Finite Group Databasebeta

← #25116901

Subgroups — #25116901

Order 11008.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583047C211yesmaximal, characteristic
2C2×#14583002C211yesmaximal, characteristic, complemented
3C2×#14582894C211yesmaximal, characteristic, complemented
4#19137635C211yesmaximal, characteristic, complemented
5#19137433C211yesmaximal, characteristic, complemented
6#19135471C211yesmaximal, characteristic, complemented
7#19135293C211yesmaximal, characteristic, complemented
8#19135215C211yesmaximal, characteristic, complemented
9#19135022C211yesmaximal, characteristic, complemented
10#19134950C211yesmaximal, characteristic, complemented
11#19134944C211yesmaximal, characteristic, complemented
12#19134865C211yesmaximal, characteristic, complemented
13#19134795C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C43×#1763C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063300C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063283C2211yescharacteristic
24#14583047C418yescomplemented
25#14583002—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063257C2211yescharacteristic
28#14582894—24no—
29C2×#13063249C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37#14582801—21no—
38#14582801—21no—
39#14582801C2211yescharacteristic
40#14582801C2211yescharacteristic
41#14582800—21no—
42#14582800C2211yescharacteristic
43#14582798C2211yescharacteristic
44#14582791—21no—
45#14582777—21no—
46#14582756—21no—
47#14582756C2211yescharacteristic
48C4×(C2×D43)⋊C4—21no—
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621902—22no—
63C2×#10621902—22no—
64C2×#10621902—22no—
65C2×#10621902—41no—
66C2×#10621902—41no—
67C2×#10621902C2×C414yescomplemented
68C22×D172—21no—
69C22×D172—21no—
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C2×#10621884—22no—
76C2×#10621884—22no—
77C2×#10621884C2×C414yes—
78C2×D344—41no—
79C2×D344—41no—
80C2×D344C2×C414yes—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85C2×C8×D43—41no—
86#13063300—22no—
87#13063300C2×C414yes—
88Q8×Dic43—22no—
89Q8×Dic43—41no—
90#13063287—22no—
91#13063287—41no—
92#13063283—22no—
93#13063283—41no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4D411yescharacteristic
109C2×(C2×D43)⋊C4D411yescharacteristic
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43C2311yescharacteristic
113#13063258—22no—
114#13063257—41no—
115#13063249—22no—
116#13063247—22no—
117#13063247—22no—
118#13063245—22no—
119#13063245—41no—
120#13063245C2×C414yescomplemented
121(C2×D43)⋊C8C2×C414yescomplemented
122#13063235—22no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95D411yescharacteristic
126C43⋊#95D411yescharacteristic
127C22×Q8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C4×Q8×C43—22no—
131C4×Q8×C43—41no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43C2311yescharacteristic
139#103×C43C2×C414yescomplemented
140#103×C43D414yescomplemented
141#97×C43—41no—
142#95×C43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43C2×D411yescharacteristic
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C22×C412yes—
150C2×Q8×C43C2×D412yes—
151C2×Q8×C43#4112yes—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164#10621902—28no—
165#10621902—44no—
166#10621902—44no—
167#10621902—44no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—24no—
171C2×D172—24no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—42no—
181C2×D172—42no—
182C2×D172—81no—
183C2×D172—81no—
184C2×D172C22×C412yes—
185C2×D172C22×C412yes—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43—24no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—81no—
196C2×C4×D43C22×C412yes—
197C2×C4×D43#4112yes—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43C22×C412yes—
203C2×C8×C43C2×D412yes—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—42no—
209C4⋊C4×C43C22×C412yes—
210C4⋊C4×C43C2×D412yes—
211C42×C43—21no—
212C42×C43—21no—
213C42×C43—42no—
214C42×C43—81no—
215#10621884—28no—
216(C2×D43)⋊C4—24no—
217(C2×D43)⋊C4—41no—
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—42no—
220(C2×D43)⋊C4—42no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—81no—
225(C2×D43)⋊C4—81no—
226(C2×D43)⋊C4—81no—
227(C2×D43)⋊C4—81no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—42no—
233C4⋊Dic43—81no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—42no—
237C4×Dic43—42no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8C22×C412yes—
244D344—44no—
245C8×D43—44no—
246C23×C43C22×D411yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43C4×D412yes—
268Q8×C43—22no—
269Q8×C43—22no—
270Q8×C43—22no—
271Q8×C43C4×D414yes—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43H(5,𝔽2)11yescharacteristic
295C2×C4×C43H(5,𝔽2)11yescharacteristic
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43C4×D412yes—
311D172—22no—
312D172—22no—
313D172—22no—
314D172—22no—
315D172—48no—
316D172—41no—
317D172—41no—
318D172—41no—
319D172—41no—
320D172—84no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—48no—
326C4×D43—84no—
327C8×C43—22no—
328C8×C43—22no—
329C43⋊C8—22no—
330C43⋊C8—41no—
331#22857—431nomaximal, Sylow
332C22×C43C2×C4×D411yescharacteristic
333C22×C43D4211yescharacteristic
334C22×C43#54611yescharacteristic
335C22×C43#57511yescharacteristic
336C22×C43#57511yescharacteristic
337C22×C43#57611yescharacteristic
338C22×C43#57711yescharacteristic
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—41no—
343C2×D43—41no—
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—42no—
347C2×D43—42no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—81no—
353C2×D43—81no—
354C2×D43—81no—
355C2×D43—81no—
356C2×D43—81no—
357C2×D43—81no—
358C2×D43—81no—
359C2×D43—81no—
360C4×C43—24no—
361C4×C43—42no—
362C4×C43—42no—
363C4×C43—41no—
364C4×C43—41no—
365C4×C43—81no—
366C4×C43C2×C4×D411yescharacteristic
367C4×C43#51811yescharacteristic
368C4×C43#54611yescharacteristic
369C4×C43#55111yescharacteristic
370Dic43—22no—
371Dic43—41no—
372Dic43—41no—
373Dic43—81no—
374Dic43—81no—
375C2×#449—431no—
376C2×#440—431no—
377C2×#416—431no—
378#2363—431no—
379#2341—431no—
380#1972—431no—
381#1936—431no—
382#1925—431no—
383#1893—431no—
384#1880—431no—
385#1879—431no—
386#1865—431no—
387#1854—431no—
388#1763D4311yescharacteristic, complemented
389#1752—431no—
390C2×C43#235811yescharacteristic
391C2×C43#294311yescharacteristic
392C2×C43#294611yescharacteristic
393C2×C43#326811yescharacteristic
394C2×C43#327111yescharacteristic
395C2×C43#330911yescharacteristic
396C2×C43#332111yescharacteristic
397D43—42no—
398D43—82no—
399D43—82no—
400C22×#41—431no—
401C22×SD16—431no—
402C22×D8—431no—
403C23×C8—431no—
404C2×#121—431no—
405C2×C4×Q8—431no—
406C2×C4×Q8C2×D4311yescharacteristic
407C2×C4×D4—431no—
408C2×#117—431no—
409#449—438no—
410#440—864no—
411C2×#107—431no—
412C2×#106—431no—
413#416—864no—
414C2×#103—431no—
415C2×#103C2×D4311yescharacteristic
416C2×#103C2×D4311yescharacteristic
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×C22⋊C8—431no—
423C2×#97—431no—
424C2×#97C2×D4311yescharacteristic
425#390—431no—
426#390—431no—
427#390—431no—
428#390—861no—
429#390—861no—
430#390—861no—
431#389—431no—
432#388—861no—
433#386—861no—
434#380—431no—
435#380—861no—
436C4×C4⋊C4C2×D4311yescharacteristic
437C4×C22⋊C4—431no—
438C4×C22⋊C4—861no—
439C4×C22⋊C4—861no—
440#340—431no—
441#340—431no—
442#340C2×D4311yescharacteristic
443#340C2×D4311yescharacteristic
444#336—431no—
445#336—431no—
446C43#2285711yescharacteristic, complemented, Sylow
447C2×#41—434no—
448C2×#41—862no—
449C2×#41—862no—
450C2×#41—862no—
451C2×#41—1721no—
452C2×#41—1721no—
453C22×Q8C22×D4311yescharacteristic
454C22×D4—431no—
455C22×D4—431no—
456C22×D4—861no—
457C22×D4—861no—
458C23×C4—431no—
459C23×C4—861no—
460C23×C4—861no—
461C2×SD16—434no—
462C2×SD16—862no—
463C2×SD16—862no—
464C2×D8—434no—
465C2×D8—1721no—
466C2×D8—1721no—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8—862no—
470C22×C8—862no—
471C22×C8—1721no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474#121—434no—
475#121—862no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×Q8—862no—
479C4×Q8—1721no—
480C4×D4—862no—
481C4×D4—1721no—
482#117—862no—
483#117—1721no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4C22×D4311yescharacteristic
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C22⋊C4—431no—
493C2×C22⋊C4—431no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—431no—
507C2×C42—861no—
508C2×C42—861no—
509C2×C42C22×D4311yescharacteristic
510#107—862no—
511#106—1721no—
512#103—862no—
513#103C4×D4314yescomplemented
514#103D17214yescomplemented
515#102—434no—
516#102—862no—
517#102—862no—
518#102—862no—
519#102—1721no—
520C22⋊C8—434no—
521#97—41no—
522#97—862no—
523#95—21no—
524#95—431no—
525#95—431no—
526#95—861no—
527#95—861no—
528C24—431no—
529C24—861no—
530C24—861no—
531#41—868no—
532#41—1724no—
533#41—1724no—
534#41—1724no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×C4×D4312yes—
539C2×Q8C2×D17212yes—
540C2×Q8#1062189812yes—
541C2×D4—432no—
542C2×D4—432no—
543C2×D4—864no—
544C2×D4—864no—
545C2×D4—861no—
546C2×D4—861no—
547C2×D4—861no—
548C2×D4—861no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—3441no—
556C2×D4—3441no—
557C2×D4—1722no—
558C2×D4—1722no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—431no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—431no—
567C22×C4—431no—
568C22×C4—864no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—3441no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4D4×D4311yescharacteristic
581C22×C4D4×D4311yescharacteristic
582C22×C4C23×D4311yescharacteristic
583SD16—868no—
584D8—1724no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—432no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—1724no—
596C2×C8C2×C4×D4312yes—
597C2×C8C2×D17212yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—861no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—3441no—
608C4⋊C4—1722no—
609C4⋊C4C2×C4×D4312yes—
610C4⋊C4C2×D17212yes—
611C22⋊C4—864no—
612C22⋊C4—3441no—
613C22⋊C4—3441no—
614C22⋊C4—3441no—
615C22⋊C4—3441no—
616C22⋊C4—1721no—
617C22⋊C4—1721no—
618C22⋊C4—1722no—
619C22⋊C4—1722no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C42—21no—
624C42—21no—
625C42—42no—
626C42—81no—
627C42—861no—
628C42—861no—
629C42—1722no—
630C42—1722no—
631C23—432no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—862no—
639C23—862no—
640C23—1721no—
641C23—1721no—
642C23—1721no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23C2×D4×D4311yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8C4×D17214yes—
657D4—862no—
658D4—862no—
659D4—862no—
660D4—862no—
661D4—3444no—
662D4—1728no—
663D4—1721no—
664D4—1721no—
665D4—1721no—
666D4—1721no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—432no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—3444no—
699C2×C4—1728no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4C22×C4×D4311yescharacteristic
707C2×C4C22×D17211yescharacteristic
708C2×C4#41×D4311yescharacteristic
709C2×C4C2×#1062189811yescharacteristic
710C2×C4#1306337011yescharacteristic
711C2×C4#1306337111yescharacteristic
712C8—22no—
713C8—22no—
714C8—862no—
715C8—1721no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—3441no—
720C22—3441no—
721C22—3441no—
722C22—3441no—
723C22—3441no—
724C22—3441no—
725C22—3441no—
726C22—3441no—
727C22—1722no—
728C22—1722no—
729C22—1722no—
730C22—1722no—
731C22—1722no—
732C22—1722no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22C4×D4×D4311yescharacteristic
738C22D4×D17211yescharacteristic
739C22#1458353911yescharacteristic
740C22#1458369811yescharacteristic
741C22#1458369811yescharacteristic
742C22#1458370311yescharacteristic
743C22#1458370811yescharacteristic
744C4—24no—
745C4—42no—
746C4—41no—
747C4—41no—
748C4—42no—
749C4—81no—
750C4—862no—
751C4—3441no—
752C4—3441no—
753C4—1721no—
754C4—1721no—
755C4C2×C4×D17211yescharacteristic
756C4#1458337111yescharacteristic
757C4#1458354411yescharacteristic
758C4#1458357311yescharacteristic
759C2—3442no—
760C2—3442no—
761C2—1722no—
762C2#1913757711yescharacteristic
763C2#1914339411yescharacteristic
764C2#1914342611yescharacteristic
765C2#1914613711yescharacteristic
766C2#1914618211yescharacteristic
767C2#1914660211yescharacteristic
768C2#1914678211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1763C2
socleC23×C43C22×D4
prime radicalC2×#14583047C2
cosocleC22×C4×C43C24
hypercenter#1763D43
hypocenterC43#22857
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×#14583002C2semidirect
3. C2×#14582894C2semidirect
4. #19137635C2semidirect
5. #19137433C2semidirect
6. #19135471C2semidirect
7. #19135293C2semidirect
8. #19135215C2semidirect
9. #19135022C2semidirect
10. #19134950C2semidirect
11. #19134944C2semidirect
12. #19134865C2semidirect
13. #19134795C2semidirect
14. #19134372C2semidirect
15. C43×#1763C2semidirect
24. #14583047C4semidirect
67. C2×#10621902C2×C4semidirect
120. #13063245C2×C4semidirect
121. (C2×D43)⋊C8C2×C4semidirect
139. #103×C43C2×C4semidirect
140. #103×C43D4semidirect
388. #1763D43semidirect
446. C43#22857semidirect
513. #103C4×D43semidirect
514. #103D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145830472
C2×#145830022
C2×#145828942
#191376352
#191374332
#191354712
#191352932
#191352152
#191350222
#191349502
#191349442
#191348652
#191347952
#191343722
C43×#17632
#2285743