Finite Group Databasebeta

← #25064388

Subgroups — #25064388

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148430C211yesmaximal, characteristic
2#19143635C211yesmaximal, characteristic, complemented
3#19137528C211yesmaximal, characteristic, complemented
4#19133170C211yesmaximal, characteristic, complemented
5#19133137C211yesmaximal, characteristic, complemented
6#19133135C211yesmaximal, characteristic, complemented
7#19133126C211yesmaximal, characteristic, complemented
8#19133122C211yesmaximal, characteristic, complemented
9#19133113C211yesmaximal, characteristic, complemented
10#19133109C211yesmaximal, characteristic, complemented
11#19133098C211yesmaximal, characteristic, complemented
12#19133096C211yesmaximal, characteristic, complemented
13#19133082C211yesmaximal, characteristic, complemented
14#19133081C211yesmaximal, characteristic, complemented
15C43×#1521C211yesmaximal, characteristic, complemented
16#14583602C411yescharacteristic, complemented
17#14583600—21no—
18#14583599C411yescharacteristic, complemented
19#14583593—21no—
20#14583590C411yescharacteristic, complemented
21#14583587C411yescharacteristic, complemented
22#14583574—21no—
23#14583573—21no—
24#14583561C411yescharacteristic, complemented
25#14583557C411yescharacteristic, complemented
26#14583544C411yescharacteristic, complemented
27#14583542C411yescharacteristic, complemented
28#14583493—21no—
29#14583482—21no—
30#14583460—21no—
31#14583433C2211yescharacteristic
32#14583412C2211yescharacteristic
33#14583409C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×D172C2211yescharacteristic
38#14582978—21no—
39#14582978—21no—
40#14582976—21no—
41#14582976—21no—
42#14582952C2211yescharacteristic, complemented
43#14582861C2211yescharacteristic
44#14582861C2211yescharacteristic
45#14582861C2211yescharacteristic, complemented
46#14582861C2211yescharacteristic, complemented
47#14582788—21no—
48#14582784—21no—
49#14582777—21no—
50#14582761C2211yescharacteristic
51#14582758C2211yescharacteristic, complemented
52#14582746—21no—
53#14582746C2211yescharacteristic
54#14582745C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582636C2211yescharacteristic, complemented
59#14582636C2211yescharacteristic, complemented
60#14582635C2211yescharacteristic, complemented
61#14582635C2211yescharacteristic, complemented
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#431C2211yescharacteristic, complemented
70C43×#383C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621900C2×C411yescharacteristic
77C2×Q8×D43C2×C411yescharacteristic, complemented
78C22×D172D411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic, complemented
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×#10621872—21no—
85C2×#10621872—21no—
86C2×#10621872—21no—
87C2×#10621872—21no—
88#13063320—21no—
89#13063320—21no—
90#13063319—21no—
91#13063319—21no—
92#13063318—21no—
93#13063317C2×C411yescharacteristic, complemented
94#13063316—21no—
95#13063315—21no—
96#13063313—21no—
97#13063313C2×C411yescharacteristic, complemented
98#13063311—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063309—21no—
104#13063308—21no—
105#13063308—21no—
106#13063307—21no—
107#13063307—21no—
108#13063305—21no—
109#13063305C2×C411yescharacteristic
110#13063305C2×C411yescharacteristic, complemented
111#13063304C2311yescharacteristic
112#13063303—21no—
113#13063302—21no—
114#13063302—21no—
115#13063301C2×C411yescharacteristic
116#13063301C2×C411yescharacteristic, complemented
117#13063300—21no—
118#13063300—21no—
119#13063300C2×C411yescharacteristic
120#13063300C2×C411yescharacteristic, complemented
121#13063299—21no—
122#13063299C2311yescharacteristic
123#13063298—21no—
124#13063298—21no—
125#13063298—21no—
126#13063298—21no—
127#13063297—21no—
128#13063296C2×C411yescharacteristic
129#13063296C2×C411yescharacteristic, complemented
130#13063295—21no—
131#13063295—21no—
132#13063295—21no—
133#13063293—21no—
134C4×Dic86C2×C411yescharacteristic, complemented
135C4×D172—21no—
136C4×D172C2×C411yescharacteristic
137C4×D172C2×C411yescharacteristic
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic, complemented
141C4×D172D411yescharacteristic
142C4×D172D411yescharacteristic
143C4×D172D411yescharacteristic
144C4×D172D411yescharacteristic
145D4×Dic43—21no—
146#13063287—21no—
147#13063287—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063283—21no—
154#13063283C2×C411yescharacteristic
155#13063283C2×C411yescharacteristic
156#13063282—21no—
157#13063282—21no—
158C2×C4⋊Dic43D411yescharacteristic
159C2×Dic43⋊C4—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43C2×C411yescharacteristic, complemented
162C4⋊C4×D43C2×C411yescharacteristic, complemented
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C2×(C2×D43)⋊C4D411yescharacteristic
169C22⋊C4×D43—21no—
170C22⋊C4×D43—21no—
171C22⋊C4×D43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43—21no—
174C4⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181C4×C43⋊C8—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic, complemented
189#124×C43C2×C411yescharacteristic, complemented
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic, complemented
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic, complemented
196#117×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201C4×C8×C43—21no—
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C23×D43—21no—
207C23×D43C2×D411yescharacteristic
208C23×D43C2×D411yescharacteristic
209C2×Q8×C43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43C22×C411yescharacteristic
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2411yescharacteristic
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228#10621902—81no—
229Q8×D43—81no—
230#10621900—81no—
231D4×D43—42no—
232D4×D43—42no—
233D4×D43—81no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—41no—
238C2×D172—41no—
239C2×D172C22⋊C411yescharacteristic
240C2×D172C22⋊C411yescharacteristic
241C2×D172C22⋊C411yescharacteristic
242C2×D172C22⋊C411yescharacteristic
243C2×D172C22×C411yescharacteristic
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—42no—
250C2×C4×D43—42no—
251C2×C4×D43—81no—
252C2×C4×D43—81no—
253C2×C4×D43—81no—
254C2×C4×D43C22×C411yescharacteristic
255C2×C4×D43C22×C411yescharacteristic
256C2×C4×D43C22×C411yescharacteristic
257C2×C4×D43C22×C411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×C4×D43C2×D411yescharacteristic
260C2×C4×D43C2×D411yescharacteristic
261C2×C4×D43C2×D411yescharacteristic
262C2×Dic86—21no—
263C2×Dic86C22×C411yescharacteristic
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43C22×C411yescharacteristic
271C4⋊C4×C43C22×C411yescharacteristic
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C42×C43—21no—
278C42×C43C22×C411yescharacteristic
279C42×C43C22×C411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—42no—
298(C2×D43)⋊C4—42no—
299(C2×D43)⋊C4—81no—
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304(C2×D43)⋊C4C22⋊C411yescharacteristic
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43C22⋊C411yescharacteristic
311C4⋊Dic43C22⋊C411yescharacteristic
312C4⋊Dic43C22⋊C411yescharacteristic
313C4⋊Dic43C22⋊C411yescharacteristic
314C4⋊Dic43C22×C411yescharacteristic
315C4⋊Dic43C22×C411yescharacteristic
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—81no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—21no—
328C4×Dic43—42no—
329C4×Dic43—81no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—21no—
332#10621872—81no—
333#10621872—81no—
334#10621872—81no—
335#10621872—81no—
336C23×C43—21no—
337C23×C43C22×D411yescharacteristic
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—41no—
344C22×D43—41no—
345C22×D43—41no—
346C22×D43—41no—
347C22×D43—42no—
348C22×D43—81no—
349C22×D43—81no—
350C22×D43C2×C22⋊C411yescharacteristic
351C22×D43C2×C22⋊C411yescharacteristic
352C22×D43C2×C22⋊C411yescharacteristic
353C22×D43C2×C22⋊C411yescharacteristic
354Q8×C43—41no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—41no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—81no—
372C2×C4×C43C2×C22⋊C411yescharacteristic
373C2×C4×C43C2×C22⋊C411yescharacteristic
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C23×C411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C22⋊D43—42no—
379C22⋊D43—41no—
380C22⋊D43—41no—
381C22⋊D43—81no—
382C22⋊D43—81no—
383C22⋊D43—81no—
384C2×Dic43—22no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—81no—
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398C2×Dic43C2×C22⋊C411yescharacteristic
399C2×Dic43C2×C22⋊C411yescharacteristic
400D172—41no—
401D172—41no—
402D172—41no—
403D172—41no—
404D172—41no—
405D172—42no—
406D172—81no—
407D172—81no—
408C4×D43—41no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—41no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—42no—
417C4×D43—81no—
418C4×D43—81no—
419C4×D43—81no—
420C4×D43—81no—
421C4×D43—84no—
422Dic86—41no—
423Dic86—81no—
424C8×C43—41no—
425C8×C43—41no—
426C43⋊C8—41no—
427C43⋊C8—41no—
428#17623—431nomaximal, Sylow
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43C22×C22⋊C411yescharacteristic
435C22×C43#57511yescharacteristic
436C22×C43#57511yescharacteristic
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—21no—
442C2×D43—21no—
443C2×D43—21no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—42no—
450C2×D43—42no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—81no—
455C2×D43—81no—
456C2×D43—162no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—21no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—41no—
466C4×C43—81no—
467C4×C43—81no—
468Dic43—21no—
469Dic43—21no—
470Dic43—21no—
471Dic43—21no—
472Dic43—42no—
473Dic43—41no—
474Dic43—41no—
475Dic43—41no—
476Dic43—81no—
477#3505—431no—
478#2975—431no—
479#2353—431no—
480#1521—431no—
481#1521D4311yescharacteristic, complemented
482#1513—431no—
483#1513—431no—
484#1511—431no—
485#1510—431no—
486#1508—431no—
487#1507—431no—
488#1504—431no—
489#1504—431no—
490#1500—431no—
491#1500—431no—
492C2×C43—21no—
493C2×C43—21no—
494C2×C43—81no—
495C2×C43#288311yescharacteristic
496C2×C43#289611yescharacteristic
497C2×C43#290111yescharacteristic
498D43—41no—
499D43—41no—
500D43—41no—
501D43—41no—
502D43—81no—
503#553—431no—
504#553—431no—
505#553—861no—
506#553—861no—
507#552—431no—
508#552—431no—
509#551—861no—
510#551—861no—
511#548—431no—
512#548—431no—
513#546—431no—
514#546—431no—
515#539—861no—
516#538—861no—
517#534—861no—
518#529—431no—
519#529C2×D4311yescharacteristic
520#525—431no—
521#525—431no—
522C2×C22⋊Q8—431no—
523C2×#121—431no—
524#518—861no—
525C2×C4×D4—431no—
526#436—861no—
527#436—861no—
528#436—861no—
529#436—861no—
530#431—431no—
531#431C2×D4311yescharacteristic, complemented
532#407—431no—
533#407—431no—
534#407—431no—
535#407—431no—
536#388—861no—
537#387—861no—
538#386—861no—
539#383C2×D4311yescharacteristic, complemented
540#381—431no—
541#380—431no—
542C4×C22⋊C4—431no—
543C4×C22⋊C4—861no—
544#376—431no—
545C2×#95—431no—
546#328—431no—
547#328—431no—
548#328—431no—
549#328—431no—
550#328—431no—
551#328—431no—
552#328C2×D4311yescharacteristic, complemented
553#328C2×D4311yescharacteristic, complemented
554#327—431no—
555#327—431no—
556#327—431no—
557#327—431no—
558#327—431no—
559#327—431no—
560#327C2×D4311yescharacteristic
561#327C2×D4311yescharacteristic
562C43#1762311yescharacteristic, complemented, Sylow
563C2×#41—431no—
564C2×#41—431no—
565C22×Q8—431no—
566C22×D4—431no—
567C22×D4—431no—
568C22×D4—861no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—861no—
572C2×M16—861no—
573C2×M16—861no—
574C2×M16—861no—
575C2×M16—861no—
576#126—21no—
577#126—861no—
578#126—861no—
579#126—861no—
580#126—861no—
581#126—861no—
582#125—431no—
583#125—861no—
584#125—861no—
585#125C4×D4311yescharacteristic, complemented
586#124—431no—
587#124—861no—
588#124—861no—
589#124C4×D4311yescharacteristic, complemented
590#123—21no—
591#123—861no—
592#123—861no—
593#123—861no—
594#123—861no—
595#123—861no—
596#123—861no—
597#123—861no—
598#123—861no—
599#123—861no—
600C22⋊Q8—431no—
601C22⋊Q8—431no—
602C22⋊Q8—431no—
603C22⋊Q8—431no—
604C22⋊Q8—431no—
605C22⋊Q8—861no—
606C22⋊Q8—861no—
607C22⋊Q8—861no—
608C22⋊Q8—861no—
609C22⋊Q8C22×D4311yescharacteristic
610#121—431no—
611#121—431no—
612#121—431no—
613#121—431no—
614#121—431no—
615#121—861no—
616#121—861no—
617#121—861no—
618#121—861no—
619#121—861no—
620#121—861no—
621#121—861no—
622#121—861no—
623#121C22×D4311yescharacteristic
624#120—861no—
625#120—861no—
626#120—861no—
627#120—861no—
628C4×Q8—431no—
629C4×Q8C4×D4311yescharacteristic, complemented
630C4×D4—21no—
631C4×D4—431no—
632C4×D4—431no—
633C4×D4—431no—
634C4×D4—431no—
635C4×D4—431no—
636C4×D4—431no—
637C4×D4—431no—
638C4×D4—431no—
639C4×D4—431no—
640C4×D4—861no—
641C4×D4—861no—
642C4×D4—861no—
643C4×D4—861no—
644C4×D4—861no—
645C4×D4—861no—
646C4×D4—861no—
647C4×D4—861no—
648C4×D4—861no—
649C4×D4C4×D4311yescharacteristic, complemented
650#117—21no—
651#117—431no—
652#117—431no—
653#117—861no—
654#117—861no—
655#117—861no—
656C2×C4⋊C4—431no—
657C2×C4⋊C4—431no—
658C2×C4⋊C4—431no—
659C2×C4⋊C4—861no—
660C2×C4⋊C4—861no—
661C2×C22⋊C4—431no—
662C2×C22⋊C4—431no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—861no—
666C2×C22⋊C4—861no—
667C2×C22⋊C4—861no—
668C2×C22⋊C4—861no—
669C2×C22⋊C4—861no—
670C2×C42—861no—
671C2×C42—861no—
672C2×C42C22×D4311yescharacteristic
673C4⋊C8—21no—
674C4⋊C8—861no—
675C22⋊C8—431no—
676C22⋊C8—431no—
677C22⋊C8—861no—
678C22⋊C8—861no—
679C22⋊C8—861no—
680C22⋊C8—861no—
681C22⋊C8C22×D4311yescharacteristic
682C22⋊C8C22×D4311yescharacteristic
683C4×C8—21no—
684C4×C8—861no—
685#95—21no—
686#95—21no—
687#95—431no—
688#95—431no—
689#95—861no—
690#95—861no—
691#95—861no—
692#95C22×D4311yescharacteristic
693#95C22×D4311yescharacteristic
694C24—431no—
695C24—431no—
696C24—861no—
697#41—3441no—
698#41—3441no—
699C2×Q8—431no—
700C2×Q8—861no—
701C2×Q8—3441no—
702C2×Q8C2×C4×D4311yescharacteristic
703C2×D4—21no—
704C2×D4—431no—
705C2×D4—431no—
706C2×D4—431no—
707C2×D4—431no—
708C2×D4—431no—
709C2×D4—861no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—861no—
716C2×D4—861no—
717C2×D4—3441no—
718C2×D4—1721no—
719C2×D4—1721no—
720C2×D4—1722no—
721C2×D4—1722no—
722C2×D4C2×C4×D4311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—3441no—
745C22×C4—3441no—
746C22×C4—3441no—
747C22×C4—1722no—
748C22×C4—1722no—
749C22×C4D4×D4311yescharacteristic
750C22×C4D4×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752M16—3441no—
753M16—3441no—
754M16—3441no—
755M16—3441no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—861no—
759C2×C8—861no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—431no—
765C4⋊C4—431no—
766C4⋊C4—431no—
767C4⋊C4—431no—
768C4⋊C4—431no—
769C4⋊C4—431no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4—861no—
773C4⋊C4—861no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C4⋊C4—861no—
777C4⋊C4—861no—
778C4⋊C4—861no—
779C4⋊C4—861no—
780C4⋊C4—3441no—
781C4⋊C4C2×C4×D4311yescharacteristic
782C4⋊C4C2×C4×D4311yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—431no—
789C22⋊C4—431no—
790C22⋊C4—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C22⋊C4—861no—
800C22⋊C4—861no—
801C22⋊C4—861no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C22⋊C4—861no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—3441no—
812C22⋊C4—1722no—
813C22⋊C4—1722no—
814C42—21no—
815C42—861no—
816C42—861no—
817C42—861no—
818C42—3441no—
819C42—1722no—
820C42C2×C4×D4311yescharacteristic
821C42C2×C4×D4311yescharacteristic
822C42D4×D4311yescharacteristic
823C42D4×D4311yescharacteristic
824C23—21no—
825C23—431no—
826C23—431no—
827C23—431no—
828C23—431no—
829C23—861no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—861no—
834C23—3441no—
835C23—3441no—
836C23—1721no—
837C23—1721no—
838C23—1721no—
839C23—1721no—
840C23—1722no—
841C23C2×D4×D4311yescharacteristic
842Q8—41no—
843Q8—3441no—
844Q8—1721no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—3441no—
849D4—3441no—
850D4—3441no—
851D4—3441no—
852D4—3441no—
853D4—1721no—
854D4—1721no—
855D4—1721no—
856D4—1721no—
857D4—1721no—
858D4—1722no—
859D4—1722no—
860D4—1721no—
861D4—1721no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—81no—
876C2×C4—431no—
877C2×C4—431no—
878C2×C4—431no—
879C2×C4—431no—
880C2×C4—862no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—3441no—
885C2×C4—3441no—
886C2×C4—3441no—
887C2×C4—3441no—
888C2×C4—3444no—
889C2×C4—3441no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1722no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4C22⋊C4×D4311yescharacteristic
907C2×C4C22⋊C4×D4311yescharacteristic
908C2×C4C22⋊C4×D4311yescharacteristic
909C2×C4C22⋊C4×D4311yescharacteristic
910C2×C4C22×C4×D4311yescharacteristic
911C2×C4C2×D4×D4311yescharacteristic
912C8—41no—
913C8—41no—
914C8—1721no—
915C8—1721no—
916C22—21no—
917C22—21no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—861no—
922C22—861no—
923C22—861no—
924C22—861no—
925C22—861no—
926C22—861no—
927C22—861no—
928C22—861no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—3441no—
934C22—3441no—
935C22—1722no—
936C22—1722no—
937C22—1721no—
938C22—1721no—
939C22—1721no—
940C22—6882no—
941C22C2×C22⋊C4×D4311yescharacteristic
942C22#1458369611yescharacteristic
943C22#1458369611yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—81no—
954C4—81no—
955C4—861no—
956C4—861no—
957C4—861no—
958C4—861no—
959C4—3441no—
960C4—1722no—
961C4—1721no—
962C4—1721no—
963C4—1721no—
964C2—21no—
965C2—21no—
966C2—81no—
967C2—3441no—
968C2—1721no—
969C2—1721no—
970C2—1721no—
971C2—1721no—
972C2#1914305411yescharacteristic
973C2#1914311011yescharacteristic
974C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1521C2
socleC22×C43C22×C22⋊C4
prime radical#19148430C2
cosocleC22×C4×C43C24
hypercenter#1521D43
hypocenterC43#17623
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #19143635C2semidirect
3. #19137528C2semidirect
4. #19133170C2semidirect
5. #19133137C2semidirect
6. #19133135C2semidirect
7. #19133126C2semidirect
8. #19133122C2semidirect
9. #19133113C2semidirect
10. #19133109C2semidirect
11. #19133098C2semidirect
12. #19133096C2semidirect
13. #19133082C2semidirect
14. #19133081C2semidirect
15. C43×#1521C2semidirect
16. #14583602C4semidirect
18. #14583599C4semidirect
20. #14583590C4semidirect
21. #14583587C4semidirect
24. #14583561C4semidirect
25. #14583557C4semidirect
26. #14583544C4semidirect
27. #14583542C4semidirect
42. #14582952C22semidirect
45. #14582861C22semidirect
46. #14582861C22semidirect
51. #14582758C22semidirect
54. #14582745C22semidirect
55. #95×D43C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C43×#431C22semidirect
70. C43×#383C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
77. C2×Q8×D43C2×C4semidirect
80. C2×D4×D43C2×C4semidirect
93. #13063317C2×C4semidirect
97. #13063313C2×C4semidirect
110. #13063305C2×C4semidirect
116. #13063301C2×C4semidirect
120. #13063300C2×C4semidirect
129. #13063296C2×C4semidirect
134. C4×Dic86C2×C4semidirect
140. C4×D172C2×C4semidirect
161. C4⋊C4×D43C2×C4semidirect
162. C4⋊C4×D43C2×C4semidirect
188. #125×C43C2×C4semidirect
189. #124×C43C2×C4semidirect
193. C4×Q8×C43C2×C4semidirect
195. C4×D4×C43C2×C4semidirect
481. #1521D43semidirect
531. #431C2×D43semidirect
539. #383C2×D43semidirect
552. #328C2×D43semidirect
553. #328C2×D43semidirect
562. C43#17623semidirect
585. #125C4×D43semidirect
589. #124C4×D43semidirect
629. C4×Q8C4×D43semidirect
649. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191484302
#191436352
#191375282
#191331702
#191331372
#191331352
#191331262
#191331222
#191331132
#191331092
#191330982
#191330962
#191330822
#191330812
C43×#15212
#1762343