Finite Group Databasebeta

← C2×#19145445 #25967248

Subgroups — C2×#19145445 #25967248

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×#14583468C211yesmaximal, characteristic, complemented
3#19145445C2116yesmaximal, direct product factor
4C2×#14583219C211yesmaximal, characteristic, complemented
5C2×#14583240C211yesmaximal, characteristic, complemented
6C2×#14583214C211yesmaximal, characteristic, complemented
7C2×#14583151C211yesmaximal, characteristic, complemented
8C2×#14583146C211yesmaximal, characteristic, complemented
9C2×#14583134C211yesmaximal, characteristic, complemented
10C2×#14583129C211yesmaximal, characteristic, complemented
11C2×#14583045C211yesmaximal, characteristic, complemented
12C2×#14583045C211yesmaximal, characteristic, complemented
13C2×#14583052C211yesmaximal, characteristic, complemented
14C2×#14583032C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#482C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×#10621900C2211yescharacteristic, complemented
19C23×D172C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621872C2211yescharacteristic, complemented
25C22×C8×D43C2211yescharacteristic, complemented
26#14583478—24no—
27#14583478C2218yescomplemented
28#14583468—24no—
29#14583468C2218yescomplemented
30C2×#13063322—21no—
31C2×#13063313—21no—
32C2×#13063305C2211yescharacteristic, complemented
33C2×#13063304C2211yescharacteristic
34C2×#13063302—21no—
35C2×#13063300C2211yescharacteristic
36C2×#13063300C2211yescharacteristic
37C2×#13063300C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×#13063298—21no—
40C2×#13063297—21no—
41C2×#13063296—21no—
42C2×#13063296C2211yescharacteristic, complemented
43C2×#13063295—21no—
44C2×#13063295—21no—
45C2×C4⋊C4×D43C2211yescharacteristic, complemented
46#14583240C2218yescomplemented
47#14583219C2218yescomplemented
48#14583214C2218yescomplemented
49#14583151C2218yescomplemented
50#14583146C2218yescomplemented
51#14583134C2218yescomplemented
52#14583129C2218yescomplemented
53#14583052C2218yescomplemented
54#14583045C2218yescomplemented
55#14583045C2218yescomplemented
56#14583032C2218yescomplemented
57C2×#13063258C2211yescharacteristic, complemented
58C2×#13063256C2211yescharacteristic, complemented
59C2×#13063248C2211yescharacteristic, complemented
60C2×#13063248C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C2×#121×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#482C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
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×D172—22no—
90C22×D172—21no—
91C22×D172—21no—
92C22×D172—21no—
93C22×D172—21no—
94C22×D172—42no—
95C22×D172—42no—
96C22×D172D411yescharacteristic
97C22×D172C2311yescharacteristic
98C22×D172C2311yescharacteristic
99C22×D172C2314yes—
100C22×C22⋊D43—21no—
101C22×C22⋊D43—21no—
102C22×C22⋊D43D411yescharacteristic
103C22×C22⋊D43D411yescharacteristic
104C23×Dic43—21no—
105C22×C4×D43—21no—
106C22×C4×D43C2311yescharacteristic
107C22×C4×D43C2311yescharacteristic
108C2×#10621873—42no—
109C2×#10621873—42no—
110C2×#10621873C2314yes—
111C2×#10621873C2314yes—
112C2×#10621882—42no—
113C2×#10621882—42no—
114C2×#10621882C2314yes—
115C2×#10621882C2314yes—
116C2×#10621872—42no—
117C2×#10621872C2314yescomplemented
118C22×C43⋊C8C2311yescharacteristic
119C22×C43⋊C8C2311yescharacteristic
120C2×C8×D43—42no—
121C2×C8×D43C2314yescomplemented
122#13063322—28no—
123#13063313—28no—
124#13063305—22no—
125#13063305C2314yescomplemented
126#13063304—22no—
127#13063304C2314yes—
128#13063302—28no—
129#13063300—22no—
130#13063300—22no—
131#13063300—22no—
132#13063300—22no—
133#13063300C2314yes—
134#13063300C2314yes—
135#13063300C2314yes—
136#13063300C2314yes—
137#13063298—28no—
138#13063297—28no—
139#13063296—28no—
140#13063296—22no—
141#13063296C2314yescomplemented
142#13063295—28no—
143#13063295—28no—
144C2×C4⋊Dic43—21no—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—21no—
148C4⋊C4×D43—22no—
149C4⋊C4×D43C2314yescomplemented
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#13063258C2314yescomplemented
158#13063256C2314yescomplemented
159#13063248C2314yescomplemented
160#13063248C2314yescomplemented
161#13063247C2314yes—
162#13063247C2314yes—
163#13063245C2314yes—
164#13063245C2314yes—
165C22⋊(C43⋊C8)C2314yes—
166(C2×D43)⋊C8C2314yescomplemented
167(C2×D43)⋊C8C2314yescomplemented
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×C43C2314yescomplemented
184#106×C43C2314yescomplemented
185#102×C43C2314yescomplemented
186#102×C43C2314yescomplemented
187C22⋊C8×C43C2314yes—
188C24×C43—21no—
189C24×C43C2×D411yescharacteristic
190C23×D43—21no—
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—24no—
200C2×D4×C43—22no—
201C2×D4×C43—22no—
202C2×D4×C43—82no—
203C2×D4×C43C2412yes—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C2×C22⋊D43—24no—
214C2×C22⋊D43—24no—
215C2×C22⋊D43—42no—
216C2×C22⋊D43—42no—
217C2×C22⋊D43—44no—
218C2×C22⋊D43—82no—
219C2×C22⋊D43C2×D414yes—
220C2×C22⋊D43C2×D414yes—
221C22×Dic43—24no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—44no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227#10621900—44no—
228#10621900—44no—
229#10621900—48no—
230#10621898—48no—
231#10621898—44no—
232#10621898—44no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172—24no—
236C2×D172—24no—
237C2×D172—24no—
238C2×D172—24no—
239C2×D172—24no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—42no—
245C2×D172—44no—
246C2×D172—44no—
247C2×D172—48no—
248C2×D172—44no—
249C2×D172—82no—
250C2×D172—82no—
251C2×D172—82no—
252C2×D172—82no—
253C2×D172C2×D414yes—
254C2×D172C2412yes—
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—
272C2×C8×C43—22no—
273C2×C8×C43—22no—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43C2412yes—
280C4⋊C4×C43C2412yes—
281C4⋊C4×C43C2412yes—
282C22⋊C4×C43—24no—
283C22⋊C4×C43—24no—
284C42×C43—24no—
285C22⋊Dic43—24no—
286C22⋊Dic43—24no—
287#10621882—44no—
288#10621882—44no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294C4⋊Dic43—21no—
295C4⋊Dic43—24no—
296C4⋊Dic43C2412yes—
297Dic43⋊C4—24no—
298Dic43⋊C4—24no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—22no—
301C2×C43⋊C8C2412yes—
302C2×C43⋊C8C2412yes—
303#10621873—44no—
304#10621873—44no—
305#10621872—44no—
306C8×D43—44no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—22no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43—42no—
314C23×C43C22×D412yes—
315C23×C43C22×D411yescharacteristic
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—48no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
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—42no—
339D4×C43—84no—
340C2×C4×C43—22no—
341C2×C4×C43—24no—
342C2×C4×C43—22no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43—42no—
350C2×C4×C43C22×D412yes—
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43H(5,𝔽2)12yes—
353C2×C4×C43H(5,𝔽2)12yes—
354C2×C4×C43C2511yescharacteristic
355C22⋊D43—44no—
356C22⋊D43—44no—
357C22⋊D43—48no—
358C22⋊D43—84no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—22no—
363C2×Dic43—48no—
364C2×Dic43—42no—
365C2×Dic43—42no—
366C2×Dic43C22×D412yes—
367C2×Dic43C22×D412yes—
368D172—22no—
369D172—22no—
370D172—22no—
371D172—22no—
372D172—44no—
373D172—48no—
374D172—42no—
375D172—42no—
376D172—84no—
377D172—84no—
378D172—84no—
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—84no—
404C22×C43#53412yes—
405C22×C43#57612yes—
406C22×C43#57712yes—
407C22×C43C23×D411yescharacteristic
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—44no—
415C2×D43—44no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C2×D43—42no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—816no—
423C2×D43—84no—
424C2×D43—84no—
425C4×C43—22no—
426C4×C43—42no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43#53412yes—
430C4×C43C2×H(5,𝔽2)11yescharacteristic
431C4×C43C2×H(5,𝔽2)11yescharacteristic
432Dic43—22no—
433Dic43—22no—
434Dic43—42no—
435Dic43—42no—
436C2×#537—431no—
437C2×#535—431no—
438#3198—4316no—
439C2×#481—431no—
440C2×#485—431no—
441C2×#482D4311yescharacteristic, complemented
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×#408—431no—
452C2×C43—42no—
453C2×C43—82no—
454C2×C43#319814yescomplemented
455C2×C43C2×#53411yescharacteristic
456C2×C43C2×#57611yescharacteristic
457C2×C43C2×#57711yescharacteristic
458D43—42no—
459D43—42no—
460D43—82no—
461D43—82no—
462C22×#41—431no—
463C22×#41—431no—
464C23×D4—431no—
465C22×SD16—431no—
466C22×SD16—431no—
467C22×D8—431no—
468C22×D8—431no—
469C22×M16—431no—
470C23×C8—431no—
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—861no—
486C2×#121—861no—
487C2×#121—861no—
488C2×#121C2×D4311yescharacteristic
489C2×#120—861no—
490C2×#120—861no—
491C2×#117C2×D4311yescharacteristic
492C22×C4⋊C4—431no—
493#485—438no—
494#482C2×D4318yescomplemented
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×#107C2×D4311yescharacteristic, complemented
507C2×#106—431no—
508C2×#106C2×D4311yescharacteristic, complemented
509C2×#103—431no—
510C2×#103—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102C2×D4311yescharacteristic, complemented
516C2×#102C2×D4311yescharacteristic, complemented
517#408—438no—
518C2×C22⋊C8—431no—
519C2×C22⋊C8—431no—
520C2×C22⋊C8—431no—
521C2×C22⋊C8C2×D4311yescharacteristic
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—431no—
536C22×D4—431no—
537C22×D4—431no—
538C22×D4—431no—
539C22×D4—431no—
540C22×D4—434no—
541C22×D4—861no—
542C22×D4—861no—
543C22×D4—861no—
544C22×D4—861no—
545C22×D4—861no—
546C22×D4—861no—
547C22×D4—861no—
548C22×D4—862no—
549C22×D4—1722no—
550C22×D4—1722no—
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—434no—
562C2×D8—434no—
563C2×D8—1722no—
564C2×D8—1722no—
565C2×M16—434no—
566C2×M16—1722no—
567C22×C8—431no—
568C22×C8—431no—
569C22×C8—434no—
570C22×C8—1722no—
571C22×C8C22×D4311yescharacteristic
572C22×C8C22×D4311yescharacteristic
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—434no—
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—862no—
591#121—862no—
592#121—868no—
593#121—868no—
594#121C22×D4314yes—
595#120—868no—
596#120—868no—
597#117—22no—
598#117C22×D4314yes—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—434no—
601C2×C4⋊C4—862no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
618#107—434no—
619#107C22×D4314yescomplemented
620#106—434no—
621#106C22×D4314yescomplemented
622#103—434no—
623#103—434no—
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102C22×D4314yescomplemented
629#102C22×D4314yescomplemented
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8C22×D4314yes—
634C24—21no—
635C24—431no—
636C24—431no—
637C24—864no—
638C24—861no—
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—21no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—82no—
661C2×D4—434no—
662C2×D4—434no—
663C2×D4—434no—
664C2×D4—432no—
665C2×D4—432no—
666C2×D4—864no—
667C2×D4—864no—
668C2×D4—864no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—864no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4—864no—
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—1724no—
685C2×D4—1724no—
686C2×D4—1722no—
687C2×D4—1724no—
688C2×D4—1728no—
689C2×D4—1722no—
690C2×D4—1722no—
691C2×D4—1724no—
692C2×D4C23×D4312yes—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—431no—
699C22×C4—431no—
700C22×C4—432no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—864no—
705C22×C4—864no—
706C22×C4—862no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
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—1724no—
721D8—1724no—
722M16—1724no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—432no—
726C2×C8—432no—
727C2×C8—862no—
728C2×C8—862no—
729C2×C8—1724no—
730C2×C8C23×D4312yes—
731C2×C8C23×D4312yes—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—432no—
736C4⋊C4—864no—
737C4⋊C4—864no—
738C4⋊C4—861no—
739C4⋊C4—864no—
740C4⋊C4C23×D4312yes—
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—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—432no—
761C23—432no—
762C23—862no—
763C23—862no—
764C23—862no—
765C23—862no—
766C23—862no—
767C23—862no—
768C23—862no—
769C23—862no—
770C23—3444no—
771C23—3444no—
772C23—34416no—
773C23—1728no—
774C23—1722no—
775C23—1722no—
776C23—1722no—
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—42no—
789D4—84no—
790D4—862no—
791D4—862no—
792D4—862no—
793D4—862no—
794D4—3444no—
795D4—3444no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—1724no—
800D4—1728no—
801D4—1724no—
802D4—1724no—
803D4—1728no—
804D4—1722no—
805D4—1722no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—432no—
817C2×C4—432no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—864no—
821C2×C4—864no—
822C2×C4—862no—
823C2×C4—862no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—3444no—
829C2×C4—1728no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4C2×D4×D4312yes—
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4#1306337112yes—
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—84no—
849C22—862no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—862no—
855C22—34416no—
856C22—3444no—
857C22—3444no—
858C22—1722no—
859C22—1722no—
860C22—1722no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1724no—
865C22—1724no—
866C22#1458346012yes—
867C22#1458370312yes—
868C22#1458370612yes—
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—862no—
875C4—862no—
876C4—1722no—
877C4—1722no—
878C4#1458346012yes—
879C4C2×#1306337111yescharacteristic
880C4C2×#1306337111yescharacteristic
881C2—42no—
882C2—82no—
883C2—3442no—
884C2—3442no—
885C2—1722no—
886C2—1722no—
887C2#1914544514yesdirect product factor
888C2C2×#1458346011yescharacteristic
889C2C2×#1458370311yescharacteristic
890C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
hypercenterC2×#482D43
hypocenterC43C2×#3198
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
1. C2×#14583478C2semidirect
2. C2×#14583468C2semidirect
3. #19145445C2direct (N × H)
4. C2×#14583219C2semidirect
5. C2×#14583240C2semidirect
6. C2×#14583214C2semidirect
7. C2×#14583151C2semidirect
8. C2×#14583146C2semidirect
9. C2×#14583134C2semidirect
10. C2×#14583129C2semidirect
11. C2×#14583045C2semidirect
12. C2×#14583045C2semidirect
13. C2×#14583052C2semidirect
14. C2×#14583032C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#482C2semidirect
18. C22×#10621900C22semidirect
24. C22×#10621872C22semidirect
25. C22×C8×D43C22semidirect
27. #14583478C22semidirect
29. #14583468C22semidirect
32. C2×#13063305C22semidirect
42. C2×#13063296C22semidirect
45. C2×C4⋊C4×D43C22semidirect
46. #14583240C22semidirect
47. #14583219C22semidirect
48. #14583214C22semidirect
49. #14583151C22semidirect
50. #14583146C22semidirect
51. #14583134C22semidirect
52. #14583129C22semidirect
53. #14583052C22semidirect
54. #14583045C22semidirect
55. #14583045C22semidirect
56. #14583032C22semidirect
57. C2×#13063258C22semidirect
58. C2×#13063256C22semidirect
59. C2×#13063248C22semidirect
60. C2×#13063248C22semidirect
65. #14582864C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
71. C43×#482C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×#102×C43C22semidirect
75. C2×#102×C43C22semidirect
85. C2×#10621900C23semidirect
117. C2×#10621872C23semidirect
121. C2×C8×D43C23semidirect
125. #13063305C23semidirect
141. #13063296C23semidirect
149. C4⋊C4×D43C23semidirect
157. #13063258C23semidirect
158. #13063256C23semidirect
159. #13063248C23semidirect
160. #13063248C23semidirect
166. (C2×D43)⋊C8C23semidirect
167. (C2×D43)⋊C8C23semidirect
183. #107×C43C23semidirect
184. #106×C43C23semidirect
185. #102×C43C23semidirect
186. #102×C43C23semidirect
441. C2×#482D43semidirect
454. C2×C43#3198semidirect
494. #482C2×D43semidirect
506. C2×#107C2×D43semidirect
508. C2×#106C2×D43semidirect
515. C2×#102C2×D43semidirect
516. C2×#102C2×D43semidirect
522. C43C2×#3198semidirect
619. #107C22×D43semidirect
621. #106C22×D43semidirect
628. #102C22×D43semidirect
629. #102C22×D43semidirect
887. C2#19145445direct (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×#145834682
#191454452
C2×#145832192
C2×#145832402
C2×#145832142
C2×#145831512
C2×#145831462
C2×#145831342
C2×#145831292
C2×#145830452
C2×#145830522
C2×#145830322
C2×#145828642
C2×C43×#4822
C2×#319843