Finite Group Databasebeta

← #25064852

Subgroups — #25064852

Order 11008.

898 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#19148517C211yesmaximal, characteristic
2#19143609C211yesmaximal, characteristic, complemented
3#19133227C211yesmaximal, characteristic, complemented
4#19133224C211yesmaximal, characteristic, complemented
5#19133221C211yesmaximal, characteristic, complemented
6#19133216C211yesmaximal, characteristic, complemented
7#19133213C211yesmaximal, characteristic, complemented
8#19133207C211yesmaximal, characteristic, complemented
9#19133205C211yesmaximal, characteristic, complemented
10#19133203C211yesmaximal, characteristic, complemented
11#19133200C211yesmaximal, characteristic, complemented
12#19133184C211yesmaximal, characteristic, complemented
13#19133181C211yesmaximal, characteristic, complemented
14C2×#14582640C211yesmaximal, characteristic, complemented
15C43×#2970C211yesmaximal, characteristic, complemented
16#14583599—21no—
17#14583599—21no—
18#14583598—21no—
19#14583598—21no—
20#14583598—21no—
21#14583598—21no—
22#14583590—21no—
23#14583590—21no—
24#14583511C411yescharacteristic
25#14583511C411yescharacteristic
26#14583504C411yescharacteristic
27#14583504C411yescharacteristic
28#14583477C411yescharacteristic
29#14583477C411yescharacteristic
30#14583449C2211yescharacteristic
31#14583433C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583433C2211yescharacteristic
34#14583433C2211yescharacteristic
35C2×#13063317C2211yescharacteristic
36#14583379C411yescharacteristic
37#14583379C411yescharacteristic
38#14583030—21no—
39#14582971—21no—
40#14582971—21no—
41D4×C43⋊C8—21no—
42#14582956C2211yescharacteristic
43#14582956C2211yescharacteristic
44#14582956C2211yescharacteristic
45C4×#10621877C2211yescharacteristic
46C2×#13063236C2211yescharacteristic
47C2×#13063236C2211yescharacteristic
48#14582640C2211yescharacteristic
49#14582640C2211yescharacteristic
50#14582640C2211yescharacteristic
51#14582640C2211yescharacteristic
52#14582640C2211yescharacteristic
53#14582640C2211yescharacteristic
54#14582640C2211yescharacteristic
55#14582640C2211yescharacteristic
56#14582638C2211yescharacteristic
57#14582638C2211yescharacteristic
58#14582638C2211yescharacteristic
59#14582638C2211yescharacteristic
60#14582638C2211yescharacteristic
61#14582638C2211yescharacteristic
62#14582638C2211yescharacteristic
63#14582638C2211yescharacteristic
64C4×#41×C43C2211yescharacteristic
65C43×#446—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#432C2211yescharacteristic
70C43×#432C2211yescharacteristic
71C43×#432C2211yescharacteristic
72C4×M16×C43C2211yescharacteristic
73C2×#97×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C2×#10621877—21no—
78C22×C43⋊C8—21no—
79C22×C43⋊C8—21no—
80#13063325C2×C411yescharacteristic
81#13063322C2×C411yescharacteristic
82#13063319—21no—
83#13063319—21no—
84#13063319—21no—
85#13063319—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063317—21no—
91#13063317—21no—
92#13063317C2×C411yescharacteristic
93#13063317C2×C411yescharacteristic
94#13063317C2311yescharacteristic
95#13063317C2311yescharacteristic
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063313C2311yescharacteristic
101#13063313C2311yescharacteristic
102#13063310—21no—
103#13063310—21no—
104#13063310—21no—
105#13063310—21no—
106#13063308—21no—
107#13063308—21no—
108#13063308—21no—
109#13063308—21no—
110#13063304C2×C411yescharacteristic
111#13063304C2×C411yescharacteristic
112#13063304C2×C411yescharacteristic
113#13063304C2×C411yescharacteristic
114#13063301—21no—
115#13063301—21no—
116#13063299—21no—
117#13063299—21no—
118#13063299C2×C411yescharacteristic
119#13063299C2×C411yescharacteristic
120#13063299C2×C411yescharacteristic
121#13063299C2×C411yescharacteristic
122#13063298—21no—
123#13063298—21no—
124#13063298—21no—
125#13063298—21no—
126#13063297—21no—
127#13063297—21no—
128#13063297—21no—
129#13063297—21no—
130#13063296—21no—
131#13063296—21no—
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86C2×C411yescharacteristic
134C4×Dic86C2×C411yescharacteristic
135C4×Dic86C2×C411yescharacteristic
136C4×D172—21no—
137C4×D172—21no—
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141C4×D172C2×C411yescharacteristic
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146(C22⋊D43)⋊C4—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063283—21no—
151#13063283—21no—
152#13063282—21no—
153#13063282—21no—
154#13063282—21no—
155#13063282—21no—
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×C4⋊Dic43C2×C411yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C4⋊C4×D43—21no—
161C4⋊C4×D43—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)—21no—
168#13063236—21no—
169#13063236—21no—
170#13063236C2311yescharacteristic
171#13063236C2311yescharacteristic
172#13063236C2311yescharacteristic
173#13063236C2311yescharacteristic
174C4×C43⋊C8—21no—
175C2×#41×C43C2×C411yescharacteristic
176C2×M16×C43—21no—
177C22×C8×C43—21no—
178C22×C8×C43—21no—
179C4×Q8×C43D411yescharacteristic
180C4×Q8×C43D411yescharacteristic
181C4×D4×C43D411yescharacteristic
182C4×D4×C43D411yescharacteristic
183C4×D4×C43D411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187#117×C43C2×C411yescharacteristic
188#117×C43C2×C411yescharacteristic
189#117×C43C2×C411yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199#97×C43—21no—
200#97×C43—21no—
201#97×C43C2311yescharacteristic
202#97×C43C2311yescharacteristic
203#97×C43C2311yescharacteristic
204#97×C43C2311yescharacteristic
205C4×C8×C43—21no—
206#41×C43—42no—
207C2×Q8×C43C22⋊C411yescharacteristic
208C2×D4×C43C22⋊C411yescharacteristic
209C2×D4×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228#10621898—42no—
229#10621898—42no—
230C2×D172—21no—
231C2×D172—21no—
232C2×D172C22×C411yescharacteristic
233C2×D172C22×C411yescharacteristic
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
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—
248C2×C8×C43—42no—
249C4⋊C4×C43C22⋊C411yescharacteristic
250C4⋊C4×C43C22⋊C411yescharacteristic
251C4⋊C4×C43C22⋊C411yescharacteristic
252C4⋊C4×C43C22⋊C411yescharacteristic
253C4⋊C4×C43C22⋊C411yescharacteristic
254C4⋊C4×C43C22⋊C411yescharacteristic
255C22⋊C4×C43C22⋊C411yescharacteristic
256C22⋊C4×C43C22⋊C411yescharacteristic
257C22⋊C4×C43C22⋊C411yescharacteristic
258C22⋊C4×C43C22⋊C411yescharacteristic
259C22⋊C4×C43C22⋊C411yescharacteristic
260C22⋊C4×C43C22⋊C411yescharacteristic
261C42×C43C22×C411yescharacteristic
262C42×C43C22×C411yescharacteristic
263C42×C43C22×C411yescharacteristic
264C42×C43C2×D411yescharacteristic
265C42×C43C2×D411yescharacteristic
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2×D411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2411yescharacteristic
271C22⋊Dic43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43C22×C411yescharacteristic
292C4⋊Dic43C22×C411yescharacteristic
293C4⋊Dic43C22×C411yescharacteristic
294C4⋊Dic43C22×C411yescharacteristic
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315#10621877—42no—
316C2×C43⋊C8—21no—
317C2×C43⋊C8—21no—
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C2×C43⋊C8—42no—
321C2×C43⋊C8—42no—
322C23×C43C2×C22⋊C411yescharacteristic
323C23×C43C2×C22⋊C411yescharacteristic
324C23×C43C2×C22⋊C411yescharacteristic
325C22×D43—21no—
326C22×D43—21no—
327Q8×C43—41no—
328D4×C43—22no—
329D4×C43—22no—
330D4×C43—41no—
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×C43—41no—
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C2×C22⋊C411yescharacteristic
348C2×C4×C43C2×C22⋊C411yescharacteristic
349C2×C4×C43C23×C411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C22⋊D43—42no—
353C22⋊D43—42no—
354C22⋊D43—81no—
355C22⋊D43—81no—
356C22⋊D43—81no—
357C22⋊D43—81no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—81no—
365C2×Dic43—81no—
366D172—41no—
367D172—41no—
368D172—81no—
369D172—81no—
370C4×D43—42no—
371C4×D43—42no—
372C4×D43—81no—
373C4×D43—81no—
374C4×D43—81no—
375C4×D43—81no—
376Dic86—41no—
377Dic86—41no—
378C8×C43—22no—
379C8×C43—41no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385C43⋊C8—41no—
386#17690—431nomaximal, Sylow
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—21no—
394C22×C43—21no—
395C22×C43#41312yes—
396C22×C43C22×C22⋊C411yescharacteristic
397C2×D43—41no—
398C2×D43—41no—
399C2×D43—41no—
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—21no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415Dic43—41no—
416Dic43—41no—
417Dic43—41no—
418Dic43—41no—
419Dic43—41no—
420Dic43—41no—
421#3512—431no—
422#2970—431no—
423#2970D4311yescharacteristic, complemented
424#1535—431no—
425#1535—431no—
426#1534—431no—
427#1532—431no—
428#1532—431no—
429#1530—431no—
430#1530—431no—
431#1529—431no—
432#1529—431no—
433#1524—431no—
434#1524—431no—
435C2×#330—431no—
436C2×C43—22no—
437C2×C43—41no—
438C2×C43—41no—
439C2×C43C2×#41311yescharacteristic
440C2×C43#290111yescharacteristic
441C2×C43#290111yescharacteristic
442D43—81no—
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#529—431no—
463C2×#125—431no—
464#520—431no—
465#520—431no—
466C4×#41C2×D4311yescharacteristic
467#446—21no—
468#446—861no—
469#435—21no—
470#435—21no—
471#435—861no—
472#435—861no—
473C8×D4—21no—
474C8×D4—861no—
475#432—431no—
476#432—431no—
477#432—431no—
478#432C2×D4311yescharacteristic
479#432C2×D4311yescharacteristic
480#432C2×D4311yescharacteristic
481C4×M16—431no—
482C4×M16C2×D4311yescharacteristic
483C2×#97—431no—
484C2×#97—431no—
485C2×#97C2×D4311yescharacteristic
486C2×#97C2×D4311yescharacteristic
487#330—431no—
488#330—431no—
489#330—431no—
490#330—431no—
491#330—431no—
492#330—431no—
493#330—431no—
494#330—431no—
495#329—431no—
496#329—431no—
497#329—431no—
498#329—431no—
499#329—431no—
500#329—431no—
501#329—431no—
502#329—431no—
503C43#1769011yescharacteristic, complemented, Sylow
504C2×#41—431no—
505C2×#41—431no—
506C2×#41C4×D4311yescharacteristic
507C2×M16—21no—
508C2×M16—861no—
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—861no—
512C22×C8—861no—
513C4⋊Q8—431no—
514#127—431no—
515#126—861no—
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—431no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125—861no—
533#124—431no—
534#124—431no—
535#123—861no—
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—431no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549#121—431no—
550#121—431no—
551#121—431no—
552#121—431no—
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#121—861no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8D17211yescharacteristic
570C4×Q8C22⋊D4311yescharacteristic
571C4×D4—431no—
572C4×D4—431no—
573C4×D4—431no—
574C4×D4—431no—
575C4×D4—861no—
576C4×D4—861no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4D17211yescharacteristic
586C4×D4D17211yescharacteristic
587C4×D4D17211yescharacteristic
588C4×D4C22⋊D4311yescharacteristic
589C4×D4C22⋊D4311yescharacteristic
590C4×D4C22⋊D4311yescharacteristic
591#117—861no—
592#117—861no—
593#117—861no—
594#117—861no—
595#117—861no—
596#117—861no—
597#117C4×D4311yescharacteristic
598#117C4×D4311yescharacteristic
599#117C4×D4311yescharacteristic
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×C42C22×D4311yescharacteristic
607C2×C42C22×D4311yescharacteristic
608C2×C42C22×D4311yescharacteristic
609C4⋊C8—21no—
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—861no—
613C4⋊C8—861no—
614C4⋊C8—861no—
615C22⋊C8—21no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—861no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621#97—21no—
622#97—21no—
623#97—431no—
624#97—431no—
625#97—431no—
626#97—431no—
627#97—861no—
628#97—861no—
629#97C22×D4311yescharacteristic
630#97C22×D4311yescharacteristic
631#97C22×D4311yescharacteristic
632#97C22×D4311yescharacteristic
633C4×C8—21no—
634C4×C8—861no—
635#41—42no—
636#41—1722no—
637#41—1722no—
638C2×Q8—431no—
639C2×Q8—431no—
640C2×Q8(C2×D43)⋊C411yescharacteristic
641C2×D4—431no—
642C2×D4—431no—
643C2×D4—861no—
644C2×D4—861no—
645C2×D4—861no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4(C2×D43)⋊C411yescharacteristic
652C2×D4(C2×D43)⋊C411yescharacteristic
653C2×D4(C2×D43)⋊C411yescharacteristic
654C22×C4—861no—
655C22×C4—861no—
656C22×C4—861no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4C2×C4×D4311yescharacteristic
663C22×C4C2×C4×D4311yescharacteristic
664C22×C4C2×C4×D4311yescharacteristic
665C22×C4C2×D17211yescharacteristic
666C22×C4C2×D17211yescharacteristic
667C22×C4C2×D17211yescharacteristic
668C22×C4C2×C22⋊D4311yescharacteristic
669C22×C4C2×C22⋊D4311yescharacteristic
670C22×C4C2×C22⋊D4311yescharacteristic
671M16—42no—
672M16—1722no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—42no—
678C2×C8—42no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—1722no—
684C2×C8—1722no—
685C4⋊C4—431no—
686C4⋊C4—431no—
687C4⋊C4—431no—
688C4⋊C4—431no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
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(C2×D43)⋊C411yescharacteristic
710C4⋊C4(C2×D43)⋊C411yescharacteristic
711C4⋊C4(C2×D43)⋊C411yescharacteristic
712C4⋊C4(C2×D43)⋊C411yescharacteristic
713C4⋊C4(C2×D43)⋊C411yescharacteristic
714C4⋊C4(C2×D43)⋊C411yescharacteristic
715C22⋊C4—861no—
716C22⋊C4—861no—
717C22⋊C4—861no—
718C22⋊C4—861no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C22⋊C4(C2×D43)⋊C411yescharacteristic
732C22⋊C4(C2×D43)⋊C411yescharacteristic
733C22⋊C4(C2×D43)⋊C411yescharacteristic
734C22⋊C4(C2×D43)⋊C411yescharacteristic
735C22⋊C4(C2×D43)⋊C411yescharacteristic
736C22⋊C4(C2×D43)⋊C411yescharacteristic
737C42—861no—
738C42—861no—
739C42—861no—
740C42—861no—
741C42C2×C4×D4311yescharacteristic
742C42C2×C4×D4311yescharacteristic
743C42C2×C4×D4311yescharacteristic
744C42C2×D17211yescharacteristic
745C42C2×D17211yescharacteristic
746C42C2×D17211yescharacteristic
747C42C2×C22⋊D4311yescharacteristic
748C42C2×C22⋊D4311yescharacteristic
749C42C2×C22⋊D4311yescharacteristic
750C42C23×D4311yescharacteristic
751C23—861no—
752C23—861no—
753C23C2×(C2×D43)⋊C411yescharacteristic
754C23C2×(C2×D43)⋊C411yescharacteristic
755C23C2×(C2×D43)⋊C411yescharacteristic
756Q8—41no—
757Q8—1721no—
758Q8—1721no—
759D4—22no—
760D4—22no—
761D4—41no—
762D4—3441no—
763D4—3441no—
764D4—3441no—
765D4—3441no—
766D4—3441no—
767D4—3441no—
768D4—1721no—
769D4—1721no—
770D4—1722no—
771D4—1722no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—3441no—
788C2×C4—3441no—
789C2×C4—3441no—
790C2×C4—3441no—
791C2×C4—3441no—
792C2×C4—3441no—
793C2×C4—1722no—
794C2×C4—1722no—
795C2×C4C2×(C2×D43)⋊C411yescharacteristic
796C2×C4C2×(C2×D43)⋊C411yescharacteristic
797C2×C4C2×(C2×D43)⋊C411yescharacteristic
798C2×C4C2×(C2×D43)⋊C411yescharacteristic
799C2×C4C2×(C2×D43)⋊C411yescharacteristic
800C2×C4C2×(C2×D43)⋊C411yescharacteristic
801C2×C4C2×(C2×D43)⋊C411yescharacteristic
802C2×C4C2×(C2×D43)⋊C411yescharacteristic
803C2×C4C2×(C2×D43)⋊C411yescharacteristic
804C2×C4C22×C4×D4311yescharacteristic
805C2×C4C22×C22⋊D4311yescharacteristic
806C2×C4C22×D17211yescharacteristic
807C8—22no—
808C8—41no—
809C8—41no—
810C8—41no—
811C8—862no—
812C8—1721no—
813C8—1721no—
814C8—1721no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—1721no—
824C22—1721no—
825C22—1721no—
826C22—1721no—
827C22—1721no—
828C22—1721no—
829C22#1458288112yes—
830C22C22×(C2×D43)⋊C411yescharacteristic
831C4—21no—
832C4—21no—
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—1721no—
844C4—1721no—
845C4—1721no—
846C4—1721no—
847C4—1721no—
848C4—1721no—
849C2—22no—
850C2—41no—
851C2—41no—
852C2—3441no—
853C2—3441no—
854C2C2×#1458288111yescharacteristic
855C2#1914314011yescharacteristic
856C2#1914314311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2970C2
socleC22×C43C22×C22⋊C4
prime radical#19148517C2
cosocleC42×C43C24
hypercenter#2970D43
hypocenterC43#17690
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #19143609C2semidirect
3. #19133227C2semidirect
4. #19133224C2semidirect
5. #19133221C2semidirect
6. #19133216C2semidirect
7. #19133213C2semidirect
8. #19133207C2semidirect
9. #19133205C2semidirect
10. #19133203C2semidirect
11. #19133200C2semidirect
12. #19133184C2semidirect
13. #19133181C2semidirect
14. C2×#14582640C2semidirect
15. C43×#2970C2semidirect
423. #2970D43semidirect
503. C43#17690semidirect

Maximal subgroups

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

subgroupindex
#191485172
#191436092
#191332272
#191332242
#191332212
#191332162
#191332132
#191332072
#191332052
#191332032
#191332002
#191331842
#191331812
C2×#145826402
C43×#29702
#1769043