Finite Group Databasebeta

← #25112743

Subgroups — #25112743

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583584C211yesmaximal, characteristic
2#19137464C211yesmaximal, characteristic, complemented
3#19135580C211yesmaximal, characteristic, complemented
4#19135579C211yesmaximal, characteristic, complemented
5#19135053C212yesmaximal
6#19135051C212yesmaximal
7#19134670C212yesmaximal, complemented
8#19134580C211yesmaximal, characteristic
9C4×#13063239C211yesmaximal, characteristic
10#19134327C212yesmaximal, complemented
11C43×#2344C211yesmaximal, characteristic, complemented
12#14583584—22no—
13#14583584—21no—
14#14583584—21no—
15#14583584—21no—
16#14583584—22no—
17#14583584—21no—
18C2×#13063320C412yescomplemented
19C2×#13063316C411yescharacteristic, complemented
20C2×#13063315C412yescomplemented
21C2×#13063308C2212yes—
22C2×#13063305C411yescharacteristic, complemented
23C2×#13063304C2211yescharacteristic
24C2×#13063290C411yescharacteristic, complemented
25C2×C4×C22⋊D43C2211yescharacteristic
26C2×#13063284C2212yes—
27C2×#13063284C2212yes—
28C2×#13063283C411yescharacteristic, complemented
29C2×#13063239C2211yescharacteristic
30C2×#13063239C2211yescharacteristic
31C2×#13063239C2212yes—
32#14582798—21no—
33#14582785—22no—
34#14582762C2212yes—
35#14582759C2211yescharacteristic
36C4⋊C4×Dic43—21no—
37C4×C22⋊Dic43C2211yescharacteristic
38#14582665C2212yes—
39#14582665C2212yes—
40#14582665C2212yes—
41#14582665C2212yes—
42#14582665C2212yes—
43#14582665C2211yescharacteristic
44#14582665C2211yescharacteristic
45C2×#117×C43C2212yes—
46C22×C4⋊C4×C43C2211yescharacteristic
47C43×#389—21no—
48C43×#387—22no—
49C43×#381C2212yes—
50C43×#380C2211yescharacteristic
51C4×C4⋊C4×C43—21no—
52C4×C22⋊C4×C43C2211yescharacteristic
53C22×Dic86C2×C411yescharacteristic
54C22×C22⋊D43C2311yescharacteristic
55C22×C4×D43C2×C411yescharacteristic
56#13063320—22no—
57#13063320—22no—
58#13063320—22no—
59#13063320—22no—
60#13063316—22no—
61#13063316—21no—
62#13063316—21no—
63#13063315—22no—
64#13063315—22no—
65#13063315—22no—
66#13063315—22no—
67#13063308—22no—
68#13063308—22no—
69#13063308—22no—
70#13063308—22no—
71#13063305—22no—
72#13063305—21no—
73#13063305—21no—
74#13063304—21no—
75#13063304—21no—
76#13063304—21no—
77#13063304—21no—
78#13063290—22no—
79#13063290—21no—
80#13063290—21no—
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83C4×C22⋊D43—21no—
84C4×C22⋊D43—21no—
85#13063284—22no—
86#13063284—22no—
87#13063284—22no—
88#13063284—22no—
89#13063284—24no—
90#13063284—42no—
91#13063283—22no—
92#13063283—21no—
93#13063283—21no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43C2×C411yescharacteristic
97C2×C4⋊Dic43C2×C412yes—
98C2×C4⋊Dic43C2×C412yes—
99C2×Dic43⋊C4C2×C411yescharacteristic
100C2×Dic43⋊C4C2×C412yes—
101C2×Dic43⋊C4C2×C412yes—
102C2×Dic43⋊C4C2×C412yes—
103C2×C22⋊Dic43C2312yes—
104C2×C22⋊Dic43C2311yescharacteristic
105C2×C22⋊Dic43C2311yescharacteristic
106C2×C22⋊Dic43C2312yes—
107C2×C22⋊Dic43C2311yescharacteristic
108C2×(C2×D43)⋊C4C2×C412yes—
109C2×(C2×D43)⋊C4C2×C411yescharacteristic
110C2×(C2×D43)⋊C4C2×C412yes—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2×C412yes—
114C2×C4×Dic43C2×C412yes—
115C2×C4×Dic43C2×C411yescharacteristic
116#13063239—22no—
117#13063239—22no—
118#13063239—42no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—22no—
122C43⋊#95—22no—
123C23×C4×C43C2312yes—
124C23×C4×C43C2311yescharacteristic
125#117×C43—24no—
126#117×C43—42no—
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2×C411yescharacteristic
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2×C412yes—
132C2×C4⋊C4×C43D412yes—
133C2×C4⋊C4×C43D411yescharacteristic
134C2×C4⋊C4×C43D411yescharacteristic
135C2×C4⋊C4×C43D411yescharacteristic
136C2×C4⋊C4×C43D412yes—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C22⋊C4×C43C2312yes—
139C2×C22⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43C2311yescharacteristic
141C2×C42×C43—22no—
142C2×C42×C43—21no—
143#95×C43—21no—
144#95×C43—22no—
145#95×C43—21no—
146#95×C43—22no—
147C24×C43C2411yescharacteristic
148C23×D43C22×C411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—42no—
157C22×C4×C43C22×C412yes—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C412yes—
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2×D412yes—
166C22×C4×C43C2×D412yes—
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C2×C22⋊D43—21no—
170C2×C22⋊D43—21no—
171C2×C22⋊D43—21no—
172C2×C22⋊D43—21no—
173C2×C22⋊D43—21no—
174C2×C22⋊D43—21no—
175C22×Dic43—21no—
176C22×Dic43—21no—
177C22×Dic43—22no—
178C22×Dic43C22×C411yescharacteristic
179C22×Dic43C22×C411yescharacteristic
180C22×Dic43C22×C411yescharacteristic
181C22×Dic43C22×C412yes—
182C22×Dic43C22×C412yes—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—42no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—42no—
189C4⋊C4×C43—44no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43C22⋊C412yes—
192C4⋊C4×C43C22⋊C411yescharacteristic
193C4⋊C4×C43C22⋊C411yescharacteristic
194C4⋊C4×C43C22⋊C412yes—
195C4⋊C4×C43C22⋊C411yescharacteristic
196C4⋊C4×C43C22⋊C411yescharacteristic
197C4⋊C4×C43C22⋊C412yes—
198C4⋊C4×C43C22⋊C412yes—
199C4⋊C4×C43C22⋊C412yes—
200C4⋊C4×C43C22⋊C412yes—
201C22⋊C4×C43—22no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—22no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43#4112yes—
207C42×C43—44no—
208C42×C43—42no—
209C22⋊Dic43—21no—
210C22⋊Dic43—21no—
211C22⋊Dic43—22no—
212C22⋊Dic43—22no—
213C22⋊Dic43—21no—
214C22⋊Dic43—22no—
215C22⋊Dic43—21no—
216C22⋊Dic43—22no—
217C22⋊Dic43—21no—
218C22⋊Dic43#4112yes—
219(C2×D43)⋊C4—22no—
220(C2×D43)⋊C4—22no—
221(C2×D43)⋊C4—21no—
222(C2×D43)⋊C4—21no—
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—22no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—22no—
228C4⋊Dic43—22no—
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—44no—
232C4⋊Dic43—42no—
233Dic43⋊C4—21no—
234Dic43⋊C4—21no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238Dic43⋊C4—22no—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241C4×Dic43—22no—
242C4×Dic43—22no—
243C4×Dic43—22no—
244C4×Dic43—22no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247C4×Dic43—44no—
248C4×Dic43—42no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43C23×C411yescharacteristic
252C23×C43C22×D411yescharacteristic
253C23×C43C22×D411yescharacteristic
254C23×C43C2×#4111yescharacteristic
255C23×C43C2×#4111yescharacteristic
256C23×C43H(5,𝔽2)11yescharacteristic
257C23×C432−1+411yescharacteristic
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—41no—
262C22×D43—41no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—22no—
268C2×C4×C43—22no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—42no—
286C2×C4×C43—41no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43—41no—
290C2×C4×C43C2×C22⋊C412yes—
291C2×C4×C43C2×C22⋊C412yes—
292C2×C4×C43C2×C22⋊C411yescharacteristic
293C2×C4×C43C2×C22⋊C411yescharacteristic
294C2×C4×C43C2×C22⋊C411yescharacteristic
295C2×C4×C43C2×C22⋊C412yes—
296C2×C4×C43C2×C22⋊C412yes—
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C22⋊D43—41no—
299C22⋊D43—41no—
300C22⋊D43—41no—
301C22⋊D43—41no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—22no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—42no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—42no—
316C2×Dic43—41no—
317C2×Dic43—42no—
318C2×Dic43—41no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—41no—
322C4×D43—42no—
323C4×D43—42no—
324Dic86—42no—
325Dic86—42no—
326#22478—431nomaximal, Sylow
327C22×C43—21no—
328C22×C43—21no—
329C22×C43—21no—
330C22×C43—21no—
331C22×C43—21no—
332C22×C43—21no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43C22×C22⋊C411yescharacteristic
338C22×C43C4×#4111yescharacteristic
339C22×C43#52011yescharacteristic
340C22×C43#54611yescharacteristic
341C22×C43#54611yescharacteristic
342C22×C43#54711yescharacteristic
343C22×C43#54711yescharacteristic
344C2×D43—41no—
345C2×D43—41no—
346C2×D43—41no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—22no—
350C4×C43—22no—
351C4×C43—22no—
352C4×C43—22no—
353C4×C43—21no—
354C4×C43—21no—
355C4×C43—21no—
356C4×C43—42no—
357C4×C43—82no—
358C4×C43—81no—
359C4×C43#41012yes—
360Dic43—42no—
361Dic43—41no—
362Dic43—42no—
363Dic43—41no—
364Dic43—41no—
365Dic43—42no—
366Dic43—82no—
367Dic43—81no—
368C2×#552—431no—
369#2344—431no—
370#2344D4311yescharacteristic, complemented
371#1996—431no—
372#1996—431no—
373#1899—432no—
374#1899—432no—
375#1820—432no—
376#1799—431no—
377C4×#99—431no—
378#1740—432no—
379C2×C43—21no—
380C2×C43—21no—
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43#233911yescharacteristic
386C2×C43C2×#41011yescharacteristic
387C2×C43#288411yescharacteristic
388D43—81no—
389#552—861no—
390#552—862no—
391#552—861no—
392#552—861no—
393#552—862no—
394#552—861no—
395C2×#126—432no—
396C2×#125—432no—
397C2×#125—431no—
398C2×#123—432no—
399C2×C22⋊Q8—431no—
400C2×C22⋊Q8—431no—
401C2×C4×Q8—431no—
402C2×C4×D4—431no—
403C2×#117—432no—
404C2×#117—431no—
405C2×#117—432no—
406C2×#117C2×D4312yes—
407C22×C4⋊C4C2×D4311yescharacteristic
408C2×#99—431no—
409C2×#99—431no—
410C2×#99—432no—
411#389—21no—
412#389—861no—
413#387—22no—
414#387—862no—
415#381—432no—
416#381C2×D4312yes—
417#380—431no—
418#380C2×D4311yescharacteristic
419C4×C4⋊C4—21no—
420C4×C4⋊C4—861no—
421C4×C22⋊C4—431no—
422C4×C22⋊C4C2×D4311yescharacteristic
423#342—432no—
424#342—431no—
425#342—432no—
426#342—432no—
427#342—432no—
428#342—432no—
429#342—431no—
430C43#2247811yescharacteristic, complemented, Sylow
431C22×Q8—431no—
432C22×D4—431no—
433C23×C4—431no—
434C23×C4C22×D4312yes—
435C23×C4C22×D4311yescharacteristic
436#126—862no—
437#126—862no—
438#126—862no—
439#126—862no—
440#125—862no—
441#125—862no—
442#125—862no—
443#125—862no—
444#125—862no—
445#125—861no—
446#125—861no—
447#123—862no—
448#123—862no—
449#123—862no—
450#123—862no—
451C22⋊Q8—861no—
452C22⋊Q8—861no—
453C22⋊Q8—861no—
454C22⋊Q8—861no—
455C22⋊Q8—862no—
456C22⋊Q8—861no—
457C22⋊Q8—861no—
458C4×Q8—862no—
459C4×Q8—861no—
460C4×Q8—861no—
461C4×D4—861no—
462C4×D4—861no—
463C4×D4—861no—
464C4×D4—861no—
465#117—24no—
466#117—42no—
467#117—862no—
468#117—862no—
469#117—862no—
470#117—862no—
471#117—862no—
472#117—861no—
473#117—861no—
474#117—864no—
475#117—1722no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—432no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—432no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4—432no—
483C2×C4⋊C4—432no—
484C2×C4⋊C4—432no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—861no—
487C2×C4⋊C4C4×D4311yescharacteristic
488C2×C4⋊C4C4×D4311yescharacteristic
489C2×C4⋊C4C4×D4312yes—
490C2×C4⋊C4D17211yescharacteristic
491C2×C4⋊C4D17212yes—
492C2×C4⋊C4D17211yescharacteristic
493C2×C4⋊C4C22⋊D4311yescharacteristic
494C2×C4⋊C4C22⋊D4312yes—
495C2×C4⋊C4C22⋊D4311yescharacteristic
496C2×C22⋊C4—431no—
497C2×C22⋊C4—431no—
498C2×C22⋊C4—432no—
499C2×C22⋊C4—432no—
500C2×C22⋊C4—431no—
501C2×C22⋊C4—432no—
502C2×C22⋊C4—432no—
503C2×C22⋊C4—431no—
504C2×C22⋊C4C22×D4312yes—
505C2×C22⋊C4C22×D4311yescharacteristic
506C2×C22⋊C4C22×D4311yescharacteristic
507C2×C42—22no—
508C2×C42—21no—
509C2×C42—432no—
510C2×C42—432no—
511C2×C42—431no—
512C2×C42—862no—
513C2×C42—861no—
514#99—862no—
515#99—862no—
516#99—1722no—
517#95—21no—
518#95—22no—
519#95—21no—
520#95—22no—
521#95—861no—
522#95—862no—
523#95—861no—
524#95—862no—
525C24—431no—
526C24C23×D4311yescharacteristic
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—1722no—
530C2×D4—861no—
531C2×D4—861no—
532C2×D4—861no—
533C2×D4—861no—
534C2×D4—861no—
535C2×D4—861no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—42no—
544C22×C4—431no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—862no—
554C22×C4—1722no—
555C22×C4C2×C4×D4312yes—
556C22×C4C2×C4×D4311yescharacteristic
557C22×C4C2×C4×D4312yes—
558C22×C4C2×C4×D4311yescharacteristic
559C22×C4C2×D17212yes—
560C22×C4C2×D17212yes—
561C22×C4C2×D17211yescharacteristic
562C22×C4C2×D17211yescharacteristic
563C22×C4C2×C22⋊D4312yes—
564C22×C4C2×C22⋊D4312yes—
565C22×C4C2×C22⋊D4311yescharacteristic
566C22×C4C2×C22⋊D4311yescharacteristic
567C4⋊C4—44no—
568C4⋊C4—42no—
569C4⋊C4—862no—
570C4⋊C4—862no—
571C4⋊C4—861no—
572C4⋊C4—861no—
573C4⋊C4—862no—
574C4⋊C4—862no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—862no—
578C4⋊C4—862no—
579C4⋊C4—862no—
580C4⋊C4—862no—
581C4⋊C4—862no—
582C4⋊C4—862no—
583C4⋊C4—1724no—
584C4⋊C4—1722no—
585C4⋊C4(C2×D43)⋊C412yes—
586C4⋊C4(C2×D43)⋊C411yescharacteristic
587C4⋊C4(C2×D43)⋊C411yescharacteristic
588C4⋊C4(C2×D43)⋊C412yes—
589C4⋊C4(C2×D43)⋊C411yescharacteristic
590C4⋊C4(C2×D43)⋊C411yescharacteristic
591C4⋊C4(C2×D43)⋊C412yes—
592C4⋊C4(C2×D43)⋊C412yes—
593C4⋊C4(C2×D43)⋊C412yes—
594C4⋊C4(C2×D43)⋊C412yes—
595C22⋊C4—21no—
596C22⋊C4—21no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—432no—
601C22⋊C4—861no—
602C22⋊C4—862no—
603C22⋊C4—861no—
604C22⋊C4—862no—
605C22⋊C4—861no—
606C22⋊C4—862no—
607C22⋊C4—862no—
608C22⋊C4—861no—
609C22⋊C4—861no—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—862no—
613C22⋊C4—861no—
614C22⋊C4—862no—
615C22⋊C4—861no—
616C22⋊C4#1062190012yes—
617C42—44no—
618C42—42no—
619C42—862no—
620C42—862no—
621C42—862no—
622C42—862no—
623C42—861no—
624C42—861no—
625C42—1724no—
626C42—1722no—
627C23—41no—
628C23—41no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—1721no—
633C23—1721no—
634C23C22×C4×D4311yescharacteristic
635C23C22×C22⋊D4311yescharacteristic
636C23C22×D17211yescharacteristic
637C23#41×D4311yescharacteristic
638C23C2×#1062190011yescharacteristic
639C23#1306337011yescharacteristic
640C23#1306337211yescharacteristic
641Q8—1722no—
642Q8—1722no—
643D4—1721no—
644D4—1721no—
645D4—1721no—
646D4—1721no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—862no—
682C2×C4—1722no—
683C2×C4—1721no—
684C2×C4—1722no—
685C2×C4—1721no—
686C2×C4—1722no—
687C2×C4—1721no—
688C2×C4—1722no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1722no—
692C2×C4—1721no—
693C2×C4—1722no—
694C2×C4—1721no—
695C2×C4—1722no—
696C2×C4C2×(C2×D43)⋊C412yes—
697C2×C4C2×(C2×D43)⋊C412yes—
698C2×C4C2×(C2×D43)⋊C411yescharacteristic
699C2×C4C2×(C2×D43)⋊C411yescharacteristic
700C2×C4C2×(C2×D43)⋊C411yescharacteristic
701C2×C4C2×(C2×D43)⋊C412yes—
702C2×C4C2×(C2×D43)⋊C412yes—
703C2×C4C2×(C2×D43)⋊C411yescharacteristic
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—3441no—
715C22—3441no—
716C22—1721no—
717C22—1721no—
718C22—1721no—
719C22C22×(C2×D43)⋊C411yescharacteristic
720C22C4×#1062190011yescharacteristic
721C22#1458337811yescharacteristic
722C22#1458354311yescharacteristic
723C22#1458354411yescharacteristic
724C22#1458354811yescharacteristic
725C22#1458355311yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—42no—
734C4—82no—
735C4—81no—
736C4—3442no—
737C4—3441no—
738C4—1722no—
739C4—1721no—
740C4—1722no—
741C4—1721no—
742C4—1721no—
743C4—1722no—
744C4#1458287212yes—
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—21no—
750C2—21no—
751C2—3441no—
752C2#1913742011yescharacteristic
753C2C2×#1458287211yescharacteristic
754C2#1914305811yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2344C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C23
cosocleC24×C43C24
hypercenter#2344D43
hypocenterC43#22478
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
2. #19137464C2semidirect
3. #19135580C2semidirect
4. #19135579C2semidirect
7. #19134670C2semidirect
10. #19134327C2semidirect
11. C43×#2344C2semidirect
18. C2×#13063320C4semidirect
19. C2×#13063316C4semidirect
20. C2×#13063315C4semidirect
22. C2×#13063305C4semidirect
24. C2×#13063290C4semidirect
28. C2×#13063283C4semidirect
370. #2344D43semidirect
430. C43#22478semidirect

Maximal subgroups

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

subgroupindex
C2×#145835842
#191374642
#191355802
#191355792
#191350532
#191350512
#191346702
#191345802
C4×#130632392
#191343272
C43×#23442
#2247843