Finite Group Databasebeta

← #25064151

Subgroups — #25064151

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#19148621C211yesmaximal, characteristic
2#19143626C211yesmaximal, characteristic, complemented
3#19137237C211yesmaximal, characteristic, complemented
4#19133161C211yesmaximal, characteristic, complemented
5#19133152C211yesmaximal, characteristic, complemented
6#19133148C211yesmaximal, characteristic, complemented
7#19133136C211yesmaximal, characteristic, complemented
8#19133135C211yesmaximal, characteristic, complemented
9#19133124C211yesmaximal, characteristic, complemented
10#19133122C211yesmaximal, characteristic, complemented
11#19133117C211yesmaximal, characteristic, complemented
12#19133101C211yesmaximal, characteristic, complemented
13#19133088C211yesmaximal, characteristic, complemented
14#19133078C211yesmaximal, characteristic, complemented
15C43×#1519C211yesmaximal, characteristic, complemented
16#14583613C411yescharacteristic, complemented
17#14583604C411yescharacteristic, complemented
18#14583597C411yescharacteristic, complemented
19#14583596C411yescharacteristic, complemented
20#14583592—21no—
21#14583567C411yescharacteristic, complemented
22#14583546C411yescharacteristic, complemented
23#14583543—21no—
24#14583543C411yescharacteristic, complemented
25#14583538—21no—
26D4×C22⋊D43—21no—
27D4×C22⋊D43C411yescharacteristic, complemented
28#14583499—21no—
29#14583487—21no—
30#14583481—21no—
31#14583444C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583409C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583372—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#14582794—21no—
49#14582789—21no—
50#14582787—21no—
51#14582762C2211yescharacteristic, complemented
52#14582761C2211yescharacteristic, complemented
53#14582758C2211yescharacteristic, complemented
54#14582750C2211yescharacteristic, complemented
55#14582744C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582635C2211yescharacteristic, complemented
59#14582635C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582633C2211yescharacteristic, complemented
65#14582633C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C2×#121×C43C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic, complemented
70C43×#380C2211yescharacteristic, complemented
71C43×#327C2211yescharacteristic
72C43×#327C2211yescharacteristic
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621898C2×C411yescharacteristic
76C2×#10621900—21no—
77C2×#10621900C2×C411yescharacteristic
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×#10621872—21no—
85C2×C8×D43—21no—
86#13063324C2×C411yescharacteristic
87#13063321—21no—
88#13063321C2×C411yescharacteristic
89#13063320—21no—
90#13063318—21no—
91#13063318—21no—
92#13063316C2×C411yescharacteristic
93#13063315—21no—
94#13063312—21no—
95#13063312C2×C411yescharacteristic
96#13063311—21no—
97#13063311—21no—
98#13063310—21no—
99#13063308—21no—
100#13063307—21no—
101#13063307—21no—
102#13063306—21no—
103#13063306—21no—
104#13063306—21no—
105#13063305C2×C411yescharacteristic
106#13063304—21no—
107#13063304C2×C411yescharacteristic
108#13063304C2311yescharacteristic
109#13063303—21no—
110#13063300C2×C411yescharacteristic
111#13063299—21no—
112#13063299C2×C411yescharacteristic
113#13063299C2311yescharacteristic
114#13063298—21no—
115#13063298—21no—
116#13063297—21no—
117#13063297—21no—
118#13063297—21no—
119#13063297—21no—
120#13063297—21no—
121#13063297—21no—
122#13063296—21no—
123#13063296—21no—
124#13063296C2×C411yescharacteristic
125#13063296C2×C411yescharacteristic
126#13063294—21no—
127#13063294—21no—
128#13063294—21no—
129#13063293—21no—
130#13063293—21no—
131#13063293—21no—
132#13063290C2×C411yescharacteristic
133D4×Dic43—21no—
134D4×Dic43—21no—
135D4×Dic43C2×C411yescharacteristic
136D4×Dic43C2×C411yescharacteristic
137#13063287C2×C411yescharacteristic
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154#13063284C2×C411yescharacteristic
155#13063283C2×C411yescharacteristic
156#13063281—21no—
157#13063281—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43C2×C411yescharacteristic
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43—21no—
164C2×C22⋊Dic43D411yescharacteristic
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43C2311yescharacteristic
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175C22⋊(C43⋊C8)—21no—
176C22⋊(C43⋊C8)C2311yescharacteristic
177C22⋊(C43⋊C8)C2311yescharacteristic
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063235—21no—
181C8×Dic43—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C22×D4×C43—21no—
188C22×D4×C43C2×C411yescharacteristic
189C23×C4×C43C2311yescharacteristic
190C22×C8×C43—21no—
191#121×C43—21no—
192#121×C43—21no—
193#121×C43C2×C411yescharacteristic
194#121×C43C2×C411yescharacteristic
195#121×C43C2311yescharacteristic
196#121×C43C2311yescharacteristic
197C2×C4⋊C4×C43—21no—
198C2×C4⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43—21no—
200C2×C22⋊C4×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C23×D43C2×D411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—81no—
216C2×D4×C43—81no—
217C2×D4×C43—81no—
218C2×D4×C43C22×C411yescharacteristic
219C2×D4×C43C22×C411yescharacteristic
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—81no—
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
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—42no—
240C2×C22⋊D43—44no—
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C2×C22⋊D43C22⋊C411yescharacteristic
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43C2×D411yescharacteristic
251C22×Dic43C2×D411yescharacteristic
252C22×Dic43C2×D411yescharacteristic
253#10621900—81no—
254#10621900—81no—
255#10621900—81no—
256D4×D43—81no—
257D4×D43—81no—
258D4×D43—81no—
259#10621898—81no—
260C2×D172—21no—
261C2×D172C22×C411yescharacteristic
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×C4×D43—81no—
266C2×C4×D43C22×C411yescharacteristic
267C2×C4×D43C22×C411yescharacteristic
268C2×C4×D43C2×D411yescharacteristic
269C2×C4×D43C2×D411yescharacteristic
270C2×Dic86—21no—
271C2×Dic86C22×C411yescharacteristic
272C2×C8×C43—21no—
273C2×C8×C43—21no—
274C2×C8×C43—81no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—81no—
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—81no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—81no—
294C22⋊Dic43C22⋊C411yescharacteristic
295C22⋊Dic43C22⋊C411yescharacteristic
296C22⋊Dic43C22⋊C411yescharacteristic
297C22⋊Dic43C22⋊C411yescharacteristic
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—81no—
305(C2×D43)⋊C4—81no—
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43C22×C411yescharacteristic
313C4⋊Dic43C22×C411yescharacteristic
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—42no—
321Dic43⋊C4—81no—
322Dic43⋊C4C22⋊C411yescharacteristic
323Dic43⋊C4C22⋊C411yescharacteristic
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326C4×Dic43—21no—
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—21no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—42no—
347C23×C43—81no—
348C23×C43—81no—
349C23×C43C2×C22⋊C411yescharacteristic
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C22×D43—21no—
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—42no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43C2×C22⋊C411yescharacteristic
361C22×D43C2×C22⋊C411yescharacteristic
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—81no—
369D4×C43—81no—
370D4×C43—81no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
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—41no—
384C2×C4×C43—41no—
385C2×C4×C43—81no—
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C2×C22⋊C411yescharacteristic
388C2×C4×C43C23×C411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C22⋊D43—22no—
391C22⋊D43—22no—
392C22⋊D43—41no—
393C22⋊D43—41no—
394C22⋊D43—42no—
395C22⋊D43—42no—
396C22⋊D43—41no—
397C22⋊D43—41no—
398C22⋊D43—42no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C22⋊D43—81no—
402C22⋊D43—81no—
403C22⋊D43—81no—
404C2×Dic43—21no—
405C2×Dic43—21no—
406C2×Dic43—22no—
407C2×Dic43—21no—
408C2×Dic43—21no—
409C2×Dic43—21no—
410C2×Dic43—41no—
411C2×Dic43—42no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—81no—
419C2×Dic43—81no—
420C2×Dic43C2×C22⋊C411yescharacteristic
421C2×Dic43C2×C22⋊C411yescharacteristic
422C2×Dic43C2×C22⋊C411yescharacteristic
423C2×Dic43C2×C22⋊C411yescharacteristic
424C2×Dic43C2×C22⋊C411yescharacteristic
425C2×Dic43C2×C22⋊C411yescharacteristic
426D172—41no—
427D172—81no—
428C4×D43—41no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—81no—
433C4×D43—81no—
434C4×D43—81no—
435Dic86—41no—
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—41no—
454C22×C43—41no—
455C22×C43—41no—
456C22×C43—81no—
457C22×C43—81no—
458C22×C43—162no—
459C22×C43C22×C22⋊C411yescharacteristic
460C22×C43#57611yescharacteristic
461C22×C43#57711yescharacteristic
462C2×D43—21no—
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—81no—
472C2×D43—81no—
473C2×D43—162no—
474C4×C43—21no—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—41no—
479C4×C43—41no—
480C4×C43—81no—
481C4×C43—81no—
482Dic43—21no—
483Dic43—21no—
484Dic43—21no—
485Dic43—21no—
486Dic43—21no—
487Dic43—41no—
488Dic43—41no—
489Dic43—41no—
490Dic43—81no—
491Dic43—81no—
492Dic43#42112yes—
493#3519—431no—
494#2974—431no—
495#2319—431no—
496#1519—431no—
497#1519D4311yescharacteristic, complemented
498#1516—431no—
499#1516—431no—
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—81no—
514C2×C43#288311yescharacteristic
515C2×C43#289711yescharacteristic
516C2×C43C2×#42111yescharacteristic
517D43—41no—
518D43—41no—
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#525—431no—
539C2×#121—431no—
540C2×#121C2×D4311yescharacteristic
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#381—431no—
559#380—431no—
560#380C2×D4311yescharacteristic, complemented
561C4×C4⋊C4—431no—
562#376—431no—
563#328—431no—
564#328—431no—
565#328—431no—
566#328—431no—
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#327C2×D4311yescharacteristic
576#327C2×D4311yescharacteristic
577#327C2×D4311yescharacteristic, complemented
578#327C2×D4311yescharacteristic, complemented
579C43#1759911yescharacteristic, complemented, Sylow
580C2×#41—431no—
581C2×#41—431no—
582C2×#41—861no—
583C22×D4—21no—
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—861no—
587C22×D4—861no—
588C22×D4C4×D4311yescharacteristic
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—861no—
608#123—861no—
609#123—861no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614C22⋊Q8—431no—
615C22⋊Q8—431no—
616C22⋊Q8—431no—
617C22⋊Q8—861no—
618C22⋊Q8—861no—
619#121—21no—
620#121—21no—
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#121C4×D4311yescharacteristic
638#121C4×D4311yescharacteristic
639#121C22×D4311yescharacteristic
640#121C22×D4311yescharacteristic
641#120—861no—
642#120—861no—
643#120—861no—
644#120—861no—
645#120—861no—
646#120—861no—
647C4×Q8—431no—
648C4×D4—431no—
649C4×D4—431no—
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—861no—
660C4×D4—861no—
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—431no—
671#117—861no—
672#117—861no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—431no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—861no—
677C2×C4⋊C4—861no—
678C2×C4⋊C4C4×D4311yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—431no—
682C2×C22⋊C4—431no—
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—431no—
705#95—431no—
706#95—861no—
707#95—861no—
708#95—861no—
709#95C22×D4311yescharacteristic
710#95C22×D4311yescharacteristic
711C24—21no—
712C24—431no—
713C24—861no—
714C24D4×D4311yescharacteristic
715#41—3441no—
716#41—3441no—
717#41—3441no—
718#41—3441no—
719C2×Q8—431no—
720C2×Q8—861no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—81no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—431no—
730C2×D4—431no—
731C2×D4—431no—
732C2×D4—431no—
733C2×D4—431no—
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—861no—
743C2×D4—861no—
744C2×D4—3441no—
745C2×D4—3441no—
746C2×D4—3441no—
747C2×D4—1722no—
748C2×D4—1724no—
749C2×D4C2×C4×D4311yescharacteristic
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—81no—
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—861no—
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—81no—
810C22⋊C4—431no—
811C22⋊C4—431no—
812C22⋊C4—431no—
813C22⋊C4—431no—
814C22⋊C4—431no—
815C22⋊C4—431no—
816C22⋊C4—431no—
817C22⋊C4—431no—
818C22⋊C4—861no—
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—431no—
837C42—431no—
838C42—431no—
839C42—431no—
840C42—861no—
841C42—861no—
842C42—861no—
843C42—3441no—
844C42—1722no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—41no—
850C23—41no—
851C23—42no—
852C23—81no—
853C23—81no—
854C23—431no—
855C23—431no—
856C23—861no—
857C23—861no—
858C23—861no—
859C23—3441no—
860C23—3441no—
861C23—1721no—
862C23—1721no—
863C23—1722no—
864C23C22⋊C4×D4311yescharacteristic
865C23C22⋊C4×D4311yescharacteristic
866C23C2×D4×D4311yescharacteristic
867Q8—3441no—
868Q8—1721no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—81no—
876D4—81no—
877D4—81no—
878D4—862no—
879D4—862no—
880D4—3441no—
881D4—3441no—
882D4—3441no—
883D4—3441no—
884D4—3441no—
885D4—3441no—
886D4—1721no—
887D4—1722no—
888D4—1721no—
889D4—1721no—
890D4—1722no—
891D4—1722no—
892D4—1721no—
893D4—1721no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—41no—
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—81no—
909C2×C4—431no—
910C2×C4—431no—
911C2×C4—431no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—862no—
916C2×C4—861no—
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—41no—
958C22—41no—
959C22—41no—
960C22—81no—
961C22—81no—
962C22—162no—
963C22—861no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—861no—
968C22—861no—
969C22—3441no—
970C22—3441no—
971C22—1721no—
972C22—1721no—
973C22—1721no—
974C22—6882no—
975C22C2×C22⋊C4×D4311yescharacteristic
976C22#1458370011yescharacteristic
977C22#1458370511yescharacteristic
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—41no—
983C4—41no—
984C4—81no—
985C4—81no—
986C4—432no—
987C4—861no—
988C4—861no—
989C4—861no—
990C4—861no—
991C4—861no—
992C4—3441no—
993C4—3441no—
994C4—1721no—
995C4—1721no—
996C4—1721no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—3441no—
1004C2—1721no—
1005C2—1721no—
1006C2#1914305311yescharacteristic
1007C2#1914311611yescharacteristic
1008C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1519C2
socleC22×C43C22×C22⋊C4
prime radical#19148621C2
cosocleC22×C4×C43C24
hypercenter#1519D43
hypocenterC43#17599
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #19143626C2semidirect
3. #19137237C2semidirect
4. #19133161C2semidirect
5. #19133152C2semidirect
6. #19133148C2semidirect
7. #19133136C2semidirect
8. #19133135C2semidirect
9. #19133124C2semidirect
10. #19133122C2semidirect
11. #19133117C2semidirect
12. #19133101C2semidirect
13. #19133088C2semidirect
14. #19133078C2semidirect
15. C43×#1519C2semidirect
16. #14583613C4semidirect
17. #14583604C4semidirect
18. #14583597C4semidirect
19. #14583596C4semidirect
21. #14583567C4semidirect
22. #14583546C4semidirect
24. #14583543C4semidirect
27. D4×C22⋊D43C4semidirect
42. #14582953C22semidirect
43. #14582949C22semidirect
44. #14582863C22semidirect
45. #14582861C22semidirect
46. C22⋊C8×D43C22semidirect
51. #14582762C22semidirect
52. #14582761C22semidirect
53. #14582758C22semidirect
54. #14582750C22semidirect
55. #14582744C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582635C22semidirect
59. #14582635C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
64. #14582633C22semidirect
65. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C2×C22⋊C8×C43C22semidirect
70. C43×#380C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
497. #1519D43semidirect
552. C2×C22⋊C8C2×D43semidirect
560. #380C2×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
#191486212
#191436262
#191372372
#191331612
#191331522
#191331482
#191331362
#191331352
#191331242
#191331222
#191331172
#191331012
#191330882
#191330782
C43×#15192
#1759943