Finite Group Databasebeta

← C2×#19144414 #25964133

Subgroups — C2×#19144414 #25964133

Order 11008.

2142 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D43C211yesmaximal, characteristic, complemented
2C2×C4×#10621902C211yesmaximal, characteristic
3#19144414C2116yesmaximal, direct product factor
4C2×#14583208C211yesmaximal, characteristic, complemented
5C2×#14583206C211yesmaximal, characteristic, complemented
6C2×#14583204C211yesmaximal, characteristic, complemented
7C2×#14583202C211yesmaximal, characteristic, complemented
8C2×#14583200C211yesmaximal, characteristic, complemented
9C2×#14583198C211yesmaximal, characteristic, complemented
10C2×#14583196C211yesmaximal, characteristic, complemented
11C2×#14582940C211yesmaximal, characteristic, complemented
12C2×#14582938C211yesmaximal, characteristic, complemented
13C2×#14582921C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic
15C2×#14582899C211yesmaximal, characteristic
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C2×#13063317C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063316C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063315—21no—
25#125×D43—24no—
26#125×D43C2218yescomplemented
27C4×#10621902—24no—
28C4×#10621902C2218yes—
29C2×Q8×Dic43C2211yescharacteristic
30C2×C4×D172—21no—
31C2×C4×D172C2211yescharacteristic
32C2×#13063287—21no—
33C2×#13063287C2211yescharacteristic
34C2×#13063283—21no—
35C2×#13063283C2211yescharacteristic
36C2×C4⋊C4×D43—21no—
37C2×C4⋊C4×D43—21no—
38C2×C4⋊C4×D43C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C42×D43—21no—
41C2×C42×D43C2211yescharacteristic
42#14583208C2218yescomplemented
43#14583206C2218yescomplemented
44#14583204C2218yescomplemented
45#14583202C2218yescomplemented
46#14583200C2218yescomplemented
47#14583198C2218yescomplemented
48#14583196C2218yescomplemented
49#14582940C2218yescomplemented
50#14582938C2218yescomplemented
51C2×#13063259C2211yescharacteristic
52C2×#13063258C2211yescharacteristic
53C2×#13063258C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57#14582921C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61#14582899C2218yes—
62#14582899C2218yes—
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#479C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902Q818yes—
80C2×#10621902C2314yes—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43D411yescharacteristic
89C22×C4×D43D411yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C2×#10621872—24no—
92C2×#10621872—24no—
93C2×#10621872C2314yes—
94C2×#10621872C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063317—22no—
98#13063317C2314yes—
99#13063316—22no—
100#13063316—22no—
101#13063316C2314yes—
102#13063316C2314yes—
103#13063315—28no—
104#13063315—28no—
105Q8×Dic43—22no—
106Q8×Dic43C2314yes—
107C4×D172—28no—
108C4×D172—22no—
109C4×D172C2314yes—
110#13063287—28no—
111#13063287—22no—
112#13063287C2314yes—
113#13063283—22no—
114#13063283—28no—
115#13063283C2314yes—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43—21no—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C4⋊C4×D43—28no—
129C4⋊C4×D43—28no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C4⋊C4×D43C2314yes—
133C4⋊C4×D43C2314yes—
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4—21no—
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43D411yescharacteristic
140C2×C4×Dic43D411yescharacteristic
141C2×C4×Dic43C2311yescharacteristic
142C42×D43—28no—
143C42×D43D414yes—
144C42×D43C2314yes—
145#13063259C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150#13063256C2314yes—
151C4⋊(C43⋊C8)C2314yes—
152Dic43⋊C8C2314yes—
153Dic43⋊C8C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160C22×Q8×C43C2311yescharacteristic
161C22×C8×C43C2311yescharacteristic
162C22×C8×C43C2311yescharacteristic
163#125×C43—22no—
164#125×C43C2314yes—
165C4×Q8×C43—22no—
166C4×Q8×C43C2314yes—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—21no—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C42×C43—21no—
174C2×C42×C43C2311yescharacteristic
175#107×C43C2314yes—
176#106×C43C2314yes—
177C4⋊C8×C43C2314yes—
178#103×C43C2314yes—
179#103×C43C2314yes—
180C23×D43—21no—
181C23×D43C2×D411yescharacteristic
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43C2×Q814yes—
185C2×Q8×C43C2412yes—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199#10621902—216no—
200#10621902—28no—
201#10621902C2×Q8116yes—
202C2×D172—21no—
203C2×D172—22no—
204C2×D172—28no—
205C2×D172—24no—
206C2×D172C2×Q814yes—
207C2×D172C2412yes—
208C2×C4×D43—28no—
209C2×C4×D43—24no—
210C2×C4×D43—24no—
211C2×C4×D43—24no—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—42no—
215C2×C4×D43—42no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×C4×D43—44no—
219C2×C4×D43—44no—
220C2×C4×D43C2×D414yes—
221C2×C4×D43C2×D414yes—
222C2×C4×D43C2×D412yes—
223C2×C4×D43C2×Q814yes—
224C2×C4×D43#4114yes—
225C2×C4×D43C2412yes—
226C2×C8×C43—22no—
227C2×C8×C43—22no—
228C2×C8×C43C2412yes—
229C2×C8×C43C2412yes—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C4⋊C4×C43C2412yes—
239C42×C43—24no—
240C42×C43C2×D412yes—
241C42×C43C2412yes—
242(C2×D43)⋊C4—24no—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245C4⋊Dic43—21no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—24no—
249C4⋊Dic43—24no—
250C4⋊Dic43—24no—
251C4⋊Dic43C2412yes—
252C4⋊Dic43C2412yes—
253C4⋊Dic43C2412yes—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260C4×Dic43—24no—
261C4×Dic43—24no—
262C4×Dic43C2×D414yes—
263C4×Dic43C2×D412yes—
264C4×Dic43C2×D414yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270#10621872—28no—
271#10621872—28no—
272C23×C43C22×D411yescharacteristic
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—24no—
276C22×D43—22no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43C22⋊Q814yes—
280C22×D43C22×D412yes—
281Q8×C43—24no—
282Q8×C43—22no—
283Q8×C43C22×Q814yes—
284C2×C4×C43—24no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43C22×D412yes—
295C2×C4×C43C22×D412yes—
296C2×C4×C43C22×D411yescharacteristic
297C2×C4×C43C22×Q812yes—
298C2×C4×C43C2×#4112yes—
299C2×C4×C43C2511yescharacteristic
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43C22⋊Q814yes—
309C2×Dic43C22×D412yes—
310C2×Dic43C22×D412yes—
311C2×Dic43C22×D412yes—
312D172—216no—
313D172—24no—
314D172—22no—
315D172C22×Q814yes—
316C4×D43—216no—
317C4×D43—44no—
318C4×D43—44no—
319C4×D43—48no—
320C4×D43—48no—
321C4×D43—48no—
322C4×D43—48no—
323C4×D43C22⋊Q818yes—
324C4×D43C22×Q814yes—
325C4×D43C2×#4114yes—
326C8×C43—22no—
327C8×C43—22no—
328C43⋊C8—22no—
329C43⋊C8—22no—
330C2×#3080—431nomaximal, Sylow
331C22×C43C2×C22⋊Q812yes—
332C22×C43#57512yes—
333C22×C43#57512yes—
334C22×C43C23×D411yescharacteristic
335C2×D43—28no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—24no—
339C2×D43—48no—
340C2×D43—42no—
341C2×D43—42no—
342C2×D43C2×C22⋊Q814yes—
343C4×C43—24no—
344C4×C43—22no—
345C4×C43—22no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43—42no—
349C4×C43C2×C22⋊Q812yes—
350C4×C43C23×Q811yescharacteristic
351C4×C43C22×#4111yescharacteristic
352Dic43—22no—
353Dic43—22no—
354Dic43—42no—
355Dic43—42no—
356Dic43—42no—
357Dic43C2×C22⋊Q814yes—
358C22×#125—431no—
359C2×C4×#41—431no—
360#3080—4316no—
361C2×#479—431no—
362C2×#479—431no—
363C2×#479—431no—
364C2×#479D4311yescharacteristic, complemented
365C2×#478—431no—
366C2×#478—431no—
367C2×#478—431no—
368C2×#478—431no—
369C2×#428—431no—
370C2×#428—431no—
371C2×#423—431no—
372C2×#417—431no—
373C2×#417—431no—
374C2×C43#308014yescomplemented
375C2×C43C22×C22⋊Q811yescharacteristic
376C2×C43C2×#57511yescharacteristic
377C2×C43C2×#57511yescharacteristic
378D43—24no—
379D43—44no—
380C22×#41—431no—
381C22×M16—431no—
382C22×M16—431no—
383C2×#125—438no—
384C2×#125—431no—
385C2×#125—431no—
386C2×#125—431no—
387C2×#125—861no—
388C2×#125—861no—
389C2×#125—864no—
390C2×#125C2×D4311yescharacteristic
391C4×#41—438no—
392C4×#41—864no—
393C2×C4×Q8—431no—
394C2×C4×Q8C2×D4311yescharacteristic
395C2×C4×D4—431no—
396C2×C4×D4—431no—
397C2×C4×D4—861no—
398C2×C4×D4—861no—
399C2×#117—431no—
400C2×#117—861no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4—861no—
404C22×C4⋊C4—861no—
405C22×C42—431no—
406C22×C42—861no—
407#479—438no—
408#479—438no—
409#479—438no—
410#479C2×D4318yescomplemented
411#478—438no—
412#478—438no—
413#478—438no—
414#478—438no—
415#428—438no—
416#428—438no—
417C2×#107—431no—
418C2×#107—431no—
419C2×#107—431no—
420C2×#107C2×D4311yescharacteristic
421C2×#106—431no—
422C2×#106—431no—
423C2×#106—431no—
424C2×#106C2×D4311yescharacteristic
425#423—438no—
426C2×C4⋊C8—431no—
427C2×C4⋊C8—431no—
428C2×C4⋊C8—431no—
429C2×C4⋊C8C2×D4311yescharacteristic
430#417—438no—
431#417—438no—
432C2×#103—431no—
433C2×#103—431no—
434C2×#103C2×D4311yescharacteristic
435C2×#103C2×D4311yescharacteristic
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C43C2×#308011yescharacteristic, complemented, Sylow
441C2×#41—438no—
442C2×#41—434no—
443C2×#41—862no—
444C2×#41—864no—
445C22×Q8C22×D4311yescharacteristic
446C22×D4—431no—
447C22×D4—861no—
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4—861no—
454C23×C4—861no—
455C23×C4—861no—
456C2×M16—434no—
457C2×M16—434no—
458C2×M16—864no—
459C2×M16—864no—
460C22×C8—431no—
461C22×C8—431no—
462C22×C8C22×D4311yescharacteristic
463C22×C8C22×D4311yescharacteristic
464#125—22no—
465#125—434no—
466#125—434no—
467#125—434no—
468#125—868no—
469#125—868no—
470#125—862no—
471#125—862no—
472#125—862no—
473#125C22×D4314yes—
474C4×Q8—22no—
475C4×Q8—434no—
476C4×Q8—862no—
477C4×Q8C22×D4314yes—
478C4×D4—434no—
479C4×D4—434no—
480C4×D4—868no—
481C4×D4—862no—
482C4×D4—868no—
483C4×D4—862no—
484#117—434no—
485#117—868no—
486#117—862no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—434no—
495C2×C4⋊C4—862no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—868no—
498C2×C4⋊C4—868no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
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⋊C4C22×D4311yescharacteristic
509C2×C4⋊C4C22×D4311yescharacteristic
510C2×C4⋊C4C22×D4311yescharacteristic
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C42—21no—
515C2×C42—431no—
516C2×C42—431no—
517C2×C42—431no—
518C2×C42—434no—
519C2×C42—434no—
520C2×C42—868no—
521C2×C42—861no—
522C2×C42—861no—
523C2×C42C22×D4311yescharacteristic
524#107—434no—
525#107—434no—
526#107—434no—
527#107C22×D4314yes—
528#106—434no—
529#106—434no—
530#106—434no—
531#106C22×D4314yes—
532C4⋊C8—434no—
533C4⋊C8—434no—
534C4⋊C8—434no—
535C4⋊C8C22×D4314yes—
536#103—434no—
537#103—434no—
538#103C22×D4314yes—
539#103C22×D4314yes—
540#102—434no—
541#102—434no—
542#102—434no—
543#102—434no—
544C24—431no—
545C24—861no—
546#41—4316no—
547#41—8616no—
548#41—868no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8Q8×D4314yes—
552C2×Q8C23×D4312yes—
553C2×D4—434no—
554C2×D4—432no—
555C2×D4—864no—
556C2×D4—868no—
557C2×D4—861no—
558C2×D4—862no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—431no—
564C22×C4—432no—
565C22×C4—434no—
566C22×C4—434no—
567C22×C4—432no—
568C22×C4—431no—
569C22×C4—431no—
570C22×C4—434no—
571C22×C4—434no—
572C22×C4—864no—
573C22×C4—868no—
574C22×C4—864no—
575C22×C4—864no—
576C22×C4—864no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—864no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4—1724no—
584C22×C4—1724no—
585C22×C4—1724no—
586C22×C4—1724no—
587C22×C4D4×D4311yescharacteristic
588C22×C4D4×D4311yescharacteristic
589C22×C4C23×D4311yescharacteristic
590M16—868no—
591M16—868no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—432no—
595C2×C8—432no—
596C2×C8—862no—
597C2×C8—862no—
598C2×C8C23×D4312yes—
599C2×C8C23×D4312yes—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—432no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—864no—
615C4⋊C4—864no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4C23×D4312yes—
622C4⋊C4C23×D4312yes—
623C4⋊C4C23×D4312yes—
624C22⋊C4—864no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C42—24no—
628C42—434no—
629C42—434no—
630C42—432no—
631C42—432no—
632C42—864no—
633C42—864no—
634C42D4×D4312yes—
635C42C23×D4312yes—
636C23—434no—
637C23—432no—
638C23—862no—
639C23—862no—
640C23—864no—
641C23—862no—
642C23—1722no—
643C23—1722no—
644C23C2×D4×D4311yescharacteristic
645Q8—24no—
646Q8—22no—
647Q8C2×Q8×D4314yes—
648D4—434no—
649D4—8616no—
650D4—864no—
651D4—862no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—434no—
663C2×C4—432no—
664C2×C4—438no—
665C2×C4—434no—
666C2×C4—434no—
667C2×C4—432no—
668C2×C4—432no—
669C2×C4—8616no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—1724no—
676C2×C4—1724no—
677C2×C4—1728no—
678C2×C4—1728no—
679C2×C4—1728no—
680C2×C4—1728no—
681C2×C4—1722no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4C2×D4×D4312yes—
685C2×C4C2×D4×D4312yes—
686C2×C4C2×D4×D4311yescharacteristic
687C2×C4C2×Q8×D4312yes—
688C2×C4#41×D4312yes—
689C2×C4C24×D4311yescharacteristic
690C8—22no—
691C8—22no—
692C8—862no—
693C8—862no—
694C22—434no—
695C22—862no—
696C22—862no—
697C22—868no—
698C22—864no—
699C22—1722no—
700C22—1722no—
701C22—1728no—
702C22C22⋊Q8×D4312yes—
703C22#1458369612yes—
704C22#1458369812yes—
705C22C22×D4×D4311yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—434no—
713C4—862no—
714C4—862no—
715C4—1722no—
716C4—1722no—
717C4—1722no—
718C4C22⋊Q8×D4312yes—
719C4C22×Q8×D4311yescharacteristic
720C4C2×#41×D4311yescharacteristic
721C2—864no—
722C2—1724no—
723C2#1914441414yesdirect product factor
724C2C2×C22⋊Q8×D4311yescharacteristic
725C2C2×#1458369611yescharacteristic
726C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
hypercenterC2×#479D43
hypocenterC43C2×#3080
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#125×D43C2semidirect
3. #19144414C2direct (N × H)
4. C2×#14583208C2semidirect
5. C2×#14583206C2semidirect
6. C2×#14583204C2semidirect
7. C2×#14583202C2semidirect
8. C2×#14583200C2semidirect
9. C2×#14583198C2semidirect
10. C2×#14583196C2semidirect
11. C2×#14582940C2semidirect
12. C2×#14582938C2semidirect
13. C2×#14582921C2semidirect
16. C2×C43×#479C2semidirect
26. #125×D43C22semidirect
42. #14583208C22semidirect
43. #14583206C22semidirect
44. #14583204C22semidirect
45. #14583202C22semidirect
46. #14583200C22semidirect
47. #14583198C22semidirect
48. #14583196C22semidirect
49. #14582940C22semidirect
50. #14582938C22semidirect
57. #14582921C22semidirect
71. C43×#479C22semidirect
364. C2×#479D43semidirect
374. C2×C43#3080semidirect
410. #479C2×D43semidirect
440. C43C2×#3080semidirect
723. C2#19144414direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D432
C2×C4×#106219022
#191444142
C2×#145832082
C2×#145832062
C2×#145832042
C2×#145832022
C2×#145832002
C2×#145831982
C2×#145831962
C2×#145829402
C2×#145829382
C2×#145829212
C2×#145828992
C2×C43×#4792
C2×#308043