Finite Group Databasebeta

← #25063642

Subgroups — #25063642

Order 11008.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148213C211yesmaximal, characteristic
2#19143717C211yesmaximal, characteristic, complemented
3#19143234C211yesmaximal, characteristic, complemented
4#19133068C211yesmaximal, characteristic, complemented
5#19133059C211yesmaximal, characteristic, complemented
6#19133054C211yesmaximal, characteristic, complemented
7#19133040C211yesmaximal, characteristic, complemented
8#19133030C211yesmaximal, characteristic, complemented
9#19133022C211yesmaximal, characteristic, complemented
10#19133007C211yesmaximal, characteristic, complemented
11#19133002C211yesmaximal, characteristic, complemented
12#19132988C211yesmaximal, characteristic, complemented
13#19132980C211yesmaximal, characteristic, complemented
14Q8⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1481C211yesmaximal, characteristic, complemented
16#14583624C411yescharacteristic
17#14583623C411yescharacteristic
18#14583620—21no—
19#14583583C411yescharacteristic
20#14583583C411yescharacteristic
21#14583581—21no—
22#14583581—21no—
23#14583564C411yescharacteristic
24#14583559C411yescharacteristic
25#14583559C411yescharacteristic
26#14583552C411yescharacteristic
27#14583551—21no—
28#14583453—21no—
29#14583436C2211yescharacteristic
30#14583436C2211yescharacteristic
31#14583427—21no—
32#14583427—21no—
33C4×#10621902—21no—
34C4×#10621898C2211yescharacteristic
35C4×#10621898C2211yescharacteristic
36C4×Q8×D43C2211yescharacteristic
37C4×Q8×D43C2211yescharacteristic
38#14583028—21no—
39#14582970—21no—
40#14582969—21no—
41C8×C22⋊D43—21no—
42#14582959—21no—
43#14582957—21no—
44#14582956C2211yescharacteristic
45#14582955C2211yescharacteristic
46#14582952C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49#14582950C2211yescharacteristic
50#14582924—21no—
51#14582921C2211yescharacteristic
52C4⋊C8×D43C2211yescharacteristic
53#14582864—21no—
54C4×#10621872C2211yescharacteristic
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
68C43×#533C2211yescharacteristic
69C43×#431C2211yescharacteristic
70C2×C4⋊C8×C43C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×Q8⋊C8C2211yescharacteristic
74C43×Q8⋊C8C2211yescharacteristic
75C2×#10621902—21no—
76C2×#10621898C2×C411yescharacteristic
77C2×#10621898D411yescharacteristic
78C2×Q8×D43C2×C411yescharacteristic
79C2×Q8×D43C2×C411yescharacteristic
80C2×#10621872—21no—
81C2×#10621872—21no—
82C2×C8×D43—21no—
83C2×C8×D43—21no—
84#13063324—21no—
85#13063323—21no—
86#13063320—21no—
87#13063320—21no—
88#13063320—21no—
89#13063320—21no—
90#13063318—21no—
91#13063318—21no—
92#13063316C2×C411yescharacteristic
93#13063316C2×C411yescharacteristic
94#13063315—21no—
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063314C2×C411yescharacteristic
99#13063314C2×C411yescharacteristic
100#13063311—21no—
101#13063311—21no—
102#13063310—21no—
103#13063310—21no—
104#13063310—21no—
105#13063310—21no—
106#13063307—21no—
107#13063307—21no—
108#13063305—21no—
109#13063303—21no—
110#13063303—21no—
111#13063303—21no—
112#13063303—21no—
113#13063301—21no—
114#13063301C2×C411yescharacteristic
115#13063301C2×C411yescharacteristic
116#13063300C2×C411yescharacteristic
117#13063300C2×C411yescharacteristic
118#13063298—21no—
119#13063298—21no—
120Q8×Dic43—21no—
121Q8×Dic43C2×C411yescharacteristic
122Q8×Dic43C2×C411yescharacteristic
123C4×Dic86—21no—
124C4×Dic86—21no—
125C4×Dic86C2×C411yescharacteristic
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86D411yescharacteristic
128C4×Dic86C2311yescharacteristic
129#13063290—21no—
130#13063290—21no—
131#13063290C2×C411yescharacteristic
132#13063290C2×C411yescharacteristic
133C4×D172—21no—
134C4×D172—21no—
135C4×D172C2×C411yescharacteristic
136C4×D172C2×C411yescharacteristic
137C4×D172D411yescharacteristic
138C4×D172C2311yescharacteristic
139#13063287—21no—
140#13063287—21no—
141#13063287—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148#13063284C2×C411yescharacteristic
149#13063284D411yescharacteristic
150#13063283—21no—
151#13063283—21no—
152#13063283—21no—
153#13063282—21no—
154#13063282—21no—
155#13063282—21no—
156#13063282D411yescharacteristic
157#13063282D411yescharacteristic
158C4⋊C4×D43—21no—
159C4⋊C4×D43—21no—
160C4⋊C4×D43C2×C411yescharacteristic
161C4⋊C4×D43C2×C411yescharacteristic
162C42×D43—21no—
163C42×D43—21no—
164C42×D43—21no—
165C42×D43C2311yescharacteristic
166C42×D43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)C2311yescharacteristic
169C4⋊(C43⋊C8)C2311yescharacteristic
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063236—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C22×C8×C43—21no—
188C4⋊Q8×C43C2×C411yescharacteristic
189C4⋊Q8×C43C2×C411yescharacteristic
190#125×C43—21no—
191C22⋊Q8×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic
193C22⋊Q8×C43C2×C411yescharacteristic
194C4×Q8×C43—21no—
195C4×Q8×C43C2311yescharacteristic
196C4×Q8×C43C2311yescharacteristic
197#117×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C4⋊C8×C43—21no—
201C4⋊C8×C43C2311yescharacteristic
202C4⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C2×Q8×C43—21no—
207C2×Q8×C43C22×C411yescharacteristic
208C2×Q8×C43C22×C411yescharacteristic
209C22×C4×C43C22×C411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C2×C22⋊D43—21no—
213C2×C22⋊D43C22⋊C411yescharacteristic
214C2×C22⋊D43C22⋊C411yescharacteristic
215#10621902—44no—
216Q8×D43—22no—
217Q8×D43—22no—
218Q8×D43—41no—
219Q8×D43—41no—
220#10621898—22no—
221#10621898—41no—
222#10621898—42no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172C22⋊C411yescharacteristic
226C2×D172C22×C411yescharacteristic
227C2×C4×D43—21no—
228C2×C4×D43—21no—
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×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86C22⋊C411yescharacteristic
243C2×Dic86C22×C411yescharacteristic
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—81no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
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
258C22⋊C4×C43—21no—
259C22⋊C4×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)⋊C4C22⋊C411yescharacteristic
280(C2×D43)⋊C4C22⋊C411yescharacteristic
281(C2×D43)⋊C4C22⋊C411yescharacteristic
282(C2×D43)⋊C4C22⋊C411yescharacteristic
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43C22⋊C411yescharacteristic
288C4⋊Dic43C22⋊C411yescharacteristic
289C4⋊Dic43C22×C411yescharacteristic
290C4⋊Dic43C22×C411yescharacteristic
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×Dic43—21no—
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43C22×C411yescharacteristic
313C4×Dic43C22×C411yescharacteristic
314C4×Dic43C2×D411yescharacteristic
315C4×Dic43C2×D411yescharacteristic
316C4×Dic43C2×D411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C2×C43⋊C8—21no—
319C2×C43⋊C8—21no—
320C2×C43⋊C8—21no—
321C2×C43⋊C8—21no—
322#10621872—42no—
323#10621872—81no—
324C8×D43—42no—
325C8×D43—81no—
326C23×C43C2×C22⋊C411yescharacteristic
327C22×D43—21no—
328C22×D43C2×C22⋊C411yescharacteristic
329C22×D43C2×C22⋊C411yescharacteristic
330Q8×C43—21no—
331Q8×C43—21no—
332Q8×C43—21no—
333Q8×C43—21no—
334Q8×C43—42no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—41no—
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C23×C411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C22⋊D43—22no—
351C22⋊D43—41no—
352C22⋊D43—42no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362D172—22no—
363D172—21no—
364D172—21no—
365D172—42no—
366D172—42no—
367C4×D43—22no—
368C4×D43—21no—
369C4×D43—21no—
370C4×D43—21no—
371C4×D43—21no—
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—21no—
375C4×D43—21no—
376C4×D43—41no—
377C4×D43—42no—
378C4×D43—42no—
379C4×D43—42no—
380C4×D43—42no—
381C4×D43—42no—
382C4×D43—42no—
383C4×D43—41no—
384C4×D43—41no—
385Dic86—21no—
386Dic86—41no—
387Dic86—42no—
388Dic86—42no—
389Dic86#13112yes—
390C8×C43—41no—
391C8×C43—41no—
392C8×C43—41no—
393C8×C43—41no—
394C43⋊C8—41no—
395C43⋊C8—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398#17524—431nomaximal, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43C22×C22⋊C411yescharacteristic
403C2×D43—21no—
404C2×D43—21no—
405C2×D43—21no—
406C2×D43—21no—
407C2×D43—21no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
411C2×D43#42112yes—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—41no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43—41no—
420C4×C43C2×#13111yescharacteristic
421C4×C43#56811yescharacteristic
422C4×C43#57711yescharacteristic
423C4×C43#57811yescharacteristic
424Dic43—22no—
425Dic43—21no—
426Dic43—21no—
427Dic43—21no—
428Dic43—21no—
429Dic43—21no—
430Dic43—21no—
431Dic43—41no—
432Dic43—41no—
433#3482—431no—
434#2990—431no—
435#2922—431no—
436#1497—431no—
437#1495—431no—
438#1494—431no—
439#1491—431no—
440#1488—431no—
441#1487—431no—
442#1483—431no—
443#1482—431no—
444#1481D4311yescharacteristic, complemented
445#1479—431no—
446#1477—431no—
447C2×Q8⋊C8—431no—
448C2×C43—41no—
449C2×C43#288011yescharacteristic
450C2×C43#289811yescharacteristic
451C2×C43C2×#42111yescharacteristic
452D43—22no—
453D43—41no—
454D43—81no—
455#557—431no—
456#556—431no—
457#556—861no—
458#552—431no—
459#552—431no—
460#552—861no—
461#552—861no—
462D4×Q8—431no—
463#548—431no—
464#548—431no—
465#547—431no—
466#547—861no—
467#533—861no—
468#533C2×D4311yescharacteristic
469#529—431no—
470#529—431no—
471#529—861no—
472#529—861no—
473C4×#41—431no—
474C4×#41—431no—
475C4×#41—861no—
476C2×C4×Q8—431no—
477C2×C4×Q8—431no—
478#446—861no—
479#435—861no—
480#435—861no—
481C8×D4—861no—
482#433—861no—
483#433—861no—
484#432—431no—
485#432—431no—
486#431—431no—
487#431—431no—
488#431—431no—
489#431—431no—
490#431C2×D4311yescharacteristic
491#424—861no—
492#423—431no—
493C2×C4⋊C8—431no—
494C2×C4⋊C8C2×D4311yescharacteristic
495#408—861no—
496C4×M16—431no—
497C2×C4×C8—431no—
498Q8⋊C8—431no—
499Q8⋊C8—431no—
500Q8⋊C8—431no—
501Q8⋊C8—431no—
502Q8⋊C8—431no—
503Q8⋊C8—431no—
504Q8⋊C8—431no—
505Q8⋊C8—431no—
506Q8⋊C8C2×D4311yescharacteristic
507Q8⋊C8C2×D4311yescharacteristic
508Q8⋊C8C2×D4311yescharacteristic
509Q8⋊C8C2×D4311yescharacteristic
510D4⋊C8—431no—
511D4⋊C8—431no—
512D4⋊C8—431no—
513D4⋊C8—431no—
514C43#1752411yescharacteristic, complemented, Sylow
515C2×#41—431no—
516C2×#41—431no—
517C2×#41—861no—
518C22×Q8—431no—
519C22×Q8—431no—
520C2×M16—861no—
521C2×M16—861no—
522C22×C8—21no—
523C22×C8—861no—
524C22×C8—861no—
525C4⋊Q8—861no—
526C4⋊Q8—861no—
527C4⋊Q8C4×D4311yescharacteristic
528C4⋊Q8C4×D4311yescharacteristic
529#126—861no—
530#126—861no—
531#126—861no—
532#126—861no—
533#126—861no—
534#126—861no—
535#125—21no—
536#125—431no—
537#125—431no—
538#125—861no—
539#125—861no—
540#125—861no—
541#125—861no—
542#124—431no—
543#124—431no—
544#124—861no—
545#124—861no—
546#123—861no—
547#123—861no—
548#123—861no—
549#123—861no—
550#123—861no—
551#123—861no—
552C22⋊Q8—21no—
553C22⋊Q8—431no—
554C22⋊Q8—431no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561C22⋊Q8C4×D4311yescharacteristic
562C22⋊Q8C4×D4311yescharacteristic
563#121—431no—
564#121—431no—
565#121—861no—
566#121—861no—
567C4×Q8—21no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—431no—
572C4×Q8—431no—
573C4×Q8—431no—
574C4×Q8—431no—
575C4×Q8—431no—
576C4×Q8—861no—
577C4×Q8—861no—
578C4×Q8—861no—
579C4×Q8—861no—
580C4×Q8—861no—
581C4×Q8C22×D4311yescharacteristic
582C4×Q8C22×D4311yescharacteristic
583C4×D4—431no—
584C4×D4—431no—
585C4×D4—431no—
586C4×D4—431no—
587C4×D4—431no—
588C4×D4—431no—
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—861no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598#117—21no—
599#117—431no—
600#117—431no—
601#117—431no—
602#117—431no—
603#117—861no—
604#117—861no—
605#117—861no—
606#117—861no—
607#117—861no—
608#117—861no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4—861no—
613C2×C42—431no—
614C2×C42—431no—
615C2×C42—861no—
616C2×C42—861no—
617C2×C42—861no—
618C2×C42C22×D4311yescharacteristic
619C4⋊C8—21no—
620C4⋊C8—21no—
621C4⋊C8—431no—
622C4⋊C8—431no—
623C4⋊C8—861no—
624C4⋊C8—861no—
625C4⋊C8—861no—
626C4⋊C8—861no—
627C4⋊C8—861no—
628C4⋊C8C22×D4311yescharacteristic
629C4⋊C8C22×D4311yescharacteristic
630C22⋊C8—21no—
631C22⋊C8—861no—
632C22⋊C8—861no—
633C22⋊C8—861no—
634C22⋊C8—861no—
635C22⋊C8—861no—
636C22⋊C8—861no—
637#97—861no—
638#97—861no—
639#97—861no—
640C4×C8—431no—
641C4×C8—431no—
642C4×C8—861no—
643C4×C8—861no—
644C4×C8C22×D4311yescharacteristic
645C4×C8C22×D4311yescharacteristic
646#41—862no—
647#41—1721no—
648#41—1722no—
649#41—1724no—
650C2×Q8—21no—
651C2×Q8—431no—
652C2×Q8—431no—
653C2×Q8—861no—
654C2×Q8—861no—
655C2×Q8—862no—
656C2×Q8—862no—
657C2×Q8—1721no—
658C2×Q8—1721no—
659C2×Q8C2×C4×D4311yescharacteristic
660C2×Q8C2×C4×D4311yescharacteristic
661C2×D4—431no—
662C2×D4—431no—
663C2×D4—431no—
664C2×D4—431no—
665C2×D4—861no—
666C2×D4—861no—
667C2×D4—861no—
668C22×C4—431no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4C2×C4×D4311yescharacteristic
682C22×C4D4×D4311yescharacteristic
683C22×C4D4×D4311yescharacteristic
684M16—3441no—
685M16—1722no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—81no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—3441no—
696C2×C8—1722no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—431no—
705C4⋊C4—431no—
706C4⋊C4—431no—
707C4⋊C4—431no—
708C4⋊C4—431no—
709C4⋊C4—431no—
710C4⋊C4—431no—
711C4⋊C4—431no—
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—861no—
724C4⋊C4—861no—
725C4⋊C4—861no—
726C4⋊C4C2×C4×D4311yescharacteristic
727C4⋊C4C2×C4×D4311yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—431no—
731C22⋊C4—431no—
732C22⋊C4—431no—
733C22⋊C4—431no—
734C22⋊C4—431no—
735C22⋊C4—431no—
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—
747C42—21no—
748C42—21no—
749C42—431no—
750C42—431no—
751C42—431no—
752C42—431no—
753C42—431no—
754C42—431no—
755C42—861no—
756C42—861no—
757C42—861no—
758C42—861no—
759C42—861no—
760C42—861no—
761C42—861no—
762C42C2×C4×D4311yescharacteristic
763C42D4×D4311yescharacteristic
764C42D4×D4311yescharacteristic
765C42C23×D4311yescharacteristic
766C23—431no—
767C23—431no—
768C23—861no—
769C23C22⋊C4×D4311yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—42no—
775Q8—432no—
776Q8—861no—
777Q8—1721no—
778Q8—1722no—
779Q8—1722no—
780D4—862no—
781D4—862no—
782D4—861no—
783D4—861no—
784D4—1722no—
785D4—1722no—
786D4—1721no—
787D4—1722no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—431no—
798C2×C4—431no—
799C2×C4—431no—
800C2×C4—431no—
801C2×C4—431no—
802C2×C4—431no—
803C2×C4—862no—
804C2×C4—861no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—861no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—861no—
814C2×C4—861no—
815C2×C4—1721no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4—1722no—
819C2×C4—1722no—
820C2×C4—1722no—
821C2×C4—1722no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4C22⋊C4×D4311yescharacteristic
825C2×C4C22⋊C4×D4311yescharacteristic
826C2×C4C22⋊C4×D4311yescharacteristic
827C2×C4C22×C4×D4311yescharacteristic
828C2×C4C2×D4×D4311yescharacteristic
829C2×C4C2×D4×D4311yescharacteristic
830C8—41no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—1721no—
835C8—1721no—
836C8—1721no—
837C8—1721no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—432no—
842C22—861no—
843C22—861no—
844C22—861no—
845C22—861no—
846C22—861no—
847C22—1721no—
848C22—1721no—
849C22—1721no—
850C22C2×C22⋊C4×D4311yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—861no—
860C4—861no—
861C4—862no—
862C4—861no—
863C4—861no—
864C4—861no—
865C4—861no—
866C4—1721no—
867C4—1721no—
868C4#131×D4311yescharacteristic
869C4#1458366411yescharacteristic
870C4#1458370511yescharacteristic
871C4#1458371211yescharacteristic
872C2—41no—
873C2—862no—
874C2—3441no—
875C2—1721no—
876C2#1914304311yescharacteristic
877C2#1914312311yescharacteristic
878C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1481C2
socleC22×C43C22×C22⋊C4
prime radical#19148213C2
cosocleC42×C43C24
hypercenter#1481D43
hypocenterC43#17524
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
2. #19143717C2semidirect
3. #19143234C2semidirect
4. #19133068C2semidirect
5. #19133059C2semidirect
6. #19133054C2semidirect
7. #19133040C2semidirect
8. #19133030C2semidirect
9. #19133022C2semidirect
10. #19133007C2semidirect
11. #19133002C2semidirect
12. #19132988C2semidirect
13. #19132980C2semidirect
14. Q8⋊C8×D43C2semidirect
15. C43×#1481C2semidirect
444. #1481D43semidirect
514. C43#17524semidirect

Maximal subgroups

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

subgroupindex
#191482132
#191437172
#191432342
#191330682
#191330592
#191330542
#191330402
#191330302
#191330222
#191330072
#191330022
#191329882
#191329802
Q8⋊C8×D432
C43×#14812
#1752443