Finite Group Databasebeta

← C2×#19145475 #25967281

Subgroups — C2×#19145475 #25967281

Order 11008.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583478C211yesmaximal, characteristic
2C2×#14583475C211yesmaximal, characteristic, complemented
3#19145475C2116yesmaximal, direct product factor
4C2×#14583236C211yesmaximal, characteristic, complemented
5C2×#14583240C211yesmaximal, characteristic, complemented
6C2×#14583231C211yesmaximal, characteristic, complemented
7C2×#14583158C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583141C211yesmaximal, characteristic, complemented
10C2×#14583127C211yesmaximal, characteristic, complemented
11C2×#14583062C211yesmaximal, characteristic, complemented
12C2×#14583062C211yesmaximal, characteristic, complemented
13C2×#14583057C211yesmaximal, characteristic, complemented
14C2×#14583037C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#482C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C23×Dic86C2211yescharacteristic
20C22×Dic172C2211yescharacteristic
21C22×Dic172C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621872C2211yescharacteristic
25C22×C8×D43C2211yescharacteristic
26#14583478—24no—
27#14583478C2218yes—
28#14583475—24no—
29#14583475C2218yescomplemented
30C2×#13063325—21no—
31C2×#13063313—21no—
32C2×#13063309—21no—
33C2×#13063309—21no—
34C2×#13063305C2211yescharacteristic
35C2×#13063305C2211yescharacteristic
36C2×#13063305C2211yescharacteristic
37C2×#13063305C2211yescharacteristic
38C2×#13063305C2211yescharacteristic
39C2×#13063304C2211yescharacteristic
40C2×#13063302—21no—
41C2×#13063298—21no—
42C2×#13063297—21no—
43C2×#13063296—21no—
44C2×#13063296C2211yescharacteristic
45C2×C4⋊C4×D43C2211yescharacteristic
46#14583240C2218yescomplemented
47#14583236C2218yescomplemented
48#14583231C2218yescomplemented
49#14583158C2218yescomplemented
50#14583144C2218yescomplemented
51#14583141C2218yescomplemented
52#14583127C2218yescomplemented
53#14583062C2218yescomplemented
54#14583062C2218yescomplemented
55#14583057C2218yescomplemented
56#14583037C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063248C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#121×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#482C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C22⋊C8×C43C2211yescharacteristic
77C2×#10621898—42no—
78C2×#10621898—42no—
79C2×#10621898D414yes—
80C2×#10621898C2314yes—
81C2×#10621900—22no—
82C2×#10621900—42no—
83C2×#10621900—42no—
84C2×#10621900C2314yes—
85C22×Dic86—21no—
86C22×Dic86—22no—
87C22×Dic86—42no—
88C22×Dic86—42no—
89C22×Dic86D411yescharacteristic
90C22×Dic86C2311yescharacteristic
91C22×Dic86C2311yescharacteristic
92C22×Dic86C2311yescharacteristic
93C22×Dic86C2314yes—
94C22×D172D411yescharacteristic
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43D411yescharacteristic
98C22×C22⋊D43D411yescharacteristic
99C23×Dic43—21no—
100C23×Dic43—21no—
101C22×C4×D43—21no—
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2311yescharacteristic
104C2×Dic172—42no—
105C2×Dic172—42no—
106C2×Dic172C2314yes—
107C2×Dic172C2314yes—
108C2×#10621883—42no—
109C2×#10621883—42no—
110C2×#10621883C2314yes—
111C2×#10621883C2314yes—
112C2×#10621872—42no—
113C2×#10621872C2314yes—
114C22×C43⋊C8C2311yescharacteristic
115C22×C43⋊C8C2311yescharacteristic
116C2×C8×D43—42no—
117C2×C8×D43C2314yes—
118#13063325—28no—
119#13063313—28no—
120#13063309—28no—
121#13063309—28no—
122#13063305—22no—
123#13063305—22no—
124#13063305—22no—
125#13063305—22no—
126#13063305—22no—
127#13063305C2314yes—
128#13063305C2314yes—
129#13063305C2314yes—
130#13063305C2314yes—
131#13063305C2314yes—
132#13063304—22no—
133#13063304C2314yes—
134#13063302—28no—
135#13063298—28no—
136#13063297—28no—
137#13063296—28no—
138#13063296—22no—
139#13063296C2314yes—
140C2×C4⋊Dic43—21no—
141C2×C4⋊Dic43—21no—
142C2×C4⋊Dic43—21no—
143C2×C4⋊Dic43—21no—
144C2×C4⋊Dic43—21no—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—21no—
148C4⋊C4×D43—22no—
149C4⋊C4×D43C2314yes—
150C2×C22⋊Dic43—21no—
151C2×C22⋊Dic43—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—21no—
157#13063258C2314yes—
158#13063256C2314yes—
159#13063250C2314yes—
160#13063250C2314yes—
161#13063248C2314yes—
162#13063248C2314yes—
163#13063248C2314yes—
164#13063248C2314yes—
165C22⋊(C43⋊C8)C2314yes—
166(C2×D43)⋊C8C2314yes—
167(C2×D43)⋊C8C2314yes—
168C22×D4×C43—21no—
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22×C8×C43C2311yescharacteristic
173#121×C43—22no—
174#121×C43C2314yes—
175#117×C43—22no—
176#117×C43C2314yes—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C42×C43—21no—
183#107×C43C2314yes—
184#106×C43C2314yes—
185#102×C43C2314yes—
186#102×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43C2×D411yescharacteristic
191C23×D43C2×D411yescharacteristic
192C2×D4×C43—21no—
193C2×D4×C43—24no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—82no—
197C2×D4×C43C2412yes—
198C22×C4×C43—22no—
199C22×C4×C43—22no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—42no—
210C2×C22⋊D43—42no—
211C2×C22⋊D43—44no—
212C2×C22⋊D43—82no—
213C2×C22⋊D43C2×D414yes—
214C2×C22⋊D43C2×D414yes—
215C22×Dic43—24no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—24no—
221C22×Dic43—44no—
222C22×Dic43—44no—
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225#10621900—44no—
226#10621900—44no—
227#10621900—48no—
228#10621898—48no—
229#10621898—44no—
230#10621898—44no—
231C2×D172—42no—
232C2×D172C2×D414yes—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—24no—
238C2×C4×D43—82no—
239C2×C4×D43C2×D412yes—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2412yes—
242C2×C4×D43C2412yes—
243C2×Dic86—22no—
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—22no—
249C2×Dic86—21no—
250C2×Dic86—21no—
251C2×Dic86—21no—
252C2×Dic86—24no—
253C2×Dic86—44no—
254C2×Dic86—44no—
255C2×Dic86—42no—
256C2×Dic86—44no—
257C2×Dic86—48no—
258C2×Dic86C2×D414yes—
259C2×Dic86C2412yes—
260C2×Dic86C2412yes—
261C2×Dic86C2412yes—
262C2×C8×C43—22no—
263C2×C8×C43—22no—
264C2×C8×C43C2412yes—
265C2×C8×C43C2412yes—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C2412yes—
270C4⋊C4×C43C2412yes—
271C4⋊C4×C43C2412yes—
272C22⋊C4×C43—24no—
273C22⋊C4×C43—24no—
274C42×C43—24no—
275C22⋊Dic43—24no—
276C22⋊Dic43—24no—
277#10621883—44no—
278#10621883—44no—
279(C2×D43)⋊C4—24no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284C4⋊Dic43—21no—
285C4⋊Dic43—24no—
286C4⋊Dic43—24no—
287C4⋊Dic43—24no—
288C4⋊Dic43—24no—
289C4⋊Dic43—24no—
290C4⋊Dic43C2412yes—
291Dic43⋊C4—24no—
292Dic43⋊C4—24no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8C2412yes—
296C2×C43⋊C8C2412yes—
297Dic172—44no—
298Dic172—44no—
299#10621872—44no—
300C8×D43—44no—
301C23×C43—22no—
302C23×C43—22no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—42no—
306C23×C43—42no—
307C23×C43—42no—
308C23×C43C22×D412yes—
309C23×C43C22×D411yescharacteristic
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43C22×D412yes—
317C22×D43C22×D412yes—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—42no—
321D4×C43—84no—
322C2×C4×C43—22no—
323C2×C4×C43—24no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—42no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43C22×D412yes—
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43H(5,𝔽2)12yes—
335C2×C4×C43H(5,𝔽2)12yes—
336C2×C4×C43C2511yescharacteristic
337C22⋊D43—44no—
338C22⋊D43—44no—
339C22⋊D43—48no—
340C22⋊D43—84no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—48no—
348C2×Dic43—48no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355D172—44no—
356C4×D43—24no—
357C4×D43—24no—
358C4×D43—22no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—84no—
363Dic86—22no—
364Dic86—22no—
365Dic86—22no—
366Dic86—22no—
367Dic86—22no—
368Dic86—22no—
369Dic86—44no—
370Dic86—48no—
371Dic86—42no—
372Dic86—42no—
373Dic86—42no—
374C8×C43—22no—
375C8×C43—22no—
376C43⋊C8—22no—
377C43⋊C8—22no—
378C2×#3201—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—44no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—84no—
387C22×C43#53412yes—
388C22×C43#57712yes—
389C22×C43#57812yes—
390C22×C43C23×D411yescharacteristic
391C2×D43—22no—
392C2×D43—22no—
393C2×D43—22no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—22no—
397C2×D43—44no—
398C2×D43—44no—
399C4×C43—22no—
400C4×C43—42no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43#53412yes—
404C4×C43C2×H(5,𝔽2)11yescharacteristic
405C4×C43C2×H(5,𝔽2)11yescharacteristic
406Dic43—22no—
407Dic43—22no—
408Dic43—42no—
409Dic43—42no—
410Dic43—42no—
411Dic43—42no—
412C2×#537—431no—
413C2×#536—431no—
414#3201—4316no—
415C2×#484—431no—
416C2×#485—431no—
417C2×#482D4311yescharacteristic, complemented
418C2×#483—431no—
419C2×#470—431no—
420C2×#468—431no—
421C2×#467—431no—
422C2×#465—431no—
423C2×#452—431no—
424C2×#452—431no—
425C2×#451—431no—
426C2×#448—431no—
427C2×#408—431no—
428C2×C43—42no—
429C2×C43—82no—
430C2×C43#320114yescomplemented
431C2×C43C2×#53411yescharacteristic
432C2×C43C2×#57711yescharacteristic
433C2×C43C2×#57811yescharacteristic
434D43—42no—
435D43—42no—
436C22×#41—431no—
437C22×#41—431no—
438C23×Q8—431no—
439C22×Q16—431no—
440C22×Q16—431no—
441C22×SD16—431no—
442C22×SD16—431no—
443C22×M16—431no—
444C23×C8—431no—
445#537—438no—
446#537—864no—
447#536—438no—
448#536—864no—
449C2×C4⋊Q8—861no—
450C2×#124—861no—
451C2×#123—861no—
452C2×#123—861no—
453C2×C22⋊Q8—431no—
454C2×C22⋊Q8—431no—
455C2×C22⋊Q8—431no—
456C2×C22⋊Q8—431no—
457C2×C22⋊Q8—431no—
458C2×C22⋊Q8—431no—
459C2×C22⋊Q8—861no—
460C2×#121—431no—
461C2×#121—861no—
462C2×#121—861no—
463C2×#121—861no—
464C2×#121C2×D4311yescharacteristic
465C2×#117C2×D4311yescharacteristic
466C22×C4⋊C4—431no—
467#485—438no—
468#484—438no—
469#483—438no—
470#482C2×D4318yescomplemented
471#470—438no—
472#468—438no—
473#467—438no—
474#465—438no—
475#452—438no—
476#452—438no—
477#451—438no—
478#448—438no—
479C2×#107—431no—
480C2×#107C2×D4311yescharacteristic
481C2×#106—431no—
482C2×#106C2×D4311yescharacteristic
483C2×#103—431no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#103—431no—
487C2×#103—431no—
488C2×#103—431no—
489C2×#102C2×D4311yescharacteristic
490C2×#102C2×D4311yescharacteristic
491#408—438no—
492C2×C22⋊C8—431no—
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×C22⋊C8C2×D4311yescharacteristic
496C43C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—434no—
498C2×#41—434no—
499C2×#41—434no—
500C2×#41—862no—
501C2×#41—1722no—
502C2×#41—1722no—
503C2×#41—1722no—
504C2×#41—1722no—
505C22×Q8—431no—
506C22×Q8—431no—
507C22×Q8—431no—
508C22×Q8—431no—
509C22×Q8—434no—
510C22×Q8—861no—
511C22×Q8—862no—
512C22×Q8—1722no—
513C22×Q8—1722no—
514C22×D4—21no—
515C22×D4—431no—
516C22×D4—431no—
517C22×D4—431no—
518C22×D4—861no—
519C22×D4—861no—
520C22×D4C22×D4311yescharacteristic
521C23×C4—431no—
522C23×C4—431no—
523C23×C4—861no—
524C23×C4—861no—
525C23×C4—861no—
526C23×C4C22×D4311yescharacteristic
527C2×Q16—434no—
528C2×Q16—434no—
529C2×Q16—1722no—
530C2×Q16—1722no—
531C2×SD16—434no—
532C2×SD16—434no—
533C2×SD16—1722no—
534C2×SD16—1722no—
535C2×M16—434no—
536C2×M16—1722no—
537C22×C8—431no—
538C22×C8—431no—
539C22×C8—434no—
540C22×C8—1722no—
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
543C4⋊Q8—868no—
544#124—868no—
545#123—868no—
546#123—868no—
547C22⋊Q8—434no—
548C22⋊Q8—434no—
549C22⋊Q8—434no—
550C22⋊Q8—434no—
551C22⋊Q8—434no—
552C22⋊Q8—434no—
553C22⋊Q8—868no—
554C22⋊Q8—862no—
555C22⋊Q8—862no—
556C22⋊Q8—862no—
557C22⋊Q8—862no—
558C22⋊Q8—862no—
559C22⋊Q8—862no—
560#121—22no—
561#121—434no—
562#121—868no—
563#121—862no—
564#121—868no—
565#121—868no—
566#121C22×D4314yes—
567#117—22no—
568#117C22×D4314yes—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—434no—
571C2×C4⋊C4—862no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4—861no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—861no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C4⋊C4C22×D4311yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C42—21no—
592#107—434no—
593#107C22×D4314yes—
594#106—434no—
595#106C22×D4314yes—
596#103—434no—
597#103—434no—
598#103—434no—
599#103—434no—
600#103—434no—
601#103—434no—
602#102C22×D4314yes—
603#102C22×D4314yes—
604C22⋊C8—434no—
605C22⋊C8—434no—
606C22⋊C8—434no—
607C22⋊C8C22×D4314yes—
608C24—21no—
609C24—431no—
610C24—431no—
611C24D4×D4311yescharacteristic
612#41—1728no—
613#41—1724no—
614#41—1724no—
615#41—1724no—
616#41—1724no—
617#41—1728no—
618C2×Q8—434no—
619C2×Q8—432no—
620C2×Q8—432no—
621C2×Q8—432no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—864no—
626C2×Q8—862no—
627C2×Q8—862no—
628C2×Q8—862no—
629C2×Q8—862no—
630C2×Q8—862no—
631C2×Q8—862no—
632C2×Q8—1722no—
633C2×Q8—1724no—
634C2×Q8—1724no—
635C2×Q8—1724no—
636C2×Q8—1728no—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—82no—
642C2×D4—434no—
643C2×D4—434no—
644C2×D4—434no—
645C2×D4—864no—
646C2×D4—864no—
647C2×D4—3442no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1724no—
652C2×D4C23×D4312yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—432no—
661C22×C4—432no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—864no—
665C22×C4—864no—
666C22×C4—862no—
667C22×C4—862no—
668C22×C4—862no—
669C22×C4—862no—
670C22×C4—864no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—3442no—
676C22×C4—1724no—
677C22×C4—1724no—
678C22×C4D4×D4312yes—
679C22×C4D4×D4311yescharacteristic
680C22×C4C23×D4312yes—
681C22×C4C23×D4311yescharacteristic
682Q16—1724no—
683Q16—1724no—
684SD16—1724no—
685SD16—1724no—
686M16—1724no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—432no—
690C2×C8—432no—
691C2×C8—862no—
692C2×C8—862no—
693C2×C8—1724no—
694C2×C8C23×D4312yes—
695C2×C8C23×D4312yes—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—432no—
700C4⋊C4—864no—
701C4⋊C4—864no—
702C4⋊C4—864no—
703C4⋊C4—864no—
704C4⋊C4—864no—
705C4⋊C4—864no—
706C4⋊C4—861no—
707C4⋊C4—864no—
708C4⋊C4C23×D4312yes—
709C4⋊C4C23×D4312yes—
710C4⋊C4C23×D4312yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C42—24no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—432no—
729C23—432no—
730C23—862no—
731C23—862no—
732C23—862no—
733C23—862no—
734C23—862no—
735C23—862no—
736C23C2×D4×D4312yes—
737C23C2×D4×D4311yescharacteristic
738Q8—862no—
739Q8—862no—
740Q8—862no—
741Q8—862no—
742Q8—862no—
743Q8—862no—
744Q8—1724no—
745Q8—1728no—
746Q8—1722no—
747Q8—1722no—
748Q8—1722no—
749D4—22no—
750D4—22no—
751D4—42no—
752D4—84no—
753D4—3444no—
754D4—1724no—
755D4—1724no—
756D4—1724no—
757D4—1728no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—864no—
773C2×C4—864no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—3444no—
783C2×C4—1728no—
784C2×C4—1728no—
785C2×C4—1722no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4C2×D4×D4312yes—
790C2×C4C2×D4×D4311yescharacteristic
791C2×C4#1306337112yes—
792C2×C4#1306337112yes—
793C2×C4C24×D4311yescharacteristic
794C8—22no—
795C8—22no—
796C8—862no—
797C8—862no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—84no—
806C22—862no—
807C22—862no—
808C22—862no—
809C22—862no—
810C22—862no—
811C22—862no—
812C22—1724no—
813C22—1724no—
814C22#1458346012yes—
815C22#1458370912yes—
816C22#1458371312yes—
817C22C22×D4×D4311yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—862no—
823C4—862no—
824C4—1722no—
825C4—1722no—
826C4—1722no—
827C4—1722no—
828C4#1458346012yes—
829C4C2×#1306337111yescharacteristic
830C4C2×#1306337111yescharacteristic
831C2—42no—
832C2—82no—
833C2—1722no—
834C2—1722no—
835C2#1914547514yesdirect product factor
836C2C2×#1458346011yescharacteristic
837C2C2×#1458370911yescharacteristic
838C2C2×#1458371311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
prime radicalC2×#14583478C2
hypercenterC2×#482D43
hypocenterC43C2×#3201
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#14583475C2semidirect
3. #19145475C2direct (N × H)
4. C2×#14583236C2semidirect
5. C2×#14583240C2semidirect
6. C2×#14583231C2semidirect
7. C2×#14583158C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583141C2semidirect
10. C2×#14583127C2semidirect
11. C2×#14583062C2semidirect
12. C2×#14583062C2semidirect
13. C2×#14583057C2semidirect
14. C2×#14583037C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#482C2semidirect
29. #14583475C22semidirect
46. #14583240C22semidirect
47. #14583236C22semidirect
48. #14583231C22semidirect
49. #14583158C22semidirect
50. #14583144C22semidirect
51. #14583141C22semidirect
52. #14583127C22semidirect
53. #14583062C22semidirect
54. #14583062C22semidirect
55. #14583057C22semidirect
56. #14583037C22semidirect
65. #14582864C22semidirect
71. C43×#482C22semidirect
417. C2×#482D43semidirect
430. C2×C43#3201semidirect
470. #482C2×D43semidirect
496. C43C2×#3201semidirect
835. C2#19145475direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834782
C2×#145834752
#191454752
C2×#145832362
C2×#145832402
C2×#145832312
C2×#145831582
C2×#145831442
C2×#145831412
C2×#145831272
C2×#145830622
C2×#145830572
C2×#145830372
C2×#145828642
C2×C43×#4822
C2×#320143