Finite Group Databasebeta

← C2×#19146174 #25971652

Subgroups — C2×#19146174 #25971652

Order 11008.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063348C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic, complemented
3C2×#14583560C211yesmaximal, characteristic, complemented
4#19146174C2116yesmaximal, direct product factor
5C2×#14583285C211yesmaximal, characteristic, complemented
6C2×#14583152C211yesmaximal, characteristic, complemented
7C2×#14583125C211yesmaximal, characteristic, complemented
8C2×#14583123C211yesmaximal, characteristic, complemented
9C2×#14583097C211yesmaximal, characteristic, complemented
10C2×#14583060C211yesmaximal, characteristic, complemented
11C2×#14583044C211yesmaximal, characteristic, complemented
12C2×#14583043C211yesmaximal, characteristic, complemented
13C2×#14583038C211yesmaximal, characteristic, complemented
14C2×#14583006C211yesmaximal, characteristic, complemented
15C2×#14582968C211yesmaximal, characteristic, complemented
16C22×#137×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic
19C2×#13063348—28no—
20C2×#13063348C2218yescomplemented
21C22×#10621884C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×#10621884C2211yescharacteristic
24C22×D344C2211yescharacteristic
25C22×#10621882C2211yescharacteristic
26C22×C8×D43C2211yescharacteristic
27#14583568—24no—
28#14583568C2218yescomplemented
29#14583560—24no—
30#14583560C2218yescomplemented
31C2×#13063321—21no—
32C2×#13063321C2211yescharacteristic
33C2×#13063314—21no—
34C2×#13063314C2211yescharacteristic
35C2×#13063301—21no—
36C2×#13063301C2211yescharacteristic
37C2×#13063299—21no—
38C2×#13063299—21no—
39C2×#13063299C2211yescharacteristic
40C2×#13063299C2211yescharacteristic
41C2×#13063296—21no—
42C2×#13063296C2211yescharacteristic
43C2×Q8×Dic43C2211yescharacteristic
44C2×Q8×Dic43C2211yescharacteristic
45C2×C4×C22⋊D43—21no—
46C2×C4×C22⋊D43—21no—
47C2×C4×C22⋊D43C2211yescharacteristic
48#14583285C2218yescomplemented
49#14583152C2218yescomplemented
50#14583125C2218yescomplemented
51#14583123C2218yescomplemented
52#14583097C2218yescomplemented
53#14583060C2218yescomplemented
54#14583044C2218yescomplemented
55#14583043C2218yescomplemented
56#14583038C2218yescomplemented
57#14583006C2218yescomplemented
58#14582968C2218yescomplemented
59C2×#13063257C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063247C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×C22⋊(C43⋊C8)C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#13063235C2211yescharacteristic
70C22×#41×C43C2211yescharacteristic
71C23×Q8×C43C2211yescharacteristic
72C2×#137×C43—28no—
73C2×#137×C43C2218yescomplemented
74C22×Q16×C43C2211yescharacteristic
75C22×Q16×C43C2211yescharacteristic
76C22×SD16×C43C2211yescharacteristic
77C22×SD16×C43C2211yescharacteristic
78C22×M16×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—24no—
83C2×#10621902—42no—
84C2×#10621902—42no—
85C2×#10621902C2314yes—
86C2×#10621902C2314yes—
87C22×D172—21no—
88C22×D172—21no—
89C22×D172C2311yescharacteristic
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×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43C2311yescharacteristic
100#13063348—232no—
101C2×#10621884—24no—
102C2×#10621884—24no—
103C2×#10621884—42no—
104C2×#10621884C2314yes—
105C2×#10621884C2314yes—
106C2×#10621884C2314yes—
107C2×D344—24no—
108C2×D344C2314yes—
109C2×#10621882—42no—
110C2×#10621882C2314yes—
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2311yescharacteristic
113C2×C8×D43—24no—
114C2×C8×D43C2314yes—
115#13063321—28no—
116#13063321—22no—
117#13063321C2314yes—
118#13063314—28no—
119#13063314—22no—
120#13063314C2314yes—
121#13063301—22no—
122#13063301—28no—
123#13063301C2314yes—
124#13063299—22no—
125#13063299—22no—
126#13063299—28no—
127#13063299—28no—
128#13063299C2314yes—
129#13063299C2314yes—
130#13063296—22no—
131#13063296—28no—
132#13063296C2314yes—
133Q8×Dic43—22no—
134Q8×Dic43—22no—
135Q8×Dic43C2314yes—
136Q8×Dic43C2314yes—
137C4×C22⋊D43—28no—
138C4×C22⋊D43—28no—
139C4×C22⋊D43D414yes—
140C4×C22⋊D43C2314yes—
141C2×C4⋊Dic43—21no—
142C2×C4⋊Dic43—21no—
143C2×C4⋊Dic43C2311yescharacteristic
144C2×C4⋊Dic43C2311yescharacteristic
145C2×Dic43⋊C4—21no—
146C2×Dic43⋊C4D411yescharacteristic
147C2×C22⋊Dic43—21no—
148C2×C22⋊Dic43D411yescharacteristic
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4D411yescharacteristic
155C2×C4×Dic43—21no—
156C2×C4×Dic43—21no—
157C2×C4×Dic43C2311yescharacteristic
158#13063257C2314yes—
159Dic43⋊C8C2314yes—
160#13063249C2314yes—
161#13063249C2314yes—
162#13063249C2314yes—
163#13063247C2314yes—
164#13063247C2314yes—
165#13063246C2314yes—
166C22⋊(C43⋊C8)C2314yes—
167(C2×D43)⋊C8C2314yes—
168#13063235C2314yes—
169C2×#41×C43—22no—
170C2×#41×C43—24no—
171C2×#41×C43—42no—
172C2×#41×C43C2314yes—
173C22×Q8×C43—22no—
174C22×Q8×C43—21no—
175C22×Q8×C43—24no—
176C22×Q8×C43—42no—
177C22×Q8×C43C2311yescharacteristic
178C22×Q8×C43C2314yes—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2311yescharacteristic
181C22×D4×C43—21no—
182C22×D4×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43—21no—
185C23×C4×C43C2311yescharacteristic
186#137×C43—232no—
187C2×Q16×C43—24no—
188C2×Q16×C43D418yescomplemented
189C2×Q16×C43C2314yes—
190C2×Q16×C43C2314yes—
191C2×SD16×C43—24no—
192C2×SD16×C43—24no—
193C2×SD16×C43C2314yes—
194C2×SD16×C43C2314yes—
195C2×M16×C43—24no—
196C2×M16×C43C2314yes—
197C22×C8×C43C2311yescharacteristic
198C22×C8×C43C2311yescharacteristic
199C24×C43—21no—
200C24×C43C2×D411yescharacteristic
201C23×D43—21no—
202C23×D43—21no—
203C23×D43C2×D411yescharacteristic
204#41×C43—28no—
205#41×C43—44no—
206#41×C43—48no—
207C2×Q8×C43—21no—
208C2×Q8×C43—21no—
209C2×Q8×C43—24no—
210C2×Q8×C43—21no—
211C2×Q8×C43—22no—
212C2×Q8×C43—22no—
213C2×Q8×C43—28no—
214C2×Q8×C43—22no—
215C2×Q8×C43—22no—
216C2×Q8×C43—44no—
217C2×Q8×C43—44no—
218C2×Q8×C43—48no—
219C2×Q8×C43C2×D414yes—
220C2×Q8×C43C2×D414yes—
221C2×Q8×C43C2412yes—
222C2×Q8×C43C2412yes—
223C2×Q8×C43C2412yes—
224C2×D4×C43—21no—
225C2×D4×C43—24no—
226C2×D4×C43—22no—
227C2×D4×C43—22no—
228C2×D4×C43—44no—
229C2×D4×C43C2412yes—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—24no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—24no—
237C22×C4×C43—44no—
238C22×C4×C43—44no—
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2×D412yes—
241C22×C4×C43C2412yes—
242C22×C4×C43C2411yescharacteristic
243C2×C22⋊D43—24no—
244C2×C22⋊D43—24no—
245C2×C22⋊D43—24no—
246C2×C22⋊D43—24no—
247C2×C22⋊D43—24no—
248C2×C22⋊D43—42no—
249C2×C22⋊D43—44no—
250C2×C22⋊D43—44no—
251C2×C22⋊D43—82no—
252C2×C22⋊D43—82no—
253C2×C22⋊D43—82no—
254C2×C22⋊D43C2×D414yes—
255C22×Dic43—21no—
256C22×Dic43—21no—
257C22×Dic43C2×D411yescharacteristic
258C22×Dic43C2×D411yescharacteristic
259C22×Dic43C2×D411yescharacteristic
260#10621902—28no—
261#10621902—28no—
262#10621902—44no—
263#10621902—44no—
264#10621902—48no—
265#10621902—48no—
266C2×D172—21no—
267C2×D172—21no—
268C2×D172—24no—
269C2×D172—24no—
270C2×D172—22no—
271C2×D172—22no—
272C2×D172—22no—
273C2×D172—22no—
274C2×D172—44no—
275C2×D172—44no—
276C2×D172C2412yes—
277C2×D172C2412yes—
278C2×C4×D43—22no—
279C2×C4×D43—22no—
280C2×C4×D43—24no—
281C2×C4×D43—24no—
282C2×C4×D43—44no—
283C2×C4×D43—44no—
284C2×C4×D43C2×D412yes—
285C2×C4×D43C2412yes—
286Q16×C43—28no—
287Q16×C43C2×D4116yescomplemented
288SD16×C43—28no—
289SD16×C43—28no—
290M16×C43—28no—
291C2×C8×C43—22no—
292C2×C8×C43C2×D414yes—
293C2×C8×C43C2412yes—
294C2×C8×C43C2412yes—
295C22⋊Dic43—24no—
296C22⋊Dic43C2×D414yes—
297#10621884—28no—
298#10621884—28no—
299#10621884—44no—
300#10621882—44no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4C2×D414yes—
307C4⋊Dic43—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43—24no—
310C4⋊Dic43—24no—
311C4⋊Dic43C2412yes—
312C4⋊Dic43C2412yes—
313Dic43⋊C4—24no—
314Dic43⋊C4C2×D414yes—
315C4×Dic43—24no—
316C4×Dic43—24no—
317C4×Dic43C2×D412yes—
318C4×Dic43C2412yes—
319C2×C43⋊C8—22no—
320C2×C43⋊C8—22no—
321C2×C43⋊C8C2412yes—
322C2×C43⋊C8C2412yes—
323D344—28no—
324C8×D43—28no—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—42no—
330C23×C43—42no—
331C23×C43—42no—
332C23×C43C22×D412yes—
333C23×C43C22×D411yescharacteristic
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43C22×D412yes—
346Q8×C43—24no—
347Q8×C43—24no—
348Q8×C43—22no—
349Q8×C43—22no—
350Q8×C43—22no—
351Q8×C43—22no—
352Q8×C43—48no—
353Q8×C43—42no—
354Q8×C43C22×D414yes—
355Q8×C43C22×D414yes—
356D4×C43—22no—
357D4×C43—22no—
358D4×C43—48no—
359D4×C43—42no—
360C2×C4×C43—24no—
361C2×C4×C43—24no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—24no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—22no—
369C2×C4×C43—48no—
370C2×C4×C43—48no—
371C2×C4×C43—42no—
372C2×C4×C43C22×D412yes—
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D412yes—
375C2×C4×C43H(5,𝔽2)12yes—
376C2×C4×C43C2511yescharacteristic
377C22⋊D43—44no—
378C22⋊D43—48no—
379C22⋊D43—48no—
380C22⋊D43—84no—
381C22⋊D43—84no—
382C22⋊D43—84no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—22no—
387C2×Dic43—22no—
388C2×Dic43—42no—
389C2×Dic43—42no—
390C2×Dic43C22×D412yes—
391C2×Dic43C22×D412yes—
392C2×Dic43C22×D412yes—
393D172—22no—
394D172—22no—
395D172—22no—
396D172—22no—
397D172—48no—
398D172—48no—
399D172—42no—
400D172—42no—
401C4×D43—24no—
402C4×D43—22no—
403C4×D43—22no—
404C4×D43—48no—
405C4×D43—48no—
406C8×C43—22no—
407C8×C43C22×D414yes—
408C43⋊C8—22no—
409C43⋊C8—22no—
410C2×#3271—431nomaximal, Sylow
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—44no—
415C22×C43—42no—
416C22×C43—42no—
417C22×C43—42no—
418C22×C43—84no—
419C22×C43D4212yes—
420C22×C43#57512yes—
421C22×C43#57712yes—
422C22×C43C23×D411yescharacteristic
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—22no—
426C2×D43—44no—
427C2×D43—42no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—42no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—84no—
434C2×D43—84no—
435C4×C43—24no—
436C4×C43—24no—
437C4×C43—22no—
438C4×C43—42no—
439C4×C43D4212yes—
440C4×C43C23×D411yescharacteristic
441C4×C43C2×H(5,𝔽2)11yescharacteristic
442Dic43—22no—
443Dic43—22no—
444Dic43—22no—
445Dic43—42no—
446Dic43—42no—
447C22×#137D4311yescharacteristic, complemented
448C22×#135—431no—
449C2×#550—431no—
450C2×#548—431no—
451#3271—4316no—
452C2×#496—431no—
453C2×#469—431no—
454C2×#465—431no—
455C2×#464—431no—
456C2×#460—431no—
457C2×#452—431no—
458C2×#449—431no—
459C2×#449—431no—
460C2×#448—431no—
461C2×#441—431no—
462C2×#435—431no—
463C2×C43—42no—
464C2×C43—82no—
465C2×C43#327114yescomplemented
466C2×C43C2×D4211yescharacteristic
467C2×C43C2×#57511yescharacteristic
468C2×C43C2×#57711yescharacteristic
469D43—42no—
470D43—82no—
471D43—82no—
472C22×#41—431no—
473C22×#41—431no—
474C22×#41C2×D4311yescharacteristic
475C23×Q8C2×D4311yescharacteristic
476C2×#137—28no—
477C2×#137C2×D4318yescomplemented
478C2×#135—438no—
479C2×#135—868no—
480C22×Q16C2×D4311yescharacteristic
481C22×Q16C2×D4311yescharacteristic
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16C2×D4311yescharacteristic
486C22×SD16C2×D4311yescharacteristic
487C22×D8—431no—
488C22×D8—431no—
489C22×M16C2×D4311yescharacteristic
490C23×C8—431no—
491#550—438no—
492#550—864no—
493#548—438no—
494#548—864no—
495C2×#127—431no—
496C2×#127—861no—
497C2×#124—431no—
498C2×#124—861no—
499C2×C22⋊Q8—431no—
500C2×C22⋊Q8—861no—
501C2×#121—431no—
502C2×#121—431no—
503C2×#121—431no—
504C2×#121—861no—
505C2×#121—861no—
506C2×#121—861no—
507C2×C4×Q8—431no—
508C2×C4×Q8—431no—
509C2×C4×D4—431no—
510C2×C4×D4—861no—
511C2×C4×D4—861no—
512#496—438no—
513#469—438no—
514#465—438no—
515#464—438no—
516#460—438no—
517#452—438no—
518#449—438no—
519#449—438no—
520#448—438no—
521#441—438no—
522#435—438no—
523C2×#106—431no—
524C2×C4⋊C8—431no—
525C2×#103—431no—
526C2×#103—431no—
527C2×#103—431no—
528C2×#102—431no—
529C2×#102—431no—
530C2×#102—431no—
531C2×C22⋊C8—431no—
532C2×C22⋊C8—431no—
533C2×#97—431no—
534C43C2×#327111yescharacteristic, complemented, Sylow
535C2×#41—22no—
536C2×#41—24no—
537C2×#41—42no—
538C2×#41—434no—
539C2×#41—434no—
540C2×#41—862no—
541C2×#41—862no—
542C2×#41—864no—
543C2×#41—864no—
544C2×#41—1722no—
545C2×#41—1722no—
546C2×#41C22×D4314yes—
547C22×Q8—21no—
548C22×Q8—22no—
549C22×Q8—24no—
550C22×Q8—42no—
551C22×Q8C22×D4311yescharacteristic
552C22×Q8C22×D4314yes—
553C22×Q8C22×D4311yescharacteristic
554C22×Q8C22×D4311yescharacteristic
555C22×D4—21no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—431no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4—861no—
566C22×D4C22×D4311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—431no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4C22×D4311yescharacteristic
573#137—232no—
574#135—8632no—
575C2×Q16—24no—
576C2×Q16C22⋊D4318yescomplemented
577C2×Q16C22×D4314yes—
578C2×Q16C22×D4314yes—
579C2×SD16—24no—
580C2×SD16—24no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—864no—
585C2×SD16—864no—
586C2×SD16—1722no—
587C2×SD16C22×D4314yes—
588C2×SD16C22×D4314yes—
589C2×D8—434no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8—1722no—
593C2×M16—24no—
594C2×M16C22×D4314yes—
595C22×C8—431no—
596C22×C8—431no—
597C22×C8—434no—
598C22×C8—864no—
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601#127—434no—
602#127—862no—
603#127—868no—
604#124—434no—
605#124—862no—
606#124—868no—
607C22⋊Q8—434no—
608C22⋊Q8—868no—
609C22⋊Q8—862no—
610#121—434no—
611#121—434no—
612#121—434no—
613#121—868no—
614#121—868no—
615#121—868no—
616#121—862no—
617#121—862no—
618#121—862no—
619C4×Q8—434no—
620C4×Q8—434no—
621C4×Q8—862no—
622C4×Q8—862no—
623C4×D4—434no—
624C4×D4—434no—
625C4×D4—868no—
626C4×D4—868no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C22⋊C4—431no—
634C2×C22⋊C4—431no—
635C2×C22⋊C4—861no—
636C2×C22⋊C4—861no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C42—431no—
642C2×C42—861no—
643C2×C42—861no—
644#106—434no—
645C4⋊C8—434no—
646#103—434no—
647#103—434no—
648#103—434no—
649#102—434no—
650#102—434no—
651#102—434no—
652C22⋊C8—434no—
653C22⋊C8—434no—
654#97—434no—
655C24—21no—
656C24—431no—
657C24—861no—
658C24—861no—
659C24D4×D4311yescharacteristic
660#41—28no—
661#41—44no—
662#41—48no—
663#41—868no—
664#41—868no—
665#41—1724no—
666#41—1724no—
667#41—1728no—
668#41—1728no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—24no—
672C2×Q8—21no—
673C2×Q8—22no—
674C2×Q8—22no—
675C2×Q8—28no—
676C2×Q8—22no—
677C2×Q8—22no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—48no—
681C2×Q8C2×C22⋊D4314yes—
682C2×Q8C2×C22⋊D4314yes—
683C2×Q8C23×D4312yes—
684C2×Q8C23×D4312yes—
685C2×Q8C23×D4312yes—
686C2×D4—24no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—44no—
691C2×D4—434no—
692C2×D4—432no—
693C2×D4—432no—
694C2×D4—864no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—864no—
699C2×D4—864no—
700C2×D4—864no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—862no—
704C2×D4—862no—
705C2×D4—862no—
706C2×D4—862no—
707C2×D4—3442no—
708C2×D4—3442no—
709C2×D4—3442no—
710C2×D4—1724no—
711C2×D4—1724no—
712C2×D4—1722no—
713C2×D4—1724no—
714C2×D4—1724no—
715C2×D4C23×D4312yes—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—432no—
729C22×C4—432no—
730C22×C4—864no—
731C22×C4—864no—
732C22×C4—862no—
733C22×C4—862no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4D4×D4312yes—
739C22×C4D4×D4311yescharacteristic
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—28no—
743Q16C2×C22⋊D43116yescomplemented
744SD16—28no—
745SD16—28no—
746SD16—868no—
747SD16—868no—
748SD16—1724no—
749D8—868no—
750D8—1724no—
751M16—28no—
752C2×C8—22no—
753C2×C8—432no—
754C2×C8—432no—
755C2×C8—862no—
756C2×C8—862no—
757C2×C8—868no—
758C2×C8C2×C22⋊D4314yes—
759C2×C8C23×D4312yes—
760C2×C8C23×D4312yes—
761C4⋊C4—434no—
762C4⋊C4—432no—
763C4⋊C4—432no—
764C4⋊C4—864no—
765C4⋊C4—864no—
766C4⋊C4—864no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C22⋊C4—434no—
770C22⋊C4—434no—
771C22⋊C4—864no—
772C22⋊C4—864no—
773C22⋊C4—864no—
774C22⋊C4—864no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C42—432no—
778C42—432no—
779C42—864no—
780C42—864no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—432no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—862no—
793C23—862no—
794C23—1722no—
795C23—1722no—
796C23—1722no—
797C23—1722no—
798C23—1722no—
799C23—1722no—
800C23C2×D4×D4312yes—
801C23C2×D4×D4311yescharacteristic
802Q8—22no—
803Q8—22no—
804Q8—24no—
805Q8—24no—
806Q8—22no—
807Q8—22no—
808Q8—48no—
809Q8—42no—
810Q8C22×C22⋊D4314yes—
811Q8C22×C22⋊D4314yes—
812D4—22no—
813D4—22no—
814D4—48no—
815D4—42no—
816D4—862no—
817D4—862no—
818D4—862no—
819D4—862no—
820D4—3444no—
821D4—3444no—
822D4—3444no—
823D4—1728no—
824D4—1728no—
825D4—1724no—
826D4—1728no—
827D4—1728no—
828D4—1722no—
829D4—1722no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—48no—
840C2×C4—48no—
841C2×C4—42no—
842C2×C4—432no—
843C2×C4—432no—
844C2×C4—432no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—864no—
851C2×C4—862no—
852C2×C4—862no—
853C2×C4—1728no—
854C2×C4—1728no—
855C2×C4—1722no—
856C2×C4—1722no—
857C2×C4C2×D4×D4312yes—
858C2×C4C2×D4×D4311yescharacteristic
859C2×C4C22×C22⋊D4312yes—
860C2×C4#1306337012yes—
861C2×C4C24×D4311yescharacteristic
862C8—22no—
863C8—862no—
864C8—862no—
865C8C22×C22⋊D4314yes—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—44no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—84no—
874C22—862no—
875C22—862no—
876C22—862no—
877C22—3444no—
878C22—3444no—
879C22—1722no—
880C22—1722no—
881C22—1722no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22—1724no—
886C22D4×C22⋊D4312yes—
887C22#1458369812yes—
888C22#1458370812yes—
889C22C22×D4×D4311yescharacteristic
890C4—22no—
891C4—24no—
892C4—24no—
893C4—42no—
894C4—862no—
895C4—862no—
896C4—862no—
897C4—1722no—
898C4—1722no—
899C4D4×C22⋊D4312yes—
900C4C23×C22⋊D4311yescharacteristic
901C4C2×#1306337011yescharacteristic
902C2—42no—
903C2—82no—
904C2—3442no—
905C2—3442no—
906C2—1722no—
907C2#1914617414yesdirect product factor
908C2C2×D4×C22⋊D4311yescharacteristic
909C2C2×#1458369811yescharacteristic
910C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#137×C43C2
socleC23×C43C22×D4
hypercenterC22×#137D43
hypocenterC43C2×#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#13063348C2semidirect
2. C2×#14583568C2semidirect
3. C2×#14583560C2semidirect
4. #19146174C2direct (N × H)
5. C2×#14583285C2semidirect
6. C2×#14583152C2semidirect
7. C2×#14583125C2semidirect
8. C2×#14583123C2semidirect
9. C2×#14583097C2semidirect
10. C2×#14583060C2semidirect
11. C2×#14583044C2semidirect
12. C2×#14583043C2semidirect
13. C2×#14583038C2semidirect
14. C2×#14583006C2semidirect
15. C2×#14582968C2semidirect
16. C22×#137×C43C2semidirect
20. C2×#13063348C22semidirect
28. #14583568C22semidirect
30. #14583560C22semidirect
48. #14583285C22semidirect
49. #14583152C22semidirect
50. #14583125C22semidirect
51. #14583123C22semidirect
52. #14583097C22semidirect
53. #14583060C22semidirect
54. #14583044C22semidirect
55. #14583043C22semidirect
56. #14583038C22semidirect
57. #14583006C22semidirect
58. #14582968C22semidirect
73. C2×#137×C43C22semidirect
188. C2×Q16×C43D4semidirect
287. Q16×C43C2×D4semidirect
447. C22×#137D43semidirect
465. C2×C43#3271semidirect
477. C2×#137C2×D43semidirect
534. C43C2×#3271semidirect
576. C2×Q16C22⋊D43semidirect
743. Q16C2×C22⋊D43semidirect
907. C2#19146174direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633482
C2×#145835682
C2×#145835602
#191461742
C2×#145832852
C2×#145831522
C2×#145831252
C2×#145831232
C2×#145830972
C2×#145830602
C2×#145830442
C2×#145830432
C2×#145830382
C2×#145830062
C2×#145829682
C22×#137×C432
C2×#327143