Finite Group Databasebeta

← C2×#19147216 #25975342

Subgroups — C2×#19147216 #25975342

Order 11008.

1930 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583613C211yesmaximal, characteristic
2C2×#14583607C211yesmaximal, characteristic, complemented
3#19147216C2116yesmaximal, direct product factor
4C2×#14583303C211yesmaximal, characteristic, complemented
5C2×#14583238C211yesmaximal, characteristic, complemented
6C2×#14583237C211yesmaximal, characteristic, complemented
7C2×#14583211C211yesmaximal, characteristic, complemented
8C2×#14583210C211yesmaximal, characteristic, complemented
9C2×#14583192C211yesmaximal, characteristic, complemented
10C2×#14583187C211yesmaximal, characteristic, complemented
11C2×#14583142C211yesmaximal, characteristic, complemented
12C2×SD16×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582975C211yesmaximal, characteristic, complemented
14C2×#14582941C211yesmaximal, characteristic, complemented
15C2×#14582940C211yesmaximal, characteristic, complemented
16C2×C43×#468C211yesmaximal, characteristic, complemented
17C22×#10621872C2211yescharacteristic
18#14583613—24no—
19#14583613C2218yes—
20#14583607—24no—
21#14583607C2218yescomplemented
22C2×#13063324C2211yescharacteristic
23C2×#13063324C2211yescharacteristic
24C2×#13063315—21no—
25C2×#13063312—21no—
26C2×#13063311—21no—
27C2×#13063305—21no—
28C2×#13063302—21no—
29C2×#13063301C2211yescharacteristic
30C2×#13063297—21no—
31C2×#13063296C2211yescharacteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×D4×Dic43C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×(C22⋊D43)⋊C4—21no—
36C2×#13063284C2211yescharacteristic
37C2×#13063283C2211yescharacteristic
38C2×#13063281—21no—
39C22×C4⋊Dic43C2211yescharacteristic
40C2×C4⋊C4×D43C2211yescharacteristic
41#14583303C2218yescomplemented
42#14583238C2218yescomplemented
43#14583237C2218yescomplemented
44#14583211C2218yescomplemented
45#14583210C2218yescomplemented
46#14583192C2218yescomplemented
47#14583187C2218yescomplemented
48#14583142C2218yescomplemented
49SD16×Dic43C2218yescomplemented
50#14582975C2218yescomplemented
51#14582941C2218yescomplemented
52#14582940C2218yescomplemented
53C2×#13063259C2211yescharacteristic
54C2×#13063259C2211yescharacteristic
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063257C2211yescharacteristic
59C2×#13063257C2211yescharacteristic
60C2×#13063256C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#468C2218yescomplemented
74C2×#107×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×Dic86—21no—
79C22×C22⋊D43—21no—
80C22×C22⋊D43D411yescharacteristic
81C23×Dic43—21no—
82C23×Dic43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—24no—
86C2×#10621872C2314yes—
87C22×C43⋊C8C2311yescharacteristic
88C22×C43⋊C8C2311yescharacteristic
89#13063324—22no—
90#13063324—22no—
91#13063324C2314yes—
92#13063324C2314yes—
93#13063315—28no—
94#13063312—28no—
95#13063311—28no—
96#13063305—28no—
97#13063302—28no—
98#13063301—22no—
99#13063301C2314yes—
100#13063297—28no—
101#13063296—22no—
102#13063296C2314yes—
103Q8×Dic43—22no—
104Q8×Dic43C2314yes—
105D4×Dic43—22no—
106D4×Dic43C2314yes—
107C4×C22⋊D43D414yes—
108C4×C22⋊D43C2314yes—
109(C22⋊D43)⋊C4—28no—
110#13063284—22no—
111#13063284C2314yes—
112#13063283—22no—
113#13063283C2314yes—
114#13063281—28no—
115C2×C4⋊Dic43—22no—
116C2×C4⋊Dic43—21no—
117C2×C4⋊Dic43—21no—
118C2×C4⋊Dic43C2311yescharacteristic
119C2×C4⋊Dic43C2314yes—
120C2×C4⋊Dic43C2311yescharacteristic
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2311yescharacteristic
123C2×Dic43⋊C4—21no—
124C2×Dic43⋊C4—21no—
125C2×Dic43⋊C4—21no—
126C2×Dic43⋊C4—21no—
127C2×Dic43⋊C4D411yescharacteristic
128C4⋊C4×D43—22no—
129C4⋊C4×D43C2314yes—
130C2×C22⋊Dic43—21no—
131C2×C22⋊Dic43—21no—
132C2×C22⋊Dic43—21no—
133C2×C22⋊Dic43D411yescharacteristic
134C2×(C2×D43)⋊C4—21no—
135C2×(C2×D43)⋊C4—21no—
136C2×(C2×D43)⋊C4D411yescharacteristic
137C2×C4×Dic43—21no—
138C2×C4×Dic43—21no—
139C2×C4×Dic43—21no—
140C2×C4×Dic43C2311yescharacteristic
141#13063259C2314yes—
142#13063259C2314yes—
143#13063258C2314yes—
144#13063258C2314yes—
145#13063258C2314yes—
146#13063257C2314yes—
147#13063257C2314yes—
148#13063256C2314yes—
149Dic43⋊C8C2314yes—
150#13063249C2314yes—
151#13063249C2314yes—
152#13063246C2314yes—
153#13063246C2314yes—
154C22⋊(C43⋊C8)C2314yes—
155(C2×D43)⋊C8C2314yes—
156C8×Dic43C2314yes—
157C22×Q8×C43C2311yescharacteristic
158C22×D4×C43—21no—
159C22×D4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C2×SD16×C43—24no—
162C2×SD16×C43C2314yes—
163C2×M16×C43—24no—
164C2×M16×C43C2314yes—
165C22×C8×C43C2311yescharacteristic
166C22×C8×C43C2311yescharacteristic
167C22⋊Q8×C43—22no—
168C22⋊Q8×C43C2314yes—
169#121×C43—22no—
170#121×C43C2314yes—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C22⋊C4×C43—21no—
175C2×C22⋊C4×C43—21no—
176#107×C43C2314yes—
177#103×C43C2314yes—
178#102×C43C2314yes—
179C24×C43—21no—
180C24×C43C2×D411yescharacteristic
181C23×D43C2×D411yescharacteristic
182C2×Q8×C43—21no—
183C2×Q8×C43—22no—
184C2×Q8×C43—22no—
185C2×Q8×C43C2412yes—
186C2×D4×C43—21no—
187C2×D4×C43—24no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43—82no—
191C2×D4×C43C2412yes—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D412yes—
199C22×C4×C43C2412yes—
200C22×C4×C43C2411yescharacteristic
201C2×C22⋊D43—24no—
202C2×C22⋊D43—24no—
203C2×C22⋊D43—82no—
204C2×C22⋊D43C2×D414yes—
205C22×Dic43—24no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—24no—
211C22×Dic43—44no—
212C22×Dic43—82no—
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—24no—
219C2×C4×D43—82no—
220C2×C4×D43C2×D412yes—
221C2×C4×D43C2412yes—
222C2×Dic86—24no—
223C2×Dic86—24no—
224C2×Dic86—82no—
225C2×Dic86—82no—
226SD16×C43—28no—
227M16×C43—28no—
228C2×C8×C43—22no—
229C2×C8×C43#4114yes—
230C2×C8×C43C2412yes—
231C2×C8×C43C2412yes—
232C4⋊C4×C43—24no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2412yes—
236C4⋊C4×C43C2412yes—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C22⋊Dic43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43C2×D414yes—
243(C2×D43)⋊C4—24no—
244(C2×D43)⋊C4—24no—
245(C2×D43)⋊C4C2×D414yes—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43—24no—
252C4⋊Dic43C2412yes—
253C4⋊Dic43C2412yes—
254C4⋊Dic43C2412yes—
255C4⋊Dic43C2412yes—
256Dic43⋊C4—24no—
257Dic43⋊C4—24no—
258Dic43⋊C4—24no—
259Dic43⋊C4—24no—
260Dic43⋊C4C2×D414yes—
261C4×Dic43—24no—
262C4×Dic43—24no—
263C4×Dic43—24no—
264C4×Dic43C2×D412yes—
265C4×Dic43C2412yes—
266C2×C43⋊C8—22no—
267C2×C43⋊C8—22no—
268C2×C43⋊C8C2412yes—
269C2×C43⋊C8C2412yes—
270#10621872—28no—
271C23×C43—22no—
272C23×C43—22no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—42no—
276C23×C43—42no—
277C23×C43—42no—
278C23×C43C22×D412yes—
279C23×C43C22×D411yescharacteristic
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43C22×D412yes—
284Q8×C43—22no—
285Q8×C43—22no—
286Q8×C43—42no—
287D4×C43—22no—
288D4×C43—22no—
289D4×C43—42no—
290D4×C43—84no—
291C2×C4×C43—22no—
292C2×C4×C43—24no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—42no—
301C2×C4×C43C22×D412yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C2×#4112yes—
304C2×C4×C432−1+412yes—
305C2×C4×C43C2511yescharacteristic
306C22⋊D43—28no—
307C22⋊D43—84no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—48no—
319C2×Dic43—84no—
320C2×Dic43#13714yes—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324C4×D43—24no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—84no—
328Dic86—84no—
329Dic86—84no—
330C8×C43—22no—
331C8×C43C2×#4114yes—
332C43⋊C8—22no—
333C43⋊C8—22no—
334C2×#3357—431nomaximal, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—44no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43—42no—
342C22×C43—84no—
343C22×C43#54712yes—
344C22×C43C2×#13712yes—
345C22×C43#57612yes—
346C22×C43C23×D411yescharacteristic
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—44no—
351C4×C43—22no—
352C4×C43—42no—
353C4×C43—42no—
354C4×C43—42no—
355C4×C43#54712yes—
356C4×C43C22×#4111yescharacteristic
357C4×C43C2×2−1+411yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—42no—
361Dic43—42no—
362Dic43—42no—
363Dic43—42no—
364Dic43C2×#13714yes—
365C2×#555—431no—
366C2×#554—431no—
367#3357—4316no—
368C2×#500—431no—
369C2×#485—431no—
370C2×#485—431no—
371C2×#480—431no—
372C2×#480—431no—
373C2×#477—431no—
374C2×#476—431no—
375C2×#468—431no—
376C2×#468D4311yescharacteristic, complemented
377C2×C4×SD16—431no—
378C2×#436—431no—
379C2×#428—431no—
380C2×#428—431no—
381C2×C43—42no—
382C2×C43—82no—
383C2×C43#335714yescomplemented
384C2×C43C2×#54711yescharacteristic
385C2×C43C22×#13711yescharacteristic
386C2×C43C2×#57611yescharacteristic
387D43—42no—
388C22×SD16C2×D4311yescharacteristic
389C22×M16—431no—
390C22×M16C2×D4311yescharacteristic
391#555—438no—
392#555—864no—
393#554—438no—
394#554—864no—
395C2×C4⋊Q8—431no—
396C2×C4⋊Q8—431no—
397C2×#125—861no—
398C2×#124—861no—
399C2×#124—861no—
400C2×C22⋊Q8—431no—
401C2×C22⋊Q8—861no—
402C2×C22⋊Q8—861no—
403C2×C22⋊Q8C2×D4311yescharacteristic
404C2×#121—431no—
405C2×#121—861no—
406C2×#121C2×D4311yescharacteristic
407C2×C4×Q8—431no—
408C2×C4×D4—431no—
409C2×C4×D4—431no—
410C2×C4×D4—861no—
411C2×#117—431no—
412C2×#117—431no—
413C2×#117—861no—
414C22×C4⋊C4—431no—
415C22×C4⋊C4—431no—
416#500—438no—
417#485—438no—
418#485—438no—
419#480—438no—
420#480—438no—
421#477—438no—
422#476—438no—
423#468—438no—
424#468C2×D4318yescomplemented
425C4×SD16—438no—
426#436—438no—
427#428—438no—
428#428—438no—
429C2×#107—431no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#107—431no—
433C2×#107—431no—
434C2×#107C2×D4311yescharacteristic
435C2×#106—431no—
436C2×#106—431no—
437C2×#106—431no—
438C2×C4⋊C8—431no—
439C2×#103—431no—
440C2×#103—431no—
441C2×#103C2×D4311yescharacteristic
442C2×#102—431no—
443C2×#102—431no—
444C2×#102C2×D4311yescharacteristic
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×C4×C8—431no—
448C43C2×#335711yescharacteristic, complemented, Sylow
449C22×Q8—861no—
450C22×Q8—861no—
451C22×Q8C22×D4311yescharacteristic
452C22×D4—21no—
453C22×D4—431no—
454C22×D4—861no—
455C22×D4C22×D4311yescharacteristic
456C23×C4—431no—
457C23×C4—861no—
458C23×C4—861no—
459C23×C4—861no—
460C23×C4C22×D4311yescharacteristic
461C2×SD16—24no—
462C2×SD16C22×D4314yes—
463C2×M16—24no—
464C2×M16—434no—
465C2×M16—864no—
466C2×M16C22×D4314yes—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4311yescharacteristic
471C4⋊Q8—434no—
472C4⋊Q8—434no—
473C4⋊Q8—862no—
474C4⋊Q8—862no—
475#125—868no—
476#124—868no—
477#124—868no—
478C22⋊Q8—22no—
479C22⋊Q8—434no—
480C22⋊Q8—868no—
481C22⋊Q8—868no—
482C22⋊Q8—862no—
483C22⋊Q8C22×D4314yes—
484#121—22no—
485#121—434no—
486#121—862no—
487#121—868no—
488#121C22×D4314yes—
489C4×Q8—434no—
490C4×Q8—862no—
491C4×D4—434no—
492C4×D4—434no—
493C4×D4—434no—
494C4×D4—862no—
495C4×D4—868no—
496#117—434no—
497#117—434no—
498#117—868no—
499#117—862no—
500#117—862no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—434no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—434no—
509C2×C4⋊C4—862no—
510C2×C4⋊C4—861no—
511C2×C4⋊C4—861no—
512C2×C4⋊C4—861no—
513C2×C4⋊C4—861no—
514C2×C4⋊C4—861no—
515C2×C4⋊C4—861no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4C22×D4311yescharacteristic
518C2×C4⋊C4C22×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—431no—
522C2×C22⋊C4—431no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C42—431no—
529C2×C42—861no—
530C2×C42—861no—
531C2×C42—861no—
532#107—434no—
533#107—434no—
534#107—434no—
535#107—434no—
536#107—434no—
537#107C22×D4314yes—
538#106—434no—
539#106—434no—
540#106—434no—
541C4⋊C8—434no—
542#103—434no—
543#103—434no—
544#103C22×D4314yes—
545#102—434no—
546#102—434no—
547#102C22×D4314yes—
548C22⋊C8—434no—
549C22⋊C8—434no—
550C4×C8—434no—
551C24—21no—
552C24—431no—
553C24D4×D4311yescharacteristic
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—864no—
558C2×Q8—864no—
559C2×Q8—3442no—
560C2×Q8—3442no—
561C2×Q8C23×D4312yes—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—82no—
567C2×D4—434no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—3442no—
571C2×D4C23×D4312yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—432no—
581C22×C4—432no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—864no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—3442no—
592C22×C4—3442no—
593C22×C4—1724no—
594C22×C4D4×D4312yes—
595C22×C4D4×D4311yescharacteristic
596C22×C4C23×D4312yes—
597C22×C4C23×D4311yescharacteristic
598SD16—28no—
599M16—28no—
600M16—868no—
601C2×C8—22no—
602C2×C8—432no—
603C2×C8—432no—
604C2×C8—862no—
605C2×C8—862no—
606C2×C8#1062190014yes—
607C2×C8C23×D4312yes—
608C2×C8C23×D4312yes—
609C4⋊C4—24no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—434no—
613C4⋊C4—432no—
614C4⋊C4—432no—
615C4⋊C4—432no—
616C4⋊C4—432no—
617C4⋊C4—864no—
618C4⋊C4—864no—
619C4⋊C4—864no—
620C4⋊C4—864no—
621C4⋊C4—864no—
622C4⋊C4—861no—
623C4⋊C4—864no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4C23×D4312yes—
628C4⋊C4C23×D4312yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—434no—
632C22⋊C4—434no—
633C22⋊C4—864no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—864no—
637C22⋊C4—864no—
638C42—432no—
639C42—432no—
640C42—864no—
641C42—864no—
642C42—864no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—432no—
651C23—862no—
652C23—862no—
653C23—862no—
654C23C2×D4×D4312yes—
655C23C2×D4×D4311yescharacteristic
656Q8—22no—
657Q8—22no—
658Q8—42no—
659Q8—3444no—
660Q8—3444no—
661D4—22no—
662D4—22no—
663D4—42no—
664D4—84no—
665D4—868no—
666D4—3444no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—434no—
678C2×C4—432no—
679C2×C4—432no—
680C2×C4—432no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—864no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—3444no—
691C2×C4—3444no—
692C2×C4—1728no—
693C2×C4—1722no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1722no—
697C2×C4C2×D4×D4312yes—
698C2×C4C2×D4×D4311yescharacteristic
699C2×C4C2×#1062190012yes—
700C2×C4#1306337212yes—
701C2×C4C24×D4311yescharacteristic
702C8—22no—
703C8—862no—
704C8—862no—
705C8C2×#1062190014yes—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—84no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—1724no—
718C22#1458354912yes—
719C22#137×D4312yes—
720C22#1458370312yes—
721C22C22×D4×D4311yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—434no—
727C4—862no—
728C4—862no—
729C4—1722no—
730C4—1722no—
731C4—1722no—
732C4—1722no—
733C4#1458354912yes—
734C4C22×#1062190011yescharacteristic
735C4C2×#1306337211yescharacteristic
736C2—42no—
737C2—82no—
738C2—1722no—
739C2#1914721614yesdirect product factor
740C2C2×#1458354911yescharacteristic
741C2C2×#137×D4311yescharacteristic
742C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#468C2
socleC23×C43C22×D4
prime radicalC2×#14583613C2
hypercenterC2×#468D43
hypocenterC43C2×#3357
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
2. C2×#14583607C2semidirect
3. #19147216C2direct (N × H)
4. C2×#14583303C2semidirect
5. C2×#14583238C2semidirect
6. C2×#14583237C2semidirect
7. C2×#14583211C2semidirect
8. C2×#14583210C2semidirect
9. C2×#14583192C2semidirect
10. C2×#14583187C2semidirect
11. C2×#14583142C2semidirect
12. C2×SD16×Dic43C2semidirect
13. C2×#14582975C2semidirect
14. C2×#14582941C2semidirect
15. C2×#14582940C2semidirect
16. C2×C43×#468C2semidirect
21. #14583607C22semidirect
41. #14583303C22semidirect
42. #14583238C22semidirect
43. #14583237C22semidirect
44. #14583211C22semidirect
45. #14583210C22semidirect
46. #14583192C22semidirect
47. #14583187C22semidirect
48. #14583142C22semidirect
49. SD16×Dic43C22semidirect
50. #14582975C22semidirect
51. #14582941C22semidirect
52. #14582940C22semidirect
73. C43×#468C22semidirect
376. C2×#468D43semidirect
383. C2×C43#3357semidirect
424. #468C2×D43semidirect
448. C43C2×#3357semidirect
739. C2#19147216direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836132
C2×#145836072
#191472162
C2×#145833032
C2×#145832382
C2×#145832372
C2×#145832112
C2×#145832102
C2×#145831922
C2×#145831872
C2×#145831422
C2×SD16×Dic432
C2×#145829752
C2×#145829412
C2×#145829402
C2×C43×#4682
C2×#335743