Finite Group Databasebeta

← #25064812

Subgroups — #25064812

Order 11008.

1152 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148382C211yesmaximal, characteristic
2#19143606C211yesmaximal, characteristic, complemented
3#19143604C211yesmaximal, characteristic, complemented
4#19133228C211yesmaximal, characteristic, complemented
5#19133218C211yesmaximal, characteristic, complemented
6#19133217C211yesmaximal, characteristic, complemented
7#19133206C211yesmaximal, characteristic, complemented
8#19133204C211yesmaximal, characteristic, complemented
9#19133204C211yesmaximal, characteristic, complemented
10#19133191C211yesmaximal, characteristic, complemented
11#19133191C211yesmaximal, characteristic, complemented
12#19133185C211yesmaximal, characteristic, complemented
13C2×#14582638C211yesmaximal, characteristic, complemented
14#329×D43C211yesmaximal, characteristic, complemented
15C43×#1530C211yesmaximal, characteristic, complemented
16C2×#13063372C411yescharacteristic
17C2×#13063371C411yescharacteristic
18#14583558—21no—
19#14583558—21no—
20#14583545—21no—
21#14583545—21no—
22#14583538—21no—
23#14583538—21no—
24#14583538—21no—
25#14583538—21no—
26#14583474C411yescharacteristic
27#14583474C411yescharacteristic
28#14583470C411yescharacteristic
29#14583463C411yescharacteristic
30#14583462C411yescharacteristic
31#14583462C411yescharacteristic
32#14583448C2211yescharacteristic
33#14583448C2211yescharacteristic
34C2×#13063313C2211yescharacteristic
35#124×D43C2211yescharacteristic
36#124×D43C2211yescharacteristic
37C4×#10621898C2211yescharacteristic
38#14583028—21no—
39#14583027—21no—
40#14582972—21no—
41#14582970—21no—
42#14582969—21no—
43#14582967—21no—
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582956C2211yescharacteristic, complemented
47#14582954C2211yescharacteristic, complemented
48#14582954C2211yescharacteristic, complemented
49#14582954C2211yescharacteristic, complemented
50#14582954C2211yescharacteristic, complemented
51#14582851C2211yescharacteristic, complemented
52#14582851C2211yescharacteristic, complemented
53C2×#13063236C2211yescharacteristic, complemented
54#97×D43C2211yescharacteristic, complemented
55#97×D43C2211yescharacteristic, complemented
56#14582639C2211yescharacteristic, complemented
57#14582639C2211yescharacteristic, complemented
58#14582639C2211yescharacteristic, complemented
59#14582639C2211yescharacteristic, complemented
60#14582638C2211yescharacteristic, complemented
61#14582638C2211yescharacteristic, complemented
62#14582638C2211yescharacteristic, complemented
63#14582638C2211yescharacteristic, complemented
64#14582638C2211yescharacteristic, complemented
65#14582638C2211yescharacteristic, complemented
66#14582638C2211yescharacteristic, complemented
67#14582638C2211yescharacteristic, complemented
68C43×#532C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C2×#97×C43C2211yescharacteristic, complemented
71C43×#329C2211yescharacteristic, complemented
72C43×#329C2211yescharacteristic, complemented
73C43×#329C2211yescharacteristic, complemented
74C43×#329C2211yescharacteristic, complemented
75#13063372—44no—
76#13063371—44no—
77C2×#10621902C2×C411yescharacteristic
78C2×#10621902C2×C411yescharacteristic
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898C2×C411yescharacteristic
82C2×#10621900—21no—
83C2×#10621900—21no—
84C2×#10621900C2×C411yescharacteristic
85C2×#10621900C2×C411yescharacteristic
86C22×Dic86—21no—
87C22×Dic86C2×C411yescharacteristic
88C2×Q8×D43C2×C411yescharacteristic
89C2×Q8×D43C2×C411yescharacteristic
90C22×D172—21no—
91C22×D172C2×C411yescharacteristic
92C2×D4×D43—21no—
93C2×D4×D43—21no—
94C2×D4×D43C2×C411yescharacteristic
95C2×D4×D43C2×C411yescharacteristic
96C2×#10621872—21no—
97C2×#10621872—21no—
98C22×C43⋊C8—21no—
99C2×C8×D43—21no—
100C2×C8×D43—21no—
101#13063323C2×C411yescharacteristic
102#13063323C2×C411yescharacteristic
103#13063321C2×C411yescharacteristic
104#13063321C2×C411yescharacteristic
105#13063314C2×C411yescharacteristic
106#13063314C2×C411yescharacteristic
107#13063313—21no—
108#13063313—21no—
109#13063313C2×C411yescharacteristic
110#13063313C2×C411yescharacteristic
111#13063313C2311yescharacteristic
112#13063313C2311yescharacteristic
113#13063312C2×C411yescharacteristic
114#13063312C2×C411yescharacteristic
115#13063311—21no—
116#13063311—21no—
117#13063311—21no—
118#13063311—21no—
119#13063310—21no—
120#13063310—21no—
121#13063310—21no—
122#13063310—21no—
123#13063306—21no—
124#13063306—21no—
125#13063304—21no—
126#13063304—21no—
127#13063303—21no—
128#13063303—21no—
129#13063303—21no—
130#13063303—21no—
131#13063299—21no—
132#13063299—21no—
133#13063298—21no—
134#13063298—21no—
135#13063298—21no—
136#13063298—21no—
137#13063297—21no—
138#13063297—21no—
139#13063297—21no—
140#13063297—21no—
141#13063293—21no—
142#13063293—21no—
143#13063293—21no—
144#13063293—21no—
145#13063293—21no—
146#13063293—21no—
147C4×Dic86D411yescharacteristic
148C4×Dic86D411yescharacteristic
149C4×D172D411yescharacteristic
150C4×D172D411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155(C22⋊D43)⋊C4—21no—
156(C22⋊D43)⋊C4—21no—
157(C22⋊D43)⋊C4—21no—
158(C22⋊D43)⋊C4—21no—
159#13063284C2×C411yescharacteristic
160#13063282C2×C411yescharacteristic
161#13063282C2×C411yescharacteristic
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C22⋊C4×D43—21no—
165C22⋊C4×D43—21no—
166C22⋊C4×D43—21no—
167C22⋊C4×D43—21no—
168C42×D43C2311yescharacteristic
169C42×D43C2311yescharacteristic
170C4⋊(C43⋊C8)—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊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#13063236C2311yescharacteristic
182#13063236C2311yescharacteristic
183#13063236C2311yescharacteristic
184#13063236C2311yescharacteristic
185#13063235—21no—
186#13063235—21no—
187C8×Dic43—21no—
188C8×Dic43—21no—
189C2×#41×C43C2×C411yescharacteristic
190C2×#41×C43C2×C411yescharacteristic
191C22×C8×C43—21no—
192C4⋊Q8×C43C2×C411yescharacteristic
193#127×C43C2×C411yescharacteristic
194#124×C43C2311yescharacteristic
195#124×C43C2311yescharacteristic
196#121×C43—21no—
197#121×C43—21no—
198C4×D4×C43—21no—
199C4×D4×C43—21no—
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203#97×C43—21no—
204#97×C43C2311yescharacteristic
205#97×C43C2311yescharacteristic
206#97×C43C2311yescharacteristic
207#97×C43C2311yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—21no—
211#41×C43—42no—
212#41×C43—42no—
213C2×Q8×C43C22×C411yescharacteristic
214C2×Q8×C43C22×C411yescharacteristic
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43C22×C411yescharacteristic
220C2×D4×C43C22×C411yescharacteristic
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43C22⋊C411yescharacteristic
235C2×C22⋊D43C22⋊C411yescharacteristic
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239#10621902—42no—
240#10621902—42no—
241Q8×D43—42no—
242Q8×D43—42no—
243#10621900—42no—
244#10621900—42no—
245#10621900—44no—
246#10621900—44no—
247D4×D43—42no—
248D4×D43—44no—
249D4×D43—44no—
250D4×D43—42no—
251#10621898—24no—
252#10621898—44no—
253#10621898—44no—
254C2×D172—21no—
255C2×D172—21no—
256C2×D172—21no—
257C2×D172—44no—
258C2×D172—42no—
259C2×D172C22⋊C411yescharacteristic
260C2×D172C22×C411yescharacteristic
261C2×D172C22×C411yescharacteristic
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×C4×D43—21no—
266C2×C4×D43C22×C411yescharacteristic
267C2×C4×D43C22×C411yescharacteristic
268C2×C4×D43C2×D411yescharacteristic
269C2×C4×D43C2×D411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×C4×D43C2×D411yescharacteristic
272C2×Dic86—21no—
273C2×Dic86—21no—
274C2×Dic86—21no—
275C2×Dic86—44no—
276C2×Dic86—42no—
277C2×Dic86C22⋊C411yescharacteristic
278C2×Dic86C22×C411yescharacteristic
279C2×Dic86C22×C411yescharacteristic
280C2×C8×C43—21no—
281C2×C8×C43—21no—
282C2×C8×C43—21no—
283C2×C8×C43—21no—
284C2×C8×C43—42no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C42×C43C22×C411yescharacteristic
292C42×C43C2×D411yescharacteristic
293C42×C43C2×D411yescharacteristic
294C42×C43C2411yescharacteristic
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43—21no—
298C22⋊Dic43—21no—
299C22⋊Dic43C22⋊C411yescharacteristic
300C22⋊Dic43C22⋊C411yescharacteristic
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—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4—21no—
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314(C2×D43)⋊C4C22⋊C411yescharacteristic
315(C2×D43)⋊C4C22⋊C411yescharacteristic
316(C2×D43)⋊C4C22⋊C411yescharacteristic
317C4⋊Dic43C22⋊C411yescharacteristic
318C4⋊Dic43C22⋊C411yescharacteristic
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4C22⋊C411yescharacteristic
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327C4×Dic43C22×C411yescharacteristic
328C4×Dic43C22×C411yescharacteristic
329C4×Dic43C2×D411yescharacteristic
330C4×Dic43C2×D411yescharacteristic
331C4×Dic43C2×D411yescharacteristic
332C4×Dic43C2×D411yescharacteristic
333C2×C43⋊C8—21no—
334C2×C43⋊C8—21no—
335C2×C43⋊C8—21no—
336C2×C43⋊C8—21no—
337C2×C43⋊C8—42no—
338#10621872—42no—
339#10621872—42no—
340C8×D43—42no—
341C8×D43—42no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43C2×C22⋊C411yescharacteristic
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43—42no—
350C22×D43—81no—
351C22×D43—81no—
352C22×D43—81no—
353C22×D43—81no—
354C22×D43—81no—
355C22×D43—81no—
356C22×D43C2×C22⋊C411yescharacteristic
357C22×D43C2×C22⋊C411yescharacteristic
358Q8×C43—41no—
359Q8×C43—41no—
360D4×C43—41no—
361D4×C43—41no—
362D4×C43—42no—
363D4×C43—42no—
364D4×C43—81no—
365D4×C43—81no—
366C2×C4×C43—22no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—42no—
372C2×C4×C43—42no—
373C2×C4×C43C2×C22⋊C411yescharacteristic
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C23×C411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C22×D411yescharacteristic
379C22⋊D43—22no—
380C22⋊D43—42no—
381C22⋊D43—42no—
382C22⋊D43—42no—
383C22⋊D43—42no—
384C22⋊D43—81no—
385C22⋊D43—81no—
386C22⋊D43—81no—
387C22⋊D43—81no—
388C22⋊D43#10014yes—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—42no—
392C2×Dic43—42no—
393C2×Dic43—42no—
394C2×Dic43C2×C22⋊C411yescharacteristic
395C2×Dic43C2×C22⋊C411yescharacteristic
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398C2×Dic43C2×C22⋊C411yescharacteristic
399C2×Dic43C2×C22⋊C411yescharacteristic
400D172—22no—
401D172—41no—
402D172—41no—
403D172—42no—
404D172—42no—
405D172—42no—
406C4×D43—22no—
407C4×D43—22no—
408C4×D43—41no—
409C4×D43—41no—
410C4×D43—41no—
411C4×D43—41no—
412C4×D43—42no—
413C4×D43—42no—
414C4×D43—42no—
415C4×D43—42no—
416Dic86—22no—
417Dic86—42no—
418Dic86—42no—
419Dic86—42no—
420Dic86—41no—
421Dic86—41no—
422C8×C43—22no—
423C8×C43—41no—
424C8×C43—41no—
425C8×C43—41no—
426C43⋊C8—22no—
427C43⋊C8—41no—
428C43⋊C8—41no—
429C43⋊C8—41no—
430#17685—431nomaximal, Sylow
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43C2×#10012yes—
440C22×C43C22×C22⋊C411yescharacteristic
441C2×D43—21no—
442C2×D43—21no—
443C2×D43—21no—
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—41no—
447C2×D43—41no—
448C2×D43—41no—
449C2×D43—41no—
450C2×D43—41no—
451C2×D43—41no—
452C2×D43—162no—
453C2×D43—162no—
454C2×D43—162no—
455C2×D43C2×#10012yes—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—41no—
463C4×C43—41no—
464Dic43—21no—
465Dic43—21no—
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—41no—
470Dic43—41no—
471Dic43C2×#10012yes—
472#3500—431no—
473#2970—431no—
474#2970—431no—
475#1536—431no—
476#1533—431no—
477#1533—431no—
478#1530—431no—
479#1530—431no—
480#1530—431no—
481#1530D4311yescharacteristic, complemented
482#1527—431no—
483#1527—431no—
484#1525—431no—
485C2×#329—431no—
486C2×#329—431no—
487C2×C43—22no—
488C2×C43—81no—
489C2×C43—81no—
490C2×C43C22×#10011yescharacteristic
491C2×C43#290111yescharacteristic
492C2×C43#290111yescharacteristic
493D43—22no—
494D43—41no—
495D43—81no—
496D43—81no—
497C2×2−1+4—431no—
498C2×H(5,𝔽2)—431no—
499#548—861no—
500#548—861no—
501#546—861no—
502#546—861no—
503#546—861no—
504#546—861no—
505#546—861no—
506#546—861no—
507#536—431no—
508#536—431no—
509#536—431no—
510#535—431no—
511#535—431no—
512#535—431no—
513#532—431no—
514#532—431no—
515#532C2×D4311yescharacteristic
516C2×#124—431no—
517C2×#124—431no—
518C2×#124—431no—
519C4×#41—431no—
520#446—861no—
521#446—861no—
522#435—861no—
523#435—861no—
524#435—861no—
525#435—861no—
526C8×D4—861no—
527C8×D4—861no—
528#432—431no—
529#432—431no—
530#432—431no—
531#432—431no—
532#432—431no—
533#432C2×D4311yescharacteristic, complemented
534C4×M16—431no—
535C4×M16—431no—
536C2×#97—431no—
537C2×#97—431no—
538C2×#97—431no—
539C2×#97C2×D4311yescharacteristic, complemented
540#329—431no—
541#329—431no—
542#329—431no—
543#329—431no—
544#329—431no—
545#329—431no—
546#329—431no—
547#329—431no—
548#329—431no—
549#329—431no—
550#329—431no—
551#329—431no—
552#329C2×D4311yescharacteristic, complemented
553#329C2×D4311yescharacteristic, complemented
554#329C2×D4311yescharacteristic, complemented
555#329C2×D4311yescharacteristic, complemented
556C43#1768511yescharacteristic, complemented, Sylow
5572−1+4—1724no—
558H(5,𝔽2)—1724no—
559C2×#41—431no—
560C2×#41—431no—
561C2×#41—431no—
562C2×#41—431no—
563C2×#41—431no—
564C2×#41—861no—
565C2×#41—861no—
566C2×#41—861no—
567C2×#41—861no—
568C2×#41C4×D4311yescharacteristic
569C2×#41C4×D4311yescharacteristic
570C22×Q8—431no—
571C22×Q8—431no—
572C22×Q8—431no—
573C22×Q8—861no—
574C22×D4—431no—
575C22×D4—431no—
576C22×D4—431no—
577C22×D4—861no—
578C22×D4—861no—
579C22×D4—861no—
580C2×M16—861no—
581C2×M16—861no—
582C22×C8—21no—
583C22×C8—861no—
584C22×C8—861no—
585C22×C8—861no—
586C4⋊Q8—431no—
587C4⋊Q8—431no—
588C4⋊Q8C4×D4311yescharacteristic
589#127—431no—
590#127—431no—
591#127C4×D4311yescharacteristic
592#124—431no—
593#124—431no—
594#124—431no—
595#124—431no—
596#124—431no—
597#124—431no—
598#124—431no—
599#124—431no—
600#124—861no—
601#124—861no—
602#124—861no—
603#124—861no—
604#124—861no—
605#124—861no—
606#124C22×D4311yescharacteristic
607#124C22×D4311yescharacteristic
608#123—861no—
609#123—861no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614C22⋊Q8—861no—
615C22⋊Q8—861no—
616C22⋊Q8—861no—
617C22⋊Q8—861no—
618C22⋊Q8—861no—
619C22⋊Q8—861no—
620#121—21no—
621#121—21no—
622#121—861no—
623#121—861no—
624#121—861no—
625#121—861no—
626#121—861no—
627#121—861no—
628#121—861no—
629#121—861no—
630#121—861no—
631#121—861no—
632#120—861no—
633#120—861no—
634#120—861no—
635#120—861no—
636#120—861no—
637#120—861no—
638C4×Q8—431no—
639C4×Q8—431no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—431no—
643C4×D4—431no—
644C4×D4—431no—
645C4×D4—431no—
646C4×D4—431no—
647C4×D4—431no—
648C4×D4—861no—
649C4×D4—861no—
650C4×D4—861no—
651C4×D4—861no—
652#117—431no—
653#117—431no—
654#117—431no—
655C2×C22⋊C4—861no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—861no—
659C2×C22⋊C4—861no—
660C2×C22⋊C4—861no—
661C2×C42—431no—
662C2×C42—431no—
663C2×C42C22×D4311yescharacteristic
664C4⋊C8—21no—
665C4⋊C8—861no—
666C4⋊C8—861no—
667C4⋊C8—861no—
668C4⋊C8—861no—
669C4⋊C8—861no—
670C22⋊C8—21no—
671C22⋊C8—861no—
672C22⋊C8—861no—
673C22⋊C8—861no—
674C22⋊C8—861no—
675C22⋊C8—861no—
676#97—21no—
677#97—431no—
678#97—431no—
679#97—431no—
680#97—431no—
681#97—861no—
682#97—861no—
683#97—861no—
684#97C22×D4311yescharacteristic
685#97C22×D4311yescharacteristic
686#97C22×D4311yescharacteristic
687#97C22×D4311yescharacteristic
688C4×C8—861no—
689C4×C8—861no—
690C24—861no—
691C24—861no—
692C24—861no—
693#41—42no—
694#41—42no—
695#41—864no—
696#41—1724no—
697#41—1724no—
698#41—1722no—
699#41—1722no—
700#41—1722no—
701#41—1722no—
702#41—1724no—
703#41—1724no—
704C2×Q8—431no—
705C2×Q8—431no—
706C2×Q8—431no—
707C2×Q8—861no—
708C2×Q8—861no—
709C2×Q8—861no—
710C2×Q8—1722no—
711C2×Q8—1724no—
712C2×Q8—1722no—
713C2×Q8—1722no—
714C2×Q8C2×C4×D4311yescharacteristic
715C2×Q8C2×C4×D4311yescharacteristic
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—431no—
721C2×D4—431no—
722C2×D4—431no—
723C2×D4—431no—
724C2×D4—431no—
725C2×D4—861no—
726C2×D4—861no—
727C2×D4—861no—
728C2×D4—861no—
729C2×D4—861no—
730C2×D4—861no—
731C2×D4—861no—
732C2×D4—861no—
733C2×D4—861no—
734C2×D4—861no—
735C2×D4—861no—
736C2×D4—1722no—
737C2×D4—1724no—
738C2×D4—1722no—
739C2×D4—1722no—
740C2×D4—1724no—
741C2×D4—1724no—
742C2×D4C2×C4×D4311yescharacteristic
743C2×D4C2×C4×D4311yescharacteristic
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—431no—
747C22×C4—431no—
748C22×C4—431no—
749C22×C4—431no—
750C22×C4—431no—
751C22×C4—431no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4C2×C4×D4311yescharacteristic
760C22×C4D4×D4311yescharacteristic
761C22×C4D4×D4311yescharacteristic
762M16—1722no—
763M16—1722no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—42no—
769C2×C8—861no—
770C2×C8—861no—
771C2×C8—861no—
772C2×C8—861no—
773C2×C8—1722no—
774C2×C8—1722no—
775C2×C8—1722no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—431no—
779C4⋊C4—431no—
780C4⋊C4—431no—
781C4⋊C4—431no—
782C4⋊C4—431no—
783C4⋊C4—431no—
784C4⋊C4—861no—
785C4⋊C4—861no—
786C4⋊C4—861no—
787C4⋊C4—861no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—431no—
797C22⋊C4—431no—
798C22⋊C4—861no—
799C22⋊C4—861no—
800C22⋊C4—861no—
801C22⋊C4—861no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C22⋊C4—861no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C42—431no—
815C42—431no—
816C42—431no—
817C42—431no—
818C42—431no—
819C42—431no—
820C42C2×C4×D4311yescharacteristic
821C42D4×D4311yescharacteristic
822C42D4×D4311yescharacteristic
823C42C23×D4311yescharacteristic
824C23—21no—
825C23—21no—
826C23—431no—
827C23—431no—
828C23—861no—
829C23—861no—
830C23—3441no—
831C23—3441no—
832C23—3441no—
833C23—3441no—
834C23—3441no—
835C23—3441no—
836C23—1722no—
837C23—1722no—
838C23—1722no—
839C23C22⋊C4×D4311yescharacteristic
840Q8—41no—
841Q8—41no—
842Q8—862no—
843Q8—1721no—
844Q8—1721no—
845Q8—1722no—
846Q8—1722no—
847Q8—1722no—
848D4—41no—
849D4—41no—
850D4—42no—
851D4—42no—
852D4—81no—
853D4—81no—
854D4—434no—
855D4—862no—
856D4—862no—
857D4—3441no—
858D4—3441no—
859D4—3441no—
860D4—3441no—
861D4—1721no—
862D4—1721no—
863D4—1722no—
864D4—1722no—
865D4—1722no—
866D4—1722no—
867D4—1722no—
868D4—1722no—
869D4—1722no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—431no—
878C2×C4—431no—
879C2×C4—431no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—431no—
883C2×C4—862no—
884C2×C4—862no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—1721no—
888C2×C4—1721no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4—1722no—
892C2×C4—1722no—
893C2×C4—1722no—
894C2×C4—1722no—
895C2×C4—1722no—
896C2×C4—1722no—
897C2×C4—1722no—
898C2×C4C22⋊C4×D4311yescharacteristic
899C2×C4C22⋊C4×D4311yescharacteristic
900C2×C4C22⋊C4×D4311yescharacteristic
901C2×C4C22×C4×D4311yescharacteristic
902C2×C4C2×D4×D4311yescharacteristic
903C2×C4C2×D4×D4311yescharacteristic
904C8—22no—
905C8—41no—
906C8—41no—
907C8—41no—
908C8—862no—
909C8—1721no—
910C8—1721no—
911C8—1721no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—432no—
921C22—861no—
922C22—861no—
923C22—861no—
924C22—861no—
925C22—861no—
926C22—1721no—
927C22—1721no—
928C22—1721no—
929C22—1721no—
930C22—1721no—
931C22—1721no—
932C22—6882no—
933C22—6882no—
934C22—6882no—
935C22#100×D4312yes—
936C22C2×C22⋊C4×D4311yescharacteristic
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—21no—
943C4—41no—
944C4—41no—
945C4—432no—
946C4—861no—
947C4—861no—
948C4—861no—
949C4—861no—
950C4—861no—
951C4—1721no—
952C4—1721no—
953C2—22no—
954C2—81no—
955C2—81no—
956C2—862no—
957C2—3441no—
958C2—3441no—
959C2—1721no—
960C2C2×#100×D4311yescharacteristic
961C2#1914313911yescharacteristic
962C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1530C2
socleC22×C43C22×C22⋊C4
prime radical#19148382C2
cosocleC42×C43C24
hypercenter#1530D43
hypocenterC43#17685
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1530

Complements

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

NH ≅ G/Ntype
2. #19143606C2semidirect
3. #19143604C2semidirect
4. #19133228C2semidirect
5. #19133218C2semidirect
6. #19133217C2semidirect
7. #19133206C2semidirect
8. #19133204C2semidirect
9. #19133204C2semidirect
10. #19133191C2semidirect
11. #19133191C2semidirect
12. #19133185C2semidirect
13. C2×#14582638C2semidirect
14. #329×D43C2semidirect
15. C43×#1530C2semidirect
46. #14582956C22semidirect
47. #14582954C22semidirect
48. #14582954C22semidirect
49. #14582954C22semidirect
50. #14582954C22semidirect
51. #14582851C22semidirect
52. #14582851C22semidirect
53. C2×#13063236C22semidirect
54. #97×D43C22semidirect
55. #97×D43C22semidirect
56. #14582639C22semidirect
57. #14582639C22semidirect
58. #14582639C22semidirect
59. #14582639C22semidirect
60. #14582638C22semidirect
61. #14582638C22semidirect
62. #14582638C22semidirect
63. #14582638C22semidirect
64. #14582638C22semidirect
65. #14582638C22semidirect
66. #14582638C22semidirect
67. #14582638C22semidirect
69. C43×#432C22semidirect
70. C2×#97×C43C22semidirect
71. C43×#329C22semidirect
72. C43×#329C22semidirect
73. C43×#329C22semidirect
74. C43×#329C22semidirect
481. #1530D43semidirect
533. #432C2×D43semidirect
539. C2×#97C2×D43semidirect
552. #329C2×D43semidirect
553. #329C2×D43semidirect
554. #329C2×D43semidirect
555. #329C2×D43semidirect
556. C43#17685semidirect

Maximal subgroups

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

subgroupindex
#191483822
#191436062
#191436042
#191332282
#191332182
#191332172
#191332062
#191332042
#191331912
#191331852
C2×#145826382
#329×D432
C43×#15302
#1768543