Finite Group Databasebeta

← #25064148

Subgroups — #25064148

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148615C211yesmaximal, characteristic
2#19143626C211yesmaximal, characteristic, complemented
3#19137235C211yesmaximal, characteristic, complemented
4#19133164C211yesmaximal, characteristic, complemented
5#19133161C211yesmaximal, characteristic, complemented
6#19133150C211yesmaximal, characteristic, complemented
7#19133138C211yesmaximal, characteristic, complemented
8#19133137C211yesmaximal, characteristic, complemented
9#19133123C211yesmaximal, characteristic, complemented
10#19133122C211yesmaximal, characteristic, complemented
11#19133119C211yesmaximal, characteristic, complemented
12#19133101C211yesmaximal, characteristic, complemented
13#19133088C211yesmaximal, characteristic, complemented
14#19133080C211yesmaximal, characteristic, complemented
15C43×#1516C211yesmaximal, characteristic, complemented
16#14583612C411yescharacteristic, complemented
17#14583607C411yescharacteristic, complemented
18#14583601C411yescharacteristic, complemented
19#14583598—21no—
20#14583593C411yescharacteristic, complemented
21#14583568C411yescharacteristic, complemented
22#14583544—21no—
23#14583540C411yescharacteristic, complemented
24#14583537C411yescharacteristic, complemented
25#14583536—21no—
26#14583533C411yescharacteristic, complemented
27#14583531—21no—
28#14583501—21no—
29#14583485—21no—
30#14583482—21no—
31#14583444C2211yescharacteristic
32#14583435C2211yescharacteristic
33#14583412C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38#14582974—21no—
39#14582973—21no—
40#14582970—21no—
41C8×C22⋊D43—21no—
42#14582953C2211yescharacteristic, complemented
43#14582949C2211yescharacteristic, complemented
44#14582863C2211yescharacteristic, complemented
45#14582861C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic, complemented
47#14582799—21no—
48#14582796—21no—
49#14582793—21no—
50#14582791—21no—
51#14582761C2211yescharacteristic, complemented
52#14582759C2211yescharacteristic, complemented
53#14582758C2211yescharacteristic, complemented
54#14582750C2211yescharacteristic, complemented
55#14582744C2211yescharacteristic, complemented
56#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic
59#14582634C2211yescharacteristic
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582632C2211yescharacteristic
65#14582632C2211yescharacteristic
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
75C2×#10621902C2×C411yescharacteristic
76C2×#10621900—21no—
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic
83C22×C4×D43C2311yescharacteristic
84C2×#10621877—21no—
85C2×#10621872—21no—
86C2×C8×D43—21no—
87#13063324C2×C411yescharacteristic
88#13063321—21no—
89#13063321C2×C411yescharacteristic
90#13063320—21no—
91#13063319—21no—
92#13063318—21no—
93#13063316C2×C411yescharacteristic
94#13063315—21no—
95#13063314C2×C411yescharacteristic
96#13063313—21no—
97#13063311—21no—
98#13063311—21no—
99#13063310—21no—
100#13063310—21no—
101#13063309—21no—
102#13063309—21no—
103#13063308—21no—
104#13063307—21no—
105#13063305—21no—
106#13063302—21no—
107#13063301C2×C411yescharacteristic
108#13063300—21no—
109#13063300C2×C411yescharacteristic
110#13063300C2×C411yescharacteristic
111#13063299—21no—
112#13063299—21no—
113#13063299—21no—
114#13063299C2×C411yescharacteristic
115#13063299C2×C411yescharacteristic
116#13063299C2311yescharacteristic
117#13063299C2311yescharacteristic
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063297—21no—
125#13063297—21no—
126#13063296—21no—
127#13063296C2×C411yescharacteristic
128#13063295—21no—
129#13063295—21no—
130#13063295—21no—
131#13063293—21no—
132#13063293—21no—
133Q8×Dic43C2×C411yescharacteristic
134C4×D172—21no—
135D4×Dic43—21no—
136D4×Dic43C2×C411yescharacteristic
137#13063287—21no—
138#13063287C2×C411yescharacteristic
139#13063287C2×C411yescharacteristic
140C4×C22⋊D43—21no—
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063283—21no—
154#13063283C2×C411yescharacteristic
155#13063282—21no—
156C2×C4⋊Dic43—21no—
157C2×C4⋊Dic43C2×C411yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43C2×C411yescharacteristic
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43D411yescharacteristic
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4D411yescharacteristic
169C22⋊C4×D43—21no—
170C22⋊C4×D43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182C8×Dic43—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic
188C23×C4×C43C2311yescharacteristic
189C22×C8×C43—21no—
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2×C411yescharacteristic
194#121×C43C2311yescharacteristic
195#120×C43—21no—
196C4×D4×C43—21no—
197C4×D4×C43—21no—
198#117×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43—21no—
200C22⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207C23×D43—21no—
208C23×D43—21no—
209C23×D43C2×D411yescharacteristic
210#41×C43—81no—
211C2×Q8×C43C22×C411yescharacteristic
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43C22×C411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—81no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2411yescharacteristic
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—42no—
235C2×C22⋊D43—81no—
236C2×C22⋊D43—81no—
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C2×C22⋊D43C22⋊C411yescharacteristic
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248#10621902—81no—
249#10621900—81no—
250#10621900—81no—
251D4×D43—44no—
252D4×D43—81no—
253D4×D43—81no—
254D4×D43—81no—
255C2×D172—21no—
256C2×D172—21no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—81no—
260C2×D172C22×C411yescharacteristic
261C2×D172C22×C411yescharacteristic
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×C4×D43—21no—
266C2×C4×D43—81no—
267C2×C4×D43C22×C411yescharacteristic
268C2×C4×D43C22×C411yescharacteristic
269C2×C4×D43C2×D411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×Dic86—21no—
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—81no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43C22×C411yescharacteristic
278C4⋊C4×C43C22×C411yescharacteristic
279C22⋊C4×C43—21no—
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C22⋊C4×C43—81no—
285C42×C43—21no—
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288C22⋊Dic43—81no—
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—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—81no—
306(C2×D43)⋊C4—81no—
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311C4⋊Dic43—21no—
312C4⋊Dic43—21no—
313C4⋊Dic43—21no—
314C4⋊Dic43—81no—
315C4⋊Dic43C22×C411yescharacteristic
316C4⋊Dic43C22×C411yescharacteristic
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—42no—
322Dic43⋊C4—81no—
323Dic43⋊C4C22⋊C411yescharacteristic
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327C4×Dic43—21no—
328C4×Dic43—21no—
329C4×Dic43—42no—
330C4×Dic43—81no—
331C4×Dic43C22×C411yescharacteristic
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335#10621877—81no—
336C2×C43⋊C8—21no—
337C2×C43⋊C8—21no—
338#10621872—81no—
339C8×D43—81no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C22×D411yescharacteristic
348C22×D43—21no—
349C22×D43—21no—
350C22×D43—21no—
351C22×D43—21no—
352C22×D43—41no—
353C22×D43—41no—
354C22×D43—42no—
355C22×D43—42no—
356C22×D43—81no—
357C22×D43—81no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43C2×C22⋊C411yescharacteristic
361C22×D43C2×C22⋊C411yescharacteristic
362Q8×C43—41no—
363D4×C43—41no—
364D4×C43—42no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—81no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
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—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—81no—
384C2×C4×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C23×C411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C22⋊D43—22no—
389C22⋊D43—22no—
390C22⋊D43—41no—
391C22⋊D43—41no—
392C22⋊D43—41no—
393C22⋊D43—41no—
394C22⋊D43—41no—
395C22⋊D43—41no—
396C22⋊D43—42no—
397C22⋊D43—81no—
398C22⋊D43—81no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C22⋊D43—81no—
402C2×Dic43—21no—
403C2×Dic43—21no—
404C2×Dic43—22no—
405C2×Dic43—21no—
406C2×Dic43—21no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—81no—
415C2×Dic43—81no—
416C2×Dic43C2×C22⋊C411yescharacteristic
417C2×Dic43C2×C22⋊C411yescharacteristic
418C2×Dic43C2×C22⋊C411yescharacteristic
419C2×Dic43C2×C22⋊C411yescharacteristic
420C2×Dic43C2×C22⋊C411yescharacteristic
421C2×Dic43C2×C22⋊C411yescharacteristic
422D172—41no—
423D172—41no—
424D172—42no—
425D172—81no—
426D172—81no—
427D172—81no—
428C4×D43—41no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—42no—
433C4×D43—81no—
434C4×D43—81no—
435C4×D43—81no—
436Dic86—81no—
437C8×C43—41no—
438C8×C43—41no—
439C43⋊C8—41no—
440C43⋊C8—41no—
441#17599—431nomaximal, Sylow
442C22×C43—21no—
443C22×C43—21no—
444C22×C43—21no—
445C22×C43—21no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—41no—
451C22×C43—41no—
452C22×C43—41no—
453C22×C43—81no—
454C22×C43—81no—
455C22×C43C22×C22⋊C411yescharacteristic
456C22×C43#57611yescharacteristic
457C22×C43#57711yescharacteristic
458C2×D43—21no—
459C2×D43—21no—
460C2×D43—21no—
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—21no—
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—81no—
471C2×D43—81no—
472C2×D43—162no—
473C2×D43—162no—
474C4×C43—21no—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—41no—
479C4×C43—41no—
480C4×C43—41no—
481C4×C43—81no—
482C4×C43—81no—
483Dic43—21no—
484Dic43—21no—
485Dic43—21no—
486Dic43—21no—
487Dic43—21no—
488Dic43—41no—
489Dic43—41no—
490Dic43—81no—
491Dic43—81no—
492Dic43#42112yes—
493#3519—431no—
494#2974—431no—
495#2319—431no—
496#1519—431no—
497#1519—431no—
498#1516—431no—
499#1516D4311yescharacteristic, complemented
500#1513—431no—
501#1513—431no—
502#1510—431no—
503#1510—431no—
504#1509—431no—
505#1505—431no—
506#1502—431no—
507#1500—431no—
508C2×C43—21no—
509C2×C43—21no—
510C2×C43—41no—
511C2×C43—41no—
512C2×C43—81no—
513C2×C43#288311yescharacteristic
514C2×C43#289711yescharacteristic
515C2×C43C2×#42111yescharacteristic
516D43—41no—
517D43—41no—
518D43—81no—
519D43—81no—
520#555—431no—
521#554—431no—
522#553—431no—
523#553—431no—
524#553—861no—
525#550—431no—
526#546—431no—
527#546—431no—
528#546—861no—
529#546—861no—
530D42—431no—
531D42—861no—
532#540—861no—
533#538—861no—
534#538—861no—
535#532—431no—
536#529—431no—
537#525—431no—
538#525C2×D4311yescharacteristic
539C2×#121—431no—
540C2×#121—431no—
541#518—861no—
542C2×C4×D4—431no—
543#436—861no—
544#435—861no—
545#435—861no—
546C8×D4—861no—
547#432—431no—
548#431—431no—
549#407—431no—
550#407—431no—
551C2×C22⋊C8—431no—
552C2×C22⋊C8C2×D4311yescharacteristic, complemented
553#390—861no—
554#389—861no—
555#388—861no—
556#388—861no—
557#381—431no—
558#381C2×D4311yescharacteristic, complemented
559#380—431no—
560#380—431no—
561C4×C4⋊C4—431no—
562#376—431no—
563#328—431no—
564#328—431no—
565#328C2×D4311yescharacteristic, complemented
566#328C2×D4311yescharacteristic, complemented
567#327—431no—
568#327—431no—
569#327—431no—
570#327—431no—
571#327—431no—
572#327—431no—
573#327—431no—
574#327—431no—
575#327—431no—
576#327—431no—
577#327C2×D4311yescharacteristic, complemented
578#327C2×D4311yescharacteristic, complemented
579C43#1759911yescharacteristic, complemented, Sylow
580C2×#41—431no—
581C2×#41—861no—
582C2×#41C4×D4311yescharacteristic
583C22×D4—431no—
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—861no—
587C22×D4—861no—
588C22×D4—861no—
589C23×C4—431no—
590C23×C4C22×D4311yescharacteristic
591C2×M16—861no—
592C2×M16—861no—
593C22×C8—21no—
594C22×C8—861no—
595C4⋊Q8—431no—
596#127—431no—
597#127—861no—
598#126—861no—
599#126—861no—
600#126—861no—
601#125—431no—
602#125—861no—
603#124—431no—
604#124—861no—
605#124—861no—
606#124—861no—
607#123—21no—
608#123—861no—
609#123—861no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614C22⋊Q8—431no—
615C22⋊Q8—861no—
616C22⋊Q8—861no—
617C22⋊Q8C4×D4311yescharacteristic
618C22⋊Q8C22×D4311yescharacteristic
619#121—431no—
620#121—431no—
621#121—431no—
622#121—431no—
623#121—431no—
624#121—431no—
625#121—431no—
626#121—861no—
627#121—861no—
628#121—861no—
629#121—861no—
630#121—861no—
631#121—861no—
632#121—861no—
633#121—861no—
634#121—861no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121C4×D4311yescharacteristic
640#121C22×D4311yescharacteristic
641#120—21no—
642#120—861no—
643#120—861no—
644#120—861no—
645#120—861no—
646#120—861no—
647C4×Q8—431no—
648C4×D4—21no—
649C4×D4—21no—
650C4×D4—431no—
651C4×D4—431no—
652C4×D4—431no—
653C4×D4—431no—
654C4×D4—431no—
655C4×D4—431no—
656C4×D4—431no—
657C4×D4—431no—
658C4×D4—431no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—861no—
662C4×D4—861no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669#117—431no—
670#117—861no—
671#117—861no—
672#117C4×D4311yescharacteristic
673C2×C4⋊C4—431no—
674C2×C4⋊C4—431no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—861no—
677C2×C4⋊C4—861no—
678C2×C4⋊C4—861no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—431no—
681C2×C22⋊C4—431no—
682C2×C22⋊C4—861no—
683C2×C22⋊C4—861no—
684C2×C22⋊C4—861no—
685C2×C22⋊C4—861no—
686C2×C22⋊C4—861no—
687C2×C22⋊C4—861no—
688C2×C22⋊C4—861no—
689C2×C42—431no—
690C2×C42—861no—
691C2×C42—861no—
692C4⋊C8—861no—
693C4⋊C8—861no—
694C22⋊C8—21no—
695C22⋊C8—431no—
696C22⋊C8—431no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8—861no—
700C22⋊C8C22×D4311yescharacteristic
701C22⋊C8C22×D4311yescharacteristic
702#97—861no—
703C4×C8—861no—
704#95—21no—
705#95—431no—
706#95—431no—
707#95—861no—
708#95—861no—
709#95C22×D4311yescharacteristic
710#95C22×D4311yescharacteristic
711C24—431no—
712C24—861no—
713C24—861no—
714C24D4×D4311yescharacteristic
715#41—81no—
716#41—3441no—
717#41—3441no—
718#41—3441no—
719C2×Q8—861no—
720C2×Q8C2×C4×D4311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—431no—
725C2×D4—431no—
726C2×D4—431no—
727C2×D4—431no—
728C2×D4—431no—
729C2×D4—431no—
730C2×D4—861no—
731C2×D4—861no—
732C2×D4—861no—
733C2×D4—861no—
734C2×D4—861no—
735C2×D4—861no—
736C2×D4—861no—
737C2×D4—861no—
738C2×D4—861no—
739C2×D4—861no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—3441no—
743C2×D4—3441no—
744C2×D4—3441no—
745C2×D4—3441no—
746C2×D4—3441no—
747C2×D4—3441no—
748C2×D4—1722no—
749C2×D4—1724no—
750C2×D4C2×C4×D4311yescharacteristic
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—81no—
755C22×C4—431no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—861no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—3441no—
771C22×C4C2×C4×D4311yescharacteristic
772C22×C4C2×C4×D4311yescharacteristic
773C22×C4D4×D4311yescharacteristic
774C22×C4D4×D4311yescharacteristic
775C22×C4D4×D4311yescharacteristic
776C22×C4C23×D4311yescharacteristic
777M16—3441no—
778M16—3441no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—81no—
782C2×C8—861no—
783C2×C8—861no—
784C2×C8—3441no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—431no—
788C4⋊C4—431no—
789C4⋊C4—431no—
790C4⋊C4—431no—
791C4⋊C4—431no—
792C4⋊C4—431no—
793C4⋊C4—861no—
794C4⋊C4—861no—
795C4⋊C4—861no—
796C4⋊C4—861no—
797C4⋊C4—861no—
798C4⋊C4—861no—
799C4⋊C4—861no—
800C4⋊C4—3441no—
801C4⋊C4—3441no—
802C4⋊C4—1722no—
803C4⋊C4C2×C4×D4311yescharacteristic
804C4⋊C4C2×C4×D4311yescharacteristic
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—81no—
811C22⋊C4—431no—
812C22⋊C4—431no—
813C22⋊C4—431no—
814C22⋊C4—431no—
815C22⋊C4—431no—
816C22⋊C4—431no—
817C22⋊C4—431no—
818C22⋊C4—431no—
819C22⋊C4—861no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—861no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—861no—
828C22⋊C4—861no—
829C22⋊C4—861no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—3441no—
834C22⋊C4—3441no—
835C22⋊C4—3441no—
836C42—21no—
837C42—431no—
838C42—431no—
839C42—431no—
840C42—431no—
841C42—861no—
842C42—861no—
843C42—3441no—
844C42—1722no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—41no—
849C23—41no—
850C23—431no—
851C23—431no—
852C23—861no—
853C23—861no—
854C23—861no—
855C23—861no—
856C23—3441no—
857C23—3441no—
858C23—3441no—
859C23—3441no—
860C23—1721no—
861C23—1721no—
862C23—1722no—
863C23—1722no—
864C23C22⋊C4×D4311yescharacteristic
865C23C22⋊C4×D4311yescharacteristic
866C23C2×D4×D4311yescharacteristic
867Q8—41no—
868Q8—3441no—
869D4—41no—
870D4—42no—
871D4—41no—
872D4—41no—
873D4—81no—
874D4—862no—
875D4—862no—
876D4—3441no—
877D4—3441no—
878D4—3441no—
879D4—3441no—
880D4—3441no—
881D4—3441no—
882D4—3441no—
883D4—3441no—
884D4—1721no—
885D4—1721no—
886D4—1722no—
887D4—1722no—
888D4—1721no—
889D4—1721no—
890D4—1721no—
891D4—1721no—
892D4—1721no—
893D4—1721no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—81no—
910C2×C4—431no—
911C2×C4—431no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—862no—
917C2×C4—861no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—861no—
921C2×C4—3441no—
922C2×C4—3441no—
923C2×C4—3441no—
924C2×C4—3441no—
925C2×C4—3441no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1722no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4C22⋊C4×D4311yescharacteristic
939C2×C4C22⋊C4×D4311yescharacteristic
940C2×C4C22×C4×D4311yescharacteristic
941C2×C4C2×D4×D4311yescharacteristic
942C8—41no—
943C8—41no—
944C8—1721no—
945C8—1721no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—81no—
958C22—81no—
959C22—861no—
960C22—861no—
961C22—861no—
962C22—861no—
963C22—861no—
964C22—861no—
965C22—3441no—
966C22—3441no—
967C22—1721no—
968C22—1721no—
969C22—1721no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22—6882no—
974C22—6882no—
975C22C2×C22⋊C4×D4311yescharacteristic
976C22#1458370111yescharacteristic
977C22#1458370611yescharacteristic
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—41no—
983C4—41no—
984C4—41no—
985C4—81no—
986C4—81no—
987C4—432no—
988C4—861no—
989C4—861no—
990C4—861no—
991C4—861no—
992C4—861no—
993C4—3441no—
994C4—3441no—
995C4—1721no—
996C4—1721no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—3441no—
1003C2—3441no—
1004C2—1721no—
1005C2—1721no—
1006C2#1914305311yescharacteristic
1007C2#1914311711yescharacteristic
1008C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1516C2
socleC22×C43C22×C22⋊C4
prime radical#19148615C2
cosocleC22×C4×C43C24
hypercenter#1516D43
hypocenterC43#17599
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. #19143626C2semidirect
3. #19137235C2semidirect
4. #19133164C2semidirect
5. #19133161C2semidirect
6. #19133150C2semidirect
7. #19133138C2semidirect
8. #19133137C2semidirect
9. #19133123C2semidirect
10. #19133122C2semidirect
11. #19133119C2semidirect
12. #19133101C2semidirect
13. #19133088C2semidirect
14. #19133080C2semidirect
15. C43×#1516C2semidirect
16. #14583612C4semidirect
17. #14583607C4semidirect
18. #14583601C4semidirect
20. #14583593C4semidirect
21. #14583568C4semidirect
23. #14583540C4semidirect
24. #14583537C4semidirect
26. #14583533C4semidirect
42. #14582953C22semidirect
43. #14582949C22semidirect
44. #14582863C22semidirect
45. #14582861C22semidirect
46. C22⋊C8×D43C22semidirect
51. #14582761C22semidirect
52. #14582759C22semidirect
53. #14582758C22semidirect
54. #14582750C22semidirect
55. #14582744C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C2×C22⋊C8×C43C22semidirect
70. C43×#381C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
499. #1516D43semidirect
552. C2×C22⋊C8C2×D43semidirect
558. #381C2×D43semidirect
565. #328C2×D43semidirect
566. #328C2×D43semidirect
577. #327C2×D43semidirect
578. #327C2×D43semidirect
579. C43#17599semidirect

Maximal subgroups

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

subgroupindex
#191486152
#191436262
#191372352
#191331642
#191331612
#191331502
#191331382
#191331372
#191331232
#191331222
#191331192
#191331012
#191330882
#191330802
C43×#15162
#1759943