Finite Group Databasebeta

← #25063514

Subgroups — #25063514

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148159C211yesmaximal, characteristic
2#19143562C211yesmaximal, characteristic, complemented
3#19133067C211yesmaximal, characteristic, complemented
4#19133058C211yesmaximal, characteristic, complemented
5#19133053C211yesmaximal, characteristic, complemented
6#19133037C211yesmaximal, characteristic, complemented
7#19133032C211yesmaximal, characteristic, complemented
8#19133027C211yesmaximal, characteristic, complemented
9#19133015C211yesmaximal, characteristic, complemented
10#19133006C211yesmaximal, characteristic, complemented
11#19133001C211yesmaximal, characteristic, complemented
12#19132985C211yesmaximal, characteristic, complemented
13#19132980C211yesmaximal, characteristic, complemented
14#19132975C211yesmaximal, characteristic, complemented
15C43×#2925C211yesmaximal, characteristic, complemented
16#14583622C411yescharacteristic
17#14583614C411yescharacteristic
18#14583609C411yescharacteristic
19#14583599—21no—
20#14583590—21no—
21#14583589C411yescharacteristic
22#14583589C411yescharacteristic
23#14583578—21no—
24#14583578—21no—
25#14583554C411yescharacteristic
26#14583545C411yescharacteristic
27#14583545C411yescharacteristic
28#14583456C2211yescharacteristic
29#14583433C2211yescharacteristic
30#14583433C2211yescharacteristic
31#14583427—21no—
32#14583427—21no—
33#14583406—21no—
34C4×#10621898C2211yescharacteristic
35C4×#10621898C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37#117×D43—21no—
38#14583030—21no—
39#14582977—21no—
40#14582971—21no—
41#14582971—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic, complemented
44#14582952C2211yescharacteristic, complemented
45C4×#10621877C2211yescharacteristic
46C4×#10621877C2211yescharacteristic, complemented
47C2×C4×C43⋊C8C2211yescharacteristic, complemented
48#14582629C2211yescharacteristic, complemented
49#14582629C2211yescharacteristic, complemented
50#14582629C2211yescharacteristic, complemented
51#14582629C2211yescharacteristic, complemented
52#14582629C2211yescharacteristic, complemented
53#14582629C2211yescharacteristic, complemented
54#14582629C2211yescharacteristic, complemented
55#14582629C2211yescharacteristic, complemented
56#14582626C2211yescharacteristic
57#14582626C2211yescharacteristic
58#14582626C2211yescharacteristic
59#14582626C2211yescharacteristic
60#14582626C2211yescharacteristic
61#14582626C2211yescharacteristic
62#14582626C2211yescharacteristic
63#14582626C2211yescharacteristic
64C4×#41×C43C2211yescharacteristic
65C43×#433—21no—
66C43×#433—21no—
67C43×#432C2211yescharacteristic
68C43×#432C2211yescharacteristic, complemented
69C43×#431C2211yescharacteristic
70C43×#431C2211yescharacteristic, complemented
71C43×#423C2211yescharacteristic, complemented
72C2×C4⋊C8×C43C2211yescharacteristic, complemented
73C43×#408—21no—
74C43×#405—21no—
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×C4×D43—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C22×C43⋊C8—21no—
82#13063325C2×C411yescharacteristic
83#13063325C2×C411yescharacteristic
84#13063320—21no—
85#13063320—21no—
86#13063319—21no—
87#13063319—21no—
88#13063318—21no—
89#13063318—21no—
90#13063317—21no—
91#13063317C2×C411yescharacteristic
92#13063317C2×C411yescharacteristic
93#13063315—21no—
94#13063315—21no—
95#13063313C2×C411yescharacteristic
96#13063313C2×C411yescharacteristic
97#13063311—21no—
98#13063311—21no—
99#13063310—21no—
100#13063310—21no—
101#13063308—21no—
102#13063308—21no—
103#13063307—21no—
104#13063307—21no—
105#13063306—21no—
106#13063306—21no—
107#13063304—21no—
108#13063304C2×C411yescharacteristic
109#13063304C2×C411yescharacteristic
110#13063304C2×C411yescharacteristic
111#13063304C2×C411yescharacteristic
112#13063303—21no—
113#13063303—21no—
114#13063301—21no—
115#13063301—21no—
116#13063299C2×C411yescharacteristic
117#13063299C2×C411yescharacteristic
118#13063298—21no—
119#13063298—21no—
120#13063296—21no—
121#13063296—21no—
122#13063293—21no—
123#13063293—21no—
124C4×Dic86—21no—
125C4×Dic86C2×C411yescharacteristic
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86C2311yescharacteristic
128C4×Dic86C2311yescharacteristic
129C4×D172—21no—
130C4×D172—21no—
131C4×D172C2×C411yescharacteristic
132C4×D172C2×C411yescharacteristic
133C4×D172C2×C411yescharacteristic
134C4×D172C2×C411yescharacteristic
135C4×D172C2311yescharacteristic
136C4×D172C2311yescharacteristic
137C4×C22⋊D43—21no—
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143#13063284—21no—
144#13063284C2×C411yescharacteristic
145#13063284C2×C411yescharacteristic
146#13063283—21no—
147#13063283—21no—
148#13063282—21no—
149#13063282—21no—
150#13063282—21no—
151#13063282—21no—
152#13063281—21no—
153#13063281—21no—
154C2×C4⋊Dic43C2×C411yescharacteristic
155C4⋊C4×D43—21no—
156C4⋊C4×D43—21no—
157C2×(C2×D43)⋊C4—21no—
158C22⋊C4×D43—21no—
159C22⋊C4×D43—21no—
160C42×D43—21no—
161C42×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—
170C4×C43⋊C8—21no—
171C4×C43⋊C8C2311yescharacteristic
172C4×C43⋊C8C2311yescharacteristic
173C4×C43⋊C8C2311yescharacteristic
174C4×C43⋊C8C2311yescharacteristic
175C2×#41×C43D411yescharacteristic
176C2×M16×C43—21no—
177C22×C8×C43—21no—
178C4×Q8×C43C2×C411yescharacteristic
179C4×Q8×C43D411yescharacteristic
180C4×D4×C43C2×C411yescharacteristic
181C4×D4×C43C2×C411yescharacteristic
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43D411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186#117×C43D411yescharacteristic
187#117×C43D411yescharacteristic
188#117×C43D411yescharacteristic
189C2×C42×C43C2311yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C4⋊C8×C43—21no—
193C4⋊C8×C43—21no—
194C4⋊C8×C43C2311yescharacteristic
195C4⋊C8×C43C2311yescharacteristic
196C4⋊C8×C43C2311yescharacteristic
197C4⋊C8×C43C2311yescharacteristic
198C22⋊C8×C43—21no—
199C22⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202#97×C43—21no—
203#97×C43—21no—
204C4×C8×C43—21no—
205C4×C8×C43—21no—
206C23×D43—21no—
207#41×C43—41no—
208#41×C43—41no—
209C2×Q8×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C2×D4×C43C22⋊C411yescharacteristic
212C2×D4×C43C22⋊C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C22×Dic43—21no—
227#10621898—22no—
228#10621898—22no—
229#10621898—41no—
230#10621898—41no—
231C2×D172—21no—
232C2×D172—22no—
233C2×D172—41no—
234C2×D172C22×C411yescharacteristic
235C2×D172C22×C411yescharacteristic
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—42no—
245C2×C4×D43—42no—
246C2×Dic86—21no—
247C2×Dic86C22×C411yescharacteristic
248C2×Dic86C22×C411yescharacteristic
249M16×C43—42no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—42no—
255C4⋊C4×C43C22⋊C411yescharacteristic
256C4⋊C4×C43C22⋊C411yescharacteristic
257C4⋊C4×C43C22⋊C411yescharacteristic
258C4⋊C4×C43C22⋊C411yescharacteristic
259C4⋊C4×C43C22⋊C411yescharacteristic
260C4⋊C4×C43C22⋊C411yescharacteristic
261C22⋊C4×C43C22⋊C411yescharacteristic
262C22⋊C4×C43C22⋊C411yescharacteristic
263C22⋊C4×C43C22⋊C411yescharacteristic
264C22⋊C4×C43C22⋊C411yescharacteristic
265C22⋊C4×C43C22⋊C411yescharacteristic
266C22⋊C4×C43C22⋊C411yescharacteristic
267C42×C43C22×C411yescharacteristic
268C42×C43C22×C411yescharacteristic
269C42×C43C22×C411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2×D411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2411yescharacteristic
277C22⋊Dic43—21no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43C22×C411yescharacteristic
300C4⋊Dic43C22×C411yescharacteristic
301C4⋊Dic43C22×C411yescharacteristic
302C4⋊Dic43C22×C411yescharacteristic
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—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321#10621877—42no—
322#10621877—42no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—42no—
328C23×C43C2×C22⋊C411yescharacteristic
329C23×C43C2×C22⋊C411yescharacteristic
330C23×C43C2×C22⋊C411yescharacteristic
331C22×D43—21no—
332C22×D43—21no—
333C22×D43—42no—
334C22×D43—42no—
335C22×D43—81no—
336Q8×C43—41no—
337D4×C43—41no—
338D4×C43—41no—
339D4×C43—41no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43C2×C22⋊C411yescharacteristic
356C2×C4×C43C2×C22⋊C411yescharacteristic
357C2×C4×C43C2×C22⋊C411yescharacteristic
358C2×C4×C43C2×C22⋊C411yescharacteristic
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×C43C23×C411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C22⋊D43—42no—
368C22⋊D43—42no—
369C22⋊D43—81no—
370C22⋊D43—81no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—42no—
378D172—21no—
379D172—21no—
380D172—21no—
381D172—42no—
382D172#13112yes—
383C4×D43—42no—
384C4×D43—42no—
385C4×D43—42no—
386C4×D43—42no—
387C4×D43—41no—
388C4×D43—41no—
389C4×D43—41no—
390C4×D43—41no—
391C4×D43—81no—
392C4×D43—81no—
393Dic86—21no—
394Dic86—21no—
395Dic86—21no—
396Dic86—21no—
397Dic86—81no—
398C8×C43—41no—
399C8×C43—41no—
400C8×C43—41no—
401C8×C43—41no—
402C43⋊C8—22no—
403C43⋊C8—41no—
404C43⋊C8—41no—
405C43⋊C8—41no—
406#17513—431nomaximal, Sylow
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—21no—
412C22×C43—21no—
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—21no—
416C22×C43C22×C22⋊C411yescharacteristic
417C2×D43—22no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C2×D43—41no—
423C2×D43—84no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—21no—
433C4×C43—21no—
434C4×C43C2×#13111yescharacteristic
435C4×C43#56811yescharacteristic
436C4×C43#57511yescharacteristic
437C4×C43#57511yescharacteristic
438Dic43—41no—
439Dic43—41no—
440Dic43—41no—
441Dic43—41no—
442Dic43—41no—
443Dic43—41no—
444#3475—431no—
445#2965—431no—
446#2925D4311yescharacteristic, complemented
447#1497—431no—
448#1495—431no—
449#1494—431no—
450#1490—431no—
451#1489—431no—
452#1488—431no—
453#1485—431no—
454#1483—431no—
455#1482—431no—
456#1478—431no—
457#1477—431no—
458#1476—431no—
459C2×C43—41no—
460C2×C43—41no—
461C2×C43—41no—
462C2×C43#288011yescharacteristic
463C2×C43#289611yescharacteristic
464C2×C43#290111yescharacteristic
465D43—42no—
466D43—81no—
467#556—431no—
468#555—431no—
469#554—431no—
470#553—861no—
471#552—431no—
472#552—431no—
473#552—861no—
474#551—861no—
475#551—861no—
476#547—431no—
477#546—431no—
478#546—431no—
479#533—431no—
480#529—431no—
481#529—431no—
482#529—861no—
483#529—861no—
484#525—861no—
485C4×#41—431no—
486C4×#41—431no—
487C4×#41C2×D4311yescharacteristic
488C2×C4×D4—431no—
489C2×#117—861no—
490#446—861no—
491#436—861no—
492#435—861no—
493#435—861no—
494#433—21no—
495#433—21no—
496#432C2×D4311yescharacteristic
497#432C2×D4311yescharacteristic, complemented
498#431—431no—
499#431—431no—
500#431—431no—
501#431C2×D4311yescharacteristic
502#431C2×D4311yescharacteristic, complemented
503#423C2×D4311yescharacteristic, complemented
504C2×C4⋊C8C2×D4311yescharacteristic, complemented
505#408—21no—
506#405—21no—
507C4×M16—431no—
508C4×M16—431no—
509C2×C4×C8—431no—
510Q8⋊C8—431no—
511Q8⋊C8—431no—
512Q8⋊C8—431no—
513Q8⋊C8—431no—
514Q8⋊C8—431no—
515Q8⋊C8—431no—
516Q8⋊C8—431no—
517Q8⋊C8—431no—
518D4⋊C8—431no—
519D4⋊C8—431no—
520D4⋊C8—431no—
521D4⋊C8—431no—
522D4⋊C8—431no—
523D4⋊C8—431no—
524D4⋊C8—431no—
525D4⋊C8—431no—
526C43#1751311yescharacteristic, complemented, Sylow
527C2×#41—431no—
528C2×#41—431no—
529C2×#41C22⋊D4311yescharacteristic
530C22×D4—431no—
531C23×C4—861no—
532C2×M16—21no—
533C2×M16—861no—
534C2×M16—861no—
535C22×C8—21no—
536C22×C8—861no—
537C4⋊Q8—431no—
538C4⋊Q8—431no—
539#126—861no—
540#126—861no—
541#126—861no—
542#126—861no—
543#126—861no—
544#126—861no—
545#125—431no—
546#125—431no—
547#125—861no—
548#125—861no—
549#125—861no—
550#124—431no—
551#124—431no—
552#124—861no—
553#124—861no—
554#123—861no—
555#123—861no—
556#123—861no—
557#123—861no—
558#123—861no—
559#123—861no—
560#123—861no—
561#123—861no—
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—
571#121—431no—
572#121—431no—
573#121—861no—
574#121—861no—
575#121—861no—
576#121—861no—
577#120—861no—
578#120—861no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—861no—
584C4×Q8C4×D4311yescharacteristic
585C4×Q8D17211yescharacteristic
586C4×D4—431no—
587C4×D4—431no—
588C4×D4—431no—
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—431no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4C4×D4311yescharacteristic
601C4×D4C4×D4311yescharacteristic
602C4×D4C4×D4311yescharacteristic
603C4×D4D17211yescharacteristic
604C4×D4D17211yescharacteristic
605C4×D4D17211yescharacteristic
606#117—431no—
607#117—431no—
608#117—861no—
609#117—861no—
610#117—861no—
611#117—861no—
612#117—861no—
613#117—861no—
614#117—861no—
615#117—861no—
616#117—861no—
617#117C22⋊D4311yescharacteristic
618#117C22⋊D4311yescharacteristic
619#117C22⋊D4311yescharacteristic
620C2×C4⋊C4—431no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4—861no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C42—861no—
627C2×C42—861no—
628C2×C42C22×D4311yescharacteristic
629C2×C42C22×D4311yescharacteristic
630C2×C42C22×D4311yescharacteristic
631C4⋊C8—21no—
632C4⋊C8—21no—
633C4⋊C8—861no—
634C4⋊C8—861no—
635C4⋊C8—861no—
636C4⋊C8C22×D4311yescharacteristic
637C4⋊C8C22×D4311yescharacteristic
638C4⋊C8C22×D4311yescharacteristic
639C4⋊C8C22×D4311yescharacteristic
640C22⋊C8—21no—
641C22⋊C8—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644C22⋊C8—861no—
645C22⋊C8—861no—
646C22⋊C8—861no—
647#97—21no—
648#97—21no—
649#97—861no—
650#97—861no—
651C4×C8—21no—
652C4×C8—21no—
653C4×C8—431no—
654C4×C8—431no—
655C4×C8—431no—
656C4×C8—431no—
657C4×C8—861no—
658C24—861no—
659#41—41no—
660#41—41no—
661#41—862no—
662#41—862no—
663#41—1721no—
664#41—1721no—
665C2×Q8—431no—
666C2×Q8—431no—
667C2×Q8—861no—
668C2×Q8(C2×D43)⋊C411yescharacteristic
669C2×D4—431no—
670C2×D4—431no—
671C2×D4—862no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4—861no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—1721no—
678C2×D4(C2×D43)⋊C411yescharacteristic
679C2×D4(C2×D43)⋊C411yescharacteristic
680C2×D4(C2×D43)⋊C411yescharacteristic
681C22×C4—861no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4C2×C4×D4311yescharacteristic
693C22×C4C2×C4×D4311yescharacteristic
694C22×C4C2×C4×D4311yescharacteristic
695C22×C4C2×D17211yescharacteristic
696C22×C4C2×D17211yescharacteristic
697C22×C4C2×D17211yescharacteristic
698C22×C4C2×C22⋊D4311yescharacteristic
699C22×C4C2×C22⋊D4311yescharacteristic
700C22×C4C2×C22⋊D4311yescharacteristic
701M16—42no—
702M16—1722no—
703M16—1722no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—42no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—861no—
713C2×C8—1722no—
714C4⋊C4—431no—
715C4⋊C4—431no—
716C4⋊C4—431no—
717C4⋊C4—431no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—861no—
728C4⋊C4—861no—
729C4⋊C4—861no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4(C2×D43)⋊C411yescharacteristic
735C4⋊C4(C2×D43)⋊C411yescharacteristic
736C4⋊C4(C2×D43)⋊C411yescharacteristic
737C4⋊C4(C2×D43)⋊C411yescharacteristic
738C4⋊C4(C2×D43)⋊C411yescharacteristic
739C4⋊C4(C2×D43)⋊C411yescharacteristic
740C22⋊C4—861no—
741C22⋊C4—861no—
742C22⋊C4—861no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—861no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C22⋊C4—861no—
758C22⋊C4(C2×D43)⋊C411yescharacteristic
759C22⋊C4(C2×D43)⋊C411yescharacteristic
760C22⋊C4(C2×D43)⋊C411yescharacteristic
761C22⋊C4(C2×D43)⋊C411yescharacteristic
762C22⋊C4(C2×D43)⋊C411yescharacteristic
763C22⋊C4(C2×D43)⋊C411yescharacteristic
764C42—861no—
765C42—861no—
766C42—861no—
767C42—861no—
768C42—861no—
769C42—861no—
770C42C2×C4×D4311yescharacteristic
771C42C2×C4×D4311yescharacteristic
772C42C2×C4×D4311yescharacteristic
773C42C2×D17211yescharacteristic
774C42C2×D17211yescharacteristic
775C42C2×D17211yescharacteristic
776C42C2×C22⋊D4311yescharacteristic
777C42C2×C22⋊D4311yescharacteristic
778C42C2×C22⋊D4311yescharacteristic
779C42C23×D4311yescharacteristic
780C23—861no—
781C23—861no—
782C23—3441no—
783C23—1722no—
784C23—1722no—
785C23C2×(C2×D43)⋊C411yescharacteristic
786C23C2×(C2×D43)⋊C411yescharacteristic
787C23C2×(C2×D43)⋊C411yescharacteristic
788Q8—41no—
789Q8—861no—
790Q8—861no—
791Q8—861no—
792Q8—861no—
793Q8—3441no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—432no—
798D4—861no—
799D4—861no—
800D4—861no—
801D4—3441no—
802D4—3441no—
803D4—1722no—
804D4—1722no—
805D4—1722no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—3441no—
828C2×C4—3441no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4—1722no—
833C2×C4—1722no—
834C2×C4—1721no—
835C2×C4—1721no—
836C2×C4—1721no—
837C2×C4—1721no—
838C2×C4C2×(C2×D43)⋊C411yescharacteristic
839C2×C4C2×(C2×D43)⋊C411yescharacteristic
840C2×C4C2×(C2×D43)⋊C411yescharacteristic
841C2×C4C2×(C2×D43)⋊C411yescharacteristic
842C2×C4C2×(C2×D43)⋊C411yescharacteristic
843C2×C4C2×(C2×D43)⋊C411yescharacteristic
844C2×C4C2×(C2×D43)⋊C411yescharacteristic
845C2×C4C2×(C2×D43)⋊C411yescharacteristic
846C2×C4C2×(C2×D43)⋊C411yescharacteristic
847C2×C4C22×C4×D4311yescharacteristic
848C2×C4C22×C22⋊D4311yescharacteristic
849C2×C4C22×D17211yescharacteristic
850C8—41no—
851C8—41no—
852C8—41no—
853C8—41no—
854C8—862no—
855C8—1721no—
856C8—1721no—
857C8—1721no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—862no—
868C22—3444no—
869C22—1721no—
870C22—1721no—
871C22—1721no—
872C22—1721no—
873C22—1721no—
874C22C22×(C2×D43)⋊C411yescharacteristic
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—21no—
882C4—21no—
883C4—21no—
884C4—21no—
885C4—1721no—
886C4—1721no—
887C4—1721no—
888C4—1721no—
889C4—1721no—
890C4—1721no—
891C4#131×D4311yescharacteristic
892C4#1458366411yescharacteristic
893C4#1458369711yescharacteristic
894C4#1458369711yescharacteristic
895C2—41no—
896C2—41no—
897C2—41no—
898C2—3441no—
899C2—1722no—
900C2#1914304211yescharacteristic
901C2#1914311211yescharacteristic
902C2#1914314011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2925C2
socleC22×C43C22×C22⋊C4
prime radical#19148159C2
cosocleC42×C43C24
hypercenter#2925D43
hypocenterC43#17513
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #19143562C2semidirect
3. #19133067C2semidirect
4. #19133058C2semidirect
5. #19133053C2semidirect
6. #19133037C2semidirect
7. #19133032C2semidirect
8. #19133027C2semidirect
9. #19133015C2semidirect
10. #19133006C2semidirect
11. #19133001C2semidirect
12. #19132985C2semidirect
13. #19132980C2semidirect
14. #19132975C2semidirect
15. C43×#2925C2semidirect
43. #14582952C22semidirect
44. #14582952C22semidirect
46. C4×#10621877C22semidirect
47. C2×C4×C43⋊C8C22semidirect
48. #14582629C22semidirect
49. #14582629C22semidirect
50. #14582629C22semidirect
51. #14582629C22semidirect
52. #14582629C22semidirect
53. #14582629C22semidirect
54. #14582629C22semidirect
55. #14582629C22semidirect
68. C43×#432C22semidirect
70. C43×#431C22semidirect
71. C43×#423C22semidirect
72. C2×C4⋊C8×C43C22semidirect
446. #2925D43semidirect
497. #432C2×D43semidirect
502. #431C2×D43semidirect
503. #423C2×D43semidirect
504. C2×C4⋊C8C2×D43semidirect
526. C43#17513semidirect

Maximal subgroups

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

subgroupindex
#191481592
#191435622
#191330672
#191330582
#191330532
#191330372
#191330322
#191330272
#191330152
#191330062
#191330012
#191329852
#191329802
#191329752
C43×#29252
#1751343