Finite Group Databasebeta

← C2×#19147029 #25975122

Subgroups — C2×#19147029 #25975122

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583589C211yesmaximal, characteristic, complemented
2#19147029C2116yesmaximal, direct product factor
3C2×#14583305C211yesmaximal, characteristic, complemented
4C2×#14583234C211yesmaximal, characteristic, complemented
5C2×#14583220C211yesmaximal, characteristic, complemented
6C2×#14583229C211yesmaximal, characteristic, complemented
7C2×#14583210C211yesmaximal, characteristic, complemented
8C2×#14583191C211yesmaximal, characteristic, complemented
9C2×#14583199C211yesmaximal, characteristic, complemented
10C2×#14583143C211yesmaximal, characteristic, complemented
11C2×#14583126C211yesmaximal, characteristic, complemented
12C2×#14582999C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic, complemented
14C2×#14582939C211yesmaximal, characteristic, complemented
15C22×#13063258C211yesmaximal, characteristic, complemented
16C2×C43×#547C211yesmaximal, characteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20#14583589—24no—
21#14583589C2218yescomplemented
22C2×#13063318—21no—
23C2×#13063317C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063306—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30C2×#13063281—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32#14583305C2218yescomplemented
33#14583234C2218yescomplemented
34#14583229C2218yescomplemented
35#14583220C2218yescomplemented
36#14583210C2218yescomplemented
37#14583199C2218yescomplemented
38#14583191C2218yescomplemented
39#14583143C2218yescomplemented
40#14583126C2218yescomplemented
41#14582999C2218yescomplemented
42#14582971C2218yescomplemented
43#14582939C2218yescomplemented
44C2×#13063258C2211yescharacteristic
45C2×#13063258C2211yescharacteristic
46C2×#13063258C2211yescharacteristic
47C2×#13063258C2211yescharacteristic
48C2×#13063258C2211yescharacteristic
49C2×#13063258C2211yescharacteristic
50C2×#13063258C2218yescomplemented
51C2×#13063256C2211yescharacteristic
52C2×#13063256C2211yescharacteristic
53C2×#13063256C2211yescharacteristic
54C2×C4⋊(C43⋊C8)C2211yescharacteristic
55C2×#13063248C2211yescharacteristic
56C2×#13063248C2211yescharacteristic
57C2×#13063248C2211yescharacteristic
58C2×#13063246C2211yescharacteristic
59C2×#13063246C2211yescharacteristic
60C2×#13063246C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C22×#41×C43—21no—
65C43×#547—24no—
66C43×#547C2218yes—
67C2×C4⋊Q8×C43C2211yescharacteristic
68C2×#123×C43—21no—
69C2×#123×C43—21no—
70C2×C22⋊Q8×C43—21no—
71C2×#121×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C2×C4×D4×C43C2211yescharacteristic
75C22×C4⋊C4×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C23×Dic43—21no—
79C2×#10621883—24no—
80C2×#10621883C2314yes—
81C2×#10621877—24no—
82C2×#10621877C2314yes—
83C22×C43⋊C8—24no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2314yes—
88C22×C43⋊C8C2311yescharacteristic
89#13063318—28no—
90#13063317—22no—
91#13063317C2314yes—
92#13063315—28no—
93#13063306—28no—
94#13063304—22no—
95#13063304—22no—
96#13063304C2314yes—
97#13063304C2314yes—
98C4×Dic86—22no—
99C4×Dic86C2314yes—
100#13063284—22no—
101#13063284C2314yes—
102#13063281—28no—
103C2×C4⋊Dic43—22no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43C2314yes—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4—21no—
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43—21no—
116C2×C22⋊Dic43—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119#13063258C2314yes—
120#13063258C2314yes—
121#13063258C2314yes—
122#13063258C2314yes—
123#13063258C2314yes—
124#13063258C2314yes—
125#13063256C2314yes—
126#13063256C2314yes—
127#13063256C2314yes—
128C4⋊(C43⋊C8)C2314yes—
129#13063248C2314yes—
130#13063248C2314yes—
131#13063248C2314yes—
132#13063246C2314yes—
133#13063246C2314yes—
134#13063246C2314yes—
135C22⋊(C43⋊C8)C2314yes—
136C22⋊(C43⋊C8)C2314yes—
137#13063236C2314yes—
138C2×#41×C43—28no—
139C2×#41×C43—48no—
140C22×Q8×C43—21no—
141C22×D4×C43—21no—
142C22×D4×C43—21no—
143C22×D4×C43D411yescharacteristic
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43—21no—
146C23×C4×C43—21no—
147C23×C4×C43—21no—
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C4⋊Q8×C43—22no—
151C4⋊Q8×C43C2314yes—
152#123×C43—28no—
153#123×C43—28no—
154C22⋊Q8×C43—28no—
155#121×C43—22no—
156#121×C43—22no—
157#121×C43C2314yes—
158#121×C43C2314yes—
159C4×D4×C43—22no—
160C4×D4×C43D414yes—
161C4×D4×C43C2314yes—
162C4×D4×C43C2314yes—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—22no—
166C2×C4⋊C4×C43—22no—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43D411yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C4⋊C4×C43C2314yes—
173C2×C4⋊C4×C43C2314yes—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176C2×C22⋊C4×C43—21no—
177C2×C22⋊C4×C43D411yescharacteristic
178C2×C22⋊C4×C43D411yescharacteristic
179C2×C42×C43C2311yescharacteristic
180C24×C43—21no—
181C24×C43C2×D411yescharacteristic
182C24×C43C2×D411yescharacteristic
183#41×C43—432no—
184C2×Q8×C43—24no—
185C2×Q8×C43—44no—
186C2×D4×C43—21no—
187C2×D4×C43—24no—
188C2×D4×C43—24no—
189C2×D4×C43—24no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—44no—
193C2×D4×C43—44no—
194C2×D4×C43C2×D414yes—
195C2×D4×C43C2412yes—
196C22×C4×C43—22no—
197C22×C4×C43—22no—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—24no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—24no—
205C22×C4×C43—24no—
206C22×C4×C43—44no—
207C22×C4×C43—44no—
208C22×C4×C43—44no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2×D412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2411yescharacteristic
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—24no—
223C22×Dic43—44no—
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—21no—
227C2×Dic86C2412yes—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43C2×D414yes—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C4⋊C4×C43C2412yes—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—24no—
241C22⋊C4×C43C2×D414yes—
242C22⋊C4×C43C2×D414yes—
243C42×C43C2×D412yes—
244C42×C43C2412yes—
245C22⋊Dic43—24no—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248#10621883—28no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261C4×Dic43—24no—
262C4×Dic43—24no—
263#10621877—28no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—22no—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—28no—
268C2×C43⋊C8#4114yescomplemented
269C2×C43⋊C8C2412yes—
270C2×C43⋊C8C2412yes—
271C2×C43⋊C8C2412yes—
272C2×C43⋊C8C2412yes—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—22no—
278C23×C43—22no—
279C23×C43—42no—
280C23×C43—42no—
281C23×C43—42no—
282C23×C43AGL(1,ℤ/8)14yes—
283C23×C43C22×D412yes—
284C23×C43C22×D412yes—
285C23×C43C22×D411yescharacteristic
286Q8×C43—48no—
287D4×C43—28no—
288D4×C43—22no—
289D4×C43—22no—
290D4×C43—48no—
291D4×C43—48no—
292D4×C43—42no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—24no—
298C2×C4×C43—24no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—48no—
307C2×C4×C43—48no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—48no—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C2×#4112yes—
318C2×C4×C432−1+412yes—
319C2×C4×C43C2511yescharacteristic
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—42no—
325C2×Dic43—48no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329Dic86—22no—
330Dic86—22no—
331Dic86—42no—
332C43⋊C8—22no—
333C43⋊C8—22no—
334C43⋊C8—22no—
335C43⋊C8C2×#4114yescomplemented
336C2×#3343—431nomaximal, Sylow
337C22×C43—28no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—44no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—84no—
348C22×C43#54712yes—
349C22×C43C2×AGL(1,ℤ/8)14yes—
350C22×C43C2×AGL(1,ℤ/8)12yes—
351C22×C43#57812yes—
352C22×C43C23×D411yescharacteristic
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—22no—
356C4×C43—22no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43#54712yes—
361C4×C43C22×#4111yescharacteristic
362C4×C43C2×2−1+411yescharacteristic
363Dic43—42no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C2×#552—431no—
368C2×#547D4311yescharacteristic
369#3343—4316no—
370C2×#501—431no—
371C2×#484—431no—
372C2×#482—431no—
373C2×#483—431no—
374C2×#480—431no—
375C2×#477—431no—
376C2×#478—431no—
377C2×#468—431no—
378C2×#465—431no—
379C2×#440—431no—
380C2×#435—431no—
381C2×#428—431no—
382C22×#107—431no—
383C2×C43—24no—
384C2×C43—42no—
385C2×C43—82no—
386C2×C43#334314yescomplemented
387C2×C43C2×#54711yescharacteristic
388C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
389C2×C43C2×#57811yescharacteristic
390C22×#41—21no—
391C22×SD16—431no—
392C22×M16—431no—
393C23×C8—431no—
394#552—438no—
395#552—864no—
396#547—24no—
397#547C2×D4318yes—
398C2×C4⋊Q8C2×D4311yescharacteristic
399C2×#126—861no—
400C2×#125—431no—
401C2×#125—861no—
402C2×#123—21no—
403C2×#123—21no—
404C2×#123—861no—
405C2×C22⋊Q8—21no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—431no—
408C2×#121C2×D4311yescharacteristic
409C2×#121C2×D4311yescharacteristic
410C2×C4×Q8—431no—
411C2×C4×D4C2×D4311yescharacteristic
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—431no—
414C2×#117—861no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4C2×D4311yescharacteristic
417C22×C4⋊C4C2×D4311yescharacteristic
418#501—438no—
419#484—438no—
420#483—438no—
421#482—438no—
422#480—438no—
423#478—438no—
424#477—438no—
425#468—438no—
426#465—438no—
427#440—438no—
428#435—438no—
429#428—438no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#107—431no—
434C2×#107—438no—
435C2×#107—431no—
436C2×#107—431no—
437C2×#106—431no—
438C2×#106—431no—
439C2×#106—431no—
440C2×C4⋊C8—431no—
441C2×#103—431no—
442C2×#103—431no—
443C2×#103—431no—
444C2×#102—431no—
445C2×#102—431no—
446C2×#102—431no—
447C2×C22⋊C8—431no—
448C2×C22⋊C8—431no—
449C2×#97—431no—
450C43C2×#334311yescharacteristic, complemented, Sylow
451C2×#41—28no—
452C2×#41—48no—
453C22×Q8—21no—
454C22×Q8—431no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C22⋊D4311yescharacteristic
458C22×D4C22×D4311yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—861no—
463C23×C4C22×D4311yescharacteristic
464C23×C4C22×D4311yescharacteristic
465C2×SD16—434no—
466C2×SD16—864no—
467C2×M16—434no—
468C2×M16—864no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8—434no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—864no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D4314yes—
477#126—868no—
478#125—434no—
479#125—868no—
480#125—862no—
481#123—28no—
482#123—28no—
483#123—868no—
484C22⋊Q8—28no—
485C22⋊Q8—434no—
486C22⋊Q8—434no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489#121—22no—
490#121—22no—
491#121C22×D4314yes—
492#121C22×D4314yes—
493C4×Q8—434no—
494C4×Q8—862no—
495C4×D4—22no—
496C4×D4C22⋊D4314yes—
497C4×D4C22×D4314yes—
498C4×D4C22×D4314yes—
499#117—434no—
500#117—862no—
501#117—868no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—862no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4C22⋊D4311yescharacteristic
519C2×C4⋊C4C22×D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4314yes—
523C2×C4⋊C4C22×D4314yes—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4C22⋊D4311yescharacteristic
531C2×C22⋊C4C22⋊D4311yescharacteristic
532C2×C42—861no—
533C2×C42—861no—
534C2×C42C22×D4311yescharacteristic
535#107—434no—
536#107—434no—
537#107—434no—
538#107—434no—
539#107—434no—
540#107—434no—
541#106—434no—
542#106—434no—
543#106—434no—
544C4⋊C8—434no—
545#103—434no—
546#103—434no—
547#103—434no—
548#102—434no—
549#102—434no—
550#102—434no—
551C22⋊C8—434no—
552C22⋊C8—434no—
553#97—434no—
554C24—21no—
555C24C2×C22⋊D4311yescharacteristic
556C24C2×C22⋊D4311yescharacteristic
557#41—432no—
558C2×Q8—24no—
559C2×Q8—44no—
560C2×Q8—432no—
561C2×Q8—861no—
562C2×Q8—862no—
563C2×Q8—862no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4C2×C22⋊D4314yes—
573C2×D4C23×D4312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—864no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—1724no—
593C22×C4C2×C22⋊D4312yes—
594C22×C4C2×C22⋊D4312yes—
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C2×C22⋊D4311yescharacteristic
598C22×C4C2×C22⋊D4311yescharacteristic
599C22×C4C23×D4312yes—
600C22×C4C23×D4312yes—
601C22×C4C23×D4311yescharacteristic
602SD16—868no—
603M16—868no—
604C2×C8—434no—
605C2×C8—432no—
606C2×C8—432no—
607C2×C8—432no—
608C2×C8—432no—
609C2×C8—868no—
610C2×C8—862no—
611C2×C8—862no—
612C2×C8—862no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—432no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—864no—
625C4⋊C4—861no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—864no—
629C4⋊C4—864no—
630C4⋊C4—864no—
631C4⋊C4C2×C22⋊D4314yes—
632C4⋊C4C23×D4312yes—
633C4⋊C4C23×D4312yes—
634C4⋊C4C23×D4312yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—864no—
641C22⋊C4C2×C22⋊D4314yes—
642C22⋊C4C2×C22⋊D4314yes—
643C42—864no—
644C42—864no—
645C42C2×C22⋊D4312yes—
646C42C23×D4312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#1306335114yes—
657C23C22×C22⋊D4312yes—
658C23C22×C22⋊D4312yes—
659C23C22×C22⋊D4311yescharacteristic
660Q8—48no—
661Q8—862no—
662Q8—862no—
663Q8—1722no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—48no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—1728no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4C22×C22⋊D4312yes—
699C2×C4C22×C22⋊D4312yes—
700C2×C4C22×C22⋊D4312yes—
701C2×C4C22×C22⋊D4312yes—
702C2×C4C22×C22⋊D4311yescharacteristic
703C2×C4#41×D4312yes—
704C2×C4#1306337212yes—
705C2×C4C24×D4311yescharacteristic
706C8—434no—
707C8—862no—
708C8—862no—
709C8—862no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22#1458354812yes—
722C22C2×#1306335114yes—
723C22C2×#1306335112yes—
724C22#1458371412yes—
725C22C23×C22⋊D4311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—1722no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4#1458354812yes—
738C4C2×#41×D4311yescharacteristic
739C4C2×#1306337211yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2#1914702914yesdirect product factor
744C2C2×#1458354811yescharacteristic
745C2C22×#1306335111yescharacteristic
746C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
Fitting, prime radicalC2×C43×#547C2
socleC23×C43C22×D4
hypercenterC2×#547D43
hypocenterC43C2×#3343
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#14583589C2semidirect
2. #19147029C2direct (N × H)
3. C2×#14583305C2semidirect
4. C2×#14583234C2semidirect
5. C2×#14583220C2semidirect
6. C2×#14583229C2semidirect
7. C2×#14583210C2semidirect
8. C2×#14583191C2semidirect
9. C2×#14583199C2semidirect
10. C2×#14583143C2semidirect
11. C2×#14583126C2semidirect
12. C2×#14582999C2semidirect
13. C2×#14582971C2semidirect
14. C2×#14582939C2semidirect
15. C22×#13063258C2semidirect
21. #14583589C22semidirect
32. #14583305C22semidirect
33. #14583234C22semidirect
34. #14583229C22semidirect
35. #14583220C22semidirect
36. #14583210C22semidirect
37. #14583199C22semidirect
38. #14583191C22semidirect
39. #14583143C22semidirect
40. #14583126C22semidirect
41. #14582999C22semidirect
42. #14582971C22semidirect
43. #14582939C22semidirect
50. C2×#13063258C22semidirect
268. C2×C43⋊C8#41semidirect
335. C43⋊C8C2×#41semidirect
386. C2×C43#3343semidirect
450. C43C2×#3343semidirect
743. C2#19147029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835892
#191470292
C2×#145833052
C2×#145832342
C2×#145832202
C2×#145832292
C2×#145832102
C2×#145831912
C2×#145831992
C2×#145831432
C2×#145831262
C2×#145829992
C2×#145829712
C2×#145829392
C22×#130632582
C2×C43×#5472
C2×#334343