Finite Group Databasebeta

← #25064378

Subgroups — #25064378

Order 11008.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148423C211yesmaximal, characteristic
2#19143622C211yesmaximal, characteristic, complemented
3#19137499C211yesmaximal, characteristic, complemented
4#19133165C211yesmaximal, characteristic, complemented
5#19133161C211yesmaximal, characteristic, complemented
6#19133136C211yesmaximal, characteristic, complemented
7#19133132C211yesmaximal, characteristic, complemented
8#19133130C211yesmaximal, characteristic, complemented
9#19133119C211yesmaximal, characteristic, complemented
10#19133117C211yesmaximal, characteristic, complemented
11#19133100C211yesmaximal, characteristic, complemented
12#19133099C211yesmaximal, characteristic, complemented
13#328×D43C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1513C211yesmaximal, characteristic, complemented
16#14583599—21no—
17#14583596C411yescharacteristic, complemented
18#14583594—21no—
19#14583593C411yescharacteristic, complemented
20#14583588C411yescharacteristic, complemented
21#14583583C411yescharacteristic, complemented
22#14583578—21no—
23#14583577—21no—
24#14583559C411yescharacteristic, complemented
25#14583556C411yescharacteristic, complemented
26#14583546C411yescharacteristic, complemented
27#14583537C411yescharacteristic, complemented
28#14583491—21no—
29#14583484—21no—
30#14583459—21no—
31#14583435C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583410C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38C2×(C22⋊D43)⋊C4—21no—
39#14582973—21no—
40#14582973—21no—
41#14582968—21no—
42#14582968—21no—
43#14582953C2211yescharacteristic, complemented
44#14582953C2211yescharacteristic, complemented
45#14582863C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic
47C22⋊C8×D43C2211yescharacteristic
48#14582794—21no—
49#14582771—21no—
50#14582770—21no—
51#14582763C2211yescharacteristic, complemented
52#14582758C2211yescharacteristic
53#14582750C2211yescharacteristic, complemented
54C2×C43⋊#95C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic
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×#525C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C43×#380C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic, complemented
76C2×Q8×D43C2×C411yescharacteristic, complemented
77C22×C22⋊D43D411yescharacteristic
78C2×D4×D43—21no—
79C2×D4×D43C2×C411yescharacteristic, complemented
80C23×Dic43—21no—
81C22×C4×D43—21no—
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86#13063320—21no—
87#13063319—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063317—21no—
93#13063316C2×C411yescharacteristic, complemented
94#13063316C2×C411yescharacteristic, complemented
95#13063315—21no—
96#13063314C2×C411yescharacteristic, complemented
97#13063312—21no—
98#13063312C2×C411yescharacteristic, complemented
99#13063311—21no—
100#13063309—21no—
101#13063308—21no—
102#13063308—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063307—21no—
107#13063306—21no—
108#13063306—21no—
109#13063305C2×C411yescharacteristic, complemented
110#13063304—21no—
111#13063304C2×C411yescharacteristic, complemented
112#13063304C2311yescharacteristic
113#13063303—21no—
114#13063303—21no—
115#13063302—21no—
116#13063301C2×C411yescharacteristic, complemented
117#13063300C2×C411yescharacteristic, complemented
118#13063299C2×C411yescharacteristic, complemented
119#13063299C2311yescharacteristic
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063297—21no—
124#13063297—21no—
125#13063296—21no—
126#13063296—21no—
127#13063296—21no—
128#13063296C2×C411yescharacteristic, complemented
129#13063294—21no—
130#13063293—21no—
131#13063293—21no—
132Q8×Dic43C2×C411yescharacteristic, complemented
133#13063290C2×C411yescharacteristic, complemented
134C4×D172—21no—
135D4×Dic43—21no—
136D4×Dic43C2×C411yescharacteristic, complemented
137#13063287—21no—
138#13063287C2×C411yescharacteristic, complemented
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
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—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—44no—
153#13063284C2×C411yescharacteristic, complemented
154#13063283—21no—
155#13063283—21no—
156#13063282—21no—
157#13063281—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C4⋊C4×D43—21no—
163C4⋊C4×D43C2×C411yescharacteristic, complemented
164C4⋊C4×D43C2×C411yescharacteristic, complemented
165C2×C22⋊Dic43D411yescharacteristic
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4D411yescharacteristic
169C22⋊C4×D43—21no—
170C22⋊C4×D43—21no—
171C22⋊C4×D43—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—
182#13063235—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C2×#41×C43C2×C411yescharacteristic, complemented
189C23×C4×C43C2311yescharacteristic
190C2×M16×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×C4⋊C4×C43—21no—
201C2×C22⋊C4×C43—21no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C23×D43C2×D411yescharacteristic
210#41×C43—81no—
211C2×Q8×C43C22×C411yescharacteristic
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43C22×C411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—81no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2411yescharacteristic
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—22no—
232C2×C22⋊D43—22no—
233C2×C22⋊D43C22⋊C411yescharacteristic
234C2×C22⋊D43C22⋊C411yescharacteristic
235C2×C22⋊D43C22⋊C411yescharacteristic
236C2×C22⋊D43C22⋊C411yescharacteristic
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—42no—
241C22×Dic43—42no—
242C22×Dic43—81no—
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246Q8×D43—81no—
247D4×D43—42no—
248D4×D43—42no—
249D4×D43—81no—
250#10621898—81no—
251C2×D172—21no—
252C2×D172C22×C411yescharacteristic
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×C4×D43—42no—
259C2×C4×D43—42no—
260C2×C4×D43—81no—
261C2×C4×D43—81no—
262C2×C4×D43C22×C411yescharacteristic
263C2×C4×D43C22×C411yescharacteristic
264C2×C4×D43C2×D411yescharacteristic
265C2×C4×D43C2×D411yescharacteristic
266C2×Dic86—21no—
267C2×Dic86C22×C411yescharacteristic
268M16×C43—81no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—81no—
274C4⋊C4×C43C22×C411yescharacteristic
275C4⋊C4×C43C22×C411yescharacteristic
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—42no—
282C42×C43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43C22⋊C411yescharacteristic
291C22⋊Dic43C22⋊C411yescharacteristic
292C22⋊Dic43C22⋊C411yescharacteristic
293C22⋊Dic43C22⋊C411yescharacteristic
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—42no—
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304(C2×D43)⋊C4C22⋊C411yescharacteristic
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307C4⋊Dic43—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43—21no—
311C4⋊Dic43C22×C411yescharacteristic
312C4⋊Dic43C22×C411yescharacteristic
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—42no—
322Dic43⋊C4—42no—
323Dic43⋊C4—81no—
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43—21no—
331C4×Dic43—42no—
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C22×C411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C4×Dic43C2×D411yescharacteristic
336#10621877—81no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8—21no—
339C8×D43—81no—
340C8×D43—81no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C2×C22⋊C411yescharacteristic
348C23×C43C22×D411yescharacteristic
349C22×D43—21no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—42no—
353C22×D43—81no—
354C22×D43—81no—
355C22×D43C2×C22⋊C411yescharacteristic
356C22×D43C2×C22⋊C411yescharacteristic
357C22×D43AGL(1,ℤ/8)12yes—
358C22×D43#13712yes—
359Q8×C43—41no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—41no—
363D4×C43—81no—
364D4×C43—81no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
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—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—81no—
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C23×C411yescharacteristic
384C2×C4×C43C22×D411yescharacteristic
385C22⋊D43—22no—
386C22⋊D43—22no—
387C22⋊D43—22no—
388C22⋊D43—22no—
389C22⋊D43—41no—
390C22⋊D43—41no—
391C22⋊D43—42no—
392C22⋊D43—81no—
393C22⋊D43—81no—
394C22⋊D43—81no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—22no—
398C2×Dic43—21no—
399C2×Dic43—21no—
400C2×Dic43—21no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—81no—
409C2×Dic43—84no—
410C2×Dic43C2×C22⋊C411yescharacteristic
411C2×Dic43C2×C22⋊C411yescharacteristic
412C2×Dic43C2×C22⋊C411yescharacteristic
413C2×Dic43C2×C22⋊C411yescharacteristic
414C2×Dic43C2×C22⋊C411yescharacteristic
415C2×Dic43C2×C22⋊C411yescharacteristic
416D172—41no—
417D172—42no—
418C4×D43—41no—
419C4×D43—41no—
420C4×D43—41no—
421C4×D43—41no—
422C4×D43—42no—
423C4×D43—81no—
424C4×D43—81no—
425C4×D43—81no—
426C4×D43—81no—
427C4×D43—84no—
428Dic86—41no—
429Dic86—81no—
430C8×C43—41no—
431C8×C43—41no—
432C43⋊C8—41no—
433C43⋊C8—41no—
434#17622—431nomaximal, Sylow
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—21no—
438C22×C43—21no—
439C22×C43—21no—
440C22×C43—21no—
441C22×C43—21no—
442C22×C43—21no—
443C22×C43—42no—
444C22×C43—42no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43C22×C22⋊C411yescharacteristic
449C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C43C2×#13711yescharacteristic
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—21no—
454C2×D43—21no—
455C2×D43—42no—
456C2×D43—42no—
457C2×D43—41no—
458C2×D43—41no—
459C2×D43—41no—
460C2×D43—162no—
461C2×D43#41712yes—
462C2×D43#41712yes—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—41no—
468C4×C43—41no—
469C4×C43—41no—
470C4×C43—81no—
471C4×C43—81no—
472Dic43—21no—
473Dic43—21no—
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—42no—
479Dic43—41no—
480Dic43—41no—
481Dic43—41no—
482Dic43—81no—
483#3505—431no—
484#2973—431no—
485#2349—431no—
486#1520—431no—
487#1519—431no—
488#1513—431no—
489#1513D4311yescharacteristic, complemented
490#1512—431no—
491#1512—431no—
492#1509—431no—
493#1509—431no—
494#1504—431no—
495#1504—431no—
496C2×#328—431no—
497C2×#327—431no—
498C2×C43—21no—
499C2×C43—21no—
500C2×C43—41no—
501C2×C43—41no—
502C2×C43—81no—
503C2×C43#288311yescharacteristic
504C2×C43C2×#41711yescharacteristic
505C2×C43#290111yescharacteristic
506D43—22no—
507D43—22no—
508D43—81no—
509#553—431no—
510#553—431no—
511#553—861no—
512#553—861no—
513#552—431no—
514#552—431no—
515#551—861no—
516#551—861no—
517#548—431no—
518#548—431no—
519#546—431no—
520#546—431no—
521#539—861no—
522#538—861no—
523#534—861no—
524#529—431no—
525#529—431no—
526#525—431no—
527#525C2×D4311yescharacteristic
528C2×C22⋊Q8—431no—
529C2×#121—431no—
530#518—861no—
531C2×C4×D4—431no—
532C2×C4×D4—861no—
533#435—861no—
534#435—861no—
535#435—861no—
536#435—861no—
537#432—431no—
538#432—431no—
539#407—431no—
540#407C2×D4311yescharacteristic, complemented
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
543#389—861no—
544#385—861no—
545#385—861no—
546#382—431no—
547#380—431no—
548#380C2×D4311yescharacteristic, complemented
549C4×C4⋊C4—431no—
550C2×#95—431no—
551C2×#95—431no—
552#328—431no—
553#328—431no—
554#328—431no—
555#328—431no—
556#328—431no—
557#328—431no—
558#328C2×D4311yescharacteristic, complemented
559#328C2×D4311yescharacteristic, complemented
560#327—431no—
561#327—431no—
562#327—431no—
563#327—431no—
564#327—431no—
565#327—431no—
566#327C2×D4311yescharacteristic
567#327C2×D4311yescharacteristic
568C43#1762211yescharacteristic, complemented, Sylow
569C2×#41—431no—
570C2×#41C4×D4311yescharacteristic, complemented
571C22×Q8—431no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4—861no—
575C23×C4—431no—
576C23×C4—861no—
577C23×C4—861no—
578C23×C4C22×D4311yescharacteristic
579C2×M16—21no—
580C2×M16—861no—
581C22×C8—861no—
582C22×C8—861no—
583#126—861no—
584#126—861no—
585#126—861no—
586#126—861no—
587#126—861no—
588#126—861no—
589#125—431no—
590#125—431no—
591#125—861no—
592#125—861no—
593#124—431no—
594#124—431no—
595#124—861no—
596#124—861no—
597#123—21no—
598#123—861no—
599#123—861no—
600#123—861no—
601#123—861no—
602#123—861no—
603#123—861no—
604#123—861no—
605#123—861no—
606#123—861no—
607C22⋊Q8—431no—
608C22⋊Q8—431no—
609C22⋊Q8—431no—
610C22⋊Q8—431no—
611C22⋊Q8—861no—
612C22⋊Q8—861no—
613C22⋊Q8—861no—
614C22⋊Q8—861no—
615C22⋊Q8C4×D4311yescharacteristic, complemented
616C22⋊Q8C22×D4311yescharacteristic
617#121—431no—
618#121—431no—
619#121—431no—
620#121—431no—
621#121—861no—
622#121—861no—
623#121—861no—
624#121—861no—
625#121—861no—
626#121—861no—
627#121—861no—
628#121—861no—
629#121C4×D4311yescharacteristic, complemented
630#121C22×D4311yescharacteristic
631#120—21no—
632#120—861no—
633#120—861no—
634#120—861no—
635C4×Q8—431no—
636C4×Q8—431no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—431no—
640C4×D4—431no—
641C4×D4—431no—
642C4×D4—431no—
643C4×D4—431no—
644C4×D4—431no—
645C4×D4—431no—
646C4×D4—431no—
647C4×D4—431no—
648C4×D4—431no—
649C4×D4—861no—
650C4×D4—861no—
651C4×D4—861no—
652C4×D4—861no—
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—1724no—
658#117—431no—
659#117—861no—
660#117—861no—
661#117—861no—
662#117—861no—
663#117C4×D4311yescharacteristic, complemented
664C2×C4⋊C4—21no—
665C2×C4⋊C4—431no—
666C2×C4⋊C4—431no—
667C2×C4⋊C4—431no—
668C2×C4⋊C4—861no—
669C2×C4⋊C4—861no—
670C2×C4⋊C4—861no—
671C2×C4⋊C4—861no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—431no—
674C2×C22⋊C4—431no—
675C2×C22⋊C4—861no—
676C2×C22⋊C4—861no—
677C2×C22⋊C4—861no—
678C2×C22⋊C4—861no—
679C2×C22⋊C4—861no—
680C2×C42—431no—
681C2×C42—861no—
682C4⋊C8—861no—
683C4⋊C8—861no—
684C22⋊C8—21no—
685C22⋊C8—431no—
686C22⋊C8—431no—
687C22⋊C8—861no—
688C22⋊C8—861no—
689C22⋊C8—861no—
690C22⋊C8C22×D4311yescharacteristic
691C22⋊C8C22×D4311yescharacteristic
692#97—861no—
693#97—861no—
694#95—431no—
695#95—431no—
696#95—861no—
697#95—861no—
698#95—861no—
699#95C22×D4311yescharacteristic
700#95C22×D4311yescharacteristic
701C24—431no—
702C24—861no—
703C24D4×D4311yescharacteristic
704#41—81no—
705#41—3441no—
706C2×Q8—431no—
707C2×Q8—861no—
708C2×Q8—3441no—
709C2×Q8C2×C4×D4311yescharacteristic
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—431no—
714C2×D4—431no—
715C2×D4—431no—
716C2×D4—431no—
717C2×D4—431no—
718C2×D4—861no—
719C2×D4—861no—
720C2×D4—862no—
721C2×D4—862no—
722C2×D4—861no—
723C2×D4—861no—
724C2×D4—861no—
725C2×D4—861no—
726C2×D4—3441no—
727C2×D4—1722no—
728C2×D4—1722no—
729C2×D4C2×C4×D4311yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—81no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—431no—
737C22×C4—431no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—431no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—3441no—
750C22×C4—3441no—
751C22×C4—3441no—
752C22×C4—1722no—
753C22×C4—1722no—
754C22×C4—1722no—
755C22×C4—1722no—
756C22×C4C2×C4×D4311yescharacteristic
757C22×C4C2×C4×D4311yescharacteristic
758C22×C4D4×D4311yescharacteristic
759C22×C4D4×D4311yescharacteristic
760C22×C4D4×D4311yescharacteristic
761C22×C4C23×D4311yescharacteristic
762M16—81no—
763M16—3441no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—861no—
767C2×C8—861no—
768C2×C8—3441no—
769C2×C8—3441no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—81no—
773C4⋊C4—431no—
774C4⋊C4—431no—
775C4⋊C4—431no—
776C4⋊C4—431no—
777C4⋊C4—431no—
778C4⋊C4—431no—
779C4⋊C4—861no—
780C4⋊C4—861no—
781C4⋊C4—861no—
782C4⋊C4—861no—
783C4⋊C4—861no—
784C4⋊C4—861no—
785C4⋊C4—861no—
786C4⋊C4—861no—
787C4⋊C4—861no—
788C4⋊C4—861no—
789C4⋊C4—861no—
790C4⋊C4—861no—
791C4⋊C4—3441no—
792C4⋊C4—1722no—
793C4⋊C4—1722no—
794C4⋊C4C2×C4×D4311yescharacteristic
795C4⋊C4C2×C4×D4311yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—431no—
803C22⋊C4—431no—
804C22⋊C4—431no—
805C22⋊C4—431no—
806C22⋊C4—431no—
807C22⋊C4—431no—
808C22⋊C4—431no—
809C22⋊C4—431no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C22⋊C4—861no—
819C22⋊C4—861no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—861no—
825C22⋊C4—1722no—
826C42—21no—
827C42—431no—
828C42—431no—
829C42—431no—
830C42—431no—
831C42—861no—
832C42—861no—
833C42—861no—
834C42—1722no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—41no—
839C23—41no—
840C23—431no—
841C23—431no—
842C23—432no—
843C23—432no—
844C23—861no—
845C23—3441no—
846C23—3441no—
847C23—1721no—
848C23—1721no—
849C23—1722no—
850C23C22⋊C4×D4311yescharacteristic
851C23C22⋊C4×D4311yescharacteristic
852C23C2×D4×D4311yescharacteristic
853Q8—41no—
854Q8—3441no—
855Q8—1721no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—81no—
860D4—81no—
861D4—862no—
862D4—862no—
863D4—862no—
864D4—862no—
865D4—3441no—
866D4—3441no—
867D4—3441no—
868D4—1721no—
869D4—1722no—
870D4—1722no—
871D4—1721no—
872D4—1721no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—81no—
889C2×C4—431no—
890C2×C4—431no—
891C2×C4—431no—
892C2×C4—431no—
893C2×C4—431no—
894C2×C4—431no—
895C2×C4—861no—
896C2×C4—861no—
897C2×C4—862no—
898C2×C4—861no—
899C2×C4—861no—
900C2×C4—861no—
901C2×C4—3441no—
902C2×C4—3441no—
903C2×C4—3441no—
904C2×C4—3441no—
905C2×C4—3444no—
906C2×C4—3441no—
907C2×C4—3444no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1722no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4—1721no—
916C2×C4—1721no—
917C2×C4—1721no—
918C2×C4—1721no—
919C2×C4—1721no—
920C2×C4C22⋊C4×D4311yescharacteristic
921C2×C4C22⋊C4×D4311yescharacteristic
922C2×C4C22×C4×D4311yescharacteristic
923C2×C4C2×D4×D4311yescharacteristic
924C8—41no—
925C8—41no—
926C8—1721no—
927C8—1721no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—21no—
934C22—21no—
935C22—21no—
936C22—42no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—432no—
942C22—432no—
943C22—861no—
944C22—861no—
945C22—861no—
946C22—861no—
947C22—1722no—
948C22—1722no—
949C22—1721no—
950C22—1721no—
951C22—1721no—
952C22—6882no—
953C22C2×C22⋊C4×D4311yescharacteristic
954C22AGL(1,ℤ/8)×D4311yescharacteristic
955C22#137×D4311yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—41no—
961C4—41no—
962C4—41no—
963C4—81no—
964C4—81no—
965C4—861no—
966C4—861no—
967C4—861no—
968C4—861no—
969C4—861no—
970C4—861no—
971C4—3441no—
972C4—1722no—
973C4—1721no—
974C4—1721no—
975C4—1721no—
976C2—21no—
977C2—21no—
978C2—41no—
979C2—41no—
980C2—81no—
981C2—862no—
982C2—862no—
983C2—3441no—
984C2#1914305311yescharacteristic
985C2#417×D4311yescharacteristic
986C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1513C2
socleC22×C43C22×C22⋊C4
prime radical#19148423C2
cosocleC22×C4×C43C24
hypercenter#1513D43
hypocenterC43#17622
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1513

Complements

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

NH ≅ G/Ntype
2. #19143622C2semidirect
3. #19137499C2semidirect
4. #19133165C2semidirect
5. #19133161C2semidirect
6. #19133136C2semidirect
7. #19133132C2semidirect
8. #19133130C2semidirect
9. #19133119C2semidirect
10. #19133117C2semidirect
11. #19133100C2semidirect
12. #19133099C2semidirect
13. #328×D43C2semidirect
14. #327×D43C2semidirect
15. C43×#1513C2semidirect
17. #14583596C4semidirect
19. #14583593C4semidirect
20. #14583588C4semidirect
21. #14583583C4semidirect
24. #14583559C4semidirect
25. #14583556C4semidirect
26. #14583546C4semidirect
27. #14583537C4semidirect
43. #14582953C22semidirect
44. #14582953C22semidirect
45. #14582863C22semidirect
51. #14582763C22semidirect
53. #14582750C22semidirect
54. C2×C43⋊#95C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C43×#407C22semidirect
70. C43×#380C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
75. C2×#10621898C2×C4semidirect
76. C2×Q8×D43C2×C4semidirect
79. C2×D4×D43C2×C4semidirect
93. #13063316C2×C4semidirect
94. #13063316C2×C4semidirect
96. #13063314C2×C4semidirect
98. #13063312C2×C4semidirect
109. #13063305C2×C4semidirect
111. #13063304C2×C4semidirect
116. #13063301C2×C4semidirect
117. #13063300C2×C4semidirect
118. #13063299C2×C4semidirect
128. #13063296C2×C4semidirect
132. Q8×Dic43C2×C4semidirect
133. #13063290C2×C4semidirect
136. D4×Dic43C2×C4semidirect
138. #13063287C2×C4semidirect
153. #13063284C2×C4semidirect
163. C4⋊C4×D43C2×C4semidirect
164. C4⋊C4×D43C2×C4semidirect
188. C2×#41×C43C2×C4semidirect
192. C22⋊Q8×C43C2×C4semidirect
194. #121×C43C2×C4semidirect
199. #117×C43C2×C4semidirect
489. #1513D43semidirect
540. #407C2×D43semidirect
548. #380C2×D43semidirect
558. #328C2×D43semidirect
559. #328C2×D43semidirect
568. C43#17622semidirect
570. C2×#41C4×D43semidirect
615. C22⋊Q8C4×D43semidirect
629. #121C4×D43semidirect
663. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191484232
#191436222
#191374992
#191331652
#191331612
#191331362
#191331322
#191331302
#191331192
#191331172
#191331002
#191330992
#328×D432
#327×D432
C43×#15132
#1762243