Finite Group Databasebeta

← C2×#19145453 #25967256

Subgroups — C2×#19145453 #25967256

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×#14583479C211yesmaximal, characteristic, complemented
2C2×#14583468C211yesmaximal, characteristic, complemented
3#19145453C2116yesmaximal, direct product factor
4C2×#14583219C211yesmaximal, characteristic, complemented
5C2×#14583223C211yesmaximal, characteristic, complemented
6C2×#14583214C211yesmaximal, characteristic, complemented
7C2×#14583153C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583136C211yesmaximal, characteristic, complemented
10C2×#14583131C211yesmaximal, characteristic, complemented
11C2×#14583047C211yesmaximal, characteristic, complemented
12C2×#14583047C211yesmaximal, characteristic, complemented
13C2×#14583049C211yesmaximal, characteristic, complemented
14C2×#14583035C211yesmaximal, characteristic, complemented
15C2×#14582864C211yesmaximal, characteristic, complemented
16C2×C43×#485C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic, complemented
18C22×#10621898C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×D344C2211yescharacteristic
23C22×D344C2211yescharacteristic
24C22×#10621872C2211yescharacteristic, complemented
25C22×C8×D43C2211yescharacteristic, complemented
26#14583479—24no—
27#14583479C2218yescomplemented
28#14583468—24no—
29#14583468C2218yescomplemented
30C2×#13063322—21no—
31C2×#13063313—21no—
32C2×#13063303—21no—
33C2×#13063301C2211yescharacteristic, complemented
34C2×#13063300—21no—
35C2×#13063300C2211yescharacteristic
36C2×#13063300C2211yescharacteristic
37C2×#13063300C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×#13063300C2211yescharacteristic, complemented
40C2×#13063299C2211yescharacteristic
41C2×#13063298—21no—
42C2×#13063298—21no—
43C2×#13063295—21no—
44C2×#13063295—21no—
45C2×C4⋊C4×D43C2211yescharacteristic, complemented
46#14583223C2218yescomplemented
47#14583219C2218yescomplemented
48#14583214C2218yescomplemented
49#14583153C2218yescomplemented
50#14583148C2218yescomplemented
51#14583136C2218yescomplemented
52#14583131C2218yescomplemented
53#14583049C2218yescomplemented
54#14583047C2218yescomplemented
55#14583047C2218yescomplemented
56#14583035C2218yescomplemented
57C2×#13063258C2211yescharacteristic, complemented
58C2×#13063256C2211yescharacteristic, complemented
59C2×#13063247C2211yescharacteristic
60C2×#13063247C2211yescharacteristic
61C2×#13063245C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×#13063245C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic, complemented
65#14582864C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#485C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—42no—
80C2×#10621902—42no—
81C2×#10621902C2314yescomplemented
82C2×#10621898—42no—
83C2×#10621898—42no—
84C2×#10621898D414yes—
85C2×#10621898C2314yes—
86C22×Dic86D411yescharacteristic
87C22×D172—21no—
88C22×D172—21no—
89C22×D172—22no—
90C22×D172—21no—
91C22×D172—21no—
92C22×D172—21no—
93C22×D172—21no—
94C22×D172—21no—
95C22×D172—42no—
96C22×D172—42no—
97C22×D172D411yescharacteristic
98C22×D172C2311yescharacteristic
99C22×D172C2311yescharacteristic
100C22×D172C2311yescharacteristic
101C22×D172C2314yes—
102C22×C22⋊D43—21no—
103C22×C22⋊D43D411yescharacteristic
104C22×C22⋊D43D411yescharacteristic
105C22×C4×D43—21no—
106C22×C4×D43—21no—
107C22×C4×D43C2311yescharacteristic
108C22×C4×D43C2311yescharacteristic
109C2×#10621884—42no—
110C2×#10621884—42no—
111C2×#10621884C2314yes—
112C2×#10621884C2314yes—
113C2×D344—42no—
114C2×D344—42no—
115C2×D344C2314yes—
116C2×D344C2314yes—
117C2×#10621872—42no—
118C2×#10621872C2314yescomplemented
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2311yescharacteristic
121C2×C8×D43—42no—
122C2×C8×D43C2314yescomplemented
123#13063322—28no—
124#13063313—28no—
125#13063303—28no—
126#13063301—22no—
127#13063301C2314yescomplemented
128#13063300—28no—
129#13063300—22no—
130#13063300—22no—
131#13063300—22no—
132#13063300—22no—
133#13063300—22no—
134#13063300C2314yes—
135#13063300C2314yes—
136#13063300C2314yes—
137#13063300C2314yes—
138#13063300C2314yescomplemented
139#13063299—22no—
140#13063299C2314yes—
141#13063298—28no—
142#13063298—28no—
143#13063295—28no—
144#13063295—28no—
145C2×C4⋊Dic43C2311yescharacteristic
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—21no—
148C4⋊C4×D43—22no—
149C4⋊C4×D43C2314yescomplemented
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—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#13063247C2314yes—
160#13063247C2314yes—
161#13063245C2314yes—
162#13063245C2314yes—
163#13063245C2314yescomplemented
164#13063245C2314yescomplemented
165C22⋊(C43⋊C8)C2314yes—
166(C2×D43)⋊C8C2314yescomplemented
167(C2×D43)⋊C8C2314yescomplemented
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22⋊Q8×C43—22no—
173C22⋊Q8×C43C2314yes—
174#117×C43—22no—
175#117×C43C2314yes—
176C2×C4⋊C4×C43—21no—
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#103×C43C2314yescomplemented
186#103×C43C2314yescomplemented
187C22⋊C8×C43C2314yes—
188C24×C43C2×D411yescharacteristic
189C23×D43—21no—
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×Q8×C43—21no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43C2412yes—
202C22×C4×C43—22no—
203C22×C4×C43—22no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—24no—
213C2×C22⋊D43—42no—
214C2×C22⋊D43—42no—
215C2×C22⋊D43—82no—
216C2×C22⋊D43C2×D414yes—
217C2×C22⋊D43C2×D414yes—
218C22×Dic43—21no—
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221#10621902—44no—
222#10621902—44no—
223#10621902—48no—
224#10621898—48no—
225#10621898—44no—
226#10621898—44no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—24no—
232C2×D172—24no—
233C2×D172—24no—
234C2×D172—24no—
235C2×D172—24no—
236C2×D172—24no—
237C2×D172—22no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172—42no—
244C2×D172—44no—
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×D172—82no—
254C2×D172C2×D414yes—
255C2×D172C2412yes—
256C2×D172C2412yes—
257C2×D172C2412yes—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—22no—
262C2×C4×D43—24no—
263C2×C4×D43—24no—
264C2×C4×D43—44no—
265C2×C4×D43—82no—
266C2×C4×D43C2×D412yes—
267C2×C4×D43C2×D412yes—
268C2×C4×D43C2412yes—
269C2×C4×D43C2412yes—
270C2×Dic86—42no—
271C2×Dic86C2×D414yes—
272C2×C8×C43—22no—
273C2×C8×C43—22no—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C4⋊C4×C43—24no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C2412yes—
281C4⋊C4×C43C2412yes—
282C4⋊C4×C43C2412yes—
283C22⋊C4×C43—24no—
284C22⋊C4×C43—24no—
285C42×C43—24no—
286#10621884—44no—
287#10621884—44no—
288(C2×D43)⋊C4—24no—
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—
294(C2×D43)⋊C4—24no—
295C4⋊Dic43—21no—
296C4⋊Dic43C2412yes—
297Dic43⋊C4—24no—
298Dic43⋊C4—24no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—22no—
301C2×C43⋊C8C2412yes—
302C2×C43⋊C8C2412yes—
303D344—44no—
304D344—44no—
305#10621872—44no—
306C8×D43—44no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43C22×D412yes—
311C23×C43C22×D411yescharacteristic
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—48no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—42no—
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—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—42no—
339C2×C4×C43—22no—
340C2×C4×C43—24no—
341C2×C4×C43—22no—
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×C43—42no—
351C2×C4×C43C22×D412yes—
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43H(5,𝔽2)12yes—
354C2×C4×C43H(5,𝔽2)12yes—
355C2×C4×C43C2511yescharacteristic
356C22⋊D43—44no—
357C22⋊D43—44no—
358C22⋊D43—84no—
359C2×Dic43—22no—
360C2×Dic43—22no—
361C2×Dic43—22no—
362C2×Dic43—42no—
363C2×Dic43C22×D412yes—
364C2×Dic43C22×D412yes—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172—22no—
371D172—44no—
372D172—48no—
373D172—48no—
374D172—42no—
375D172—42no—
376D172—42no—
377D172—84no—
378D172—84no—
379D172—84no—
380D172—84no—
381D172—84no—
382C4×D43—24no—
383C4×D43—24no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—22no—
387C4×D43—22no—
388C4×D43—48no—
389C4×D43—84no—
390Dic86—44no—
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#53412yes—
401C22×C43#57612yes—
402C22×C43#57712yes—
403C22×C43C23×D411yescharacteristic
404C2×D43—22no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—44no—
411C2×D43—44no—
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—42no—
427C4×C43—42no—
428C4×C43—42no—
429C4×C43—42no—
430C4×C43#53412yes—
431C4×C43C2×H(5,𝔽2)11yescharacteristic
432C4×C43C2×H(5,𝔽2)11yescharacteristic
433Dic43—22no—
434Dic43—22no—
435Dic43—42no—
436C2×#537—431no—
437C2×#535—431no—
438#3198—4316no—
439C2×#481—431no—
440C2×#485D4311yescharacteristic, complemented
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×#408—431no—
452C2×C43—42no—
453C2×C43#319814yescomplemented
454C2×C43C2×#53411yescharacteristic
455C2×C43C2×#57611yescharacteristic
456C2×C43C2×#57711yescharacteristic
457D43—42no—
458D43—42no—
459D43—82no—
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—861no—
479C2×C22⋊Q8C2×D4311yescharacteristic
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×#117C2×D4311yescharacteristic
492C22×C4⋊C4—431no—
493#485C2×D4318yescomplemented
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×#107C2×D4311yescharacteristic, complemented
507C2×#106—431no—
508C2×#106C2×D4311yescharacteristic, complemented
509C2×#103C2×D4311yescharacteristic, complemented
510C2×#103C2×D4311yescharacteristic, complemented
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102—431no—
515C2×#102—431no—
516C2×#102—431no—
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×Q8C22×D4311yescharacteristic
534C22×D4—431no—
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—861no—
549C22×D4—862no—
550C22×D4—1722no—
551C22×D4—1722no—
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—22no—
576C22⋊Q8—434no—
577C22⋊Q8—868no—
578C22⋊Q8—862no—
579C22⋊Q8C22×D4314yes—
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—862no—
589#121—862no—
590#121—862no—
591#121—862no—
592#121—862no—
593#121—868no—
594#121—862no—
595#120—868no—
596#120—868no—
597#117—22no—
598#117C22×D4314yes—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—434no—
602C2×C4⋊C4—862no—
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#103C22×D4314yescomplemented
623#103C22×D4314yescomplemented
624#102—434no—
625#102—434no—
626#102—434no—
627#102—434no—
628#102—434no—
629#102—434no—
630C22⋊C8—434no—
631C22⋊C8—434no—
632C22⋊C8—434no—
633C22⋊C8C22×D4314yes—
634C24—431no—
635C24—431no—
636C24—864no—
637C24—861no—
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—21no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—434no—
654C2×Q8—1722no—
655C2×Q8C23×D4312yes—
656C2×D4—434no—
657C2×D4—434no—
658C2×D4—434no—
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—1722no—
688C2×D4—1724no—
689C2×D4—1728no—
690C2×D4—1724no—
691C2×D4—1722no—
692C2×D4—1722no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—431no—
700C22×C4—431no—
701C22×C4—432no—
702C22×C4—432no—
703C22×C4—432no—
704C22×C4—432no—
705C22×C4—864no—
706C22×C4—864no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—862no—
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—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—432no—
737C4⋊C4—864no—
738C4⋊C4—864no—
739C4⋊C4—861no—
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—432no—
757C23—432no—
758C23—862no—
759C23—862no—
760C23—862no—
761C23—862no—
762C23—862no—
763C23—862no—
764C23—862no—
765C23—862no—
766C23—862no—
767C23—3444no—
768C23—3444no—
769C23—34416no—
770C23—1728no—
771C23—1722no—
772C23—1722no—
773C23—1722no—
774C23—1722no—
775C23—1722no—
776C23—1722no—
777C23—1722no—
778C23—1722no—
779C23—1722no—
780C23C2×D4×D4312yes—
781C23C2×D4×D4311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—1724no—
786D4—862no—
787D4—862no—
788D4—862no—
789D4—862no—
790D4—862no—
791D4—862no—
792D4—3444no—
793D4—3444no—
794D4—3444no—
795D4—3444no—
796D4—3444no—
797D4—3444no—
798D4—1724no—
799D4—1728no—
800D4—1728no—
801D4—1724no—
802D4—1724no—
803D4—1722no—
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—22no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—432no—
819C2×C4—432no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—864no—
823C2×C4—864no—
824C2×C4—862no—
825C2×C4—862no—
826C2×C4—862no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—3444no—
830C2×C4—1728no—
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—862no—
846C22—862no—
847C22—862no—
848C22—862no—
849C22—862no—
850C22—862no—
851C22—34416no—
852C22—3444no—
853C22—3444no—
854C22—3444no—
855C22—1722no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22—1722no—
860C22—1722no—
861C22—1722no—
862C22—1722no—
863C22—1722no—
864C22—1724no—
865C22—1724no—
866C22#1458346012yes—
867C22#1458370112yes—
868C22#1458370812yes—
869C22C22×D4×D4311yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—862no—
876C4—862no—
877C4—1722no—
878C4#1458346012yes—
879C4C2×#1306337111yescharacteristic
880C4C2×#1306337111yescharacteristic
881C2—42no—
882C2—3442no—
883C2—3442no—
884C2—3442no—
885C2—1722no—
886C2—1722no—
887C2#1914545314yesdirect product factor
888C2C2×#1458346011yescharacteristic
889C2C2×#1458370111yescharacteristic
890C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
hypercenterC2×#485D43
hypocenterC43C2×#3198
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
1. C2×#14583479C2semidirect
2. C2×#14583468C2semidirect
3. #19145453C2direct (N × H)
4. C2×#14583219C2semidirect
5. C2×#14583223C2semidirect
6. C2×#14583214C2semidirect
7. C2×#14583153C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583136C2semidirect
10. C2×#14583131C2semidirect
11. C2×#14583047C2semidirect
12. C2×#14583047C2semidirect
13. C2×#14583049C2semidirect
14. C2×#14583035C2semidirect
15. C2×#14582864C2semidirect
16. C2×C43×#485C2semidirect
17. C22×#10621902C22semidirect
24. C22×#10621872C22semidirect
25. C22×C8×D43C22semidirect
27. #14583479C22semidirect
29. #14583468C22semidirect
33. C2×#13063301C22semidirect
39. C2×#13063300C22semidirect
45. C2×C4⋊C4×D43C22semidirect
46. #14583223C22semidirect
47. #14583219C22semidirect
48. #14583214C22semidirect
49. #14583153C22semidirect
50. #14583148C22semidirect
51. #14583136C22semidirect
52. #14583131C22semidirect
53. #14583049C22semidirect
54. #14583047C22semidirect
55. #14583047C22semidirect
56. #14583035C22semidirect
57. C2×#13063258C22semidirect
58. C2×#13063256C22semidirect
63. C2×#13063245C22semidirect
64. C2×#13063245C22semidirect
65. #14582864C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
71. C43×#485C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×#103×C43C22semidirect
75. C2×#103×C43C22semidirect
81. C2×#10621902C23semidirect
118. C2×#10621872C23semidirect
122. C2×C8×D43C23semidirect
127. #13063301C23semidirect
138. #13063300C23semidirect
149. C4⋊C4×D43C23semidirect
157. #13063258C23semidirect
158. #13063256C23semidirect
163. #13063245C23semidirect
164. #13063245C23semidirect
166. (C2×D43)⋊C8C23semidirect
167. (C2×D43)⋊C8C23semidirect
183. #107×C43C23semidirect
184. #106×C43C23semidirect
185. #103×C43C23semidirect
186. #103×C43C23semidirect
440. C2×#485D43semidirect
453. C2×C43#3198semidirect
493. #485C2×D43semidirect
506. C2×#107C2×D43semidirect
508. C2×#106C2×D43semidirect
509. C2×#103C2×D43semidirect
510. C2×#103C2×D43semidirect
522. C43C2×#3198semidirect
619. #107C22×D43semidirect
621. #106C22×D43semidirect
622. #103C22×D43semidirect
623. #103C22×D43semidirect
887. C2#19145453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834792
C2×#145834682
#191454532
C2×#145832192
C2×#145832232
C2×#145832142
C2×#145831532
C2×#145831482
C2×#145831362
C2×#145831312
C2×#145830472
C2×#145830492
C2×#145830352
C2×#145828642
C2×C43×#4852
C2×#319843