Finite Group Databasebeta

← #25064826

Subgroups — #25064826

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148510C211yesmaximal, characteristic
2#19143613C211yesmaximal, characteristic, complemented
3#19143606C211yesmaximal, characteristic, complemented
4#19133228C211yesmaximal, characteristic, complemented
5#19133226C211yesmaximal, characteristic, complemented
6#19133223C211yesmaximal, characteristic, complemented
7#19133214C211yesmaximal, characteristic, complemented
8#19133213C211yesmaximal, characteristic, complemented
9#19133201C211yesmaximal, characteristic, complemented
10#19133200C211yesmaximal, characteristic, complemented
11#19133195C211yesmaximal, characteristic, complemented
12#19133195C211yesmaximal, characteristic, complemented
13#19133185C211yesmaximal, characteristic, complemented
14#19133180C211yesmaximal, characteristic, complemented
15C43×#1524C211yesmaximal, characteristic, complemented
16#14583600—21no—
17#14583599—21no—
18#14583598—21no—
19#14583594—21no—
20#14583594—21no—
21#14583593—21no—
22#14583585—21no—
23#14583582—21no—
24#14583509C411yescharacteristic
25#14583507C411yescharacteristic
26#14583502C411yescharacteristic
27#14583500C411yescharacteristic
28#14583479C411yescharacteristic
29#14583478C411yescharacteristic
30#14583448C2211yescharacteristic
31#14583434C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583428C2211yescharacteristic
34#125×D43C2211yescharacteristic
35#14583381C411yescharacteristic
36#14583378C411yescharacteristic
37C4×#10621898C2211yescharacteristic
38#14583027—21no—
39C8×Dic86—21no—
40#14582978—21no—
41#14582975—21no—
42#14582975—21no—
43#14582972—21no—
44#14582970—21no—
45C8×C22⋊D43—21no—
46#14582956C2211yescharacteristic
47#14582956C2211yescharacteristic
48#14582954C2211yescharacteristic
49#14582954C2211yescharacteristic
50#14582954C2211yescharacteristic
51#14582954C2211yescharacteristic
52#14582851C2211yescharacteristic
53#14582851C2211yescharacteristic
54#14582851C2211yescharacteristic
55#97×D43C2211yescharacteristic
56#14582641C2211yescharacteristic
57#14582641C2211yescharacteristic
58#14582640C2211yescharacteristic
59#14582640C2211yescharacteristic
60#14582640C2211yescharacteristic
61#14582640C2211yescharacteristic
62#14582639C2211yescharacteristic
63#14582639C2211yescharacteristic
64#14582638C2211yescharacteristic
65#14582638C2211yescharacteristic
66#14582638C2211yescharacteristic
67#14582638C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C4×M16×C43C2211yescharacteristic
70C2×#97×C43C2211yescharacteristic
71C43×#330C2211yescharacteristic
72C43×#330C2211yescharacteristic
73C43×#329C2211yescharacteristic
74C43×#329C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C2×#10621900C2×C411yescharacteristic
78C2×#10621872—21no—
79C2×#10621872—21no—
80C2×#10621872—21no—
81C2×C8×D43—21no—
82#13063323C2×C411yescharacteristic
83#13063321C2×C411yescharacteristic
84#13063320—21no—
85#13063320—21no—
86#13063319—21no—
87#13063319—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063317—21no—
92#13063317C2311yescharacteristic
93#13063316—21no—
94#13063316C2×C411yescharacteristic
95#13063316C2×C411yescharacteristic
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063313C2311yescharacteristic
101#13063310—21no—
102#13063309—21no—
103#13063308—21no—
104#13063308—21no—
105#13063307—21no—
106#13063307—21no—
107#13063307—21no—
108#13063305C2×C411yescharacteristic
109#13063304C2×C411yescharacteristic
110#13063303—21no—
111#13063302—21no—
112#13063301C2×C411yescharacteristic
113#13063300—21no—
114#13063300C2×C411yescharacteristic
115#13063299—21no—
116#13063299C2×C411yescharacteristic
117#13063298—21no—
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063297—21no—
124#13063297—21no—
125#13063296—21no—
126#13063296—21no—
127#13063296C2×C411yescharacteristic
128Q8×Dic43C2×C411yescharacteristic
129C4×Dic86C2×C411yescharacteristic
130C4×Dic86D411yescharacteristic
131C4×Dic86D411yescharacteristic
132#13063290C2×C411yescharacteristic
133C4×D172—21no—
134C4×D172C2×C411yescharacteristic
135C4×D172D411yescharacteristic
136C4×D172D411yescharacteristic
137D4×Dic43C2×C411yescharacteristic
138#13063287—21no—
139#13063287—21no—
140#13063287C2×C411yescharacteristic
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43D411yescharacteristic
144C4×C22⋊D43D411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151#13063284C2×C411yescharacteristic
152#13063283—21no—
153#13063282—21no—
154#13063282—21no—
155#13063282C2×C411yescharacteristic
156#13063282C2×C411yescharacteristic
157#13063281—21no—
158#13063281—21no—
159C2×Dic43⋊C4—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43—21no—
162C4⋊C4×D43—21no—
163C4⋊C4×D43C2×C411yescharacteristic
164C4⋊C4×D43C2×C411yescharacteristic
165C42×D43C2311yescharacteristic
166C42×D43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063236C2311yescharacteristic
180#13063236C2311yescharacteristic
181#13063236C2311yescharacteristic
182#13063236C2311yescharacteristic
183#13063235—21no—
184C8×Dic43—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C2×M16×C43—21no—
188C22×C8×C43—21no—
189#126×C43—21no—
190#125×C43C2311yescharacteristic
191#124×C43C2311yescharacteristic
192#123×C43—21no—
193C22⋊Q8×C43C2×C411yescharacteristic
194#121×C43C2×C411yescharacteristic
195C4×Q8×C43C2×C411yescharacteristic
196C4×D4×C43—21no—
197C4×D4×C43C2×C411yescharacteristic
198#117×C43—21no—
199C2×C42×C43C2311yescharacteristic
200#97×C43—21no—
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205C4×C8×C43—21no—
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43C22×C411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43C2×D411yescharacteristic
213C2×C22⋊D43—21no—
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43C22⋊C411yescharacteristic
219C2×C22⋊D43C22⋊C411yescharacteristic
220C22×Dic43—21no—
221C22×Dic43—21no—
222#10621902—42no—
223#10621900—42no—
224#10621898—42no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172C22⋊C411yescharacteristic
228C2×D172C22×C411yescharacteristic
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C2×D411yescharacteristic
237C2×C4×D43C2×D411yescharacteristic
238C2×C4×D43C2×D411yescharacteristic
239C2×C4×D43C2×D411yescharacteristic
240C2×Dic86C22⋊C411yescharacteristic
241C2×Dic86C22×C411yescharacteristic
242M16×C43—42no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—42no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43C22×C411yescharacteristic
253C4⋊C4×C43C22×C411yescharacteristic
254C22⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C22⋊C4×C43—21no—
257C22⋊C4×C43—21no—
258C22⋊C4×C43—21no—
259C42×C43—21no—
260C42×C43C22×C411yescharacteristic
261C42×C43C2×D411yescharacteristic
262C42×C43C2×D411yescharacteristic
263C42×C43C2411yescharacteristic
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266C22⋊Dic43—21no—
267C22⋊Dic43C22⋊C411yescharacteristic
268C22⋊Dic43C22⋊C411yescharacteristic
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4C22⋊C411yescharacteristic
278(C2×D43)⋊C4C22⋊C411yescharacteristic
279(C2×D43)⋊C4C22⋊C411yescharacteristic
280(C2×D43)⋊C4C22⋊C411yescharacteristic
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43C22⋊C411yescharacteristic
286C4⋊Dic43C22⋊C411yescharacteristic
287C4⋊Dic43C22×C411yescharacteristic
288C4⋊Dic43C22×C411yescharacteristic
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4C22⋊C411yescharacteristic
302Dic43⋊C4C22⋊C411yescharacteristic
303Dic43⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4C22⋊C411yescharacteristic
305C4×Dic43—21no—
306C4×Dic43—21no—
307C4×Dic43—21no—
308C4×Dic43C22×C411yescharacteristic
309C4×Dic43C22×C411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313C4×Dic43C2×D411yescharacteristic
314C2×C43⋊C8—21no—
315C2×C43⋊C8—21no—
316C2×C43⋊C8—21no—
317C2×C43⋊C8—21no—
318#10621872—42no—
319#10621872—42no—
320#10621872—42no—
321C8×D43—42no—
322C23×C43—21no—
323C23×C43C2×C22⋊C411yescharacteristic
324C22×D43—21no—
325C22×D43C2×C22⋊C411yescharacteristic
326C22×D43C2×C22⋊C411yescharacteristic
327Q8×C43—41no—
328D4×C43—41no—
329D4×C43—81no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—81no—
337C2×C4×C43C2×C22⋊C411yescharacteristic
338C2×C4×C43C2×C22⋊C411yescharacteristic
339C2×C4×C43C2×C22⋊C411yescharacteristic
340C2×C4×C43C23×C411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C22⋊D43—22no—
344C22⋊D43—41no—
345C22⋊D43—42no—
346C22⋊D43—81no—
347C22⋊D43—81no—
348C22⋊D43—81no—
349C22⋊D43—81no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—42no—
354C2×Dic43—81no—
355C2×Dic43C2×C22⋊C411yescharacteristic
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361D172—41no—
362D172—41no—
363D172—42no—
364D172—81no—
365C4×D43—22no—
366C4×D43—41no—
367C4×D43—41no—
368C4×D43—41no—
369C4×D43—41no—
370C4×D43—41no—
371C4×D43—42no—
372C4×D43—81no—
373C4×D43—81no—
374C4×D43—81no—
375C4×D43—81no—
376Dic86—22no—
377Dic86—41no—
378C8×C43—22no—
379C8×C43—22no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385C43⋊C8—41no—
386#17687—431nomaximal, Sylow
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43C22×C22⋊C411yescharacteristic
394C2×D43—21no—
395C2×D43—21no—
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—21no—
400C2×D43—41no—
401C2×D43—41no—
402C2×D43—41no—
403C4×C43—21no—
404C4×C43—21no—
405C4×C43—21no—
406C4×C43—21no—
407C4×C43—21no—
408C4×C43—21no—
409C4×C43—41no—
410C4×C43—41no—
411C4×C43—41no—
412Dic43—21no—
413Dic43—21no—
414Dic43—21no—
415Dic43—21no—
416Dic43—21no—
417Dic43—41no—
418Dic43—41no—
419Dic43—41no—
420Dic43#41312yes—
421#3512—431no—
422#2971—431no—
423#2970—431no—
424#1536—431no—
425#1535—431no—
426#1535—431no—
427#1532—431no—
428#1532—431no—
429#1529—431no—
430#1529—431no—
431#1528—431no—
432#1528—431no—
433#1525—431no—
434#1524—431no—
435#1524D4311yescharacteristic, complemented
436C2×C43—41no—
437C2×C43—81no—
438C2×C43C2×#41311yescharacteristic
439C2×C43#290111yescharacteristic
440C2×C43#290111yescharacteristic
441D43—41no—
442D43—41no—
443D43—81no—
444#553—861no—
445#553—861no—
446#553—861no—
447#553—861no—
448#553—861no—
449#553—861no—
450#552—861no—
451#552—861no—
452#541—431no—
453#541—431no—
454#540—431no—
455#540—431no—
456#537—431no—
457#537—431no—
458#532—431no—
459#529—431no—
460#529—431no—
461#529—431no—
462#529C2×D4311yescharacteristic
463C2×#125—431no—
464#520—431no—
465#520—431no—
466C4×#41—431no—
467#446—861no—
468C8×Q8—861no—
469#436—861no—
470#436—861no—
471#436—861no—
472#435—861no—
473#435—861no—
474C8×D4—861no—
475#432—431no—
476#432—431no—
477#432—431no—
478#432—431no—
479#432—431no—
480#432—431no—
481C4×M16—431no—
482C4×M16—431no—
483C4×M16—431no—
484C4×M16C2×D4311yescharacteristic
485C2×#97—431no—
486C2×#97C2×D4311yescharacteristic
487#330—431no—
488#330—431no—
489#330—431no—
490#330—431no—
491#330—431no—
492#330—431no—
493#330C2×D4311yescharacteristic
494#330C2×D4311yescharacteristic
495#329—431no—
496#329—431no—
497#329—431no—
498#329—431no—
499#329—431no—
500#329—431no—
501#329C2×D4311yescharacteristic
502#329C2×D4311yescharacteristic
503C43#1768711yescharacteristic, complemented, Sylow
504C2×#41—431no—
505C2×#41—431no—
506C2×#41—431no—
507C2×M16—21no—
508C2×M16—861no—
509C2×M16—861no—
510C2×M16—861no—
511C22×C8—21no—
512C22×C8—861no—
513C4⋊Q8—431no—
514#127—431no—
515#126—21no—
516#126—861no—
517#126—861no—
518#126—861no—
519#126—861no—
520#126—861no—
521#126—861no—
522#126—861no—
523#125—431no—
524#125—431no—
525#125—431no—
526#125—861no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125C22×D4311yescharacteristic
533#124—431no—
534#124C22×D4311yescharacteristic
535#123—21no—
536#123—861no—
537#123—861no—
538#123—861no—
539#123—861no—
540#123—861no—
541#123—861no—
542#123—861no—
543C22⋊Q8—431no—
544C22⋊Q8—431no—
545C22⋊Q8—431no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8C4×D4311yescharacteristic
549#121—431no—
550#121—431no—
551#121—431no—
552#121—861no—
553#121—861no—
554#121—861no—
555#121—861no—
556#121—861no—
557#121—861no—
558#121—861no—
559#121—861no—
560#121—861no—
561#121—861no—
562#121—861no—
563#121—861no—
564#121C4×D4311yescharacteristic
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8C4×D4311yescharacteristic
571C4×D4—21no—
572C4×D4—431no—
573C4×D4—431no—
574C4×D4—431no—
575C4×D4—431no—
576C4×D4—431no—
577C4×D4—431no—
578C4×D4—431no—
579C4×D4—431no—
580C4×D4—431no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4—861no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4C4×D4311yescharacteristic
591#117—21no—
592#117—431no—
593#117—431no—
594#117—431no—
595#117—861no—
596#117—861no—
597#117—861no—
598#117—861no—
599#117—861no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—861no—
606C2×C42—431no—
607C2×C42—431no—
608C2×C42C22×D4311yescharacteristic
609C4⋊C8—861no—
610C4⋊C8—861no—
611C4⋊C8—861no—
612C4⋊C8—861no—
613C4⋊C8—861no—
614C4⋊C8—861no—
615C22⋊C8—861no—
616C22⋊C8—861no—
617C22⋊C8—861no—
618C22⋊C8—861no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621#97—21no—
622#97—431no—
623#97—431no—
624#97—431no—
625#97—431no—
626#97—861no—
627#97C22×D4311yescharacteristic
628#97C22×D4311yescharacteristic
629#97C22×D4311yescharacteristic
630#97C22×D4311yescharacteristic
631C4×C8—21no—
632C4×C8—861no—
633C4×C8—861no—
634C4×C8—861no—
635#41—1722no—
636#41—1722no—
637#41—1722no—
638C2×Q8—431no—
639C2×Q8—431no—
640C2×Q8C2×C4×D4311yescharacteristic
641C2×D4—21no—
642C2×D4—431no—
643C2×D4—431no—
644C2×D4—431no—
645C2×D4—431no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—861no—
652C2×D4—861no—
653C2×D4C2×C4×D4311yescharacteristic
654C22×C4—21no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4C2×C4×D4311yescharacteristic
669C22×C4D4×D4311yescharacteristic
670C22×C4D4×D4311yescharacteristic
671M16—42no—
672M16—1722no—
673M16—1722no—
674M16—1722no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—861no—
684C2×C8—1722no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—431no—
690C4⋊C4—431no—
691C4⋊C4—431no—
692C4⋊C4—431no—
693C4⋊C4—431no—
694C4⋊C4—431no—
695C4⋊C4—431no—
696C4⋊C4—431no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4C2×C4×D4311yescharacteristic
714C4⋊C4C2×C4×D4311yescharacteristic
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—431no—
721C22⋊C4—431no—
722C22⋊C4—431no—
723C22⋊C4—431no—
724C22⋊C4—431no—
725C22⋊C4—431no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C42—21no—
738C42—431no—
739C42—431no—
740C42—431no—
741C42—431no—
742C42—431no—
743C42—431no—
744C42—861no—
745C42—861no—
746C42—861no—
747C42C2×C4×D4311yescharacteristic
748C42D4×D4311yescharacteristic
749C42D4×D4311yescharacteristic
750C42C23×D4311yescharacteristic
751C23—21no—
752C23—431no—
753C23—431no—
754C23—861no—
755C23C22⋊C4×D4311yescharacteristic
756Q8—41no—
757Q8—862no—
758Q8—1721no—
759D4—41no—
760D4—81no—
761D4—862no—
762D4—3441no—
763D4—3441no—
764D4—3441no—
765D4—3441no—
766D4—3441no—
767D4—1721no—
768D4—1721no—
769D4—1722no—
770D4—1721no—
771D4—1722no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—81no—
779C2×C4—431no—
780C2×C4—431no—
781C2×C4—431no—
782C2×C4—431no—
783C2×C4—431no—
784C2×C4—431no—
785C2×C4—862no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—3441no—
790C2×C4—3441no—
791C2×C4—3441no—
792C2×C4—3441no—
793C2×C4—3441no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1722no—
800C2×C4—1722no—
801C2×C4C22⋊C4×D4311yescharacteristic
802C2×C4C22⋊C4×D4311yescharacteristic
803C2×C4C22⋊C4×D4311yescharacteristic
804C2×C4C22×C4×D4311yescharacteristic
805C2×C4C2×D4×D4311yescharacteristic
806C2×C4C2×D4×D4311yescharacteristic
807C8—22no—
808C8—22no—
809C8—41no—
810C8—41no—
811C8—1721no—
812C8—1721no—
813C8—1721no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—861no—
822C22—861no—
823C22—861no—
824C22—861no—
825C22—861no—
826C22—861no—
827C22—1721no—
828C22—1721no—
829C22—1721no—
830C22C2×C22⋊C4×D4311yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—432no—
841C4—861no—
842C4—861no—
843C4—861no—
844C4—861no—
845C4—861no—
846C4—1721no—
847C4—1721no—
848C4—1721no—
849C2—41no—
850C2—81no—
851C2—3441no—
852C2—1721no—
853C2—1721no—
854C2#413×D4311yescharacteristic
855C2#1914313911yescharacteristic
856C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1524C2
socleC22×C43C22×C22⋊C4
prime radical#19148510C2
cosocleC42×C43C24
hypercenter#1524D43
hypocenterC43#17687
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1524

Complements

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

NH ≅ G/Ntype
2. #19143613C2semidirect
3. #19143606C2semidirect
4. #19133228C2semidirect
5. #19133226C2semidirect
6. #19133223C2semidirect
7. #19133214C2semidirect
8. #19133213C2semidirect
9. #19133201C2semidirect
10. #19133200C2semidirect
11. #19133195C2semidirect
12. #19133195C2semidirect
13. #19133185C2semidirect
14. #19133180C2semidirect
15. C43×#1524C2semidirect
435. #1524D43semidirect
503. C43#17687semidirect

Maximal subgroups

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

subgroupindex
#191485102
#191436132
#191436062
#191332282
#191332262
#191332232
#191332142
#191332132
#191332012
#191332002
#191331952
#191331852
#191331802
C43×#15242
#1768743