Finite Group Databasebeta

← C2×#479×D43 #25964082

Subgroups — C2×#479×D43 #25964082

Order 11008.

2142 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D43C211yesmaximal, characteristic
2C2×C4×Q8×D43C211yesmaximal, characteristic
3C2×#14583209C211yesmaximal, characteristic, complemented
4C2×#14583208C211yesmaximal, characteristic, complemented
5C2×#14583207C211yesmaximal, characteristic, complemented
6C2×#14583206C211yesmaximal, characteristic, complemented
7C2×#14583205C211yesmaximal, characteristic, complemented
8C2×#14583204C211yesmaximal, characteristic, complemented
9C2×#14583203C211yesmaximal, characteristic, complemented
10#479×D43C2116yesmaximal, direct product factor
11C2×#107×D43C211yesmaximal, characteristic
12C2×#106×D43C211yesmaximal, characteristic
13C2×C4⋊C8×D43C211yesmaximal, characteristic
14C2×#103×D43C211yesmaximal, characteristic
15C2×#103×D43C211yesmaximal, characteristic
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20C2×#13063317C2211yescharacteristic
21C2×#13063316C2211yescharacteristic
22C2×#13063316C2211yescharacteristic
23C2×#13063315—21no—
24C2×#13063315—21no—
25#125×D43—24no—
26#125×D43C2218yes—
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×Dic86—21no—
29C2×C4×Dic86C2211yescharacteristic
30C2×#13063290—21no—
31C2×#13063290C2211yescharacteristic
32C4×Q8×D43—24no—
33C4×Q8×D43C2218yes—
34C2×C4⋊C4×D43—21no—
35C2×C4⋊C4×D43—21no—
36C2×C4⋊C4×D43—21no—
37C2×C4⋊C4×D43C2211yescharacteristic
38C2×C4⋊C4×D43C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40C2×C42×D43—21no—
41C2×C42×D43C2211yescharacteristic
42#14583209C2218yescomplemented
43#14583208C2218yescomplemented
44#14583207C2218yescomplemented
45#14583206C2218yescomplemented
46#14583205C2218yescomplemented
47#14583204C2218yescomplemented
48#14583203C2218yescomplemented
49C2×#13063259C2211yescharacteristic
50C2×#13063258C2211yescharacteristic
51C2×#13063258C2211yescharacteristic
52#107×D43C2218yes—
53C2×#13063257C2211yescharacteristic
54C2×#13063256C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56#106×D43C2218yes—
57C2×C4⋊(C43⋊C8)C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C4⋊C8×D43C2218yes—
61C2×#13063250C2211yescharacteristic
62C2×#13063250C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063249C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063248C2211yescharacteristic
67#103×D43C2218yes—
68#103×D43C2218yes—
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
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C2×Q8×D43—22no—
80C2×Q8×D43—24no—
81C2×Q8×D43Q818yes—
82C2×Q8×D43C2314yes—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43D411yescharacteristic
88C22×C4×D43D411yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C2×C8×D43—24no—
93C2×C8×D43—24no—
94C2×C8×D43C2314yes—
95C2×C8×D43C2314yes—
96#13063317—22no—
97#13063317C2314yes—
98#13063316—22no—
99#13063316—22no—
100#13063316C2314yes—
101#13063316C2314yes—
102#13063315—28no—
103#13063315—28no—
104Q8×Dic43—22no—
105Q8×Dic43C2314yes—
106C4×Dic86—22no—
107C4×Dic86—28no—
108C4×Dic86C2314yes—
109#13063290—22no—
110#13063290—28no—
111#13063290C2314yes—
112C2×C4⋊Dic43—21no—
113C2×C4⋊Dic43—21no—
114C2×C4⋊Dic43—21no—
115C2×C4⋊Dic43C2311yescharacteristic
116C2×C4⋊Dic43C2311yescharacteristic
117C2×C4⋊Dic43C2311yescharacteristic
118C2×Dic43⋊C4—21no—
119C2×Dic43⋊C4—21no—
120C2×Dic43⋊C4—21no—
121C2×Dic43⋊C4—21no—
122C2×Dic43⋊C4—21no—
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C4⋊C4×D43—28no—
128C4⋊C4×D43—28no—
129C4⋊C4×D43—28no—
130C4⋊C4×D43—22no—
131C4⋊C4×D43—22no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43C2314yes—
134C4⋊C4×D43C2314yes—
135C4⋊C4×D43C2314yes—
136C2×C4×Dic43—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#13063250C2314yes—
155#13063250C2314yes—
156#13063249C2314yes—
157#13063249C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
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×D43C2×D411yescharacteristic
181C2×Q8×C43—21no—
182C2×Q8×C43—22no—
183C2×Q8×C43C2×Q814yes—
184C2×Q8×C43C2412yes—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2411yescharacteristic
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43C2×D411yescharacteristic
197C22×Dic43C2×D411yescharacteristic
198C22×Dic43C2×D411yescharacteristic
199Q8×D43—216no—
200Q8×D43—28no—
201Q8×D43C2×Q8116yes—
202C2×C4×D43—28no—
203C2×C4×D43—24no—
204C2×C4×D43—24no—
205C2×C4×D43—24no—
206C2×C4×D43—24no—
207C2×C4×D43—24no—
208C2×C4×D43—24no—
209C2×C4×D43—44no—
210C2×C4×D43—44no—
211C2×C4×D43—44no—
212C2×C4×D43C2×D414yes—
213C2×C4×D43C2×D414yes—
214C2×C4×D43C2×D412yes—
215C2×C4×D43C2×Q814yes—
216C2×C4×D43#4114yes—
217C2×C4×D43C2412yes—
218C2×Dic86—21no—
219C2×Dic86—22no—
220C2×Dic86—28no—
221C2×Dic86—24no—
222C2×Dic86C2×Q814yes—
223C2×Dic86C2412yes—
224C2×C8×C43—22no—
225C2×C8×C43—22no—
226C2×C8×C43C2412yes—
227C2×C8×C43C2412yes—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2412yes—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C42×C43—24no—
238C42×C43C2×D412yes—
239C42×C43C2412yes—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—24no—
244C4⋊Dic43—24no—
245C4⋊Dic43—24no—
246C4⋊Dic43C2412yes—
247C4⋊Dic43C2412yes—
248C4⋊Dic43C2412yes—
249Dic43⋊C4—24no—
250Dic43⋊C4—24no—
251Dic43⋊C4—24no—
252Dic43⋊C4—24no—
253Dic43⋊C4—24no—
254Dic43⋊C4—24no—
255Dic43⋊C4—24no—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—24no—
261C4×Dic43C2×D412yes—
262C4×Dic43C2×D414yes—
263C4×Dic43C2×D414yes—
264C4×Dic43C2412yes—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8C2412yes—
268C2×C43⋊C8C2412yes—
269C8×D43—28no—
270C8×D43—28no—
271C23×C43C22×D411yescharacteristic
272C22×D43C22⋊Q814yes—
273C22×D43#13514yes—
274C22×D43#13714yes—
275C22×D43C22×D412yes—
276Q8×C43—24no—
277Q8×C43—22no—
278Q8×C43C22×Q814yes—
279C2×C4×C43—24no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43C22×D412yes—
290C2×C4×C43C22×D412yes—
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C22×Q812yes—
293C2×C4×C43C2×#4112yes—
294C2×C4×C43C2511yescharacteristic
295C2×Dic43—24no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—42no—
303C2×Dic43—42no—
304C2×Dic43—42no—
305C2×Dic43C22⋊Q814yes—
306C2×Dic43C22×D412yes—
307C2×Dic43C22×D412yes—
308C2×Dic43C22×D412yes—
309C4×D43—216no—
310C4×D43—28no—
311C4×D43—28no—
312C4×D43—48no—
313C4×D43—48no—
314C4×D43—48no—
315C4×D43C22⋊Q818yes—
316C4×D43C22×Q814yes—
317C4×D43C2×#4114yes—
318Dic86—24no—
319Dic86—22no—
320Dic86—216no—
321Dic86C22×Q814yes—
322C8×C43—22no—
323C8×C43—22no—
324C43⋊C8—22no—
325C43⋊C8—22no—
326C22×#479—431nomaximal, Sylow
327C22×C43C2×C22⋊Q812yes—
328C22×C43C2×#13512yes—
329C22×C43C2×#13712yes—
330C22×C43C23×D411yescharacteristic
331C2×D43#479116yesdirect product factor
332C2×D43C2×C22⋊Q814yes—
333C2×D43C2×#13514yes—
334C2×D43C2×#13714yes—
335C4×C43—24no—
336C4×C43—22no—
337C4×C43—22no—
338C4×C43—42no—
339C4×C43—42no—
340C4×C43—42no—
341C4×C43C2×C22⋊Q812yes—
342C4×C43C23×Q811yescharacteristic
343C4×C43C22×#4111yescharacteristic
344Dic43—24no—
345Dic43—22no—
346Dic43—22no—
347Dic43—42no—
348Dic43—42no—
349Dic43—42no—
350Dic43C2×C22⋊Q814yes—
351C22×#125—431no—
352C22×C4×Q8—431no—
353C2×#479—4316no—
354C2×#479—431no—
355C2×#479—431no—
356C2×#479—431no—
357C2×#479—431no—
358C2×#479—431no—
359C2×#479—431no—
360C2×#479—431no—
361C2×#479D4311yescharacteristic, direct product factor
362C22×#107—431no—
363C22×#106—431no—
364C22×C4⋊C8—431no—
365C22×#103—431no—
366C22×#103—431no—
367C2×C43C2×#47914yescomplemented
368C2×C43C22×C22⋊Q811yescharacteristic
369C2×C43C22×#13511yescharacteristic
370C2×C43C22×#13711yescharacteristic
371D43C2×#47918yesdirect product factor
372C23×Q8—431no—
373C23×C8—431no—
374C23×C8—431no—
375C2×#125—438no—
376C2×#125—431no—
377C2×#125—431no—
378C2×#125—431no—
379C2×#125—861no—
380C2×#125—861no—
381C2×#125—864no—
382C2×#125C2×D4311yescharacteristic
383C2×C4×Q8—431no—
384C2×C4×Q8—438no—
385C2×C4×Q8—431no—
386C2×C4×Q8—431no—
387C2×C4×Q8—861no—
388C2×C4×Q8—861no—
389C2×C4×Q8—864no—
390C2×C4×Q8C2×D4311yescharacteristic
391C22×C4⋊C4—431no—
392C22×C4⋊C4—431no—
393C22×C4⋊C4—431no—
394C22×C4⋊C4—861no—
395C22×C4⋊C4—861no—
396C22×C4⋊C4—861no—
397C22×C42—431no—
398C22×C42—861no—
399#479—438no—
400#479—438no—
401#479—438no—
402#479—438no—
403#479—438no—
404#479—438no—
405#479—438no—
406#479C2×D4318yesdirect product factor
407C2×#107—431no—
408C2×#107—431no—
409C2×#107—431no—
410C2×#107—438no—
411C2×#107C2×D4311yescharacteristic
412C2×#106—431no—
413C2×#106—431no—
414C2×#106—431no—
415C2×#106—438no—
416C2×#106C2×D4311yescharacteristic
417C2×C4⋊C8—431no—
418C2×C4⋊C8—431no—
419C2×C4⋊C8—431no—
420C2×C4⋊C8—438no—
421C2×C4⋊C8C2×D4311yescharacteristic
422C2×#103—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—438no—
429C2×#103—438no—
430C2×#103C2×D4311yescharacteristic
431C2×#103C2×D4311yescharacteristic
432C43C22×#47911yescharacteristic, complemented, Sylow
433C22×Q8—438no—
434C22×Q8—434no—
435C22×Q8—431no—
436C22×Q8—861no—
437C22×Q8—862no—
438C22×Q8—864no—
439C22×Q8C22×D4311yescharacteristic
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4—861no—
446C23×C4—861no—
447C22×C8—431no—
448C22×C8—431no—
449C22×C8—434no—
450C22×C8—434no—
451C22×C8—864no—
452C22×C8—864no—
453C22×C8C22×D4311yescharacteristic
454C22×C8C22×D4311yescharacteristic
455#125—22no—
456#125—434no—
457#125—434no—
458#125—434no—
459#125—868no—
460#125—868no—
461#125—862no—
462#125—862no—
463#125—862no—
464#125C22×D4314yes—
465C4×Q8—22no—
466C4×Q8—434no—
467C4×Q8—434no—
468C4×Q8—434no—
469C4×Q8—868no—
470C4×Q8—868no—
471C4×Q8—862no—
472C4×Q8—862no—
473C4×Q8—862no—
474C4×Q8C22×D4314yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—434no—
482C2×C4⋊C4—434no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4—862no—
486C2×C4⋊C4—862no—
487C2×C4⋊C4—868no—
488C2×C4⋊C4—868no—
489C2×C4⋊C4—868no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4C22×D4311yescharacteristic
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C42—21no—
506C2×C42—431no—
507C2×C42—431no—
508C2×C42—431no—
509C2×C42—434no—
510C2×C42—434no—
511C2×C42—868no—
512C2×C42—861no—
513C2×C42—861no—
514C2×C42—861no—
515C2×C42C22×D4311yescharacteristic
516#107—434no—
517#107—434no—
518#107—434no—
519#107C22×D4314yes—
520#106—434no—
521#106—434no—
522#106—434no—
523#106C22×D4314yes—
524C4⋊C8—434no—
525C4⋊C8—434no—
526C4⋊C8—434no—
527C4⋊C8C22×D4314yes—
528#103—434no—
529#103—434no—
530#103—434no—
531#103—434no—
532#103—434no—
533#103—434no—
534#103C22×D4314yes—
535#103C22×D4314yes—
536C24—431no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—4316no—
540C2×Q8—434no—
541C2×Q8—432no—
542C2×Q8—864no—
543C2×Q8—868no—
544C2×Q8—8616no—
545C2×Q8—868no—
546C2×Q8—861no—
547C2×Q8—862no—
548C2×Q8Q8×D4314yes—
549C2×Q8C23×D4312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—431no—
555C22×C4—432no—
556C22×C4—434no—
557C22×C4—434no—
558C22×C4—432no—
559C22×C4—431no—
560C22×C4—431no—
561C22×C4—434no—
562C22×C4—434no—
563C22×C4—864no—
564C22×C4—864no—
565C22×C4—864no—
566C22×C4—868no—
567C22×C4—864no—
568C22×C4—864no—
569C22×C4—864no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—1724no—
575C22×C4—1724no—
576C22×C4—1724no—
577C22×C4D4×D4311yescharacteristic
578C22×C4D4×D4311yescharacteristic
579C22×C4C23×D4311yescharacteristic
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—432no—
583C2×C8—432no—
584C2×C8—868no—
585C2×C8—868no—
586C2×C8—862no—
587C2×C8—862no—
588C2×C8C23×D4312yes—
589C2×C8C23×D4312yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—432no—
597C4⋊C4—432no—
598C4⋊C4—432no—
599C4⋊C4—864no—
600C4⋊C4—864no—
601C4⋊C4—864no—
602C4⋊C4—864no—
603C4⋊C4—864no—
604C4⋊C4—864no—
605C4⋊C4—864no—
606C4⋊C4—864no—
607C4⋊C4—864no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—864no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4C23×D4312yes—
615C4⋊C4C23×D4312yes—
616C4⋊C4C23×D4312yes—
617C42—24no—
618C42—434no—
619C42—434no—
620C42—432no—
621C42—432no—
622C42—864no—
623C42—864no—
624C42—864no—
625C42D4×D4312yes—
626C42C23×D4312yes—
627C23—434no—
628C23—434no—
629C23—434no—
630C23—432no—
631C23C2×D4×D4311yescharacteristic
632Q8—24no—
633Q8—22no—
634Q8—434no—
635Q8—8616no—
636Q8—864no—
637Q8—862no—
638Q8C2×Q8×D4314yes—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—434no—
650C2×C4—432no—
651C2×C4—438no—
652C2×C4—434no—
653C2×C4—434no—
654C2×C4—432no—
655C2×C4—432no—
656C2×C4—868no—
657C2×C4—868no—
658C2×C4—8616no—
659C2×C4—864no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—1728no—
667C2×C4—1728no—
668C2×C4—1728no—
669C2×C4—1722no—
670C2×C4—1722no—
671C2×C4—1722no—
672C2×C4C2×D4×D4312yes—
673C2×C4C2×D4×D4312yes—
674C2×C4C2×D4×D4311yescharacteristic
675C2×C4C2×Q8×D4312yes—
676C2×C4#41×D4312yes—
677C2×C4C24×D4311yescharacteristic
678C8—22no—
679C8—22no—
680C8—862no—
681C8—862no—
682C22—434no—
683C22—434no—
684C22—434no—
685C22—4316no—
686C22C22⋊Q8×D4312yes—
687C22#135×D4312yes—
688C22#137×D4312yes—
689C22C22×D4×D4311yescharacteristic
690C4—22no—
691C4—22no—
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—434no—
697C4—862no—
698C4—862no—
699C4—864no—
700C4—1722no—
701C4—1722no—
702C4—1722no—
703C4C22⋊Q8×D4312yes—
704C4C22×Q8×D4311yescharacteristic
705C4C2×#41×D4311yescharacteristic
706C2—438no—
707C2#479×D4314yesdirect product factor
708C2C2×C22⋊Q8×D4311yescharacteristic
709C2C2×#135×D4311yescharacteristic
710C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenterC2×#479D43
hypocenterC43C22×#479
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
3. C2×#14583209C2semidirect
4. C2×#14583208C2semidirect
5. C2×#14583207C2semidirect
6. C2×#14583206C2semidirect
7. C2×#14583205C2semidirect
8. C2×#14583204C2semidirect
9. C2×#14583203C2semidirect
10. #479×D43C2direct (N × H)
16. C2×C43×#479C2semidirect
42. #14583209C22semidirect
43. #14583208C22semidirect
44. #14583207C22semidirect
45. #14583206C22semidirect
46. #14583205C22semidirect
47. #14583204C22semidirect
48. #14583203C22semidirect
71. C43×#479C22semidirect
331. C2×D43#479direct (N × H)
361. C2×#479D43direct (N × H)
367. C2×C43C2×#479semidirect
371. D43C2×#479direct (N × H)
406. #479C2×D43direct (N × H)
432. C43C22×#479semidirect
707. C2#479×D43direct (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×Q8×D432
C2×#145832092
C2×#145832082
C2×#145832072
C2×#145832062
C2×#145832052
C2×#145832042
C2×#145832032
#479×D432
C2×#107×D432
C2×#106×D432
C2×C4⋊C8×D432
C2×#103×D432
C2×C43×#4792
C22×#47943