Finite Group Databasebeta

← #25096701

Subgroups — #25096701

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
2C2×#14582960C211yesmaximal, characteristic, complemented
3#19134683C211yesmaximal, characteristic, complemented
4#19134679C211yesmaximal, characteristic, complemented
5#19134607C211yesmaximal, characteristic, complemented
6#19134602C211yesmaximal, characteristic, complemented
7#19134597C211yesmaximal, characteristic, complemented
8#19134592C211yesmaximal, characteristic, complemented
9#19134533C211yesmaximal, characteristic
10#19134533C211yesmaximal, characteristic
11#19134428C211yesmaximal, characteristic, complemented
12#19134423C211yesmaximal, characteristic, complemented
13C4×#13063248C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic, complemented
15C43×#2314C211yesmaximal, 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—
28#14582960—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×#13063236C2211yescharacteristic
42C2×C4×C43⋊C8C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C2×#117×C43C2211yescharacteristic
52C43×#388—21no—
53C43×#388—21no—
54C43×#387—21no—
55C43×#387—21no—
56C43×#384C2211yescharacteristic
57C43×#382C2211yescharacteristic
58C43×#380C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C4×C4⋊C4×C43C2211yescharacteristic
61C4×C4⋊C4×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—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C4×Dic86—22no—
80C4×Dic86—22no—
81C4×Dic86C2×C414yes—
82C4×Dic86C2×C414yes—
83C4×D172—22no—
84C4×D172—22no—
85C4×D172C2×C414yes—
86C4×D172C2×C414yes—
87(C22⋊D43)⋊C4—28no—
88(C22⋊D43)⋊C4—28no—
89#13063283—28no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2×C414yes—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C4⋊C4×D43—28no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C4⋊(C43⋊C8)—22no—
103C4⋊(C43⋊C8)—22no—
104#13063248—22no—
105#13063248—22no—
106#13063248—22no—
107#13063248—22no—
108#13063245—22no—
109#13063245—22no—
110#13063245—22no—
111#13063245—22no—
112C22⋊(C43⋊C8)—22no—
113C22⋊(C43⋊C8)—22no—
114#13063236—22no—
115C4×C43⋊C8—22no—
116C23×C4×C43C2311yescharacteristic
117#117×C43C2×C414yes—
118#117×C43D414yes—
119C2×C4⋊C4×C43—21no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43D411yescharacteristic
122C2×C4⋊C4×C43D411yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43—21no—
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C22⋊C4×C43D411yescharacteristic
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#95×C43—21no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D412yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—24no—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—24no—
162C22×Dic43—24no—
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—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—81no—
202C4⋊C4×C43—81no—
203C4⋊C4×C43C22⋊C414yes—
204C4⋊C4×C43C22⋊C414yes—
205C22⋊C4×C43—81no—
206C22⋊C4×C43—81no—
207C22⋊C4×C43C22⋊C414yes—
208C22⋊C4×C43C22⋊C414yes—
209C42×C43—81no—
210C42×C43—81no—
211C42×C43C22×C412yes—
212C42×C43C22×C412yes—
213C42×C43C2×D412yes—
214C42×C43C2×D412yes—
215(C2×D43)⋊C4—24no—
216(C2×D43)⋊C4—24no—
217C4⋊Dic43—24no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43C22×C412yes—
221C4⋊Dic43C22×C412yes—
222Dic43⋊C4—24no—
223Dic43⋊C4—24no—
224C4×Dic43—24no—
225C4×Dic43—24no—
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—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
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×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—41no—
278C2×C4×C43—41no—
279C2×C4×C43C2×C22⋊C412yes—
280C2×C4×C43C2×C22⋊C412yes—
281C2×C4×C43C2×C22⋊C412yes—
282C2×C4×C43C2×C22⋊C412yes—
283C2×C4×C43C2×C22⋊C412yes—
284C2×C4×C43C23×C411yescharacteristic
285C2×C4×C43C22×D411yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×C4×C43C2×#4111yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C22⋊D43—216no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—22no—
294C2×Dic43—22no—
295C2×Dic43—22no—
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—
312C43⋊C8—41no—
313C43⋊C8—41no—
314C43⋊C8—41no—
315C43⋊C8—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×C43—81no—
344C4×C43—81no—
345C4×C43—81no—
346C4×C43—81no—
347C4×C43C2×#11711yescharacteristic
348C4×C43C2×#11711yescharacteristic
349C4×C43#52511yescharacteristic
350C4×C43#52511yescharacteristic
351Dic43—24no—
352Dic43—42no—
353Dic43—42no—
354C2×#520—431no—
355C2×#433—431no—
356#2314D4311yescharacteristic, complemented
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—864no—
392C2×C4⋊C8—431no—
393C2×C4⋊C8—431no—
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⋊C8—431no—
403C2×C22⋊C8—431no—
404C2×#97—431no—
405C2×C4×C8—431no—
406#388—21no—
407#388—21no—
408#387—21no—
409#387—21no—
410#384C2×D4311yescharacteristic
411#382C2×D4311yescharacteristic
412#380C2×D4311yescharacteristic
413#380C2×D4311yescharacteristic
414C4×C4⋊C4C2×D4311yescharacteristic
415C4×C4⋊C4C2×D4311yescharacteristic
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×C8—431no—
440C22×C8—431no—
441C22×C8—431no—
442C22×C8—431no—
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#117D17214yes—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—434no—
459C2×C4⋊C4—431no—
460C2×C4⋊C4—431no—
461C2×C4⋊C4—862no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4—868no—
466C2×C4⋊C4C22⋊D4311yescharacteristic
467C2×C4⋊C4C22⋊D4311yescharacteristic
468C2×C4⋊C4C22×D4311yescharacteristic
469C2×C4⋊C4C22×D4311yescharacteristic
470C2×C4⋊C4C22×D4311yescharacteristic
471C2×C4⋊C4C22×D4311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4C22⋊D4311yescharacteristic
477C2×C22⋊C4C22⋊D4311yescharacteristic
478C2×C42—21no—
479C2×C42—21no—
480C2×C42—861no—
481C2×C42—861no—
482C2×C42C22×D4311yescharacteristic
483C2×C42C22×D4311yescharacteristic
484C4⋊C8—862no—
485C4⋊C8—862no—
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—862no—
495C22⋊C8—862no—
496#97—862no—
497C4×C8—862no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504C24—861no—
505C24C2×C22⋊D4311yescharacteristic
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—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—864no—
534C22×C4—864no—
535C22×C4—861no—
536C22×C4—864no—
537C22×C4—864no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—864no—
541C22×C4—864no—
542C22×C4—3441no—
543C22×C4—3441no—
544C22×C4—3441no—
545C22×C4—3441no—
546C22×C4—3441no—
547C22×C4—3441no—
548C22×C4C2×C4×D4312yes—
549C22×C4C2×D17212yes—
550C22×C4C2×C22⋊D4311yescharacteristic
551C22×C4C2×C22⋊D4311yescharacteristic
552C22×C4C2×C22⋊D4311yescharacteristic
553C22×C4C2×C22⋊D4311yescharacteristic
554C22×C4C2×C22⋊D4311yescharacteristic
555C22×C4C23×D4311yescharacteristic
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—861no—
560C2×C8—861no—
561C2×C8—861no—
562C2×C8—861no—
563C2×C8—861no—
564C2×C8—861no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—81no—
577C4⋊C4—81no—
578C4⋊C4—432no—
579C4⋊C4—432no—
580C4⋊C4—864no—
581C4⋊C4—864no—
582C4⋊C4—864no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4(C2×D43)⋊C414yes—
586C4⋊C4(C2×D43)⋊C414yes—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C22⋊C4—864no—
590C22⋊C4—864no—
591C22⋊C4(C2×D43)⋊C414yes—
592C22⋊C4(C2×D43)⋊C414yes—
593C42—81no—
594C42—81no—
595C42—864no—
596C42—864no—
597C42C2×C4×D4312yes—
598C42C2×C4×D4312yes—
599C42C2×D17212yes—
600C42C2×D17212yes—
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×C22⋊D4311yescharacteristic
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—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—8616no—
652C2×C4—862no—
653C2×C4—862no—
654C2×C4—862no—
655C2×C4—862no—
656C2×C4—862no—
657C2×C4—3444no—
658C2×C4—3444no—
659C2×C4—3444no—
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×D17211yescharacteristic
671C2×C4#41×D4311yescharacteristic
672C2×C4#41×D4311yescharacteristic
673C2×C4#41×D4311yescharacteristic
674C2×C4#41×D4311yescharacteristic
675C8—1721no—
676C8—1721no—
677C8—1721no—
678C8—1721no—
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#1458340611yescharacteristic
695C22#1458340611yescharacteristic
696C22#1458370211yescharacteristic
697C22#1458370711yescharacteristic
698C22#1458371011yescharacteristic
699C22#1458371411yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—864no—
710C4—1722no—
711C4—1722no—
712C4#117×D4311yescharacteristic
713C4#117×D4311yescharacteristic
714C4#1458341111yescharacteristic
715C4#1458341111yescharacteristic
716C2—42no—
717C2—1724no—
718C2#1913697411yescharacteristic
719C2#1914311811yescharacteristic
720C2#1914312511yescharacteristic
721C2#1914478811yescharacteristic
722C2#1914480311yescharacteristic
723C2#1914485111yescharacteristic
724C2#1914486611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2314C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#2314D43
hypocenterC43#20746
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#14582960C2semidirect
3. #19134683C2semidirect
4. #19134679C2semidirect
5. #19134607C2semidirect
6. #19134602C2semidirect
7. #19134597C2semidirect
8. #19134592C2semidirect
11. #19134428C2semidirect
12. #19134423C2semidirect
13. C4×#13063248C2semidirect
14. C4×#13063245C2semidirect
15. C43×#2314C2semidirect
18. #14583379C4semidirect
356. #2314D43semidirect
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
C2×#145829602
#191346832
#191346792
#191346072
#191346022
#191345972
#191345922
#191345332
#191344282
#191344232
C4×#130632482
C4×#130632452
C43×#23142
#2074643