semidirect
38. #14582798C22semidirect
45. C4⋊C4×Dic43C22semidirect
46. #14582662C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
56. C43×#447C4semidirect
117. C22×D4×C43C2×C4semidirect
134. #102×C43C2×C4semidirect
135. #102×C43C2×C4semidirect
136. C22⋊C8×C43C2×C4semidirect
424. #447Dic43semidirect
461. C43#22056semidirect
470. C22×D4C2×Dic43semidirect
530. #102C2×Dic43semidirect
531. #102C2×Dic43semidirect
533. C22⋊C8C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
#191372902
#191371772
#191354722
#191354622
#191352942
#191352802
#191352242
#191352172
#191349452
#191349182
#191347962
#191345262
#191343632
C2×C43×#4472
#2205643