Finite Group Databasebeta

← #25130653

Subgroups — #25130653

Order 11008.

1184 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583177C211yesmaximal, characteristic, complemented
3C2×#14583000C211yesmaximal, characteristic, complemented
4#19139494C211yesmaximal, characteristic
5#19135797C211yesmaximal, characteristic, complemented
6#19135795C211yesmaximal, characteristic, complemented
7#19135595C211yesmaximal, characteristic, complemented
8#19135566C211yesmaximal, characteristic, complemented
9#19135391C211yesmaximal, characteristic, complemented
10#19134913C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134785C211yesmaximal, characteristic, complemented
13#19134784C211yesmaximal, characteristic, complemented
14#19134608C211yesmaximal, characteristic, complemented
15C43×#2000C211yesmaximal, characteristic, complemented
16#14583607—24no—
17#14583607—24no—
18C2×#13063324C2211yescharacteristic
19C2×#13063315—21no—
20C2×#13063305—21no—
21C2×#13063302—21no—
22C2×#13063301C2211yescharacteristic
23C2×#13063296C2211yescharacteristic
24C2×Q8×Dic43C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×C4×C22⋊D43C2211yescharacteristic
27C2×(C22⋊D43)⋊C4—21no—
28C22×C4⋊Dic43C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30#14583177—24no—
31#14583000—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063259C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44#14582827—21no—
45#14582807—21no—
46#14582779—21no—
47#14582776—21no—
48#14582764C2211yescharacteristic
49#14582759C2211yescharacteristic
50#14582756C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56C22×SD16×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#121×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86—21no—
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C23×Dic43—21no—
67C23×Dic43—21no—
68C22×C4×D43—21no—
69C22×C4×D43C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72#13063324—22no—
73#13063324D414yescomplemented
74#13063315—28no—
75#13063305—28no—
76#13063302—28no—
77#13063301—22no—
78#13063301—22no—
79#13063296—22no—
80#13063296—41no—
81Q8×Dic43—22no—
82Q8×Dic43D414yescomplemented
83D4×Dic43—22no—
84D4×Dic43—22no—
85C4×C22⋊D43—22no—
86C4×C22⋊D43—22no—
87(C22⋊D43)⋊C4—28no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4D411yescharacteristic
100C4⋊C4×D43—22no—
101C4⋊C4×D43—22no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43—21no—
104C2×C22⋊Dic43—21no—
105C2×C22⋊Dic43D411yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111#13063259—22no—
112#13063259—22no—
113#13063258—22no—
114Dic43⋊C8—22no—
115#13063249—22no—
116#13063249—41no—
117#13063246—22no—
118#13063246—22no—
119C22⋊(C43⋊C8)—41no—
120(C2×D43)⋊C8—22no—
121(C2×D43)⋊C8—41no—
122#13063235—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×Q8×C43C2311yescharacteristic
128C22×D4×C43—21no—
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C2×SD16×C43—22no—
132C2×SD16×C43—22no—
133C2×SD16×C43—22no—
134C22×C8×C43C2311yescharacteristic
135C22×C8×C43C2311yescharacteristic
136C22⋊Q8×C43—22no—
137C22⋊Q8×C43—22no—
138#121×C43—22no—
139#121×C43—41no—
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145#103×C43—41no—
146#102×C43—22no—
147C22⋊C8×C43—22no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C23×D43C2×D411yescharacteristic
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—81no—
165C2×D4×C43#4112yes—
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×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2411yescharacteristic
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—22no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—42no—
182C2×C22⋊D43—81no—
183C22×Dic43—24no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—42no—
189C22×Dic43—81no—
190C22×Dic43—81no—
191C22×Dic43—81no—
192C22×Dic43—81no—
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C22×Dic43C2×D411yescharacteristic
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43—24no—
203C2×C4×D43—81no—
204C2×C4×D43—81no—
205C2×Dic86—24no—
206C2×Dic86—81no—
207C2×Dic86—81no—
208SD16×C43—28no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43#4112yes—
215C4⋊C4×C43—24no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—24no—
221C22⋊C4×C43—42no—
222C22⋊Dic43—22no—
223C22⋊Dic43—42no—
224C22⋊Dic43—42no—
225C22⋊Dic43—81no—
226(C2×D43)⋊C4—24no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—81no—
229C4⋊Dic43—24no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—24no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43C2×D412yes—
238C4⋊Dic43C2×D412yes—
239Dic43⋊C4—24no—
240Dic43⋊C4—24no—
241Dic43⋊C4—24no—
242Dic43⋊C4—22no—
243C4×Dic43—24no—
244C4×Dic43C2×D412yes—
245C4×Dic43C2×D412yes—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—22no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43#13712yes—
266C23×C43C22×D411yescharacteristic
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43#13712yes—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—41no—
277Q8×C43—41no—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—41no—
281D4×C43—41no—
282D4×C43—84no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C432−1+411yescharacteristic
305C22⋊D43—28no—
306C22⋊D43—84no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—22no—
312C2×Dic43—21no—
313C2×Dic43—22no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—84no—
327C2×Dic43—84no—
328C2×Dic43#12012yes—
329C2×Dic43#12012yes—
330C4×D43—41no—
331C4×D43—41no—
332C4×D43—41no—
333C4×D43—41no—
334C4×D43—84no—
335Dic86—84no—
336C8×C43—22no—
337C8×C43—41no—
338C43⋊C8—41no—
339C43⋊C8—41no—
340#24130—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—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43C2×#12011yescharacteristic
356C22×C43#54611yescharacteristic
357C22×C43#54711yescharacteristic
358C22×C43C2×#13711yescharacteristic
359C22×C43C2×#13711yescharacteristic
360C22×C43#57611yescharacteristic
361C22×C43#57611yescharacteristic
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C4×C43—41no—
370C4×C43—42no—
371C4×C43—42no—
372C4×C43—81no—
373C4×C43#52511yescharacteristic
374C4×C43#53711yescharacteristic
375C4×C43#54811yescharacteristic
376C4×C43#55011yescharacteristic
377Dic43—22no—
378Dic43—22no—
379Dic43—41no—
380Dic43—42no—
381Dic43—42no—
382Dic43—81no—
383Dic43—81no—
384C2×#554—431no—
385C2×#474—431no—
386C2×#440—431no—
387#2535—431no—
388#2036—431no—
389#2036—431no—
390#2000—431no—
391#2000D4311yescharacteristic, complemented
392#1993—431no—
393#1955—431no—
394#1874—431no—
395#1874—431no—
396#1852—431no—
397#1852—431no—
398#1805—431no—
399C2×C43—42no—
400C2×C43—82no—
401C2×C43#240711yescharacteristic
402C2×C43#300411yescharacteristic
403C2×C43#300811yescharacteristic
404C2×C43#331411yescharacteristic
405C2×C43#331411yescharacteristic
406C2×C43#334611yescharacteristic
407C2×C43#334611yescharacteristic
408D43—42no—
409C22×SD16C2×D4311yescharacteristic
410#554—864no—
411#554—864no—
412C2×C4⋊Q8—431no—
413C2×#125—861no—
414C2×C22⋊Q8—431no—
415C2×C22⋊Q8—861no—
416C2×C22⋊Q8—861no—
417C2×C22⋊Q8C2×D4311yescharacteristic
418C2×#121—431no—
419C2×#121C2×D4311yescharacteristic
420C2×C4×Q8—431no—
421C2×C4×D4—431no—
422C2×C4×D4—431no—
423C2×C4×D4—861no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—431no—
426#474—864no—
427#440—864no—
428C2×#107—431no—
429C2×#107—431no—
430C2×#107—431no—
431C2×C4⋊C8—431no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103C2×D4311yescharacteristic
435C2×#102—431no—
436C2×#102—431no—
437C2×#102C2×D4311yescharacteristic
438C2×C22⋊C8—431no—
439C2×C22⋊C8—431no—
440C2×C22⋊C8—431no—
441C2×C22⋊C8C2×D4311yescharacteristic
442C2×#97—431no—
443#397—861no—
444#392—861no—
445#386—861no—
446#386—861no—
447#382—431no—
448#380—431no—
449#380—431no—
450#340—431no—
451#340—431no—
452#340—431no—
453#340—431no—
454#340—431no—
455#340C2×D4311yescharacteristic
456C43#2413011yescharacteristic, complemented, Sylow
457C22×Q8—861no—
458C22×Q8C22×D4311yescharacteristic
459C22×D4—21no—
460C22×D4—431no—
461C22×D4—861no—
462C22×D4C22×D4311yescharacteristic
463C23×C4—431no—
464C23×C4—861no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4C22×D4311yescharacteristic
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—22no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477#125—868no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—868no—
481C22⋊Q8—868no—
482C22⋊Q8—862no—
483C22⋊Q8—862no—
484#121—22no—
485#121—41no—
486#121—862no—
487#121—1721no—
488C4×Q8—434no—
489C4×Q8—862no—
490C4×D4—862no—
491C4×D4—862no—
492C4×D4—862no—
493C4×D4—862no—
494C4×D4—868no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—862no—
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C22⋊C4—21no—
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×C42—431no—
522C2×C42—861no—
523#107—862no—
524#107—862no—
525#107—862no—
526C4⋊C8—862no—
527#103—41no—
528#103—862no—
529#103—1721no—
530#102—22no—
531#102—862no—
532#102—862no—
533C22⋊C8—22no—
534C22⋊C8—862no—
535C22⋊C8—1721no—
536C22⋊C8—1721no—
537#97—862no—
538#95—861no—
539#95—861no—
540#95—861no—
541#95—861no—
542C24—21no—
543C24—431no—
544C24D4×D4311yescharacteristic
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—864no—
551C2×Q8—3441no—
552C2×Q8—3441no—
553C2×Q8D4×D4312yes—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—81no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—3441no—
566C2×D4—1722no—
567C2×D4—1722no—
568C2×D4#1062190012yes—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—3441no—
594C22×C4—3441no—
595C22×C4—3441no—
596C22×C4—3441no—
597C22×C4—3441no—
598C22×C4—3441no—
599C22×C4—1722no—
600C22×C4D4×D4311yescharacteristic
601C22×C4C23×D4311yescharacteristic
602SD16—28no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8#1062190012yes—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—862no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4D4×D4312yes—
634C22⋊C4—24no—
635C22⋊C4—42no—
636C22⋊C4—862no—
637C22⋊C4—864no—
638C22⋊C4—862no—
639C22⋊C4—3441no—
640C22⋊C4—3441no—
641C22⋊C4—1722no—
642C22⋊C4—1722no—
643C42—432no—
644C42—432no—
645C42—864no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—432no—
660C23—861no—
661C23—861no—
662C23—861no—
663C23—861no—
664C23—861no—
665C23—861no—
666C23#1306335412yes—
667C23C2×D4×D4311yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—3444no—
673D4—22no—
674D4—22no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—868no—
679D4—3444no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—3444no—
708C2×C4—3444no—
709C2×C4—3444no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4C2×D4×D4311yescharacteristic
725C2×C4C2×D4×D4311yescharacteristic
726C2×C4C2×#1062190011yescharacteristic
727C2×C4C2×#1062190011yescharacteristic
728C2×C4#1306337011yescharacteristic
729C2×C4#1306337211yescharacteristic
730C8—22no—
731C8—41no—
732C8—1721no—
733C8—1721no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—862no—
749C22—862no—
750C22—862no—
751C22—1721no—
752C22—1721no—
753C22—1721no—
754C22—1721no—
755C22#120×D4311yescharacteristic
756C22#1458353611yescharacteristic
757C22#1458354911yescharacteristic
758C22#137×D4311yescharacteristic
759C22C2×#1306335411yescharacteristic
760C22#1458370111yescharacteristic
761C22#1458370311yescharacteristic
762C4—41no—
763C4—42no—
764C4—42no—
765C4—81no—
766C4—862no—
767C4—862no—
768C4—3441no—
769C4—3441no—
770C4—1721no—
771C4—1722no—
772C4—1722no—
773C4#1458340511yescharacteristic
774C4#1458347611yescharacteristic
775C4#1458355511yescharacteristic
776C4#1458356911yescharacteristic
777C2—42no—
778C2—82no—
779C2—1722no—
780C2#1913793311yescharacteristic
781C2#1914382611yescharacteristic
782C2#1914386011yescharacteristic
783C2#1914666911yescharacteristic
784C2#1914668011yescharacteristic
785C2#1914707511yescharacteristic
786C2#1914708611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2000C2
socleC23×C43C22×D4
prime radical#19139494C2
hypercenter#2000D43
hypocenterC43#24130
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#14583607C2semidirect
2. C2×#14583177C2semidirect
3. C2×#14583000C2semidirect
5. #19135797C2semidirect
6. #19135795C2semidirect
7. #19135595C2semidirect
8. #19135566C2semidirect
9. #19135391C2semidirect
10. #19134913C2semidirect
11. #19134909C2semidirect
12. #19134785C2semidirect
13. #19134784C2semidirect
14. #19134608C2semidirect
15. C43×#2000C2semidirect
73. #13063324D4semidirect
82. Q8×Dic43D4semidirect
391. #2000D43semidirect
456. C43#24130semidirect

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145831772
C2×#145830002
#191394942
#191357972
#191357952
#191355952
#191355662
#191353912
#191349132
#191349092
#191347852
#191347842
#191346082
C43×#20002
#2413043