Finite Group Databasebeta

← C2×#19145449 #25967252

Subgroups — C2×#19145449 #25967252

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×#14583477C211yesmaximal, characteristic, complemented
2C2×#14583463C211yesmaximal, characteristic, complemented
3#19145449C2116yesmaximal, direct product factor
4C2×#14583218C211yesmaximal, characteristic, complemented
5C2×#14583241C211yesmaximal, characteristic, complemented
6C2×#14583224C211yesmaximal, characteristic, complemented
7C2×#14583213C211yesmaximal, characteristic, complemented
8C2×#14583152C211yesmaximal, characteristic, complemented
9C2×#14583145C211yesmaximal, characteristic, complemented
10C2×#14583135C211yesmaximal, characteristic, complemented
11C2×#14583128C211yesmaximal, characteristic, complemented
12C2×#14583046C211yesmaximal, characteristic, complemented
13C2×#14583046C211yesmaximal, characteristic, complemented
14C2×#14583052C211yesmaximal, characteristic, complemented
15C2×#14583035C211yesmaximal, characteristic, complemented
16C2×C43×#408C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic, complemented
18C23×D172C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×D344C2211yescharacteristic
22C22×D344C2211yescharacteristic
23#14583477—24no—
24#14583477C2218yescomplemented
25#14583463—24no—
26#14583463C2218yescomplemented
27C2×#13063321—21no—
28C2×#13063314—21no—
29C2×#13063304C2211yescharacteristic
30C2×#13063304C2211yescharacteristic, complemented
31C2×#13063301—21no—
32C2×#13063299C2211yescharacteristic
33C2×#13063299C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063299C2211yescharacteristic
37C2×#13063299C2211yescharacteristic, complemented
38C2×#13063297—21no—
39C2×#13063297—21no—
40C2×#13063296—21no—
41C2×#13063293—21no—
42C2×#13063293—21no—
43C2×#13063284C2211yescharacteristic
44C22×C4⋊Dic43C2211yescharacteristic, complemented
45#14583241C2218yescomplemented
46#14583224C2218yescomplemented
47#14583218C2218yescomplemented
48#14583213C2218yescomplemented
49#14583152C2218yescomplemented
50#14583145C2218yescomplemented
51#14583135C2218yescomplemented
52#14583128C2218yescomplemented
53#14583052C2218yescomplemented
54#14583046C2218yescomplemented
55#14583046C2218yescomplemented
56#14583035C2218yescomplemented
57C2×#13063259C2211yescharacteristic, complemented
58C2×#13063259C2211yescharacteristic, complemented
59C2×#13063257C2211yescharacteristic, complemented
60C2×#13063257C2211yescharacteristic, complemented
61C2×#13063250C2211yescharacteristic, complemented
62C2×#13063250C2211yescharacteristic, complemented
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic, complemented
68C2×#13063247C2211yescharacteristic, complemented
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic, complemented
71C23×C8×C43C2211yescharacteristic, complemented
72C43×#408C2218yescomplemented
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×C22⋊C8×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621898—22no—
79C2×#10621898—42no—
80C2×#10621898—42no—
81C2×#10621898C2314yescomplemented
82C22×Dic86C2311yescharacteristic
83C22×D172—21no—
84C22×D172—22no—
85C22×D172—42no—
86C22×D172—42no—
87C22×D172C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×D172C2311yescharacteristic
90C22×D172C2314yes—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C23×Dic43—21no—
99C22×C4×D43—21no—
100C2×#10621873—42no—
101C2×#10621873—42no—
102C2×#10621873C2314yes—
103C2×#10621873C2314yes—
104C2×D344—42no—
105C2×D344—42no—
106C2×D344C2314yes—
107C2×D344C2314yes—
108#13063321—28no—
109#13063314—28no—
110#13063304—22no—
111#13063304—22no—
112#13063304C2314yes—
113#13063304C2314yescomplemented
114#13063301—28no—
115#13063299—22no—
116#13063299—22no—
117#13063299—22no—
118#13063299—22no—
119#13063299—22no—
120#13063299—22no—
121#13063299C2314yes—
122#13063299C2314yes—
123#13063299C2314yes—
124#13063299C2314yes—
125#13063299C2314yes—
126#13063299C2314yescomplemented
127#13063297—28no—
128#13063297—28no—
129#13063296—28no—
130#13063293—28no—
131#13063293—28no—
132#13063284—22no—
133#13063284C2314yes—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43—22no—
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×C4⋊Dic43C2311yescharacteristic
139C2×C4⋊Dic43C2311yescharacteristic
140C2×C4⋊Dic43C2314yescomplemented
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—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#13063259C2314yescomplemented
154#13063259C2314yescomplemented
155#13063257C2314yescomplemented
156#13063257C2314yescomplemented
157#13063250C2314yescomplemented
158#13063250C2314yescomplemented
159#13063247C2314yes—
160#13063247C2314yes—
161#13063247C2314yes—
162#13063247C2314yes—
163#13063247C2314yescomplemented
164#13063247C2314yescomplemented
165C2×#41×C43—42no—
166C2×#41×C43—42no—
167C2×#41×C43D414yes—
168C2×#41×C43C2314yes—
169C22×Q8×C43D411yescharacteristic
170C22×D4×C43D411yescharacteristic
171C22×D4×C43D411yescharacteristic
172C22×D4×C43D411yescharacteristic
173C23×C4×C43C2311yescharacteristic
174C23×C4×C43C2311yescharacteristic
175C23×C4×C43C2311yescharacteristic
176C2×M16×C43—42no—
177C2×M16×C43C2314yescomplemented
178C22×C8×C43—42no—
179C22×C8×C43C2311yescharacteristic
180C22×C8×C43C2311yescharacteristic
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183C22×C8×C43C2314yescomplemented
184C22⋊C8×C43C2314yes—
185C22⋊C8×C43C2314yes—
186C22⋊C8×C43C2314yescomplemented
187C22⋊C8×C43C2314yescomplemented
188C24×C43C2×D411yescharacteristic
189C24×C43C2×D411yescharacteristic
190C24×C43C2×D411yescharacteristic
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—21no—
194C23×D43—24no—
195C23×D43—44no—
196C23×D43—82no—
197C23×D43—82no—
198#41×C43—48no—
199#41×C43—44no—
200#41×C43—44no—
201C2×Q8×C43—42no—
202C2×Q8×C43C2×D414yes—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—42no—
206C2×D4×C43C2×D414yes—
207C2×D4×C43C2×D414yes—
208C2×D4×C43C2×D414yes—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D412yes—
219C22×C4×C43C2×D412yes—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—24no—
226C2×C22⋊D43—24no—
227C2×C22⋊D43—24no—
228C2×C22⋊D43—24no—
229C2×C22⋊D43—24no—
230C2×C22⋊D43—24no—
231C2×C22⋊D43—24no—
232C2×C22⋊D43—44no—
233C2×C22⋊D43—82no—
234C2×C22⋊D43—82no—
235C2×C22⋊D43—82no—
236C2×C22⋊D43—82no—
237C2×C22⋊D43—82no—
238C2×C22⋊D43—82no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—24no—
245C22×Dic43—82no—
246#10621898—44no—
247#10621898—44no—
248#10621898—48no—
249C2×D172—21no—
250C2×D172—21no—
251C2×D172—21no—
252C2×D172—24no—
253C2×D172—22no—
254C2×D172—22no—
255C2×D172—22no—
256C2×D172—22no—
257C2×D172—22no—
258C2×D172—22no—
259C2×D172—44no—
260C2×D172—44no—
261C2×D172—48no—
262C2×D172—44no—
263C2×D172C2412yes—
264C2×D172C2412yes—
265C2×D172C2412yes—
266C2×C4×D43—24no—
267C2×C4×D43—44no—
268C2×Dic86—22no—
269C2×Dic86—22no—
270C2×Dic86—21no—
271C2×Dic86C2412yes—
272M16×C43—44no—
273C2×C8×C43—22no—
274C2×C8×C43—22no—
275C2×C8×C43—22no—
276C2×C8×C43—22no—
277C2×C8×C43—44no—
278C2×C8×C43C2412yes—
279C2×C8×C43C2412yes—
280C2×C8×C43C2412yes—
281C2×C8×C43C2412yes—
282C22⋊Dic43—24no—
283C22⋊Dic43—24no—
284C22⋊Dic43—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291C4⋊Dic43—21no—
292C4⋊Dic43—21no—
293C4⋊Dic43—24no—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43C2412yes—
297C4⋊Dic43C2412yes—
298C4⋊Dic43C2412yes—
299C4⋊Dic43C2412yes—
300Dic43⋊C4—24no—
301Dic43⋊C4—24no—
302C4×Dic43—24no—
303D344—44no—
304D344—44no—
305#10621873—44no—
306#10621873—44no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—22no—
312C23×C43—22no—
313C23×C43—22no—
314C23×C43—22no—
315C23×C43—22no—
316C23×C43C22×D412yes—
317C23×C43C22×D412yes—
318C23×C43C22×D412yes—
319C23×C43C22×D411yescharacteristic
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—48no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—84no—
334C22×D43—84no—
335C22×D43—816no—
336Q8×C43—44no—
337D4×C43—44no—
338D4×C43—44no—
339D4×C43—44no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—24no—
344C2×C4×C43—24no—
345C2×C4×C43—24no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D412yes—
354C2×C4×C43C22×D412yes—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43H(5,𝔽2)12yes—
357C2×C4×C43H(5,𝔽2)12yes—
358C2×C4×C43C2511yescharacteristic
359C22⋊D43—48no—
360C22⋊D43—84no—
361C22⋊D43—84no—
362C22⋊D43—84no—
363C22⋊D43—84no—
364C22⋊D43—84no—
365C22⋊D43—84no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43—42no—
375C2×Dic43—42no—
376C2×Dic43—84no—
377D172—22no—
378D172—22no—
379D172—22no—
380D172—22no—
381D172—22no—
382D172—22no—
383D172—48no—
384D172—42no—
385D172—42no—
386D172—42no—
387C4×D43—48no—
388Dic86—22no—
389Dic86—22no—
390Dic86—42no—
391C8×C43—22no—
392C8×C43—22no—
393C8×C43—22no—
394C8×C43—22no—
395C2×#3198—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—22no—
402C22×C43—22no—
403C22×C43—22no—
404C22×C43—22no—
405C22×C43—44no—
406C22×C43—44no—
407C22×C43—44no—
408C22×C43#53412yes—
409C22×C43#57612yes—
410C22×C43#57712yes—
411C22×C43C23×D411yescharacteristic
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—816no—
422C2×D43—84no—
423C2×D43—84no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—22no—
427C4×C43—22no—
428C4×C43#53412yes—
429C4×C43C2×H(5,𝔽2)11yescharacteristic
430C4×C43C2×H(5,𝔽2)11yescharacteristic
431Dic43—42no—
432Dic43—42no—
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×#466—431no—
446C2×#465—431no—
447C2×#449—431no—
448C2×#449—431no—
449C2×#450—431no—
450C2×#447—431no—
451C2×#408D4311yescharacteristic, complemented
452C2×C43—42no—
453C2×C43—42no—
454C2×C43—42no—
455C2×C43#319814yescomplemented
456C2×C43C2×#53411yescharacteristic
457C2×C43C2×#57611yescharacteristic
458C2×C43C2×#57711yescharacteristic
459D43—82no—
460D43—82no—
461D43—82no—
462C22×#41—431no—
463C22×#41C2×D4311yescharacteristic
464C23×D4—431no—
465C22×SD16—431no—
466C22×SD16—431no—
467C22×D8—431no—
468C22×D8—431no—
469C22×M16C2×D4311yescharacteristic, complemented
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—431no—
485C2×#121—431no—
486C2×#121—861no—
487C2×#121—861no—
488C2×#121—861no—
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#466—438no—
500#465—438no—
501#450—438no—
502#449—438no—
503#449—438no—
504#447—438no—
505C2×#107—431no—
506C2×#107—431no—
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×#102—431no—
516C2×#102—431no—
517#408C2×D4318yescomplemented
518C2×C22⋊C8C2×D4311yescharacteristic
519C2×C22⋊C8C2×D4311yescharacteristic
520C2×C22⋊C8C2×D4311yescharacteristic, complemented
521C2×C22⋊C8C2×D4311yescharacteristic, complemented
522C43C2×#319811yescharacteristic, complemented, Sylow
523C25—861no—
524C2×#41—42no—
525C2×#41—42no—
526C2×#41—434no—
527C2×#41—862no—
528C2×#41—1722no—
529C2×#41—1722no—
530C2×#41D17214yes—
531C2×#41C22×D4314yes—
532C22×Q8—431no—
533C22×Q8D17211yescharacteristic
534C22×D4—431no—
535C22×D4—431no—
536C22×D4—431no—
537C22×D4—434no—
538C22×D4—861no—
539C22×D4—861no—
540C22×D4—861no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4—861no—
544C22×D4—861no—
545C22×D4—861no—
546C22×D4—862no—
547C22×D4—1722no—
548C22×D4—1722no—
549C22×D4D17211yescharacteristic
550C22×D4D17211yescharacteristic
551C22×D4D17211yescharacteristic
552C23×C4—861no—
553C23×C4—861no—
554C23×C4C22×D4311yescharacteristic
555C23×C4C22×D4311yescharacteristic
556C23×C4C22×D4311yescharacteristic
557C2×SD16—434no—
558C2×SD16—434no—
559C2×SD16—1722no—
560C2×SD16—1722no—
561C2×D8—434no—
562C2×D8—434no—
563C2×D8—1722no—
564C2×D8—1722no—
565C2×M16—42no—
566C2×M16C22×D4314yescomplemented
567C22×C8—42no—
568C22×C8C22×D4311yescharacteristic
569C22×C8C22×D4311yescharacteristic
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—434no—
581#121—434no—
582#121—434no—
583#121—434no—
584#121—434no—
585#121—434no—
586#121—868no—
587#121—868no—
588#121—868no—
589#121—862no—
590#121—862no—
591#121—862no—
592#121—862no—
593#121—862no—
594#121—862no—
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—431no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4—861no—
608C2×C22⋊C4—861no—
609C2×C22⋊C4—861no—
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#107—434no—
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#102—434no—
629#102—434no—
630C22⋊C8C22×D4314yes—
631C22⋊C8C22×D4314yes—
632C22⋊C8C22×D4314yescomplemented
633C22⋊C8C22×D4314yescomplemented
634C24—864no—
635C24—861no—
636C24—861no—
637C24—861no—
638C24—3442no—
639C24—3442no—
640C24—1724no—
641C24C2×D17211yescharacteristic
642C24C2×D17211yescharacteristic
643C24C2×D17211yescharacteristic
644#41—44no—
645#41—44no—
646#41—48no—
647#41—1724no—
648#41—1724no—
649#41—1728no—
650C2×Q8—42no—
651C2×Q8—432no—
652C2×Q8—861no—
653C2×Q8—862no—
654C2×Q8—862no—
655C2×Q8C2×D17214yes—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—432no—
660C2×D4—432no—
661C2×D4—432no—
662C2×D4—864no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—864no—
668C2×D4—864no—
669C2×D4—861no—
670C2×D4—861no—
671C2×D4—861no—
672C2×D4—864no—
673C2×D4—862no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—862no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—3442no—
680C2×D4—3442no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—3442no—
684C2×D4—3442no—
685C2×D4—1724no—
686C2×D4—1724no—
687C2×D4—1724no—
688C2×D4—1728no—
689C2×D4—1724no—
690C2×D4C2×D17214yes—
691C2×D4C2×D17214yes—
692C2×D4C2×D17214yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—864no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—864no—
706C22×C4—3442no—
707C22×C4—1724no—
708C22×C4C2×D17212yes—
709C22×C4C2×D17212yes—
710C22×C4C2×D17212yes—
711C22×C4C2×D17211yescharacteristic
712C22×C4C2×D17211yescharacteristic
713C22×C4C2×D17211yescharacteristic
714C22×C4C23×D4312yes—
715C22×C4C23×D4312yes—
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718SD16—1724no—
719SD16—1724no—
720D8—1724no—
721D8—1724no—
722M16—44no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—44no—
728C2×C8C23×D4312yes—
729C2×C8C23×D4312yes—
730C2×C8C23×D4312yes—
731C2×C8C23×D4312yes—
732C4⋊C4—432no—
733C4⋊C4—432no—
734C4⋊C4—432no—
735C4⋊C4—432no—
736C4⋊C4—864no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—864no—
742C4⋊C4—864no—
743C22⋊C4—864no—
744C22⋊C4—864no—
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—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—862no—
763C23—862no—
764C23—862no—
765C23—3444no—
766C23—3444no—
767C23—34416no—
768C23—1728no—
769C23—1722no—
770C23—1722no—
771C23—1722no—
772C23—1722no—
773C23—1722no—
774C23—1722no—
775C23—1722no—
776C23—1722no—
777C23—1722no—
778C23C22×D17212yes—
779C23C22×D17212yes—
780C23C22×D17212yes—
781C23C22×D17211yescharacteristic
782Q8—44no—
783Q8—862no—
784Q8—862no—
785Q8—1722no—
786D4—44no—
787D4—44no—
788D4—44no—
789D4—862no—
790D4—862no—
791D4—862no—
792D4—862no—
793D4—862no—
794D4—862no—
795D4—3444no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—3444no—
800D4—3444no—
801D4—1728no—
802D4—1728no—
803D4—1722no—
804D4—1722no—
805D4—1722no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—862no—
823C2×C4—3444no—
824C2×C4—1728no—
825C2×C4—1722no—
826C2×C4—1722no—
827C2×C4—1722no—
828C2×C4—1722no—
829C2×C4—1722no—
830C2×C4C22×D17212yes—
831C2×C4C22×D17212yes—
832C2×C4C22×D17212yes—
833C2×C4C22×D17211yescharacteristic
834C2×C4#1306337012yes—
835C2×C4#1306337012yes—
836C2×C4C24×D4311yescharacteristic
837C8—22no—
838C8—22no—
839C8—22no—
840C8—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—34416no—
854C22—3444no—
855C22—3444no—
856C22—3444no—
857C22—1722no—
858C22—1722no—
859C22—1722no—
860C22—1722no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1722no—
865C22—1722no—
866C22#1458346112yes—
867C22#1458370412yes—
868C22#1458371112yes—
869C22C23×D17211yescharacteristic
870C4—22no—
871C4—22no—
872C4—22no—
873C4—1722no—
874C4—1722no—
875C4—1722no—
876C4—1722no—
877C4—1722no—
878C4#1458346112yes—
879C4C2×#1306337011yescharacteristic
880C4C2×#1306337011yescharacteristic
881C2—42no—
882C2—42no—
883C2—42no—
884C2—3442no—
885C2—3442no—
886C2—3442no—
887C2#1914544914yesdirect product factor
888C2C2×#1458346111yescharacteristic
889C2C2×#1458370411yescharacteristic
890C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#408C2
socleC23×C43C22×D4
hypercenterC2×#408D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
1. C2×#14583477C2semidirect
2. C2×#14583463C2semidirect
3. #19145449C2direct (N × H)
4. C2×#14583218C2semidirect
5. C2×#14583241C2semidirect
6. C2×#14583224C2semidirect
7. C2×#14583213C2semidirect
8. C2×#14583152C2semidirect
9. C2×#14583145C2semidirect
10. C2×#14583135C2semidirect
11. C2×#14583128C2semidirect
12. C2×#14583046C2semidirect
13. C2×#14583046C2semidirect
14. C2×#14583052C2semidirect
15. C2×#14583035C2semidirect
16. C2×C43×#408C2semidirect
17. C22×#10621898C22semidirect
24. #14583477C22semidirect
26. #14583463C22semidirect
30. C2×#13063304C22semidirect
37. C2×#13063299C22semidirect
44. C22×C4⋊Dic43C22semidirect
45. #14583241C22semidirect
46. #14583224C22semidirect
47. #14583218C22semidirect
48. #14583213C22semidirect
49. #14583152C22semidirect
50. #14583145C22semidirect
51. #14583135C22semidirect
52. #14583128C22semidirect
53. #14583052C22semidirect
54. #14583046C22semidirect
55. #14583046C22semidirect
56. #14583035C22semidirect
57. C2×#13063259C22semidirect
58. C2×#13063259C22semidirect
59. C2×#13063257C22semidirect
60. C2×#13063257C22semidirect
61. C2×#13063250C22semidirect
62. C2×#13063250C22semidirect
67. C2×#13063247C22semidirect
68. C2×#13063247C22semidirect
70. C22×M16×C43C22semidirect
71. C23×C8×C43C22semidirect
72. C43×#408C22semidirect
75. C2×C22⋊C8×C43C22semidirect
76. C2×C22⋊C8×C43C22semidirect
81. C2×#10621898C23semidirect
113. #13063304C23semidirect
126. #13063299C23semidirect
140. C2×C4⋊Dic43C23semidirect
153. #13063259C23semidirect
154. #13063259C23semidirect
155. #13063257C23semidirect
156. #13063257C23semidirect
157. #13063250C23semidirect
158. #13063250C23semidirect
163. #13063247C23semidirect
164. #13063247C23semidirect
177. C2×M16×C43C23semidirect
183. C22×C8×C43C23semidirect
186. C22⋊C8×C43C23semidirect
187. C22⋊C8×C43C23semidirect
451. C2×#408D43semidirect
455. C2×C43#3198semidirect
469. C22×M16C2×D43semidirect
470. C23×C8C2×D43semidirect
517. #408C2×D43semidirect
520. C2×C22⋊C8C2×D43semidirect
521. C2×C22⋊C8C2×D43semidirect
522. C43C2×#3198semidirect
566. C2×M16C22×D43semidirect
572. C22×C8C22×D43semidirect
632. C22⋊C8C22×D43semidirect
633. C22⋊C8C22×D43semidirect
887. C2#19145449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145834632
#191454492
C2×#145832182
C2×#145832412
C2×#145832242
C2×#145832132
C2×#145831522
C2×#145831452
C2×#145831352
C2×#145831282
C2×#145830462
C2×#145830522
C2×#145830352
C2×C43×#4082
C2×#319843