Finite Group Databasebeta

← #25096709

Subgroups — #25096709

Order 11008.

1298 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2#19137204C211yesmaximal, characteristic, complemented
3#19134686C211yesmaximal, characteristic, complemented
4#19134682C211yesmaximal, characteristic, complemented
5#19134611C211yesmaximal, characteristic, complemented
6#19134606C211yesmaximal, characteristic, complemented
7#19134601C211yesmaximal, characteristic, complemented
8#19134596C211yesmaximal, characteristic, complemented
9#19134536C211yesmaximal, characteristic
10#19134536C211yesmaximal, characteristic
11#19134426C211yesmaximal, characteristic, complemented
12#19134421C211yesmaximal, characteristic, complemented
13C4×#13063250C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C2×C43×#433C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583379—24no—
18#14583379C418yescomplemented
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×(C22⋊D43)⋊C4—21no—
24C2×(C22⋊D43)⋊C4—21no—
25C2×#13063283—21no—
26C22×C4⋊Dic43C2211yescharacteristic
27C2×C4⋊C4×D43—21no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36#14582792—21no—
37#14582792—21no—
38#14582785—21no—
39#14582785—21no—
40#14582769C2211yescharacteristic
41#14582765C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic
55C43×#433—24no—
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×#97×C43C2211yescharacteristic
61C2×C4×C8×C43C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898C2×C414yes—
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C4×Dic86C2×C414yes—
78C4×Dic86C2×C414yes—
79C4×D172—22no—
80C4×D172—22no—
81C4×D172C2×C414yes—
82C4×D172C2×C414yes—
83(C22⋊D43)⋊C4—28no—
84(C22⋊D43)⋊C4—28no—
85#13063283—28no—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43C2×C414yes—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C4⋊C4×D43—28no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108#13063250—22no—
109#13063250—22no—
110#13063250—22no—
111#13063250—22no—
112#13063247—22no—
113#13063247—22no—
114#13063247—22no—
115#13063247—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127#117×C43C2×C414yes—
128#117×C43D414yes—
129C2×C4⋊C4×C43D411yescharacteristic
130C2×C4⋊C4×C43D411yescharacteristic
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—22no—
136C4⋊C8×C43—22no—
137C22⋊C8×C43—22no—
138C22⋊C8×C43—22no—
139#97×C43—22no—
140C4×C8×C43—22no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C22×C412yes—
148C22×C4×C43C2×D412yes—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C2×C22⋊D43—24no—
156C2×C22⋊D43—24no—
157C2×C22⋊D43—24no—
158C22×Dic43—24no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—81no—
167C22×Dic43—81no—
168#10621898—28no—
169#10621898—28no—
170#10621898—28no—
171#10621898—28no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172C22×C412yes—
176C2×D172#4112yes—
177C2×D172#4112yes—
178C2×C4×D43—24no—
179C2×C4×D43—24no—
180C2×C4×D43—24no—
181C2×C4×D43—24no—
182C2×C4×D43—24no—
183C2×C4×D43—81no—
184C2×C4×D43—81no—
185C2×C4×D43—81no—
186C2×C4×D43—81no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86C22×C412yes—
191C2×Dic86#4112yes—
192C2×Dic86#4112yes—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C4⋊C4×C43C22⋊C414yes—
206C4⋊C4×C43C22⋊C414yes—
207C22⋊C4×C43C22⋊C414yes—
208C22⋊C4×C43C22⋊C414yes—
209C42×C43C22×C412yes—
210C42×C43C22×C412yes—
211C42×C43C2×D412yes—
212C42×C43C2×D412yes—
213C22⋊Dic43—81no—
214C22⋊Dic43—81no—
215(C2×D43)⋊C4—24no—
216(C2×D43)⋊C4—24no—
217C4⋊Dic43—24no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—81no—
229C4⋊Dic43—81no—
230C4⋊Dic43C22×C412yes—
231C4⋊Dic43C22×C412yes—
232Dic43⋊C4—24no—
233Dic43⋊C4—24no—
234C4×Dic43—24no—
235C4×Dic43—24no—
236C4×Dic43—81no—
237C4×Dic43—81no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43C2×C22⋊C412yes—
245C23×C43C22×D411yescharacteristic
246C22×D43—22no—
247C22×D43—22no—
248C22×D43—22no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43—41no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—22no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43C2×C22⋊C412yes—
268C2×C4×C43C2×C22⋊C412yes—
269C2×C4×C43C2×C22⋊C412yes—
270C2×C4×C43C2×C22⋊C412yes—
271C2×C4×C43C2×C22⋊C412yes—
272C2×C4×C43C23×C411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C22⋊D43—216no—
279C2×Dic43—22no—
280C2×Dic43—22no—
281C2×Dic43—22no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—84no—
301D172—22no—
302D172—22no—
303D172—22no—
304D172#11714yes—
305C4×D43—216no—
306C4×D43—84no—
307C4×D43—84no—
308Dic86—22no—
309Dic86—22no—
310Dic86—22no—
311Dic86#11714yes—
312C8×C43—41no—
313C8×C43—41no—
314C8×C43—41no—
315C8×C43—41no—
316#20746—431nomaximal, Sylow
317C22×C43—22no—
318C22×C43—22no—
319C22×C43—22no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43C22×C22⋊C411yescharacteristic
325C22×C43#52511yescharacteristic
326C22×C43#52511yescharacteristic
327C22×C43#57611yescharacteristic
328C22×C43#57711yescharacteristic
329C22×C43#57711yescharacteristic
330C22×C43#57811yescharacteristic
331C2×D43—24no—
332C2×D43—42no—
333C2×D43—42no—
334C2×D43—42no—
335C2×D43—42no—
336C2×D43—42no—
337C2×D43—42no—
338C4×C43—22no—
339C4×C43—22no—
340C4×C43—22no—
341C4×C43—22no—
342C4×C43—22no—
343C4×C43C2×#11711yescharacteristic
344C4×C43C2×#11711yescharacteristic
345C4×C43#52511yescharacteristic
346C4×C43#52511yescharacteristic
347Dic43—24no—
348Dic43—42no—
349Dic43—42no—
350Dic43—81no—
351Dic43—81no—
352Dic43—81no—
353Dic43—81no—
354C2×#520—431no—
355C2×#433D4311yescharacteristic, complemented
356#2314—431no—
357#1824—431no—
358#1823—431no—
359#1805—431no—
360#1804—431no—
361#1803—431no—
362#1802—431no—
363#1788—431no—
364#1788—431no—
365#1763—431no—
366#1762—431no—
367C4×#103—431no—
368C4×#102—431no—
369C2×C43—42no—
370C2×C43#228011yescharacteristic
371C2×C43#289711yescharacteristic
372C2×C43#289811yescharacteristic
373C2×C43#311911yescharacteristic
374C2×C43#312011yescharacteristic
375C2×C43#312411yescharacteristic
376C2×C43#312511yescharacteristic
377D43—44no—
378C22×#41—431no—
379#520—438no—
380#520—864no—
381C2×C4×Q8—431no—
382C2×C4×Q8—431no—
383C2×C4×D4—431no—
384C2×C4×D4—431no—
385C2×C4×D4—861no—
386C2×C4×D4—861no—
387C2×#117—861no—
388C2×#117C2×D4311yescharacteristic
389C22×C4⋊C4—431no—
390C22×C4⋊C4—861no—
391#433—24no—
392C2×C4⋊C8C2×D4311yescharacteristic
393C2×C4⋊C8C2×D4311yescharacteristic
394C2×#103—431no—
395C2×#103—431no—
396C2×#103—431no—
397C2×#103—431no—
398C2×#102—431no—
399C2×#102—431no—
400C2×#102—431no—
401C2×#102—431no—
402C2×C22⋊C8C2×D4311yescharacteristic
403C2×C22⋊C8C2×D4311yescharacteristic
404C2×#97C2×D4311yescharacteristic
405C2×C4×C8C2×D4311yescharacteristic
406#388—861no—
407#388—861no—
408#387—861no—
409#387—861no—
410#384—431no—
411#382—431no—
412#380—431no—
413#380—431no—
414C4×C4⋊C4—431no—
415C4×C4⋊C4—431no—
416#340—431no—
417#340—431no—
418#340—431no—
419#340—431no—
420#340—431no—
421#340—431no—
422#340—431no—
423#340—431no—
424C43#2074611yescharacteristic, complemented, Sylow
425C2×#41—434no—
426C2×#41—862no—
427C2×#41—862no—
428C2×#41—862no—
429C2×#41—862no—
430C2×#41—862no—
431C22×Q8—431no—
432C22×D4—431no—
433C22×D4—861no—
434C23×C4—861no—
435C23×C4—861no—
436C23×C4—861no—
437C23×C4—861no—
438C23×C4C22×D4311yescharacteristic
439C22×C8C22×D4311yescharacteristic
440C22×C8C22×D4311yescharacteristic
441C22×C8C22×D4311yescharacteristic
442C22×C8C22×D4311yescharacteristic
443C4×Q8—434no—
444C4×Q8—434no—
445C4×Q8—862no—
446C4×Q8—862no—
447C4×D4—434no—
448C4×D4—434no—
449C4×D4—868no—
450C4×D4—868no—
451C4×D4—862no—
452C4×D4—862no—
453#117—868no—
454#117C4×D4314yes—
455#117C22⋊D4314yes—
456C2×C4⋊C4—434no—
457C2×C4⋊C4—431no—
458C2×C4⋊C4—431no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—431no—
462C2×C4⋊C4—431no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4—861no—
466C2×C4⋊C4—862no—
467C2×C4⋊C4—868no—
468C2×C4⋊C4—861no—
469C2×C4⋊C4—861no—
470C2×C4⋊C4D17211yescharacteristic
471C2×C4⋊C4D17211yescharacteristic
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4D17211yescharacteristic
477C2×C22⋊C4D17211yescharacteristic
478C2×C42—861no—
479C2×C42—861no—
480C2×C42—861no—
481C2×C42—861no—
482C2×C42C22×D4311yescharacteristic
483C2×C42C22×D4311yescharacteristic
484C4⋊C8—22no—
485C4⋊C8—22no—
486#103—862no—
487#103—862no—
488#103—862no—
489#103—862no—
490#102—862no—
491#102—862no—
492#102—862no—
493#102—862no—
494C22⋊C8—22no—
495C22⋊C8—22no—
496#97—22no—
497C4×C8—22no—
498#95—861no—
499#95—861no—
500#95—861no—
501#95—861no—
502#95—861no—
503#95—861no—
504C24—861no—
505C24C2×D17211yescharacteristic
506#41—868no—
507#41—868no—
508#41—868no—
509#41—868no—
510C2×Q8—432no—
511C2×Q8—432no—
512C2×Q8—432no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×D4—432no—
517C2×D4—432no—
518C2×D4—432no—
519C2×D4—864no—
520C2×D4—864no—
521C2×D4—864no—
522C2×D4—861no—
523C2×D4—861no—
524C2×D4—861no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—864no—
530C22×C4—864no—
531C22×C4—861no—
532C22×C4—864no—
533C22×C4—864no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—864no—
537C22×C4—864no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—3441no—
543C22×C4—3441no—
544C22×C4—3441no—
545C22×C4—3441no—
546C22×C4—3441no—
547C22×C4—3441no—
548C22×C4C2×C4×D4312yes—
549C22×C4C2×D17211yescharacteristic
550C22×C4C2×D17211yescharacteristic
551C22×C4C2×D17211yescharacteristic
552C22×C4C2×D17211yescharacteristic
553C22×C4C2×D17211yescharacteristic
554C22×C4C2×C22⋊D4312yes—
555C22×C4C23×D4311yescharacteristic
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C4⋊C4—432no—
569C4⋊C4—432no—
570C4⋊C4—864no—
571C4⋊C4—864no—
572C4⋊C4—864no—
573C4⋊C4—861no—
574C4⋊C4—861no—
575C4⋊C4—861no—
576C4⋊C4—861no—
577C4⋊C4—861no—
578C4⋊C4—861no—
579C4⋊C4—861no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—3441no—
584C4⋊C4—3441no—
585C4⋊C4(C2×D43)⋊C414yes—
586C4⋊C4(C2×D43)⋊C414yes—
587C22⋊C4—864no—
588C22⋊C4—864no—
589C22⋊C4—3441no—
590C22⋊C4—3441no—
591C22⋊C4(C2×D43)⋊C414yes—
592C22⋊C4(C2×D43)⋊C414yes—
593C42—864no—
594C42—864no—
595C42—3441no—
596C42—3441no—
597C42C2×C4×D4312yes—
598C42C2×C4×D4312yes—
599C42C2×C22⋊D4312yes—
600C42C2×C22⋊D4312yes—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—862no—
608C23—862no—
609C23—862no—
610C23—1721no—
611C23—1721no—
612C23—1721no—
613C23—1721no—
614C23C2×(C2×D43)⋊C412yes—
615C23C22×D17211yescharacteristic
616Q8—434no—
617Q8—862no—
618Q8—862no—
619Q8—862no—
620D4—434no—
621D4—8616no—
622D4—862no—
623D4—862no—
624D4—862no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—8616no—
640C2×C4—862no—
641C2×C4—862no—
642C2×C4—862no—
643C2×C4—862no—
644C2×C4—862no—
645C2×C4—3444no—
646C2×C4—3444no—
647C2×C4—3444no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4—1721no—
653C2×C4—1721no—
654C2×C4—1721no—
655C2×C4—1721no—
656C2×C4—1721no—
657C2×C4—1721no—
658C2×C4—1721no—
659C2×C4—1721no—
660C2×C4—1721no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1721no—
664C2×C4C2×(C2×D43)⋊C412yes—
665C2×C4C2×(C2×D43)⋊C412yes—
666C2×C4C2×(C2×D43)⋊C412yes—
667C2×C4C2×(C2×D43)⋊C412yes—
668C2×C4C2×(C2×D43)⋊C412yes—
669C2×C4C22×C4×D4311yescharacteristic
670C2×C4C22×C22⋊D4311yescharacteristic
671C2×C4#41×D4311yescharacteristic
672C2×C4#41×D4311yescharacteristic
673C2×C4#41×D4311yescharacteristic
674C2×C4#41×D4311yescharacteristic
675C8—41no—
676C8—41no—
677C8—41no—
678C8—41no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—864no—
687C22—1722no—
688C22—1722no—
689C22—1722no—
690C22—1722no—
691C22—1722no—
692C22—1722no—
693C22C22×(C2×D43)⋊C411yescharacteristic
694C22#1458341111yescharacteristic
695C22#1458341111yescharacteristic
696C22#1458370411yescharacteristic
697C22#1458371111yescharacteristic
698C22#1458371111yescharacteristic
699C22#1458371611yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—864no—
706C4—3441no—
707C4—3441no—
708C4—3441no—
709C4—3441no—
710C4—1722no—
711C4—1722no—
712C4#117×D4311yescharacteristic
713C4#117×D4311yescharacteristic
714C4#1458340611yescharacteristic
715C4#1458340611yescharacteristic
716C2—42no—
717C2—1724no—
718C2#1913697411yescharacteristic
719C2#1914312211yescharacteristic
720C2#1914312911yescharacteristic
721C2#1914479611yescharacteristic
722C2#1914481111yescharacteristic
723C2#1914485911yescharacteristic
724C2#1914487411yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#433C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×#433D43
hypocenterC43#20746
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #19137204C2semidirect
3. #19134686C2semidirect
4. #19134682C2semidirect
5. #19134611C2semidirect
6. #19134606C2semidirect
7. #19134601C2semidirect
8. #19134596C2semidirect
11. #19134426C2semidirect
12. #19134421C2semidirect
13. C4×#13063250C2semidirect
14. C4×#13063247C2semidirect
15. C2×C43×#433C2semidirect
18. #14583379C4semidirect
355. C2×#433D43semidirect
424. C43#20746semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
#191372042
#191346862
#191346822
#191346112
#191346062
#191346012
#191345962
#191345362
#191344262
#191344212
C4×#130632502
C4×#130632472
C2×C43×#4332
#2074643