Finite Group Databasebeta

← #25064372

Subgroups — #25064372

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#19137502C211yesmaximal, characteristic, complemented
4#19133165C211yesmaximal, characteristic, complemented
5#19133161C211yesmaximal, characteristic, complemented
6#19133139C211yesmaximal, characteristic, complemented
7#19133138C211yesmaximal, characteristic, complemented
8#19133132C211yesmaximal, characteristic, complemented
9#19133130C211yesmaximal, characteristic, complemented
10#19133119C211yesmaximal, characteristic, complemented
11#19133117C211yesmaximal, characteristic, complemented
12#19133097C211yesmaximal, characteristic, complemented
13#328×D43C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1504C211yesmaximal, 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⋊D43—21no—
38C2×C4×C22⋊D43C2211yescharacteristic
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#14582796—21no—
49#14582773—21no—
50#14582772—21no—
51#14582763C2211yescharacteristic, complemented
52#14582759C2211yescharacteristic, complemented
53#14582758C2211yescharacteristic
54#14582750C2211yescharacteristic, 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
70C2×#95×C43C2211yescharacteristic, 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
80C22×C4×D43—21no—
81C22×C4×D43C2311yescharacteristic
82C2×#10621877—21no—
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85#13063320—21no—
86#13063319—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063317—21no—
92#13063316C2×C411yescharacteristic, complemented
93#13063316C2×C411yescharacteristic, complemented
94#13063315—21no—
95#13063314C2×C411yescharacteristic, complemented
96#13063312—21no—
97#13063312C2×C411yescharacteristic, complemented
98#13063311—21no—
99#13063309—21no—
100#13063308—21no—
101#13063308—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063306—21no—
107#13063306—21no—
108#13063305C2×C411yescharacteristic, complemented
109#13063304—21no—
110#13063304C2×C411yescharacteristic, complemented
111#13063304C2311yescharacteristic
112#13063303—21no—
113#13063303—21no—
114#13063302—21no—
115#13063301C2×C411yescharacteristic, complemented
116#13063300C2×C411yescharacteristic, complemented
117#13063299C2×C411yescharacteristic, complemented
118#13063299C2311yescharacteristic
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063296—21no—
125#13063296—21no—
126#13063296—21no—
127#13063296C2×C411yescharacteristic, complemented
128#13063294—21no—
129#13063293—21no—
130#13063293—21no—
131Q8×Dic43C2×C411yescharacteristic, complemented
132#13063290C2×C411yescharacteristic, complemented
133C4×D172—21no—
134D4×Dic43—21no—
135D4×Dic43C2×C411yescharacteristic, complemented
136#13063287—21no—
137#13063287C2×C411yescharacteristic, complemented
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—44no—
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#13063284C2×C411yescharacteristic, complemented
153#13063283—21no—
154#13063283—21no—
155#13063282—21no—
156#13063281—21no—
157C2×C4⋊Dic43—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⋊Dic43—21no—
166C2×C22⋊Dic43D411yescharacteristic
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4D411yescharacteristic
170C22⋊C4×D43—21no—
171C22⋊C4×D43—21no—
172C22⋊C4×D43—21no—
173C2×C4×Dic43—21no—
174C2×C4×Dic43C2311yescharacteristic
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177C22⋊(C43⋊C8)—21no—
178C22⋊(C43⋊C8)C2311yescharacteristic
179C22⋊(C43⋊C8)C2311yescharacteristic
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182#13063235—21no—
183#13063235—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C2×#41×C43C2×C411yescharacteristic, complemented
189C23×C4×C43—21no—
190C23×C4×C43C2311yescharacteristic
191C2×M16×C43—21no—
192#123×C43—21no—
193C22⋊Q8×C43C2×C411yescharacteristic, complemented
194C22⋊Q8×C43C2311yescharacteristic
195#121×C43C2×C411yescharacteristic, complemented
196#121×C43C2311yescharacteristic
197#120×C43—21no—
198C4×D4×C43—21no—
199C4×D4×C43—21no—
200#117×C43C2×C411yescharacteristic, complemented
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#95×C43—21no—
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—42no—
220C22×C4×C43—42no—
221C22×C4×C43—81no—
222C22×C4×C43—81no—
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2411yescharacteristic
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—22no—
235C2×C22⋊D43—22no—
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
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×C43C22×C411yescharacteristic
274C4⋊C4×C43C22×C411yescharacteristic
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—21no—
280C42×C43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288C22⋊Dic43—42no—
289C22⋊Dic43C22⋊C411yescharacteristic
290C22⋊Dic43C22⋊C411yescharacteristic
291C22⋊Dic43C22⋊C411yescharacteristic
292C22⋊Dic43C22⋊C411yescharacteristic
293(C2×D43)⋊C4—21no—
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—42no—
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304(C2×D43)⋊C4C22⋊C411yescharacteristic
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43—81no—
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—22no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
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×C43—84no—
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C23×C411yescharacteristic
385C2×C4×C43C22×D411yescharacteristic
386C22⋊D43—22no—
387C22⋊D43—22no—
388C22⋊D43—22no—
389C22⋊D43—22no—
390C22⋊D43—41no—
391C22⋊D43—41no—
392C22⋊D43—42no—
393C22⋊D43—81no—
394C22⋊D43—81no—
395C22⋊D43—81no—
396C2×Dic43—21no—
397C2×Dic43—21no—
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—41no—
409C2×Dic43—81no—
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—42no—
468C4×C43—41no—
469C4×C43—41no—
470C4×C43—41no—
471C4×C43—81no—
472Dic43—21no—
473Dic43—21no—
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—41no—
479Dic43—41no—
480Dic43—41no—
481Dic43—81no—
482Dic43—81no—
483#3505—431no—
484#2973—431no—
485#2349—431no—
486#1520—431no—
487#1519—431no—
488#1513—431no—
489#1513—431no—
490#1512—431no—
491#1512—431no—
492#1509—431no—
493#1509—431no—
494#1504—431no—
495#1504D4311yescharacteristic, complemented
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#380—431no—
549C4×C4⋊C4—431no—
550C2×#95—431no—
551C2×#95C2×D4311yescharacteristic, complemented
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—21no—
576C23×C4—431no—
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—431no—
665C2×C4⋊C4—431no—
666C2×C4⋊C4—431no—
667C2×C4⋊C4—861no—
668C2×C4⋊C4—861no—
669C2×C4⋊C4—861no—
670C2×C4⋊C4—861no—
671C2×C4⋊C4—861no—
672C2×C22⋊C4—431no—
673C2×C22⋊C4—431no—
674C2×C22⋊C4—861no—
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—21no—
695#95—431no—
696#95—431no—
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—42no—
734C22×C4—42no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4—431no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—431no—
743C22×C4—431no—
744C22×C4—861no—
745C22×C4—861no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—3441no—
753C22×C4—3441no—
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—431no—
773C4⋊C4—431no—
774C4⋊C4—431no—
775C4⋊C4—431no—
776C4⋊C4—431no—
777C4⋊C4—431no—
778C4⋊C4—861no—
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—3441no—
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—431no—
802C22⋊C4—431no—
803C22⋊C4—431no—
804C22⋊C4—431no—
805C22⋊C4—431no—
806C22⋊C4—431no—
807C22⋊C4—431no—
808C22⋊C4—431no—
809C22⋊C4—861no—
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—1722no—
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—22no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
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—84no—
890C2×C4—431no—
891C2×C4—431no—
892C2×C4—431no—
893C2×C4—431no—
894C2×C4—431no—
895C2×C4—431no—
896C2×C4—861no—
897C2×C4—861no—
898C2×C4—861no—
899C2×C4—861no—
900C2×C4—861no—
901C2×C4—3441no—
902C2×C4—3441no—
903C2×C4—3444no—
904C2×C4—3441no—
905C2×C4—3441no—
906C2×C4—3441no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1722no—
912C2×C4—1721no—
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—42no—
961C4—41no—
962C4—41no—
963C4—41no—
964C4—81no—
965C4—861no—
966C4—861no—
967C4—861no—
968C4—861no—
969C4—861no—
970C4—861no—
971C4—3441no—
972C4—3441no—
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#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1504C2
socleC22×C43C22×C22⋊C4
prime radical#19148423C2
cosocleC22×C4×C43C24
hypercenter#1504D43
hypocenterC43#17622
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #19143622C2semidirect
3. #19137502C2semidirect
4. #19133165C2semidirect
5. #19133161C2semidirect
6. #19133139C2semidirect
7. #19133138C2semidirect
8. #19133132C2semidirect
9. #19133130C2semidirect
10. #19133119C2semidirect
11. #19133117C2semidirect
12. #19133097C2semidirect
13. #328×D43C2semidirect
14. #327×D43C2semidirect
15. C43×#1504C2semidirect
17. #14583596C4semidirect
19. #14583593C4semidirect
20. #14583588C4semidirect
21. #14583583C4semidirect
24. #14583559C4semidirect
25. #14583556C4semidirect
26. #14583546C4semidirect
27. #14583537C4semidirect
43. #14582953C22semidirect
44. #14582953C22semidirect
45. #14582863C22semidirect
51. #14582763C22semidirect
52. #14582759C22semidirect
54. #14582750C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C43×#407C22semidirect
70. C2×#95×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
75. C2×#10621898C2×C4semidirect
76. C2×Q8×D43C2×C4semidirect
79. C2×D4×D43C2×C4semidirect
92. #13063316C2×C4semidirect
93. #13063316C2×C4semidirect
95. #13063314C2×C4semidirect
97. #13063312C2×C4semidirect
108. #13063305C2×C4semidirect
110. #13063304C2×C4semidirect
115. #13063301C2×C4semidirect
116. #13063300C2×C4semidirect
117. #13063299C2×C4semidirect
127. #13063296C2×C4semidirect
131. Q8×Dic43C2×C4semidirect
132. #13063290C2×C4semidirect
135. D4×Dic43C2×C4semidirect
137. #13063287C2×C4semidirect
152. #13063284C2×C4semidirect
163. C4⋊C4×D43C2×C4semidirect
164. C4⋊C4×D43C2×C4semidirect
188. C2×#41×C43C2×C4semidirect
193. C22⋊Q8×C43C2×C4semidirect
195. #121×C43C2×C4semidirect
200. #117×C43C2×C4semidirect
495. #1504D43semidirect
540. #407C2×D43semidirect
551. C2×#95C2×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
#191375022
#191331652
#191331612
#191331392
#191331382
#191331322
#191331302
#191331192
#191331172
#191330972
#328×D432
#327×D432
C43×#15042
#1762243