Finite Group Databasebeta

← C2×#19146904 #25973511

Subgroups — C2×#19146904 #25973511

Order 11008.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583607C211yesmaximal, characteristic, complemented
2C2×#14583548C211yesmaximal, characteristic
3#19146904C2116yesmaximal, direct product factor
4C2×#14583248C211yesmaximal, characteristic, complemented
5C2×#14583230C211yesmaximal, characteristic, complemented
6C2×#14583228C211yesmaximal, characteristic, complemented
7C2×#14583187C211yesmaximal, characteristic, complemented
8C2×#14583155C211yesmaximal, characteristic, complemented
9C2×#14583154C211yesmaximal, characteristic, complemented
10C2×#14583107C211yesmaximal, characteristic, complemented
11C2×#14583058C211yesmaximal, characteristic, complemented
12C2×SD16×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582974C211yesmaximal, characteristic, complemented
14C2×#14582900C211yesmaximal, characteristic, complemented
15C2×#14582897C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C22×#10621872C2211yescharacteristic
21#14583607—24no—
22#14583607C2218yescomplemented
23#14583548—24no—
24#14583548C2218yes—
25C2×#13063324C2211yescharacteristic
26C2×#13063323C2211yescharacteristic
27C2×#13063315—21no—
28C2×#13063308—21no—
29C2×#13063306—21no—
30C2×#13063305—21no—
31C2×#13063304C2211yescharacteristic
32C2×#13063302—21no—
33C2×#13063301C2211yescharacteristic
34C2×#13063301C2211yescharacteristic
35C2×#13063297—21no—
36C2×Q8×Dic43C2211yescharacteristic
37C2×D4×Dic43C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×(C22⋊D43)⋊C4—21no—
40C22×C4⋊Dic43C2211yescharacteristic
41C22×Dic43⋊C4—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43#14583248C2218yescomplemented
44#14583230C2218yescomplemented
45#14583228C2218yescomplemented
46#14583187C2218yescomplemented
47#14583155C2218yescomplemented
48#14583154C2218yescomplemented
49#14583107C2218yescomplemented
50#14583058C2218yescomplemented
51SD16×Dic43C2218yescomplemented
52#14582974C2218yescomplemented
53C2×#13063257C2211yescharacteristic
54C2×#13063257C2211yescharacteristic
55C2×#13063256C2211yescharacteristic
56C2×Dic43⋊C8C2211yescharacteristic
57#14582900C2218yescomplemented
58#14582897C2218yescomplemented
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×Q16×C43C2211yescharacteristic
71C22×SD16×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#452C2218yescomplemented
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621900—24no—
78C2×#10621900—22no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43D411yescharacteristic
85C23×Dic43—21no—
86C23×Dic43—21no—
87C23×Dic43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621885—42no—
91C2×#10621885C2314yes—
92C2×#10621877—42no—
93C2×#10621877C2314yes—
94C2×#10621872—42no—
95C2×#10621872C2314yes—
96C22×C43⋊C8C2311yescharacteristic
97C22×C43⋊C8C2311yescharacteristic
98#13063324—22no—
99#13063324C2314yes—
100#13063323—22no—
101#13063323C2314yes—
102#13063315—28no—
103#13063308—28no—
104#13063306—28no—
105#13063305—28no—
106#13063304—22no—
107#13063304C2314yes—
108#13063302—28no—
109#13063301—22no—
110#13063301—22no—
111#13063301C2314yes—
112#13063301C2314yes—
113#13063297—28no—
114Q8×Dic43—22no—
115Q8×Dic43C2314yes—
116D4×Dic43—22no—
117D4×Dic43C2314yes—
118C4×C22⋊D43D414yes—
119C4×C22⋊D43C2314yes—
120(C22⋊D43)⋊C4—28no—
121C2×C4⋊Dic43—22no—
122C2×C4⋊Dic43—21no—
123C2×C4⋊Dic43—21no—
124C2×C4⋊Dic43C2311yescharacteristic
125C2×C4⋊Dic43C2314yes—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2311yescharacteristic
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—28no—
136C2×Dic43⋊C4D411yescharacteristic
137C4⋊C4×D43—22no—
138C4⋊C4×D43C2314yes—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43—21no—
141C2×C22⋊Dic43D411yescharacteristic
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43C2311yescharacteristic
147#13063257C2314yes—
148#13063257C2314yes—
149#13063256C2314yes—
150Dic43⋊C8C2314yes—
151#13063250C2314yes—
152#13063250C2314yes—
153#13063249C2314yes—
154#13063249C2314yes—
155#13063249C2314yes—
156#13063248C2314yes—
157#13063246C2314yes—
158#13063246C2314yes—
159(C2×D43)⋊C8C2314yes—
160C8×Dic43C2314yes—
161C2×#41×C43—22no—
162C2×#41×C43—24no—
163C2×#41×C43—42no—
164C2×#41×C43C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43C2311yescharacteristic
171C2×Q16×C43—42no—
172C2×Q16×C43C2314yes—
173C2×SD16×C43—24no—
174C2×SD16×C43C2314yes—
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2311yescharacteristic
177C22⋊Q8×C43—22no—
178C22⋊Q8×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182#103×C43C2314yes—
183#102×C43C2314yes—
184C22⋊C8×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43C2×D411yescharacteristic
188#41×C43—28no—
189#41×C43—44no—
190#41×C43—48no—
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43C2412yes—
198C2×Q8×C43C2412yes—
199C2×D4×C43—21no—
200C2×D4×C43—22no—
201C2×D4×C43—24no—
202C2×D4×C43—44no—
203C2×D4×C43#4114yes—
204C2×D4×C43C2412yes—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—24no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—44no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—44no—
219C2×C22⋊D43C2×D414yes—
220C22×Dic43—24no—
221C22×Dic43—24no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—24no—
227C22×Dic43—44no—
228C22×Dic43—44no—
229C22×Dic43—82no—
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233#10621900—28no—
234#10621900—44no—
235#10621900—48no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—24no—
239C2×C4×D43—82no—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2412yes—
242C2×Dic86—22no—
243C2×Dic86—22no—
244C2×Dic86—21no—
245C2×Dic86—24no—
246C2×Dic86—82no—
247C2×Dic86C2412yes—
248Q16×C43—44no—
249SD16×C43—28no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C2412yes—
257C22⋊C4×C43—24no—
258C22⋊Dic43—24no—
259C22⋊Dic43—24no—
260C22⋊Dic43C2×D414yes—
261#10621885—44no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4C2×D414yes—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—24no—
268C4⋊Dic43—21no—
269C4⋊Dic43—24no—
270C4⋊Dic43C2412yes—
271C4⋊Dic43C2412yes—
272C4⋊Dic43C2412yes—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4—24no—
276Dic43⋊C4—24no—
277Dic43⋊C4—24no—
278Dic43⋊C4—24no—
279Dic43⋊C4—24no—
280Dic43⋊C4C2×D414yes—
281C4×Dic43—24no—
282C4×Dic43C2×D412yes—
283C4×Dic43C2412yes—
284#10621877—44no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8—22no—
287C2×C43⋊C8C2412yes—
288C2×C43⋊C8C2412yes—
289#10621872—44no—
290C23×C43—24no—
291C23×C43—22no—
292C23×C43—22no—
293C23×C43—22no—
294C23×C43—22no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43C22×D412yes—
298C23×C43C22×D411yescharacteristic
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43C22×D412yes—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—42no—
308Q8×C43—42no—
309D4×C43—24no—
310D4×C43—22no—
311D4×C43—48no—
312D4×C43C2×#4114yes—
313C2×C4×C43—22no—
314C2×C4×C43—24no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—48no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43C22×D412yes—
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4112yes—
327C2×C4×C43H(5,𝔽2)12yes—
328C2×C4×C43C2511yescharacteristic
329C22⋊D43—28no—
330C22⋊D43—48no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—48no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—48no—
343C2×Dic43—84no—
344C2×Dic43#13714yes—
345C2×Dic43C22×D412yes—
346C2×Dic43C22×D412yes—
347C2×Dic43C22×D412yes—
348C4×D43—24no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—84no—
352Dic86—22no—
353Dic86—22no—
354Dic86—42no—
355Dic86—84no—
356C8×C43—22no—
357C8×C43—22no—
358C43⋊C8—22no—
359C43⋊C8—22no—
360C2×#3331—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—44no—
366C22×C43—48no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43#54612yes—
370C22×C43C2×#13712yes—
371C22×C43#57712yes—
372C22×C43C23×D411yescharacteristic
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—44no—
377C4×C43—22no—
378C4×C43—42no—
379C4×C43—42no—
380C4×C43—42no—
381C4×C43#54612yes—
382C4×C43C22×#4111yescharacteristic
383C4×C43C2×H(5,𝔽2)11yescharacteristic
384Dic43—22no—
385Dic43—22no—
386Dic43—42no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390Dic43C2×#13714yes—
391C2×#554—431no—
392C2×#547—431no—
393#3331—4316no—
394C2×#487—431no—
395C2×#483—431no—
396C2×#483—431no—
397C2×#476—431no—
398C2×#470—431no—
399C2×#470—431no—
400C2×#462—431no—
401C2×#452—431no—
402C2×#452D4311yescharacteristic, complemented
403C2×C4×SD16—431no—
404C2×#436—431no—
405C2×#417—431no—
406C2×#417—431no—
407C2×C43—42no—
408C2×C43—44no—
409C2×C43#333114yescomplemented
410C2×C43C2×#54611yescharacteristic
411C2×C43C22×#13711yescharacteristic
412C2×C43C2×#57711yescharacteristic
413D43—42no—
414C22×#41—431no—
415C22×#41C2×D4311yescharacteristic
416C22×Q16—431no—
417C22×Q16C2×D4311yescharacteristic
418C22×SD16C2×D4311yescharacteristic
419C22×M16—431no—
420C22×M16—431no—
421#554—438no—
422#554—864no—
423#547—438no—
424#547—864no—
425C2×C4⋊Q8—431no—
426C2×C4⋊Q8—431no—
427C2×#125—861no—
428C2×#123—861no—
429C2×#123—861no—
430C2×C22⋊Q8—431no—
431C2×C22⋊Q8—431no—
432C2×C22⋊Q8—431no—
433C2×C22⋊Q8—861no—
434C2×C22⋊Q8—861no—
435C2×C22⋊Q8C2×D4311yescharacteristic
436C2×#121—861no—
437C2×C4×Q8—431no—
438C2×C4×D4—431no—
439C2×C4×D4—431no—
440C2×C4×D4—861no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—861no—
444#487—438no—
445#483—438no—
446#483—438no—
447#476—438no—
448#470—438no—
449#470—438no—
450#462—438no—
451#452—438no—
452#452C2×D4318yescomplemented
453C4×SD16—438no—
454#436—438no—
455C2×#106—431no—
456C2×#106—431no—
457C2×#106—431no—
458C2×C4⋊C8—431no—
459#417—438no—
460#417—438no—
461C2×#103—431no—
462C2×#103—431no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103C2×D4311yescharacteristic
468C2×#102—431no—
469C2×#102—431no—
470C2×#102C2×D4311yescharacteristic
471C2×C22⋊C8—431no—
472C2×C22⋊C8C2×D4311yescharacteristic
473C2×C4×C8—431no—
474C43C2×#333111yescharacteristic, complemented, Sylow
475C2×#41—22no—
476C2×#41—24no—
477C2×#41—42no—
478C2×#41—434no—
479C2×#41—862no—
480C2×#41—864no—
481C2×#41—1722no—
482C2×#41C22×D4314yes—
483C22×Q8—431no—
484C22×Q8—861no—
485C22×Q8C22×D4311yescharacteristic
486C22×Q8C22×D4311yescharacteristic
487C22×D4—21no—
488C22×D4—431no—
489C22×D4—861no—
490C22×D4C22×D4311yescharacteristic
491C23×C4—21no—
492C23×C4—431no—
493C23×C4—861no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C23×C4C22×D4311yescharacteristic
498C2×Q16—42no—
499C2×Q16—434no—
500C2×Q16—1722no—
501C2×Q16C22×D4314yes—
502C2×SD16—24no—
503C2×SD16C22×D4314yes—
504C2×M16—434no—
505C2×M16—434no—
506C2×M16—1722no—
507C2×M16—1722no—
508C22×C8—431no—
509C22×C8—431no—
510C22×C8C22×D4311yescharacteristic
511C22×C8C22×D4311yescharacteristic
512C4⋊Q8—434no—
513C4⋊Q8—434no—
514C4⋊Q8—862no—
515C4⋊Q8—862no—
516#125—868no—
517#123—868no—
518#123—868no—
519C22⋊Q8—22no—
520C22⋊Q8—434no—
521C22⋊Q8—434no—
522C22⋊Q8—434no—
523C22⋊Q8—868no—
524C22⋊Q8—868no—
525C22⋊Q8—862no—
526C22⋊Q8—862no—
527C22⋊Q8—862no—
528C22⋊Q8C22×D4314yes—
529#121—868no—
530C4×Q8—434no—
531C4×Q8—862no—
532C4×D4—434no—
533C4×D4—434no—
534C4×D4—434no—
535C4×D4—862no—
536C4×D4—868no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—431no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—434no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—434no—
544C2×C4⋊C4—862no—
545C2×C4⋊C4—868no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4—861no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4—862no—
555C2×C4⋊C4—861no—
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—431no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C42—431no—
565C2×C42—861no—
566#106—434no—
567#106—434no—
568#106—434no—
569C4⋊C8—434no—
570#103—434no—
571#103—434no—
572#103—434no—
573#103—434no—
574#103—434no—
575#103—434no—
576#103C22×D4314yes—
577#102—434no—
578#102—434no—
579#102C22×D4314yes—
580C22⋊C8—434no—
581C22⋊C8C22×D4314yes—
582C4×C8—434no—
583C24—21no—
584C24—431no—
585C24D4×D4311yescharacteristic
586#41—28no—
587#41—44no—
588#41—48no—
589#41—868no—
590#41—1724no—
591#41—1728no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—432no—
599C2×Q8—864no—
600C2×Q8—861no—
601C2×Q8—862no—
602C2×Q8—862no—
603C2×Q8—3442no—
604C2×Q8C23×D4312yes—
605C2×Q8C23×D4312yes—
606C2×D4—24no—
607C2×D4—21no—
608C2×D4—22no—
609C2×D4—44no—
610C2×D4—434no—
611C2×D4—864no—
612C2×D4—864no—
613C2×D4—1724no—
614C2×D4#1062190014yes—
615C2×D4C23×D4312yes—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—24no—
622C22×C4—44no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—432no—
627C22×C4—432no—
628C22×C4—864no—
629C22×C4—864no—
630C22×C4—864no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—864no—
634C22×C4—861no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—861no—
638C22×C4—3442no—
639C22×C4—3442no—
640C22×C4—1724no—
641C22×C4—1724no—
642C22×C4D4×D4312yes—
643C22×C4D4×D4311yescharacteristic
644C22×C4C23×D4312yes—
645C22×C4C23×D4311yescharacteristic
646Q16—44no—
647Q16—1724no—
648SD16—28no—
649M16—1724no—
650M16—1724no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—432no—
654C2×C8—432no—
655C2×C8—862no—
656C2×C8—862no—
657C2×C8C23×D4312yes—
658C2×C8C23×D4312yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—434no—
662C4⋊C4—432no—
663C4⋊C4—432no—
664C4⋊C4—432no—
665C4⋊C4—864no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—864no—
669C4⋊C4—864no—
670C4⋊C4—864no—
671C4⋊C4—864no—
672C4⋊C4—861no—
673C4⋊C4—864no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4—864no—
677C4⋊C4C23×D4312yes—
678C22⋊C4—24no—
679C22⋊C4—434no—
680C22⋊C4—434no—
681C22⋊C4—864no—
682C22⋊C4—864no—
683C22⋊C4—864no—
684C22⋊C4—864no—
685C42—432no—
686C42—432no—
687C42—864no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—42no—
694C23—42no—
695C23—432no—
696C23—862no—
697C23—862no—
698C23—862no—
699C23C2×D4×D4312yes—
700C23C2×D4×D4311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—862no—
708Q8—862no—
709Q8—3444no—
710Q8—1722no—
711D4—22no—
712D4—24no—
713D4—48no—
714D4—868no—
715D4—1728no—
716D4C2×#1062190014yes—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—48no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—434no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—864no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—3444no—
742C2×C4—3444no—
743C2×C4—1728no—
744C2×C4—1728no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4C2×D4×D4312yes—
750C2×C4C2×D4×D4311yescharacteristic
751C2×C4C2×#1062190012yes—
752C2×C4#1306337012yes—
753C2×C4C24×D4311yescharacteristic
754C8—22no—
755C8—22no—
756C8—862no—
757C8—862no—
758C22—22no—
759C22—24no—
760C22—22no—
761C22—22no—
762C22—42no—
763C22—42no—
764C22—44no—
765C22—48no—
766C22—862no—
767C22—862no—
768C22—862no—
769C22—1724no—
770C22#1458353612yes—
771C22#137×D4312yes—
772C22#1458370612yes—
773C22C22×D4×D4311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—434no—
779C4—862no—
780C4—862no—
781C4—1722no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C4#1458353612yes—
786C4C22×#1062190011yescharacteristic
787C4C2×#1306337011yescharacteristic
788C2—42no—
789C2—44no—
790C2—1722no—
791C2#1914690414yesdirect product factor
792C2C2×#1458353611yescharacteristic
793C2C2×#137×D4311yescharacteristic
794C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC2×#14583548C2
hypercenterC2×#452D43
hypocenterC43C2×#3331
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#14583607C2semidirect
3. #19146904C2direct (N × H)
4. C2×#14583248C2semidirect
5. C2×#14583230C2semidirect
6. C2×#14583228C2semidirect
7. C2×#14583187C2semidirect
8. C2×#14583155C2semidirect
9. C2×#14583154C2semidirect
10. C2×#14583107C2semidirect
11. C2×#14583058C2semidirect
12. C2×SD16×Dic43C2semidirect
13. C2×#14582974C2semidirect
14. C2×#14582900C2semidirect
15. C2×#14582897C2semidirect
16. C2×C43×#452C2semidirect
22. #14583607C22semidirect
43. #14583248C22semidirect
44. #14583230C22semidirect
45. #14583228C22semidirect
46. #14583187C22semidirect
47. #14583155C22semidirect
48. #14583154C22semidirect
49. #14583107C22semidirect
50. #14583058C22semidirect
51. SD16×Dic43C22semidirect
52. #14582974C22semidirect
57. #14582900C22semidirect
58. #14582897C22semidirect
73. C43×#452C22semidirect
402. C2×#452D43semidirect
409. C2×C43#3331semidirect
452. #452C2×D43semidirect
474. C43C2×#3331semidirect
791. C2#19146904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836072
C2×#145835482
#191469042
C2×#145832482
C2×#145832302
C2×#145832282
C2×#145831872
C2×#145831552
C2×#145831542
C2×#145831072
C2×#145830582
C2×SD16×Dic432
C2×#145829742
C2×#145829002
C2×#145828972
C2×C43×#4522
C2×#333143