Finite Group Databasebeta

← C2×#19147035 #25975128

Subgroups — C2×#19147035 #25975128

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×#14583553C211yesmaximal, characteristic
2#19147035C2116yesmaximal, direct product factor
3C2×#14583309C211yesmaximal, characteristic, complemented
4C2×#14583232C211yesmaximal, characteristic, complemented
5C2×#14583223C211yesmaximal, characteristic, complemented
6C2×#14583227C211yesmaximal, characteristic, complemented
7C2×#14583212C211yesmaximal, characteristic, complemented
8C2×#14583194C211yesmaximal, characteristic, complemented
9C2×#14583196C211yesmaximal, characteristic, complemented
10C2×#14583147C211yesmaximal, characteristic, complemented
11C2×#14583130C211yesmaximal, characteristic, complemented
12C2×#14582997C211yesmaximal, characteristic, complemented
13C2×#14582971C211yesmaximal, characteristic, complemented
14C2×#14582942C211yesmaximal, characteristic, complemented
15C22×#13063258C211yesmaximal, characteristic, complemented
16C2×C43×#552C211yesmaximal, characteristic, complemented
17C22×#10621900—21no—
18C22×#10621884C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C23×C43⋊C8C2211yescharacteristic
21#14583553—24no—
22#14583553C2218yes—
23C2×#13063325C2211yescharacteristic
24C2×#13063309—21no—
25C2×#13063309—21no—
26C2×#13063305—21no—
27C2×#13063299C2211yescharacteristic
28C2×#13063299C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32#14583309C2218yescomplemented
33#14583232C2218yescomplemented
34#14583227C2218yescomplemented
35#14583223C2218yescomplemented
36#14583212C2218yescomplemented
37#14583196C2218yescomplemented
38#14583194C2218yescomplemented
39#14583147C2218yescomplemented
40#14583130C2218yescomplemented
41#14582997C2218yescomplemented
42#14582971C2218yescomplemented
43#14582942C2218yescomplemented
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×#13063249C2211yescharacteristic
56C2×#13063249C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063245C2211yescharacteristic
59C2×#13063245C2211yescharacteristic
60C2×#13063245C2211yescharacteristic
61C2×C22⋊(C43⋊C8)C2211yescharacteristic
62C2×C22⋊(C43⋊C8)C2211yescharacteristic
63C2×#13063236C2211yescharacteristic
64C43×#552—24no—
65C43×#552C2218yescomplemented
66C2×#126×C43—21no—
67C2×#125×C43—21no—
68C2×#125×C43C2211yescharacteristic
69C2×#123×C43—21no—
70C2×C22⋊Q8×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C4×Q8×C43C2211yescharacteristic
73C2×C4×D4×C43C2211yescharacteristic
74C2×#117×C43—21no—
75C2×#117×C43C2211yescharacteristic
76C22×C4⋊C4×C43C2211yescharacteristic
77C2×#10621900—28no—
78C2×#10621900—48no—
79C22×Dic86—21no—
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C23×Dic43—21no—
84C23×Dic43—21no—
85C22×C4×D43—21no—
86C2×#10621884—24no—
87C2×#10621884C2314yes—
88C2×#10621877—24no—
89C2×#10621877C2314yes—
90C22×C43⋊C8—24no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C22×C43⋊C8C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96#13063325—22no—
97#13063325C2314yes—
98#13063309—28no—
99#13063309—28no—
100#13063305—28no—
101#13063299—22no—
102#13063299—22no—
103#13063299C2314yes—
104#13063299C2314yes—
105C4×D172—22no—
106C4×D172C2314yes—
107C2×C4⋊Dic43—22no—
108C2×C4⋊Dic43—22no—
109C2×C4⋊Dic43—21no—
110C2×C4⋊Dic43—21no—
111C2×C4⋊Dic43—21no—
112C2×C4⋊Dic43C2314yes—
113C2×C4⋊Dic43C2314yes—
114C2×C4⋊Dic43C2311yescharacteristic
115C2×C4⋊Dic43C2311yescharacteristic
116C2×C4⋊Dic43C2311yescharacteristic
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120#13063258C2314yes—
121#13063258C2314yes—
122#13063258C2314yes—
123#13063258C2314yes—
124#13063258C2314yes—
125#13063258C2314yes—
126#13063256C2314yes—
127#13063256C2314yes—
128#13063256C2314yes—
129C4⋊(C43⋊C8)C2314yes—
130#13063249C2314yes—
131#13063249C2314yes—
132#13063249C2314yes—
133#13063245C2314yes—
134#13063245C2314yes—
135#13063245C2314yes—
136C22⋊(C43⋊C8)C2314yes—
137C22⋊(C43⋊C8)C2314yes—
138#13063236C2314yes—
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43D411yescharacteristic
141C23×C4×C43—21no—
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144#126×C43—28no—
145#125×C43—28no—
146#125×C43—22no—
147#125×C43C2314yes—
148#123×C43—28no—
149C22⋊Q8×C43—22no—
150C22⋊Q8×C43—22no—
151C22⋊Q8×C43C2314yes—
152C22⋊Q8×C43C2314yes—
153C4×Q8×C43—22no—
154C4×Q8×C43C2314yes—
155C4×D4×C43D414yes—
156C4×D4×C43C2314yes—
157#117×C43—22no—
158#117×C43—28no—
159#117×C43C2314yes—
160C2×C4⋊C4×C43—21no—
161C2×C4⋊C4×C43—22no—
162C2×C4⋊C4×C43—21no—
163C2×C4⋊C4×C43—21no—
164C2×C4⋊C4×C43—21no—
165C2×C4⋊C4×C43—21no—
166C2×C4⋊C4×C43—21no—
167C2×C4⋊C4×C43D411yescharacteristic
168C2×C4⋊C4×C43C2311yescharacteristic
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2314yes—
171C2×C4⋊C4×C43C2311yescharacteristic
172C2×C22⋊C4×C43—21no—
173C2×C22⋊C4×C43—21no—
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43D411yescharacteristic
176C2×C22⋊C4×C43D411yescharacteristic
177C2×C42×C43—21no—
178C2×C42×C43—21no—
179C2×C42×C43C2311yescharacteristic
180C24×C43C2×D411yescharacteristic
181C24×C43C2×D411yescharacteristic
182C23×D43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43C2412yes—
187C2×D4×C43—24no—
188C2×D4×C43C2×D414yes—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—24no—
198C22×C4×C43—44no—
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D412yes—
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—44no—
211C2×C22⋊D43—44no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—24no—
216C22×Dic43—24no—
217C22×Dic43—44no—
218C22×Dic43—44no—
219#10621900—432no—
220C2×D172—21no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172C2412yes—
224C2×C4×D43—24no—
225C2×C4×D43—44no—
226C2×Dic86—24no—
227C2×Dic86—44no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—24no—
231C4⋊C4×C43—24no—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—24no—
234C4⋊C4×C43—24no—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43C2×D414yes—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—24no—
244C22⋊C4×C43C2×D414yes—
245C22⋊C4×C43C2×D414yes—
246C42×C43—24no—
247C42×C43—24no—
248C42×C43C2×D412yes—
249C42×C43C2412yes—
250#10621884—28no—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—24no—
258C4⋊Dic43—24no—
259C4⋊Dic43—24no—
260C4⋊Dic43C2412yes—
261C4⋊Dic43C2412yes—
262C4⋊Dic43C2412yes—
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×C43AGL(1,ℤ/8)14yes—
279C23×C43C22×D412yes—
280C23×C43C22×D412yes—
281C23×C43C22×D411yescharacteristic
282C22×D43—22no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—42no—
289D4×C43—28no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—24no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—42no—
305C2×C4×C43—48no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D412yes—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C2×#4112yes—
315C2×C4×C432−1+412yes—
316C2×C4×C43C2511yescharacteristic
317C22⋊D43—48no—
318C22⋊D43—48no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—48no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—48no—
327D172—22no—
328D172—22no—
329D172—42no—
330C4×D43—48no—
331Dic86—48no—
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#54712yes—
345C22×C43C2×AGL(1,ℤ/8)14yes—
346C22×C43C2×AGL(1,ℤ/8)12yes—
347C22×C43#57812yes—
348C22×C43C23×D411yescharacteristic
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—84no—
353C4×C43—22no—
354C4×C43—22no—
355C4×C43—22no—
356C4×C43—22no—
357C4×C43—42no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43—42no—
361C4×C43#54712yes—
362C4×C43C22×#4111yescharacteristic
363C4×C43C2×2−1+411yescharacteristic
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C2×#552D4311yescharacteristic, complemented
368C2×#547—431no—
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#334314yescomplemented
386C2×C43C2×#54711yescharacteristic
387C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
388C2×C43C2×#57811yescharacteristic
389D43—82no—
390C22×#41—861no—
391C22×SD16—431no—
392C22×M16—431no—
393C23×C8—431no—
394#552—24no—
395#552C2×D4318yescomplemented
396#547—438no—
397#547—864no—
398C2×C4⋊Q8—431no—
399C2×#126—21no—
400C2×#125—21no—
401C2×#125C2×D4311yescharacteristic
402C2×#123—21no—
403C2×#123—861no—
404C2×#123—861no—
405C2×C22⋊Q8—861no—
406C2×C22⋊Q8C2×D4311yescharacteristic
407C2×C22⋊Q8C2×D4311yescharacteristic
408C2×#121—431no—
409C2×#121—431no—
410C2×C4×Q8C2×D4311yescharacteristic
411C2×C4×D4—431no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×#117—21no—
414C2×#117C2×D4311yescharacteristic
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
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—868no—
452C2×#41—1728no—
453C22×Q8—861no—
454C22×Q8C22×D4311yescharacteristic
455C22×D4—431no—
456C22×D4—861no—
457C22×D4—861no—
458C22×D4C22⋊D4311yescharacteristic
459C23×C4—21no—
460C23×C4—861no—
461C23×C4—861no—
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—434no—
476C4⋊Q8—862no—
477#126—28no—
478#125—28no—
479#125—22no—
480#125C22×D4314yes—
481#123—28no—
482#123—868no—
483#123—868no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—868no—
487C22⋊Q8C22×D4314yes—
488C22⋊Q8C22×D4314yes—
489#121—434no—
490#121—434no—
491#121—862no—
492#121—862no—
493C4×Q8—22no—
494C4×Q8C22×D4314yes—
495C4×D4—434no—
496C4×D4—862no—
497C4×D4C22⋊D4314yes—
498C4×D4C22×D4314yes—
499#117—22no—
500#117—28no—
501#117C22×D4314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—434no—
513C2×C4⋊C4—434no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—862no—
518C2×C4⋊C4—861no—
519C2×C4⋊C4C22⋊D4311yescharacteristic
520C2×C4⋊C4C22×D4311yescharacteristic
521C2×C4⋊C4C22×D4311yescharacteristic
522C2×C4⋊C4C22×D4314yes—
523C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
533C2×C42—21no—
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—861no—
555C24C2×C22⋊D4311yescharacteristic
556C24C2×C22⋊D4311yescharacteristic
557#41—17232no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—864no—
562C2×Q8—1724no—
563C2×Q8C23×D4312yes—
564C2×D4—24no—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—864no—
568C2×D4—861no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—1724no—
572C2×D4—1724no—
573C2×D4C2×C22⋊D4314yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—44no—
584C22×C4—864no—
585C22×C4—864no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—864no—
590C22×C4—1724no—
591C22×C4—1724no—
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—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—21no—
622C4⋊C4—432no—
623C4⋊C4—432no—
624C4⋊C4—432no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
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—24no—
644C42—24no—
645C42C2×C22⋊D4312yes—
646C42C23×D4312yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—862no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23#1306335014yes—
657C23C22×C22⋊D4312yes—
658C23C22×C22⋊D4312yes—
659C23C22×C22⋊D4311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—1728no—
664D4—28no—
665D4—862no—
666D4—862no—
667D4—1728no—
668D4—1728no—
669D4—1722no—
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—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—1728no—
693C2×C4—1728no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4—1728no—
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—3444no—
718C22—1722no—
719C22—1722no—
720C22—1722no—
721C22#1458354812yes—
722C22C2×#1306335014yes—
723C22C2×#1306335012yes—
724C22#1458371412yes—
725C22C23×C22⋊D4311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4#1458354812yes—
738C4C2×#41×D4311yescharacteristic
739C4C2×#1306337211yescharacteristic
740C2—24no—
741C2—42no—
742C2—3442no—
743C2#1914703514yesdirect product factor
744C2C2×#1458354811yescharacteristic
745C2C22×#1306335011yescharacteristic
746C2C2×#1458371411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radicalC2×#14583553C2
hypercenterC2×#552D43
hypocenterC43C2×#3343
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #19147035C2direct (N × H)
3. C2×#14583309C2semidirect
4. C2×#14583232C2semidirect
5. C2×#14583223C2semidirect
6. C2×#14583227C2semidirect
7. C2×#14583212C2semidirect
8. C2×#14583194C2semidirect
9. C2×#14583196C2semidirect
10. C2×#14583147C2semidirect
11. C2×#14583130C2semidirect
12. C2×#14582997C2semidirect
13. C2×#14582971C2semidirect
14. C2×#14582942C2semidirect
15. C22×#13063258C2semidirect
16. C2×C43×#552C2semidirect
32. #14583309C22semidirect
33. #14583232C22semidirect
34. #14583227C22semidirect
35. #14583223C22semidirect
36. #14583212C22semidirect
37. #14583196C22semidirect
38. #14583194C22semidirect
39. #14583147C22semidirect
40. #14583130C22semidirect
41. #14582997C22semidirect
42. #14582971C22semidirect
43. #14582942C22semidirect
50. C2×#13063258C22semidirect
65. C43×#552C22semidirect
268. C2×C43⋊C8#41semidirect
335. C43⋊C8C2×#41semidirect
367. C2×#552D43semidirect
385. C2×C43#3343semidirect
395. #552C2×D43semidirect
450. C43C2×#3343semidirect
743. C2#19147035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835532
#191470352
C2×#145833092
C2×#145832322
C2×#145832232
C2×#145832272
C2×#145832122
C2×#145831942
C2×#145831962
C2×#145831472
C2×#145831302
C2×#145829972
C2×#145829712
C2×#145829422
C22×#130632582
C2×C43×#5522
C2×#334343