Finite Group Databasebeta

← #25063602

Subgroups — #25063602

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148205C211yesmaximal, characteristic
2#19143239C211yesmaximal, characteristic, complemented
3#19133063C211yesmaximal, characteristic, complemented
4#19133058C211yesmaximal, characteristic, complemented
5#19133053C211yesmaximal, characteristic, complemented
6#19133037C211yesmaximal, characteristic, complemented
7#19133027C211yesmaximal, characteristic, complemented
8#19133019C211yesmaximal, characteristic, complemented
9#19133006C211yesmaximal, characteristic, complemented
10#19133001C211yesmaximal, characteristic, complemented
11#19132993C211yesmaximal, characteristic, complemented
12#19132985C211yesmaximal, characteristic, complemented
13#19132980C211yesmaximal, characteristic, complemented
14C2×#14582626C211yesmaximal, characteristic, complemented
15C43×#2990C211yesmaximal, characteristic, complemented
16#14583634C411yescharacteristic
17#14583609C411yescharacteristic
18#14583606C411yescharacteristic
19#14583595C411yescharacteristic
20#14583595C411yescharacteristic
21#14583593—21no—
22#14583573—21no—
23#14583573—21no—
24#14583545C411yescharacteristic
25#14583545C411yescharacteristic
26#14583537—21no—
27D4×D172C411yescharacteristic
28#14583449C2211yescharacteristic
29#14583436—21no—
30#14583433C2211yescharacteristic
31#14583433C2211yescharacteristic
32#14583408—21no—
33#14583408—21no—
34C4×#10621898C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C4×D4×D43—21no—
38#14582960—21no—
39#14582960—21no—
40#14582952C2211yescharacteristic, complemented
41#14582952C2211yescharacteristic, complemented
42#14582952C2211yescharacteristic, complemented
43#14582952C2211yescharacteristic, complemented
44#14582926—21no—
45#14582866—21no—
46C4×#10621877C2211yescharacteristic, complemented
47C2×C4×C43⋊C8C2211yescharacteristic, complemented
48#14582629C2211yescharacteristic, complemented
49#14582629C2211yescharacteristic, complemented
50#14582629C2211yescharacteristic, complemented
51#14582629C2211yescharacteristic, complemented
52#14582626C2211yescharacteristic
53#14582626C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582626C2211yescharacteristic
56#14582626C2211yescharacteristic, complemented
57#14582626C2211yescharacteristic, complemented
58#14582626C2211yescharacteristic, complemented
59#14582626C2211yescharacteristic, complemented
60#14582626C2211yescharacteristic, complemented
61#14582626C2211yescharacteristic, complemented
62#14582626C2211yescharacteristic, complemented
63#14582626C2211yescharacteristic, complemented
64C4×#41×C43C2211yescharacteristic
65C43×#446—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#432C2211yescharacteristic, complemented
70C43×#432C2211yescharacteristic, complemented
71C43×#431C2211yescharacteristic, complemented
72C43×#423C2211yescharacteristic, complemented
73C2×C4⋊C8×C43C2211yescharacteristic, complemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#10621898—21no—
76C2×#10621898C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×D172C2×C411yescharacteristic
79C2×D4×D43—21no—
80C22×C4×D43—21no—
81C22×C4×D43—21no—
82C2×#10621877—21no—
83C22×C43⋊C8—21no—
84#13063325C2×C411yescharacteristic
85#13063322C2×C411yescharacteristic
86#13063320—21no—
87#13063320—21no—
88#13063319—21no—
89#13063319—21no—
90#13063317C2×C411yescharacteristic
91#13063317C2×C411yescharacteristic
92#13063316—21no—
93#13063314—21no—
94#13063313—21no—
95#13063313C2×C411yescharacteristic
96#13063313C2×C411yescharacteristic
97#13063310—21no—
98#13063310—21no—
99#13063310—21no—
100#13063310—21no—
101#13063308—21no—
102#13063308—21no—
103#13063307—21no—
104#13063307—21no—
105#13063304C2×C411yescharacteristic
106#13063304C2×C411yescharacteristic
107#13063303—21no—
108#13063303—21no—
109#13063302—21no—
110#13063302—21no—
111#13063301—21no—
112#13063300—21no—
113#13063299—21no—
114#13063299C2×C411yescharacteristic
115#13063299C2×C411yescharacteristic
116#13063299C2×C411yescharacteristic
117#13063299C2×C411yescharacteristic
118#13063298—21no—
119#13063298—21no—
120#13063297—21no—
121#13063297—21no—
122#13063295—21no—
123#13063295—21no—
124#13063293—21no—
125#13063293—21no—
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86C2311yescharacteristic
128C4×D172—21no—
129C4×D172—21no—
130C4×D172—21no—
131C4×D172—21no—
132C4×D172—21no—
133C4×D172C2×C411yescharacteristic
134C4×D172C2×C411yescharacteristic
135C4×D172C2×C411yescharacteristic
136C4×D172C2×C411yescharacteristic
137C4×D172C2×C411yescharacteristic
138C4×D172C2311yescharacteristic
139C4×D172C2311yescharacteristic
140C4×D172C2311yescharacteristic
141D4×Dic43—21no—
142#13063287—21no—
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#13063284C2×C411yescharacteristic
150#13063282—21no—
151#13063282—21no—
152#13063282—21no—
153C2×C4⋊Dic43C2×C411yescharacteristic
154C2×C4⋊Dic43C2×C411yescharacteristic
155C4⋊C4×D43—21no—
156C2×(C2×D43)⋊C4—21no—
157C2×(C2×D43)⋊C4—21no—
158C22⋊C4×D43—21no—
159C22⋊C4×D43—21no—
160C42×D43—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)—21no—
168C22⋊(C43⋊C8)—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—
178C22×C8×C43—21no—
179C4×Q8×C43C2×C411yescharacteristic
180C4×Q8×C43D411yescharacteristic
181C4×D4×C43C2×C411yescharacteristic
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43C2×C411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187#117×C43D411yescharacteristic
188#117×C43D411yescharacteristic
189#117×C43D411yescharacteristic
190C2×C42×C43C2311yescharacteristic
191C2×C42×C43C2311yescharacteristic
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43—21no—
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C4⋊C8×C43C2311yescharacteristic
197C4⋊C8×C43C2311yescharacteristic
198C4⋊C8×C43C2311yescharacteristic
199C4⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203#97×C43—21no—
204#97×C43—21no—
205C4×C8×C43—21no—
206C23×D43—21no—
207C23×D43—21no—
208#41×C43—42no—
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—
226C2×C22⋊D43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229D4×D43—44no—
230#10621898—22no—
231#10621898—41no—
232#10621898—81no—
233#10621898—81no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—41no—
241C2×D172—41no—
242C2×D172C22×C411yescharacteristic
243C2×D172C22×C411yescharacteristic
244C2×D172C22×C411yescharacteristic
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—81no—
255C2×C4×D43—81no—
256C2×C4×D43—81no—
257C2×C4×D43—81no—
258C2×Dic86—21no—
259C2×Dic86C22×C411yescharacteristic
260M16×C43—81no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—81no—
266C2×C8×C43—81no—
267C4⋊C4×C43C22⋊C411yescharacteristic
268C4⋊C4×C43C22⋊C411yescharacteristic
269C4⋊C4×C43C22⋊C411yescharacteristic
270C4⋊C4×C43C22⋊C411yescharacteristic
271C4⋊C4×C43C22⋊C411yescharacteristic
272C4⋊C4×C43C22⋊C411yescharacteristic
273C22⋊C4×C43C22⋊C411yescharacteristic
274C22⋊C4×C43C22⋊C411yescharacteristic
275C22⋊C4×C43C22⋊C411yescharacteristic
276C22⋊C4×C43C22⋊C411yescharacteristic
277C22⋊C4×C43C22⋊C411yescharacteristic
278C22⋊C4×C43C22⋊C411yescharacteristic
279C42×C43C22×C411yescharacteristic
280C42×C43C22×C411yescharacteristic
281C42×C43C22×C411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C42×C43C2×D411yescharacteristic
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C42×C43C2411yescharacteristic
289C22⋊Dic43—21no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308C4⋊Dic43—21no—
309C4⋊Dic43—21no—
310C4⋊Dic43—21no—
311C4⋊Dic43C22×C411yescharacteristic
312C4⋊Dic43C22×C411yescharacteristic
313C4⋊Dic43C22×C411yescharacteristic
314C4⋊Dic43C22×C411yescharacteristic
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326#10621877—42no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—42no—
332C23×C43C2×C22⋊C411yescharacteristic
333C23×C43C2×C22⋊C411yescharacteristic
334C23×C43C2×C22⋊C411yescharacteristic
335C22×D43—21no—
336C22×D43—21no—
337C22×D43—21no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—42no—
341C22×D43—42no—
342C22×D43—81no—
343C22×D43—81no—
344Q8×C43—41no—
345D4×C43—22no—
346D4×C43—22no—
347D4×C43—41no—
348C2×C4×C43—22no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
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×C43C2×C22⋊C411yescharacteristic
370C2×C4×C43C2×C22⋊C411yescharacteristic
371C2×C4×C43C2×C22⋊C411yescharacteristic
372C2×C4×C43C23×C411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C22×D411yescharacteristic
375C22⋊D43—42no—
376C22⋊D43—42no—
377C22⋊D43—42no—
378C22⋊D43—81no—
379C22⋊D43—81no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—81no—
386C2×Dic43—81no—
387D172—21no—
388D172—21no—
389D172—21no—
390D172—21no—
391D172—21no—
392D172—42no—
393D172—42no—
394D172—42no—
395D172—81no—
396D172#13112yes—
397C4×D43—42no—
398C4×D43—42no—
399C4×D43—41no—
400C4×D43—41no—
401C4×D43—41no—
402C4×D43—41no—
403C4×D43—41no—
404C4×D43—41no—
405C4×D43—81no—
406C4×D43—81no—
407C4×D43—81no—
408C4×D43—81no—
409Dic86—21no—
410Dic86—21no—
411Dic86—81no—
412C8×C43—41no—
413C8×C43—41no—
414C8×C43—41no—
415C8×C43—41no—
416C43⋊C8—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17521—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—21no—
429C22×C43#42112yes—
430C22×C43C22×C22⋊C411yescharacteristic
431C2×D43—22no—
432C2×D43—41no—
433C2×D43—41no—
434C2×D43—41no—
435C2×D43—41no—
436C2×D43—41no—
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—41no—
440C2×D43—84no—
441C2×D43—84no—
442C4×C43—21no—
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—21no—
452C4×C43C2×#13111yescharacteristic
453C4×C43#56811yescharacteristic
454C4×C43#57611yescharacteristic
455C4×C43#57711yescharacteristic
456Dic43—41no—
457Dic43—41no—
458Dic43—41no—
459Dic43—41no—
460Dic43—41no—
461#3481—431no—
462#2990D4311yescharacteristic, complemented
463#2922—431no—
464#1496—431no—
465#1495—431no—
466#1494—431no—
467#1490—431no—
468#1488—431no—
469#1486—431no—
470#1483—431no—
471#1482—431no—
472#1480—431no—
473#1478—431no—
474#1477—431no—
475C2×D4⋊C8—431no—
476C2×C43—22no—
477C2×C43—41no—
478C2×C43—41no—
479C2×C43#288011yescharacteristic
480C2×C43#289711yescharacteristic
481C2×C43C2×#42111yescharacteristic
482D43—42no—
483D43—81no—
484D43—81no—
485#559—431no—
486#554—431no—
487#554—431no—
488#553—431no—
489#553—431no—
490#553—861no—
491#551—861no—
492#551—861no—
493#546—431no—
494#546—431no—
495#546—861no—
496D42—431no—
497#532—431no—
498#529—431no—
499#529—431no—
500#529—861no—
501#525—861no—
502#525—861no—
503C4×#41—431no—
504C4×#41C2×D4311yescharacteristic
505C2×C4×D4—431no—
506C2×C4×D4—431no—
507C2×C4×D4—861no—
508#446—21no—
509#435—21no—
510#435—21no—
511C8×D4—21no—
512#433—861no—
513#433—861no—
514#432C2×D4311yescharacteristic, complemented
515#432C2×D4311yescharacteristic, complemented
516#431—431no—
517#431—431no—
518#431—431no—
519#431—431no—
520#431C2×D4311yescharacteristic, complemented
521#424—861no—
522#423C2×D4311yescharacteristic, complemented
523C2×C4⋊C8C2×D4311yescharacteristic, complemented
524C2×C4⋊C8C2×D4311yescharacteristic, complemented
525#408—861no—
526C4×M16—431no—
527C2×C4×C8—431no—
528Q8⋊C8—431no—
529Q8⋊C8—431no—
530Q8⋊C8—431no—
531Q8⋊C8—431no—
532D4⋊C8—431no—
533D4⋊C8—431no—
534D4⋊C8—431no—
535D4⋊C8—431no—
536D4⋊C8—431no—
537D4⋊C8—431no—
538D4⋊C8—431no—
539D4⋊C8—431no—
540D4⋊C8—431no—
541D4⋊C8—431no—
542D4⋊C8—431no—
543D4⋊C8—431no—
544C43#1752111yescharacteristic, complemented, Sylow
545C2×#41—431no—
546C2×#41—861no—
547C2×#41D17211yescharacteristic
548C22×D4—431no—
549C22×D4—431no—
550C22×D4—861no—
551C23×C4—861no—
552C23×C4—861no—
553C2×M16—21no—
554C2×M16—861no—
555C22×C8—21no—
556C22×C8—21no—
557C22×C8—861no—
558C4⋊Q8—431no—
559#127—431no—
560#126—861no—
561#126—861no—
562#126—861no—
563#126—861no—
564#125—431no—
565#125—431no—
566#125—861no—
567#124—431no—
568#124—431no—
569#124—861no—
570#124—861no—
571#123—861no—
572#123—861no—
573#123—861no—
574#123—861no—
575#123—861no—
576#123—861no—
577#123—861no—
578#123—861no—
579C22⋊Q8—431no—
580C22⋊Q8—431no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C22⋊Q8—861no—
584C22⋊Q8—861no—
585C22⋊Q8—861no—
586#121—431no—
587#121—431no—
588#121—431no—
589#121—431no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121—861no—
594#121—861no—
595#121—861no—
596#120—861no—
597#120—861no—
598#120—861no—
599#120—861no—
600C4×Q8—431no—
601C4×Q8—431no—
602C4×Q8C4×D4311yescharacteristic
603C4×Q8C22⋊D4311yescharacteristic
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—431no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4C4×D4311yescharacteristic
626C4×D4C4×D4311yescharacteristic
627C4×D4C4×D4311yescharacteristic
628C4×D4C22⋊D4311yescharacteristic
629C4×D4C22⋊D4311yescharacteristic
630C4×D4C22⋊D4311yescharacteristic
631#117—431no—
632#117—861no—
633#117—861no—
634#117—861no—
635#117D17211yescharacteristic
636#117D17211yescharacteristic
637#117D17211yescharacteristic
638C2×C4⋊C4—431no—
639C2×C4⋊C4—431no—
640C2×C4⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C22⋊C4—861no—
644C2×C22⋊C4—861no—
645C2×C42—861no—
646C2×C42C22×D4311yescharacteristic
647C2×C42C22×D4311yescharacteristic
648C2×C42C22×D4311yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—861no—
653C4⋊C8—861no—
654C4⋊C8—861no—
655C4⋊C8—861no—
656C4⋊C8C22×D4311yescharacteristic
657C4⋊C8C22×D4311yescharacteristic
658C4⋊C8C22×D4311yescharacteristic
659C4⋊C8C22×D4311yescharacteristic
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—861no—
664C22⋊C8—861no—
665C22⋊C8—861no—
666C22⋊C8—861no—
667#97—21no—
668#97—21no—
669#97—861no—
670C4×C8—21no—
671C4×C8—431no—
672C4×C8—431no—
673C4×C8—431no—
674C4×C8—431no—
675C4×C8—861no—
676C24—861no—
677C24—861no—
678#41—42no—
679#41—862no—
680#41—3441no—
681#41—3441no—
682#41—1721no—
683C2×Q8—431no—
684C2×Q8—861no—
685C2×Q8(C2×D43)⋊C411yescharacteristic
686C2×D4—431no—
687C2×D4—431no—
688C2×D4—431no—
689C2×D4—862no—
690C2×D4—862no—
691C2×D4—861no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—1721no—
701C2×D4—1721no—
702C2×D4—1724no—
703C2×D4(C2×D43)⋊C411yescharacteristic
704C2×D4(C2×D43)⋊C411yescharacteristic
705C2×D4(C2×D43)⋊C411yescharacteristic
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—3441no—
718C22×C4—3441no—
719C22×C4—3441no—
720C22×C4—3441no—
721C22×C4C2×C4×D4311yescharacteristic
722C22×C4C2×C4×D4311yescharacteristic
723C22×C4C2×C4×D4311yescharacteristic
724C22×C4C2×D17211yescharacteristic
725C22×C4C2×D17211yescharacteristic
726C22×C4C2×D17211yescharacteristic
727C22×C4C2×C22⋊D4311yescharacteristic
728C22×C4C2×C22⋊D4311yescharacteristic
729C22×C4C2×C22⋊D4311yescharacteristic
730M16—81no—
731M16—1722no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—81no—
737C2×C8—81no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—861no—
742C2×C8—1722no—
743C4⋊C4—431no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4(C2×D43)⋊C411yescharacteristic
759C4⋊C4(C2×D43)⋊C411yescharacteristic
760C4⋊C4(C2×D43)⋊C411yescharacteristic
761C4⋊C4(C2×D43)⋊C411yescharacteristic
762C4⋊C4(C2×D43)⋊C411yescharacteristic
763C4⋊C4(C2×D43)⋊C411yescharacteristic
764C22⋊C4—861no—
765C22⋊C4—861no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—861no—
769C22⋊C4—861no—
770C22⋊C4—861no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C22⋊C4—861no—
774C22⋊C4—861no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—861no—
778C22⋊C4—861no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C22⋊C4(C2×D43)⋊C411yescharacteristic
784C22⋊C4(C2×D43)⋊C411yescharacteristic
785C22⋊C4(C2×D43)⋊C411yescharacteristic
786C22⋊C4(C2×D43)⋊C411yescharacteristic
787C22⋊C4(C2×D43)⋊C411yescharacteristic
788C22⋊C4(C2×D43)⋊C411yescharacteristic
789C42—861no—
790C42—861no—
791C42—861no—
792C42C2×C4×D4311yescharacteristic
793C42C2×C4×D4311yescharacteristic
794C42C2×C4×D4311yescharacteristic
795C42C2×D17211yescharacteristic
796C42C2×D17211yescharacteristic
797C42C2×D17211yescharacteristic
798C42C2×C22⋊D4311yescharacteristic
799C42C2×C22⋊D4311yescharacteristic
800C42C2×C22⋊D4311yescharacteristic
801C42C23×D4311yescharacteristic
802C23—861no—
803C23—861no—
804C23—861no—
805C23—3441no—
806C23—3441no—
807C23—1722no—
808C23—1722no—
809C23—1722no—
810C23—1722no—
811C23C2×(C2×D43)⋊C411yescharacteristic
812C23C2×(C2×D43)⋊C411yescharacteristic
813C23C2×(C2×D43)⋊C411yescharacteristic
814Q8—41no—
815Q8—861no—
816Q8—861no—
817Q8—3441no—
818D4—22no—
819D4—22no—
820D4—41no—
821D4—432no—
822D4—861no—
823D4—861no—
824D4—861no—
825D4—861no—
826D4—861no—
827D4—3441no—
828D4—3441no—
829D4—3441no—
830D4—1722no—
831D4—1722no—
832D4—1722no—
833D4—1722no—
834D4—1722no—
835D4—1722no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—861no—
852C2×C4—861no—
853C2×C4—861no—
854C2×C4—861no—
855C2×C4—861no—
856C2×C4—3441no—
857C2×C4—3441no—
858C2×C4—3441no—
859C2×C4—3441no—
860C2×C4—3441no—
861C2×C4—3441no—
862C2×C4—1722no—
863C2×C4—1722no—
864C2×C4—1721no—
865C2×C4—1721no—
866C2×C4—1721no—
867C2×C4—1721no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4C2×(C2×D43)⋊C411yescharacteristic
871C2×C4C2×(C2×D43)⋊C411yescharacteristic
872C2×C4C2×(C2×D43)⋊C411yescharacteristic
873C2×C4C2×(C2×D43)⋊C411yescharacteristic
874C2×C4C2×(C2×D43)⋊C411yescharacteristic
875C2×C4C2×(C2×D43)⋊C411yescharacteristic
876C2×C4C2×(C2×D43)⋊C411yescharacteristic
877C2×C4C2×(C2×D43)⋊C411yescharacteristic
878C2×C4C2×(C2×D43)⋊C411yescharacteristic
879C2×C4C22×C4×D4311yescharacteristic
880C2×C4C22×C22⋊D4311yescharacteristic
881C2×C4C22×D17211yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—1721no—
887C8—1721no—
888C8—1721no—
889C8—1721no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—862no—
899C22—3444no—
900C22—3444no—
901C22—1721no—
902C22—1721no—
903C22—1721no—
904C22—1721no—
905C22—1721no—
906C22—1721no—
907C22—1721no—
908C22—1721no—
909C22#1458291512yes—
910C22C22×(C2×D43)⋊C411yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—1721no—
922C4—1721no—
923C4—1721no—
924C4—1721no—
925C4—1721no—
926C4#131×D4311yescharacteristic
927C4#1458366411yescharacteristic
928C4#1458370211yescharacteristic
929C4#1458370711yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—3441no—
934C2—3441no—
935C2—1722no—
936C2#1914304211yescharacteristic
937C2#1914311811yescharacteristic
938C2C2×#1458291511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2990C2
socleC22×C43C22×C22⋊C4
prime radical#19148205C2
cosocleC42×C43C24
hypercenter#2990D43
hypocenterC43#17521
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #19143239C2semidirect
3. #19133063C2semidirect
4. #19133058C2semidirect
5. #19133053C2semidirect
6. #19133037C2semidirect
7. #19133027C2semidirect
8. #19133019C2semidirect
9. #19133006C2semidirect
10. #19133001C2semidirect
11. #19132993C2semidirect
12. #19132985C2semidirect
13. #19132980C2semidirect
14. C2×#14582626C2semidirect
15. C43×#2990C2semidirect
40. #14582952C22semidirect
41. #14582952C22semidirect
42. #14582952C22semidirect
43. #14582952C22semidirect
46. C4×#10621877C22semidirect
47. C2×C4×C43⋊C8C22semidirect
48. #14582629C22semidirect
49. #14582629C22semidirect
50. #14582629C22semidirect
51. #14582629C22semidirect
56. #14582626C22semidirect
57. #14582626C22semidirect
58. #14582626C22semidirect
59. #14582626C22semidirect
60. #14582626C22semidirect
61. #14582626C22semidirect
62. #14582626C22semidirect
63. #14582626C22semidirect
69. C43×#432C22semidirect
70. C43×#432C22semidirect
71. C43×#431C22semidirect
72. C43×#423C22semidirect
73. C2×C4⋊C8×C43C22semidirect
74. C2×C4⋊C8×C43C22semidirect
462. #2990D43semidirect
514. #432C2×D43semidirect
515. #432C2×D43semidirect
520. #431C2×D43semidirect
522. #423C2×D43semidirect
523. C2×C4⋊C8C2×D43semidirect
524. C2×C4⋊C8C2×D43semidirect
544. C43#17521semidirect

Maximal subgroups

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

subgroupindex
#191482052
#191432392
#191330632
#191330582
#191330532
#191330372
#191330272
#191330192
#191330062
#191330012
#191329932
#191329852
#191329802
C2×#145826262
C43×#29902
#1752143