Finite Group Databasebeta

← #25063581

Subgroups — #25063581

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148212C211yesmaximal, characteristic
2#19143717C211yesmaximal, characteristic, complemented
3C4×#13063331C211yesmaximal, characteristic, complemented
4#19133056C211yesmaximal, characteristic, complemented
5#19133054C211yesmaximal, characteristic, complemented
6#19133048C211yesmaximal, characteristic, complemented
7#19133042C211yesmaximal, characteristic, complemented
8#19133040C211yesmaximal, characteristic, complemented
9#19133033C211yesmaximal, characteristic, complemented
10#19133014C211yesmaximal, characteristic, complemented
11#19133007C211yesmaximal, characteristic, complemented
12#19133006C211yesmaximal, characteristic, complemented
13#19132976C211yesmaximal, characteristic, complemented
14Q8⋊C8×D43C211yesmaximal, characteristic, complemented
15C2×C43×Q8⋊C8C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583625C411yescharacteristic
18#14583621—21no—
19#14583621C411yescharacteristic
20#14583590—21no—
21#14583590C411yescharacteristic
22#14583584—21no—
23#14583584C411yescharacteristic
24Q8×C22⋊D43C411yescharacteristic
25#14583561C411yescharacteristic
26#14583560C411yescharacteristic
27#14583550—21no—
28#14583550C411yescharacteristic
29#14583453—21no—
30#14583453C2211yescharacteristic
31#14583436—21no—
32#14583436C2211yescharacteristic
33#14583433—21no—
34#14583433C2211yescharacteristic
35C4×#10621902C2211yescharacteristic
36C4×#10621898—21no—
37C4×#10621898C2211yescharacteristic
38C4×Q8×D43C2211yescharacteristic
39#14583028—21no—
40#14582970—21no—
41#14582969—21no—
42C8×C22⋊D43—21no—
43#14582956C2211yescharacteristic
44#14582955C2211yescharacteristic
45#14582951C2211yescharacteristic
46#14582921C2211yescharacteristic
47C4⋊C8×D43C2211yescharacteristic
48#14582854—21no—
49#14582853—21no—
50#14582853—21no—
51C4×#10621877C2211yescharacteristic
52C4×#10621872C2211yescharacteristic
53C4×#10621872C2211yescharacteristic
54C4×C8×D43C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58Q8⋊(C43⋊C8)C2211yescharacteristic
59Q8⋊(C43⋊C8)C2211yescharacteristic
60Q8⋊(C43⋊C8)C2211yescharacteristic
61Q8⋊(C43⋊C8)C2211yescharacteristic
62#14582629C2211yescharacteristic
63#14582629C2211yescharacteristic
64#14582628C2211yescharacteristic
65#14582628C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C2×C4×Q8×C43C2211yescharacteristic
69C2×C4⋊C8×C43C2211yescharacteristic
70C2×C4×C8×C43C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×Q8⋊C8C2211yescharacteristic
74C43×Q8⋊C8C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898—21no—
77C2×#10621898D411yescharacteristic
78C2×Q8×D43C2×C411yescharacteristic
79#13063331—28no—
80C2×#10621877—21no—
81C2×#10621872—21no—
82C2×#10621872—21no—
83C2×#10621872—21no—
84C2×C8×D43—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063324—21no—
88#13063324C2×C411yescharacteristic
89#13063323—21no—
90#13063323C2×C411yescharacteristic
91#13063320—21no—
92#13063320—21no—
93#13063320—21no—
94#13063319—21no—
95#13063319—21no—
96#13063319—21no—
97#13063317—21no—
98#13063317C2×C411yescharacteristic
99#13063316—21no—
100#13063316C2×C411yescharacteristic
101#13063315—21no—
102#13063315—21no—
103#13063315—21no—
104#13063314—21no—
105#13063314C2×C411yescharacteristic
106#13063313—21no—
107#13063313C2×C411yescharacteristic
108#13063310—21no—
109#13063310—21no—
110#13063310—21no—
111#13063308—21no—
112#13063308—21no—
113#13063308—21no—
114#13063305—21no—
115#13063305C2×C411yescharacteristic
116#13063304—21no—
117#13063304C2×C411yescharacteristic
118#13063303—21no—
119#13063303—21no—
120#13063303—21no—
121#13063301—21no—
122#13063301—21no—
123#13063301C2×C411yescharacteristic
124#13063301C2×C411yescharacteristic
125#13063300—21no—
126#13063300C2×C411yescharacteristic
127#13063299—21no—
128#13063299C2×C411yescharacteristic
129Q8×Dic43C2×C411yescharacteristic
130Q8×Dic43C2×C411yescharacteristic
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86C2×C411yescharacteristic
135C4×Dic86D411yescharacteristic
136C4×Dic86C2311yescharacteristic
137#13063290—21no—
138#13063290C2×C411yescharacteristic
139C4×D172—21no—
140C4×D172—21no—
141C4×D172—21no—
142C4×D172C2×C411yescharacteristic
143C4×D172D411yescharacteristic
144C4×D172C2311yescharacteristic
145#13063287—21no—
146#13063287C2×C411yescharacteristic
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43C2×C411yescharacteristic
151C4×C22⋊D43C2×C411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154#13063284—21no—
155#13063284D411yescharacteristic
156#13063283—21no—
157#13063283C2×C411yescharacteristic
158#13063282—21no—
159#13063282—21no—
160#13063282—21no—
161#13063282—21no—
162#13063282—21no—
163#13063282D411yescharacteristic
164#13063282D411yescharacteristic
165C4⋊C4×D43—21no—
166C4⋊C4×D43C2×C411yescharacteristic
167C42×D43—21no—
168C42×D43—21no—
169C42×D43C2311yescharacteristic
170C42×D43C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172C4⋊(C43⋊C8)C2311yescharacteristic
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175C22⋊(C43⋊C8)—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063236—21no—
179#13063236—21no—
180#13063235—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C8×Dic43—21no—
188C22×Q8×C43C2×C411yescharacteristic
189C22×C8×C43—21no—
190C22×C8×C43—21no—
191C4×Q8×C43—21no—
192C4×Q8×C43—21no—
193C4×Q8×C43C2×C411yescharacteristic
194C4×Q8×C43C2×C411yescharacteristic
195C4×Q8×C43C2311yescharacteristic
196C4×Q8×C43C2311yescharacteristic
197C2×C4⋊C4×C43—21no—
198C2×C4⋊C4×C43C2×C411yescharacteristic
199C2×C42×C43—21no—
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43—21no—
202C4⋊C8×C43C2311yescharacteristic
203C4⋊C8×C43C2311yescharacteristic
204C4×C8×C43—21no—
205C4×C8×C43C2311yescharacteristic
206C4×C8×C43C2311yescharacteristic
207C2×Q8×C43—21no—
208C2×Q8×C43—22no—
209C2×Q8×C43—41no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×Q8×C43C22×C411yescharacteristic
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2×D411yescharacteristic
217C2×C22⋊D43—21no—
218C2×C22⋊D43C22⋊C411yescharacteristic
219C2×C22⋊D43C22⋊C411yescharacteristic
220#10621902—22no—
221#10621902—41no—
222Q8×D43—22no—
223Q8×D43—41no—
224#10621898—24no—
225#10621898—44no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172C22⋊C411yescharacteristic
229C2×D172C22×C411yescharacteristic
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C22×C411yescharacteristic
237C2×C4×D43C2×D411yescharacteristic
238C2×C4×D43C2×D411yescharacteristic
239C2×C4×D43C2×D411yescharacteristic
240C2×C4×D43C2×D411yescharacteristic
241C2×Dic86—21no—
242C2×Dic86—21no—
243C2×Dic86C22⋊C411yescharacteristic
244C2×Dic86C22×C411yescharacteristic
245C2×C8×C43—24no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—81no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43C22×C411yescharacteristic
257C4⋊C4×C43C22×C411yescharacteristic
258C42×C43—21no—
259C42×C43—21no—
260C42×C43—21no—
261C42×C43—21no—
262C42×C43C22×C411yescharacteristic
263C42×C43C2×D411yescharacteristic
264C42×C43C2×D411yescharacteristic
265C42×C43C2411yescharacteristic
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)⋊C4—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4C22⋊C411yescharacteristic
282(C2×D43)⋊C4C22⋊C411yescharacteristic
283(C2×D43)⋊C4C22⋊C411yescharacteristic
284(C2×D43)⋊C4C22⋊C411yescharacteristic
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43C22⋊C411yescharacteristic
290C4⋊Dic43C22⋊C411yescharacteristic
291C4⋊Dic43C22×C411yescharacteristic
292C4⋊Dic43C22×C411yescharacteristic
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⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4C22⋊C411yescharacteristic
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43C22×C411yescharacteristic
315C4×Dic43C22×C411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320#10621877—24no—
321C2×C43⋊C8—21no—
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325#10621872—24no—
326#10621872—24no—
327#10621872—81no—
328C8×D43—24no—
329C8×D43—24no—
330C8×D43—81no—
331C23×C43C2×C22⋊C411yescharacteristic
332C22×D43—21no—
333C22×D43C2×C22⋊C411yescharacteristic
334C22×D43C2×C22⋊C411yescharacteristic
335Q8×C43—21no—
336Q8×C43—21no—
337Q8×C43—21no—
338Q8×C43—42no—
339Q8×C43#13112yescomplemented
340C2×C4×C43—21no—
341C2×C4×C43—22no—
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—42no—
350C2×C4×C43—42no—
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C2×C22⋊C411yescharacteristic
353C2×C4×C43C2×C22⋊C411yescharacteristic
354C2×C4×C43C23×C411yescharacteristic
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D411yescharacteristic
357C22⋊D43—22no—
358C22⋊D43—42no—
359C22⋊D43#10414yes—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43C2×C22⋊C411yescharacteristic
364C2×Dic43C2×C22⋊C411yescharacteristic
365C2×Dic43C2×C22⋊C411yescharacteristic
366C2×Dic43C2×C22⋊C411yescharacteristic
367C2×Dic43C2×C22⋊C411yescharacteristic
368C2×Dic43C2×C22⋊C411yescharacteristic
369D172—22no—
370D172—21no—
371D172—21no—
372D172—42no—
373D172—42no—
374C4×D43—22no—
375C4×D43—21no—
376C4×D43—21no—
377C4×D43—21no—
378C4×D43—21no—
379C4×D43—21no—
380C4×D43—21no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—22no—
384C4×D43—42no—
385C4×D43—42no—
386C4×D43—42no—
387C4×D43—41no—
388C4×D43—41no—
389C4×D43—42no—
390Dic86—22no—
391Dic86—21no—
392Dic86—21no—
393Dic86—42no—
394Dic86—42no—
395C8×C43—22no—
396C8×C43—22no—
397C8×C43—41no—
398C8×C43—41no—
399C43⋊C8—22no—
400C43⋊C8—22no—
401C43⋊C8—41no—
402C43⋊C8—41no—
403#17519—431nomaximal, Sylow
404C22×C43—21no—
405C22×C43—21no—
406C22×C43C2×#10412yes—
407C22×C43C22×C22⋊C411yescharacteristic
408C2×D43—21no—
409C2×D43—21no—
410C2×D43—21no—
411C2×D43—21no—
412C2×D43—21no—
413C2×D43—41no—
414C2×D43—41no—
415C2×D43—41no—
416C2×D43C2×#10412yes—
417C4×C43—22no—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—21no—
421C4×C43—21no—
422C4×C43—41no—
423C4×C43—41no—
424C4×C43—41no—
425C4×C43C2×#13111yescharacteristic
426C4×C43#56811yescharacteristic
427C4×C43#57711yescharacteristic
428C4×C43#57811yescharacteristic
429Dic43—21no—
430Dic43—21no—
431Dic43—21no—
432Dic43—21no—
433Dic43—21no—
434Dic43—41no—
435Dic43—41no—
436Dic43—41no—
437Dic43C2×#10412yes—
438#3482—431no—
439#2990—431no—
440C4×#131—431no—
441#1494—431no—
442#1494—431no—
443#1493—431no—
444#1491—431no—
445#1491—431no—
446#1489—431no—
447#1485—431no—
448#1483—431no—
449#1483—431no—
450#1476—431no—
451C2×Q8⋊C8—431no—
452C2×Q8⋊C8D4311yescharacteristic, complemented
453C2×C43—22no—
454C2×C43#288011yescharacteristic
455C2×C43#289811yescharacteristic
456C2×C43C22×#10411yescharacteristic
457D43—22no—
458D43—41no—
459D43—81no—
460C2×#131—861no—
461#557—431no—
462#556—431no—
463#556—861no—
464#552—431no—
465#552—431no—
466#552—861no—
467#552—861no—
468D4×Q8—431no—
469#548—431no—
470#548—431no—
471#547—431no—
472#547—861no—
473#533—431no—
474#533—861no—
475#529—431no—
476#529—431no—
477#529—861no—
478#529—861no—
479C4×#41—431no—
480C4×#41—431no—
481C4×#41—861no—
482C2×C4×Q8—431no—
483C2×C4×Q8C2×D4311yescharacteristic
484#446—861no—
485#435—861no—
486#435—861no—
487C8×D4—861no—
488#432—431no—
489#432—431no—
490#431—431no—
491#423—431no—
492C2×C4⋊C8—431no—
493C2×C4⋊C8C2×D4311yescharacteristic
494#405—861no—
495#405—861no—
496#405—861no—
497C4×M16—431no—
498C4×M16—431no—
499C4×M16—431no—
500C2×C4×C8—431no—
501C2×C4×C8—431no—
502C2×C4×C8C2×D4311yescharacteristic
503Q8⋊C8—431no—
504Q8⋊C8—431no—
505Q8⋊C8—431no—
506Q8⋊C8—431no—
507Q8⋊C8—431no—
508Q8⋊C8—431no—
509Q8⋊C8—431no—
510Q8⋊C8—431no—
511Q8⋊C8C2×D4311yescharacteristic
512Q8⋊C8C2×D4311yescharacteristic
513Q8⋊C8C2×D4311yescharacteristic
514Q8⋊C8C2×D4311yescharacteristic
515D4⋊C8—431no—
516D4⋊C8—431no—
517D4⋊C8—431no—
518D4⋊C8—431no—
519C43#1751911yescharacteristic, complemented, Sylow
520C2×#41—431no—
521C2×#41—431no—
522C2×#41—861no—
523C22×Q8—431no—
524C22×Q8C4×D4311yescharacteristic
525#131—868no—
526C2×M16—861no—
527C2×M16—861no—
528C2×M16—861no—
529C2×M16—861no—
530C22×C8—21no—
531C22×C8—21no—
532C22×C8—861no—
533C22×C8—861no—
534C22×C8—861no—
535C4⋊Q8—431no—
536C4⋊Q8—431no—
537C4⋊Q8—861no—
538C4⋊Q8—861no—
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#125—861no—
551#125—861no—
552#124—431no—
553#124—431no—
554#124—861no—
555#124—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—
571C22⋊Q8—861no—
572C22⋊Q8—861no—
573#121—431no—
574#121—431no—
575#121—861no—
576#121—861no—
577C4×Q8—21no—
578C4×Q8—21no—
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×Q8C4×D4311yescharacteristic
590C4×Q8C4×D4311yescharacteristic
591C4×Q8C22×D4311yescharacteristic
592C4×Q8C22×D4311yescharacteristic
593C4×D4—431no—
594C4×D4—431no—
595C4×D4—431no—
596C4×D4—431no—
597C4×D4—431no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608#117—431no—
609#117—431no—
610#117—431no—
611#117—431no—
612#117—861no—
613#117—861no—
614#117—861no—
615#117—861no—
616#117—861no—
617#117—861no—
618#117—861no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4C4×D4311yescharacteristic
623C2×C42—21no—
624C2×C42—431no—
625C2×C42—431no—
626C2×C42—861no—
627C2×C42—861no—
628C2×C42C22×D4311yescharacteristic
629C4⋊C8—21no—
630C4⋊C8—431no—
631C4⋊C8—431no—
632C4⋊C8—861no—
633C4⋊C8—861no—
634C4⋊C8C22×D4311yescharacteristic
635C4⋊C8C22×D4311yescharacteristic
636C22⋊C8—861no—
637C22⋊C8—861no—
638C22⋊C8—861no—
639#97—861no—
640#97—861no—
641#97—861no—
642#97—861no—
643#97—861no—
644C4×C8—21no—
645C4×C8—431no—
646C4×C8—431no—
647C4×C8—861no—
648C4×C8—861no—
649C4×C8—861no—
650C4×C8C22×D4311yescharacteristic
651C4×C8C22×D4311yescharacteristic
652#41—864no—
653#41—862no—
654#41—1724no—
655#41—1721no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—41no—
659C2×Q8—431no—
660C2×Q8—431no—
661C2×Q8—861no—
662C2×Q8—861no—
663C2×Q8—862no—
664C2×Q8—1721no—
665C2×Q8C2×C4×D4311yescharacteristic
666C2×Q8C2×C4×D4311yescharacteristic
667C2×D4—431no—
668C2×D4—431no—
669C2×D4—431no—
670C2×D4—431no—
671C2×D4—861no—
672C2×D4—861no—
673C2×D4—861no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—431no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—861no—
683C22×C4—861no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4C2×C4×D4311yescharacteristic
688C22×C4D4×D4311yescharacteristic
689C22×C4D4×D4311yescharacteristic
690M16—864no—
691M16—864no—
692M16—864no—
693M16—3441no—
694C2×C8—24no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—81no—
700C2×C8—864no—
701C2×C8—864no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—3441no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—431no—
713C4⋊C4—431no—
714C4⋊C4—431no—
715C4⋊C4—431no—
716C4⋊C4—431no—
717C4⋊C4—431no—
718C4⋊C4—431no—
719C4⋊C4—431no—
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—861no—
735C4⋊C4—861no—
736C4⋊C4C2×C4×D4311yescharacteristic
737C4⋊C4C2×C4×D4311yescharacteristic
738C22⋊C4—431no—
739C22⋊C4—431no—
740C22⋊C4—431no—
741C22⋊C4—431no—
742C22⋊C4—431no—
743C22⋊C4—431no—
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—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C42—431no—
762C42—431no—
763C42—431no—
764C42—431no—
765C42—431no—
766C42—431no—
767C42—861no—
768C42—861no—
769C42—861no—
770C42—861no—
771C42—861no—
772C42C2×C4×D4311yescharacteristic
773C42D4×D4311yescharacteristic
774C42D4×D4311yescharacteristic
775C42C23×D4311yescharacteristic
776C23—431no—
777C23—431no—
778C23—861no—
779C23C22⋊C4×D4311yescharacteristic
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—42no—
784Q8—862no—
785Q8—861no—
786Q8—861no—
787Q8—1722no—
788Q8—1722no—
789Q8#1306333112yescomplemented
790D4—434no—
791D4—862no—
792D4—862no—
793D4—861no—
794D4—861no—
795D4—1722no—
796D4—1722no—
797D4—1722no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—431no—
810C2×C4—431no—
811C2×C4—431no—
812C2×C4—431no—
813C2×C4—431no—
814C2×C4—431no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—861no—
828C2×C4—1722no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4—1722no—
832C2×C4—1721no—
833C2×C4—1721no—
834C2×C4C22⋊C4×D4311yescharacteristic
835C2×C4C22⋊C4×D4311yescharacteristic
836C2×C4C22⋊C4×D4311yescharacteristic
837C2×C4C22×C4×D4311yescharacteristic
838C2×C4C2×D4×D4311yescharacteristic
839C2×C4C2×D4×D4311yescharacteristic
840C8—22no—
841C8—22no—
842C8—41no—
843C8—41no—
844C8—862no—
845C8—862no—
846C8—1721no—
847C8—1721no—
848C22—21no—
849C22—21no—
850C22—432no—
851C22—861no—
852C22—861no—
853C22—861no—
854C22—861no—
855C22—861no—
856C22—1721no—
857C22—1721no—
858C22—1721no—
859C22#104×D4312yes—
860C22C2×C22⋊C4×D4311yescharacteristic
861C4—21no—
862C4—22no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—41no—
867C4—41no—
868C4—41no—
869C4—432no—
870C4—861no—
871C4—861no—
872C4—861no—
873C4—861no—
874C4—861no—
875C4—1721no—
876C4—1721no—
877C4—1721no—
878C4C2×#1306333111yescharacteristic
879C4#1458366511yescharacteristic
880C4#1458370511yescharacteristic
881C4#1458371211yescharacteristic
882C2—22no—
883C2—862no—
884C2—3441no—
885C2—1721no—
886C2#1914304111yescharacteristic
887C2#1914312311yescharacteristic
888C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC2×C43×Q8⋊C8C2
socleC22×C43C22×C22⋊C4
prime radical#19148212C2
cosocleC42×C43C24
hypercenterC2×Q8⋊C8D43
hypocenterC43#17519
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. #19143717C2semidirect
3. C4×#13063331C2semidirect
4. #19133056C2semidirect
5. #19133054C2semidirect
6. #19133048C2semidirect
7. #19133042C2semidirect
8. #19133040C2semidirect
9. #19133033C2semidirect
10. #19133014C2semidirect
11. #19133007C2semidirect
12. #19133006C2semidirect
13. #19132976C2semidirect
14. Q8⋊C8×D43C2semidirect
15. C2×C43×Q8⋊C8C2semidirect
339. Q8×C43#131semidirect
452. C2×Q8⋊C8D43semidirect
519. C43#17519semidirect
789. Q8#13063331semidirect

Maximal subgroups

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

subgroupindex
#191482122
#191437172
C4×#130633312
#191330562
#191330542
#191330482
#191330422
#191330402
#191330332
#191330142
#191330072
#191330062
#191329762
Q8⋊C8×D432
C2×C43×Q8⋊C82
#1751943