Finite Group Databasebeta

← #25117346

Subgroups — #25117346

Order 11008.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143811C211yesmaximal, characteristic
2C2×#14583018C211yesmaximal, characteristic, complemented
3#19143322C211yesmaximal, characteristic, complemented
4C2×#14582917C211yesmaximal, characteristic, complemented
5#19143045C211yesmaximal, characteristic, complemented
6#19135480C211yesmaximal, characteristic, complemented
7#19135307C211yesmaximal, characteristic, complemented
8#19135241C211yesmaximal, characteristic, complemented
9#19134920C211yesmaximal, characteristic, complemented
10#19134919C211yesmaximal, characteristic, complemented
11#19134871C211yesmaximal, characteristic, complemented
12#19134799C211yesmaximal, characteristic, complemented
13#19134429C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#1897C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063333C2211yescharacteristic
21C2×#13063332C2211yescharacteristic, complemented
22C22×#10621877C2211yescharacteristic
23#14583059C411yescharacteristic, complemented
24#14583059C411yescharacteristic, complemented
25#14583054C411yescharacteristic, complemented
26#14583049C411yescharacteristic, complemented
27#14583042C411yescharacteristic, complemented
28#14583042C411yescharacteristic, complemented
29#14583037C411yescharacteristic, complemented
30#14583032C411yescharacteristic, complemented
31#14583018—24no—
32#14582977—21no—
33#14582971—21no—
34#14582971—21no—
35D4×C43⋊C8—21no—
36C2×#13063260C2211yescharacteristic, complemented
37C2×#13063260C2211yescharacteristic, complemented
38#14582926C2211yescharacteristic, complemented
39#14582917—24no—
40C2×#13063253C2211yescharacteristic
41C2×#13063253C2211yescharacteristic
42C2×#13063253C2211yescharacteristic
43C2×#13063253C2211yescharacteristic
44#14582893C2211yescharacteristic
45#14582893C2211yescharacteristic
46#14582867C2211yescharacteristic
47#14582867C2211yescharacteristic
48#14582866C2211yescharacteristic, complemented
49#14582864—21no—
50#14582864—21no—
51#14582861—21no—
52C2×C22⋊(C43⋊C8)C2211yescharacteristic
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C22⋊C8×D43—21no—
55#14582855C2211yescharacteristic, complemented
56C2×#13063236C2211yescharacteristic, complemented
57C2×C4×C43⋊C8C2211yescharacteristic, complemented
58#14582663C2211yescharacteristic, complemented
59#14582663C2211yescharacteristic, complemented
60#14582654C2211yescharacteristic, complemented
61#14582654C2211yescharacteristic, complemented
62C43×#525C2211yescharacteristic
63C2×#117×C43C2211yescharacteristic
64C2×#104×C43C2211yescharacteristic, complemented
65C2×#104×C43C2211yescharacteristic, complemented
66C43×#407C2211yescharacteristic
67C43×#339C2211yescharacteristic, complemented
68C43×#339C2211yescharacteristic, complemented
69C2×#10621898—21no—
70C2×#10621898—21no—
71C2×#10621898—22no—
72C2×#10621898—22no—
73C2×#10621898—41no—
74C2×#10621898—41no—
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898C2311yescharacteristic
78C2×#10621898C2311yescharacteristic
79C22×Dic86C2×C411yescharacteristic
80C22×D172C2×C411yescharacteristic
81C22×C22⋊D43—21no—
82C22×C4×D43—21no—
83#13063345—22no—
84#13063345—22no—
85#13063345—41no—
86#13063345—41no—
87C2×#10621885C2×C411yescharacteristic
88C2×#10621885C2×C411yescharacteristic
89C2×#10621883C2×C411yescharacteristic
90C2×#10621883C2×C411yescharacteristic
91C2×#10621884C2×C411yescharacteristic
92C2×#10621884C2×C411yescharacteristic
93C2×#10621882C2×C411yescharacteristic
94C2×#10621882C2×C411yescharacteristic
95#13063333—22no—
96#13063333—22no—
97#13063333—41no—
98#13063333—41no—
99#13063332—22no—
100#13063332—41no—
101C2×#10621877—21no—
102C2×#10621877—21no—
103C2×#10621877—22no—
104C2×#10621877—41no—
105C2×#10621877C2311yescharacteristic
106C2×#10621877C2311yescharacteristic
107C2×#10621872—21no—
108C2×#10621872—21no—
109C22×C43⋊C8—21no—
110C22×C43⋊C8—21no—
111C22×C43⋊C8C2311yescharacteristic
112C22×C43⋊C8C2311yescharacteristic
113C22×C43⋊C8C2311yescharacteristic
114C22×C43⋊C8C2311yescharacteristic
115C2×C8×D43—21no—
116C2×C8×D43—21no—
117#13063260—22no—
118#13063260—41no—
119C4⋊(C43⋊C8)—21no—
120C4⋊(C43⋊C8)—21no—
121#13063253—22no—
122#13063253—22no—
123#13063253—22no—
124#13063253D414yescomplemented
125#13063248C2×C411yescharacteristic
126#13063248C2×C411yescharacteristic
127#13063248C2×C411yescharacteristic
128#13063248C2×C411yescharacteristic
129#13063245C2×C411yescharacteristic
130#13063245C2×C411yescharacteristic
131#13063245C2×C411yescharacteristic
132#13063245C2×C411yescharacteristic
133C22⋊(C43⋊C8)—21no—
134C22⋊(C43⋊C8)—21no—
135C22⋊(C43⋊C8)C2×C411yescharacteristic
136C22⋊(C43⋊C8)C2×C411yescharacteristic
137C22⋊(C43⋊C8)C2×C411yescharacteristic
138C22⋊(C43⋊C8)C2×C411yescharacteristic
139C22⋊(C43⋊C8)D411yescharacteristic
140C22⋊(C43⋊C8)D411yescharacteristic
141C22⋊(C43⋊C8)D411yescharacteristic
142C22⋊(C43⋊C8)D411yescharacteristic
143(C2×D43)⋊C8—21no—
144(C2×D43)⋊C8—21no—
145(C2×D43)⋊C8—21no—
146(C2×D43)⋊C8—21no—
147#13063236—22no—
148#13063236—21no—
149C4×C43⋊C8—21no—
150C4×C43⋊C8—41no—
151C2×#41×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C2×M16×C43C2311yescharacteristic
154C2×M16×C43C2311yescharacteristic
155#123×C43—21no—
156C22⋊Q8×C43C2×C411yescharacteristic
157C22⋊Q8×C43C2×C411yescharacteristic
158#121×C43C2×C411yescharacteristic
159#121×C43C2×C411yescharacteristic
160#120×C43—21no—
161C4×D4×C43—21no—
162C4×D4×C43—21no—
163#117×C43—22no—
164#117×C43—41no—
165#117×C43C2311yescharacteristic
166C2×C4⋊C4×C43—21no—
167C2×C22⋊C4×C43—21no—
168C2×C42×C43C2311yescharacteristic
169C2×C42×C43C2311yescharacteristic
170#104×C43—22no—
171#104×C43—41no—
172C22⋊C8×C43—21no—
173C22⋊C8×C43—21no—
174C24×C43#4111yescharacteristic
175C23×D43—21no—
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—21no—
179#41×C43—21no—
180C2×Q8×C43C22×C411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43C22×C411yescharacteristic
193C22×C4×C43C22×C411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43#4111yescharacteristic
197C22×C4×C43C2411yescharacteristic
198C2×C22⋊D43—21no—
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C22×Dic43—21no—
205#10621898—21no—
206#10621898—21no—
207#10621898—21no—
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—22no—
212#10621898—22no—
213#10621898—41no—
214#10621898—41no—
215#10621898—42no—
216#10621898—42no—
217#10621898—42no—
218#10621898—42no—
219#10621898C2×D412yes—
220#10621898#4112yes—
221C2×D172—21no—
222C2×D172—22no—
223C2×D172—41no—
224C2×D172C22×C411yescharacteristic
225C2×D172C22×C411yescharacteristic
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×Dic86—22no—
233C2×Dic86—21no—
234C2×Dic86—41no—
235C2×Dic86C22×C411yescharacteristic
236C2×Dic86C22×C411yescharacteristic
237M16×C43—21no—
238M16×C43—21no—
239M16×C43—21no—
240M16×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—42no—
246C4⋊C4×C43C22×C411yescharacteristic
247C4⋊C4×C43C22×C411yescharacteristic
248C22⋊C4×C43—21no—
249C22⋊C4×C43—21no—
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—42no—
254C42×C43—21no—
255C42×C43—21no—
256C42×C43—21no—
257C42×C43—21no—
258C42×C43C2×D412yes—
259#10621885—22no—
260#10621885—41no—
261#10621884—22no—
262#10621884—41no—
263#10621883—22no—
264#10621883—41no—
265#10621882—22no—
266#10621882—41no—
267#10621877—21no—
268#10621877—21no—
269#10621877—21no—
270#10621877—42no—
271#10621877—42no—
272#10621877C2×D412yes—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—42no—
284C2×C43⋊C8—42no—
285C2×C43⋊C8C22×C411yescharacteristic
286C2×C43⋊C8C22×C411yescharacteristic
287C2×C43⋊C8C22×C411yescharacteristic
288C2×C43⋊C8C22×C411yescharacteristic
289C2×C43⋊C8C2×D411yescharacteristic
290C2×C43⋊C8C2×D411yescharacteristic
291C2×C43⋊C8C2×D411yescharacteristic
292C2×C43⋊C8C2×D411yescharacteristic
293#10621872—42no—
294#10621872—42no—
295C8×D43—42no—
296C8×D43—42no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43C4×D411yescharacteristic
303C23×C43C4×D411yescharacteristic
304C23×C43C2×#4111yescharacteristic
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—81no—
310Q8×C43—21no—
311Q8×C43—21no—
312D4×C43—21no—
313D4×C43—21no—
314D4×C43—42no—
315D4×C43—41no—
316D4×C43—41no—
317D4×C43—81no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—22no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43C4×D411yescharacteristic
340C2×C4×C43C4×D411yescharacteristic
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C22⋊D43—22no—
348C22⋊D43—22no—
349C22⋊D43—42no—
350C22⋊D43—42no—
351C22⋊D43—41no—
352C22⋊D43—41no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—42no—
356D172—21no—
357D172—21no—
358D172—21no—
359D172—42no—
360D172C4×D412yes—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—42no—
364C4×D43—42no—
365C4×D43—41no—
366C4×D43—41no—
367Dic86—21no—
368Dic86—21no—
369Dic86—21no—
370Dic86—42no—
371Dic86C4×D412yes—
372C8×C43—41no—
373C8×C43—41no—
374C43⋊C8—21no—
375C43⋊C8—21no—
376C43⋊C8—21no—
377C43⋊C8—21no—
378C43⋊C8—21no—
379C43⋊C8—21no—
380C43⋊C8—22no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—41no—
384#22887—431nomaximal, Sylow
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43C2×C4×D411yescharacteristic
399C22×C43#54611yescharacteristic
400C22×C43#55111yescharacteristic
401C2×D43—22no—
402C2×D43—41no—
403C2×D43—41no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—84no—
408C4×C43—21no—
409C4×C43—21no—
410C4×C43—42no—
411C4×C43—41no—
412C4×C43—41no—
413C4×C43—41no—
414C4×C43—81no—
415C4×C43C2×C4×D411yescharacteristic
416C4×C43#51811yescharacteristic
417C4×C43D4211yescharacteristic
418C4×C43#54611yescharacteristic
419Dic43—22no—
420Dic43—41no—
421#3002—431no—
422C2×#444—431no—
423#2933—431no—
424C2×#421—431no—
425#2880—431no—
426#1974—431no—
427#1938—431no—
428#1929—431no—
429#1897D4311yescharacteristic, complemented
430#1876—431no—
431#1876—431no—
432#1866—431no—
433#1855—431no—
434#1764—431no—
435#1750—431no—
436C2×C43—21no—
437C2×C43—21no—
438C2×C43—41no—
439C2×C43—41no—
440C2×C43—81no—
441C2×C43#235811yescharacteristic
442C2×C43#295511yescharacteristic
443C2×C43#295711yescharacteristic
444D43—42no—
445D43—81no—
446C22×#41—431no—
447C2×#135—431no—
448C2×#135—431no—
449C2×#131—431no—
450C2×#131—431no—
451C2×#131—431no—
452C22×M16—431no—
453#525C2×D4311yescharacteristic
454C2×#117C2×D4311yescharacteristic
455#452—431no—
456#452—431no—
457#451—431no—
458#450—431no—
459#449—431no—
460#449—431no—
461#448—431no—
462#447—431no—
463#444—864no—
464#436—861no—
465#435—861no—
466#435—861no—
467C8×D4—861no—
468C2×#108—431no—
469C2×#108—431no—
470#424—431no—
471#421—864no—
472C2×#104—431no—
473C2×#104—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104C2×D4311yescharacteristic, complemented
477C2×#104C2×D4311yescharacteristic, complemented
478#416—431no—
479#416—431no—
480#408—431no—
481#408—431no—
482#408—431no—
483#408—861no—
484#408—861no—
485#407—861no—
486#407C2×D4311yescharacteristic
487C2×C22⋊C8—431no—
488C2×C22⋊C8—431no—
489C2×C22⋊C8—861no—
490#405—431no—
491C2×#97—431no—
492C2×C4×C8—431no—
493#341—431no—
494#341—431no—
495#339C2×D4311yescharacteristic, complemented
496#339C2×D4311yescharacteristic, complemented
497#336—431no—
498#336—431no—
499C43#2288711yescharacteristic, complemented, Sylow
500C2×#41—431no—
501C2×#41—431no—
502C2×#41—431no—
503C2×#41—431no—
504C2×#41—862no—
505C2×#41—862no—
506C2×#41—861no—
507C2×#41—861no—
508C2×#41—1721no—
509C2×#41—1721no—
510C2×#41C22×D4311yescharacteristic
511C22×Q8—431no—
512C22×D4—431no—
513C22×D4—861no—
514C23×C4—861no—
515C23×C4C22×D4311yescharacteristic
516#135—862no—
517#135—862no—
518#135—1721no—
519#135—1721no—
520C2×Q16—431no—
521C2×Q16—431no—
522C2×SD16—431no—
523C2×SD16—431no—
524C2×SD16—431no—
525C2×SD16—431no—
526C2×D8—431no—
527C2×D8—431no—
528#131—862no—
529#131—862no—
530#131—862no—
531#131—1721no—
532#131—1721no—
533#131—1721no—
534C2×M16—431no—
535C2×M16—431no—
536C2×M16—861no—
537C2×M16—861no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—862no—
541C2×M16—1721no—
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C22×C8—431no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—431no—
548C22×C8—861no—
549C22×C8—861no—
550C22×C8—861no—
551C22×C8—861no—
552#123—21no—
553C22⋊Q8C4×D4311yescharacteristic
554C22⋊Q8C4×D4311yescharacteristic
555#121C4×D4311yescharacteristic
556#121C4×D4311yescharacteristic
557#120—21no—
558C4×D4—21no—
559C4×D4—21no—
560#117—22no—
561#117—41no—
562#117C22×D4311yescharacteristic
563C2×C4⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C42C22×D4311yescharacteristic
566C2×C42C22×D4311yescharacteristic
567#108—862no—
568#108—1721no—
569C4⋊C8—861no—
570C4⋊C8—861no—
571#104—22no—
572#104—41no—
573#104—434no—
574#104—862no—
575#104—862no—
576#104—862no—
577#103—431no—
578#103—431no—
579#103—431no—
580#103—431no—
581#102—431no—
582#102—431no—
583#102—431no—
584#102—431no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—431no—
588C22⋊C8—431no—
589C22⋊C8—431no—
590C22⋊C8—431no—
591C22⋊C8—431no—
592C22⋊C8—431no—
593C22⋊C8—431no—
594C22⋊C8—431no—
595C22⋊C8—861no—
596C22⋊C8—861no—
597C22⋊C8—861no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8—861no—
601#97—861no—
602#97—862no—
603C4×C8—861no—
604C4×C8—1721no—
605C24—861no—
606C24#1062190011yescharacteristic
607#41—21no—
608#41—21no—
609#41—21no—
610#41—21no—
611#41—432no—
612#41—432no—
613#41—862no—
614#41—862no—
615#41—861no—
616#41—861no—
617#41—861no—
618#41—861no—
619#41—861no—
620#41—861no—
621#41—1722no—
622#41—1722no—
623#41—1721no—
624#41—1721no—
625#41—1722no—
626#41—1722no—
627C2×Q8—431no—
628C2×Q8—431no—
629C2×Q8—862no—
630C2×Q8—861no—
631C2×Q8—1721no—
632C2×Q8C2×C4×D4311yescharacteristic
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—431no—
637C2×D4—431no—
638C2×D4—862no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—1721no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4C2×C4×D4311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—1722no—
661C22×C4—1722no—
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4C2×C4×D4311yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4D4×D4311yescharacteristic
666C22×C4#1062190011yescharacteristic
667C22×C4C23×D4311yescharacteristic
668Q16—862no—
669Q16—1721no—
670SD16—862no—
671SD16—862no—
672SD16—1721no—
673SD16—1721no—
674D8—862no—
675D8—1721no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—432no—
681M16—861no—
682M16—861no—
683M16—861no—
684M16—1722no—
685M16—1722no—
686M16—1722no—
687M16—1722no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—431no—
691C2×C8—431no—
692C2×C8—431no—
693C2×C8—431no—
694C2×C8—431no—
695C2×C8—431no—
696C2×C8—431no—
697C2×C8—431no—
698C2×C8—861no—
699C2×C8—861no—
700C2×C8—861no—
701C2×C8—861no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—1722no—
709C2×C8—1722no—
710C2×C8—1722no—
711C2×C8—1722no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4C2×C4×D4311yescharacteristic
716C4⋊C4C2×C4×D4311yescharacteristic
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—42no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42D4×D4312yes—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—861no—
734C23—861no—
735C23—3441no—
736C23—1722no—
737C23—1722no—
738C23(C22⋊D43)⋊C411yescharacteristic
739C23(C22⋊D43)⋊C411yescharacteristic
740C23C2×#1062190011yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—432no—
744Q8—861no—
745Q8—861no—
746Q8—861no—
747Q8—1722no—
748D4—21no—
749D4—21no—
750D4—42no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—432no—
755D4—862no—
756D4—862no—
757D4—861no—
758D4—861no—
759D4—861no—
760D4—1722no—
761D4—1722no—
762D4—1722no—
763D4—1721no—
764D4—1721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—861no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—861no—
790C2×C4—1722no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4(C22⋊D43)⋊C411yescharacteristic
796C2×C4(C22⋊D43)⋊C411yescharacteristic
797C2×C4C22×C4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4#41×D4311yescharacteristic
801C2×C4#1306337011yescharacteristic
802C2×C4#1306337111yescharacteristic
803C8—41no—
804C8—41no—
805C8—861no—
806C8—861no—
807C8—861no—
808C8—861no—
809C8—861no—
810C8—861no—
811C8—862no—
812C8—861no—
813C8—861no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—81no—
827C22—81no—
828C22—862no—
829C22—3444no—
830C22—1721no—
831C22—1721no—
832C22—1721no—
833C22—1721no—
834C22—1721no—
835C22C2×(C22⋊D43)⋊C411yescharacteristic
836C22#1458353611yescharacteristic
837C22#1458357211yescharacteristic
838C4—21no—
839C4—21no—
840C4—42no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—81no—
845C4—862no—
846C4—1721no—
847C4C4×D4×D4311yescharacteristic
848C4#1458337111yescharacteristic
849C4#1458353311yescharacteristic
850C4#1458353811yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—3441no—
857C2—1722no—
858C2#1913757511yescharacteristic
859C2#1914349411yescharacteristic
860C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1897C2
socleC22×C43C2×C4×D4
prime radical#19143811C2
cosocleC22×C4×C43C24
hypercenter#1897D43
hypocenterC43#22887
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. C2×#14583018C2semidirect
3. #19143322C2semidirect
4. C2×#14582917C2semidirect
5. #19143045C2semidirect
6. #19135480C2semidirect
7. #19135307C2semidirect
8. #19135241C2semidirect
9. #19134920C2semidirect
10. #19134919C2semidirect
11. #19134871C2semidirect
12. #19134799C2semidirect
13. #19134429C2semidirect
14. #19134361C2semidirect
15. C43×#1897C2semidirect
21. C2×#13063332C22semidirect
23. #14583059C4semidirect
24. #14583059C4semidirect
25. #14583054C4semidirect
26. #14583049C4semidirect
27. #14583042C4semidirect
28. #14583042C4semidirect
29. #14583037C4semidirect
30. #14583032C4semidirect
36. C2×#13063260C22semidirect
37. C2×#13063260C22semidirect
38. #14582926C22semidirect
48. #14582866C22semidirect
55. #14582855C22semidirect
56. C2×#13063236C22semidirect
57. C2×C4×C43⋊C8C22semidirect
58. #14582663C22semidirect
59. #14582663C22semidirect
60. #14582654C22semidirect
61. #14582654C22semidirect
64. C2×#104×C43C22semidirect
65. C2×#104×C43C22semidirect
67. C43×#339C22semidirect
68. C43×#339C22semidirect
124. #13063253D4semidirect
429. #1897D43semidirect
476. C2×#104C2×D43semidirect
477. C2×#104C2×D43semidirect
495. #339C2×D43semidirect
496. #339C2×D43semidirect
499. C43#22887semidirect

Maximal subgroups

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

subgroupindex
#191438112
C2×#145830182
#191433222
C2×#145829172
#191430452
#191354802
#191353072
#191352412
#191349202
#191349192
#191348712
#191347992
#191344292
#191343612
C43×#18972
#2288743