Finite Group Databasebeta

← C2×#19145494 #25967302

Subgroups — C2×#19145494 #25967302

Order 11008.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583478C211yesmaximal, characteristic, complemented
2C2×#14583477C211yesmaximal, characteristic, complemented
3#19145494C2116yesmaximal, direct product factor
4C2×#14583235C211yesmaximal, characteristic, complemented
5C2×#14583233C211yesmaximal, characteristic, complemented
6C2×#14583211C211yesmaximal, characteristic, complemented
7C2×#14583210C211yesmaximal, characteristic, complemented
8C2×#14583144C211yesmaximal, characteristic, complemented
9C2×#14583142C211yesmaximal, characteristic, complemented
10C2×#14583139C211yesmaximal, characteristic, complemented
11C2×#14583132C211yesmaximal, characteristic, complemented
12C2×#14583061C211yesmaximal, characteristic, complemented
13C2×#14583058C211yesmaximal, characteristic, complemented
14C2×#14583041C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#449C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621883C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583478—24no—
24#14583478C2218yescomplemented
25#14583477—24no—
26#14583477C2218yescomplemented
27C2×#13063305C2211yescharacteristic
28C2×#13063304—21no—
29C2×#13063304C2211yescharacteristic
30C2×#13063302—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063301C2211yescharacteristic
33C2×#13063299—21no—
34C2×#13063298—21no—
35C2×#13063297—21no—
36C2×#13063297—21no—
37C2×#13063297—21no—
38C2×#13063296—21no—
39C2×#13063296C2211yescharacteristic
40C2×#13063296C2211yescharacteristic
41C2×#13063296C2211yescharacteristic
42C22×C4⋊Dic43C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic
44#14583235C2218yescomplemented
45#14583233C2218yescomplemented
46#14583211C2218yescomplemented
47#14583210C2218yescomplemented
48#14583144C2218yescomplemented
49#14583142C2218yescomplemented
50#14583139C2218yescomplemented
51#14583132C2218yescomplemented
52#14583061C2218yescomplemented
53#14583058C2218yescomplemented
54#14583041C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063259C2211yescharacteristic
57C2×#13063258C2211yescharacteristic
58C2×#13063258C2211yescharacteristic
59C2×#13063250C2211yescharacteristic
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063246C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063246C2211yescharacteristic
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×SD16×C43C2211yescharacteristic
71C22×D8×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic
73C43×#449C2218yescomplemented
74C2×#103×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×Dic86D411yescharacteristic
86C22×Dic86C2311yescharacteristic
87C22×D172D411yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43D411yescharacteristic
93C22×C22⋊D43D411yescharacteristic
94C23×Dic43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C22×C4×D43C2311yescharacteristic
99C2×#10621885—42no—
100C2×#10621885C2314yes—
101C2×#10621883—42no—
102C2×#10621883C2314yes—
103C2×#10621872—42no—
104C2×#10621872C2314yes—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C2×C8×D43—42no—
108C2×C8×D43C2314yes—
109#13063305—22no—
110#13063305C2314yes—
111#13063304—22no—
112#13063304—28no—
113#13063304C2314yes—
114#13063302—28no—
115#13063301—22no—
116#13063301—22no—
117#13063301C2314yes—
118#13063301C2314yes—
119#13063299—28no—
120#13063298—28no—
121#13063297—28no—
122#13063297—28no—
123#13063297—28no—
124#13063296—28no—
125#13063296—22no—
126#13063296—22no—
127#13063296—22no—
128#13063296C2314yes—
129#13063296C2314yes—
130#13063296C2314yes—
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—22no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2314yes—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C2×Dic43⋊C4—21no—
142C4⋊C4×D43—22no—
143C4⋊C4×D43C2314yes—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43—21no—
146C2×C22⋊Dic43—21no—
147C2×C22⋊Dic43—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151#13063259C2314yes—
152#13063259C2314yes—
153#13063258C2314yes—
154#13063258C2314yes—
155#13063250C2314yes—
156#13063250C2314yes—
157#13063249C2314yes—
158#13063246C2314yes—
159#13063246C2314yes—
160#13063246C2314yes—
161C22⋊(C43⋊C8)C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164C2×#41×C43—22no—
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C22×D4×C43—21no—
170C22×D4×C43—21no—
171C22×D4×C43C2311yescharacteristic
172C22×D4×C43C2311yescharacteristic
173C23×C4×C43—21no—
174C23×C4×C43C2311yescharacteristic
175C2×SD16×C43—42no—
176C2×SD16×C43C2314yes—
177C2×D8×C43—42no—
178C2×D8×C43C2314yes—
179C22×C8×C43C2311yescharacteristic
180C22×C8×C43C2311yescharacteristic
181#121×C43—22no—
182#121×C43C2314yes—
183C2×C4⋊C4×C43C2311yescharacteristic
184C2×C22⋊C4×C43—21no—
185#103×C43C2314yes—
186#102×C43C2314yes—
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43C2×D411yescharacteristic
191C23×D43C2×D411yescharacteristic
192C23×D43C2×D411yescharacteristic
193#41×C43—44no—
194#41×C43—44no—
195#41×C43—48no—
196C2×Q8×C43—21no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43C2412yes—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—24no—
203C2×D4×C43—24no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—22no—
208C2×D4×C43—44no—
209C2×D4×C43—82no—
210C2×D4×C43C2412yes—
211C2×D4×C43C2412yes—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—24no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—44no—
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D412yes—
220C22×C4×C43C2412yes—
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—24no—
226C2×C22⋊D43—42no—
227C2×C22⋊D43—42no—
228C2×C22⋊D43—44no—
229C2×C22⋊D43—82no—
230C2×C22⋊D43—82no—
231C2×C22⋊D43—82no—
232C2×C22⋊D43C2×D414yes—
233C2×C22⋊D43C2×D414yes—
234C22×Dic43—24no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—24no—
240C22×Dic43—44no—
241C22×Dic43—82no—
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244#10621900—44no—
245#10621900—44no—
246#10621900—48no—
247#10621898—48no—
248#10621898—44no—
249#10621898—44no—
250C2×D172—42no—
251C2×D172C2×D414yes—
252C2×C4×D43—22no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—24no—
257C2×C4×D43—82no—
258C2×C4×D43C2×D412yes—
259C2×C4×D43C2×D412yes—
260C2×C4×D43C2412yes—
261C2×C4×D43C2412yes—
262C2×Dic86—22no—
263C2×Dic86—22no—
264C2×Dic86—21no—
265C2×Dic86—42no—
266C2×Dic86C2×D414yes—
267C2×Dic86C2412yes—
268SD16×C43—44no—
269D8×C43—44no—
270C2×C8×C43—22no—
271C2×C8×C43—22no—
272C2×C8×C43C2412yes—
273C2×C8×C43C2412yes—
274C4⋊C4×C43—21no—
275C4⋊C4×C43C2412yes—
276C22⋊C4×C43—24no—
277C22⋊Dic43—24no—
278C22⋊Dic43—24no—
279C22⋊Dic43—24no—
280C22⋊Dic43—24no—
281#10621885—44no—
282#10621883—44no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—24no—
290C4⋊Dic43—24no—
291C4⋊Dic43C2412yes—
292C4⋊Dic43C2412yes—
293C4⋊Dic43C2412yes—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296Dic43⋊C4—24no—
297Dic43⋊C4—24no—
298C2×C43⋊C8—22no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8C2412yes—
301C2×C43⋊C8C2412yes—
302#10621872—44no—
303C8×D43—44no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43C22×D412yes—
316C23×C43C22×D411yescharacteristic
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43C22×D412yes—
324C22×D43C22×D412yes—
325Q8×C43—22no—
326Q8×C43—22no—
327Q8×C43—42no—
328D4×C43—22no—
329D4×C43—22no—
330D4×C43—22no—
331D4×C43—22no—
332D4×C43—48no—
333D4×C43—42no—
334D4×C43—42no—
335D4×C43—84no—
336C2×C4×C43—22no—
337C2×C4×C43—24no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—48no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43C22×D412yes—
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43H(5,𝔽2)12yes—
348C2×C4×C43H(5,𝔽2)12yes—
349C2×C4×C43C2511yescharacteristic
350C22⋊D43—44no—
351C22⋊D43—44no—
352C22⋊D43—48no—
353C22⋊D43—84no—
354C22⋊D43—84no—
355C22⋊D43—84no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—48no—
363C2×Dic43—42no—
364C2×Dic43—42no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367C2×Dic43—84no—
368C2×Dic43C22×D412yes—
369C2×Dic43C22×D412yes—
370D172—44no—
371C4×D43—24no—
372C4×D43—24no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—84no—
378Dic86—22no—
379Dic86—22no—
380Dic86—44no—
381Dic86—42no—
382C8×C43—22no—
383C8×C43—22no—
384C43⋊C8—22no—
385C43⋊C8—22no—
386C2×#3203—431nomaximal, Sylow
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—44no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—84no—
398C22×C43—84no—
399C22×C43#53412yes—
400C22×C43#57612yes—
401C22×C43#57812yes—
402C22×C43C23×D411yescharacteristic
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—44no—
410C2×D43—44no—
411C4×C43—22no—
412C4×C43—42no—
413C4×C43—42no—
414C4×C43#53412yes—
415C4×C43C2×H(5,𝔽2)11yescharacteristic
416C4×C43C2×H(5,𝔽2)11yescharacteristic
417Dic43—22no—
418Dic43—22no—
419Dic43—42no—
420Dic43—42no—
421Dic43—42no—
422Dic43—42no—
423C2×#537—431no—
424C2×#537—431no—
425#3203—4316no—
426C2×#484—431no—
427C2×#484—431no—
428C2×#480—431no—
429C2×#480—431no—
430C2×#468—431no—
431C2×#468—431no—
432C2×#467—431no—
433C2×#466—431no—
434C2×#452—431no—
435C2×#452—431no—
436C2×#449—431no—
437C2×#449D4311yescharacteristic, complemented
438C2×#408—431no—
439C2×C43—42no—
440C2×C43—82no—
441C2×C43—82no—
442C2×C43#320314yescomplemented
443C2×C43C2×#53411yescharacteristic
444C2×C43C2×#57611yescharacteristic
445C2×C43C2×#57811yescharacteristic
446D43—42no—
447D43—42no—
448C22×#41—431no—
449C22×#41—431no—
450C22×#41C2×D4311yescharacteristic
451C22×Q16—431no—
452C22×SD16—431no—
453C22×SD16C2×D4311yescharacteristic
454C22×D8C2×D4311yescharacteristic
455C22×M16—431no—
456C23×C8—431no—
457#537—438no—
458#537—438no—
459#537—864no—
460#537—864no—
461C2×C22⋊Q8—431no—
462C2×C22⋊Q8—431no—
463C2×C22⋊Q8—431no—
464C2×C22⋊Q8—431no—
465C2×C22⋊Q8—861no—
466C2×C22⋊Q8—861no—
467C2×#121—431no—
468C2×#121—431no—
469C2×#121—431no—
470C2×#121—861no—
471C2×#121—861no—
472C2×#121—861no—
473C2×#121—861no—
474C2×#121—861no—
475C2×#121—861no—
476C2×#121C2×D4311yescharacteristic
477C22×C4⋊C4—431no—
478C22×C4⋊C4—431no—
479#484—438no—
480#484—438no—
481#480—438no—
482#480—438no—
483#468—438no—
484#468—438no—
485#467—438no—
486#466—438no—
487#452—438no—
488#452—438no—
489#449—438no—
490#449C2×D4318yescomplemented
491C2×#107—431no—
492C2×#107—431no—
493C2×#107—431no—
494C2×#107—431no—
495C2×#103—431no—
496C2×#103—431no—
497C2×#103—431no—
498C2×#103C2×D4311yescharacteristic
499C2×#102—431no—
500C2×#102—431no—
501C2×#102—431no—
502C2×#102C2×D4311yescharacteristic
503#408—438no—
504C2×C22⋊C8—431no—
505C2×C22⋊C8—431no—
506C2×C22⋊C8—431no—
507C2×C22⋊C8C2×D4311yescharacteristic
508C43C2×#320311yescharacteristic, complemented, Sylow
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41—434no—
513C2×#41—434no—
514C2×#41—434no—
515C2×#41—862no—
516C2×#41—1722no—
517C2×#41—1722no—
518C2×#41—1722no—
519C2×#41—1722no—
520C2×#41C22×D4314yes—
521C22×Q8—431no—
522C22×Q8—431no—
523C22×Q8C22×D4311yescharacteristic
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—431no—
527C22×D4—431no—
528C22×D4—431no—
529C22×D4—861no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4C22×D4311yescharacteristic
534C22×D4C22×D4311yescharacteristic
535C23×C4—21no—
536C23×C4—431no—
537C23×C4—431no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4C22×D4311yescharacteristic
542C2×Q16—434no—
543C2×Q16—1722no—
544C2×SD16—42no—
545C2×SD16—434no—
546C2×SD16—1722no—
547C2×SD16C22×D4314yes—
548C2×D8—42no—
549C2×D8C22×D4314yes—
550C2×M16—434no—
551C2×M16—1722no—
552C22×C8—431no—
553C22×C8—431no—
554C22×C8—434no—
555C22×C8—1722no—
556C22×C8C22×D4311yescharacteristic
557C22×C8C22×D4311yescharacteristic
558C22⋊Q8—434no—
559C22⋊Q8—434no—
560C22⋊Q8—434no—
561C22⋊Q8—434no—
562C22⋊Q8—868no—
563C22⋊Q8—862no—
564C22⋊Q8—868no—
565C22⋊Q8—862no—
566C22⋊Q8—862no—
567C22⋊Q8—862no—
568#121—22no—
569#121—434no—
570#121—434no—
571#121—434no—
572#121—868no—
573#121—868no—
574#121—862no—
575#121—862no—
576#121—862no—
577#121—868no—
578#121—868no—
579#121—868no—
580#121—868no—
581#121C22×D4314yes—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—431no—
584C2×C4⋊C4—431no—
585C2×C4⋊C4—434no—
586C2×C4⋊C4—434no—
587C2×C4⋊C4—862no—
588C2×C4⋊C4—861no—
589C2×C4⋊C4—861no—
590C2×C4⋊C4—861no—
591C2×C4⋊C4—861no—
592C2×C4⋊C4—861no—
593C2×C4⋊C4—862no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4C22×D4311yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—861no—
598C2×C22⋊C4—861no—
599C2×C22⋊C4—861no—
600C2×C22⋊C4—861no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604#107—434no—
605#107—434no—
606#107—434no—
607#107—434no—
608#103—434no—
609#103—434no—
610#103—434no—
611#103C22×D4314yes—
612#102—434no—
613#102—434no—
614#102—434no—
615#102C22×D4314yes—
616C22⋊C8—434no—
617C22⋊C8—434no—
618C22⋊C8—434no—
619C22⋊C8C22×D4314yes—
620C24—21no—
621C24—21no—
622C24—431no—
623C24—431no—
624C24D4×D4311yescharacteristic
625#41—44no—
626#41—44no—
627#41—48no—
628#41—1728no—
629#41—1724no—
630#41—1724no—
631#41—1724no—
632#41—1724no—
633#41—1728no—
634C2×Q8—21no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—434no—
638C2×Q8—432no—
639C2×Q8—861no—
640C2×Q8—862no—
641C2×Q8—862no—
642C2×Q8—1722no—
643C2×Q8C23×D4312yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—44no—
653C2×D4—82no—
654C2×D4—434no—
655C2×D4—434no—
656C2×D4—434no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—864no—
661C2×D4—3442no—
662C2×D4—3442no—
663C2×D4—3442no—
664C2×D4—1722no—
665C2×D4—1722no—
666C2×D4—1722no—
667C2×D4—1724no—
668C2×D4C23×D4312yes—
669C2×D4C23×D4312yes—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—24no—
675C22×C4—44no—
676C22×C4—431no—
677C22×C4—431no—
678C22×C4—432no—
679C22×C4—432no—
680C22×C4—432no—
681C22×C4—432no—
682C22×C4—864no—
683C22×C4—864no—
684C22×C4—862no—
685C22×C4—862no—
686C22×C4—862no—
687C22×C4—862no—
688C22×C4—864no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—861no—
692C22×C4—861no—
693C22×C4—3442no—
694C22×C4—3442no—
695C22×C4—1724no—
696C22×C4D4×D4312yes—
697C22×C4D4×D4311yescharacteristic
698C22×C4C23×D4312yes—
699C22×C4C23×D4311yescharacteristic
700Q16—1724no—
701SD16—44no—
702SD16—1724no—
703D8—44no—
704M16—1724no—
705C2×C8—22no—
706C2×C8—22no—
707C2×C8—432no—
708C2×C8—432no—
709C2×C8—862no—
710C2×C8—862no—
711C2×C8—1724no—
712C2×C8C23×D4312yes—
713C2×C8C23×D4312yes—
714C4⋊C4—21no—
715C4⋊C4—432no—
716C4⋊C4—432no—
717C4⋊C4—432no—
718C4⋊C4—864no—
719C4⋊C4—864no—
720C4⋊C4—864no—
721C4⋊C4—864no—
722C4⋊C4—864no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—864no—
727C4⋊C4C23×D4312yes—
728C22⋊C4—24no—
729C22⋊C4—864no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—432no—
748C23—432no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—862no—
754C23—862no—
755C23C2×D4×D4312yes—
756C23C2×D4×D4311yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—42no—
760Q8—862no—
761Q8—862no—
762Q8—1724no—
763Q8—1722no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—42no—
770D4—42no—
771D4—84no—
772D4—3444no—
773D4—3444no—
774D4—3444no—
775D4—1724no—
776D4—1724no—
777D4—1724no—
778D4—1728no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—48no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—432no—
789C2×C4—432no—
790C2×C4—862no—
791C2×C4—862no—
792C2×C4—864no—
793C2×C4—864no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—3444no—
803C2×C4—3444no—
804C2×C4—1728no—
805C2×C4—1722no—
806C2×C4—1722no—
807C2×C4—1722no—
808C2×C4—1722no—
809C2×C4C2×D4×D4312yes—
810C2×C4C2×D4×D4311yescharacteristic
811C2×C4#1306337012yes—
812C2×C4#1306337012yes—
813C2×C4C24×D4311yescharacteristic
814C8—22no—
815C8—22no—
816C8—862no—
817C8—862no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—84no—
829C22—84no—
830C22—862no—
831C22—862no—
832C22—862no—
833C22—862no—
834C22—862no—
835C22—862no—
836C22—1724no—
837C22—1724no—
838C22#1458345912yes—
839C22#1458370312yes—
840C22#1458371312yes—
841C22C22×D4×D4311yescharacteristic
842C4—22no—
843C4—42no—
844C4—42no—
845C4—862no—
846C4—862no—
847C4—1722no—
848C4—1722no—
849C4—1722no—
850C4—1722no—
851C4#1458345912yes—
852C4C2×#1306337011yescharacteristic
853C4C2×#1306337011yescharacteristic
854C2—42no—
855C2—82no—
856C2—82no—
857C2—1722no—
858C2—1722no—
859C2#1914549414yesdirect product factor
860C2C2×#1458345911yescharacteristic
861C2C2×#1458370311yescharacteristic
862C2C2×#1458371311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#449C2
socleC23×C43C22×D4
hypercenterC2×#449D43
hypocenterC43C2×#3203
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#14583478C2semidirect
2. C2×#14583477C2semidirect
3. #19145494C2direct (N × H)
4. C2×#14583235C2semidirect
5. C2×#14583233C2semidirect
6. C2×#14583211C2semidirect
7. C2×#14583210C2semidirect
8. C2×#14583144C2semidirect
9. C2×#14583142C2semidirect
10. C2×#14583139C2semidirect
11. C2×#14583132C2semidirect
12. C2×#14583061C2semidirect
13. C2×#14583058C2semidirect
14. C2×#14583041C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#449C2semidirect
24. #14583478C22semidirect
26. #14583477C22semidirect
44. #14583235C22semidirect
45. #14583233C22semidirect
46. #14583211C22semidirect
47. #14583210C22semidirect
48. #14583144C22semidirect
49. #14583142C22semidirect
50. #14583139C22semidirect
51. #14583132C22semidirect
52. #14583061C22semidirect
53. #14583058C22semidirect
54. #14583041C22semidirect
65. #14582864C22semidirect
73. C43×#449C22semidirect
437. C2×#449D43semidirect
442. C2×C43#3203semidirect
490. #449C2×D43semidirect
508. C43C2×#3203semidirect
859. C2#19145494direct (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×#145834772
#191454942
C2×#145832352
C2×#145832332
C2×#145832112
C2×#145832102
C2×#145831442
C2×#145831422
C2×#145831392
C2×#145831322
C2×#145830612
C2×#145830582
C2×#145830412
C2×#145828642
C2×C43×#4492
C2×#320343