Finite Group Databasebeta

← C2×#19147036 #25975129

Subgroups — C2×#19147036 #25975129

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×#14583588C211yesmaximal, characteristic, complemented
2C2×#14583550C211yesmaximal, characteristic
3#19147036C2116yesmaximal, direct product factor
4C2×#14583306C211yesmaximal, characteristic, complemented
5C2×#14583234C211yesmaximal, characteristic, complemented
6C2×#14583223C211yesmaximal, characteristic, complemented
7C2×#14583231C211yesmaximal, characteristic, complemented
8C2×#14583214C211yesmaximal, characteristic, complemented
9C2×#14583193C211yesmaximal, characteristic, complemented
10C2×#14583198C211yesmaximal, characteristic, complemented
11C2×#14583145C211yesmaximal, characteristic, complemented
12C2×#14583129C211yesmaximal, characteristic, complemented
13C2×#14582998C211yesmaximal, characteristic, complemented
14C2×#14582968C211yesmaximal, characteristic, complemented
15C2×#107×D43C211yesmaximal, characteristic, complemented
16C2×C43×#428C211yesmaximal, characteristic, complemented
17C22×#10621898—21no—
18C22×#10621873C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583588—24no—
21#14583588C2218yescomplemented
22#14583550—24no—
23#14583550C2218yes—
24C2×#13063324C2211yescharacteristic
25C2×#13063318—21no—
26C2×#13063317—21no—
27C2×#13063316C2211yescharacteristic
28C2×#13063310—21no—
29C2×#13063308—21no—
30C2×#13063307—21no—
31C2×#13063305C2211yescharacteristic
32C2×#13063304C2211yescharacteristic
33C2×#13063303—21no—
34C2×#13063300C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063290C2211yescharacteristic
37C2×#13063287C2211yescharacteristic
38C2×C4×C22⋊D43C2211yescharacteristic
39C2×#13063282—21no—
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C4⋊C4×D43C2211yescharacteristic
42#14583306C2218yescomplemented
43#14583234C2218yescomplemented
44#14583231C2218yescomplemented
45#14583223C2218yescomplemented
46#14583214C2218yescomplemented
47#14583198C2218yescomplemented
48#14583193C2218yescomplemented
49#14583145C2218yescomplemented
50#14583129C2218yescomplemented
51#14582998C2218yescomplemented
52#14582968C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063258C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57#107×D43C2218yescomplemented
58C2×#13063256C2211yescharacteristic
59C2×Dic43⋊C8C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×M16×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#428C2218yescomplemented
73C2×#107×C43C2211yescharacteristic
74C2×#107×C43C2211yescharacteristic
75C2×#106×C43C2211yescharacteristic
76C2×#106×C43C2211yescharacteristic
77C2×#10621898—28no—
78C2×#10621898—48no—
79C22×Dic86—21no—
80C22×Dic86C2311yescharacteristic
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×C22⋊D43—21no—
84C22×C22⋊D43D411yescharacteristic
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43C2311yescharacteristic
89C2×#10621873—24no—
90C2×#10621873C2314yes—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—24no—
94C2×C8×D43C2314yes—
95#13063324—22no—
96#13063324C2314yes—
97#13063318—28no—
98#13063317—28no—
99#13063316—22no—
100#13063316C2314yes—
101#13063310—28no—
102#13063308—28no—
103#13063307—28no—
104#13063305—22no—
105#13063305C2314yes—
106#13063304—22no—
107#13063304C2314yes—
108#13063303—28no—
109#13063300—22no—
110#13063300C2314yes—
111#13063299—22no—
112#13063299C2314yes—
113#13063290—22no—
114#13063290C2314yes—
115#13063287—22no—
116#13063287C2314yes—
117C4×C22⋊D43D414yes—
118C4×C22⋊D43C2314yes—
119#13063282—28no—
120C2×C4⋊Dic43—21no—
121C2×C4⋊Dic43—21no—
122C2×C4⋊Dic43C2311yescharacteristic
123C2×C4⋊Dic43C2311yescharacteristic
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4—21no—
128C2×Dic43⋊C4—21no—
129C2×Dic43⋊C4—21no—
130C2×Dic43⋊C4D411yescharacteristic
131C4⋊C4×D43—22no—
132C4⋊C4×D43—22no—
133C4⋊C4×D43C2314yes—
134C4⋊C4×D43C2314yes—
135C2×C22⋊Dic43—21no—
136C2×C22⋊Dic43D411yescharacteristic
137C2×(C2×D43)⋊C4—21no—
138C2×(C2×D43)⋊C4—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4D411yescharacteristic
142C2×C4×Dic43—21no—
143C2×C4×Dic43C2311yescharacteristic
144#13063259C2314yes—
145#13063258C2314yes—
146#13063258C2314yes—
147#13063258C2314yes—
148#13063256C2314yes—
149Dic43⋊C8C2314yes—
150#13063250C2314yes—
151#13063248C2314yes—
152#13063248C2314yes—
153#13063247C2314yes—
154#13063245C2314yes—
155#13063245C2314yes—
156C22⋊(C43⋊C8)C2314yes—
157(C2×D43)⋊C8C2314yes—
158#13063235C2314yes—
159C23×C4×C43—21no—
160C23×C4×C43C2311yescharacteristic
161C2×M16×C43—24no—
162C2×M16×C43C2314yes—
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165#117×C43—22no—
166#117×C43C2314yes—
167C2×C4⋊C4×C43—21no—
168C2×C4⋊C4×C43—22no—
169C2×C4⋊C4×C43C2311yescharacteristic
170C2×C4⋊C4×C43C2311yescharacteristic
171C2×C4⋊C4×C43C2314yes—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C42×C43—21no—
176#107×C43C2314yes—
177#107×C43C2314yes—
178#106×C43C2314yes—
179#106×C43C2314yes—
180C24×C43C2×D411yescharacteristic
181C23×D43—21no—
182C23×D43C2×D411yescharacteristic
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—24no—
190C22×C4×C43—44no—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—44no—
198C2×C22⋊D43C2×D414yes—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205#10621898—432no—
206C2×D172—21no—
207C2×D172—24no—
208C2×D172—22no—
209C2×D172—22no—
210C2×D172—44no—
211C2×D172C2412yes—
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—24no—
215C2×C4×D43—24no—
216C2×C4×D43—24no—
217C2×C4×D43—44no—
218C2×C4×D43—44no—
219C2×C4×D43—44no—
220C2×C4×D43C2×D412yes—
221C2×C4×D43C2412yes—
222C2×Dic86—22no—
223C2×Dic86—22no—
224C2×Dic86—21no—
225C2×Dic86—24no—
226C2×Dic86—44no—
227C2×Dic86C2412yes—
228M16×C43—28no—
229C2×C8×C43—22no—
230C2×C8×C43#4114yescomplemented
231C2×C8×C43C2412yes—
232C2×C8×C43C2412yes—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43—24no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—21no—
238C4⋊C4×C43C2412yes—
239C4⋊C4×C43C2412yes—
240C4⋊C4×C43C2412yes—
241C4⋊C4×C43C2412yes—
242C22⋊C4×C43—24no—
243C42×C43—24no—
244C22⋊Dic43—24no—
245C22⋊Dic43C2×D414yes—
246(C2×D43)⋊C4—24no—
247(C2×D43)⋊C4—24no—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4C2×D414yes—
251C4⋊Dic43—21no—
252C4⋊Dic43—21no—
253C4⋊Dic43—24no—
254C4⋊Dic43—24no—
255C4⋊Dic43C2412yes—
256C4⋊Dic43C2412yes—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4—24no—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263Dic43⋊C4C2×D414yes—
264C4×Dic43—24no—
265C4×Dic43C2×D412yes—
266C4×Dic43C2412yes—
267C2×C43⋊C8—22no—
268C2×C43⋊C8—22no—
269C2×C43⋊C8C2412yes—
270C2×C43⋊C8C2412yes—
271#10621873—28no—
272C8×D43—28no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43C22×D412yes—
277C23×C43C22×D411yescharacteristic
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43AGL(1,ℤ/8)14yes—
285C22×D43C22×D412yes—
286C2×C4×C43—22no—
287C2×C4×C43—24no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—48no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43C22×D412yes—
300C2×C4×C43C22×D411yescharacteristic
301C2×C4×C43C2×#4112yes—
302C2×C4×C432−1+412yes—
303C2×C4×C43C2511yescharacteristic
304C22⋊D43—28no—
305C22⋊D43—48no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43C22×D412yes—
316C2×Dic43C22×D412yes—
317C2×Dic43C22×D412yes—
318D172—22no—
319D172—22no—
320D172—48no—
321D172—42no—
322C4×D43—24no—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—48no—
326C4×D43—48no—
327C4×D43—48no—
328Dic86—22no—
329Dic86—22no—
330Dic86—48no—
331Dic86—42no—
332C8×C43—22no—
333C8×C43C2×#4114yescomplemented
334C43⋊C8—22no—
335C43⋊C8—22no—
336C2×#3343—431nomaximal, Sylow
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—44no—
341C22×C43#54712yes—
342C22×C43C2×AGL(1,ℤ/8)12yes—
343C22×C43#57812yes—
344C22×C43C23×D411yescharacteristic
345C2×D43—28no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—84no—
352C2×D43C2×AGL(1,ℤ/8)14yes—
353C4×C43—22no—
354C4×C43—42no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358C4×C43#54712yes—
359C4×C43C22×#4111yescharacteristic
360C4×C43C2×2−1+411yescharacteristic
361Dic43—22no—
362Dic43—22no—
363Dic43—22no—
364Dic43—42no—
365Dic43—42no—
366Dic43—42no—
367C2×#552—431no—
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×#428D4311yescharacteristic, complemented
382C22×#107—431no—
383C2×C43—42no—
384C2×C43#334314yescomplemented
385C2×C43C2×#54711yescharacteristic
386C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
387C2×C43C2×#57811yescharacteristic
388D43—24no—
389D43—82no—
390C22×#41—861no—
391C22×SD16—431no—
392C22×M16C2×D4311yescharacteristic
393C23×C8—431no—
394#552—438no—
395#552—864no—
396#547—438no—
397#547—864no—
398C2×C4⋊Q8—431no—
399C2×#126—861no—
400C2×#125—431no—
401C2×#125—861no—
402C2×#123—861no—
403C2×#123—861no—
404C2×#123—861no—
405C2×C22⋊Q8—431no—
406C2×C22⋊Q8—431no—
407C2×C22⋊Q8—861no—
408C2×#121—431no—
409C2×#121—431no—
410C2×C4×Q8—431no—
411C2×C4×D4—431no—
412C2×C4×D4—431no—
413C2×#117—861no—
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#428C2×D4318yescomplemented
430C2×#107—431no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#107—431no—
434C2×#107—438no—
435C2×#107C2×D4311yescharacteristic
436C2×#107C2×D4311yescharacteristic
437C2×#106—431no—
438C2×#106C2×D4311yescharacteristic
439C2×#106C2×D4311yescharacteristic
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—431no—
454C22×Q8—861no—
455C22×D4—431no—
456C22×D4—431no—
457C22×D4—861no—
458C22×D4—861no—
459C23×C4—21no—
460C23×C4—431no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×SD16—434no—
466C2×SD16—864no—
467C2×M16—24no—
468C2×M16C22×D4314yes—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8—434no—
472C22×C8—864no—
473C22×C8C22×D4311yescharacteristic
474C22×C8C22×D4311yescharacteristic
475C4⋊Q8—434no—
476C4⋊Q8—862no—
477#126—868no—
478#125—434no—
479#125—868no—
480#125—862no—
481#123—868no—
482#123—868no—
483#123—868no—
484C22⋊Q8—434no—
485C22⋊Q8—434no—
486C22⋊Q8—868no—
487C22⋊Q8—862no—
488C22⋊Q8—862no—
489#121—434no—
490#121—434no—
491#121—862no—
492#121—862no—
493C4×Q8—434no—
494C4×Q8—862no—
495C4×D4—434no—
496C4×D4—434no—
497C4×D4—434no—
498C4×D4—862no—
499#117—22no—
500#117—868no—
501#117C22×D4314yes—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—434no—
508C2×C4⋊C4—434no—
509C2×C4⋊C4—862no—
510C2×C4⋊C4—862no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—861no—
517C2×C4⋊C4—861no—
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—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—861no—
532C2×C42—21no—
533C2×C42—431no—
534C2×C42—861no—
535#107—434no—
536#107—434no—
537#107—434no—
538#107—434no—
539#107C22×D4314yes—
540#107C22×D4314yes—
541#106—434no—
542#106C22×D4314yes—
543#106C22×D4314yes—
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—431no—
555C24—861no—
556C24D4×D4311yescharacteristic
557#41—17232no—
558C2×Q8—432no—
559C2×Q8—864no—
560C2×Q8—861no—
561C2×Q8—862no—
562C2×Q8—862no—
563C2×Q8—1724no—
564C2×D4—434no—
565C2×D4—432no—
566C2×D4—864no—
567C2×D4—864no—
568C2×D4—864no—
569C2×D4—861no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—1724no—
573C2×D4—1724no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—44no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—431no—
585C22×C4—432no—
586C22×C4—432no—
587C22×C4—864no—
588C22×C4—864no—
589C22×C4—864no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—1724no—
596C22×C4—1724no—
597C22×C4—1724no—
598C22×C4D4×D4312yes—
599C22×C4D4×D4311yescharacteristic
600C22×C4C23×D4312yes—
601C22×C4C23×D4311yescharacteristic
602SD16—868no—
603M16—28no—
604C2×C8—22no—
605C2×C8—432no—
606C2×C8—432no—
607C2×C8—862no—
608C2×C8—862no—
609C2×C8—868no—
610C2×C8#1062189814yescomplemented
611C2×C8C23×D4312yes—
612C2×C8C23×D4312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—434no—
619C4⋊C4—432no—
620C4⋊C4—432no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—864no—
624C4⋊C4—864no—
625C4⋊C4—864no—
626C4⋊C4—864no—
627C4⋊C4—864no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—864no—
631C4⋊C4C23×D4312yes—
632C4⋊C4C23×D4312yes—
633C4⋊C4C23×D4312yes—
634C4⋊C4C23×D4312yes—
635C22⋊C4—24no—
636C22⋊C4—434no—
637C22⋊C4—434no—
638C22⋊C4—864no—
639C22⋊C4—864no—
640C22⋊C4—864no—
641C22⋊C4—864no—
642C22⋊C4—864no—
643C42—24no—
644C42—432no—
645C42—432no—
646C42—864no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—434no—
651C23—432no—
652C23—862no—
653C23—862no—
654C23—862no—
655C23—1722no—
656C23—1722no—
657C23—1722no—
658C23C2×D4×D4312yes—
659C23C2×D4×D4311yescharacteristic
660Q8—862no—
661Q8—862no—
662Q8—1728no—
663Q8—1722no—
664D4—868no—
665D4—862no—
666D4—862no—
667D4—1728no—
668D4—1728no—
669D4—1722no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—48no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—432no—
684C2×C4—432no—
685C2×C4—432no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—864no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—1728no—
696C2×C4—1728no—
697C2×C4—1728no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4—1722no—
701C2×C4C2×D4×D4312yes—
702C2×C4C2×D4×D4311yescharacteristic
703C2×C4C2×#1062189812yes—
704C2×C4#1306337312yes—
705C2×C4C24×D4311yescharacteristic
706C8—22no—
707C8—862no—
708C8—862no—
709C8C2×#1062189814yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—434no—
715C22—862no—
716C22—868no—
717C22—862no—
718C22—3444no—
719C22—1722no—
720C22—1722no—
721C22—1722no—
722C22#1458355012yes—
723C22AGL(1,ℤ/8)×D4312yes—
724C22#1458371512yes—
725C22C22×D4×D4311yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—862no—
732C4—862no—
733C4—862no—
734C4—1722no—
735C4—1722no—
736C4—1722no—
737C4#1458355012yes—
738C4C22×#1062189811yescharacteristic
739C4C2×#1306337311yescharacteristic
740C2—42no—
741C2—864no—
742C2—3442no—
743C2#1914703614yesdirect product factor
744C2C2×#1458355011yescharacteristic
745C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
746C2C2×#1458371511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radicalC2×#14583550C2
hypercenterC2×#428D43
hypocenterC43C2×#3343
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#14583588C2semidirect
3. #19147036C2direct (N × H)
4. C2×#14583306C2semidirect
5. C2×#14583234C2semidirect
6. C2×#14583223C2semidirect
7. C2×#14583231C2semidirect
8. C2×#14583214C2semidirect
9. C2×#14583193C2semidirect
10. C2×#14583198C2semidirect
11. C2×#14583145C2semidirect
12. C2×#14583129C2semidirect
13. C2×#14582998C2semidirect
14. C2×#14582968C2semidirect
15. C2×#107×D43C2semidirect
16. C2×C43×#428C2semidirect
21. #14583588C22semidirect
42. #14583306C22semidirect
43. #14583234C22semidirect
44. #14583231C22semidirect
45. #14583223C22semidirect
46. #14583214C22semidirect
47. #14583198C22semidirect
48. #14583193C22semidirect
49. #14583145C22semidirect
50. #14583129C22semidirect
51. #14582998C22semidirect
52. #14582968C22semidirect
57. #107×D43C22semidirect
72. C43×#428C22semidirect
230. C2×C8×C43#41semidirect
333. C8×C43C2×#41semidirect
381. C2×#428D43semidirect
384. C2×C43#3343semidirect
429. #428C2×D43semidirect
450. C43C2×#3343semidirect
610. C2×C8#10621898semidirect
709. C8C2×#10621898semidirect
743. C2#19147036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835882
C2×#145835502
#191470362
C2×#145833062
C2×#145832342
C2×#145832232
C2×#145832312
C2×#145832142
C2×#145831932
C2×#145831982
C2×#145831452
C2×#145831292
C2×#145829982
C2×#145829682
C2×#107×D432
C2×C43×#4282
C2×#334343