Finite Group Databasebeta

← #25130775

Subgroups — #25130775

Order 11008.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583587C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3#19139513C211yesmaximal, characteristic
4#19135800C211yesmaximal, characteristic, complemented
5#19135793C211yesmaximal, characteristic, complemented
6#19135604C211yesmaximal, characteristic, complemented
7#19135604C211yesmaximal, characteristic, complemented
8#19135565C211yesmaximal, characteristic, complemented
9#19135392C211yesmaximal, characteristic
10#19134904C211yesmaximal, characteristic, complemented
11#19134899C211yesmaximal, characteristic, complemented
12#19134791C211yesmaximal, characteristic, complemented
13#19134786C211yesmaximal, characteristic, complemented
14#19134601C211yesmaximal, characteristic, complemented
15C2×C43×#479C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17#14583587—24no—
18#14583587—24no—
19C2×#13063320—21no—
20C2×#13063316—21no—
21C2×#13063310—21no—
22C2×#13063305C2211yescharacteristic
23C2×#13063305C2211yescharacteristic
24C2×#13063301C2211yescharacteristic
25C2×#13063301C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063283—21no—
29C2×#13063283C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31#14583004—24no—
32C2×#13063256C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42#14582821—21no—
43#14582821—21no—
44#14582801—21no—
45#14582797—21no—
46#14582769C2211yescharacteristic
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C43×#479—24no—
58C2×#107×C43C2211yescharacteristic
59C2×#106×C43C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×#103×C43C2211yescharacteristic
62C2×#103×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172D411yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43C2311yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063320—28no—
74#13063316—28no—
75#13063310—28no—
76#13063305—22no—
77#13063305—22no—
78#13063305—22no—
79#13063305—22no—
80#13063301—22no—
81#13063301—22no—
82#13063301—41no—
83#13063301—41no—
84C4×Dic86—22no—
85C4×Dic86D414yes—
86C4×D172—22no—
87C4×D172—22no—
88#13063283—28no—
89#13063283—22no—
90#13063283—22no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43D411yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C4⋊C4×D43—22no—
104C4⋊C4×D43—22no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×(C2×D43)⋊C4—21no—
110C2×(C2×D43)⋊C4—21no—
111C2×(C2×D43)⋊C4—21no—
112C2×(C2×D43)⋊C4D411yescharacteristic
113C2×(C2×D43)⋊C4D411yescharacteristic
114C2×C4×Dic43—21no—
115C2×C4×Dic43—21no—
116#13063256—22no—
117#13063250—41no—
118#13063250—41no—
119#13063249—22no—
120#13063248—22no—
121(C2×D43)⋊C8—22no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—41no—
124(C2×D43)⋊C8—41no—
125#13063236—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C22×Q8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131#125×C43—22no—
132#125×C43D414yes—
133C4×Q8×C43—22no—
134C4×Q8×C43—22no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C42×C43—21no—
142C2×C42×C43C2311yescharacteristic
143#107×C43—22no—
144#106×C43—22no—
145C4⋊C8×C43—22no—
146#103×C43—22no—
147#103×C43—22no—
148C23×D43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43#4112yes—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×D172—22no—
170C2×D172—22no—
171C2×D172—41no—
172C2×C4×D43—24no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86C2×D412yes—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C4⋊C4×C43—24no—
200C4⋊C4×C43—24no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—42no—
206C4⋊C4×C43C2×D412yes—
207C4⋊C4×C43C2×D412yes—
208C42×C43—42no—
209C42×C43C2×D412yes—
210C42×C43C2×D412yes—
211#10621885—28no—
212(C2×D43)⋊C4—24no—
213(C2×D43)⋊C4—24no—
214(C2×D43)⋊C4—24no—
215(C2×D43)⋊C4—22no—
216(C2×D43)⋊C4—22no—
217(C2×D43)⋊C4—42no—
218(C2×D43)⋊C4—42no—
219(C2×D43)⋊C4—81no—
220(C2×D43)⋊C4—81no—
221C4⋊Dic43—24no—
222C4⋊Dic43—24no—
223C4⋊Dic43—22no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—42no—
230C4⋊Dic43—81no—
231C4⋊Dic43C2×D412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234Dic43⋊C4—42no—
235Dic43⋊C4—42no—
236C4×Dic43—24no—
237C4×Dic43—24no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8#4112yes—
244C23×C43C22×D411yescharacteristic
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43#13712yes—
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—41no—
262Q8×C43—41no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43#12012yes—
280C2×C4×C43#12012yes—
281C2×C4×C43C22×D411yescharacteristic
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C432−1+411yescharacteristic
287C2×Dic43—22no—
288C2×Dic43—21no—
289C2×Dic43—22no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305D172—44no—
306C4×D43—48no—
307C4×D43—41no—
308C4×D43—41no—
309C4×D43—41no—
310C4×D43—41no—
311C4×D43—41no—
312C4×D43—41no—
313C4×D43—41no—
314C4×D43—41no—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319C8×C43—41no—
320C8×C43—41no—
321C43⋊C8—22no—
322C43⋊C8—41no—
323#24139—431nomaximal, Sylow
324C22×C43C2×#12011yescharacteristic
325C22×C43#54611yescharacteristic
326C22×C43#54711yescharacteristic
327C22×C43C2×#13711yescharacteristic
328C22×C43#57511yescharacteristic
329C22×C43#57711yescharacteristic
330C22×C43#57811yescharacteristic
331C2×D43—22no—
332C2×D43—22no—
333C2×D43—22no—
334C2×D43—41no—
335C2×D43—41no—
336C2×D43—41no—
337C2×D43—41no—
338C2×D43—41no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—42no—
348C4×C43—42no—
349C4×C43—42no—
350C4×C43—81no—
351C4×C43#52511yescharacteristic
352C4×C43#53711yescharacteristic
353C4×C43#54811yescharacteristic
354C4×C43#55011yescharacteristic
355Dic43—42no—
356Dic43—41no—
357Dic43—41no—
358Dic43—42no—
359Dic43—81no—
360Dic43—81no—
361C2×#552—431no—
362C2×#479D4311yescharacteristic, complemented
363C2×#441—431no—
364#2538—431no—
365#2036—431no—
366#2035—431no—
367#2001—431no—
368#2001—431no—
369#1992—431no—
370#1955—431no—
371#1873—431no—
372#1872—431no—
373#1854—431no—
374#1853—431no—
375#1803—431no—
376C2×C43#240711yescharacteristic
377C2×C43#300711yescharacteristic
378C2×C43#301311yescharacteristic
379C2×C43#331211yescharacteristic
380C2×C43#331711yescharacteristic
381C2×C43#334411yescharacteristic
382C2×C43#334911yescharacteristic
383D43—42no—
384D43—81no—
385C22×Q16—431no—
386#552—864no—
387#552—864no—
388C2×#126—861no—
389C2×#125—861no—
390C2×#125C2×D4311yescharacteristic
391C2×#123—861no—
392C2×C22⋊Q8—431no—
393C2×C22⋊Q8—431no—
394C2×C22⋊Q8—431no—
395C2×C22⋊Q8—431no—
396C2×C4×Q8—431no—
397C2×C4×Q8C2×D4311yescharacteristic
398C2×C4×D4—431no—
399C2×#117—431no—
400C2×#117—861no—
401C22×C4⋊C4—431no—
402#479—24no—
403#441—864no—
404C2×#107C2×D4311yescharacteristic
405C2×#106—431no—
406C2×#106C2×D4311yescharacteristic
407C2×C4⋊C8C2×D4311yescharacteristic
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103C2×D4311yescharacteristic
413C2×#103C2×D4311yescharacteristic
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×#97—431no—
419#396—861no—
420#396—861no—
421#390—861no—
422#389—861no—
423#384—431no—
424#380—431no—
425#380—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432C43#2413911yescharacteristic, complemented, Sylow
433C22×Q8—431no—
434C22×Q8C22×D4311yescharacteristic
435C22×D4—431no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—861no—
439C2×Q16—862no—
440C2×Q16—862no—
441C2×Q16—862no—
442C22×C8—431no—
443C22×C8—431no—
444C22×C8C22×D4311yescharacteristic
445C22×C8C22×D4311yescharacteristic
446#126—868no—
447#125—22no—
448#125—868no—
449#125C22⋊D4314yes—
450#123—868no—
451C22⋊Q8—862no—
452C22⋊Q8—862no—
453C22⋊Q8—862no—
454C22⋊Q8—862no—
455C22⋊Q8—862no—
456C22⋊Q8—862no—
457C22⋊Q8—1721no—
458C22⋊Q8—1721no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—434no—
462C4×Q8—862no—
463C4×D4—862no—
464C4×D4—862no—
465#117—862no—
466#117—868no—
467#117—862no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—862no—
476C2×C4⋊C4—861no—
477C2×C4⋊C4—861no—
478C2×C4⋊C4—861no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—862no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C22⋊C4—431no—
489C2×C22⋊C4—431no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C42—21no—
498C2×C42—861no—
499C2×C42—861no—
500C2×C42C22×D4311yescharacteristic
501#107—22no—
502#106—22no—
503#106—862no—
504C4⋊C8—22no—
505#103—22no—
506#103—22no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#103—1721no—
511C22⋊C8—862no—
512C22⋊C8—862no—
513C22⋊C8—1721no—
514C22⋊C8—1721no—
515#97—862no—
516#95—861no—
517#95—861no—
518C24—431no—
519C24—431no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—432no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8#1062190212yes—
532C2×D4—862no—
533C2×D4—862no—
534C2×D4—1721no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—431no—
540C22×C4—431no—
541C22×C4—864no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4D4×D4311yescharacteristic
561C22×C4D4×D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563Q16—868no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—432no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—432no—
584C4⋊C4—864no—
585C4⋊C4—864no—
586C4⋊C4—864no—
587C4⋊C4—862no—
588C4⋊C4—864no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—861no—
593C4⋊C4—861no—
594C4⋊C4—3441no—
595C4⋊C4—1722no—
596C4⋊C4—1722no—
597C4⋊C4—1722no—
598C4⋊C4C2×C22⋊D4312yes—
599C4⋊C4C2×C22⋊D4312yes—
600C22⋊C4—864no—
601C22⋊C4—864no—
602C22⋊C4—864no—
603C22⋊C4—862no—
604C22⋊C4—862no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C42—42no—
610C42—864no—
611C42—864no—
612C42D4×D4312yes—
613C42C2×C22⋊D4312yes—
614C23—432no—
615C23—861no—
616C23—861no—
617C23—861no—
618C23—861no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23C2×D4×D4311yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—862no—
634Q8—862no—
635Q8—1721no—
636Q8—1721no—
637D4—1724no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—862no—
655C2×C4—861no—
656C2×C4—862no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—861no—
661C2×C4—861no—
662C2×C4—1728no—
663C2×C4—1721no—
664C2×C4—1721no—
665C2×C4—1721no—
666C2×C4—1721no—
667C2×C4—1721no—
668C2×C4—1721no—
669C2×C4—1721no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4#1306329312yes—
682C2×C4#1306329312yes—
683C2×C4C2×D4×D4311yescharacteristic
684C2×C4C22×C22⋊D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4C2×#1062190211yescharacteristic
687C2×C4#1306337111yescharacteristic
688C2×C4#1306337311yescharacteristic
689C8—41no—
690C8—41no—
691C8—862no—
692C8—1721no—
693C22—862no—
694C22—862no—
695C22—862no—
696C22—1721no—
697C22—1721no—
698C22—1721no—
699C22—1721no—
700C22—1721no—
701C22—1721no—
702C22—1721no—
703C22—1721no—
704C22—1721no—
705C22—1721no—
706C22—1721no—
707C22C2×#1306329311yescharacteristic
708C22#1458354011yescharacteristic
709C22#1458355111yescharacteristic
710C22#137×D4311yescharacteristic
711C22#1458369811yescharacteristic
712C22#1458370611yescharacteristic
713C22#1458371311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—81no—
720C4—3441no—
721C4—3441no—
722C4—1721no—
723C4—1721no—
724C4—1722no—
725C4—1722no—
726C4#1458341211yescharacteristic
727C4#1458347911yescharacteristic
728C4#1458356011yescharacteristic
729C4#1458356811yescharacteristic
730C2—3441no—
731C2—1722no—
732C2#1913794211yescharacteristic
733C2#1914385111yescharacteristic
734C2#1914390611yescharacteristic
735C2#1914664311yescharacteristic
736C2#1914671811yescharacteristic
737C2#1914705711yescharacteristic
738C2#1914713211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenterC2×#479D43
hypocenterC43#24139
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
4. #19135800C2semidirect
5. #19135793C2semidirect
6. #19135604C2semidirect
7. #19135604C2semidirect
8. #19135565C2semidirect
10. #19134904C2semidirect
11. #19134899C2semidirect
12. #19134791C2semidirect
13. #19134786C2semidirect
14. #19134601C2semidirect
15. C2×C43×#479C2semidirect
362. C2×#479D43semidirect
432. C43#24139semidirect

Maximal subgroups

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

subgroupindex
C2×#145835872
C2×#145830042
#191395132
#191358002
#191357932
#191356042
#191355652
#191353922
#191349042
#191348992
#191347912
#191347862
#191346012
C2×C43×#4792
#2413943