Finite Group Databasebeta

← C2×#19147136 #25975236

Subgroups — C2×#19147136 #25975236

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×#14583617C211yesmaximal, characteristic, complemented
2C2×#14583593C211yesmaximal, characteristic
3#19147136C2116yesmaximal, direct product factor
4C2×#14583307C211yesmaximal, characteristic, complemented
5C2×#14583240C211yesmaximal, characteristic, complemented
6C2×#14583225C211yesmaximal, characteristic, complemented
7C2×#14583223C211yesmaximal, characteristic, complemented
8C2×#14583231C211yesmaximal, characteristic, complemented
9C2×#14583209C211yesmaximal, characteristic, complemented
10C2×#14583188C211yesmaximal, characteristic, complemented
11C2×#14583146C211yesmaximal, characteristic, complemented
12C2×#14583128C211yesmaximal, characteristic, complemented
13C2×#14582998C211yesmaximal, characteristic, complemented
14C2×#14582970C211yesmaximal, characteristic, complemented
15C2×#14582940C211yesmaximal, characteristic, complemented
16C2×C43×#427C211yesmaximal, characteristic, complemented
17C22×#10621873C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19#14583617—24no—
20#14583617C2218yescomplemented
21#14583593—24no—
22#14583593C2218yes—
23C2×#13063324C2211yescharacteristic
24C2×#13063319—21no—
25C2×#13063319—21no—
26C2×#13063318—21no—
27C2×#13063316C2211yescharacteristic
28C2×#13063311—21no—
29C2×#13063307—21no—
30C2×#13063305C2211yescharacteristic
31C2×#13063304C2211yescharacteristic
32C2×#13063300C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063298—21no—
35C2×C4×Dic86—21no—
36C2×#13063290C2211yescharacteristic
37C2×C4×D172—21no—
38C2×#13063287C2211yescharacteristic
39C2×C4×C22⋊D43C2211yescharacteristic
40C2×#13063283C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583307C2218yescomplemented
43#14583240C2218yescomplemented
44#14583231C2218yescomplemented
45#14583225C2218yescomplemented
46#14583223C2218yescomplemented
47#14583209C2218yescomplemented
48#14583188C2218yescomplemented
49#14583146C2218yescomplemented
50#14583128C2218yescomplemented
51#14582998C2218yescomplemented
52#14582970C2218yescomplemented
53#14582940C2218yescomplemented
54C2×#13063258C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×C8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C2×#117×C43C2211yescharacteristic
72C43×#427C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#107×C43C2211yescharacteristic
75C2×#106×C43C2211yescharacteristic
76C2×#106×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43D411yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×#10621873—24no—
87C2×#10621873C2314yes—
88C2×#10621872—24no—
89C2×#10621872C2314yes—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92#13063324—22no—
93#13063324C2314yes—
94#13063319—28no—
95#13063319—28no—
96#13063318—28no—
97#13063316—22no—
98#13063316C2314yes—
99#13063311—28no—
100#13063307—28no—
101#13063305—22no—
102#13063305C2314yes—
103#13063304—22no—
104#13063304C2314yes—
105#13063300—22no—
106#13063300C2314yes—
107#13063299—22no—
108#13063299C2314yes—
109#13063298—28no—
110C4×Dic86—28no—
111#13063290—22no—
112#13063290C2314yes—
113C4×D172—28no—
114#13063287—22no—
115#13063287C2314yes—
116C4×C22⋊D43D414yes—
117C4×C22⋊D43C2314yes—
118#13063283—22no—
119#13063283C2314yes—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4D411yescharacteristic
130C4⋊C4×D43—22no—
131C4⋊C4×D43C2314yes—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43D411yescharacteristic
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4D411yescharacteristic
140C2×C4×Dic43—21no—
141C2×C4×Dic43—21no—
142C2×C4×Dic43C2311yescharacteristic
143#13063258C2314yes—
144#13063258C2314yes—
145#13063257C2314yes—
146#13063256C2314yes—
147#13063256C2314yes—
148Dic43⋊C8C2314yes—
149#13063250C2314yes—
150#13063248C2314yes—
151#13063248C2314yes—
152#13063247C2314yes—
153#13063245C2314yes—
154#13063245C2314yes—
155C22⋊(C43⋊C8)C2314yes—
156(C2×D43)⋊C8C2314yes—
157#13063235C2314yes—
158C23×C4×C43C2311yescharacteristic
159C22×C8×C43—24no—
160C22×C8×C43C2311yescharacteristic
161C22×C8×C43C2314yes—
162C22×C8×C43C2311yescharacteristic
163#117×C43—22no—
164#117×C43—22no—
165#117×C43C2314yes—
166#117×C43C2314yes—
167C2×C4⋊C4×C43C2311yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C22⋊C4×C43—21no—
172C2×C22⋊C4×C43—21no—
173C2×C42×C43—21no—
174C2×C42×C43—21no—
175#107×C43C2314yes—
176#107×C43C2314yes—
177#106×C43C2314yes—
178#106×C43C2314yes—
179C24×C43C2×D411yescharacteristic
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2411yescharacteristic
192C2×C22⋊D43—24no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—82no—
195C2×C22⋊D43C2×D414yes—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201C22×Dic43C2×D411yescharacteristic
202C2×D172—21no—
203C2×D172—24no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—44no—
207C2×D172C2412yes—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—82no—
213C2×C4×D43—82no—
214C2×C4×D43C2×D412yes—
215C2×C4×D43C2412yes—
216C2×Dic86—22no—
217C2×Dic86—22no—
218C2×Dic86—21no—
219C2×Dic86—24no—
220C2×Dic86—44no—
221C2×Dic86C2412yes—
222C2×C8×C43—22no—
223C2×C8×C43—28no—
224C2×C8×C43#4114yes—
225C2×C8×C43C2412yes—
226C2×C8×C43C2412yes—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43C2412yes—
232C4⋊C4×C43C2412yes—
233C4⋊C4×C43C2412yes—
234C4⋊C4×C43C2412yes—
235C22⋊C4×C43—24no—
236C22⋊C4×C43—24no—
237C42×C43—24no—
238C42×C43—24no—
239C22⋊Dic43—24no—
240C22⋊Dic43C2×D414yes—
241(C2×D43)⋊C4—24no—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4—24no—
246(C2×D43)⋊C4C2×D414yes—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43C2412yes—
252C4⋊Dic43C2412yes—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4C2×D414yes—
259C4×Dic43—24no—
260C4×Dic43—24no—
261C4×Dic43C2×D412yes—
262C4×Dic43C2412yes—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8C2412yes—
266C2×C43⋊C8C2412yes—
267#10621873—28no—
268#10621872—28no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43C22×D412yes—
273C23×C43C22×D411yescharacteristic
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43C22×D412yes—
282C2×C4×C43—22no—
283C2×C4×C43—24no—
284C2×C4×C43—22no—
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—42no—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4112yes—
297C2×C4×C432−1+412yes—
298C2×C4×C43C2511yescharacteristic
299C22⋊D43—44no—
300C22⋊D43—84no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43C22×D412yes—
311C2×Dic43C22×D412yes—
312C2×Dic43C22×D412yes—
313D172—22no—
314D172—22no—
315D172—48no—
316D172—42no—
317C4×D43—24no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—84no—
321C4×D43—84no—
322Dic86—22no—
323Dic86—22no—
324Dic86—48no—
325Dic86—42no—
326C8×C43—22no—
327C8×C43C2×#4114yes—
328C43⋊C8—22no—
329C43⋊C8—22no—
330C2×#3350—431nomaximal, Sylow
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—44no—
335C22×C43#54712yes—
336C22×C43#57512yes—
337C22×C43#57712yes—
338C22×C43C23×D411yescharacteristic
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—44no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—42no—
346C2×D43—84no—
347C4×C43—22no—
348C4×C43—42no—
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—22no—
358Dic43—42no—
359Dic43—42no—
360Dic43—42no—
361C2×#556—431no—
362C2×#553—431no—
363#3350—4316no—
364C2×#501—431no—
365C2×#485—431no—
366C2×#482—431no—
367C2×#482—431no—
368C2×#483—431no—
369C2×#479—431no—
370C2×#476—431no—
371C2×#468—431no—
372C2×#465—431no—
373C2×#440—431no—
374C2×#435—431no—
375C2×#428—431no—
376C2×#427D4311yescharacteristic, complemented
377C2×C43—42no—
378C2×C43#335014yescomplemented
379C2×C43C2×#54711yescharacteristic
380C2×C43C2×#57511yescharacteristic
381C2×C43C2×#57711yescharacteristic
382D43—42no—
383D43—82no—
384C22×SD16—431no—
385C22×M16—431no—
386C23×C8C2×D4311yescharacteristic
387#556—438no—
388#556—864no—
389#553—438no—
390#553—864no—
391C2×C4⋊Q8—431no—
392C2×#126—861no—
393C2×#126—861no—
394C2×#126—861no—
395C2×#125—431no—
396C2×#124—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×Q8—861no—
405C2×C4×D4—431no—
406C2×C4×D4—431no—
407C2×C4×D4—861no—
408C2×#117—431no—
409C2×#117C2×D4311yescharacteristic
410C2×#117C2×D4311yescharacteristic
411C22×C4⋊C4—431no—
412#501—438no—
413#485—438no—
414#483—438no—
415#482—438no—
416#482—438no—
417#479—438no—
418#476—438no—
419#468—438no—
420#465—438no—
421#440—438no—
422#435—438no—
423#428—438no—
424#427C2×D4318yescomplemented
425C2×#107—431no—
426C2×#107—431no—
427C2×#107C2×D4311yescharacteristic
428C2×#107C2×D4311yescharacteristic
429C2×#106—431no—
430C2×#106—431no—
431C2×#106—431no—
432C2×#106C2×D4311yescharacteristic
433C2×#106C2×D4311yescharacteristic
434C2×C4⋊C8—431no—
435C2×#103—431no—
436C2×#103—431no—
437C2×#103—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×C22⋊C8—431no—
442C2×C22⋊C8—431no—
443C2×#97—431no—
444C43C2×#335011yescharacteristic, complemented, Sylow
445C22×Q8—431no—
446C22×Q8—861no—
447C22×D4—431no—
448C22×D4—431no—
449C22×D4—861no—
450C22×D4—861no—
451C23×C4—431no—
452C23×C4—861no—
453C23×C4—861no—
454C23×C4C22×D4311yescharacteristic
455C2×SD16—434no—
456C2×SD16—864no—
457C2×M16—434no—
458C2×M16—864no—
459C22×C8—24no—
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4314yes—
464C22×C8C22×D4311yescharacteristic
465C4⋊Q8—434no—
466C4⋊Q8—862no—
467#126—868no—
468#126—868no—
469#126—868no—
470#125—434no—
471#125—862no—
472#124—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—868no—
485C4×Q8—862no—
486C4×D4—434no—
487C4×D4—434no—
488C4×D4—434no—
489C4×D4—868no—
490C4×D4—862no—
491#117—22no—
492#117—22no—
493#117—434no—
494#117—862no—
495#117C22×D4314yes—
496#117C22×D4314yes—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—434no—
501C2×C4⋊C4—862no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C4⋊C4C22×D4311yescharacteristic
512C2×C4⋊C4C22×D4311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—431no—
516C2×C22⋊C4—431no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42—431no—
526C2×C42—861no—
527C2×C42—861no—
528#107—434no—
529#107—434no—
530#107C22×D4314yes—
531#107C22×D4314yes—
532#106—434no—
533#106—434no—
534#106—434no—
535#106C22×D4314yes—
536#106C22×D4314yes—
537C4⋊C8—434no—
538#103—434no—
539#103—434no—
540#103—434no—
541#102—434no—
542#102—434no—
543#102—434no—
544C22⋊C8—434no—
545C22⋊C8—434no—
546#97—434no—
547C24—431no—
548C24—861no—
549C24D4×D4311yescharacteristic
550C2×Q8—432no—
551C2×Q8—864no—
552C2×Q8—861no—
553C2×Q8—862no—
554C2×Q8—862no—
555C2×Q8—1724no—
556C2×D4—434no—
557C2×D4—432no—
558C2×D4—864no—
559C2×D4—864no—
560C2×D4—861no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—3442no—
564C2×D4—1724no—
565C2×D4—1722no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—431no—
573C22×C4—431no—
574C22×C4—431no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—864no—
578C22×C4—864no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—3442no—
585C22×C4—3442no—
586C22×C4D4×D4312yes—
587C22×C4D4×D4311yescharacteristic
588C22×C4C23×D4312yes—
589C22×C4C23×D4311yescharacteristic
590SD16—868no—
591M16—868no—
592C2×C8—22no—
593C2×C8—28no—
594C2×C8—432no—
595C2×C8—432no—
596C2×C8—862no—
597C2×C8—862no—
598C2×C8#1062189814yes—
599C2×C8C23×D4312yes—
600C2×C8C23×D4312yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—434no—
606C4⋊C4—432no—
607C4⋊C4—432no—
608C4⋊C4—864no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—864no—
617C4⋊C4C23×D4312yes—
618C4⋊C4C23×D4312yes—
619C4⋊C4C23×D4312yes—
620C4⋊C4C23×D4312yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—434no—
624C22⋊C4—434no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—864no—
628C22⋊C4—864no—
629C22⋊C4—864no—
630C22⋊C4—864no—
631C42—24no—
632C42—24no—
633C42—432no—
634C42—432no—
635C42—864no—
636C42—864no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—432no—
641C23—862no—
642C23—862no—
643C23—862no—
644C23—862no—
645C23—1722no—
646C23—1722no—
647C23—1722no—
648C23C2×D4×D4312yes—
649C23C2×D4×D4311yescharacteristic
650Q8—862no—
651Q8—862no—
652Q8—1728no—
653Q8—1722no—
654D4—862no—
655D4—862no—
656D4—3444no—
657D4—1728no—
658D4—1724no—
659D4—1722no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—432no—
673C2×C4—432no—
674C2×C4—432no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—864no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—3444no—
685C2×C4—3444no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4C2×D4×D4312yes—
690C2×C4C2×D4×D4311yescharacteristic
691C2×C4C2×#1062189812yes—
692C2×C4#1306337312yes—
693C2×C4C24×D4311yescharacteristic
694C8—22no—
695C8—862no—
696C8—862no—
697C8C2×#1062189814yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—44no—
702C22—862no—
703C22—862no—
704C22—862no—
705C22—3444no—
706C22—1722no—
707C22—1722no—
708C22—1722no—
709C22—1724no—
710C22#1458355012yes—
711C22#1458369612yes—
712C22#1458370612yes—
713C22C22×D4×D4311yescharacteristic
714C4—22no—
715C4—42no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—862no—
720C4—862no—
721C4—862no—
722C4—1722no—
723C4—1722no—
724C4—1722no—
725C4#1458355012yes—
726C4C22×#1062189811yescharacteristic
727C4C2×#1306337311yescharacteristic
728C2—42no—
729C2—3442no—
730C2—1722no—
731C2#1914713614yesdirect product factor
732C2C2×#1458355011yescharacteristic
733C2C2×#1458369611yescharacteristic
734C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#427C2
socleC23×C43C22×D4
prime radicalC2×#14583593C2
hypercenterC2×#427D43
hypocenterC43C2×#3350
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#14583617C2semidirect
3. #19147136C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583240C2semidirect
6. C2×#14583225C2semidirect
7. C2×#14583223C2semidirect
8. C2×#14583231C2semidirect
9. C2×#14583209C2semidirect
10. C2×#14583188C2semidirect
11. C2×#14583146C2semidirect
12. C2×#14583128C2semidirect
13. C2×#14582998C2semidirect
14. C2×#14582970C2semidirect
15. C2×#14582940C2semidirect
16. C2×C43×#427C2semidirect
20. #14583617C22semidirect
42. #14583307C22semidirect
43. #14583240C22semidirect
44. #14583231C22semidirect
45. #14583225C22semidirect
46. #14583223C22semidirect
47. #14583209C22semidirect
48. #14583188C22semidirect
49. #14583146C22semidirect
50. #14583128C22semidirect
51. #14582998C22semidirect
52. #14582970C22semidirect
53. #14582940C22semidirect
72. C43×#427C22semidirect
376. C2×#427D43semidirect
378. C2×C43#3350semidirect
424. #427C2×D43semidirect
444. C43C2×#3350semidirect
731. C2#19147136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836172
C2×#145835932
#191471362
C2×#145833072
C2×#145832402
C2×#145832252
C2×#145832232
C2×#145832312
C2×#145832092
C2×#145831882
C2×#145831462
C2×#145831282
C2×#145829982
C2×#145829702
C2×#145829402
C2×C43×#4272
C2×#335043