Finite Group Databasebeta

← C2×#19145440 #25967243

Subgroups — C2×#19145440 #25967243

Order 11008.

2378 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583478C211yesmaximal, characteristic, complemented
2C2×#14583465C211yesmaximal, characteristic, complemented
3#19145440C2116yesmaximal, direct product factor
4C2×#14583216C211yesmaximal, characteristic, complemented
5C2×#14583242C211yesmaximal, characteristic, complemented
6C2×#14583222C211yesmaximal, characteristic, complemented
7C2×#14583214C211yesmaximal, characteristic, complemented
8C2×#14583150C211yesmaximal, characteristic, complemented
9C2×#14583143C211yesmaximal, characteristic, complemented
10C2×#14583128C211yesmaximal, characteristic, complemented
11C2×#14583045C211yesmaximal, characteristic, complemented
12C2×#14583041C211yesmaximal, characteristic, complemented
13C2×#14583051C211yesmaximal, characteristic, complemented
14C2×#14583031C211yesmaximal, characteristic, complemented
15C2×#14582865C211yesmaximal, characteristic, complemented
16C2×C43×#466C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic, complemented
19C22×D4×D43C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621877C2211yescharacteristic, complemented
24#14583478—24no—
25#14583478C2218yescomplemented
26#14583465—24no—
27#14583465C2218yescomplemented
28C2×#13063321—21no—
29C2×#13063311—21no—
30C2×#13063305C2211yescharacteristic
31C2×#13063304C2211yescharacteristic, complemented
32C2×#13063302—21no—
33C2×#13063300C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35C2×#13063298—21no—
36C2×#13063297—21no—
37C2×#13063296—21no—
38C2×#13063296C2211yescharacteristic
39C2×#13063296C2211yescharacteristic
40C2×#13063295—21no—
41C2×#13063293—21no—
42C2×#13063283C2211yescharacteristic
43C2×C4⋊C4×D43C2211yescharacteristic, complemented
44#14583242C2218yescomplemented
45#14583222C2218yescomplemented
46#14583216C2218yescomplemented
47#14583214C2218yescomplemented
48#14583150C2218yescomplemented
49#14583143C2218yescomplemented
50#14583128C2218yescomplemented
51#14583051C2218yescomplemented
52#14583045C2218yescomplemented
53#14583041C2218yescomplemented
54#14583031C2218yescomplemented
55C2×#13063258C2211yescharacteristic, complemented
56C2×#13063257C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×#13063250C2211yescharacteristic, complemented
59C2×#13063248C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063246C2211yescharacteristic
62C2×#13063246C2211yescharacteristic, complemented
63C2×#13063245C2211yescharacteristic
64#14582865C2218yescomplemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C22×D8×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic, complemented
71C2×#121×C43C2211yescharacteristic
72C2×#121×C43C2211yescharacteristic, complemented
73C43×#466C2218yescomplemented
74C2×#107×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—42no—
79C2×#10621898—42no—
80C2×#10621898D414yes—
81C2×#10621898C2314yes—
82C2×#10621900—22no—
83C2×#10621900—42no—
84C2×#10621900—42no—
85C2×#10621900C2314yescomplemented
86C22×Dic86D411yescharacteristic
87C22×Dic86C2311yescharacteristic
88C22×D172—21no—
89C22×D172D411yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C22×C22⋊D43D411yescharacteristic
97C22×C22⋊D43D411yescharacteristic
98C2×D4×D43—22no—
99C2×D4×D43—42no—
100C2×D4×D43—42no—
101C2×D4×D43C2314yes—
102C23×Dic43—21no—
103C22×C4×D43—21no—
104C22×C4×D43C2311yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×#10621873—42no—
107C2×#10621873C2314yes—
108C2×#10621883—42no—
109C2×#10621883C2314yes—
110C2×#10621882—42no—
111C2×#10621882C2314yes—
112C2×#10621877—42no—
113C2×#10621877C2314yescomplemented
114C22×C43⋊C8C2311yescharacteristic
115C22×C43⋊C8C2311yescharacteristic
116#13063321—28no—
117#13063311—28no—
118#13063305—22no—
119#13063305C2314yes—
120#13063304—22no—
121#13063304C2314yescomplemented
122#13063302—28no—
123#13063300—22no—
124#13063300C2314yes—
125#13063299—22no—
126#13063299C2314yes—
127#13063298—28no—
128#13063297—28no—
129#13063296—28no—
130#13063296—22no—
131#13063296—22no—
132#13063296C2314yes—
133#13063296C2314yes—
134#13063295—28no—
135#13063293—28no—
136#13063283—22no—
137#13063283C2314yes—
138C2×C4⋊Dic43—21no—
139C2×C4⋊Dic43C2311yescharacteristic
140C2×C4⋊Dic43C2311yescharacteristic
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C4⋊C4×D43—22no—
144C4⋊C4×D43C2314yescomplemented
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—
151C2×(C2×D43)⋊C4—21no—
152C2×C4×Dic43—21no—
153#13063258C2314yescomplemented
154#13063257C2314yescomplemented
155#13063256C2314yescomplemented
156#13063250C2314yescomplemented
157#13063248C2314yescomplemented
158#13063247C2314yes—
159#13063246C2314yes—
160#13063246C2314yescomplemented
161#13063245C2314yes—
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yescomplemented
165(C2×D43)⋊C8C2314yescomplemented
166C22×D4×C43—21no—
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C22×D4×C43C2311yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C2×D8×C43—42no—
172C2×D8×C43C2314yes—
173C22×C8×C43—42no—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C22×C8×C43C2314yescomplemented
177#121×C43—22no—
178#121×C43—22no—
179#121×C43C2314yes—
180#121×C43C2314yescomplemented
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C4⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43—21no—
184C2×C22⋊C4×C43—21no—
185#107×C43C2314yescomplemented
186#102×C43C2314yes—
187#102×C43C2314yescomplemented
188C24×C43—21no—
189C24×C43—21no—
190C24×C43C2×D411yescharacteristic
191C23×D43—21no—
192C23×D43—24no—
193C23×D43—44no—
194C23×D43—82no—
195C23×D43—82no—
196C23×D43C2×D411yescharacteristic
197C23×D43C2×D411yescharacteristic
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—24no—
201C2×D4×C43—24no—
202C2×D4×C43—22no—
203C2×D4×C43—22no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—82no—
207C2×D4×C43—82no—
208C2×D4×C43C2412yes—
209C2×D4×C43C2412yes—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—42no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—44no—
226C2×C22⋊D43—44no—
227C2×C22⋊D43—82no—
228C2×C22⋊D43—82no—
229C2×C22⋊D43—82no—
230C2×C22⋊D43C2×D414yes—
231C2×C22⋊D43C2×D414yes—
232C22×Dic43—24no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—44no—
237C22×Dic43C2×D411yescharacteristic
238C22×Dic43C2×D411yescharacteristic
239#10621900—44no—
240#10621900—44no—
241#10621900—48no—
242D4×D43—44no—
243D4×D43—44no—
244D4×D43—48no—
245#10621898—48no—
246#10621898—44no—
247#10621898—44no—
248C2×D172—21no—
249C2×D172—24no—
250C2×D172—22no—
251C2×D172—22no—
252C2×D172—42no—
253C2×D172—82no—
254C2×D172C2×D414yes—
255C2×D172C2412yes—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—24no—
261C2×C4×D43—82no—
262C2×C4×D43C2×D412yes—
263C2×C4×D43C2×D412yes—
264C2×C4×D43C2412yes—
265C2×C4×D43C2412yes—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—21no—
269C2×Dic86—42no—
270C2×Dic86C2×D414yes—
271C2×Dic86C2412yes—
272D8×C43—44no—
273C2×C8×C43—22no—
274C2×C8×C43—22no—
275C2×C8×C43—44no—
276C2×C8×C43C2412yes—
277C2×C8×C43C2412yes—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C2412yes—
281C4⋊C4×C43C2412yes—
282C22⋊C4×C43—24no—
283C22⋊C4×C43—24no—
284C22⋊Dic43—24no—
285C22⋊Dic43—24no—
286C22⋊Dic43—24no—
287#10621883—44no—
288#10621882—44no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293C4⋊Dic43—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43—24no—
296C4⋊Dic43C2412yes—
297C4⋊Dic43C2412yes—
298Dic43⋊C4—24no—
299Dic43⋊C4—24no—
300C4×Dic43—24no—
301#10621877—44no—
302C2×C43⋊C8—22no—
303C2×C43⋊C8—22no—
304C2×C43⋊C8C2412yes—
305C2×C43⋊C8C2412yes—
306#10621873—44no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43—42no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43C22×D412yes—
319C23×C43C22×D411yescharacteristic
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—48no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—84no—
332C22×D43—84no—
333C22×D43—816no—
334C22×D43C22×D412yes—
335C22×D43C22×D412yes—
336D4×C43—22no—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—22no—
340D4×C43—42no—
341D4×C43—42no—
342D4×C43—84no—
343D4×C43—84no—
344C2×C4×C43—22no—
345C2×C4×C43—24no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43H(5,𝔽2)12yes—
355C2×C4×C43H(5,𝔽2)12yes—
356C2×C4×C43C2511yescharacteristic
357C22⋊D43—44no—
358C22⋊D43—44no—
359C22⋊D43—48no—
360C22⋊D43—48no—
361C22⋊D43—84no—
362C22⋊D43—84no—
363C22⋊D43—84no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—48no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375D172—22no—
376D172—22no—
377D172—44no—
378D172—42no—
379D172—84no—
380C4×D43—24no—
381C4×D43—24no—
382C4×D43—22no—
383C4×D43—22no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—84no—
387Dic86—22no—
388Dic86—22no—
389Dic86—44no—
390Dic86—42no—
391C8×C43—22no—
392C8×C43—22no—
393C43⋊C8—22no—
394C43⋊C8—22no—
395C2×#3198—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—44no—
400C22×C43—42no—
401C22×C43—42no—
402C22×C43—42no—
403C22×C43—42no—
404C22×C43—42no—
405C22×C43—42no—
406C22×C43—84no—
407C22×C43—84no—
408C22×C43#53412yes—
409C22×C43#57612yes—
410C22×C43#57712yes—
411C22×C43C23×D411yescharacteristic
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—44no—
419C2×D43—44no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—42no—
423C2×D43—816no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43#53412yes—
429C4×C43C2×H(5,𝔽2)11yescharacteristic
430C4×C43C2×H(5,𝔽2)11yescharacteristic
431Dic43—22no—
432Dic43—22no—
433Dic43—42no—
434Dic43—42no—
435Dic43—42no—
436C2×#537—431no—
437C2×#535—431no—
438#3198—4316no—
439C2×#481—431no—
440C2×#485—431no—
441C2×#482—431no—
442C2×#480—431no—
443C2×#469—431no—
444C2×#468—431no—
445C2×#466D4311yescharacteristic, complemented
446C2×#465—431no—
447C2×#449—431no—
448C2×#449—431no—
449C2×#450—431no—
450C2×#447—431no—
451C2×#408—431no—
452C2×C43—42no—
453C2×C43—82no—
454C2×C43—82no—
455C2×C43#319814yescomplemented
456C2×C43C2×#53411yescharacteristic
457C2×C43C2×#57611yescharacteristic
458C2×C43C2×#57711yescharacteristic
459D43—42no—
460D43—42no—
461D43—82no—
462C22×#41—431no—
463C22×#41—431no—
464C23×D4—431no—
465C22×SD16—431no—
466C22×SD16—431no—
467C22×D8—431no—
468C22×D8C2×D4311yescharacteristic
469C22×M16—431no—
470C23×C8C2×D4311yescharacteristic, complemented
471#537—438no—
472#537—864no—
473#535—438no—
474#535—864no—
475C2×#127—861no—
476C2×#124—861no—
477C2×C22⋊Q8—431no—
478C2×C22⋊Q8—431no—
479C2×C22⋊Q8—861no—
480C2×#121—431no—
481C2×#121—431no—
482C2×#121—431no—
483C2×#121—431no—
484C2×#121—861no—
485C2×#121—861no—
486C2×#121—861no—
487C2×#121C2×D4311yescharacteristic
488C2×#121C2×D4311yescharacteristic, complemented
489C2×#120—861no—
490C2×#120—861no—
491C2×#117—431no—
492C22×C4⋊C4—431no—
493#485—438no—
494#482—438no—
495#481—438no—
496#480—438no—
497#469—438no—
498#468—438no—
499#466C2×D4318yescomplemented
500#465—438no—
501#450—438no—
502#449—438no—
503#449—438no—
504#447—438no—
505C2×#107—431no—
506C2×#107C2×D4311yescharacteristic, complemented
507C2×#106—431no—
508C2×#106—431no—
509C2×#103—431no—
510C2×#103—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102C2×D4311yescharacteristic
516C2×#102C2×D4311yescharacteristic, complemented
517#408—438no—
518C2×C22⋊C8—431no—
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×C22⋊C8—431no—
522C43C2×#319811yescharacteristic, complemented, Sylow
523C25—861no—
524C2×#41—434no—
525C2×#41—434no—
526C2×#41—434no—
527C2×#41—862no—
528C2×#41—1722no—
529C2×#41—1722no—
530C2×#41—1722no—
531C2×#41—1722no—
532C22×Q8—431no—
533C22×Q8—431no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—431no—
537C22×D4—431no—
538C22×D4—434no—
539C22×D4—431no—
540C22×D4—431no—
541C22×D4—861no—
542C22×D4—862no—
543C22×D4—861no—
544C22×D4—861no—
545C22×D4—861no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—1722no—
549C22×D4—1722no—
550C22×D4C22×D4311yescharacteristic
551C22×D4C22×D4311yescharacteristic
552C23×C4—431no—
553C23×C4—431no—
554C23×C4—861no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×SD16—434no—
558C2×SD16—434no—
559C2×SD16—1722no—
560C2×SD16—1722no—
561C2×D8—42no—
562C2×D8—434no—
563C2×D8—1722no—
564C2×D8C22×D4314yes—
565C2×M16—434no—
566C2×M16—1722no—
567C22×C8—42no—
568C22×C8—431no—
569C22×C8—431no—
570C22×C8C22×D4311yescharacteristic
571C22×C8C22×D4311yescharacteristic
572C22×C8C22×D4314yescomplemented
573#127—868no—
574#124—868no—
575C22⋊Q8—434no—
576C22⋊Q8—434no—
577C22⋊Q8—868no—
578C22⋊Q8—862no—
579C22⋊Q8—862no—
580#121—22no—
581#121—22no—
582#121—434no—
583#121—434no—
584#121—434no—
585#121—434no—
586#121—868no—
587#121—862no—
588#121—862no—
589#121—862no—
590#121—868no—
591#121—868no—
592#121—862no—
593#121C22×D4314yes—
594#121C22×D4314yescomplemented
595#120—868no—
596#120—868no—
597#117—434no—
598#117—862no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—434no—
602C2×C4⋊C4—862no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4C22×D4311yescharacteristic
607C2×C4⋊C4C22×D4311yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C42—861no—
618#107—434no—
619#107C22×D4314yescomplemented
620#106—434no—
621#106—434no—
622#103—434no—
623#103—434no—
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102C22×D4314yes—
629#102C22×D4314yescomplemented
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8—434no—
634C24—21no—
635C24—21no—
636C24—431no—
637C24—431no—
638C24—864no—
639C24—861no—
640C24—3442no—
641C24—3442no—
642C24—1724no—
643C24D4×D4311yescharacteristic
644#41—1728no—
645#41—1724no—
646#41—1724no—
647#41—1724no—
648#41—1724no—
649#41—1728no—
650C2×Q8—434no—
651C2×Q8—432no—
652C2×Q8—861no—
653C2×Q8—862no—
654C2×Q8—862no—
655C2×Q8—1722no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—82no—
665C2×D4—82no—
666C2×D4—434no—
667C2×D4—434no—
668C2×D4—434no—
669C2×D4—432no—
670C2×D4—864no—
671C2×D4—864no—
672C2×D4—864no—
673C2×D4—864no—
674C2×D4—864no—
675C2×D4—864no—
676C2×D4—861no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—3442no—
680C2×D4—3442no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—1722no—
684C2×D4—1724no—
685C2×D4—1724no—
686C2×D4—1728no—
687C2×D4—1722no—
688C2×D4—1722no—
689C2×D4—1724no—
690C2×D4—1724no—
691C2×D4C23×D4312yes—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—431no—
698C22×C4—431no—
699C22×C4—432no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—864no—
704C22×C4—864no—
705C22×C4—862no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—3442no—
713C22×C4—1724no—
714C22×C4D4×D4312yes—
715C22×C4D4×D4311yescharacteristic
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718SD16—1724no—
719SD16—1724no—
720D8—44no—
721D8—1724no—
722M16—1724no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—44no—
726C2×C8—432no—
727C2×C8—432no—
728C2×C8—862no—
729C2×C8—862no—
730C2×C8C23×D4312yes—
731C2×C8C23×D4312yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—432no—
735C4⋊C4—432no—
736C4⋊C4—864no—
737C4⋊C4—864no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—864no—
741C4⋊C4C23×D4312yes—
742C4⋊C4C23×D4312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—864no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C42—864no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—432no—
765C23—432no—
766C23—862no—
767C23—862no—
768C23—862no—
769C23—862no—
770C23—862no—
771C23—862no—
772C23—862no—
773C23—3444no—
774C23—3444no—
775C23—34416no—
776C23—1728no—
777C23—1722no—
778C23—1722no—
779C23—1722no—
780C23C2×D4×D4312yes—
781C23C2×D4×D4311yescharacteristic
782Q8—862no—
783Q8—862no—
784Q8—1724no—
785Q8—1722no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—42no—
791D4—42no—
792D4—84no—
793D4—84no—
794D4—862no—
795D4—862no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—3444no—
800D4—1724no—
801D4—1724no—
802D4—1724no—
803D4—1728no—
804D4—1728no—
805D4—1722no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—432no—
815C2×C4—432no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—864no—
819C2×C4—864no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—3444no—
828C2×C4—1728no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4C2×D4×D4312yes—
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4#1306337012yes—
835C2×C4#1306337112yes—
836C2×C4C24×D4311yescharacteristic
837C8—22no—
838C8—22no—
839C8—862no—
840C8—862no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—862no—
858C22—862no—
859C22—34416no—
860C22—3444no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1724no—
865C22—1724no—
866C22#1458345712yes—
867C22#1458370012yes—
868C22#1458370612yes—
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—862no—
874C4—862no—
875C4—1722no—
876C4—1722no—
877C4—1722no—
878C4#1458345712yes—
879C4C2×#1306337011yescharacteristic
880C4C2×#1306337111yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—3442no—
885C2—1722no—
886C2—1722no—
887C2#1914544014yesdirect product factor
888C2C2×#1458345711yescharacteristic
889C2C2×#1458370011yescharacteristic
890C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#466C2
socleC23×C43C22×D4
hypercenterC2×#466D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#14583478C2semidirect
2. C2×#14583465C2semidirect
3. #19145440C2direct (N × H)
4. C2×#14583216C2semidirect
5. C2×#14583242C2semidirect
6. C2×#14583222C2semidirect
7. C2×#14583214C2semidirect
8. C2×#14583150C2semidirect
9. C2×#14583143C2semidirect
10. C2×#14583128C2semidirect
11. C2×#14583045C2semidirect
12. C2×#14583041C2semidirect
13. C2×#14583051C2semidirect
14. C2×#14583031C2semidirect
15. C2×#14582865C2semidirect
16. C2×C43×#466C2semidirect
18. C22×#10621900C22semidirect
23. C22×#10621877C22semidirect
25. #14583478C22semidirect
27. #14583465C22semidirect
31. C2×#13063304C22semidirect
43. C2×C4⋊C4×D43C22semidirect
44. #14583242C22semidirect
45. #14583222C22semidirect
46. #14583216C22semidirect
47. #14583214C22semidirect
48. #14583150C22semidirect
49. #14583143C22semidirect
50. #14583128C22semidirect
51. #14583051C22semidirect
52. #14583045C22semidirect
53. #14583041C22semidirect
54. #14583031C22semidirect
55. C2×#13063258C22semidirect
56. C2×#13063257C22semidirect
57. C2×#13063256C22semidirect
58. C2×#13063250C22semidirect
59. C2×#13063248C22semidirect
62. C2×#13063246C22semidirect
64. #14582865C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
70. C23×C8×C43C22semidirect
72. C2×#121×C43C22semidirect
73. C43×#466C22semidirect
74. C2×#107×C43C22semidirect
76. C2×#102×C43C22semidirect
85. C2×#10621900C23semidirect
113. C2×#10621877C23semidirect
121. #13063304C23semidirect
144. C4⋊C4×D43C23semidirect
153. #13063258C23semidirect
154. #13063257C23semidirect
155. #13063256C23semidirect
156. #13063250C23semidirect
157. #13063248C23semidirect
160. #13063246C23semidirect
164. (C2×D43)⋊C8C23semidirect
165. (C2×D43)⋊C8C23semidirect
176. C22×C8×C43C23semidirect
180. #121×C43C23semidirect
185. #107×C43C23semidirect
187. #102×C43C23semidirect
445. C2×#466D43semidirect
455. C2×C43#3198semidirect
470. C23×C8C2×D43semidirect
488. C2×#121C2×D43semidirect
499. #466C2×D43semidirect
506. C2×#107C2×D43semidirect
516. C2×#102C2×D43semidirect
522. C43C2×#3198semidirect
572. C22×C8C22×D43semidirect
594. #121C22×D43semidirect
619. #107C22×D43semidirect
629. #102C22×D43semidirect
887. C2#19145440direct (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×#145834652
#191454402
C2×#145832162
C2×#145832422
C2×#145832222
C2×#145832142
C2×#145831502
C2×#145831432
C2×#145831282
C2×#145830452
C2×#145830412
C2×#145830512
C2×#145830312
C2×#145828652
C2×C43×#4662
C2×#319843