Finite Group Databasebeta

← C2×#19147162 #25975282

Subgroups — C2×#19147162 #25975282

Order 11008.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583599C211yesmaximal, characteristic
2C2×#14583587C211yesmaximal, characteristic, complemented
3#19147162C2116yesmaximal, direct product factor
4C2×#14583298C211yesmaximal, characteristic, complemented
5C2×#14583216C211yesmaximal, characteristic, complemented
6C2×#14583242C211yesmaximal, characteristic, complemented
7C2×#14583221C211yesmaximal, characteristic, complemented
8C2×#14583231C211yesmaximal, characteristic, complemented
9C2×#14583207C211yesmaximal, characteristic, complemented
10C2×#14583144C211yesmaximal, characteristic, complemented
11C2×#14583144C211yesmaximal, characteristic, complemented
12C2×C4×#10621883C211yesmaximal, characteristic, complemented
13C2×#14582976C211yesmaximal, characteristic, complemented
14C2×#14582940C211yesmaximal, characteristic, complemented
15C2×#14582938C211yesmaximal, characteristic, complemented
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C22×#10621883C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20#14583599—24no—
21#14583599C2218yes—
22#14583587—24no—
23#14583587C2218yescomplemented
24C2×#13063320—21no—
25C2×#13063318—21no—
26C2×#13063317C2211yescharacteristic
27C2×#13063316—21no—
28C2×#13063310—21no—
29C2×#13063308—21no—
30C2×#13063305C2211yescharacteristic
31C2×#13063305C2211yescharacteristic
32C2×#13063298—21no—
33C2×#13063296C2211yescharacteristic
34C2×#13063296C2211yescharacteristic
35C2×C4×Dic86C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C2×#13063283—21no—
39C2×#13063283C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583298C2218yescomplemented
44#14583242C2218yescomplemented
45#14583231C2218yescomplemented
46#14583221C2218yescomplemented
47#14583216C2218yescomplemented
48#14583207C2218yescomplemented
49#14583144C2218yescomplemented
50#14583144C2218yescomplemented
51C4×#10621883C2218yescomplemented
52#14582976C2218yescomplemented
53#14582940C2218yescomplemented
54#14582938C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063256C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×#13063256C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C4×C43⋊C8C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×D172D411yescharacteristic
79C22×C22⋊D43—21no—
80C22×C22⋊D43—21no—
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83C22×C4×D43C2311yescharacteristic
84C22×C4×D43C2311yescharacteristic
85C2×#10621883—24no—
86C2×#10621883C2314yes—
87C2×#10621872—24no—
88C2×#10621872—24no—
89C2×#10621872C2314yes—
90C2×#10621872C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063320—28no—
94#13063318—28no—
95#13063317—22no—
96#13063317C2314yes—
97#13063316—28no—
98#13063310—28no—
99#13063308—28no—
100#13063305—22no—
101#13063305—22no—
102#13063305C2314yes—
103#13063305C2314yes—
104#13063298—28no—
105#13063296—22no—
106#13063296—22no—
107#13063296C2314yes—
108#13063296C2314yes—
109C4×Dic86—22no—
110C4×Dic86C2314yes—
111C4×D172D414yes—
112C4×D172C2314yes—
113C4×C22⋊D43—28no—
114#13063283—22no—
115#13063283—22no—
116#13063283—28no—
117#13063283C2314yes—
118#13063283C2314yes—
119C2×C4⋊Dic43—21no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43D411yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2311yescharacteristic
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C4⋊C4×D43C2314yes—
133C4⋊C4×D43C2314yes—
134C2×C22⋊Dic43—21no—
135C2×C22⋊Dic43—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4D411yescharacteristic
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×C4×Dic43—21no—
143C2×C4×Dic43—21no—
144C2×C4×Dic43—21no—
145#13063259C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152#13063250C2314yes—
153#13063250C2314yes—
154#13063248C2314yes—
155#13063246C2314yes—
156(C2×D43)⋊C8C2314yes—
157(C2×D43)⋊C8C2314yes—
158C4×C43⋊C8C2314yes—
159C22×D4×C43C2311yescharacteristic
160C23×C4×C43—21no—
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163#125×C43—22no—
164#125×C43C2314yes—
165C4×D4×C43—22no—
166C4×D4×C43C2314yes—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C42×C43C2311yescharacteristic
174#107×C43C2314yes—
175#106×C43C2314yes—
176C4⋊C8×C43C2314yes—
177#102×C43C2314yes—
178#102×C43C2314yes—
179C24×C43—21no—
180C23×D43C2×D411yescharacteristic
181C23×D43C2×D411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43—22no—
184C2×D4×C43—22no—
185C2×D4×C43C2412yes—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—82no—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—24no—
195C2×C22⋊D43—24no—
196C2×C22⋊D43—44no—
197C2×C22⋊D43—82no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C2×D172—42no—
205C2×D172C2×D414yes—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—44no—
213C2×C4×D43—82no—
214C2×C4×D43C2×D412yes—
215C2×C4×D43C2×D412yes—
216C2×C4×D43C2412yes—
217C2×C4×D43C2412yes—
218C2×Dic86—22no—
219C2×Dic86—22no—
220C2×Dic86—21no—
221C2×Dic86C2412yes—
222C2×C8×C43—22no—
223C2×C8×C43—22no—
224C2×C8×C43C2412yes—
225C2×C8×C43C2412yes—
226C4⋊C4×C43—24no—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C2412yes—
232C4⋊C4×C43C2412yes—
233C4⋊C4×C43C2412yes—
234C22⋊C4×C43—24no—
235C42×C43C2×D412yes—
236C42×C43C2412yes—
237C22⋊Dic43—24no—
238C22⋊Dic43—24no—
239#10621883—28no—
240(C2×D43)⋊C4—24no—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4C2×D414yes—
245(C2×D43)⋊C4C2×D414yes—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43C2×D414yes—
252C4⋊Dic43C2412yes—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260C4×Dic43—24no—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8#4114yes—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267#10621872—28no—
268#10621872—28no—
269C23×C43—22no—
270C23×C43—42no—
271C23×C43—42no—
272C23×C43—42no—
273C23×C43C22×D411yescharacteristic
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43C22×D412yes—
281C22×D43C22×D412yes—
282D4×C43—22no—
283D4×C43—22no—
284D4×C43—42no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—84no—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C2×#4112yes—
298C2×C4×C432−1+412yes—
299C2×C4×C43C2511yescharacteristic
300C22⋊D43—48no—
301C22⋊D43—84no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43C22×D412yes—
313C2×Dic43C22×D412yes—
314D172—44no—
315C4×D43—24no—
316C4×D43—24no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—48no—
322C4×D43—84no—
323Dic86—22no—
324Dic86—22no—
325Dic86—42no—
326C8×C43—22no—
327C8×C43—22no—
328C43⋊C8—22no—
329C43⋊C8C2×#4114yes—
330C2×#3351—431nomaximal, Sylow
331C22×C43—42no—
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—84no—
335C22×C43#54712yes—
336C22×C43#57512yes—
337C22×C43#57712yes—
338C22×C43C23×D411yescharacteristic
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—44no—
346C2×D43—44no—
347C4×C43—22no—
348C4×C43—22no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43#54712yes—
353C4×C43C22×#4111yescharacteristic
354C4×C43C2×2−1+411yescharacteristic
355Dic43—22no—
356Dic43—22no—
357Dic43—42no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#553—431no—
362C2×#552—431no—
363#3351—4316no—
364C2×#499—431no—
365C2×#481—431no—
366C2×#485—431no—
367C2×#482—431no—
368C2×#483—431no—
369C2×#479—431no—
370C2×#478D4311yescharacteristic, complemented
371C2×#468—431no—
372C2×#468—431no—
373C2×C4×SD16—431no—
374C2×#436—431no—
375C2×#428—431no—
376C2×#428—431no—
377C2×C43—82no—
378C2×C43#335114yescomplemented
379C2×C43C2×#54711yescharacteristic
380C2×C43C2×#57511yescharacteristic
381C2×C43C2×#57711yescharacteristic
382D43—42no—
383D43—42no—
384C22×SD16—431no—
385C22×M16—431no—
386C22×M16—431no—
387#553—438no—
388#553—864no—
389#552—438no—
390#552—864no—
391C2×#126—861no—
392C2×#126—861no—
393C2×#125—431no—
394C2×#125—861no—
395C2×#125C2×D4311yescharacteristic
396C2×#123—861no—
397C2×#123—861no—
398C2×C22⋊Q8—431no—
399C2×C22⋊Q8—431no—
400C2×#121—431no—
401C2×#121—431no—
402C2×#121—861no—
403C2×C4×Q8—431no—
404C2×C4×D4—431no—
405C2×C4×D4—861no—
406C2×C4×D4C2×D4311yescharacteristic
407C2×#117—431no—
408C2×#117—431no—
409C2×#117—861no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4—431no—
412#499—438no—
413#485—438no—
414#483—438no—
415#482—438no—
416#481—438no—
417#479—438no—
418#478C2×D4318yescomplemented
419#468—438no—
420#468—438no—
421C4×SD16—438no—
422#436—438no—
423#428—438no—
424#428—438no—
425C2×#107—431no—
426C2×#107—431no—
427C2×#107—431no—
428C2×#107C2×D4311yescharacteristic
429C2×#106—431no—
430C2×#106—431no—
431C2×#106—431no—
432C2×#106—431no—
433C2×#106C2×D4311yescharacteristic
434C2×C4⋊C8C2×D4311yescharacteristic
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#102—431no—
439C2×#102C2×D4311yescharacteristic
440C2×#102C2×D4311yescharacteristic
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×C4×C8—431no—
444C43C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8—431no—
446C22×D4—431no—
447C22×D4—861no—
448C22×D4—861no—
449C22×D4C22×D4311yescharacteristic
450C23×C4—21no—
451C23×C4—431no—
452C23×C4—431no—
453C23×C4—861no—
454C23×C4—861no—
455C2×SD16—434no—
456C2×SD16—864no—
457C2×M16—434no—
458C2×M16—434no—
459C2×M16—864no—
460C2×M16—864no—
461C22×C8—431no—
462C22×C8—431no—
463C22×C8C22×D4311yescharacteristic
464C22×C8C22×D4311yescharacteristic
465#126—868no—
466#126—868no—
467#125—22no—
468#125—434no—
469#125—868no—
470#125—862no—
471#125C22×D4314yes—
472#123—868no—
473#123—868no—
474C22⋊Q8—434no—
475C22⋊Q8—434no—
476C22⋊Q8—862no—
477C22⋊Q8—862no—
478#121—434no—
479#121—434no—
480#121—868no—
481#121—862no—
482#121—862no—
483C4×Q8—434no—
484C4×Q8—862no—
485C4×D4—22no—
486C4×D4—434no—
487C4×D4—434no—
488C4×D4—868no—
489C4×D4C22×D4314yes—
490#117—434no—
491#117—434no—
492#117—868no—
493#117—862no—
494#117—862no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4—861no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C4⋊C4C22×D4311yescharacteristic
514C2×C4⋊C4C22×D4311yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—431no—
517C2×C22⋊C4—431no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C42—861no—
525C2×C42—861no—
526C2×C42—861no—
527C2×C42C22×D4311yescharacteristic
528#107—434no—
529#107—434no—
530#107—434no—
531#107C22×D4314yes—
532#106—434no—
533#106—434no—
534#106—434no—
535#106—434no—
536#106C22×D4314yes—
537C4⋊C8C22×D4314yes—
538#103—434no—
539#103—434no—
540#103—434no—
541#102—434no—
542#102C22×D4314yes—
543#102C22×D4314yes—
544C22⋊C8—434no—
545C22⋊C8—434no—
546C4×C8—434no—
547C24—21no—
548C24—431no—
549C24—431no—
550C2×Q8—432no—
551C2×Q8—861no—
552C2×Q8—862no—
553C2×Q8—862no—
554C2×D4—21no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—434no—
558C2×D4—864no—
559C2×D4—864no—
560C2×D4—3442no—
561C2×D4—1722no—
562C2×D4—1724no—
563C2×D4C23×D4312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—864no—
576C22×C4—864no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—3442no—
586C22×C4—1724no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591M16—868no—
592M16—868no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—434no—
596C2×C8—432no—
597C2×C8—432no—
598C2×C8—862no—
599C2×C8C23×D4312yes—
600C2×C8C23×D4312yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—434no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—432no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4C23×D4312yes—
621C4⋊C4C23×D4312yes—
622C4⋊C4C23×D4312yes—
623C22⋊C4—24no—
624C22⋊C4—434no—
625C22⋊C4—434no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C22⋊C4—864no—
632C42—864no—
633C42—864no—
634C42—864no—
635C42D4×D4312yes—
636C42C23×D4312yes—
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—432no—
642C23—432no—
643C23—862no—
644C23—862no—
645C23—862no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23C2×D4×D4311yescharacteristic
650Q8—862no—
651Q8—862no—
652Q8—1722no—
653D4—22no—
654D4—22no—
655D4—42no—
656D4—3444no—
657D4—1724no—
658D4—1728no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—84no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—864no—
677C2×C4—864no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—3444no—
683C2×C4—1728no—
684C2×C4—1722no—
685C2×C4—1722no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4C2×D4×D4312yes—
689C2×C4C2×D4×D4312yes—
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4#41×D4312yes—
692C2×C4#1306337312yes—
693C2×C4C24×D4311yescharacteristic
694C8—22no—
695C8—22no—
696C8—434no—
697C8—862no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—84no—
702C22—862no—
703C22—862no—
704C22—862no—
705C22—862no—
706C22—862no—
707C22—862no—
708C22—1724no—
709C22—1724no—
710C22#1458355112yes—
711C22#1458369612yes—
712C22#1458370912yes—
713C22C22×D4×D4311yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—862no—
720C4—862no—
721C4—1722no—
722C4—1722no—
723C4—1722no—
724C4—1722no—
725C4#1458355112yes—
726C4C2×#41×D4311yescharacteristic
727C4C2×#1306337311yescharacteristic
728C2—82no—
729C2—1722no—
730C2—1722no—
731C2#1914716214yesdirect product factor
732C2C2×#1458355111yescharacteristic
733C2C2×#1458369611yescharacteristic
734C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
prime radicalC2×#14583599C2
hypercenterC2×#478D43
hypocenterC43C2×#3351
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. C2×#14583587C2semidirect
3. #19147162C2direct (N × H)
4. C2×#14583298C2semidirect
5. C2×#14583216C2semidirect
6. C2×#14583242C2semidirect
7. C2×#14583221C2semidirect
8. C2×#14583231C2semidirect
9. C2×#14583207C2semidirect
10. C2×#14583144C2semidirect
11. C2×#14583144C2semidirect
12. C2×C4×#10621883C2semidirect
13. C2×#14582976C2semidirect
14. C2×#14582940C2semidirect
15. C2×#14582938C2semidirect
16. C2×C43×#478C2semidirect
23. #14583587C22semidirect
43. #14583298C22semidirect
44. #14583242C22semidirect
45. #14583231C22semidirect
46. #14583221C22semidirect
47. #14583216C22semidirect
48. #14583207C22semidirect
49. #14583144C22semidirect
50. #14583144C22semidirect
51. C4×#10621883C22semidirect
52. #14582976C22semidirect
53. #14582940C22semidirect
54. #14582938C22semidirect
71. C43×#478C22semidirect
370. C2×#478D43semidirect
378. C2×C43#3351semidirect
418. #478C2×D43semidirect
444. C43C2×#3351semidirect
731. C2#19147162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835992
C2×#145835872
#191471622
C2×#145832982
C2×#145832162
C2×#145832422
C2×#145832212
C2×#145832312
C2×#145832072
C2×#145831442
C2×C4×#106218832
C2×#145829762
C2×#145829402
C2×#145829382
C2×C43×#4782
C2×#335143