Finite Group Databasebeta

← #25064258

Subgroups — #25064258

Order 11008.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148347C211yesmaximal, characteristic
2#19143253C211yesmaximal, characteristic, complemented
3#19133170C211yesmaximal, characteristic, complemented
4#19133158C211yesmaximal, characteristic, complemented
5#19133149C211yesmaximal, characteristic
6#19133145C211yesmaximal, characteristic, complemented
7#19133131C211yesmaximal, characteristic, complemented
8#19133127C211yesmaximal, characteristic, complemented
9#19133118C211yesmaximal, characteristic, complemented
10#19133106C211yesmaximal, characteristic, complemented
11#19133097C211yesmaximal, characteristic
12#19133093C211yesmaximal, characteristic, complemented
13#19133079C211yesmaximal, characteristic, complemented
14C2×#14582635C211yesmaximal, characteristic, complemented
15C43×#2343C211yesmaximal, characteristic, complemented
16#14583617—21no—
17#14583604—21no—
18#14583588—21no—
19#14583584—21no—
20#14583582—21no—
21#14583582—21no—
22#14583575—21no—
23#14583575—21no—
24#14583527C411yescharacteristic, complemented
25#14583520C411yescharacteristic, complemented
26#14583520C411yescharacteristic, complemented
27#14583511C411yescharacteristic, complemented
28#14583511C411yescharacteristic, complemented
29#14583475C411yescharacteristic, complemented
30#14583456C2211yescharacteristic
31#14583456C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583433C2211yescharacteristic
34#14583410C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36#14583379C411yescharacteristic, complemented
37#14583376C411yescharacteristic, complemented
38#14582960—21no—
39#14582960—21no—
40#14582956C2211yescharacteristic
41#14582956C2211yescharacteristic
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582926—21no—
45#14582863C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47#14582855—21no—
48#14582635C2211yescharacteristic
49#14582635C2211yescharacteristic
50#14582635C2211yescharacteristic
51#14582635C2211yescharacteristic
52#14582635C2211yescharacteristic
53#14582635C2211yescharacteristic
54#14582635C2211yescharacteristic
55#14582635C2211yescharacteristic
56#14582635C2211yescharacteristic
57#14582635C2211yescharacteristic
58#14582635C2211yescharacteristic
59#14582635C2211yescharacteristic
60#14582632C2211yescharacteristic
61#14582632C2211yescharacteristic
62#14582632C2211yescharacteristic
63#14582632C2211yescharacteristic
64C2×#117×C43C2211yescharacteristic
65C43×#387—21no—
66C43×#387—21no—
67C43×#385—21no—
68C43×#383C2211yescharacteristic
69C43×#382C2211yescharacteristic
70C43×#381C2211yescharacteristic
71C4×C4⋊C4×C43C2211yescharacteristic
72C4×C22⋊C4×C43—21no—
73C43×#376C2211yescharacteristic
74C2×#95×C43C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C2×#10621877—21no—
78C22×C43⋊C8—21no—
79#13063325C2×C411yescharacteristic, complemented
80#13063325C2×C411yescharacteristic, complemented
81#13063325C2×C411yescharacteristic, complemented
82#13063325C2×C411yescharacteristic, complemented
83#13063324—21no—
84#13063320—21no—
85#13063320—21no—
86#13063319—21no—
87#13063319—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063317—21no—
93#13063317—21no—
94#13063317C2×C411yescharacteristic, complemented
95#13063317C2×C411yescharacteristic, complemented
96#13063316—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063315—21no—
101#13063313C2×C411yescharacteristic, complemented
102#13063313C2×C411yescharacteristic, complemented
103#13063311—21no—
104#13063311—21no—
105#13063309—21no—
106#13063309—21no—
107#13063308—21no—
108#13063308—21no—
109#13063308—21no—
110#13063307—21no—
111#13063307—21no—
112#13063305—21no—
113#13063305—21no—
114#13063304—21no—
115#13063304—21no—
116#13063304—21no—
117#13063304—21no—
118#13063304C2×C411yescharacteristic
119#13063304C2×C411yescharacteristic
120#13063304C2×C411yescharacteristic
121#13063304C2311yescharacteristic
122#13063304C2311yescharacteristic
123#13063304C2311yescharacteristic
124#13063303—21no—
125#13063303—21no—
126#13063302—21no—
127#13063302—21no—
128#13063299C2×C411yescharacteristic
129#13063299C2311yescharacteristic
130#13063294—21no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86C2×C411yescharacteristic, complemented
134C4×Dic86C2×C411yescharacteristic, complemented
135C4×Dic86C2×C411yescharacteristic, complemented
136C4×Dic86C2×C411yescharacteristic, complemented
137C4×Dic86C2×C411yescharacteristic, complemented
138C4×Dic86C2×C411yescharacteristic, complemented
139#13063290—21no—
140#13063290—21no—
141C4×D172C2×C411yescharacteristic, complemented
142C4×D172C2×C411yescharacteristic, complemented
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149#13063284—21no—
150#13063284—21no—
151#13063284C2×C411yescharacteristic
152#13063283—21no—
153#13063282—21no—
154#13063282—21no—
155#13063281—21no—
156#13063281—21no—
157C2×C4⋊Dic43C2×C411yescharacteristic
158C2×Dic43⋊C4—21no—
159C4⋊C4×D43—21no—
160C2×C22⋊Dic43—21no—
161C4⋊(C43⋊C8)—21no—
162C4⋊(C43⋊C8)—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)C2311yescharacteristic
168C22⋊(C43⋊C8)C2311yescharacteristic
169C22⋊(C43⋊C8)C2311yescharacteristic
170C22⋊(C43⋊C8)C2311yescharacteristic
171#13063236—21no—
172#13063236—21no—
173C4×C43⋊C8—21no—
174C4×C43⋊C8—21no—
175C23×C4×C43—21no—
176C23×C4×C43C2311yescharacteristic
177#117×C43C2×C411yescharacteristic
178#117×C43C2×C411yescharacteristic
179#117×C43C2×C411yescharacteristic
180#117×C43C2×C411yescharacteristic
181#117×C43D411yescharacteristic
182#117×C43D411yescharacteristic
183#117×C43D411yescharacteristic
184#117×C43D411yescharacteristic
185C2×C4⋊C4×C43—21no—
186C2×C4⋊C4×C43—21no—
187C2×C4⋊C4×C43D411yescharacteristic
188C2×C4⋊C4×C43D411yescharacteristic
189C2×C22⋊C4×C43—21no—
190C2×C22⋊C4×C43D411yescharacteristic
191C2×C22⋊C4×C43D411yescharacteristic
192C2×C42×C43—21no—
193C2×C42×C43—21no—
194C2×C42×C43C2311yescharacteristic
195C2×C42×C43C2311yescharacteristic
196#95×C43—21no—
197#95×C43—21no—
198#95×C43—21no—
199#95×C43—21no—
200#95×C43—21no—
201#95×C43—21no—
202#95×C43C2311yescharacteristic
203#95×C43C2311yescharacteristic
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—42no—
212C22×C4×C43—42no—
213C22×C4×C43—42no—
214C22×C4×C43—81no—
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230#10621898—42no—
231C2×D172C22×C411yescharacteristic
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—42no—
239C2×Dic86C22×C411yescharacteristic
240C2×Dic86C22×C411yescharacteristic
241C2×Dic86C22×C411yescharacteristic
242C4⋊C4×C43—42no—
243C4⋊C4×C43—81no—
244C4⋊C4×C43C22⋊C411yescharacteristic
245C4⋊C4×C43C22⋊C411yescharacteristic
246C4⋊C4×C43C22⋊C411yescharacteristic
247C4⋊C4×C43C22⋊C411yescharacteristic
248C4⋊C4×C43C22⋊C411yescharacteristic
249C4⋊C4×C43C22⋊C411yescharacteristic
250C4⋊C4×C43C22⋊C411yescharacteristic
251C4⋊C4×C43C22⋊C411yescharacteristic
252C22⋊C4×C43—42no—
253C22⋊C4×C43C22⋊C411yescharacteristic
254C22⋊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×C43—42no—
262C42×C43—81no—
263C42×C43C22×C411yescharacteristic
264C42×C43C22×C411yescharacteristic
265C42×C43C22×C411yescharacteristic
266C42×C43C22×C411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2×D411yescharacteristic
269C42×C43C2×D411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C22⋊Dic43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43—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—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292C4⋊Dic43—21no—
293C4⋊Dic43C22×C411yescharacteristic
294C4⋊Dic43C22×C411yescharacteristic
295C4⋊Dic43C22×C411yescharacteristic
296C4⋊Dic43C22×C411yescharacteristic
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—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320#10621877—42no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—42no—
326C23×C43—21no—
327C23×C43—21no—
328C23×C43—22no—
329C23×C43—41no—
330C23×C43C2×C22⋊C411yescharacteristic
331C23×C43C2×C22⋊C411yescharacteristic
332C23×C43C22×D411yescharacteristic
333C22×D43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—84no—
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C2×C22⋊C411yescharacteristic
362C2×C4×C43C2×C22⋊C411yescharacteristic
363C2×C4×C43C2×C22⋊C411yescharacteristic
364C2×C4×C43C2×C22⋊C411yescharacteristic
365C2×C4×C43C2×C22⋊C411yescharacteristic
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C23×C411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C22⋊D43—41no—
372C22⋊D43—41no—
373C22⋊D43—42no—
374C22⋊D43—81no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—21no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—42no—
383C2×Dic43—81no—
384D172—41no—
385C4×D43—42no—
386C4×D43—81no—
387C4×D43—81no—
388Dic86—42no—
389Dic86—41no—
390Dic86—41no—
391Dic86—41no—
392Dic86—81no—
393Dic86—81no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398#17609—431nomaximal, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—42no—
407C22×C43—42no—
408C22×C43#41012yes—
409C22×C43C22×C22⋊C411yescharacteristic
410C22×C43#57711yescharacteristic
411C22×C43#57811yescharacteristic
412C2×D43—41no—
413C2×D43—41no—
414C2×D43—41no—
415C4×C43—21no—
416C4×C43—21no—
417C4×C43—21no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—21no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—42no—
428C4×C43—81no—
429C4×C43—81no—
430C4×C43—81no—
431Dic43—41no—
432Dic43—41no—
433Dic43—41no—
434Dic43—41no—
435Dic43—41no—
436Dic43—41no—
437Dic43—41no—
438#3495—431no—
439#2924—431no—
440#2343D4311yescharacteristic, complemented
441#1521—431no—
442#1518—431no—
443#1516—431no—
444#1515—431no—
445#1512—431no—
446#1511—431no—
447#1509—431no—
448#1506—431no—
449#1504—431no—
450#1503—431no—
451#1500—431no—
452C2×#328—431no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—22no—
456C2×C43—41no—
457C2×C43C2×#41011yescharacteristic
458C2×C43#289811yescharacteristic
459C2×C43#290111yescharacteristic
460D43—81no—
461#556—861no—
462#554—861no—
463#552—861no—
464#552—861no—
465#552—861no—
466#552—861no—
467#551—861no—
468#551—861no—
469#544—431no—
470#542—431no—
471#542—431no—
472#541—431no—
473#541—431no—
474#536—431no—
475#533—431no—
476#533—431no—
477#529—431no—
478#529—431no—
479#525—431no—
480C2×C22⋊Q8—431no—
481#520—431no—
482#519—431no—
483C2×#117C2×D4311yescharacteristic
484#433—861no—
485#433—861no—
486#432—431no—
487#432—431no—
488#431—431no—
489#431—431no—
490#424—861no—
491#407—431no—
492C2×C22⋊C8—431no—
493#405—861no—
494#387—21no—
495#387—21no—
496#385—21no—
497#383C2×D4311yescharacteristic
498#382C2×D4311yescharacteristic
499#381C2×D4311yescharacteristic
500C4×C4⋊C4C2×D4311yescharacteristic
501C4×C22⋊C4—21no—
502#376C2×D4311yescharacteristic
503C2×#95C2×D4311yescharacteristic
504#328—431no—
505#328—431no—
506#328—431no—
507#328—431no—
508#328—431no—
509#328—431no—
510#328—431no—
511#328—431no—
512#328—431no—
513#328—431no—
514#328—431no—
515#328—431no—
516#327—431no—
517#327—431no—
518#327—431no—
519#327—431no—
520C43#1760911yescharacteristic, complemented, Sylow
521C2×#41—431no—
522C22×Q8—431no—
523C23×C4—21no—
524C23×C4C22×D4311yescharacteristic
525C2×M16—861no—
526C22×C8—861no—
527C4⋊Q8—431no—
528C4⋊Q8—431no—
529C4⋊Q8—431no—
530C4⋊Q8—431no—
531C4⋊Q8—861no—
532#126—861no—
533#126—861no—
534#126—861no—
535#126—861no—
536#126—861no—
537#126—861no—
538#126—861no—
539#126—861no—
540#125—431no—
541#125—431no—
542#125—861no—
543#125—861no—
544#125—861no—
545#125—861no—
546#125—861no—
547#125—861no—
548#125—861no—
549#124—431no—
550#124—431no—
551#124—861no—
552#124—861no—
553#123—861no—
554#123—861no—
555#123—861no—
556#123—861no—
557#123—861no—
558#123—861no—
559#123—861no—
560C22⋊Q8—431no—
561C22⋊Q8—431no—
562C22⋊Q8—431no—
563C22⋊Q8—431no—
564C22⋊Q8—431no—
565C22⋊Q8—431no—
566C22⋊Q8—861no—
567C22⋊Q8—861no—
568C22⋊Q8—861no—
569C22⋊Q8—861no—
570C22⋊Q8—861no—
571C22⋊Q8—861no—
572C22⋊Q8—861no—
573C22⋊Q8—861no—
574C22⋊Q8—861no—
575C22⋊Q8—861no—
576#121—431no—
577#121—431no—
578#120—861no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—431no—
584C4×Q8—431no—
585C4×Q8—861no—
586C4×Q8—861no—
587C4×Q8—861no—
588C4×Q8—861no—
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597#117—431no—
598#117—861no—
599#117—861no—
600#117—861no—
601#117—861no—
602#117—861no—
603#117—861no—
604#117—861no—
605#117C4×D4311yescharacteristic
606#117C4×D4311yescharacteristic
607#117C4×D4311yescharacteristic
608#117C4×D4311yescharacteristic
609#117D17211yescharacteristic
610#117D17211yescharacteristic
611#117D17211yescharacteristic
612#117D17211yescharacteristic
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—431no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4C22⋊D4311yescharacteristic
619C2×C4⋊C4C22⋊D4311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—861no—
622C2×C22⋊C4C22⋊D4311yescharacteristic
623C2×C22⋊C4C22⋊D4311yescharacteristic
624C2×C42—21no—
625C2×C42—21no—
626C2×C42C22×D4311yescharacteristic
627C2×C42C22×D4311yescharacteristic
628C4⋊C8—861no—
629C4⋊C8—861no—
630C4⋊C8—861no—
631C4⋊C8—861no—
632C22⋊C8—431no—
633C22⋊C8—431no—
634C22⋊C8—431no—
635C22⋊C8—431no—
636C22⋊C8—861no—
637C22⋊C8—861no—
638#97—861no—
639#97—861no—
640C4×C8—861no—
641C4×C8—861no—
642#95—21no—
643#95—21no—
644#95—21no—
645#95—21no—
646#95—21no—
647#95—21no—
648#95C22×D4311yescharacteristic
649#95C22×D4311yescharacteristic
650#95C22×D4311yescharacteristic
651#95C22×D4311yescharacteristic
652C24C2×C22⋊D4311yescharacteristic
653#41—1722no—
654C2×Q8—431no—
655C2×Q8—431no—
656C2×Q8—431no—
657C2×Q8—861no—
658C2×Q8—861no—
659C2×Q8—861no—
660C2×Q8—1722no—
661C2×D4—431no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—81no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4C2×C4×D4311yescharacteristic
679C22×C4C2×C4×D4311yescharacteristic
680C22×C4C2×D17211yescharacteristic
681C22×C4C2×D17211yescharacteristic
682C22×C4C2×C22⋊D4311yescharacteristic
683C22×C4C2×C22⋊D4311yescharacteristic
684C22×C4C2×C22⋊D4311yescharacteristic
685C22×C4C2×C22⋊D4311yescharacteristic
686C22×C4C2×C22⋊D4311yescharacteristic
687C22×C4C23×D4311yescharacteristic
688M16—1722no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—1722no—
694C4⋊C4—42no—
695C4⋊C4—81no—
696C4⋊C4—431no—
697C4⋊C4—431no—
698C4⋊C4—431no—
699C4⋊C4—431no—
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⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4(C2×D43)⋊C411yescharacteristic
724C4⋊C4(C2×D43)⋊C411yescharacteristic
725C4⋊C4(C2×D43)⋊C411yescharacteristic
726C4⋊C4(C2×D43)⋊C411yescharacteristic
727C4⋊C4(C2×D43)⋊C411yescharacteristic
728C4⋊C4(C2×D43)⋊C411yescharacteristic
729C4⋊C4(C2×D43)⋊C411yescharacteristic
730C4⋊C4(C2×D43)⋊C411yescharacteristic
731C22⋊C4—42no—
732C22⋊C4—861no—
733C22⋊C4—861no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C22⋊C4—861no—
742C22⋊C4—861no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4(C2×D43)⋊C411yescharacteristic
748C22⋊C4(C2×D43)⋊C411yescharacteristic
749C22⋊C4(C2×D43)⋊C411yescharacteristic
750C22⋊C4(C2×D43)⋊C411yescharacteristic
751C22⋊C4(C2×D43)⋊C411yescharacteristic
752C22⋊C4(C2×D43)⋊C411yescharacteristic
753C22⋊C4(C2×D43)⋊C411yescharacteristic
754C22⋊C4(C2×D43)⋊C411yescharacteristic
755C42—42no—
756C42—81no—
757C42—861no—
758C42—861no—
759C42—861no—
760C42—861no—
761C42—861no—
762C42—861no—
763C42—861no—
764C42C2×C4×D4311yescharacteristic
765C42C2×C4×D4311yescharacteristic
766C42C2×C4×D4311yescharacteristic
767C42C2×C4×D4311yescharacteristic
768C42C2×D17211yescharacteristic
769C42C2×D17211yescharacteristic
770C42C2×D17211yescharacteristic
771C42C2×D17211yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—861no—
777C23C2×(C2×D43)⋊C411yescharacteristic
778C23C2×(C2×D43)⋊C411yescharacteristic
779C23C22×C22⋊D4311yescharacteristic
780Q8—3441no—
781Q8—3441no—
782Q8—1721no—
783Q8—1721no—
784Q8—1721no—
785Q8—1722no—
786D4—3441no—
787D4—1721no—
788D4—1722no—
789D4—1721no—
790D4—1721no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—84no—
816C2×C4—861no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—3441no—
824C2×C4—3441no—
825C2×C4—3441no—
826C2×C4—1722no—
827C2×C4—1722no—
828C2×C4C2×(C2×D43)⋊C411yescharacteristic
829C2×C4C2×(C2×D43)⋊C411yescharacteristic
830C2×C4C2×(C2×D43)⋊C411yescharacteristic
831C2×C4C2×(C2×D43)⋊C411yescharacteristic
832C2×C4C2×(C2×D43)⋊C411yescharacteristic
833C2×C4C2×(C2×D43)⋊C411yescharacteristic
834C2×C4C2×(C2×D43)⋊C411yescharacteristic
835C2×C4C2×(C2×D43)⋊C411yescharacteristic
836C2×C4C2×(C2×D43)⋊C411yescharacteristic
837C2×C4C2×(C2×D43)⋊C411yescharacteristic
838C2×C4C22×C4×D4311yescharacteristic
839C2×C4C22×D17211yescharacteristic
840C8—1721no—
841C8—1721no—
842C8—1721no—
843C8—1721no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—1721no—
854C22—1721no—
855C22—1721no—
856C22#1458287212yes—
857C22C22×(C2×D43)⋊C411yescharacteristic
858C22#1458371011yescharacteristic
859C22#1458371411yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—1721no—
877C4—1721no—
878C4—1721no—
879C4—1721no—
880C4—1721no—
881C4—1721no—
882C4—1721no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—3441no—
888C2C2×#1458287211yescharacteristic
889C2#1914312511yescharacteristic
890C2#1914314311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2343C2
socleC22×C43C22×C22⋊C4
prime radical#14583410C22
cosocleC22×C4×C43C24
hypercenter#2343D43
hypocenterC43#17609
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2343

Complements

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

NH ≅ G/Ntype
2. #19143253C2semidirect
3. #19133170C2semidirect
4. #19133158C2semidirect
6. #19133145C2semidirect
7. #19133131C2semidirect
8. #19133127C2semidirect
9. #19133118C2semidirect
10. #19133106C2semidirect
12. #19133093C2semidirect
13. #19133079C2semidirect
14. C2×#14582635C2semidirect
15. C43×#2343C2semidirect
24. #14583527C4semidirect
25. #14583520C4semidirect
26. #14583520C4semidirect
27. #14583511C4semidirect
28. #14583511C4semidirect
29. #14583475C4semidirect
36. #14583379C4semidirect
37. #14583376C4semidirect
79. #13063325C2×C4semidirect
80. #13063325C2×C4semidirect
81. #13063325C2×C4semidirect
82. #13063325C2×C4semidirect
94. #13063317C2×C4semidirect
95. #13063317C2×C4semidirect
101. #13063313C2×C4semidirect
102. #13063313C2×C4semidirect
133. C4×Dic86C2×C4semidirect
134. C4×Dic86C2×C4semidirect
135. C4×Dic86C2×C4semidirect
136. C4×Dic86C2×C4semidirect
137. C4×Dic86C2×C4semidirect
138. C4×Dic86C2×C4semidirect
141. C4×D172C2×C4semidirect
142. C4×D172C2×C4semidirect
440. #2343D43semidirect
520. C43#17609semidirect

Maximal subgroups

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

subgroupindex
#191483472
#191432532
#191331702
#191331582
#191331492
#191331452
#191331312
#191331272
#191331182
#191331062
#191330972
#191330932
#191330792
C2×#145826352
C43×#23432
#1760943