Finite Group Databasebeta

← C2×#19146319 #25971844

Subgroups — C2×#19146319 #25971844

Order 11008.

2858 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×#13063346C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic, complemented
3C2×#14583548C211yesmaximal, characteristic, complemented
4#19146319C2116yesmaximal, direct product factor
5C2×#14583270C211yesmaximal, characteristic, complemented
6C2×#14583128C211yesmaximal, characteristic, complemented
7C2×#14583125C211yesmaximal, characteristic, complemented
8C2×#14583107C211yesmaximal, characteristic, complemented
9C2×#14583092C211yesmaximal, characteristic, complemented
10C2×#14583061C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583041C211yesmaximal, characteristic, complemented
14C2×SD16×Dic43C211yesmaximal, characteristic, complemented
15C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
16C22×#135×C43C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C2×#13063346—28no—
20C2×#13063346C2218yescomplemented
21C22×#10621885C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621884C2211yescharacteristic
25C22×#10621882C2211yescharacteristic
26C22×C8×D43C2211yescharacteristic
27#14583568—24no—
28#14583568C2218yescomplemented
29#14583548—24no—
30#14583548C2218yescomplemented
31C2×#13063323C2211yescharacteristic
32C2×#13063321—21no—
33C2×#13063321C2211yescharacteristic
34C2×#13063308—21no—
35C2×#13063306—21no—
36C2×#13063304C2211yescharacteristic
37C2×#13063301C2211yescharacteristic
38C2×#13063299—21no—
39C2×#13063299C2211yescharacteristic
40C2×#13063297—21no—
41C2×#13063296—21no—
42C2×#13063296C2211yescharacteristic
43C2×Q8×Dic43C2211yescharacteristic
44C2×D4×Dic43C2211yescharacteristic
45C2×C4×C22⋊D43—21no—
46C2×C4×C22⋊D43C2211yescharacteristic
47C22×Dic43⋊C4—21no—
48#14583270C2218yescomplemented
49#14583128C2218yescomplemented
50#14583125C2218yescomplemented
51#14583107C2218yescomplemented
52#14583092C2218yescomplemented
53#14583061C2218yescomplemented
54#14583060C2218yescomplemented
55#14583044C2218yescomplemented
56#14583041C2218yescomplemented
57SD16×Dic43C2218yescomplemented
58C8×C22⋊D43C2218yescomplemented
59C2×#13063257C2211yescharacteristic
60C2×Dic43⋊C8C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×C22⋊(C43⋊C8)C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×C8×Dic43C2211yescharacteristic
70C22×#41×C43C2211yescharacteristic
71C22×#41×C43C2211yescharacteristic
72C2×#135×C43—28no—
73C2×#135×C43C2218yescomplemented
74C22×Q16×C43C2211yescharacteristic
75C22×SD16×C43C2211yescharacteristic
76C22×SD16×C43C2211yescharacteristic
77C22×D8×C43C2211yescharacteristic
78C23×C8×C43C2211yescharacteristic
79C2×#10621902—22no—
80C2×#10621902—24no—
81C2×#10621902—42no—
82C2×#10621902C2314yes—
83C2×#10621900—24no—
84C2×#10621900—22no—
85C2×#10621900—42no—
86C2×#10621900C2314yes—
87C22×Dic86C2311yescharacteristic
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C22×C22⋊D43D411yescharacteristic
96C23×Dic43—21no—
97C23×Dic43—21no—
98C22×C4×D43—21no—
99C22×C4×D43C2311yescharacteristic
100#13063346—232no—
101C2×#10621885—24no—
102C2×#10621885C2314yes—
103C2×#10621873—24no—
104C2×#10621873C2314yes—
105C2×#10621883—42no—
106C2×#10621883C2314yes—
107C2×#10621884—42no—
108C2×#10621884C2314yes—
109C2×#10621882—24no—
110C2×#10621882C2314yes—
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2311yescharacteristic
113C2×C8×D43—24no—
114C2×C8×D43C2314yes—
115#13063323—22no—
116#13063323C2314yes—
117#13063321—28no—
118#13063321—22no—
119#13063321C2314yes—
120#13063308—28no—
121#13063306—28no—
122#13063304—22no—
123#13063304C2314yes—
124#13063301—22no—
125#13063301C2314yes—
126#13063299—22no—
127#13063299—28no—
128#13063299C2314yes—
129#13063297—28no—
130#13063296—22no—
131#13063296—28no—
132#13063296C2314yes—
133Q8×Dic43—22no—
134Q8×Dic43C2314yes—
135D4×Dic43—22no—
136D4×Dic43C2314yes—
137C4×C22⋊D43—28no—
138C4×C22⋊D43D414yes—
139C4×C22⋊D43C2314yes—
140C2×C4⋊Dic43—21no—
141C2×C4⋊Dic43C2311yescharacteristic
142C2×C4⋊Dic43C2311yescharacteristic
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊C4—21no—
146C2×Dic43⋊C4—21no—
147C2×Dic43⋊C4—28no—
148C2×Dic43⋊C4D411yescharacteristic
149C2×C22⋊Dic43—21no—
150C2×C22⋊Dic43—21no—
151C2×C22⋊Dic43—21no—
152C2×C22⋊Dic43D411yescharacteristic
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4D411yescharacteristic
156C2×C4×Dic43—21no—
157C2×C4×Dic43C2311yescharacteristic
158#13063257C2314yes—
159Dic43⋊C8C2314yes—
160#13063250C2314yes—
161#13063249C2314yes—
162#13063249C2314yes—
163#13063247C2314yes—
164#13063246C2314yes—
165#13063246C2314yes—
166C22⋊(C43⋊C8)C2314yes—
167(C2×D43)⋊C8C2314yes—
168C8×Dic43C2314yes—
169C2×#41×C43—22no—
170C2×#41×C43—22no—
171C2×#41×C43—24no—
172C2×#41×C43—24no—
173C2×#41×C43—42no—
174C2×#41×C43—42no—
175C2×#41×C43C2314yes—
176C2×#41×C43C2314yes—
177C22×Q8×C43C2311yescharacteristic
178C22×Q8×C43C2311yescharacteristic
179C22×D4×C43—21no—
180C22×D4×C43—21no—
181C22×D4×C43C2311yescharacteristic
182C22×D4×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43—21no—
185C23×C4×C43C2311yescharacteristic
186#135×C43—232no—
187C2×Q16×C43—24no—
188C2×Q16×C43C2314yes—
189C2×SD16×C43—24no—
190C2×SD16×C43D418yescomplemented
191C2×SD16×C43C2314yes—
192C2×SD16×C43C2314yes—
193C2×D8×C43—24no—
194C2×D8×C43C2314yes—
195C22×C8×C43—24no—
196C22×C8×C43C2311yescharacteristic
197C22×C8×C43C2314yes—
198C22×C8×C43C2311yescharacteristic
199C24×C43—21no—
200C24×C43—21no—
201C24×C43C2×D411yescharacteristic
202C23×D43—21no—
203C23×D43C2×D411yescharacteristic
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—21no—
212C2×Q8×C43—22no—
213C2×Q8×C43—22no—
214C2×Q8×C43—22no—
215C2×Q8×C43C2×D414yes—
216C2×Q8×C43C2412yes—
217C2×Q8×C43C2412yes—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—22no—
221C2×D4×C43—24no—
222C2×D4×C43—24no—
223C2×D4×C43—22no—
224C2×D4×C43—22no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43C2×D414yes—
228C2×D4×C43C2412yes—
229C2×D4×C43C2412yes—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—24no—
233C22×C4×C43—24no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—44no—
237C22×C4×C43—44no—
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D412yes—
240C22×C4×C43C2412yes—
241C22×C4×C43C2411yescharacteristic
242C2×C22⋊D43—24no—
243C2×C22⋊D43—24no—
244C2×C22⋊D43—24no—
245C2×C22⋊D43—24no—
246C2×C22⋊D43—24no—
247C2×C22⋊D43—24no—
248C2×C22⋊D43—44no—
249C2×C22⋊D43—44no—
250C2×C22⋊D43—82no—
251C2×C22⋊D43—82no—
252C2×C22⋊D43—82no—
253C2×C22⋊D43C2×D414yes—
254C22×Dic43—24no—
255C22×Dic43—24no—
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—44no—
260C22×Dic43—44no—
261C22×Dic43C2×D411yescharacteristic
262C22×Dic43C2×D411yescharacteristic
263C22×Dic43C2×D411yescharacteristic
264#10621902—28no—
265#10621902—44no—
266#10621902—48no—
267#10621900—28no—
268#10621900—44no—
269#10621900—48no—
270C2×D172—21no—
271C2×D172—24no—
272C2×D172—22no—
273C2×D172—22no—
274C2×D172—44no—
275C2×D172C2412yes—
276C2×C4×D43—22no—
277C2×C4×D43—22no—
278C2×C4×D43—24no—
279C2×C4×D43—44no—
280C2×C4×D43C2×D412yes—
281C2×C4×D43C2412yes—
282C2×Dic86—22no—
283C2×Dic86—22no—
284C2×Dic86—21no—
285C2×Dic86C2412yes—
286Q16×C43—28no—
287SD16×C43—28no—
288SD16×C43C2×D4116yescomplemented
289D8×C43—28no—
290C2×C8×C43—22no—
291C2×C8×C43—28no—
292C2×C8×C43C2×D414yes—
293C2×C8×C43C2412yes—
294C2×C8×C43C2412yes—
295C22⋊Dic43—24no—
296C22⋊Dic43—24no—
297C22⋊Dic43—24no—
298C22⋊Dic43C2×D414yes—
299#10621885—28no—
300#10621884—44no—
301#10621883—44no—
302#10621882—28no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4C2×D414yes—
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308C4⋊Dic43—24no—
309C4⋊Dic43C2412yes—
310C4⋊Dic43C2412yes—
311Dic43⋊C4—24no—
312Dic43⋊C4—24no—
313Dic43⋊C4—24no—
314Dic43⋊C4—24no—
315Dic43⋊C4C2×D414yes—
316C4×Dic43—24no—
317C4×Dic43C2×D412yes—
318C4×Dic43C2412yes—
319C2×C43⋊C8—22no—
320C2×C43⋊C8—22no—
321C2×C43⋊C8C2412yes—
322C2×C43⋊C8C2412yes—
323#10621873—28no—
324C8×D43—28no—
325C23×C43—24no—
326C23×C43—22no—
327C23×C43—22no—
328C23×C43—22no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—42no—
332C23×C43—42no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43—42no—
336C23×C43C22×D412yes—
337C23×C43C22×D411yescharacteristic
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43C22×D412yes—
346Q8×C43—24no—
347Q8×C43—22no—
348Q8×C43—22no—
349Q8×C43—22no—
350Q8×C43—42no—
351Q8×C43C22×D414yes—
352D4×C43—24no—
353D4×C43—22no—
354D4×C43—22no—
355D4×C43—22no—
356D4×C43—48no—
357D4×C43—48no—
358D4×C43—42no—
359D4×C43C22×D414yes—
360C2×C4×C43—24no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—24no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—48no—
368C2×C4×C43—48no—
369C2×C4×C43—42no—
370C2×C4×C43C22×D412yes—
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43C22×D412yes—
373C2×C4×C43H(5,𝔽2)12yes—
374C2×C4×C43C2511yescharacteristic
375C22⋊D43—28no—
376C22⋊D43—48no—
377C22⋊D43—48no—
378C22⋊D43—84no—
379C22⋊D43—84no—
380C22⋊D43—84no—
381C2×Dic43—22no—
382C2×Dic43—22no—
383C2×Dic43—22no—
384C2×Dic43—22no—
385C2×Dic43—22no—
386C2×Dic43—48no—
387C2×Dic43—42no—
388C2×Dic43—42no—
389C2×Dic43—42no—
390C2×Dic43—48no—
391C2×Dic43#13514yescomplemented
392C2×Dic43C22×D412yes—
393C2×Dic43C22×D412yes—
394C2×Dic43C22×D412yes—
395D172—22no—
396D172—22no—
397D172—48no—
398D172—42no—
399C4×D43—24no—
400C4×D43—22no—
401C4×D43—22no—
402C4×D43—48no—
403Dic86—22no—
404Dic86—22no—
405Dic86—42no—
406C8×C43—22no—
407C8×C43C22×D414yes—
408C43⋊C8—22no—
409C43⋊C8—22no—
410C2×#3284—431nomaximal, Sylow
411C22×C43—24no—
412C22×C43—22no—
413C22×C43—22no—
414C22×C43—22no—
415C22×C43—44no—
416C22×C43—48no—
417C22×C43—42no—
418C22×C43—42no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—42no—
422C22×C43—84no—
423C22×C43D4212yes—
424C22×C43C2×#13512yes—
425C22×C43#57712yes—
426C22×C43C23×D411yescharacteristic
427C2×D43—22no—
428C2×D43—22no—
429C2×D43—22no—
430C2×D43—44no—
431C2×D43—42no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—84no—
435C4×C43—24no—
436C4×C43—22no—
437C4×C43—42no—
438C4×C43D4212yes—
439C4×C43C23×D411yescharacteristic
440C4×C43C2×H(5,𝔽2)11yescharacteristic
441Dic43—22no—
442Dic43—22no—
443Dic43—42no—
444Dic43—42no—
445Dic43—42no—
446Dic43C2×#13514yescomplemented
447C22×#135—431no—
448C22×#135D4311yescharacteristic, complemented
449C2×#550—431no—
450C2×#547—431no—
451#3284—4316no—
452C2×#492—431no—
453C2×#465—431no—
454C2×#465—431no—
455C2×#462—431no—
456C2×#459—431no—
457C2×#452—431no—
458C2×#452—431no—
459C2×#449—431no—
460C2×#449—431no—
461C2×C4×SD16—431no—
462C2×C8×D4—431no—
463C2×C43—42no—
464C2×C43—44no—
465C2×C43—82no—
466C2×C43#328414yescomplemented
467C2×C43C2×D4211yescharacteristic
468C2×C43C22×#13511yescharacteristic
469C2×C43C2×#57711yescharacteristic
470D43—42no—
471D43—82no—
472C22×#41—431no—
473C22×#41—431no—
474C22×#41C2×D4311yescharacteristic
475C22×#41C2×D4311yescharacteristic
476C2×#135—28no—
477C2×#135—438no—
478C2×#135—868no—
479C2×#135C2×D4318yescomplemented
480C22×Q16—431no—
481C22×Q16C2×D4311yescharacteristic
482C22×SD16—431no—
483C22×SD16—431no—
484C22×SD16—431no—
485C22×SD16C2×D4311yescharacteristic
486C22×SD16C2×D4311yescharacteristic
487C22×D8—431no—
488C22×D8C2×D4311yescharacteristic
489C23×C8—431no—
490C23×C8C2×D4311yescharacteristic
491#550—438no—
492#550—864no—
493#547—438no—
494#547—864no—
495C2×C4⋊Q8—431no—
496C2×#127—431no—
497C2×#127—861no—
498C2×#123—861no—
499C2×#123—861no—
500C2×C22⋊Q8—431no—
501C2×C22⋊Q8—431no—
502C2×#121—431no—
503C2×#121—431no—
504C2×#121—861no—
505C2×#121—861no—
506C2×#121—861no—
507C2×C4×Q8—431no—
508C2×C4×D4—431no—
509C2×C4×D4—431no—
510C2×C4×D4—861no—
511C22×C4⋊C4—861no—
512#492—438no—
513#465—438no—
514#465—438no—
515#462—438no—
516#459—438no—
517#452—438no—
518#452—438no—
519#449—438no—
520#449—438no—
521C4×SD16—438no—
522C8×D4—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×C4×C8—431no—
534C43C2×#328411yescharacteristic, 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—434no—
543C2×#41—862no—
544C2×#41—862no—
545C2×#41—864no—
546C2×#41—864no—
547C2×#41—1722no—
548C2×#41—1722no—
549C2×#41C22×D4314yes—
550C2×#41C22×D4314yes—
551C22×Q8—431no—
552C22×Q8C22×D4311yescharacteristic
553C22×Q8C22×D4311yescharacteristic
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—861no—
559C22×D4—861no—
560C22×D4—861no—
561C22×D4—861no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4C22×D4311yescharacteristic
565C22×D4C22×D4311yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4—431no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4C22×D4311yescharacteristic
573#135—232no—
574#135—8632no—
575C2×Q16—24no—
576C2×Q16—434no—
577C2×Q16—864no—
578C2×Q16C22×D4314yes—
579C2×SD16—24no—
580C2×SD16—434no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—864no—
584C2×SD16—1722no—
585C2×SD16—1722no—
586C2×SD16C22⋊D4318yescomplemented
587C2×SD16C22×D4314yes—
588C2×SD16C22×D4314yes—
589C2×D8—24no—
590C2×D8—434no—
591C2×D8—864no—
592C2×D8C22×D4314yes—
593C22×C8—24no—
594C22×C8—431no—
595C22×C8—431no—
596C22×C8—434no—
597C22×C8—864no—
598C22×C8C22×D4311yescharacteristic
599C22×C8C22×D4314yes—
600C22×C8C22×D4311yescharacteristic
601C4⋊Q8—434no—
602C4⋊Q8—862no—
603#127—434no—
604#127—862no—
605#127—868no—
606#123—868no—
607#123—868no—
608C22⋊Q8—434no—
609C22⋊Q8—434no—
610C22⋊Q8—862no—
611C22⋊Q8—862no—
612#121—434no—
613#121—434no—
614#121—868no—
615#121—868no—
616#121—862no—
617#121—868no—
618#121—862no—
619C4×Q8—434no—
620C4×Q8—862no—
621C4×D4—434no—
622C4×D4—434no—
623C4×D4—434no—
624C4×D4—862no—
625C4×D4—868no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—868no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4—861no—
635C2×C22⋊C4—431no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—861no—
638C2×C22⋊C4—861no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C42—431no—
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—
654C4×C8—434no—
655C24—21no—
656C24—21no—
657C24—431no—
658C24—861no—
659C24D4×D4311yescharacteristic
660#41—28no—
661#41—28no—
662#41—44no—
663#41—44no—
664#41—48no—
665#41—48no—
666#41—868no—
667#41—868no—
668#41—1724no—
669#41—1728no—
670#41—1724no—
671#41—1728no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—22no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8—432no—
678C2×Q8—861no—
679C2×Q8—862no—
680C2×Q8—862no—
681C2×Q8C2×C22⋊D4314yes—
682C2×Q8C23×D4312yes—
683C2×Q8C23×D4312yes—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—434no—
694C2×D4—432no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—864no—
699C2×D4—864no—
700C2×D4—864no—
701C2×D4—864no—
702C2×D4—861no—
703C2×D4—862no—
704C2×D4—862no—
705C2×D4—3442no—
706C2×D4—3442no—
707C2×D4—3442no—
708C2×D4—1724no—
709C2×D4—1724no—
710C2×D4—1724no—
711C2×D4C2×C22⋊D4314yes—
712C2×D4C23×D4312yes—
713C2×D4C23×D4312yes—
714C22×C4—21no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—432no—
726C22×C4—432no—
727C22×C4—864no—
728C22×C4—864no—
729C22×C4—864no—
730C22×C4—862no—
731C22×C4—862no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—1724no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4D4×D4312yes—
739C22×C4D4×D4311yescharacteristic
740C22×C4C23×D4312yes—
741C22×C4C23×D4311yescharacteristic
742Q16—28no—
743Q16—868no—
744SD16—28no—
745SD16—868no—
746SD16—1724no—
747SD16—1724no—
748SD16C2×C22⋊D43116yescomplemented
749D8—28no—
750D8—868no—
751C2×C8—22no—
752C2×C8—28no—
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—864no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—864no—
771C22⋊C4—434no—
772C22⋊C4—434no—
773C22⋊C4—864no—
774C22⋊C4—864no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C22⋊C4—864no—
778C42—432no—
779C42—432no—
780C42—864no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—24no—
786C23—22no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—432no—
793C23—862no—
794C23—862no—
795C23—862no—
796C23—862no—
797C23—1722no—
798C23—1722no—
799C23—1722no—
800C23C2×D4×D4312yes—
801C23C2×D4×D4311yescharacteristic
802Q8—22no—
803Q8—24no—
804Q8—22no—
805Q8—22no—
806Q8—42no—
807Q8—862no—
808Q8—862no—
809Q8—1722no—
810Q8C22×C22⋊D4314yes—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—24no—
815D4—48no—
816D4—48no—
817D4—42no—
818D4—868no—
819D4—862no—
820D4—862no—
821D4—3444no—
822D4—3444no—
823D4—3444no—
824D4—1728no—
825D4—1728no—
826D4—1728no—
827D4—1722no—
828D4C22×C22⋊D4314yes—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—48no—
837C2×C4—48no—
838C2×C4—42no—
839C2×C4—434no—
840C2×C4—432no—
841C2×C4—432no—
842C2×C4—432no—
843C2×C4—862no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—864no—
848C2×C4—862no—
849C2×C4—862no—
850C2×C4—862no—
851C2×C4—1728no—
852C2×C4—1728no—
853C2×C4—1728no—
854C2×C4—1722no—
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—24no—
868C22—22no—
869C22—22no—
870C22—42no—
871C22—42no—
872C22—44no—
873C22—48no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—84no—
878C22—862no—
879C22—862no—
880C22—862no—
881C22—3444no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22—1724no—
886C22D4×C22⋊D4312yes—
887C22#135×D4312yes—
888C22#1458370612yes—
889C22C22×D4×D4311yescharacteristic
890C4—22no—
891C4—24no—
892C4—42no—
893C4—434no—
894C4—862no—
895C4—862no—
896C4—1722no—
897C4—1722no—
898C4—1722no—
899C4D4×C22⋊D4312yes—
900C4C23×C22⋊D4311yescharacteristic
901C4C2×#1306337011yescharacteristic
902C2—42no—
903C2—44no—
904C2—82no—
905C2—3442no—
906C2—1722no—
907C2#1914631914yesdirect product factor
908C2C2×D4×C22⋊D4311yescharacteristic
909C2C2×#135×D4311yescharacteristic
910C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#135×C43C2
socleC23×C43C22×D4
hypercenterC22×#135D43
hypocenterC43C2×#3284
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×#13063346C2semidirect
2. C2×#14583568C2semidirect
3. C2×#14583548C2semidirect
4. #19146319C2direct (N × H)
5. C2×#14583270C2semidirect
6. C2×#14583128C2semidirect
7. C2×#14583125C2semidirect
8. C2×#14583107C2semidirect
9. C2×#14583092C2semidirect
10. C2×#14583061C2semidirect
11. C2×#14583060C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583041C2semidirect
14. C2×SD16×Dic43C2semidirect
15. C2×C8×C22⋊D43C2semidirect
16. C22×#135×C43C2semidirect
20. C2×#13063346C22semidirect
28. #14583568C22semidirect
30. #14583548C22semidirect
48. #14583270C22semidirect
49. #14583128C22semidirect
50. #14583125C22semidirect
51. #14583107C22semidirect
52. #14583092C22semidirect
53. #14583061C22semidirect
54. #14583060C22semidirect
55. #14583044C22semidirect
56. #14583041C22semidirect
57. SD16×Dic43C22semidirect
58. C8×C22⋊D43C22semidirect
73. C2×#135×C43C22semidirect
190. C2×SD16×C43D4semidirect
288. SD16×C43C2×D4semidirect
391. C2×Dic43#135semidirect
446. Dic43C2×#135semidirect
448. C22×#135D43semidirect
466. C2×C43#3284semidirect
479. C2×#135C2×D43semidirect
534. C43C2×#3284semidirect
586. C2×SD16C22⋊D43semidirect
748. SD16C2×C22⋊D43semidirect
907. C2#19146319direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633462
C2×#145835682
C2×#145835482
#191463192
C2×#145832702
C2×#145831282
C2×#145831252
C2×#145831072
C2×#145830922
C2×#145830612
C2×#145830602
C2×#145830442
C2×#145830412
C2×SD16×Dic432
C2×C8×C22⋊D432
C22×#135×C432
C2×#328443