Finite Group Databasebeta

← C2×#19146176 #25971654

Subgroups — C2×#19146176 #25971654

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×#13063355C211yesmaximal, characteristic, complemented
2C22×#13063345C211yesmaximal, characteristic, complemented
3C2×#14583558C211yesmaximal, characteristic, complemented
4#19146176C2116yesmaximal, direct product factor
5C2×#14583286C211yesmaximal, characteristic, complemented
6C2×#14583150C211yesmaximal, characteristic, complemented
7C2×#14583126C211yesmaximal, characteristic, complemented
8C2×#14583121C211yesmaximal, characteristic, complemented
9C2×#14583096C211yesmaximal, characteristic, complemented
10C2×#14583061C211yesmaximal, characteristic, complemented
11C2×#14583044C211yesmaximal, characteristic, complemented
12C2×#14583042C211yesmaximal, characteristic, complemented
13C2×#14583037C211yesmaximal, characteristic, complemented
14C2×#14583004C211yesmaximal, characteristic, complemented
15C2×#14582971C211yesmaximal, characteristic, complemented
16C2×C43×#550C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C23×Dic86C2211yescharacteristic
19C2×#13063355—28no—
20C2×#13063355C2218yescomplemented
21C2×#13063345—28no—
22C2×#13063345C2218yescomplemented
23C22×#10621885C2211yescharacteristic
24C22×#10621885C2211yescharacteristic
25C22×#10621883C2211yescharacteristic
26C22×#10621883C2211yescharacteristic
27C22×#10621883C2211yescharacteristic
28C22×#10621883C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621882C2211yescharacteristic
31C22×#10621882C2211yescharacteristic
32C22×#10621877C2211yescharacteristic
33C23×C43⋊C8C2211yescharacteristic
34#14583558—24no—
35#14583558C2218yescomplemented
36C2×#13063313C2211yescharacteristic
37C2×#13063311—21no—
38C2×#13063304C2211yescharacteristic
39C2×#13063303—21no—
40C2×#13063299C2211yescharacteristic
41C2×#13063297—21no—
42C2×C4×Dic86C2211yescharacteristic
43C2×(C22⋊D43)⋊C4—21no—
44#14583286C2218yescomplemented
45#14583150C2218yescomplemented
46#14583126C2218yescomplemented
47#14583121C2218yescomplemented
48#14583096C2218yescomplemented
49#14583061C2218yescomplemented
50#14583044C2218yescomplemented
51#14583042C2218yescomplemented
52#14583037C2218yescomplemented
53#14583004C2218yescomplemented
54#14582971C2218yescomplemented
55C2×#13063256C2211yescharacteristic
56C2×C4⋊(C43⋊C8)C2211yescharacteristic
57C2×#13063249C2211yescharacteristic
58C2×#13063248C2211yescharacteristic
59C2×#13063248C2211yescharacteristic
60C2×#13063246C2211yescharacteristic
61C2×#13063246C2211yescharacteristic
62C2×#13063245C2211yescharacteristic
63C2×C22⋊(C43⋊C8)C2211yescharacteristic
64C2×C22⋊(C43⋊C8)C2211yescharacteristic
65C2×#13063236C2211yescharacteristic
66C22×#41×C43C2211yescharacteristic
67C22×#41×C43C2211yescharacteristic
68C43×#550—24no—
69C43×#550C2218yescomplemented
70C2×#127×C43—21no—
71C2×#127×C43C2211yescharacteristic
72C2×#121×C43—21no—
73C2×#121×C43—21no—
74C2×#121×C43C2211yescharacteristic
75C2×#121×C43C2211yescharacteristic
76C2×C4×Q8×C43C2211yescharacteristic
77C2×C4×D4×C43—21no—
78C2×C4×D4×C43C2211yescharacteristic
79C2×#10621898—22no—
80C2×#10621898—24no—
81C2×#10621898—42no—
82C2×#10621898C2314yes—
83C22×Dic86—24no—
84C22×Dic86—22no—
85C22×Dic86—21no—
86C22×Dic86—42no—
87C22×Dic86C2311yescharacteristic
88C22×Dic86C2314yes—
89C22×Dic86C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95#13063355—232no—
96#13063345—232no—
97C2×#10621885—24no—
98C2×#10621885D418yescomplemented
99C2×#10621885C2314yes—
100C2×#10621885C2314yes—
101C2×#10621883—24no—
102C2×#10621883—24no—
103C2×#10621883—24no—
104C2×#10621883—42no—
105C2×#10621883C2314yes—
106C2×#10621883C2314yes—
107C2×#10621883C2314yes—
108C2×#10621883C2314yes—
109C2×#10621884—24no—
110C2×#10621884C2314yes—
111C2×#10621882—24no—
112C2×#10621882—42no—
113C2×#10621882C2314yes—
114C2×#10621882C2314yes—
115C2×#10621877—24no—
116C2×#10621877C2314yes—
117C22×C43⋊C8—24no—
118C22×C43⋊C8C2311yescharacteristic
119C22×C43⋊C8C2311yescharacteristic
120C22×C43⋊C8C2311yescharacteristic
121C22×C43⋊C8C2314yes—
122C22×C43⋊C8C2311yescharacteristic
123#13063313—22no—
124#13063313C2314yes—
125#13063311—28no—
126#13063304—22no—
127#13063304C2314yes—
128#13063303—28no—
129#13063299—22no—
130#13063299C2314yes—
131#13063297—28no—
132C4×Dic86—22no—
133C4×Dic86C2314yes—
134(C22⋊D43)⋊C4—28no—
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×C22⋊Dic43—21no—
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×C4×Dic43—21no—
143#13063256C2314yes—
144C4⋊(C43⋊C8)C2314yes—
145#13063249C2314yes—
146#13063248C2314yes—
147#13063248C2314yes—
148#13063246C2314yes—
149#13063246C2314yes—
150#13063245C2314yes—
151C22⋊(C43⋊C8)C2314yes—
152C22⋊(C43⋊C8)C2314yes—
153#13063236C2314yes—
154C2×#41×C43—22no—
155C2×#41×C43—22no—
156C2×#41×C43—24no—
157C2×#41×C43—24no—
158C2×#41×C43—42no—
159C2×#41×C43—42no—
160C2×#41×C43C2314yes—
161C2×#41×C43C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×D4×C43—21no—
164C22×D4×C43—21no—
165C22×D4×C43—21no—
166C22×D4×C43—21no—
167C22×D4×C43—21no—
168C22×D4×C43—21no—
169C22×D4×C43D411yescharacteristic
170C22×D4×C43C2311yescharacteristic
171C22×D4×C43C2311yescharacteristic
172C23×C4×C43—21no—
173C23×C4×C43—21no—
174C23×C4×C43C2311yescharacteristic
175C23×C4×C43C2311yescharacteristic
176#127×C43—28no—
177#127×C43—22no—
178#127×C43C2314yes—
179#121×C43—22no—
180#121×C43—22no—
181#121×C43—28no—
182#121×C43—28no—
183#121×C43C2314yes—
184#121×C43C2314yes—
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yes—
187C4×D4×C43—28no—
188C4×D4×C43D414yes—
189C4×D4×C43C2314yes—
190C2×C4⋊C4×C43—21no—
191C2×C4⋊C4×C43D411yescharacteristic
192C2×C4⋊C4×C43C2311yescharacteristic
193C2×C22⋊C4×C43—21no—
194C2×C22⋊C4×C43—21no—
195C2×C22⋊C4×C43D411yescharacteristic
196C2×C22⋊C4×C43D411yescharacteristic
197C2×C42×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C24×C43—21no—
200C24×C43—21no—
201C24×C43C2×D411yescharacteristic
202C24×C43C2×D411yescharacteristic
203C23×D43—21no—
204#41×C43—28no—
205#41×C43—28no—
206#41×C43—44no—
207#41×C43—44no—
208#41×C43—48no—
209#41×C43—48no—
210C2×Q8×C43—21no—
211C2×Q8×C43—22no—
212C2×Q8×C43C2×D414yes—
213C2×Q8×C43C2412yes—
214C2×D4×C43—24no—
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—24no—
218C2×D4×C43—24no—
219C2×D4×C43—24no—
220C2×D4×C43—24no—
221C2×D4×C43—24no—
222C2×D4×C43—22no—
223C2×D4×C43—22no—
224C2×D4×C43—22no—
225C2×D4×C43—22no—
226C2×D4×C43—42no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—44no—
230C2×D4×C43—82no—
231C2×D4×C43—82no—
232C2×D4×C43—82no—
233C2×D4×C43C2×D414yes—
234C2×D4×C43C2412yes—
235C2×D4×C43C2412yes—
236C22×C4×C43—22no—
237C22×C4×C43—22no—
238C22×C4×C43—22no—
239C22×C4×C43—22no—
240C22×C4×C43—24no—
241C22×C4×C43—24no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—44no—
245C22×C4×C43—44no—
246C22×C4×C43C2×D411yescharacteristic
247C22×C4×C43C2×D411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D412yes—
251C22×C4×C43C2×D412yes—
252C22×C4×C43C2412yes—
253C22×C4×C43C2412yes—
254C22×C4×C43C2411yescharacteristic
255C2×C22⋊D43—24no—
256C2×C22⋊D43—24no—
257C2×C22⋊D43—44no—
258C2×C22⋊D43—44no—
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—24no—
263C22×Dic43—44no—
264#10621898—28no—
265#10621898—44no—
266#10621898—48no—
267C2×D172—21no—
268C2×D172—22no—
269C2×D172—22no—
270C2×D172C2412yes—
271C2×C4×D43—24no—
272C2×C4×D43—44no—
273C2×Dic86—21no—
274C2×Dic86—22no—
275C2×Dic86—22no—
276C2×Dic86—22no—
277C2×Dic86—28no—
278C2×Dic86—24no—
279C2×Dic86—21no—
280C2×Dic86—44no—
281C2×Dic86—48no—
282C2×Dic86—44no—
283C2×Dic86C2×D414yes—
284C2×Dic86C2412yes—
285C2×Dic86C2412yes—
286C4⋊C4×C43—24no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43C2×D414yes—
289C4⋊C4×C43C2412yes—
290C22⋊C4×C43—24no—
291C22⋊C4×C43—24no—
292C22⋊C4×C43C2×D414yes—
293C22⋊C4×C43C2×D414yes—
294C42×C43—24no—
295C42×C43C2×D412yes—
296C42×C43C2412yes—
297C22⋊Dic43—24no—
298#10621885—28no—
299#10621885C2×D4116yescomplemented
300#10621884—28no—
301#10621883—28no—
302#10621883—28no—
303#10621883—28no—
304#10621883—44no—
305#10621882—28no—
306#10621882—44no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4—24no—
309(C2×D43)⋊C4—24no—
310C4⋊Dic43—21no—
311C4⋊Dic43C2412yes—
312Dic43⋊C4—24no—
313Dic43⋊C4—24no—
314C4×Dic43—24no—
315#10621877—28no—
316C2×C43⋊C8—22no—
317C2×C43⋊C8—22no—
318C2×C43⋊C8—22no—
319C2×C43⋊C8—28no—
320C2×C43⋊C8C2×D414yes—
321C2×C43⋊C8C2412yes—
322C2×C43⋊C8C2412yes—
323C2×C43⋊C8C2412yes—
324C2×C43⋊C8C2412yes—
325C23×C43—22no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43—42no—
337C23×C43—42no—
338C23×C43—42no—
339C23×C43C22×D412yes—
340C23×C43C22×D412yes—
341C23×C43C22×D411yescharacteristic
342C22×D43—22no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43—42no—
346Q8×C43—24no—
347Q8×C43—22no—
348Q8×C43C22×D414yes—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—22no—
352D4×C43—22no—
353D4×C43—44no—
354D4×C43—48no—
355D4×C43—48no—
356D4×C43—48no—
357D4×C43—42no—
358D4×C43—42no—
359D4×C43—84no—
360D4×C43—84no—
361D4×C43—84no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—24no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—22no—
368C2×C4×C43—24no—
369C2×C4×C43—24no—
370C2×C4×C43—22no—
371C2×C4×C43—22no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—48no—
376C2×C4×C43—48no—
377C2×C4×C43—42no—
378C2×C4×C43C22×D412yes—
379C2×C4×C43C22×D412yes—
380C2×C4×C43C22×D412yes—
381C2×C4×C43C22×D412yes—
382C2×C4×C43C22×D412yes—
383C2×C4×C43C22×D411yescharacteristic
384C2×C4×C43H(5,𝔽2)12yes—
385C2×C4×C43C2511yescharacteristic
386C22⋊D43—48no—
387C22⋊D43—48no—
388C2×Dic43—24no—
389C2×Dic43—22no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—48no—
393C2×Dic43—42no—
394C2×Dic43—42no—
395D172—22no—
396D172—22no—
397D172—42no—
398C4×D43—48no—
399Dic86—24no—
400Dic86—22no—
401Dic86—22no—
402Dic86—22no—
403Dic86—48no—
404Dic86—42no—
405Dic86C22×D414yes—
406C43⋊C8—22no—
407C43⋊C8—22no—
408C43⋊C8—22no—
409C43⋊C8C22×D414yes—
410C2×#3271—431nomaximal, Sylow
411C22×C43—22no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—22no—
416C22×C43—22no—
417C22×C43—44no—
418C22×C43—44no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—42no—
423C22×C43—42no—
424C22×C43—42no—
425C22×C43—84no—
426C22×C43—84no—
427C22×C43D4212yes—
428C22×C43#57512yes—
429C22×C43#57712yes—
430C22×C43C23×D411yescharacteristic
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—84no—
435C4×C43—22no—
436C4×C43—22no—
437C4×C43—24no—
438C4×C43—22no—
439C4×C43—22no—
440C4×C43—42no—
441C4×C43D4212yes—
442C4×C43C23×D411yescharacteristic
443C4×C43C2×H(5,𝔽2)11yescharacteristic
444Dic43—24no—
445Dic43—42no—
446Dic43—42no—
447C22×#137—431no—
448C22×#135—431no—
449C2×#550D4311yescharacteristic, complemented
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—42no—
465C2×C43—82no—
466C2×C43—82no—
467C2×C43#327114yescomplemented
468C2×C43C2×D4211yescharacteristic
469C2×C43C2×#57511yescharacteristic
470C2×C43C2×#57711yescharacteristic
471D43—82no—
472C22×#41—431no—
473C22×#41C2×D4311yescharacteristic
474C22×#41C2×D4311yescharacteristic
475C23×Q8—431no—
476C2×#137—438no—
477C2×#137—868no—
478C2×#135—438no—
479C2×#135—868no—
480C22×Q16—431no—
481C22×Q16—431no—
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16—431no—
487C22×D8—431no—
488C22×D8—431no—
489C22×M16—431no—
490C23×C8—431no—
491#550—24no—
492#550C2×D4318yescomplemented
493#548—438no—
494#548—864no—
495C2×#127—21no—
496C2×#127C2×D4311yescharacteristic
497C2×#124—431no—
498C2×#124—861no—
499C2×C22⋊Q8—431no—
500C2×C22⋊Q8—861no—
501C2×#121—21no—
502C2×#121—21no—
503C2×#121—431no—
504C2×#121—861no—
505C2×#121C2×D4311yescharacteristic
506C2×#121C2×D4311yescharacteristic
507C2×C4×Q8—431no—
508C2×C4×Q8C2×D4311yescharacteristic
509C2×C4×D4—21no—
510C2×C4×D4—861no—
511C2×C4×D4C2×D4311yescharacteristic
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—22no—
537C2×#41—24no—
538C2×#41—24no—
539C2×#41—42no—
540C2×#41—42no—
541C2×#41—434no—
542C2×#41—864no—
543C2×#41—862no—
544C2×#41—1722no—
545C2×#41C22×D4314yes—
546C2×#41C22×D4314yes—
547C22×Q8—431no—
548C22×Q8—431no—
549C22×Q8—434no—
550C22×Q8—864no—
551C22×Q8—861no—
552C22×Q8—862no—
553C22×Q8—1722no—
554C22×Q8C22×D4311yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—431no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4C22⋊D4311yescharacteristic
565C22×D4C22×D4311yescharacteristic
566C22×D4C22×D4311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4C22×D4311yescharacteristic
572C23×C4C22×D4311yescharacteristic
573#137—8632no—
574#135—8632no—
575C2×Q16—438no—
576C2×Q16—434no—
577C2×Q16—434no—
578C2×Q16—864no—
579C2×SD16—434no—
580C2×SD16—434no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—864no—
585C2×SD16—864no—
586C2×SD16—864no—
587C2×SD16—864no—
588C2×SD16—1722no—
589C2×D8—434no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8—1722no—
593C2×M16—434no—
594C2×M16—864no—
595C22×C8—431no—
596C22×C8—431no—
597C22×C8—434no—
598C22×C8—431no—
599C22×C8—431no—
600C22×C8—864no—
601#127—28no—
602#127—22no—
603#127C22×D4314yes—
604#124—434no—
605#124—868no—
606#124—862no—
607C22⋊Q8—434no—
608C22⋊Q8—862no—
609C22⋊Q8—868no—
610#121—22no—
611#121—22no—
612#121—28no—
613#121—28no—
614#121—434no—
615#121—868no—
616#121—862no—
617#121C22×D4314yes—
618#121C22×D4314yes—
619C4×Q8—22no—
620C4×Q8—434no—
621C4×Q8—862no—
622C4×Q8C22×D4314yes—
623C4×D4—28no—
624C4×D4—868no—
625C4×D4C22⋊D4314yes—
626C4×D4C22×D4314yes—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4C22⋊D4311yescharacteristic
632C2×C4⋊C4C22×D4311yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—861no—
636C2×C22⋊C4—861no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4C22⋊D4311yescharacteristic
640C2×C22⋊C4C22⋊D4311yescharacteristic
641C2×C42—21no—
642C2×C42—861no—
643C2×C42C22×D4311yescharacteristic
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—21no—
657C24—861no—
658C24C2×C22⋊D4311yescharacteristic
659C24C2×C22⋊D4311yescharacteristic
660#41—28no—
661#41—28no—
662#41—44no—
663#41—44no—
664#41—48no—
665#41—48no—
666#41—868no—
667#41—1724no—
668#41—1728no—
669C2×Q8—21no—
670C2×Q8—22no—
671C2×Q8—434no—
672C2×Q8—432no—
673C2×Q8—432no—
674C2×Q8—868no—
675C2×Q8—861no—
676C2×Q8—864no—
677C2×Q8—861no—
678C2×Q8—862no—
679C2×Q8—862no—
680C2×Q8—862no—
681C2×Q8—1724no—
682C2×Q8—1724no—
683C2×Q8—1728no—
684C2×Q8D4×D4314yes—
685C2×Q8C23×D4312yes—
686C2×D4—24no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—24no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—24no—
696C2×D4—22no—
697C2×D4—22no—
698C2×D4—42no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—82no—
703C2×D4—82no—
704C2×D4—82no—
705C2×D4—432no—
706C2×D4—864no—
707C2×D4—864no—
708C2×D4—862no—
709C2×D4—861no—
710C2×D4—862no—
711C2×D4—1724no—
712C2×D4—1724no—
713C2×D4C2×C22⋊D4314yes—
714C2×D4C23×D4312yes—
715C2×D4C23×D4312yes—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—861no—
727C22×C4—864no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—864no—
731C22×C4—1724no—
732C22×C4—1724no—
733C22×C4C2×C22⋊D4312yes—
734C22×C4C2×C22⋊D4312yes—
735C22×C4C2×C22⋊D4311yescharacteristic
736C22×C4C2×C22⋊D4311yescharacteristic
737C22×C4C2×C22⋊D4311yescharacteristic
738C22×C4C2×C22⋊D4311yescharacteristic
739C22×C4C23×D4312yes—
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—4316no—
743Q16—868no—
744SD16—868no—
745SD16—868no—
746SD16—868no—
747SD16—868no—
748SD16—1724no—
749D8—868no—
750D8—1724no—
751M16—868no—
752C2×C8—434no—
753C2×C8—432no—
754C2×C8—432no—
755C2×C8—432no—
756C2×C8—432no—
757C2×C8—868no—
758C2×C8—862no—
759C2×C8—862no—
760C2×C8—862no—
761C4⋊C4—24no—
762C4⋊C4—21no—
763C4⋊C4—432no—
764C4⋊C4—861no—
765C4⋊C4—864no—
766C4⋊C4—864no—
767C4⋊C4C2×C22⋊D4314yes—
768C4⋊C4C23×D4312yes—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—864no—
772C22⋊C4—864no—
773C22⋊C4—864no—
774C22⋊C4—864no—
775C22⋊C4C2×C22⋊D4314yes—
776C22⋊C4C2×C22⋊D4314yes—
777C42—24no—
778C42—864no—
779C42C2×C22⋊D4312yes—
780C42C23×D4312yes—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—862no—
796C23—1722no—
797C23—1722no—
798C23—1722no—
799C23C22×C22⋊D4312yes—
800C23C22×C22⋊D4312yes—
801C23C22×C22⋊D4311yescharacteristic
802Q8—22no—
803Q8—24no—
804Q8—434no—
805Q8—862no—
806Q8—864no—
807Q8—862no—
808Q8—862no—
809Q8—1728no—
810Q8—1722no—
811Q8C2×D4×D4314yes—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—44no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—42no—
821D4—42no—
822D4—84no—
823D4—84no—
824D4—84no—
825D4—862no—
826D4—862no—
827D4—1728no—
828D4—1728no—
829D4—1722no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—48no—
844C2×C4—48no—
845C2×C4—42no—
846C2×C4—862no—
847C2×C4—864no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—1728no—
851C2×C4—1728no—
852C2×C4—1722no—
853C2×C4—1722no—
854C2×C4C2×D4×D4312yes—
855C2×C4C22×C22⋊D4312yes—
856C2×C4C22×C22⋊D4312yes—
857C2×C4C22×C22⋊D4312yes—
858C2×C4C22×C22⋊D4312yes—
859C2×C4C22×C22⋊D4311yescharacteristic
860C2×C4#1306337012yes—
861C2×C4C24×D4311yescharacteristic
862C8—434no—
863C8—862no—
864C8—862no—
865C8—862no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—84no—
881C22—84no—
882C22—3444no—
883C22—1722no—
884C22—1722no—
885C22—1722no—
886C22D4×C22⋊D4312yes—
887C22#1458369712yes—
888C22#1458371012yes—
889C22C23×C22⋊D4311yescharacteristic
890C4—22no—
891C4—22no—
892C4—24no—
893C4—22no—
894C4—22no—
895C4—42no—
896C4—864no—
897C4—1722no—
898C4—1722no—
899C4D4×C22⋊D4312yes—
900C4C22×D4×D4311yescharacteristic
901C4C2×#1306337011yescharacteristic
902C2—42no—
903C2—42no—
904C2—82no—
905C2—82no—
906C2—3442no—
907C2#1914617614yesdirect product factor
908C2C2×D4×C22⋊D4311yescharacteristic
909C2C2×#1458369711yescharacteristic
910C2C2×#1458371011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#550C2
socleC23×C43C22×D4
hypercenterC2×#550D43
hypocenterC43C2×#3271
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#13063355C2semidirect
2. C22×#13063345C2semidirect
3. C2×#14583558C2semidirect
4. #19146176C2direct (N × H)
5. C2×#14583286C2semidirect
6. C2×#14583150C2semidirect
7. C2×#14583126C2semidirect
8. C2×#14583121C2semidirect
9. C2×#14583096C2semidirect
10. C2×#14583061C2semidirect
11. C2×#14583044C2semidirect
12. C2×#14583042C2semidirect
13. C2×#14583037C2semidirect
14. C2×#14583004C2semidirect
15. C2×#14582971C2semidirect
16. C2×C43×#550C2semidirect
20. C2×#13063355C22semidirect
22. C2×#13063345C22semidirect
35. #14583558C22semidirect
44. #14583286C22semidirect
45. #14583150C22semidirect
46. #14583126C22semidirect
47. #14583121C22semidirect
48. #14583096C22semidirect
49. #14583061C22semidirect
50. #14583044C22semidirect
51. #14583042C22semidirect
52. #14583037C22semidirect
53. #14583004C22semidirect
54. #14582971C22semidirect
69. C43×#550C22semidirect
98. C2×#10621885D4semidirect
299. #10621885C2×D4semidirect
449. C2×#550D43semidirect
467. C2×C43#3271semidirect
492. #550C2×D43semidirect
534. C43C2×#3271semidirect
907. C2#19146176direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633552
C22×#130633452
C2×#145835582
#191461762
C2×#145832862
C2×#145831502
C2×#145831262
C2×#145831212
C2×#145830962
C2×#145830612
C2×#145830442
C2×#145830422
C2×#145830372
C2×#145830042
C2×#145829712
C2×C43×#5502
C2×#327143