Finite Group Databasebeta

← #25063569

Subgroups — #25063569

Order 11008.

1096 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148199C211yesmaximal, characteristic
2#19143722C211yesmaximal, characteristic, complemented
3C4×#13063333C211yesmaximal, characteristic, complemented
4#19133053C211yesmaximal, characteristic, complemented
5#19133052C211yesmaximal, characteristic, complemented
6#19133044C211yesmaximal, characteristic, complemented
7#19133036C211yesmaximal, characteristic, complemented
8#19133031C211yesmaximal, characteristic, complemented
9#19133010C211yesmaximal, characteristic, complemented
10#19133009C211yesmaximal, characteristic, complemented
11#19133005C211yesmaximal, characteristic, complemented
12#19132974C211yesmaximal, characteristic, complemented
13C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1490C211yesmaximal, characteristic, complemented
16C2×#13063333—21no—
17#14583632C411yescharacteristic
18#14583608C411yescharacteristic
19#14583604C411yescharacteristic
20#14583599C411yescharacteristic
21#14583598—21no—
22#14583597C411yescharacteristic
23#14583578—21no—
24#14583575—21no—
25#14583544C411yescharacteristic
26#14583543C411yescharacteristic
27#14583539—21no—
28D4×C22⋊D43C411yescharacteristic
29#14583446C2211yescharacteristic
30#14583433C2211yescharacteristic
31#14583431C2211yescharacteristic
32#14583429—21no—
33#14583410—21no—
34#14583408—21no—
35C4×#10621898C2211yescharacteristic
36C4×#10621900C2211yescharacteristic
37C2×C4×C22⋊D43—21no—
38C4×D4×D43C2211yescharacteristic
39#14583027—21no—
40#14582972—21no—
41#14582967—21no—
42(C22⋊D43)⋊C8—21no—
43#14582955C2211yescharacteristic, complemented
44#14582951C2211yescharacteristic, complemented
45#14582921C2211yescharacteristic, complemented
46C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
47C4⋊C8×D43C2211yescharacteristic, complemented
48#14582857—21no—
49#14582856—21no—
50#14582856—21no—
51C4×#10621872C2211yescharacteristic, complemented
52C4×#10621872C2211yescharacteristic, complemented
53C2×C4×C43⋊C8C2211yescharacteristic, complemented
54C4×C8×D43C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic, complemented
56#14582631C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58#14582629C2211yescharacteristic, complemented
59#14582629C2211yescharacteristic, complemented
60#14582628C2211yescharacteristic, complemented
61#14582628C2211yescharacteristic, complemented
62D4⋊(C43⋊C8)C2211yescharacteristic
63D4⋊(C43⋊C8)C2211yescharacteristic
64D4⋊(C43⋊C8)C2211yescharacteristic, complemented
65D4⋊(C43⋊C8)C2211yescharacteristic, complemented
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C2×C4×D4×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C4×M16×C43C2211yescharacteristic, complemented
71C43×D4⋊C8C2211yescharacteristic
72C43×D4⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic, complemented
74C43×D4⋊C8C2211yescharacteristic, complemented
75C2×#10621898—21no—
76C2×#10621898D411yescharacteristic
77C2×#10621900C2×C411yescharacteristic
78C22×C22⋊D43—21no—
79C2×D4×D43C2×C411yescharacteristic
80C22×C4×D43—21no—
81#13063333—28no—
82C2×#10621872—21no—
83C2×#10621872—21no—
84C2×#10621872—21no—
85C22×C43⋊C8—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89C2×C8×D43—21no—
90#13063324C2×C411yescharacteristic
91#13063321C2×C411yescharacteristic
92#13063320—21no—
93#13063319—21no—
94#13063318—21no—
95#13063318—21no—
96#13063317C2×C411yescharacteristic
97#13063316C2×C411yescharacteristic
98#13063315—21no—
99#13063313C2×C411yescharacteristic
100#13063312C2×C411yescharacteristic
101#13063311—21no—
102#13063311—21no—
103#13063310—21no—
104#13063309—21no—
105#13063308—21no—
106#13063308—21no—
107#13063308—21no—
108#13063307—21no—
109#13063307—21no—
110#13063306—21no—
111#13063305C2×C411yescharacteristic
112#13063304—21no—
113#13063304—21no—
114#13063304C2×C411yescharacteristic
115#13063303—21no—
116#13063302—21no—
117#13063302—21no—
118#13063300C2×C411yescharacteristic
119#13063299—21no—
120#13063299—21no—
121#13063299C2×C411yescharacteristic
122#13063298—21no—
123#13063298—21no—
124#13063297—21no—
125#13063297—21no—
126#13063296C2×C411yescharacteristic
127#13063296C2×C411yescharacteristic
128#13063295—21no—
129#13063294—21no—
130#13063294—21no—
131#13063293—21no—
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86D411yescharacteristic
134C4×Dic86C2311yescharacteristic
135#13063290C2×C411yescharacteristic
136C4×D172C2×C411yescharacteristic
137C4×D172D411yescharacteristic
138C4×D172C2311yescharacteristic
139D4×Dic43C2×C411yescharacteristic
140D4×Dic43C2×C411yescharacteristic
141#13063287C2×C411yescharacteristic
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43C2×C411yescharacteristic
152C4×C22⋊D43C2×C411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155(C22⋊D43)⋊C4—21no—
156(C22⋊D43)⋊C4—21no—
157#13063284—21no—
158#13063284D411yescharacteristic
159#13063283C2×C411yescharacteristic
160#13063282—21no—
161#13063282D411yescharacteristic
162#13063282D411yescharacteristic
163#13063281—21no—
164C2×Dic43⋊C4—21no—
165C4⋊C4×D43C2×C411yescharacteristic
166C2×C22⋊Dic43—21no—
167C2×(C2×D43)⋊C4—21no—
168C22⋊C4×D43—21no—
169C2×C4×Dic43—21no—
170C42×D43C2311yescharacteristic
171C42×D43C2311yescharacteristic
172C4⋊(C43⋊C8)—21no—
173C4⋊(C43⋊C8)C2311yescharacteristic
174C4⋊(C43⋊C8)C2311yescharacteristic
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063235—21no—
180#13063235—21no—
181#13063235—21no—
182C4×C43⋊C8—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C8×Dic43—21no—
188C22×D4×C43C2×C411yescharacteristic
189C23×C4×C43—21no—
190C2×M16×C43—21no—
191C4×D4×C43—21no—
192C4×D4×C43—21no—
193C4×D4×C43C2×C411yescharacteristic
194C4×D4×C43C2×C411yescharacteristic
195C4×D4×C43C2311yescharacteristic
196C4×D4×C43C2311yescharacteristic
197C2×C4⋊C4×C43C2×C411yescharacteristic
198C2×C22⋊C4×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C4⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43—21no—
203#97×C43—21no—
204#97×C43—21no—
205C4×C8×C43C2311yescharacteristic
206C4×C8×C43C2311yescharacteristic
207C24×C43—21no—
208C23×D43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—22no—
211C2×D4×C43—41no—
212C2×D4×C43C22×C411yescharacteristic
213C2×D4×C43C22×C411yescharacteristic
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—81no—
220C22×C4×C43—81no—
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—44no—
232C2×C22⋊D43C22⋊C411yescharacteristic
233C2×C22⋊D43C22⋊C411yescharacteristic
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237#10621900—22no—
238#10621900—41no—
239D4×D43—22no—
240D4×D43—41no—
241#10621898—24no—
242#10621898—81no—
243#10621898—81no—
244C2×D172—21no—
245C2×D172C22⋊C411yescharacteristic
246C2×D172C22×C411yescharacteristic
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—81no—
251C2×C4×D43—81no—
252C2×C4×D43C22×C411yescharacteristic
253C2×C4×D43C22×C411yescharacteristic
254C2×C4×D43C2×D411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×Dic86—21no—
259C2×Dic86C22⋊C411yescharacteristic
260C2×Dic86C22×C411yescharacteristic
261M16×C43—24no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43C22×C411yescharacteristic
268C4⋊C4×C43C22×C411yescharacteristic
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C42×C43C22×C411yescharacteristic
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—
283C22⋊Dic43—21no—
284C22⋊Dic43C22⋊C411yescharacteristic
285C22⋊Dic43C22⋊C411yescharacteristic
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)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43C22⋊C411yescharacteristic
301C4⋊Dic43C22⋊C411yescharacteristic
302C4⋊Dic43C22×C411yescharacteristic
303C4⋊Dic43C22×C411yescharacteristic
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⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43C22×C411yescharacteristic
320C4×Dic43C22×C411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C4×Dic43C2×D411yescharacteristic
325C2×C43⋊C8—24no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—81no—
331#10621872—24no—
332#10621872—24no—
333#10621872—81no—
334C8×D43—24no—
335C8×D43—24no—
336C8×D43—81no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—42no—
340C23×C43—42no—
341C23×C43—81no—
342C23×C43C2×C22⋊C411yescharacteristic
343C22×D43—21no—
344C22×D43—42no—
345C22×D43—42no—
346C22×D43—81no—
347C22×D43C2×C22⋊C411yescharacteristic
348C22×D43C2×C22⋊C411yescharacteristic
349D4×C43—21no—
350D4×C43—21no—
351D4×C43—21no—
352D4×C43—42no—
353D4×C43#13112yescomplemented
354C2×C4×C43—22no—
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×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—81no—
366C2×C4×C43—81no—
367C2×C4×C43—81no—
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C2×C22⋊C411yescharacteristic
370C2×C4×C43C2×C22⋊C411yescharacteristic
371C2×C4×C43C23×C411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C22⋊D43—22no—
375C22⋊D43—42no—
376C22⋊D43—42no—
377C22⋊D43—42no—
378C22⋊D43—42no—
379C22⋊D43—42no—
380C22⋊D43—81no—
381C22⋊D43—81no—
382C22⋊D43#10414yes—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—42no—
387C2×Dic43—42no—
388C2×Dic43—81no—
389C2×Dic43C2×C22⋊C411yescharacteristic
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393C2×Dic43C2×C22⋊C411yescharacteristic
394C2×Dic43C2×C22⋊C411yescharacteristic
395D172—22no—
396D172—21no—
397D172—21no—
398D172—81no—
399C4×D43—22no—
400C4×D43—21no—
401C4×D43—21no—
402C4×D43—21no—
403C4×D43—21no—
404C4×D43—21no—
405C4×D43—21no—
406C4×D43—21no—
407C4×D43—21no—
408C4×D43—22no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—81no—
412C4×D43—81no—
413Dic86—22no—
414Dic86—21no—
415Dic86—21no—
416Dic86—81no—
417C8×C43—22no—
418C8×C43—22no—
419C8×C43—41no—
420C8×C43—41no—
421C43⋊C8—22no—
422C43⋊C8—22no—
423C43⋊C8—41no—
424C43⋊C8—41no—
425#17517—431nomaximal, Sylow
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—22no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—84no—
435C22×C43C2×#10412yes—
436C22×C43C22×C22⋊C411yescharacteristic
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—21no—
440C2×D43—21no—
441C2×D43—21no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—41no—
445C2×D43—84no—
446C2×D43C2×#10412yes—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—41no—
452C4×C43—41no—
453C4×C43C2×#13111yescharacteristic
454C4×C43#56811yescharacteristic
455C4×C43#57611yescharacteristic
456C4×C43#57711yescharacteristic
457Dic43—21no—
458Dic43—21no—
459Dic43—21no—
460Dic43—21no—
461Dic43—21no—
462Dic43—41no—
463Dic43—41no—
464Dic43—41no—
465Dic43C2×#10412yes—
466#3481—431no—
467#2990—431no—
468C4×#131—431no—
469#1494—431no—
470#1494—431no—
471#1492—431no—
472#1490—431no—
473#1490D4311yescharacteristic, complemented
474#1489—431no—
475#1484—431no—
476#1483—431no—
477#1483—431no—
478#1476—431no—
479C2×D4⋊C8—431no—
480C2×D4⋊C8—431no—
481C2×C43—22no—
482C2×C43—42no—
483C2×C43—81no—
484C2×C43#288011yescharacteristic
485C2×C43#289711yescharacteristic
486C2×C43C22×#10411yescharacteristic
487D43—22no—
488D43—41no—
489D43—81no—
490C2×#131—861no—
491#559—431no—
492#554—431no—
493#554—431no—
494#553—431no—
495#553—431no—
496#553—861no—
497#551—861no—
498#551—861no—
499#546—431no—
500#546—431no—
501#546—861no—
502D42—431no—
503#532—431no—
504#529—431no—
505#529—431no—
506#529—861no—
507#525—861no—
508#525—861no—
509C4×#41—431no—
510C4×#41—431no—
511C2×C4×D4—431no—
512C2×C4×D4—861no—
513C2×C4×D4C2×D4311yescharacteristic
514#446—861no—
515#435—861no—
516#435—861no—
517C8×D4—861no—
518#432—431no—
519#432C2×D4311yescharacteristic, complemented
520#431—431no—
521#423—431no—
522C2×C4⋊C8—431no—
523C2×C4⋊C8—431no—
524#405—861no—
525#405—861no—
526#405—861no—
527C4×M16—431no—
528C4×M16—431no—
529C4×M16C2×D4311yescharacteristic, complemented
530C2×C4×C8—431no—
531C2×C4×C8—431no—
532C2×C4×C8—431no—
533Q8⋊C8—431no—
534Q8⋊C8—431no—
535Q8⋊C8—431no—
536Q8⋊C8—431no—
537D4⋊C8—431no—
538D4⋊C8—431no—
539D4⋊C8—431no—
540D4⋊C8—431no—
541D4⋊C8—431no—
542D4⋊C8—431no—
543D4⋊C8—431no—
544D4⋊C8—431no—
545D4⋊C8C2×D4311yescharacteristic
546D4⋊C8C2×D4311yescharacteristic
547D4⋊C8C2×D4311yescharacteristic, complemented
548D4⋊C8C2×D4311yescharacteristic, complemented
549C43#1751711yescharacteristic, complemented, Sylow
550C2×#41—431no—
551C2×#41—431no—
552C2×#41—861no—
553C22×D4—431no—
554C22×D4—861no—
555C22×D4C4×D4311yescharacteristic
556C23×C4—21no—
557C23×C4—861no—
558#131—868no—
559C2×M16—21no—
560C2×M16—861no—
561C2×M16—861no—
562C2×M16—861no—
563C22×C8—861no—
564C22×C8—861no—
565C22×C8—861no—
566C22×C8—861no—
567C22×C8—861no—
568C4⋊Q8—431no—
569#127—431no—
570#126—861no—
571#126—861no—
572#126—861no—
573#126—861no—
574#125—431no—
575#125—431no—
576#125—861no—
577#124—431no—
578#124—431no—
579#124—861no—
580#124—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586#123—861no—
587#123—861no—
588#123—861no—
589C22⋊Q8—431no—
590C22⋊Q8—431no—
591C22⋊Q8—861no—
592C22⋊Q8—861no—
593C22⋊Q8—861no—
594C22⋊Q8—861no—
595C22⋊Q8—861no—
596#121—431no—
597#121—431no—
598#121—431no—
599#121—431no—
600#121—861no—
601#121—861no—
602#121—861no—
603#121—861no—
604#121—861no—
605#121—861no—
606#120—861no—
607#120—861no—
608#120—861no—
609#120—861no—
610C4×Q8—431no—
611C4×Q8—431no—
612C4×Q8—431no—
613C4×Q8—431no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—431no—
617C4×D4—431no—
618C4×D4—431no—
619C4×D4—431no—
620C4×D4—431no—
621C4×D4—431no—
622C4×D4—431no—
623C4×D4—431no—
624C4×D4—431no—
625C4×D4—431no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4—861no—
631C4×D4—861no—
632C4×D4—861no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4—861no—
636C4×D4—861no—
637C4×D4C4×D4311yescharacteristic
638C4×D4C4×D4311yescharacteristic
639C4×D4C22×D4311yescharacteristic
640C4×D4C22×D4311yescharacteristic
641#117—431no—
642#117—431no—
643#117—431no—
644#117—431no—
645#117—861no—
646#117—861no—
647#117—861no—
648C2×C4⋊C4—431no—
649C2×C4⋊C4—861no—
650C2×C4⋊C4C4×D4311yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—861no—
653C2×C22⋊C4—861no—
654C2×C22⋊C4—861no—
655C2×C42—431no—
656C2×C42—431no—
657C2×C42—861no—
658C2×C42C22×D4311yescharacteristic
659C4⋊C8—431no—
660C4⋊C8—431no—
661C4⋊C8—861no—
662C4⋊C8—861no—
663C4⋊C8—861no—
664C4⋊C8C22×D4311yescharacteristic
665C4⋊C8C22×D4311yescharacteristic
666C22⋊C8—21no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669#97—21no—
670#97—21no—
671#97—861no—
672#97—861no—
673#97—861no—
674C4×C8—431no—
675C4×C8—431no—
676C4×C8—861no—
677C4×C8—861no—
678C4×C8—861no—
679C4×C8—861no—
680C4×C8C22×D4311yescharacteristic
681C4×C8C22×D4311yescharacteristic
682C24—21no—
683C24—861no—
684#41—864no—
685#41—862no—
686#41—3441no—
687#41—3441no—
688#41—1721no—
689C2×Q8—431no—
690C2×Q8—431no—
691C2×Q8—861no—
692C2×D4—22no—
693C2×D4—21no—
694C2×D4—41no—
695C2×D4—431no—
696C2×D4—431no—
697C2×D4—431no—
698C2×D4—431no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—862no—
704C2×D4—861no—
705C2×D4—861no—
706C2×D4—861no—
707C2×D4—861no—
708C2×D4—1721no—
709C2×D4—1724no—
710C2×D4C2×C4×D4311yescharacteristic
711C2×D4C2×C4×D4311yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—3441no—
732C22×C4—3441no—
733C22×C4C2×C4×D4311yescharacteristic
734C22×C4D4×D4311yescharacteristic
735C22×C4D4×D4311yescharacteristic
736M16—24no—
737M16—864no—
738M16—864no—
739M16—3441no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—864no—
745C2×C8—864no—
746C2×C8—864no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—861no—
750C2×C8—861no—
751C2×C8—3441no—
752C2×C8—3441no—
753C4⋊C4—21no—
754C4⋊C4—431no—
755C4⋊C4—431no—
756C4⋊C4—431no—
757C4⋊C4—431no—
758C4⋊C4—431no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—431no—
762C4⋊C4—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4C2×C4×D4311yescharacteristic
773C4⋊C4C2×C4×D4311yescharacteristic
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—431no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—431no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C42—431no—
800C42—431no—
801C42—431no—
802C42—431no—
803C42—431no—
804C42—431no—
805C42—861no—
806C42—861no—
807C42—861no—
808C42C2×C4×D4311yescharacteristic
809C42D4×D4311yescharacteristic
810C42D4×D4311yescharacteristic
811C42C23×D4311yescharacteristic
812C23—21no—
813C23—21no—
814C23—42no—
815C23—42no—
816C23—81no—
817C23—431no—
818C23—431no—
819C23—861no—
820C23—3441no—
821C23—1722no—
822C23—1722no—
823C23C22⋊C4×D4311yescharacteristic
824Q8—862no—
825Q8—861no—
826Q8—861no—
827Q8—3441no—
828D4—21no—
829D4—21no—
830D4—21no—
831D4—42no—
832D4—434no—
833D4—862no—
834D4—862no—
835D4—861no—
836D4—861no—
837D4—3441no—
838D4—3441no—
839D4—3441no—
840D4—1722no—
841D4—1722no—
842D4—1722no—
843D4—1722no—
844D4—1722no—
845D4#1306333312yescomplemented
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—431no—
861C2×C4—431no—
862C2×C4—431no—
863C2×C4—431no—
864C2×C4—431no—
865C2×C4—431no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—861no—
869C2×C4—861no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
879C2×C4—3441no—
880C2×C4—3441no—
881C2×C4—3441no—
882C2×C4—1722no—
883C2×C4—1722no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4C22⋊C4×D4311yescharacteristic
887C2×C4C22⋊C4×D4311yescharacteristic
888C2×C4C22⋊C4×D4311yescharacteristic
889C2×C4C22×C4×D4311yescharacteristic
890C2×C4C2×D4×D4311yescharacteristic
891C2×C4C2×D4×D4311yescharacteristic
892C8—22no—
893C8—22no—
894C8—41no—
895C8—41no—
896C8—862no—
897C8—862no—
898C8—1721no—
899C8—1721no—
900C22—21no—
901C22—21no—
902C22—22no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—84no—
909C22—432no—
910C22—861no—
911C22—861no—
912C22—861no—
913C22—861no—
914C22—861no—
915C22—3444no—
916C22—1721no—
917C22—1721no—
918C22—1721no—
919C22#104×D4312yes—
920C22C2×C22⋊C4×D4311yescharacteristic
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—41no—
926C4—41no—
927C4—432no—
928C4—861no—
929C4—861no—
930C4—861no—
931C4—861no—
932C4—861no—
933C4—1721no—
934C4—1721no—
935C4—1721no—
936C4C2×#1306333311yescharacteristic
937C4#1458366511yescharacteristic
938C4#1458370311yescharacteristic
939C4#1458370911yescharacteristic
940C2—22no—
941C2—42no—
942C2—81no—
943C2—862no—
944C2—3441no—
945C2—1721no—
946C2#1914304511yescharacteristic
947C2#1914312011yescharacteristic
948C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1490C2
socleC22×C43C22×C22⋊C4
prime radical#19148199C2
cosocleC42×C43C24
hypercenter#1490D43
hypocenterC43#17517
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #19143722C2semidirect
3. C4×#13063333C2semidirect
4. #19133053C2semidirect
5. #19133052C2semidirect
6. #19133044C2semidirect
7. #19133036C2semidirect
8. #19133031C2semidirect
9. #19133010C2semidirect
10. #19133009C2semidirect
11. #19133005C2semidirect
12. #19132974C2semidirect
13. C2×D4⋊(C43⋊C8)C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1490C2semidirect
43. #14582955C22semidirect
44. #14582951C22semidirect
45. #14582921C22semidirect
46. C2×C4⋊(C43⋊C8)C22semidirect
47. C4⋊C8×D43C22semidirect
51. C4×#10621872C22semidirect
52. C4×#10621872C22semidirect
53. C2×C4×C43⋊C8C22semidirect
54. C4×C8×D43C22semidirect
55. C4×C8×D43C22semidirect
56. #14582631C22semidirect
57. #14582631C22semidirect
58. #14582629C22semidirect
59. #14582629C22semidirect
60. #14582628C22semidirect
61. #14582628C22semidirect
64. D4⋊(C43⋊C8)C22semidirect
65. D4⋊(C43⋊C8)C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#432C22semidirect
70. C4×M16×C43C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
353. D4×C43#131semidirect
473. #1490D43semidirect
519. #432C2×D43semidirect
529. C4×M16C2×D43semidirect
547. D4⋊C8C2×D43semidirect
548. D4⋊C8C2×D43semidirect
549. C43#17517semidirect
845. D4#13063333semidirect

Maximal subgroups

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

subgroupindex
#191481992
#191437222
C4×#130633332
#191330532
#191330522
#191330442
#191330362
#191330312
#191330102
#191330092
#191330052
#191329742
C2×D4⋊(C43⋊C8)2
D4⋊C8×D432
C43×#14902
#1751743