Finite Group Databasebeta

← #25064198

Subgroups — #25064198

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#19148256C211yesmaximal, characteristic
2#19143041C211yesmaximal, characteristic, complemented
3#19137419C211yesmaximal, characteristic, complemented
4#19133161C211yesmaximal, characteristic, complemented
5#19133150C211yesmaximal, characteristic, complemented
6#19133137C211yesmaximal, characteristic, complemented
7#19133123C211yesmaximal, characteristic, complemented
8#19133122C211yesmaximal, characteristic, complemented
9#19133109C211yesmaximal, characteristic, complemented
10#19133099C211yesmaximal, characteristic, complemented
11#19133098C211yesmaximal, characteristic, complemented
12#19133085C211yesmaximal, characteristic, complemented
13C2×#14582634C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1516C211yesmaximal, characteristic, complemented
16C2×#13063371C411yescharacteristic, complemented
17C22×#10621898C2211yescharacteristic
18C2×#13063331—21no—
19#14583570—21no—
20#14583558—21no—
21#14583545—21no—
22#14583541—21no—
23#14583541—21no—
24D4×D172—21no—
25#14583531—21no—
26#14583531—21no—
27#14583479C411yescharacteristic, complemented
28#14583479C411yescharacteristic, complemented
29#14583477C411yescharacteristic, complemented
30#14583468C411yescharacteristic, complemented
31#14583465C411yescharacteristic, complemented
32#14583465C411yescharacteristic, complemented
33#14583412C2211yescharacteristic
34#14583412C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36#121×D43C2211yescharacteristic
37#121×D43C2211yescharacteristic
38#14583379C411yescharacteristic, complemented
39C2×(C22⋊D43)⋊C4—21no—
40#14582865—21no—
41#14582864—21no—
42#14582864—21no—
43#14582863C2211yescharacteristic, complemented
44#14582861C2211yescharacteristic, complemented
45#14582861C2211yescharacteristic, 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#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic, complemented
59#14582634C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582632C2211yescharacteristic, complemented
65#14582632C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C43×#525C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic, complemented
70C43×#381C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75#13063371—44no—
76C2×#10621902C2×C411yescharacteristic, complemented
77C2×#10621902C2×C411yescharacteristic, complemented
78C2×#10621898—21no—
79C2×#10621898—44no—
80C2×#10621898C2×C411yescharacteristic
81C2×#10621898C2×C411yescharacteristic
82C2×#10621898C2×C411yescharacteristic
83C2×#10621898C2×C411yescharacteristic
84C2×#10621898D411yescharacteristic
85C2×#10621898D411yescharacteristic
86C2×#10621898D411yescharacteristic
87C2×#10621898D411yescharacteristic
88C22×Dic86D411yescharacteristic
89C22×D172—21no—
90C22×D172C2×C411yescharacteristic, complemented
91C22×D172D411yescharacteristic
92C22×C22⋊D43—21no—
93C22×C22⋊D43D411yescharacteristic
94C22×C22⋊D43D411yescharacteristic
95C2×D4×D43—21no—
96C2×D4×D43—21no—
97C2×D4×D43—21no—
98C2×D4×D43—21no—
99C2×D4×D43C2×C411yescharacteristic, complemented
100C2×D4×D43C2×C411yescharacteristic, complemented
101C23×Dic43—21no—
102C22×C4×D43—21no—
103C22×C4×D43C2311yescharacteristic
104C22×C4×D43C2311yescharacteristic
105#13063331—44no—
106C2×#10621877—21no—
107C2×#10621872—21no—
108C2×#10621872—21no—
109C2×C8×D43—21no—
110C2×C8×D43—21no—
111#13063322—21no—
112#13063321—21no—
113#13063321—21no—
114#13063313—21no—
115#13063311—21no—
116#13063311—21no—
117#13063310—21no—
118#13063310—21no—
119#13063304—21no—
120#13063303—21no—
121#13063303—21no—
122#13063301C2×C411yescharacteristic, complemented
123#13063301C2×C411yescharacteristic, complemented
124#13063300—21no—
125#13063300—21no—
126#13063300C2×C411yescharacteristic, complemented
127#13063300C2×C411yescharacteristic, complemented
128#13063300C2×C411yescharacteristic, complemented
129#13063300C2×C411yescharacteristic, complemented
130#13063299—21no—
131#13063299—21no—
132#13063299—21no—
133#13063299C2×C411yescharacteristic, complemented
134#13063299C2×C411yescharacteristic, complemented
135#13063299C2311yescharacteristic
136#13063299C2311yescharacteristic
137#13063298—21no—
138#13063298—21no—
139#13063298—21no—
140#13063298—21no—
141#13063298—21no—
142#13063298—21no—
143#13063297—21no—
144#13063297—21no—
145#13063297—21no—
146#13063297—21no—
147#13063296C2×C411yescharacteristic, complemented
148#13063296C2×C411yescharacteristic, complemented
149#13063295—21no—
150#13063295—21no—
151#13063295—21no—
152#13063295—21no—
153#13063295—21no—
154#13063295—21no—
155#13063293—21no—
156#13063293—21no—
157C4×Dic86—21no—
158C4×D172—21no—
159#13063287—21no—
160#13063287—21no—
161(C22⋊D43)⋊C4—21no—
162(C22⋊D43)⋊C4—21no—
163(C22⋊D43)⋊C4—21no—
164(C22⋊D43)⋊C4—21no—
165(C22⋊D43)⋊C4—44no—
166#13063283C2×C411yescharacteristic, complemented
167#13063283C2×C411yescharacteristic, complemented
168C2×C4⋊Dic43C2×C411yescharacteristic, complemented
169C2×Dic43⋊C4—21no—
170C4⋊C4×D43C2×C411yescharacteristic, complemented
171C4⋊C4×D43C2×C411yescharacteristic, complemented
172C2×(C2×D43)⋊C4—21no—
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
191C2×#41×C43C2×C411yescharacteristic, complemented
192C23×C4×C43C2311yescharacteristic
193C22×C8×C43—21no—
194#123×C43—21no—
195C22⋊Q8×C43C2×C411yescharacteristic, complemented
196C22⋊Q8×C43C2311yescharacteristic
197#121×C43C2×C411yescharacteristic, complemented
198#121×C43C2311yescharacteristic
199#120×C43—21no—
200C4×D4×C43—21no—
201C4×D4×C43—21no—
202#117×C43C2×C411yescharacteristic, complemented
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×C43C2×D411yescharacteristic
211C23×D43—21no—
212C23×D43—21no—
213C23×D43—21no—
214C23×D43C2×D411yescharacteristic
215C23×D43C2×D411yescharacteristic
216#41×C43—42no—
217C2×Q8×C43C22×C411yescharacteristic
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43C22×C411yescharacteristic
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—42no—
226C22×C4×C43C22×C411yescharacteristic
227C22×C4×C43C22×C411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2411yescharacteristic
232C2×C22⋊D43—24no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C2×C22⋊D43—21no—
241C2×C22⋊D43—42no—
242C2×C22⋊D43—81no—
243C2×C22⋊D43—81no—
244C2×C22⋊D43C22⋊C411yescharacteristic
245C2×C22⋊D43C22⋊C411yescharacteristic
246C2×C22⋊D43C22⋊C411yescharacteristic
247C2×C22⋊D43C22⋊C411yescharacteristic
248C2×C22⋊D43C22⋊C411yescharacteristic
249C2×C22⋊D43C22⋊C411yescharacteristic
250C2×C22⋊D43C22⋊C411yescharacteristic
251C2×C22⋊D43C22⋊C411yescharacteristic
252C22×Dic43—21no—
253C22×Dic43—21no—
254C22×Dic43—21no—
255C22×Dic43—42no—
256C22×Dic43—42no—
257C22×Dic43—81no—
258C22×Dic43C2×D411yescharacteristic
259C22×Dic43C2×D411yescharacteristic
260#10621902—42no—
261#10621902—42no—
262D4×D43—42no—
263D4×D43—44no—
264D4×D43—44no—
265D4×D43—42no—
266D4×D43—81no—
267D4×D43—81no—
268D4×D43—81no—
269D4×D43—81no—
270#10621898—24no—
271#10621898—24no—
272#10621898—42no—
273#10621898—42no—
274#10621898—44no—
275#10621898—42no—
276#10621898—42no—
277#10621898—42no—
278#10621898—42no—
279C2×D172—21no—
280C2×D172—21no—
281C2×D172—21no—
282C2×D172—21no—
283C2×D172—21no—
284C2×D172—21no—
285C2×D172—21no—
286C2×D172—42no—
287C2×D172—44no—
288C2×D172—42no—
289C2×D172C22⋊C411yescharacteristic
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—21no—
299C2×C4×D43—42no—
300C2×C4×D43—42no—
301C2×C4×D43—42no—
302C2×C4×D43—42no—
303C2×C4×D43—81no—
304C2×C4×D43C22×C411yescharacteristic
305C2×C4×D43C22×C411yescharacteristic
306C2×C4×D43C22×C411yescharacteristic
307C2×C4×D43C22×C411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2×D411yescharacteristic
311C2×C4×D43C2×D411yescharacteristic
312C2×Dic86—42no—
313C2×Dic86C22⋊C411yescharacteristic
314C2×Dic86C22⋊C411yescharacteristic
315C2×Dic86C22⋊C411yescharacteristic
316C2×Dic86C22⋊C411yescharacteristic
317C2×C8×C43—21no—
318C2×C8×C43—21no—
319C2×C8×C43—42no—
320C4⋊C4×C43—21no—
321C4⋊C4×C43—21no—
322C4⋊C4×C43C22×C411yescharacteristic
323C4⋊C4×C43C22×C411yescharacteristic
324C22⋊C4×C43—21no—
325C22⋊C4×C43—21no—
326C22⋊C4×C43—21no—
327C22⋊C4×C43—21no—
328C22⋊C4×C43—21no—
329C22⋊C4×C43—42no—
330C42×C43—21no—
331C22⋊Dic43—21no—
332C22⋊Dic43—21no—
333(C2×D43)⋊C4—21no—
334(C2×D43)⋊C4—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—21no—
344(C2×D43)⋊C4—21no—
345(C2×D43)⋊C4—42no—
346(C2×D43)⋊C4—42no—
347(C2×D43)⋊C4—81no—
348C4⋊Dic43—21no—
349C4⋊Dic43C22×C411yescharacteristic
350C4⋊Dic43C22×C411yescharacteristic
351Dic43⋊C4—21no—
352Dic43⋊C4—21no—
353Dic43⋊C4—21no—
354Dic43⋊C4—21no—
355Dic43⋊C4—42no—
356C4×Dic43—21no—
357C4×Dic43—21no—
358C4×Dic43—42no—
359#10621877—42no—
360C2×C43⋊C8—21no—
361C2×C43⋊C8—21no—
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—41no—
371C23×C43C2×C22⋊C411yescharacteristic
372C23×C43C2×C22⋊C411yescharacteristic
373C23×C43C22×D411yescharacteristic
374C22×D43—21no—
375C22×D43—21no—
376C22×D43—21no—
377C22×D43—21no—
378C22×D43—22no—
379C22×D43—21no—
380C22×D43—21no—
381C22×D43—41no—
382C22×D43—41no—
383C22×D43—41no—
384C22×D43—42no—
385C22×D43—42no—
386C22×D43—42no—
387C22×D43—81no—
388C22×D43—81no—
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
397Q8×C43—41no—
398D4×C43—41no—
399D4×C43—41no—
400D4×C43—41no—
401D4×C43—42no—
402D4×C43—81no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—21no—
406C2×C4×C43—21no—
407C2×C4×C43—21no—
408C2×C4×C43—41no—
409C2×C4×C43—41no—
410C2×C4×C43—41no—
411C2×C4×C43—41no—
412C2×C4×C43—42no—
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×C43C2×C22⋊C411yescharacteristic
420C2×C4×C43C2×C22⋊C411yescharacteristic
421C2×C4×C43C23×C411yescharacteristic
422C2×C4×C43C22×D411yescharacteristic
423C22⋊D43—22no—
424C22⋊D43—22no—
425C22⋊D43—22no—
426C22⋊D43—22no—
427C22⋊D43—22no—
428C22⋊D43—41no—
429C22⋊D43—41no—
430C22⋊D43—42no—
431C22⋊D43—41no—
432C22⋊D43—41no—
433C22⋊D43—41no—
434C22⋊D43—41no—
435C22⋊D43—42no—
436C22⋊D43—81no—
437C22⋊D43—81no—
438C22⋊D43—81no—
439C22⋊D43—81no—
440C22⋊D43#9914yes—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—21no—
444C2×Dic43—21no—
445C2×Dic43—41no—
446C2×Dic43—41no—
447C2×Dic43—41no—
448C2×Dic43—41no—
449C2×Dic43—41no—
450C2×Dic43—41no—
451C2×Dic43—81no—
452C2×Dic43—84no—
453C2×Dic43C2×C22⋊C411yescharacteristic
454C2×Dic43C2×C22⋊C411yescharacteristic
455C2×Dic43C2×C22⋊C411yescharacteristic
456C2×Dic43C2×C22⋊C411yescharacteristic
457D172—22no—
458D172—22no—
459D172—41no—
460D172—41no—
461D172—41no—
462D172—41no—
463D172—42no—
464D172—42no—
465D172—42no—
466D172—81no—
467D172—81no—
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—42no—
480C4×D43—81no—
481C4×D43—81no—
482C4×D43—84no—
483Dic86—22no—
484Dic86—22no—
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×C43C2×#9912yes—
505C22×C43C22×C22⋊C411yescharacteristic
506C22×C43#57611yescharacteristic
507C22×C43#57711yescharacteristic
508C2×D43—21no—
509C2×D43—21no—
510C2×D43—21no—
511C2×D43—21no—
512C2×D43—21no—
513C2×D43—21no—
514C2×D43—21no—
515C2×D43—21no—
516C2×D43—21no—
517C2×D43—21no—
518C2×D43—21no—
519C2×D43—42no—
520C2×D43—42no—
521C2×D43—41no—
522C2×D43—41no—
523C2×D43—41no—
524C2×D43—41no—
525C2×D43—41no—
526C2×D43—41no—
527C2×D43—81no—
528C2×D43—81no—
529C2×D43—162no—
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—41no—
540C4×C43—81no—
541C4×C43—81no—
542Dic43—21no—
543Dic43—21no—
544Dic43—21no—
545Dic43—42no—
546Dic43—41no—
547Dic43—41no—
548Dic43—81no—
549Dic43C2×#9912yes—
550#3488—431no—
551#2880—431no—
552#2339—431no—
553#1519—431no—
554#1516—431no—
555#1516D4311yescharacteristic, complemented
556#1513—431no—
557#1510—431no—
558#1510—431no—
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×C43C22×#9911yescharacteristic
571C2×C43#289711yescharacteristic
572C2×C43#290111yescharacteristic
573D43—22no—
574D43—41no—
575D43—41no—
576D43—41no—
577D43—81no—
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#525C2×D4311yescharacteristic
599C2×#121—431no—
600C2×#121—431no—
601C2×#121—431no—
602#520—431no—
603C2×C4×D4—861no—
604#408—861no—
605#408—861no—
606#408—861no—
607#407—431no—
608#407—431no—
609#407—431no—
610C2×C22⋊C8—431no—
611C2×C22⋊C8—431no—
612C2×C22⋊C8C2×D4311yescharacteristic, complemented
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#328C2×D4311yescharacteristic, complemented
625#328C2×D4311yescharacteristic, complemented
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#327—431no—
635#327—431no—
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—861no—
651C2×#41—1724no—
652C2×#41C4×D4311yescharacteristic, complemented
653C22×Q8—431no—
654C22×D4—431no—
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×D4—861no—
666C23×C4—431no—
667C23×C4—431no—
668C23×C4—861no—
669C23×C4—861no—
670C23×C4C22×D4311yescharacteristic
671#131—1724no—
672C2×M16—861no—
673C2×M16—861no—
674C2×M16—861no—
675C22×C8—21no—
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—21no—
685#123—861no—
686#123—861no—
687C22⋊Q8—431no—
688C22⋊Q8—431no—
689C22⋊Q8—861no—
690C22⋊Q8—861no—
691C22⋊Q8—861no—
692C22⋊Q8C4×D4311yescharacteristic, complemented
693C22⋊Q8C22×D4311yescharacteristic
694#121—431no—
695#121—431no—
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#121—861no—
718#121—861no—
719#121C4×D4311yescharacteristic, complemented
720#121C22×D4311yescharacteristic
721#120—21no—
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—21no—
732C4×D4—21no—
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#117C4×D4311yescharacteristic, complemented
744C2×C4⋊C4—431no—
745C2×C4⋊C4—431no—
746C2×C4⋊C4—431no—
747C2×C4⋊C4—861no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—861no—
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—431no—
775C24—431no—
776C24—861no—
777C24—861no—
778C24—861no—
779C24D4×D4311yescharacteristic
780#41—42no—
781#41—864no—
782#41—864no—
783#41—1722no—
784#41—1722no—
785#41—1722no—
786#41—1722no—
787#41—1722no—
788#41—1722no—
789#41—1724no—
790#41—1722no—
791#41—1722no—
792C2×Q8—431no—
793C2×Q8—431no—
794C2×Q8—431no—
795C2×Q8—431no—
796C2×Q8—1722no—
797C2×Q8C2×C4×D4311yescharacteristic
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—431no—
802C2×D4—431no—
803C2×D4—431no—
804C2×D4—431no—
805C2×D4—431no—
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—861no—
816C2×D4—861no—
817C2×D4—861no—
818C2×D4—861no—
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—3441no—
832C2×D4—3441no—
833C2×D4—3441no—
834C2×D4—3441no—
835C2×D4—3441no—
836C2×D4—3441no—
837C2×D4—1722no—
838C2×D4—1722no—
839C2×D4—1724no—
840C2×D4—1722no—
841C2×D4—1722no—
842C2×D4—1724no—
843C2×D4—1724no—
844C2×D4—1722no—
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—1722no—
882M16—1722no—
883M16—1722no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C2×C8—861no—
888C2×C8—861no—
889C2×C8—1722no—
890C2×C8—1722no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—431no—
894C4⋊C4—431no—
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—21no—
908C22⋊C4—42no—
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—21no—
927C42—861no—
928C42—861no—
929C42—1722no—
930C23—22no—
931C23—21no—
932C23—21no—
933C23—21no—
934C23—41no—
935C23—431no—
936C23—431no—
937C23—431no—
938C23—431no—
939C23—862no—
940C23—861no—
941C23—861no—
942C23—861no—
943C23—861no—
944C23—861no—
945C23—861no—
946C23—3441no—
947C23—3441no—
948C23—3441no—
949C23—3441no—
950C23—3441no—
951C23—3441no—
952C23—1721no—
953C23—1721no—
954C23—1721no—
955C23—1722no—
956C23—1722no—
957C23—1722no—
958C23C22⋊C4×D4311yescharacteristic
959C23C22⋊C4×D4311yescharacteristic
960C23C2×D4×D4311yescharacteristic
961Q8—41no—
962Q8—862no—
963Q8—862no—
964Q8—1721no—
965Q8—1721no—
966D4—41no—
967D4—42no—
968D4—41no—
969D4—41no—
970D4—81no—
971D4—434no—
972D4—862no—
973D4—862no—
974D4—862no—
975D4—862no—
976D4—862no—
977D4—862no—
978D4—862no—
979D4—3441no—
980D4—3441no—
981D4—3441no—
982D4—3441no—
983D4—3441no—
984D4—3441no—
985D4—3441no—
986D4—3441no—
987D4—1721no—
988D4—1721no—
989D4—1721no—
990D4—1721no—
991D4—1722no—
992D4—1722no—
993D4—1722no—
994D4—1722no—
995D4—1721no—
996D4—1721no—
997D4—1722no—
998D4—1721no—
999D4—1721no—
1000D4—1721no—
1001D4—1721no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—42no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—431no—
1019C2×C4—431no—
1020C2×C4—431no—
1021C2×C4—431no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—861no—
1029C2×C4—861no—
1030C2×C4—3441no—
1031C2×C4—3441no—
1032C2×C4—3444no—
1033C2×C4—3444no—
1034C2×C4—3441no—
1035C2×C4—1721no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1722no—
1040C2×C4—1722no—
1041C2×C4—1721no—
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—432no—
1068C22—861no—
1069C22—861no—
1070C22—861no—
1071C22—861no—
1072C22—861no—
1073C22—861no—
1074C22—861no—
1075C22—861no—
1076C22—861no—
1077C22—861no—
1078C22—861no—
1079C22—3441no—
1080C22—3441no—
1081C22—1722no—
1082C22—1722no—
1083C22—1721no—
1084C22—1721no—
1085C22—1721no—
1086C22—1721no—
1087C22—1721no—
1088C22—1721no—
1089C22—6882no—
1090C22—6882no—
1091C22—6882no—
1092C22#99×D4312yes—
1093C22C2×C22⋊C4×D4311yescharacteristic
1094C22#1458370111yescharacteristic
1095C22#1458370611yescharacteristic
1096C4—21no—
1097C4—21no—
1098C4—21no—
1099C4—21no—
1100C4—41no—
1101C4—41no—
1102C4—41no—
1103C4—81no—
1104C4—81no—
1105C4—432no—
1106C4—861no—
1107C4—861no—
1108C4—861no—
1109C4—3441no—
1110C4—1722no—
1111C4—1721no—
1112C4—1721no—
1113C2—21no—
1114C2—21no—
1115C2—22no—
1116C2—41no—
1117C2—81no—
1118C2—862no—
1119C2—3441no—
1120C2—3441no—
1121C2—1721no—
1122C2—1721no—
1123C2—1721no—
1124C2C2×#99×D4311yescharacteristic
1125C2#1914311711yescharacteristic
1126C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1516C2
socleC22×C43C22×C22⋊C4
prime radical#19148256C2
cosocleC22×C4×C43C24
hypercenter#1516D43
hypocenterC43#17603
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #19143041C2semidirect
3. #19137419C2semidirect
4. #19133161C2semidirect
5. #19133150C2semidirect
6. #19133137C2semidirect
7. #19133123C2semidirect
8. #19133122C2semidirect
9. #19133109C2semidirect
10. #19133099C2semidirect
11. #19133098C2semidirect
12. #19133085C2semidirect
13. C2×#14582634C2semidirect
14. #327×D43C2semidirect
15. C43×#1516C2semidirect
16. C2×#13063371C4semidirect
27. #14583479C4semidirect
28. #14583479C4semidirect
29. #14583477C4semidirect
30. #14583468C4semidirect
31. #14583465C4semidirect
32. #14583465C4semidirect
38. #14583379C4semidirect
43. #14582863C22semidirect
44. #14582861C22semidirect
45. #14582861C22semidirect
46. C22⋊C8×D43C22semidirect
47. C22⋊C8×D43C22semidirect
51. #14582761C22semidirect
52. #14582758C22semidirect
53. #14582746C22semidirect
54. C2×C43⋊#95C22semidirect
55. #95×D43C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
58. #14582634C22semidirect
59. #14582634C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
64. #14582632C22semidirect
65. #14582632C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C2×C22⋊C8×C43C22semidirect
70. C43×#381C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
76. C2×#10621902C2×C4semidirect
77. C2×#10621902C2×C4semidirect
90. C22×D172C2×C4semidirect
99. C2×D4×D43C2×C4semidirect
100. C2×D4×D43C2×C4semidirect
122. #13063301C2×C4semidirect
123. #13063301C2×C4semidirect
126. #13063300C2×C4semidirect
127. #13063300C2×C4semidirect
128. #13063300C2×C4semidirect
129. #13063300C2×C4semidirect
133. #13063299C2×C4semidirect
134. #13063299C2×C4semidirect
147. #13063296C2×C4semidirect
148. #13063296C2×C4semidirect
166. #13063283C2×C4semidirect
167. #13063283C2×C4semidirect
168. C2×C4⋊Dic43C2×C4semidirect
170. C4⋊C4×D43C2×C4semidirect
171. C4⋊C4×D43C2×C4semidirect
191. C2×#41×C43C2×C4semidirect
195. C22⋊Q8×C43C2×C4semidirect
197. #121×C43C2×C4semidirect
202. #117×C43C2×C4semidirect
555. #1516D43semidirect
612. C2×C22⋊C8C2×D43semidirect
617. #381C2×D43semidirect
624. #328C2×D43semidirect
625. #328C2×D43semidirect
636. #327C2×D43semidirect
637. #327C2×D43semidirect
638. C43#17603semidirect
652. C2×#41C4×D43semidirect
692. C22⋊Q8C4×D43semidirect
719. #121C4×D43semidirect
743. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191482562
#191430412
#191374192
#191331612
#191331502
#191331372
#191331232
#191331222
#191331092
#191330992
#191330982
#191330852
C2×#145826342
#327×D432
C43×#15162
#1760343