Finite Group Databasebeta

← #25064195

Subgroups — #25064195

Order 11008.

1366 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148260C211yesmaximal, characteristic
2#19143045C211yesmaximal, characteristic, complemented
3#19137419C211yesmaximal, characteristic, complemented
4#19133161C211yesmaximal, characteristic, complemented
5#19133149C211yesmaximal, characteristic, complemented
6#19133148C211yesmaximal, characteristic, complemented
7#19133135C211yesmaximal, characteristic, complemented
8#19133122C211yesmaximal, characteristic, complemented
9#19133109C211yesmaximal, characteristic, complemented
10#19133100C211yesmaximal, characteristic, complemented
11#19133096C211yesmaximal, characteristic, complemented
12#19133083C211yesmaximal, characteristic, complemented
13C2×#14582633C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1510C211yesmaximal, characteristic, complemented
16C2×#13063370C411yescharacteristic, complemented
17C22×#10621898C2211yescharacteristic
18C2×#13063333—21no—
19#14583567—21no—
20#14583555—21no—
21#14583546—21no—
22#14583539—21no—
23#14583539—21no—
24#14583533—21no—
25D4×C22⋊D43—21no—
26D4×C22⋊D43—21no—
27#14583480C411yescharacteristic, complemented
28#14583478C411yescharacteristic, complemented
29#14583478C411yescharacteristic, complemented
30#14583466C411yescharacteristic, complemented
31#14583465C411yescharacteristic, complemented
32#14583465C411yescharacteristic, complemented
33#14583410C2211yescharacteristic
34#14583409C2211yescharacteristic
35#14583409C2211yescharacteristic
36#121×D43C2211yescharacteristic
37#121×D43C2211yescharacteristic
38#14583380C411yescharacteristic, complemented
39C2×(C22⋊D43)⋊C4—21no—
40#14582867—21no—
41#14582864—21no—
42#14582864—21no—
43#14582861C2211yescharacteristic, complemented
44#14582861C2211yescharacteristic, complemented
45C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic, complemented
47C22⋊C8×D43C2211yescharacteristic, complemented
48#14582803—21no—
49#14582777—21no—
50#14582776—21no—
51#14582761C2211yescharacteristic, complemented
52#14582758C2211yescharacteristic, complemented
53#14582746C2211yescharacteristic, complemented
54C2×C43⋊#95C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582635C2211yescharacteristic, complemented
59#14582635C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582633C2211yescharacteristic, complemented
65#14582633C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C2×#121×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C43×#381C2211yescharacteristic, complemented
71C43×#327C2211yescharacteristic, complemented
72C43×#327C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75#13063370—44no—
76C2×#10621898—44no—
77C2×#10621898C2×C411yescharacteristic
78C2×#10621898C2×C411yescharacteristic
79C2×#10621898C2×C411yescharacteristic
80C2×#10621898C2×C411yescharacteristic
81C2×#10621898C2×C411yescharacteristic, complemented
82C2×#10621898D411yescharacteristic
83C2×#10621898D411yescharacteristic
84C2×#10621898D411yescharacteristic
85C2×#10621898D411yescharacteristic
86C2×#10621900—21no—
87C2×#10621900C2×C411yescharacteristic, complemented
88C2×#10621900C2×C411yescharacteristic, complemented
89C22×Dic86D411yescharacteristic
90C22×D172D411yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43D411yescharacteristic
94C22×C22⋊D43D411yescharacteristic
95C2×D4×D43—21no—
96C2×D4×D43—21no—
97C2×D4×D43—21no—
98C2×D4×D43C2×C411yescharacteristic, complemented
99C2×D4×D43C2×C411yescharacteristic, complemented
100C23×Dic43—21no—
101C22×C4×D43—21no—
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2311yescharacteristic
104#13063333—44no—
105C2×#10621872—21no—
106C2×#10621872—21no—
107C22×C43⋊C8—21no—
108C2×C8×D43—21no—
109C2×C8×D43—21no—
110#13063321—21no—
111#13063321—21no—
112#13063321—21no—
113#13063312—21no—
114#13063311—21no—
115#13063311—21no—
116#13063308—21no—
117#13063307—21no—
118#13063307—21no—
119#13063305—21no—
120#13063305C2×C411yescharacteristic, complemented
121#13063305C2×C411yescharacteristic, complemented
122#13063304C2×C411yescharacteristic, complemented
123#13063304C2311yescharacteristic
124#13063302—21no—
125#13063302—21no—
126#13063300—21no—
127#13063300C2×C411yescharacteristic, complemented
128#13063300C2×C411yescharacteristic, complemented
129#13063299—21no—
130#13063299—21no—
131#13063299C2×C411yescharacteristic, complemented
132#13063299C2311yescharacteristic
133#13063298—21no—
134#13063298—21no—
135#13063298—21no—
136#13063298—21no—
137#13063297—21no—
138#13063297—21no—
139#13063297—21no—
140#13063297—21no—
141#13063296—21no—
142#13063296—21no—
143#13063296C2×C411yescharacteristic, complemented
144#13063296C2×C411yescharacteristic, complemented
145#13063296C2×C411yescharacteristic, complemented
146#13063296C2×C411yescharacteristic, complemented
147#13063295—21no—
148#13063295—21no—
149#13063294—21no—
150#13063294—21no—
151#13063294—21no—
152#13063293—21no—
153#13063293—21no—
154#13063293—21no—
155#13063293—21no—
156#13063290—21no—
157D4×Dic43—21no—
158D4×Dic43—21no—
159#13063287—21no—
160C4×C22⋊D43—21no—
161C4×C22⋊D43—21no—
162C4×C22⋊D43—21no—
163C4×C22⋊D43—21no—
164(C22⋊D43)⋊C4—21no—
165(C22⋊D43)⋊C4—21no—
166(C22⋊D43)⋊C4—44no—
167#13063284C2×C411yescharacteristic, complemented
168#13063283C2×C411yescharacteristic, complemented
169#13063283C2×C411yescharacteristic, complemented
170C2×Dic43⋊C4—21no—
171C4⋊C4×D43C2×C411yescharacteristic, complemented
172C4⋊C4×D43C2×C411yescharacteristic, complemented
173C2×(C2×D43)⋊C4—21no—
174C2×(C2×D43)⋊C4—21no—
175C2×(C2×D43)⋊C4—21no—
176C22⋊C4×D43—21no—
177C22⋊C4×D43—21no—
178C2×C4×Dic43—21no—
179C22⋊(C43⋊C8)—21no—
180C22⋊(C43⋊C8)C2311yescharacteristic
181C22⋊(C43⋊C8)C2311yescharacteristic
182(C2×D43)⋊C8—21no—
183(C2×D43)⋊C8—21no—
184(C2×D43)⋊C8—21no—
185(C2×D43)⋊C8—21no—
186C43⋊#95—21no—
187C43⋊#95—21no—
188C43⋊#95—21no—
189C43⋊#95C2311yescharacteristic
190C43⋊#95C2311yescharacteristic
191C22×D4×C43—21no—
192C22×D4×C43C2×C411yescharacteristic, complemented
193C23×C4×C43C2311yescharacteristic
194C2×M16×C43—21no—
195#121×C43—21no—
196#121×C43—21no—
197#121×C43C2×C411yescharacteristic, complemented
198#121×C43C2×C411yescharacteristic, complemented
199#121×C43C2311yescharacteristic
200#121×C43C2311yescharacteristic
201C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
202C2×C22⋊C4×C43—21no—
203C2×C22⋊C4×C43—21no—
204C22⋊C8×C43—21no—
205C22⋊C8×C43C2311yescharacteristic
206C22⋊C8×C43C2311yescharacteristic
207#95×C43—21no—
208#95×C43C2311yescharacteristic
209#95×C43C2311yescharacteristic
210C24×C43—21no—
211C24×C43C2×D411yescharacteristic
212C23×D43—21no—
213C23×D43—21no—
214C23×D43C2×D411yescharacteristic
215C23×D43C2×D411yescharacteristic
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—42no—
222C2×D4×C43—81no—
223C2×D4×C43—81no—
224C2×D4×C43C22×C411yescharacteristic
225C2×D4×C43C22×C411yescharacteristic
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—42no—
230C22×C4×C43C22×C411yescharacteristic
231C22×C4×C43C22×C411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2411yescharacteristic
236C2×C22⋊D43—24no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C2×C22⋊D43—21no—
241C2×C22⋊D43—21no—
242C2×C22⋊D43—21no—
243C2×C22⋊D43—21no—
244C2×C22⋊D43—21no—
245C2×C22⋊D43—21no—
246C2×C22⋊D43—21no—
247C2×C22⋊D43—21no—
248C2×C22⋊D43—42no—
249C2×C22⋊D43—44no—
250C2×C22⋊D43—44no—
251C2×C22⋊D43C22⋊C411yescharacteristic
252C2×C22⋊D43C22⋊C411yescharacteristic
253C2×C22⋊D43C22⋊C411yescharacteristic
254C2×C22⋊D43C22⋊C411yescharacteristic
255C2×C22⋊D43C22⋊C411yescharacteristic
256C2×C22⋊D43C22⋊C411yescharacteristic
257C2×C22⋊D43C22⋊C411yescharacteristic
258C2×C22⋊D43C22⋊C411yescharacteristic
259C22×Dic43—21no—
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43—21no—
263C22×Dic43—42no—
264C22×Dic43—42no—
265C22×Dic43—81no—
266C22×Dic43C2×D411yescharacteristic
267C22×Dic43C2×D411yescharacteristic
268#10621900—44no—
269#10621900—42no—
270#10621900—42no—
271D4×D43—42no—
272D4×D43—44no—
273D4×D43—42no—
274D4×D43—81no—
275D4×D43—81no—
276D4×D43—81no—
277D4×D43—81no—
278#10621898—24no—
279#10621898—24no—
280#10621898—42no—
281#10621898—42no—
282#10621898—42no—
283#10621898—42no—
284#10621898—42no—
285#10621898—42no—
286#10621898—42no—
287C2×D172—21no—
288C2×D172—21no—
289C2×D172—42no—
290C2×D172C22⋊C411yescharacteristic
291C2×D172C22⋊C411yescharacteristic
292C2×D172C22⋊C411yescharacteristic
293C2×D172C22⋊C411yescharacteristic
294C2×D172C22×C411yescharacteristic
295C2×C4×D43—21no—
296C2×C4×D43—21no—
297C2×C4×D43—21no—
298C2×C4×D43—42no—
299C2×C4×D43—42no—
300C2×C4×D43—42no—
301C2×C4×D43—42no—
302C2×C4×D43—81no—
303C2×C4×D43C22×C411yescharacteristic
304C2×C4×D43C22×C411yescharacteristic
305C2×C4×D43C22×C411yescharacteristic
306C2×C4×D43C22×C411yescharacteristic
307C2×C4×D43C2×D411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2×D411yescharacteristic
311C2×Dic86—42no—
312C2×Dic86C22⋊C411yescharacteristic
313C2×Dic86C22⋊C411yescharacteristic
314C2×Dic86C22⋊C411yescharacteristic
315C2×Dic86C22⋊C411yescharacteristic
316C2×Dic86C22×C411yescharacteristic
317M16×C43—42no—
318C2×C8×C43—21no—
319C2×C8×C43—21no—
320C4⋊C4×C43—21no—
321C4⋊C4×C43C22×C411yescharacteristic
322C4⋊C4×C43C22×C411yescharacteristic
323C22⋊C4×C43—21no—
324C22⋊C4×C43—21no—
325C22⋊C4×C43—21no—
326C22⋊C4×C43—21no—
327C22⋊C4×C43—42no—
328C22⋊Dic43—21no—
329C22⋊Dic43—21no—
330C22⋊Dic43—21no—
331C22⋊Dic43—21no—
332C22⋊Dic43—21no—
333C22⋊Dic43—21no—
334C22⋊Dic43—21no—
335(C2×D43)⋊C4—21no—
336(C2×D43)⋊C4—21no—
337(C2×D43)⋊C4—21no—
338(C2×D43)⋊C4—21no—
339(C2×D43)⋊C4—21no—
340(C2×D43)⋊C4—21no—
341(C2×D43)⋊C4—21no—
342(C2×D43)⋊C4—21no—
343(C2×D43)⋊C4—42no—
344(C2×D43)⋊C4—42no—
345(C2×D43)⋊C4—81no—
346C4⋊Dic43—21no—
347C4⋊Dic43—21no—
348C4⋊Dic43C22×C411yescharacteristic
349C4⋊Dic43C22×C411yescharacteristic
350Dic43⋊C4—21no—
351Dic43⋊C4—21no—
352Dic43⋊C4—21no—
353Dic43⋊C4—21no—
354Dic43⋊C4—42no—
355C4×Dic43—21no—
356C4×Dic43—21no—
357C4×Dic43—21no—
358C4×Dic43—42no—
359C2×C43⋊C8—21no—
360C2×C43⋊C8—21no—
361C2×C43⋊C8—42no—
362#10621872—42no—
363#10621872—42no—
364C8×D43—42no—
365C8×D43—42no—
366C23×C43—21no—
367C23×C43—21no—
368C23×C43—22no—
369C23×C43—21no—
370C23×C43—21no—
371C23×C43—41no—
372C23×C43—42no—
373C23×C43—81no—
374C23×C43—81no—
375C23×C43C2×C22⋊C411yescharacteristic
376C23×C43C2×C22⋊C411yescharacteristic
377C23×C43C22×D411yescharacteristic
378C22×D43—21no—
379C22×D43—21no—
380C22×D43—21no—
381C22×D43—21no—
382C22×D43—22no—
383C22×D43—21no—
384C22×D43—41no—
385C22×D43—41no—
386C22×D43—41no—
387C22×D43—42no—
388C22×D43—42no—
389C22×D43—81no—
390C22×D43—81no—
391C22×D43—81no—
392C22×D43—81no—
393C22×D43C2×C22⋊C411yescharacteristic
394C22×D43C2×C22⋊C411yescharacteristic
395C22×D43C2×C22⋊C411yescharacteristic
396C22×D43C2×C22⋊C411yescharacteristic
397D4×C43—41no—
398D4×C43—41no—
399D4×C43—42no—
400D4×C43—41no—
401D4×C43—41no—
402D4×C43—41no—
403D4×C43—41no—
404D4×C43—81no—
405D4×C43—81no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—21no—
409C2×C4×C43—21no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43—41no—
414C2×C4×C43—41no—
415C2×C4×C43—41no—
416C2×C4×C43—41no—
417C2×C4×C43—41no—
418C2×C4×C43—41no—
419C2×C4×C43—41no—
420C2×C4×C43—81no—
421C2×C4×C43C2×C22⋊C411yescharacteristic
422C2×C4×C43C2×C22⋊C411yescharacteristic
423C2×C4×C43C23×C411yescharacteristic
424C2×C4×C43C22×D411yescharacteristic
425C22⋊D43—22no—
426C22⋊D43—22no—
427C22⋊D43—22no—
428C22⋊D43—22no—
429C22⋊D43—22no—
430C22⋊D43—41no—
431C22⋊D43—41no—
432C22⋊D43—42no—
433C22⋊D43—42no—
434C22⋊D43—41no—
435C22⋊D43—41no—
436C22⋊D43—42no—
437C22⋊D43—42no—
438C22⋊D43—42no—
439C22⋊D43—81no—
440C22⋊D43—81no—
441C22⋊D43—81no—
442C22⋊D43—81no—
443C22⋊D43—81no—
444C22⋊D43#9914yes—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—21no—
448C2×Dic43—21no—
449C2×Dic43—21no—
450C2×Dic43—41no—
451C2×Dic43—42no—
452C2×Dic43—41no—
453C2×Dic43—41no—
454C2×Dic43—42no—
455C2×Dic43—41no—
456C2×Dic43—41no—
457C2×Dic43—41no—
458C2×Dic43—84no—
459C2×Dic43C2×C22⋊C411yescharacteristic
460C2×Dic43C2×C22⋊C411yescharacteristic
461C2×Dic43C2×C22⋊C411yescharacteristic
462C2×Dic43C2×C22⋊C411yescharacteristic
463D172—22no—
464D172—22no—
465D172—41no—
466D172—41no—
467D172—41no—
468D172—81no—
469D172—81no—
470C4×D43—22no—
471C4×D43—22no—
472C4×D43—22no—
473C4×D43—22no—
474C4×D43—41no—
475C4×D43—41no—
476C4×D43—41no—
477C4×D43—41no—
478C4×D43—42no—
479C4×D43—81no—
480C4×D43—81no—
481C4×D43—84no—
482Dic86—22no—
483Dic86—22no—
484Dic86—41no—
485Dic86—41no—
486Dic86—41no—
487C8×C43—41no—
488C8×C43—41no—
489C43⋊C8—41no—
490C43⋊C8—41no—
491#17603—431nomaximal, Sylow
492C22×C43—21no—
493C22×C43—21no—
494C22×C43—21no—
495C22×C43—21no—
496C22×C43—21no—
497C22×C43—21no—
498C22×C43—21no—
499C22×C43—42no—
500C22×C43—42no—
501C22×C43—41no—
502C22×C43—41no—
503C22×C43—41no—
504C22×C43—41no—
505C22×C43—41no—
506C22×C43—41no—
507C22×C43—162no—
508C22×C43C2×#9912yes—
509C22×C43C22×C22⋊C411yescharacteristic
510C22×C43#57611yescharacteristic
511C22×C43#57711yescharacteristic
512C2×D43—21no—
513C2×D43—21no—
514C2×D43—21no—
515C2×D43—21no—
516C2×D43—21no—
517C2×D43—21no—
518C2×D43—21no—
519C2×D43—21no—
520C2×D43—21no—
521C2×D43—21no—
522C2×D43—21no—
523C2×D43—42no—
524C2×D43—42no—
525C2×D43—41no—
526C2×D43—41no—
527C2×D43—41no—
528C2×D43—81no—
529C2×D43—81no—
530C2×D43—162no—
531C2×D43—162no—
532C2×D43C2×#9912yes—
533C4×C43—21no—
534C4×C43—21no—
535C4×C43—21no—
536C4×C43—21no—
537C4×C43—41no—
538C4×C43—41no—
539C4×C43—81no—
540C4×C43—81no—
541Dic43—21no—
542Dic43—21no—
543Dic43—21no—
544Dic43—42no—
545Dic43—41no—
546Dic43—41no—
547Dic43—41no—
548Dic43—81no—
549Dic43C2×#9912yes—
550#3488—431no—
551#2880—431no—
552#2339—431no—
553#1519—431no—
554#1516—431no—
555#1516—431no—
556#1513—431no—
557#1510—431no—
558#1510D4311yescharacteristic, complemented
559#1507—431no—
560#1504—431no—
561#1504—431no—
562#1501—431no—
563C2×#327—431no—
564C2×#327—431no—
565C2×C43—21no—
566C2×C43—21no—
567C2×C43—22no—
568C2×C43—41no—
569C2×C43—81no—
570C2×C43—81no—
571C2×C43C22×#9911yescharacteristic
572C2×C43#289711yescharacteristic
573C2×C43#290111yescharacteristic
574D43—22no—
575D43—41no—
576D43—41no—
577D43—41no—
578D43—81no—
579C2×H(5,𝔽2)—431no—
580C22×#41—431no—
581C2×#131—861no—
582#550—861no—
583#548—861no—
584#546—861no—
585#546—861no—
586#546—861no—
587D42—861no—
588D42—861no—
589D42—861no—
590#537—431no—
591#537—431no—
592#537—431no—
593#535—431no—
594#535—431no—
595#535—431no—
596#525—431no—
597#525—431no—
598#525—431no—
599C2×#121—431no—
600C2×#121—431no—
601C2×#121C2×D4311yescharacteristic
602#520—431no—
603C2×C4×D4—861no—
604#408—861no—
605#408—861no—
606#408—861no—
607#407—431no—
608#407—431no—
609#407C2×D4311yescharacteristic, complemented
610C2×C22⋊C8—431no—
611C2×C22⋊C8—431no—
612C2×C22⋊C8—431no—
613#391—861no—
614#386—861no—
615#386—861no—
616#381—431no—
617#381C2×D4311yescharacteristic, complemented
618#380—431no—
619C4×C22⋊C4—431no—
620C2×#95—431no—
621C2×#95—431no—
622#328—431no—
623#328—431no—
624#328—431no—
625#328—431no—
626#327—431no—
627#327—431no—
628#327—431no—
629#327—431no—
630#327—431no—
631#327—431no—
632#327—431no—
633#327—431no—
634#327C2×D4311yescharacteristic, complemented
635#327C2×D4311yescharacteristic, complemented
636#327C2×D4311yescharacteristic, complemented
637#327C2×D4311yescharacteristic, complemented
638C43#1760311yescharacteristic, complemented, Sylow
639H(5,𝔽2)—1724no—
640C2×#41—431no—
641C2×#41—431no—
642C2×#41—431no—
643C2×#41—431no—
644C2×#41—431no—
645C2×#41—431no—
646C2×#41—431no—
647C2×#41—431no—
648C2×#41—431no—
649C2×#41—431no—
650C2×#41—431no—
651C2×#41—861no—
652C2×#41—1724no—
653C22×Q8—431no—
654C22×D4—21no—
655C22×D4—431no—
656C22×D4—431no—
657C22×D4—431no—
658C22×D4—431no—
659C22×D4—431no—
660C22×D4—861no—
661C22×D4—861no—
662C22×D4—861no—
663C22×D4—861no—
664C22×D4—861no—
665C22×D4C4×D4311yescharacteristic, complemented
666C23×C4—431no—
667C23×C4—431no—
668C23×C4—861no—
669C23×C4—861no—
670C23×C4C22×D4311yescharacteristic
671#131—1724no—
672C2×M16—21no—
673C2×M16—861no—
674C2×M16—861no—
675C22×C8—861no—
676C22×C8—861no—
677C22×C8—861no—
678#127—861no—
679#127—861no—
680#127—861no—
681#124—861no—
682#124—861no—
683#124—861no—
684#123—861no—
685#123—861no—
686#123—861no—
687C22⋊Q8—431no—
688C22⋊Q8—431no—
689C22⋊Q8—431no—
690C22⋊Q8—431no—
691C22⋊Q8—861no—
692C22⋊Q8—861no—
693C22⋊Q8—861no—
694#121—21no—
695#121—21no—
696#121—431no—
697#121—431no—
698#121—431no—
699#121—431no—
700#121—431no—
701#121—431no—
702#121—431no—
703#121—431no—
704#121—861no—
705#121—861no—
706#121—861no—
707#121—861no—
708#121—861no—
709#121—861no—
710#121—861no—
711#121—861no—
712#121—861no—
713#121—861no—
714#121—861no—
715#121—861no—
716#121—861no—
717#121C4×D4311yescharacteristic, complemented
718#121C4×D4311yescharacteristic, complemented
719#121C22×D4311yescharacteristic
720#121C22×D4311yescharacteristic
721#120—861no—
722#120—861no—
723#120—861no—
724#120—861no—
725#120—861no—
726#120—861no—
727#120—861no—
728#120—861no—
729#120—861no—
730C4×Q8—861no—
731C4×D4—861no—
732C4×D4—861no—
733C4×D4—861no—
734C4×D4—861no—
735C4×D4—861no—
736C4×D4—861no—
737C4×D4—861no—
738C4×D4—861no—
739C4×D4—861no—
740C4×D4—1724no—
741#117—431no—
742#117—431no—
743#117—431no—
744C2×C4⋊C4—431no—
745C2×C4⋊C4—431no—
746C2×C4⋊C4—861no—
747C2×C4⋊C4C4×D4311yescharacteristic, complemented
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—861no—
751C2×C22⋊C4—861no—
752C2×C22⋊C4—861no—
753C2×C22⋊C4—861no—
754C2×C22⋊C4—861no—
755C2×C42—861no—
756C22⋊C8—21no—
757C22⋊C8—431no—
758C22⋊C8—431no—
759C22⋊C8—861no—
760C22⋊C8—861no—
761C22⋊C8—861no—
762C22⋊C8—861no—
763C22⋊C8—861no—
764C22⋊C8C22×D4311yescharacteristic
765C22⋊C8C22×D4311yescharacteristic
766#95—21no—
767#95—431no—
768#95—431no—
769#95—861no—
770#95—861no—
771#95—861no—
772#95C22×D4311yescharacteristic
773#95C22×D4311yescharacteristic
774C24—21no—
775C24—431no—
776C24—431no—
777C24—861no—
778C24—861no—
779C24D4×D4311yescharacteristic
780#41—864no—
781#41—864no—
782#41—1722no—
783#41—1722no—
784#41—1722no—
785#41—1722no—
786#41—1722no—
787#41—1722no—
788#41—1722no—
789#41—1722no—
790#41—1722no—
791#41—1724no—
792C2×Q8—431no—
793C2×Q8—431no—
794C2×Q8—431no—
795C2×Q8—431no—
796C2×Q8—431no—
797C2×Q8—1722no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—42no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—431no—
807C2×D4—431no—
808C2×D4—431no—
809C2×D4—431no—
810C2×D4—431no—
811C2×D4—431no—
812C2×D4—431no—
813C2×D4—431no—
814C2×D4—431no—
815C2×D4—431no—
816C2×D4—431no—
817C2×D4—431no—
818C2×D4—431no—
819C2×D4—861no—
820C2×D4—861no—
821C2×D4—861no—
822C2×D4—861no—
823C2×D4—864no—
824C2×D4—861no—
825C2×D4—861no—
826C2×D4—861no—
827C2×D4—861no—
828C2×D4—861no—
829C2×D4—861no—
830C2×D4—861no—
831C2×D4—861no—
832C2×D4—861no—
833C2×D4—3441no—
834C2×D4—3441no—
835C2×D4—3441no—
836C2×D4—3441no—
837C2×D4—1722no—
838C2×D4—1722no—
839C2×D4—1722no—
840C2×D4—1724no—
841C2×D4—1724no—
842C2×D4—1722no—
843C2×D4—1724no—
844C2×D4C2×C4×D4311yescharacteristic
845C2×D4C2×C4×D4311yescharacteristic
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—861no—
861C22×C4—861no—
862C22×C4—861no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—861no—
867C22×C4—3441no—
868C22×C4—3441no—
869C22×C4—1722no—
870C22×C4—1722no—
871C22×C4—1722no—
872C22×C4—1722no—
873C22×C4—1722no—
874C22×C4—1722no—
875C22×C4C2×C4×D4311yescharacteristic
876C22×C4C2×C4×D4311yescharacteristic
877C22×C4D4×D4311yescharacteristic
878C22×C4D4×D4311yescharacteristic
879C22×C4D4×D4311yescharacteristic
880C22×C4C23×D4311yescharacteristic
881M16—42no—
882M16—1722no—
883M16—1722no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—861no—
887C2×C8—861no—
888C2×C8—1722no—
889C2×C8—1722no—
890C2×C8—1722no—
891C4⋊C4—21no—
892C4⋊C4—431no—
893C4⋊C4—431no—
894C4⋊C4—861no—
895C4⋊C4—861no—
896C4⋊C4—861no—
897C4⋊C4—861no—
898C4⋊C4—861no—
899C4⋊C4—861no—
900C4⋊C4—1722no—
901C4⋊C4C2×C4×D4311yescharacteristic
902C4⋊C4C2×C4×D4311yescharacteristic
903C22⋊C4—21no—
904C22⋊C4—21no—
905C22⋊C4—21no—
906C22⋊C4—21no—
907C22⋊C4—42no—
908C22⋊C4—861no—
909C22⋊C4—861no—
910C22⋊C4—861no—
911C22⋊C4—861no—
912C22⋊C4—861no—
913C22⋊C4—861no—
914C22⋊C4—861no—
915C22⋊C4—861no—
916C22⋊C4—861no—
917C22⋊C4—861no—
918C22⋊C4—861no—
919C22⋊C4—861no—
920C22⋊C4—861no—
921C22⋊C4—861no—
922C22⋊C4—861no—
923C22⋊C4—3441no—
924C22⋊C4—1722no—
925C22⋊C4—1722no—
926C42—861no—
927C42—861no—
928C42—861no—
929C42—1722no—
930C23—22no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—21no—
935C23—41no—
936C23—42no—
937C23—81no—
938C23—81no—
939C23—431no—
940C23—431no—
941C23—431no—
942C23—431no—
943C23—862no—
944C23—861no—
945C23—861no—
946C23—861no—
947C23—861no—
948C23—861no—
949C23—3441no—
950C23—3441no—
951C23—3441no—
952C23—3441no—
953C23—1721no—
954C23—1721no—
955C23—1721no—
956C23—1722no—
957C23—1722no—
958C23C22⋊C4×D4311yescharacteristic
959C23C22⋊C4×D4311yescharacteristic
960C23C2×D4×D4311yescharacteristic
961Q8—862no—
962Q8—862no—
963Q8—1721no—
964Q8—1721no—
965Q8—1721no—
966D4—41no—
967D4—41no—
968D4—42no—
969D4—41no—
970D4—41no—
971D4—41no—
972D4—41no—
973D4—81no—
974D4—81no—
975D4—434no—
976D4—862no—
977D4—862no—
978D4—862no—
979D4—862no—
980D4—862no—
981D4—862no—
982D4—862no—
983D4—3441no—
984D4—3441no—
985D4—3441no—
986D4—3441no—
987D4—3441no—
988D4—3441no—
989D4—3441no—
990D4—1721no—
991D4—1721no—
992D4—1721no—
993D4—1722no—
994D4—1721no—
995D4—1721no—
996D4—1722no—
997D4—1722no—
998D4—1722no—
999D4—1722no—
1000D4—1721no—
1001D4—1721no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—81no—
1017C2×C4—431no—
1018C2×C4—431no—
1019C2×C4—431no—
1020C2×C4—431no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—861no—
1028C2×C4—861no—
1029C2×C4—861no—
1030C2×C4—3441no—
1031C2×C4—3441no—
1032C2×C4—3444no—
1033C2×C4—3444no—
1034C2×C4—1721no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1722no—
1039C2×C4—1722no—
1040C2×C4—1721no—
1041C2×C4—1722no—
1042C2×C4—1721no—
1043C2×C4—1721no—
1044C2×C4—1721no—
1045C2×C4—1721no—
1046C2×C4—1721no—
1047C2×C4C22⋊C4×D4311yescharacteristic
1048C2×C4C22⋊C4×D4311yescharacteristic
1049C2×C4C22×C4×D4311yescharacteristic
1050C2×C4C2×D4×D4311yescharacteristic
1051C8—41no—
1052C8—41no—
1053C8—1721no—
1054C8—1721no—
1055C22—21no—
1056C22—21no—
1057C22—21no—
1058C22—21no—
1059C22—21no—
1060C22—21no—
1061C22—21no—
1062C22—42no—
1063C22—42no—
1064C22—41no—
1065C22—41no—
1066C22—41no—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—162no—
1071C22—432no—
1072C22—861no—
1073C22—861no—
1074C22—861no—
1075C22—861no—
1076C22—861no—
1077C22—861no—
1078C22—861no—
1079C22—861no—
1080C22—861no—
1081C22—861no—
1082C22—861no—
1083C22—3441no—
1084C22—3441no—
1085C22—1722no—
1086C22—1722no—
1087C22—1721no—
1088C22—1721no—
1089C22—1721no—
1090C22—6882no—
1091C22—6882no—
1092C22#99×D4312yes—
1093C22C2×C22⋊C4×D4311yescharacteristic
1094C22#1458370311yescharacteristic
1095C22#1458370911yescharacteristic
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—41no—
1101C4—41no—
1102C4—81no—
1103C4—81no—
1104C4—432no—
1105C4—861no—
1106C4—861no—
1107C4—861no—
1108C4—3441no—
1109C4—1722no—
1110C4—1721no—
1111C4—1721no—
1112C4—1721no—
1113C2—21no—
1114C2—21no—
1115C2—22no—
1116C2—41no—
1117C2—81no—
1118C2—81no—
1119C2—862no—
1120C2—3441no—
1121C2—1721no—
1122C2—1721no—
1123C2—1721no—
1124C2C2×#99×D4311yescharacteristic
1125C2#1914312011yescharacteristic
1126C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1510C2
socleC22×C43C22×C22⋊C4
prime radical#19148260C2
cosocleC22×C4×C43C24
hypercenter#1510D43
hypocenterC43#17603
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #19143045C2semidirect
3. #19137419C2semidirect
4. #19133161C2semidirect
5. #19133149C2semidirect
6. #19133148C2semidirect
7. #19133135C2semidirect
8. #19133122C2semidirect
9. #19133109C2semidirect
10. #19133100C2semidirect
11. #19133096C2semidirect
12. #19133083C2semidirect
13. C2×#14582633C2semidirect
14. #327×D43C2semidirect
15. C43×#1510C2semidirect
16. C2×#13063370C4semidirect
27. #14583480C4semidirect
28. #14583478C4semidirect
29. #14583478C4semidirect
30. #14583466C4semidirect
31. #14583465C4semidirect
32. #14583465C4semidirect
38. #14583380C4semidirect
43. #14582861C22semidirect
44. #14582861C22semidirect
45. C2×C22⋊(C43⋊C8)C22semidirect
46. C22⋊C8×D43C22semidirect
47. C22⋊C8×D43C22semidirect
51. #14582761C22semidirect
52. #14582758C22semidirect
53. #14582746C22semidirect
54. C2×C43⋊#95C22semidirect
55. #95×D43C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582635C22semidirect
59. #14582635C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
64. #14582633C22semidirect
65. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#407C22semidirect
70. C43×#381C22semidirect
71. C43×#327C22semidirect
72. C43×#327C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
81. C2×#10621898C2×C4semidirect
87. C2×#10621900C2×C4semidirect
88. C2×#10621900C2×C4semidirect
98. C2×D4×D43C2×C4semidirect
99. C2×D4×D43C2×C4semidirect
120. #13063305C2×C4semidirect
121. #13063305C2×C4semidirect
122. #13063304C2×C4semidirect
127. #13063300C2×C4semidirect
128. #13063300C2×C4semidirect
131. #13063299C2×C4semidirect
143. #13063296C2×C4semidirect
144. #13063296C2×C4semidirect
145. #13063296C2×C4semidirect
146. #13063296C2×C4semidirect
167. #13063284C2×C4semidirect
168. #13063283C2×C4semidirect
169. #13063283C2×C4semidirect
171. C4⋊C4×D43C2×C4semidirect
172. C4⋊C4×D43C2×C4semidirect
192. C22×D4×C43C2×C4semidirect
197. #121×C43C2×C4semidirect
198. #121×C43C2×C4semidirect
201. C2×C4⋊C4×C43C2×C4semidirect
558. #1510D43semidirect
609. #407C2×D43semidirect
617. #381C2×D43semidirect
634. #327C2×D43semidirect
635. #327C2×D43semidirect
636. #327C2×D43semidirect
637. #327C2×D43semidirect
638. C43#17603semidirect
665. C22×D4C4×D43semidirect
717. #121C4×D43semidirect
718. #121C4×D43semidirect
747. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191482602
#191430452
#191374192
#191331612
#191331492
#191331482
#191331352
#191331222
#191331092
#191331002
#191330962
#191330832
C2×#145826332
#327×D432
C43×#15102
#1760343