Finite Group Databasebeta

← #25063809

Subgroups — #25063809

Order 11008.

1102 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148632C211yesmaximal, characteristic
2#19143626C211yesmaximal, characteristic, complemented
3#19136954C211yesmaximal, characteristic, complemented
4#19133117C211yesmaximal, characteristic, complemented
5#19133114C211yesmaximal, characteristic, complemented
6#19133113C211yesmaximal, characteristic, complemented
7#19133105C211yesmaximal, characteristic, complemented
8#19133099C211yesmaximal, characteristic, complemented
9#19133096C211yesmaximal, characteristic, complemented
10#19133092C211yesmaximal, characteristic, complemented
11#19133083C211yesmaximal, characteristic, complemented
12#19133078C211yesmaximal, characteristic, complemented
13C2×#14582637C211yesmaximal, characteristic, complemented
14#328×D43C211yesmaximal, characteristic, complemented
15C43×#1501C211yesmaximal, characteristic, complemented
16#14583617C411yescharacteristic, complemented
17#14583608—21no—
18#14583591C411yescharacteristic, complemented
19#14583588C411yescharacteristic, complemented
20#14583580—21no—
21#14583578—21no—
22#14583562C411yescharacteristic, complemented
23#14583556C411yescharacteristic, complemented
24#14583555C411yescharacteristic, complemented
25#14583549C411yescharacteristic, complemented
26#14583548C411yescharacteristic, complemented
27#14583536—21no—
28#14583517—21no—
29#14583492—21no—
30#14583491—21no—
31#14583451C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583409C2211yescharacteristic
34C2×#13063304C2211yescharacteristic
35C22⋊Q8×D43C2211yescharacteristic
36#14583378—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38C2×(C22⋊D43)⋊C4—21no—
39#14582974—21no—
40#14582973—21no—
41#14582970—21no—
42C8×C22⋊D43—21no—
43#14582953C2211yescharacteristic
44#14582949C2211yescharacteristic
45#14582863C2211yescharacteristic
46#14582861C2211yescharacteristic
47C22⋊C8×D43C2211yescharacteristic
48C4×Dic43⋊C4—21no—
49#14582750C2211yescharacteristic
50C22⋊C4×Dic43—21no—
51C4×(C2×D43)⋊C4—21no—
52#14582746C2211yescharacteristic
53#14582744C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55#95×D43C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582637C2211yescharacteristic
59#14582637C2211yescharacteristic
60#14582636C2211yescharacteristic
61#14582636C2211yescharacteristic
62#14582635C2211yescharacteristic
63#14582635C2211yescharacteristic
64#14582635C2211yescharacteristic
65#14582635C2211yescharacteristic
66#14582633C2211yescharacteristic
67#14582633C2211yescharacteristic
68C43×#525C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic
70C4×C22⋊C4×C43C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621900—21no—
76C2×#10621900C2×C411yescharacteristic, complemented
77C22×Dic86C2×C411yescharacteristic, complemented
78C2×Q8×D43C2×C411yescharacteristic, complemented
79C22×C22⋊D43D411yescharacteristic
80C23×Dic43—21no—
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×#10621872—21no—
85C2×C8×D43—21no—
86#13063324—21no—
87#13063324C2×C411yescharacteristic, complemented
88#13063323C2×C411yescharacteristic, complemented
89#13063320—21no—
90#13063319—21no—
91#13063318—21no—
92#13063318—21no—
93#13063318—21no—
94#13063317—21no—
95#13063316—21no—
96#13063316C2×C411yescharacteristic, complemented
97#13063315—21no—
98#13063312—21no—
99#13063312C2×C411yescharacteristic, complemented
100#13063311—21no—
101#13063311—21no—
102#13063309—21no—
103#13063308—21no—
104#13063307—21no—
105#13063307—21no—
106#13063307—21no—
107#13063306—21no—
108#13063306—21no—
109#13063306—21no—
110#13063305C2×C411yescharacteristic, complemented
111#13063305C2×C411yescharacteristic, complemented
112#13063304—21no—
113#13063304—21no—
114#13063304—21no—
115#13063304C2×C411yescharacteristic, complemented
116#13063304C2×C411yescharacteristic, complemented
117#13063304C2311yescharacteristic
118#13063304C2311yescharacteristic
119#13063303—21no—
120#13063303—21no—
121#13063302—21no—
122#13063302—21no—
123#13063302—21no—
124#13063302—21no—
125#13063302—21no—
126#13063301C2×C411yescharacteristic, complemented
127#13063297—21no—
128#13063297—21no—
129#13063296—21no—
130#13063296C2×C411yescharacteristic, complemented
131#13063293—21no—
132Q8×Dic43C2×C411yescharacteristic, complemented
133C4×Dic86—21no—
134#13063290—21no—
135#13063290C2×C411yescharacteristic, complemented
136#13063290C2×C411yescharacteristic, complemented
137D4×Dic43—21no—
138D4×Dic43—21no—
139D4×Dic43—21no—
140D4×Dic43C2×C411yescharacteristic, complemented
141C4×C22⋊D43—21no—
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150(C22⋊D43)⋊C4—28no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063283C2×C411yescharacteristic, complemented
154#13063282—21no—
155#13063281—21no—
156#13063281—21no—
157#13063281—21no—
158C2×C4⋊Dic43C2×C411yescharacteristic, complemented
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4D411yescharacteristic
163C4⋊C4×D43—21no—
164C4⋊C4×D43C2×C411yescharacteristic, complemented
165C2×C22⋊Dic43—21no—
166C2×C22⋊Dic43D411yescharacteristic
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4D411yescharacteristic
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182C8×Dic43—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C2×#41×C43C2×C411yescharacteristic, complemented
189C23×C4×C43C2311yescharacteristic
190C22×C8×C43—21no—
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic, complemented
193C22⋊Q8×C43C2311yescharacteristic
194#121×C43C2×C411yescharacteristic, complemented
195#121×C43C2311yescharacteristic
196#120×C43—21no—
197C4×D4×C43—21no—
198C4×D4×C43—21no—
199#117×C43C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C43—21no—
201C2×C42×C43—21no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43C2×D411yescharacteristic
209#41×C43—81no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43C22×C411yescharacteristic
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—81no—
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—24no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43C22⋊C411yescharacteristic
229C2×C22⋊D43C22⋊C411yescharacteristic
230C2×C22⋊D43C22⋊C411yescharacteristic
231C2×C22⋊D43C22⋊C411yescharacteristic
232C22×Dic43—24no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—81no—
240C22×Dic43—81no—
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244Q8×D43—81no—
245#10621900—44no—
246#10621900—81no—
247C2×C4×D43—24no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—81no—
251C2×C4×D43—81no—
252C2×C4×D43—81no—
253C2×C4×D43C22×C411yescharacteristic
254C2×C4×D43C22×C411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×Dic86—21no—
258C2×Dic86—21no—
259C2×Dic86—21no—
260C2×Dic86—81no—
261C2×Dic86C22×C411yescharacteristic
262C2×Dic86C22×C411yescharacteristic
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—81no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43C22×C411yescharacteristic
269C4⋊C4×C43C22×C411yescharacteristic
270C22⋊C4×C43—24no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C42×C43—21no—
277C42×C43—81no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289C22⋊Dic43C22⋊C411yescharacteristic
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C22×C411yescharacteristic
305C4⋊Dic43C22×C411yescharacteristic
306Dic43⋊C4—24no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4C22⋊C411yescharacteristic
320Dic43⋊C4C22⋊C411yescharacteristic
321Dic43⋊C4C22⋊C411yescharacteristic
322Dic43⋊C4C22⋊C411yescharacteristic
323C4×Dic43—24no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—21no—
328C4×Dic43—81no—
329C4×Dic43—81no—
330C4×Dic43C22×C411yescharacteristic
331C4×Dic43C22×C411yescharacteristic
332C4×Dic43C2×D411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334#10621877—81no—
335C2×C43⋊C8—21no—
336C2×C43⋊C8—21no—
337#10621872—81no—
338C8×D43—81no—
339C23×C43—21no—
340C23×C43—21no—
341C23×C43—22no—
342C23×C43—21no—
343C23×C43—41no—
344C23×C43C2×C22⋊C411yescharacteristic
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C22×D411yescharacteristic
347C22×D43—21no—
348C22×D43—21no—
349C22×D43—22no—
350C22×D43—41no—
351C22×D43C2×C22⋊C411yescharacteristic
352C22×D43C2×C22⋊C411yescharacteristic
353Q8×C43—41no—
354D4×C43—41no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—42no—
358D4×C43—81no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
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—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—81no—
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C2×C22⋊C411yescharacteristic
377C2×C4×C43C23×C411yescharacteristic
378C2×C4×C43C22×D411yescharacteristic
379C22⋊D43—22no—
380C22⋊D43—22no—
381C22⋊D43—22no—
382C22⋊D43—42no—
383C22⋊D43—81no—
384C22⋊D43#10414yes—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—22no—
388C2×Dic43—22no—
389C2×Dic43—22no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—42no—
400C2×Dic43—42no—
401C2×Dic43—81no—
402C2×Dic43—81no—
403C2×Dic43—84no—
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C2×Dic43C2×C22⋊C411yescharacteristic
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—41no—
413C4×D43—41no—
414C4×D43—42no—
415C4×D43—81no—
416C4×D43—84no—
417Dic86—42no—
418Dic86—41no—
419Dic86—41no—
420Dic86—81no—
421Dic86—81no—
422C8×C43—41no—
423C8×C43—41no—
424C43⋊C8—41no—
425C43⋊C8—41no—
426#17548—431nomaximal, Sylow
427C22×C43—21no—
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43C2×#10412yes—
440C22×C43C22×C22⋊C411yescharacteristic
441C22×C43#57711yescharacteristic
442C22×C43#57811yescharacteristic
443C2×D43—21no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43C2×#10412yes—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455C4×C43—42no—
456C4×C43—42no—
457C4×C43—41no—
458C4×C43—41no—
459C4×C43—41no—
460Dic43—21no—
461Dic43—21no—
462Dic43—21no—
463Dic43—21no—
464Dic43—21no—
465Dic43—42no—
466Dic43—42no—
467Dic43—41no—
468Dic43—41no—
469Dic43—41no—
470Dic43—41no—
471Dic43C2×#10412yes—
472#3520—431no—
473#2974—431no—
474#2275—431no—
475#1509—431no—
476#1508—431no—
477#1508—431no—
478#1506—431no—
479#1504—431no—
480#1504—431no—
481#1503—431no—
482#1501—431no—
483#1501D4311yescharacteristic, complemented
484#1500—431no—
485C2×#328—431no—
486C2×#328—431no—
487C2×C43—21no—
488C2×C43—21no—
489C2×C43—22no—
490C2×C43—41no—
491C2×C43—81no—
492C2×C43#288311yescharacteristic
493C2×C43#289811yescharacteristic
494C2×C43C22×#10411yescharacteristic
495D43—22no—
496D43—41no—
497#556—431no—
498#554—861no—
499#552—431no—
500#552—431no—
501#551—861no—
502#551—861no—
503D4×Q8—431no—
504#548—431no—
505#548—431no—
506#547—431no—
507#547—431no—
508#546—861no—
509#542—861no—
510#539—861no—
511#539—861no—
512#533—431no—
513#529—431no—
514#525—431no—
515#525C2×D4311yescharacteristic
516C2×C22⋊Q8—431no—
517C2×C22⋊Q8—431no—
518#520—861no—
519C2×C4×D4—431no—
520C2×C4×D4—861no—
521#436—861no—
522#435—861no—
523#435—861no—
524C8×D4—861no—
525#432—431no—
526#431—431no—
527#407—431no—
528#407—431no—
529C2×C22⋊C8—431no—
530C2×C22⋊C8C2×D4311yescharacteristic
531C4×C4⋊C4—431no—
532C4×C4⋊C4—861no—
533C4×C22⋊C4—431no—
534C4×C22⋊C4—861no—
535C4×C22⋊C4—861no—
536C4×C22⋊C4C2×D4311yescharacteristic
537#376—431no—
538C2×#95—431no—
539C2×#95—431no—
540#328—431no—
541#328—431no—
542#328—431no—
543#328—431no—
544#328—431no—
545#328—431no—
546#328—431no—
547#328—431no—
548#328—431no—
549#328—431no—
550#328C2×D4311yescharacteristic
551#328C2×D4311yescharacteristic
552#327—431no—
553#327—431no—
554#327C2×D4311yescharacteristic
555#327C2×D4311yescharacteristic
556C43#1754811yescharacteristic, complemented, Sylow
557C2×#41—431no—
558C2×#41—861no—
559C2×#41C4×D4311yescharacteristic, complemented
560C22×Q8—431no—
561C22×Q8—431no—
562C22×D4—431no—
563C23×C4—431no—
564C23×C4—861no—
565C23×C4—861no—
566C23×C4C22×D4311yescharacteristic
567C2×M16—861no—
568C2×M16—861no—
569C22×C8—21no—
570C22×C8—861no—
571C4⋊Q8—431no—
572C4⋊Q8—431no—
573C4⋊Q8—861no—
574#126—861no—
575#126—861no—
576#126—861no—
577#126—861no—
578#126—861no—
579#125—431no—
580#125—861no—
581#125—861no—
582#125—861no—
583#124—431no—
584#124—861no—
585#124—861no—
586#124—861no—
587#123—21no—
588#123—861no—
589#123—861no—
590#123—861no—
591#123—861no—
592#123—861no—
593#123—861no—
594#123—861no—
595#123—861no—
596C22⋊Q8—431no—
597C22⋊Q8—431no—
598C22⋊Q8—431no—
599C22⋊Q8—431no—
600C22⋊Q8—431no—
601C22⋊Q8—431no—
602C22⋊Q8—431no—
603C22⋊Q8—861no—
604C22⋊Q8—861no—
605C22⋊Q8—861no—
606C22⋊Q8—861no—
607C22⋊Q8—861no—
608C22⋊Q8—861no—
609C22⋊Q8—861no—
610C22⋊Q8—861no—
611C22⋊Q8—861no—
612C22⋊Q8—861no—
613C22⋊Q8C4×D4311yescharacteristic, complemented
614C22⋊Q8C22×D4311yescharacteristic
615#121—431no—
616#121—861no—
617#121—861no—
618#121—861no—
619#121C4×D4311yescharacteristic, complemented
620#121C22×D4311yescharacteristic
621#120—21no—
622#120—861no—
623C4×Q8—431no—
624C4×Q8—431no—
625C4×Q8—431no—
626C4×Q8—861no—
627C4×Q8—861no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—431no—
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—861no—
640C4×D4—861no—
641C4×D4—868no—
642C4×D4—861no—
643C4×D4—861no—
644C4×D4—861no—
645C4×D4—861no—
646#117—431no—
647#117—861no—
648#117—861no—
649#117—861no—
650#117—861no—
651#117C4×D4311yescharacteristic, complemented
652C2×C4⋊C4—431no—
653C2×C4⋊C4—431no—
654C2×C4⋊C4—431no—
655C2×C4⋊C4—861no—
656C2×C4⋊C4—861no—
657C2×C4⋊C4—861no—
658C2×C4⋊C4—861no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—431no—
661C2×C22⋊C4—431no—
662C2×C22⋊C4—861no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C42—21no—
666C2×C42—431no—
667C2×C42—861no—
668C2×C42—861no—
669C2×C42—861no—
670C4⋊C8—861no—
671C4⋊C8—861no—
672C22⋊C8—21no—
673C22⋊C8—431no—
674C22⋊C8—431no—
675C22⋊C8—861no—
676C22⋊C8—861no—
677C22⋊C8—861no—
678C22⋊C8C22×D4311yescharacteristic
679C22⋊C8C22×D4311yescharacteristic
680#97—861no—
681C4×C8—861no—
682#95—431no—
683#95—431no—
684#95—861no—
685#95—861no—
686#95—861no—
687#95C22×D4311yescharacteristic
688#95C22×D4311yescharacteristic
689C24—431no—
690C24D4×D4311yescharacteristic
691#41—81no—
692#41—3441no—
693#41—1724no—
694C2×Q8—431no—
695C2×Q8—431no—
696C2×Q8—861no—
697C2×Q8—861no—
698C2×Q8—861no—
699C2×Q8—3441no—
700C2×Q8—3441no—
701C2×Q8C2×C4×D4311yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—431no—
706C2×D4—431no—
707C2×D4—431no—
708C2×D4—431no—
709C2×D4—864no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4C2×C4×D4311yescharacteristic
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—81no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—861no—
725C22×C4—864no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—864no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—3441no—
735C22×C4—3441no—
736C22×C4—3441no—
737C22×C4—3441no—
738C22×C4—3441no—
739C22×C4C2×C4×D4311yescharacteristic
740C22×C4C2×C4×D4311yescharacteristic
741C22×C4D4×D4311yescharacteristic
742C22×C4D4×D4311yescharacteristic
743C22×C4D4×D4311yescharacteristic
744C22×C4C23×D4311yescharacteristic
745M16—3441no—
746M16—3441no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—81no—
750C2×C8—861no—
751C2×C8—861no—
752C2×C8—3441no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—431no—
756C4⋊C4—431no—
757C4⋊C4—431no—
758C4⋊C4—431no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—861no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4—861no—
773C4⋊C4—864no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C4⋊C4—861no—
777C4⋊C4—861no—
778C4⋊C4—861no—
779C4⋊C4C2×C4×D4311yescharacteristic
780C4⋊C4C2×C4×D4311yescharacteristic
781C22⋊C4—24no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—431no—
788C22⋊C4—431no—
789C22⋊C4—431no—
790C22⋊C4—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C22⋊C4—864no—
800C22⋊C4—861no—
801C22⋊C4—861no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C42—21no—
809C42—81no—
810C42—431no—
811C42—431no—
812C42—431no—
813C42—431no—
814C42—861no—
815C42—861no—
816C42—861no—
817C42—861no—
818C42—864no—
819C42—3441no—
820C42—3441no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—41no—
826C23—431no—
827C23—431no—
828C23—862no—
829C23—861no—
830C23—861no—
831C23—1721no—
832C23C22⋊C4×D4311yescharacteristic
833C23C22⋊C4×D4311yescharacteristic
834C23C2×D4×D4311yescharacteristic
835Q8—41no—
836Q8—3441no—
837Q8—3441no—
838Q8—1721no—
839Q8—1721no—
840Q8—1722no—
841D4—41no—
842D4—42no—
843D4—41no—
844D4—41no—
845D4—81no—
846D4—434no—
847D4—862no—
848D4—862no—
849D4—862no—
850D4—3441no—
851D4—1722no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—81no—
868C2×C4—431no—
869C2×C4—431no—
870C2×C4—431no—
871C2×C4—431no—
872C2×C4—431no—
873C2×C4—431no—
874C2×C4—862no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—3441no—
884C2×C4—3444no—
885C2×C4—3441no—
886C2×C4—3441no—
887C2×C4—3444no—
888C2×C4—1721no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1722no—
893C2×C4—1722no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1722no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4C22⋊C4×D4311yescharacteristic
901C2×C4C22⋊C4×D4311yescharacteristic
902C2×C4C22×C4×D4311yescharacteristic
903C2×C4C2×D4×D4311yescharacteristic
904C8—41no—
905C8—41no—
906C8—1721no—
907C8—1721no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—432no—
921C22—861no—
922C22—861no—
923C22—861no—
924C22—861no—
925C22—861no—
926C22—1722no—
927C22—1722no—
928C22#104×D4312yes—
929C22C2×C22⋊C4×D4311yescharacteristic
930C22#1458370611yescharacteristic
931C22#1458371311yescharacteristic
932C4—21no—
933C4—21no—
934C4—21no—
935C4—21no—
936C4—42no—
937C4—42no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—432no—
942C4—861no—
943C4—861no—
944C4—861no—
945C4—861no—
946C4—861no—
947C4—1722no—
948C4—1722no—
949C4—1721no—
950C4—1721no—
951C4—1721no—
952C4—1721no—
953C2—21no—
954C2—21no—
955C2—22no—
956C2—41no—
957C2—81no—
958C2—862no—
959C2—1721no—
960C2#1914305311yescharacteristic
961C2#1914312411yescharacteristic
962C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1501C2
socleC22×C43C22×C22⋊C4
prime radical#19148632C2
cosocleC22×C4×C43C24
hypercenter#1501D43
hypocenterC43#17548
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #19143626C2semidirect
3. #19136954C2semidirect
4. #19133117C2semidirect
5. #19133114C2semidirect
6. #19133113C2semidirect
7. #19133105C2semidirect
8. #19133099C2semidirect
9. #19133096C2semidirect
10. #19133092C2semidirect
11. #19133083C2semidirect
12. #19133078C2semidirect
13. C2×#14582637C2semidirect
14. #328×D43C2semidirect
15. C43×#1501C2semidirect
16. #14583617C4semidirect
18. #14583591C4semidirect
19. #14583588C4semidirect
22. #14583562C4semidirect
23. #14583556C4semidirect
24. #14583555C4semidirect
25. #14583549C4semidirect
26. #14583548C4semidirect
76. C2×#10621900C2×C4semidirect
77. C22×Dic86C2×C4semidirect
78. C2×Q8×D43C2×C4semidirect
87. #13063324C2×C4semidirect
88. #13063323C2×C4semidirect
96. #13063316C2×C4semidirect
99. #13063312C2×C4semidirect
110. #13063305C2×C4semidirect
111. #13063305C2×C4semidirect
115. #13063304C2×C4semidirect
116. #13063304C2×C4semidirect
126. #13063301C2×C4semidirect
130. #13063296C2×C4semidirect
132. Q8×Dic43C2×C4semidirect
135. #13063290C2×C4semidirect
136. #13063290C2×C4semidirect
140. D4×Dic43C2×C4semidirect
153. #13063283C2×C4semidirect
158. C2×C4⋊Dic43C2×C4semidirect
164. C4⋊C4×D43C2×C4semidirect
188. C2×#41×C43C2×C4semidirect
192. C22⋊Q8×C43C2×C4semidirect
194. #121×C43C2×C4semidirect
199. #117×C43C2×C4semidirect
483. #1501D43semidirect
556. C43#17548semidirect
559. C2×#41C4×D43semidirect
613. C22⋊Q8C4×D43semidirect
619. #121C4×D43semidirect
651. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486322
#191436262
#191369542
#191331172
#191331142
#191331132
#191331052
#191330992
#191330962
#191330922
#191330832
#191330782
C2×#145826372
#328×D432
C43×#15012
#1754843