Finite Group Databasebeta

← #25112999

Subgroups — #25112999

Order 11008.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic
2C2×#14582977C211yesmaximal, characteristic
3#19135559C211yesmaximal, characteristic, complemented
4#19135552C211yesmaximal, characteristic, complemented
5#19135026C211yesmaximal, characteristic, complemented
6#19135026C211yesmaximal, characteristic, complemented
7#19134907C211yesmaximal, characteristic, complemented
8#19134902C211yesmaximal, characteristic, complemented
9#19134687C211yesmaximal, characteristic, complemented
10#19134683C211yesmaximal, characteristic, complemented
11#19134607C211yesmaximal, characteristic, complemented
12C4×#13063248C211yesmaximal, characteristic, complemented
13#19134316C211yesmaximal, characteristic, complemented
14#19134314C211yesmaximal, characteristic, complemented
15C43×#2352C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18#14583589—24no—
19#14583589C418yescomplemented
20C2×#13063318—21no—
21C2×#13063317C2211yescharacteristic
22C2×#13063315—21no—
23C2×#13063306—21no—
24C2×#13063304C2211yescharacteristic
25C2×#13063304C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063281—21no—
29C22×C4⋊Dic43C2211yescharacteristic
30#14582977—24no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C4×C43⋊C8C2211yescharacteristic
39#14582661C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×C4×D4×C43C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C43×#388—21no—
55C43×#387—21no—
56C43×#386—21no—
57C43×#382C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C22⋊C4×C43—21no—
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621877—22no—
65C2×#10621877—22no—
66C2×#10621877—22no—
67C2×#10621877—22no—
68C2×#10621877—41no—
69C2×#10621877—41no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063318—28no—
75#13063317—22no—
76#13063317C2×C414yescomplemented
77#13063315—28no—
78#13063306—28no—
79#13063304—22no—
80#13063304—22no—
81#13063304C2×C414yes—
82#13063304C2×C414yescomplemented
83C4×Dic86—22no—
84C4×Dic86C2×C414yescomplemented
85#13063284—22no—
86#13063284C2×C414yes—
87#13063281—28no—
88C2×C4⋊Dic43—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2×C414yescomplemented
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C4⋊(C43⋊C8)—22no—
105#13063248—22no—
106#13063248—22no—
107#13063248—41no—
108#13063248—41no—
109C22⋊(C43⋊C8)—22no—
110C22⋊(C43⋊C8)—22no—
111C4×C43⋊C8—22no—
112C22×D4×C43D411yescharacteristic
113C23×C4×C43—21no—
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116C4×D4×C43C2×C414yes—
117C4×D4×C43D414yes—
118#117×C43—22no—
119#117×C43—41no—
120C2×C4⋊C4×C43—22no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43—41no—
123C2×C4⋊C4×C43D411yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C42×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D411yescharacteristic
143C2×D4×C43—41no—
144C2×D4×C43—41no—
145C2×D4×C43C22⋊C414yes—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—42no—
159C22×C4×C43—42no—
160C22×C4×C43—81no—
161C22×C4×C43C22×C412yes—
162C22×C4×C43C22×C412yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43C2×D412yes—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
170C22×Dic43—24no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86C22×C412yes—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—42no—
191C4⋊C4×C43C22⋊C414yes—
192C4⋊C4×C43#4112yes—
193C22⋊C4×C43—42no—
194C22⋊C4×C43—42no—
195C22⋊C4×C43—81no—
196C22⋊C4×C43C22⋊C414yes—
197C22⋊C4×C43C22⋊C414yes—
198C42×C43—42no—
199C42×C43—81no—
200C42×C43C22×C412yes—
201C42×C43C2×D412yes—
202C22⋊Dic43—24no—
203C22⋊Dic43—24no—
204C22⋊Dic43—24no—
205C4⋊Dic43—24no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43C22×C412yes—
210C4⋊Dic43C22×C412yes—
211C4⋊Dic43C22×C412yes—
212Dic43⋊C4—24no—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217C4×Dic43—24no—
218C4×Dic43—24no—
219#10621877—44no—
220#10621877—44no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8#4112yes—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43C2×C22⋊C412yes—
246C23×C43C2×C22⋊C412yes—
247C23×C43C22×D411yescharacteristic
248D4×C43—44no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—22no—
258C2×C4×C43—22no—
259C2×C4×C43—22no—
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—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—84no—
278C2×C4×C43C2×C22⋊C412yes—
279C2×C4×C43C2×C22⋊C412yes—
280C2×C4×C43C2×C22⋊C412yes—
281C2×C4×C43C2×C22⋊C412yes—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C432−1+411yescharacteristic
288C2×Dic43—22no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—48no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301Dic86—22no—
302Dic86—22no—
303Dic86—41no—
304Dic86—41no—
305C43⋊C8—22no—
306C43⋊C8—41no—
307C43⋊C8—41no—
308C43⋊C8—41no—
309#22499—431nomaximal, Sylow
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43C22×C22⋊C411yescharacteristic
325C22×C43#54611yescharacteristic
326C22×C43#54711yescharacteristic
327C22×C43#57511yescharacteristic
328C22×C43#57511yescharacteristic
329C22×C43#57711yescharacteristic
330C22×C43#57811yescharacteristic
331C4×C43—22no—
332C4×C43—22no—
333C4×C43—22no—
334C4×C43—22no—
335C4×C43—42no—
336C4×C43—81no—
337C4×C43—81no—
338C4×C43—81no—
339C4×C43C4×#4111yescharacteristic
340C4×C43#52011yescharacteristic
341C4×C43#54611yescharacteristic
342C4×C43#54711yescharacteristic
343Dic43—42no—
344Dic43—42no—
345Dic43—42no—
346Dic43—42no—
347C2×#552—431no—
348C2×#436—431no—
349#2352D4311yescharacteristic
350#1991—431no—
351#1989—431no—
352#1894—431no—
353#1894—431no—
354#1873—431no—
355#1872—431no—
356#1825—431no—
357#1824—431no—
358#1805—431no—
359C4×#103—431no—
360#1736—431no—
361#1736—431no—
362C2×C43—42no—
363C2×C43—42no—
364C2×C43#233911yescharacteristic
365C2×C43#289611yescharacteristic
366C2×C43#289811yescharacteristic
367C2×C43#332311yescharacteristic
368C2×C43#332711yescharacteristic
369C2×C43#335111yescharacteristic
370C2×C43#335211yescharacteristic
371C22×M16—431no—
372C22×M16—431no—
373#552—438no—
374#552—864no—
375C2×#126—861no—
376C2×#125—431no—
377C2×#125—861no—
378C2×#123—861no—
379C2×C22⋊Q8—431no—
380C2×C22⋊Q8—431no—
381C2×C4×Q8—431no—
382C2×C4×D4C2×D4311yescharacteristic
383C2×#117—431no—
384C2×#117—861no—
385C2×#117C2×D4311yescharacteristic
386C22×C4⋊C4—431no—
387C22×C4⋊C4C2×D4311yescharacteristic
388#436—864no—
389C2×C4⋊C8—431no—
390C2×#103—431no—
391C2×#103—431no—
392C2×#103—431no—
393C2×#103—431no—
394C2×C22⋊C8—431no—
395C2×C22⋊C8—431no—
396C2×C4×C8—431no—
397#388—21no—
398#387—21no—
399#386—21no—
400#382C2×D4311yescharacteristic
401#380C2×D4311yescharacteristic
402#380C2×D4311yescharacteristic
403C4×C4⋊C4C2×D4311yescharacteristic
404C4×C22⋊C4—21no—
405#340—431no—
406#340—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#340—431no—
411#340—431no—
412#340—431no—
413#340—431no—
414#340—431no—
415#340—431no—
416#340—431no—
417C43#2249911yescharacteristic, complemented, Sylow
418C22×Q8—431no—
419C22×D4C22⋊D4311yescharacteristic
420C23×C4—21no—
421C23×C4—861no—
422C23×C4C22×D4311yescharacteristic
423C23×C4C22×D4311yescharacteristic
424C2×M16—862no—
425C2×M16—862no—
426C2×M16—862no—
427C2×M16—862no—
428C2×M16—1721no—
429C2×M16—1721no—
430C22×C8—431no—
431C22×C8—431no—
432C22×C8—431no—
433C22×C8—431no—
434#126—868no—
435#125—434no—
436#125—868no—
437#125—862no—
438#123—868no—
439C22⋊Q8—434no—
440C22⋊Q8—434no—
441C22⋊Q8—862no—
442C22⋊Q8—862no—
443C4×Q8—434no—
444C4×Q8—862no—
445C4×D4C4×D4314yes—
446C4×D4D17214yes—
447#117—22no—
448#117—41no—
449#117—434no—
450#117—862no—
451#117—868no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—434no—
456C2×C4⋊C4—431no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—862no—
460C2×C4⋊C4—861no—
461C2×C4⋊C4—861no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4—861no—
466C2×C4⋊C4C22⋊D4311yescharacteristic
467C2×C4⋊C4C22×D4311yescharacteristic
468C2×C4⋊C4C22×D4311yescharacteristic
469C2×C4⋊C4C22×D4311yescharacteristic
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4C22⋊D4311yescharacteristic
478C2×C22⋊C4C22⋊D4311yescharacteristic
479C2×C42—21no—
480C2×C42—21no—
481C2×C42—861no—
482C2×C42—861no—
483C2×C42C22×D4311yescharacteristic
484C4⋊C8—862no—
485#103—862no—
486#103—862no—
487#103—1721no—
488#103—1721no—
489C22⋊C8—862no—
490C22⋊C8—862no—
491C4×C8—862no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497C24C2×C22⋊D4311yescharacteristic
498C24C2×C22⋊D4311yescharacteristic
499C2×Q8—432no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×D4—41no—
506C2×D4—41no—
507C2×D4(C2×D43)⋊C414yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—864no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—1722no—
529C22×C4—1722no—
530C22×C4C2×C4×D4312yes—
531C22×C4C2×C4×D4312yes—
532C22×C4C2×D17212yes—
533C22×C4C2×D17212yes—
534C22×C4C2×C22⋊D4311yescharacteristic
535C22×C4C2×C22⋊D4311yescharacteristic
536C22×C4C2×C22⋊D4311yescharacteristic
537C22×C4C2×C22⋊D4311yescharacteristic
538C22×C4C23×D4311yescharacteristic
539M16—1724no—
540M16—1724no—
541C2×C8—432no—
542C2×C8—861no—
543C2×C8—861no—
544C2×C8—861no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—432no—
562C4⋊C4—432no—
563C4⋊C4—432no—
564C4⋊C4—864no—
565C4⋊C4—864no—
566C4⋊C4—864no—
567C4⋊C4—864no—
568C4⋊C4—864no—
569C4⋊C4—864no—
570C4⋊C4—861no—
571C4⋊C4—861no—
572C4⋊C4—861no—
573C4⋊C4(C2×D43)⋊C414yes—
574C4⋊C4#1062190012yes—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—81no—
578C22⋊C4—864no—
579C22⋊C4—864no—
580C22⋊C4—864no—
581C22⋊C4(C2×D43)⋊C414yes—
582C22⋊C4(C2×D43)⋊C414yes—
583C42—42no—
584C42—81no—
585C42—864no—
586C42—864no—
587C42C2×C4×D4312yes—
588C42C2×D17212yes—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×(C2×D43)⋊C412yes—
602C23C2×(C2×D43)⋊C412yes—
603C23C22×C22⋊D4311yescharacteristic
604Q8—862no—
605Q8—862no—
606Q8—1721no—
607Q8—1721no—
608D4—44no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—84no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—1728no—
643C2×C4—1721no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4C2×(C2×D43)⋊C412yes—
652C2×C4C2×(C2×D43)⋊C412yes—
653C2×C4C2×(C2×D43)⋊C412yes—
654C2×C4C2×(C2×D43)⋊C412yes—
655C2×C4C22×C4×D4311yescharacteristic
656C2×C4C22×D17211yescharacteristic
657C2×C4#41×D4311yescharacteristic
658C2×C4C2×#1062190011yescharacteristic
659C2×C4#1306337011yescharacteristic
660C2×C4#1306337211yescharacteristic
661C8—862no—
662C8—1721no—
663C8—1721no—
664C8—1721no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22C22×(C2×D43)⋊C411yescharacteristic
680C22#1458354311yescharacteristic
681C22#1458354811yescharacteristic
682C22#1458369711yescharacteristic
683C22#1458369711yescharacteristic
684C22#1458371011yescharacteristic
685C22#1458371411yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—1722no—
695C4—1722no—
696C4—1722no—
697C4—1722no—
698C4C4×#1062190011yescharacteristic
699C4#1458337811yescharacteristic
700C4#1458354411yescharacteristic
701C4#1458355311yescharacteristic
702C2—42no—
703C2—42no—
704C2#1913742011yescharacteristic
705C2#1914311211yescharacteristic
706C2#1914312511yescharacteristic
707C2#1914681111yescharacteristic
708C2#1914686311yescharacteristic
709C2#1914714911yescharacteristic
710C2#1914716411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2352C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
cosocleC22×C4×C43C24
hypercenter#2352D43
hypocenterC43#22499
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. #19135559C2semidirect
4. #19135552C2semidirect
5. #19135026C2semidirect
6. #19135026C2semidirect
7. #19134907C2semidirect
8. #19134902C2semidirect
9. #19134687C2semidirect
10. #19134683C2semidirect
11. #19134607C2semidirect
12. C4×#13063248C2semidirect
13. #19134316C2semidirect
14. #19134314C2semidirect
19. #14583589C4semidirect
76. #13063317C2×C4semidirect
82. #13063304C2×C4semidirect
84. C4×Dic86C2×C4semidirect
90. C2×C4⋊Dic43C2×C4semidirect
417. C43#22499semidirect

Maximal subgroups

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

subgroupindex
C2×#145835892
C2×#145829772
#191355592
#191355522
#191350262
#191349072
#191349022
#191346872
#191346832
#191346072
C4×#130632482
#191343162
#191343142
C43×#23522
#2249943