Finite Group Databasebeta

← #25113151

Subgroups — #25113151

Order 11008.

1114 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic
2#19137474C211yesmaximal, characteristic, complemented
3#19137470C211yesmaximal, characteristic, complemented
4#19135581C211yesmaximal, characteristic, complemented
5#19135578C212yesmaximal, complemented
6#19135578C212yesmaximal, complemented
7#19134582C212yesmaximal
8#19134580C211yesmaximal, characteristic
9C4×#13063239C211yesmaximal, characteristic
10#19134382C212yesmaximal
11C43×#1996C211yesmaximal, characteristic, complemented
12#14583607—22no—
13#14583607—21no—
14#14583607—21no—
15#14583607—21no—
16#14583607—21no—
17#14583607—22no—
18C2×#13063324C411yescharacteristic, complemented
19C2×#13063315C412yescomplemented
20C2×#13063305C412yescomplemented
21C2×#13063302C2212yes—
22C2×#13063301C411yescharacteristic, complemented
23C2×Q8×Dic43C411yescharacteristic, complemented
24C2×C4×C22⋊D43C2211yescharacteristic
25C2×(C22⋊D43)⋊C4C2212yes—
26C22×C4⋊Dic43C2211yescharacteristic
27C2×C4⋊C4×D43C411yescharacteristic, complemented
28C2×#13063239C2212yes—
29C2×#13063239C2211yescharacteristic
30C2×#13063239C2211yescharacteristic
31#14582797—21no—
32#14582795—21no—
33#14582784—22no—
34#14582782—22no—
35#14582759C2211yescharacteristic
36#14582757C2212yes—
37#14582757C2212yes—
38C4⋊C4×Dic43—21no—
39C4×C4⋊Dic43—21no—
40C22⋊C4×Dic43C2212yes—
41C22⋊C4×Dic43C2212yes—
42C4×C22⋊Dic43C2211yescharacteristic
43#14582666C2212yes—
44#14582666C2212yes—
45#14582665C2212yes—
46#14582665C2211yescharacteristic
47#14582665C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C43×#380C2211yescharacteristic
50C4×C22⋊C4×C43C2211yescharacteristic
51C43×#342C2212yes—
52C43×#342C2212yes—
53C22×Dic86C2×C412yes—
54C22×C22⋊D43C2311yescharacteristic
55C23×Dic43C2312yes—
56C22×C4×D43C2×C411yescharacteristic
57C22×C4×D43C2×C412yes—
58#13063324—22no—
59#13063324—21no—
60#13063324—21no—
61#13063315—22no—
62#13063315—22no—
63#13063315—22no—
64#13063315—22no—
65#13063305—22no—
66#13063305—22no—
67#13063305—22no—
68#13063305—22no—
69#13063302—22no—
70#13063302—22no—
71#13063302—22no—
72#13063302—22no—
73#13063301—22no—
74#13063301—21no—
75#13063301—21no—
76Q8×Dic43—22no—
77Q8×Dic43—21no—
78Q8×Dic43—21no—
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81C4×C22⋊D43—21no—
82C4×C22⋊D43—21no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86(C22⋊D43)⋊C4—22no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2×C412yes—
89C2×C4⋊Dic43C2×C411yescharacteristic
90C2×C4⋊Dic43C2×C411yescharacteristic
91C2×C4⋊Dic43C2×C412yes—
92C2×C4⋊Dic43D412yes—
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43D411yescharacteristic
95C2×C4⋊Dic43D411yescharacteristic
96C2×C4⋊Dic43D411yescharacteristic
97C2×C4⋊Dic43D412yes—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4C2×C412yes—
101C2×Dic43⋊C4C2×C412yes—
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C412yes—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—21no—
106C4⋊C4×D43—21no—
107C2×C22⋊Dic43C2311yescharacteristic
108C2×C22⋊Dic43C2312yes—
109C2×C22⋊Dic43C2311yescharacteristic
110C2×C22⋊Dic43C2311yescharacteristic
111C2×(C2×D43)⋊C4C2×C412yes—
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×C4×Dic43—21no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43—22no—
116C2×C4×Dic43C2×C412yes—
117C2×C4×Dic43C2×C411yescharacteristic
118#13063239—24no—
119#13063239—22no—
120#13063239Q814yescomplemented
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—22no—
124C43⋊#95—22no—
125C43⋊#95—22no—
126C43⋊#95—22no—
127C22×Q8×C43C2×C411yescharacteristic
128C23×C4×C43C2311yescharacteristic
129C22⋊Q8×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2×C411yescharacteristic
135C2×C4⋊C4×C43C2×C412yes—
136C2×C22⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43C2312yes—
138C2×C22⋊C4×C43C2312yes—
139C2×C22⋊C4×C43C2311yescharacteristic
140C2×C42×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143C24×C43C2411yescharacteristic
144C23×D43C22×C411yescharacteristic
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—42no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—42no—
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C22×C412yes—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C22×C411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2×D411yescharacteristic
159C22×C4×C43C2×D411yescharacteristic
160C2×C22⋊D43—21no—
161C2×C22⋊D43—21no—
162C2×C22⋊D43—21no—
163C2×C22⋊D43—21no—
164C2×C22⋊D43C2×Q812yes—
165C2×C22⋊D43#4112yes—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—22no—
169C22×Dic43—82no—
170C22×Dic43C22×C411yescharacteristic
171C22×Dic43C22×C411yescharacteristic
172C22×Dic43C22×C411yescharacteristic
173C22×Dic43C22×C412yes—
174C22×Dic43C22×C412yes—
175C22×Dic43C2×D412yes—
176C22×Dic43C2×D412yes—
177C22×Dic43C2×D412yes—
178C22×Dic43C2×D412yes—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—22no—
182C2×C4×D43—22no—
183C2×C4×D43—42no—
184C2×C4×D43—82no—
185C2×Dic86—22no—
186C2×Dic86—22no—
187C2×Dic86—82no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—22no—
191C4⋊C4×C43—22no—
192C4⋊C4×C43—42no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—21no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—21no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—21no—
200C22⋊C4×C43C2×Q812yes—
201C42×C43—42no—
202C22⋊Dic43—21no—
203C22⋊Dic43—21no—
204C22⋊Dic43—21no—
205C22⋊Dic43—22no—
206C22⋊Dic43—21no—
207C22⋊Dic43—21no—
208C22⋊Dic43—22no—
209C22⋊Dic43C2×Q812yes—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—21no—
212(C2×D43)⋊C4—22no—
213(C2×D43)⋊C4—22no—
214C4⋊Dic43—22no—
215C4⋊Dic43—22no—
216C4⋊Dic43—42no—
217C4⋊Dic43C22⋊C412yes—
218C4⋊Dic43C22⋊C411yescharacteristic
219C4⋊Dic43C22⋊C411yescharacteristic
220C4⋊Dic43C22⋊C412yes—
221C4⋊Dic43C22⋊C411yescharacteristic
222C4⋊Dic43C22⋊C411yescharacteristic
223C4⋊Dic43C22⋊C412yes—
224C4⋊Dic43C22⋊C412yes—
225C4⋊Dic43C22⋊C412yes—
226C4⋊Dic43C22⋊C412yes—
227Dic43⋊C4—21no—
228Dic43⋊C4—21no—
229Dic43⋊C4—22no—
230Dic43⋊C4—22no—
231Dic43⋊C4—22no—
232Dic43⋊C4—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—82no—
236Dic43⋊C4—82no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43—42no—
242C4×Dic43—82no—
243C4×Dic43—82no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43C23×C411yescharacteristic
247C23×C43C22×D411yescharacteristic
248C23×C43C22×D411yescharacteristic
249C23×C43C22×Q811yescharacteristic
250C23×C43C2×#4111yescharacteristic
251C23×C432−1+411yescharacteristic
252C23×C432−1+411yescharacteristic
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43C4×Q812yes—
258Q8×C43—42no—
259Q8×C43—42no—
260C2×C4×C43—22no—
261C2×C4×C43—22no—
262C2×C4×C43—22no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—41no—
279C2×C4×C43C2×C22⋊C411yescharacteristic
280C2×C4×C43C2×C22⋊C411yescharacteristic
281C2×C4×C43C2×C22⋊C411yescharacteristic
282C2×C4×C43C2×C22⋊C411yescharacteristic
283C22⋊D43—22no—
284C22⋊D43—22no—
285C22⋊D43—22no—
286C22⋊D43—22no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—22no—
292C2×Dic43—42no—
293C2×Dic43—42no—
294C2×Dic43—42no—
295C2×Dic43—42no—
296C2×Dic43—42no—
297C2×Dic43—42no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43—42no—
304C2×Dic43—41no—
305C2×Dic43—42no—
306C2×Dic43—41no—
307C2×Dic43—42no—
308C2×Dic43C2×C22⋊C412yes—
309C2×Dic43C2×C22⋊C412yes—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312C2×Dic43C4×Q812yes—
313C4×D43—42no—
314C4×D43—42no—
315C4×D43—82no—
316C4×D43—82no—
317Dic86—82no—
318Dic86—82no—
319#22513—431nomaximal, Sylow
320C22×C43—21no—
321C22×C43—21no—
322C22×C43—21no—
323C22×C43—21no—
324C22×C43—21no—
325C22×C43—21no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43C22×C22⋊C411yescharacteristic
331C22×C43C2×C4×Q811yescharacteristic
332C22×C43#51911yescharacteristic
333C22×C43#54811yescharacteristic
334C22×C43#54811yescharacteristic
335C22×C43D4×Q811yescharacteristic
336C22×C43D4×Q811yescharacteristic
337C2×D43—22no—
338C2×D43—42no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—42no—
342C4×C43—21no—
343C4×C43—21no—
344C4×C43—21no—
345C4×C43—42no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43—81no—
349C4×C43—82no—
350C4×C43#41012yes—
351Dic43—22no—
352Dic43—22no—
353Dic43—22no—
354Dic43—22no—
355Dic43—22no—
356Dic43—42no—
357Dic43—41no—
358Dic43—41no—
359Dic43—82no—
360Dic43—81no—
361C2×#554—431no—
362#2345—431no—
363#2345—431no—
364#1996—432no—
365#1996—432no—
366#1996—431no—
367#1996D4311yescharacteristic, complemented
368#1799—431no—
369#1799—432no—
370C4×#99—431no—
371C4×#99—432no—
372C2×C43—21no—
373C2×C43—21no—
374C2×C43—21no—
375C2×C43—21no—
376C2×C43—21no—
377C2×C43—21no—
378C2×C43Q8×C22⋊C411yescharacteristic
379C2×C43C2×#41011yescharacteristic
380C2×C43#288311yescharacteristic
381D43—42no—
382#554—861no—
383#554—861no—
384#554—862no—
385#554—862no—
386#554—861no—
387#554—861no—
388C2×C4⋊Q8—431no—
389C2×#125—432no—
390C2×C22⋊Q8—431no—
391C2×C22⋊Q8—432no—
392C2×C22⋊Q8—432no—
393C2×C22⋊Q8C2×D4311yescharacteristic
394C2×C4×Q8—431no—
395C2×C4×D4—431no—
396C2×C4×D4—432no—
397C22×C4⋊C4—431no—
398C22×C4⋊C4—431no—
399C2×#99—431no—
400C2×#99—432no—
401C2×#99—431no—
402#389—861no—
403#389—861no—
404#387—862no—
405#387—862no—
406#380—431no—
407#380—432no—
408#380—432no—
409#380C2×D4311yescharacteristic
410C4×C4⋊C4—861no—
411C4×C4⋊C4—861no—
412C4×C22⋊C4—431no—
413C4×C22⋊C4—432no—
414C4×C22⋊C4—432no—
415C4×C22⋊C4C2×D4311yescharacteristic
416#342—432no—
417#342—432no—
418#342—431no—
419#342—431no—
420#342—432no—
421#342C2×D4312yes—
422#342C2×D4312yes—
423C43#2251311yescharacteristic, complemented, Sylow
424C22×Q8—432no—
425C22×Q8C4×D4311yescharacteristic
426C22×D4—431no—
427C23×C4—432no—
428C23×C4—432no—
429C23×C4—431no—
430C23×C4C22×D4311yescharacteristic
431C4⋊Q8—862no—
432C4⋊Q8—861no—
433C4⋊Q8—861no—
434#125—862no—
435#125—862no—
436#125—862no—
437#125—862no—
438C22⋊Q8—21no—
439C22⋊Q8—21no—
440C22⋊Q8—21no—
441C22⋊Q8—21no—
442C22⋊Q8—862no—
443C22⋊Q8—862no—
444C22⋊Q8—862no—
445C22⋊Q8—862no—
446C22⋊Q8—862no—
447C22⋊Q8—862no—
448C22⋊Q8—862no—
449C22⋊Q8—862no—
450C22⋊Q8—862no—
451C22⋊Q8—861no—
452C22⋊Q8—861no—
453C4×Q8—862no—
454C4×Q8—861no—
455C4×Q8—861no—
456C4×D4—862no—
457C4×D4—862no—
458C4×D4—862no—
459C4×D4—862no—
460C4×D4—861no—
461C4×D4—861no—
462C4×D4—861no—
463C4×D4—861no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—432no—
467C2×C4⋊C4—431no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—432no—
471C2×C4⋊C4—432no—
472C2×C4⋊C4—431no—
473C2×C4⋊C4—431no—
474C2×C4⋊C4—432no—
475C2×C4⋊C4—431no—
476C2×C4⋊C4—432no—
477C2×C4⋊C4—432no—
478C2×C4⋊C4—432no—
479C2×C4⋊C4—862no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—861no—
485C2×C4⋊C4C4×D4311yescharacteristic
486C2×C4⋊C4C4×D4312yes—
487C2×C22⋊C4—431no—
488C2×C22⋊C4—431no—
489C2×C22⋊C4—432no—
490C2×C22⋊C4—431no—
491C2×C22⋊C4—431no—
492C2×C22⋊C4—432no—
493C2×C22⋊C4C22×D4312yes—
494C2×C22⋊C4C22×D4311yescharacteristic
495C2×C22⋊C4C22×D4312yes—
496C2×C22⋊C4C22×D4311yescharacteristic
497C2×C42—21no—
498C2×C42—432no—
499C2×C42—431no—
500C2×C42—862no—
501C2×C42—862no—
502C2×C42—861no—
503#99—434no—
504#99—864no—
505#99—862no—
506#95—21no—
507#95—21no—
508#95—862no—
509#95—862no—
510#95—862no—
511#95—862no—
512#95—861no—
513#95—861no—
514C24—431no—
515C24C23×D4311yescharacteristic
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—42no—
519C2×Q8—862no—
520C2×Q8—862no—
521C2×Q8—3442no—
522C2×D4—432no—
523C2×D4—432no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—42no—
532C22×C4—431no—
533C22×C4—432no—
534C22×C4—432no—
535C22×C4—432no—
536C22×C4—432no—
537C22×C4—432no—
538C22×C4—432no—
539C22×C4—431no—
540C22×C4—431no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—862no—
547C22×C4—861no—
548C22×C4—3442no—
549C22×C4—3442no—
550C22×C4—1722no—
551C22×C4C2×C4×D4311yescharacteristic
552C22×C4C2×C4×D4312yes—
553C22×C4C2×C4×D4312yes—
554C22×C4C2×C4×D4311yescharacteristic
555C22×C4D4×D4311yescharacteristic
556C22×C4D4×D4311yescharacteristic
557C22×C4D4×D4311yescharacteristic
558C22×C4D4×D4311yescharacteristic
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—42no—
564C4⋊C4—432no—
565C4⋊C4—431no—
566C4⋊C4—431no—
567C4⋊C4—432no—
568C4⋊C4—432no—
569C4⋊C4—432no—
570C4⋊C4—432no—
571C4⋊C4—432no—
572C4⋊C4—431no—
573C4⋊C4—431no—
574C4⋊C4—862no—
575C4⋊C4—862no—
576C4⋊C4—862no—
577C4⋊C4—862no—
578C4⋊C4—862no—
579C4⋊C4—862no—
580C4⋊C4—862no—
581C4⋊C4—862no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—3442no—
585C4⋊C4—3442no—
586C4⋊C4—1722no—
587C22⋊C4—22no—
588C22⋊C4—22no—
589C22⋊C4—21no—
590C22⋊C4—22no—
591C22⋊C4—21no—
592C22⋊C4—22no—
593C22⋊C4—21no—
594C22⋊C4—432no—
595C22⋊C4—862no—
596C22⋊C4—862no—
597C22⋊C4—861no—
598C22⋊C4—861no—
599C22⋊C4—861no—
600C22⋊C4—861no—
601C22⋊C4—861no—
602C22⋊C4—861no—
603C22⋊C4—862no—
604C22⋊C4—861no—
605C22⋊C4—862no—
606C22⋊C4Q8×D4312yes—
607C42—42no—
608C42—862no—
609C42—862no—
610C42—861no—
611C42—861no—
612C42—3442no—
613C42—3442no—
614C42—1722no—
615C23—41no—
616C23—41no—
617C23—432no—
618C23—861no—
619C23—861no—
620C23—1721no—
621C23—1721no—
622C23C22×C4×D4311yescharacteristic
623C23C2×D4×D4311yescharacteristic
624C23C2×D4×D4311yescharacteristic
625C23C2×Q8×D4311yescharacteristic
626C23#41×D4311yescharacteristic
627C23#1306337211yescharacteristic
628C23#1306337311yescharacteristic
629Q8—42no—
630Q8—42no—
631Q8—3442no—
632Q8—3442no—
633D4—862no—
634D4—862no—
635D4—862no—
636D4—862no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—432no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—862no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—3442no—
667C2×C4—3442no—
668C2×C4—1722no—
669C2×C4—1722no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4—1722no—
673C2×C4—1722no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1722no—
679C2×C4—1721no—
680C2×C4—1722no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1722no—
684C2×C4—1721no—
685C2×C4—1721no—
686C2×C4C22⋊C4×D4311yescharacteristic
687C2×C4C22⋊C4×D4311yescharacteristic
688C2×C4C22⋊C4×D4311yescharacteristic
689C2×C4C22⋊C4×D4311yescharacteristic
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—862no—
701C22—1722no—
702C22—1722no—
703C22—1721no—
704C22—1721no—
705C22C2×C22⋊C4×D4311yescharacteristic
706C22C4×Q8×D4311yescharacteristic
707C22#1458337511yescharacteristic
708C22#1458355711yescharacteristic
709C22#1458355911yescharacteristic
710C22#1458356211yescharacteristic
711C22#1458356411yescharacteristic
712C4—21no—
713C4—21no—
714C4—21no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—82no—
719C4—81no—
720C4—862no—
721C4—862no—
722C4—862no—
723C4—862no—
724C4—862no—
725C4—3441no—
726C4—3442no—
727C4—1722no—
728C4—1721no—
729C4—1721no—
730C4#1458287112yes—
731C2—21no—
732C2—21no—
733C2—21no—
734C2—21no—
735C2—21no—
736C2—21no—
737C2—1722no—
738C2#1913742911yescharacteristic
739C2C2×#1458287111yescharacteristic
740C2#1914305411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1996C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C23
cosocleC24×C43C24
hypercenter#1996D43
hypocenterC43#22513
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #19137474C2semidirect
3. #19137470C2semidirect
4. #19135581C2semidirect
5. #19135578C2semidirect
6. #19135578C2semidirect
11. C43×#1996C2semidirect
18. C2×#13063324C4semidirect
19. C2×#13063315C4semidirect
20. C2×#13063305C4semidirect
22. C2×#13063301C4semidirect
23. C2×Q8×Dic43C4semidirect
27. C2×C4⋊C4×D43C4semidirect
120. #13063239Q8semidirect
367. #1996D43semidirect
423. C43#22513semidirect

Maximal subgroups

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

subgroupindex
C2×#145836072
#191374742
#191374702
#191355812
#191355782
#191345822
#191345802
C4×#130632392
#191343822
C43×#19962
#2251343