Finite Group Databasebeta

← #25062820

Subgroups — #25062820

Order 11008.

1290 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583547C211yesmaximal, characteristic
2#19143045C211yesmaximal, characteristic, complemented
3#19143041C211yesmaximal, characteristic, complemented
4#19132957C211yesmaximal, characteristic, complemented
5#19132957C211yesmaximal, characteristic, complemented
6#19132943C211yesmaximal, characteristic, complemented
7#19132940C211yesmaximal, characteristic, complemented
8#19132940C211yesmaximal, characteristic, complemented
9#19132930C211yesmaximal, characteristic, complemented
10#19132924C211yesmaximal, characteristic, complemented
11#19132923C211yesmaximal, characteristic, complemented
12#19132910C211yesmaximal, characteristic, complemented
13C2×#14582624C211yesmaximal, characteristic, complemented
14#324×D43C211yesmaximal, characteristic, complemented
15C43×#1468C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621900C411yescharacteristic
18C2×#13063333—21no—
19C2×#13063331—21no—
20#14583547—21no—
21#14583547—21no—
22#14583547—21no—
23#14583547—21no—
24#14583547—21no—
25#14583547—21no—
26#14583547—21no—
27#14583547—21no—
28C2×#13063324C411yescharacteristic
29C2×#13063310C411yescharacteristic
30C2×#13063309C411yescharacteristic
31C2×#13063307C2211yescharacteristic
32C2×#13063303C2211yescharacteristic
33C2×#13063302C411yescharacteristic
34C2×#13063298C411yescharacteristic
35C2×#13063297C411yescharacteristic
36C2×(C22⋊D43)⋊C4C411yescharacteristic
37C2×(C22⋊D43)⋊C4C2211yescharacteristic
38C22×Dic43⋊C4C2211yescharacteristic
39C2×C4⋊C4×D43C2211yescharacteristic
40#14582867—21no—
41#14582865—21no—
42#14582864—21no—
43#14582864—21no—
44#14582864—21no—
45#14582864—21no—
46#14582863C2211yescharacteristic
47#14582861C2211yescharacteristic
48#14582861C2211yescharacteristic
49#14582861C2211yescharacteristic
50#14582861C2211yescharacteristic
51C2×C22⋊(C43⋊C8)C2211yescharacteristic
52C22⋊C8×D43C2211yescharacteristic
53C22⋊C8×D43C2211yescharacteristic
54C22⋊C8×D43C2211yescharacteristic
55C22⋊C8×D43C2211yescharacteristic
56#14582625C2211yescharacteristic
57#14582625C2211yescharacteristic
58#14582624C2211yescharacteristic
59#14582624C2211yescharacteristic
60#14582624C2211yescharacteristic
61#14582624C2211yescharacteristic
62#14582624C2211yescharacteristic
63#14582624C2211yescharacteristic
64#14582624C2211yescharacteristic
65#14582624C2211yescharacteristic
66#14582623C2211yescharacteristic
67#14582623C2211yescharacteristic
68C2×#123×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C2×C22⋊C8×C43C2211yescharacteristic
71C43×#324C2211yescharacteristic
72C43×#324C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C2×#10621898—44no—
76C2×#10621898D411yescharacteristic
77C2×#10621898D411yescharacteristic
78C2×#10621898D411yescharacteristic
79C2×#10621898D411yescharacteristic
80C2×#10621898D411yescharacteristic
81C2×#10621898D411yescharacteristic
82C2×#10621898D411yescharacteristic
83C2×#10621898D411yescharacteristic
84C2×#10621900—21no—
85C2×#10621900—21no—
86C2×#10621900—21no—
87C2×#10621900—21no—
88C2×#10621900—44no—
89C22×Dic86C2×C411yescharacteristic
90C22×Dic86C2×C411yescharacteristic
91C22×D172C2×C411yescharacteristic
92C22×C22⋊D43C2×C411yescharacteristic
93C22×C22⋊D43C2×C411yescharacteristic
94C22×C22⋊D43C2×C411yescharacteristic
95C22×C22⋊D43C2×C411yescharacteristic
96C23×Dic43C2×C411yescharacteristic
97C23×Dic43C2×C411yescharacteristic
98C23×Dic43C2×C411yescharacteristic
99C22×C4×D43C2×C411yescharacteristic
100C22×C4×D43C2×C411yescharacteristic
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2311yescharacteristic
103#13063333—44no—
104#13063331—44no—
105C2×#10621877—21no—
106C2×#10621872—21no—
107C2×#10621872—21no—
108C2×#10621872—21no—
109C2×#10621872—21no—
110C22×C43⋊C8—21no—
111C2×C8×D43—21no—
112C2×C8×D43—21no—
113C2×C8×D43—21no—
114C2×C8×D43—21no—
115#13063324—21no—
116#13063324—21no—
117#13063324—21no—
118#13063324—21no—
119#13063310—21no—
120#13063310—21no—
121#13063310—21no—
122#13063310—21no—
123#13063309—21no—
124#13063309—21no—
125#13063309—21no—
126#13063309—21no—
127#13063307—21no—
128#13063307—21no—
129#13063307—21no—
130#13063307—21no—
131#13063303—21no—
132#13063303—21no—
133#13063303—21no—
134#13063303—21no—
135#13063302—21no—
136#13063302—21no—
137#13063302—21no—
138#13063302—21no—
139#13063298—21no—
140#13063298—21no—
141#13063298—21no—
142#13063298—21no—
143#13063297—21no—
144#13063297—21no—
145#13063297—21no—
146#13063297—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155C2×C4⋊Dic43C2×C411yescharacteristic
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4C2×C411yescharacteristic
162C2×Dic43⋊C4C2×C411yescharacteristic
163C2×Dic43⋊C4C2×C411yescharacteristic
164C2×Dic43⋊C4C2×C411yescharacteristic
165C2×Dic43⋊C4C2311yescharacteristic
166C2×Dic43⋊C4C2311yescharacteristic
167C4⋊C4×D43—21no—
168C4⋊C4×D43—21no—
169C4⋊C4×D43—21no—
170C4⋊C4×D43—21no—
171C2×C22⋊Dic43C2×C411yescharacteristic
172C2×(C2×D43)⋊C4C2×C411yescharacteristic
173C2×(C2×D43)⋊C4C2×C411yescharacteristic
174C2×(C2×D43)⋊C4C2×C411yescharacteristic
175C2×(C2×D43)⋊C4C2×C411yescharacteristic
176C2×C4×Dic43C2×C411yescharacteristic
177C22⋊(C43⋊C8)—21no—
178C22⋊(C43⋊C8)—21no—
179C22⋊(C43⋊C8)C2311yescharacteristic
180C22⋊(C43⋊C8)C2311yescharacteristic
181C22⋊(C43⋊C8)C2311yescharacteristic
182C22⋊(C43⋊C8)C2311yescharacteristic
183(C2×D43)⋊C8—21no—
184(C2×D43)⋊C8—21no—
185(C2×D43)⋊C8—21no—
186(C2×D43)⋊C8—21no—
187(C2×D43)⋊C8—21no—
188(C2×D43)⋊C8—21no—
189(C2×D43)⋊C8—21no—
190(C2×D43)⋊C8—21no—
191C22×D4×C43C2×C411yescharacteristic
192C23×C4×C43C2311yescharacteristic
193C2×M16×C43—21no—
194C22×C8×C43—21no—
195#123×C43—21no—
196#123×C43—21no—
197#123×C43—21no—
198#123×C43—21no—
199C2×C4⋊C4×C43C2×C411yescharacteristic
200C2×C4⋊C4×C43C2311yescharacteristic
201C2×C22⋊C4×C43C2×C411yescharacteristic
202C2×C22⋊C4×C43C2×C411yescharacteristic
203C2×C22⋊C4×C43C2311yescharacteristic
204C22⋊C8×C43—21no—
205C22⋊C8×C43—21no—
206C22⋊C8×C43C2311yescharacteristic
207C22⋊C8×C43C2311yescharacteristic
208C22⋊C8×C43C2311yescharacteristic
209C22⋊C8×C43C2311yescharacteristic
210C24×C43C22×C411yescharacteristic
211C24×C43C22×C411yescharacteristic
212C23×D43C22×C411yescharacteristic
213C23×D43C22×C411yescharacteristic
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—42no—
217C22×C4×C43—42no—
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—24no—
228C2×C22⋊D43—22no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—41no—
234C2×C22⋊D43—42no—
235C2×C22⋊D43—42no—
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C2×C22⋊D43C22⋊C411yescharacteristic
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—22no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—21no—
251C22×Dic43—41no—
252C22×Dic43—42no—
253C22×Dic43—42no—
254C22×Dic43C22×C411yescharacteristic
255C22×Dic43C22×C411yescharacteristic
256C22×Dic43C22×C411yescharacteristic
257C22×Dic43C22×C411yescharacteristic
258C22×Dic43C22×C411yescharacteristic
259C22×Dic43C22×C411yescharacteristic
260#10621900—44no—
261#10621900—44no—
262#10621900—44no—
263#10621900—44no—
264#10621898—24no—
265#10621898—24no—
266#10621898—42no—
267#10621898—42no—
268#10621898—42no—
269#10621898—42no—
270#10621898—42no—
271#10621898—42no—
272C2×D172—42no—
273C2×D172C22⋊C411yescharacteristic
274C2×D172C22⋊C411yescharacteristic
275C2×D172C22⋊C411yescharacteristic
276C2×D172C22⋊C411yescharacteristic
277C2×C4×D43—22no—
278C2×C4×D43—21no—
279C2×C4×D43—21no—
280C2×C4×D43—21no—
281C2×C4×D43—21no—
282C2×C4×D43—42no—
283C2×C4×D43—41no—
284C2×C4×D43—42no—
285C2×C4×D43—42no—
286C2×C4×D43C2×D411yescharacteristic
287C2×C4×D43C2×D411yescharacteristic
288C2×C4×D43C2×D411yescharacteristic
289C2×C4×D43C2×D411yescharacteristic
290C2×C4×D43C2×D411yescharacteristic
291C2×C4×D43C2×D411yescharacteristic
292C2×C4×D43C2×D411yescharacteristic
293C2×C4×D43C2×D411yescharacteristic
294C2×Dic86—21no—
295C2×Dic86—21no—
296C2×Dic86—42no—
297C2×Dic86—42no—
298C2×Dic86C22⋊C411yescharacteristic
299C2×Dic86C22⋊C411yescharacteristic
300C2×Dic86C22⋊C411yescharacteristic
301C2×Dic86C22⋊C411yescharacteristic
302M16×C43—42no—
303C2×C8×C43—21no—
304C2×C8×C43—21no—
305C2×C8×C43—21no—
306C2×C8×C43—21no—
307C2×C8×C43—42no—
308C4⋊C4×C43—21no—
309C4⋊C4×C43—21no—
310C4⋊C4×C43—21no—
311C4⋊C4×C43—21no—
312C22⋊C4×C43—21no—
313C22⋊C4×C43—21no—
314C22⋊C4×C43—21no—
315C22⋊C4×C43—21no—
316C22⋊C4×C43—21no—
317C22⋊C4×C43—21no—
318C22⋊Dic43—21no—
319C22⋊Dic43—21no—
320(C2×D43)⋊C4—21no—
321(C2×D43)⋊C4—21no—
322(C2×D43)⋊C4—21no—
323(C2×D43)⋊C4—21no—
324(C2×D43)⋊C4—21no—
325(C2×D43)⋊C4—21no—
326(C2×D43)⋊C4—21no—
327(C2×D43)⋊C4—21no—
328C4⋊Dic43—21no—
329C4⋊Dic43—21no—
330C4⋊Dic43—21no—
331C4⋊Dic43—21no—
332Dic43⋊C4—21no—
333Dic43⋊C4—21no—
334Dic43⋊C4—21no—
335Dic43⋊C4—21no—
336Dic43⋊C4—21no—
337Dic43⋊C4—21no—
338Dic43⋊C4—21no—
339Dic43⋊C4—21no—
340Dic43⋊C4—21no—
341Dic43⋊C4—21no—
342Dic43⋊C4—21no—
343Dic43⋊C4—21no—
344C4×Dic43—21no—
345C4×Dic43—21no—
346#10621877—42no—
347C2×C43⋊C8—21no—
348C2×C43⋊C8—21no—
349C2×C43⋊C8—21no—
350C2×C43⋊C8—21no—
351C2×C43⋊C8—42no—
352#10621872—42no—
353#10621872—42no—
354#10621872—42no—
355#10621872—42no—
356C8×D43—42no—
357C8×D43—42no—
358C8×D43—42no—
359C8×D43—42no—
360C23×C43—21no—
361C23×C43—21no—
362C23×C43—22no—
363C23×C43—21no—
364C23×C43—21no—
365C23×C43—21no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43C2×C22⋊C411yescharacteristic
370C23×C43C2×C22⋊C411yescharacteristic
371C23×C43C23×C411yescharacteristic
372C22×D43—21no—
373C22×D43—21no—
374C22×D43—21no—
375C22×D43—21no—
376C22×D43—22no—
377C22×D43—41no—
378C22×D43—41no—
379C22×D43—41no—
380C22×D43C2×C22⋊C411yescharacteristic
381C22×D43C2×C22⋊C411yescharacteristic
382C22×D43C2×C22⋊C411yescharacteristic
383C22×D43C2×C22⋊C411yescharacteristic
384D4×C43—42no—
385D4×C43—42no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43C2×C22⋊C411yescharacteristic
400C2×C4×C43C2×C22⋊C411yescharacteristic
401C2×C4×C43C22×D411yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C22⋊D43—22no—
404C22⋊D43—22no—
405C22⋊D43—22no—
406C22⋊D43—22no—
407C22⋊D43—22no—
408C22⋊D43—41no—
409C22⋊D43—41no—
410C22⋊D43—42no—
411C22⋊D43—42no—
412C22⋊D43—42no—
413C22⋊D43—42no—
414C22⋊D43#9914yes—
415C2×Dic43—21no—
416C2×Dic43—21no—
417C2×Dic43—22no—
418C2×Dic43—21no—
419C2×Dic43—21no—
420C2×Dic43—21no—
421C2×Dic43—21no—
422C2×Dic43—21no—
423C2×Dic43—41no—
424C2×Dic43—42no—
425C2×Dic43—42no—
426C2×Dic43—42no—
427C2×Dic43—42no—
428C2×Dic43—42no—
429C2×Dic43—42no—
430C2×Dic43—41no—
431C2×Dic43—41no—
432C2×Dic43C2×C22⋊C411yescharacteristic
433C2×Dic43C2×C22⋊C411yescharacteristic
434C2×Dic43C2×C22⋊C411yescharacteristic
435C2×Dic43C2×C22⋊C411yescharacteristic
436C2×Dic43#13112yescomplemented
437D172—22no—
438D172—22no—
439D172—41no—
440D172—41no—
441C4×D43—22no—
442C4×D43—22no—
443C4×D43—22no—
444C4×D43—22no—
445C4×D43—41no—
446C4×D43—41no—
447C4×D43—41no—
448C4×D43—41no—
449C4×D43—42no—
450C4×D43—42no—
451C4×D43—42no—
452C4×D43—42no—
453Dic86—22no—
454Dic86—22no—
455Dic86—41no—
456Dic86—41no—
457Dic86—42no—
458Dic86—42no—
459C8×C43—41no—
460C8×C43—41no—
461C8×C43—41no—
462C8×C43—41no—
463C43⋊C8—41no—
464C43⋊C8—41no—
465C43⋊C8—41no—
466C43⋊C8—41no—
467#17416—431nomaximal, Sylow
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—42no—
476C22×C43—42no—
477C22×C43—41no—
478C22×C43—41no—
479C22×C43—41no—
480C22×C43—81no—
481C22×C43—81no—
482C22×C43C2×#9912yes—
483C22×C43C22×C22⋊C411yescharacteristic
484C22×C43C2×#13111yescharacteristic
485C22×C43#56811yescharacteristic
486C2×D43—21no—
487C2×D43—21no—
488C2×D43—21no—
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—21no—
492C2×D43—21no—
493C2×D43—21no—
494C2×D43—21no—
495C2×D43—21no—
496C2×D43—21no—
497C2×D43—42no—
498C2×D43—42no—
499C2×D43—81no—
500C2×D43—81no—
501C2×D43C2×#9912yes—
502C4×C43—21no—
503C4×C43—21no—
504C4×C43—21no—
505C4×C43—21no—
506C4×C43—41no—
507C4×C43—41no—
508C4×C43—41no—
509Dic43—22no—
510Dic43—21no—
511Dic43—21no—
512Dic43—21no—
513Dic43—41no—
514Dic43—41no—
515Dic43—41no—
516Dic43C2×#9912yes—
517C2×#547—431no—
518#2880—431no—
519#2880—431no—
520#1472—431no—
521#1472—431no—
522#1468—431no—
523#1468—431no—
524#1468—431no—
525#1468D4311yescharacteristic, complemented
526#1465—431no—
527#1463—431no—
528#1463—431no—
529#1459—431no—
530C2×#324—431no—
531C2×#324—431no—
532C2×C43—21no—
533C2×C43—21no—
534C2×C43—22no—
535C2×C43—41no—
536C2×C43—81no—
537C2×C43#288011yescharacteristic
538C2×C43C22×#9911yescharacteristic
539C2×C43#288911yescharacteristic
540D43—22no—
541D43—41no—
542D43—41no—
543D43—41no—
544C22×#41—431no—
545C22×#41—431no—
546C2×#131—861no—
547C2×#131—861no—
548#547—861no—
549#547—861no—
550#547—861no—
551#547—861no—
552#547—861no—
553#547—861no—
554#547—861no—
555#547—861no—
556C2×C4⋊Q8—431no—
557C2×#123—431no—
558C2×#123—431no—
559C2×#123—431no—
560C2×#123C2×D4311yescharacteristic
561C2×C22⋊Q8—431no—
562C2×C22⋊Q8—431no—
563C2×#121—431no—
564C2×#121—431no—
565C2×C4×D4—431no—
566C2×C4×D4—431no—
567C22×C4⋊C4—431no—
568C22×C4⋊C4—431no—
569#408—861no—
570#408—861no—
571#408—861no—
572#408—861no—
573#408—861no—
574#408—861no—
575#407—431no—
576#407—431no—
577#407—431no—
578#407—431no—
579#407—431no—
580#407C2×D4311yescharacteristic
581C2×C22⋊C8—431no—
582C2×C22⋊C8—431no—
583C2×C22⋊C8—431no—
584C2×C22⋊C8—431no—
585C2×C22⋊C8—431no—
586C2×C22⋊C8C2×D4311yescharacteristic
587#324—431no—
588#324—431no—
589#324—431no—
590#324—431no—
591#324—431no—
592#324—431no—
593#324—431no—
594#324—431no—
595#324—431no—
596#324—431no—
597#324C2×D4311yescharacteristic
598#324C2×D4311yescharacteristic
599#323—431no—
600#323—431no—
601#323C2×D4311yescharacteristic
602#323C2×D4311yescharacteristic
603C43#1741611yescharacteristic, complemented, Sylow
604C2×#41—431no—
605C2×#41—431no—
606C2×#41—431no—
607C2×#41—431no—
608C2×#41—431no—
609C2×#41—431no—
610C2×#41—431no—
611C2×#41—431no—
612C2×#41—861no—
613C2×#41—861no—
614C2×#41—861no—
615C2×#41—861no—
616C2×#41—1724no—
617C2×#41—1724no—
618C22×Q8—431no—
619C22×Q8—431no—
620C22×D4—431no—
621C22×D4—431no—
622C22×D4—431no—
623C22×D4—431no—
624C22×D4—431no—
625C22×D4C4×D4311yescharacteristic
626C23×C4—431no—
627C23×C4—431no—
628C23×C4—431no—
629C23×C4—431no—
630C23×C4—431no—
631C23×C4—431no—
632C23×C4—431no—
633C23×C4C22×D4311yescharacteristic
634#131—1724no—
635#131—1724no—
636C2×M16—21no—
637C2×M16—861no—
638C2×M16—861no—
639C2×M16—861no—
640C2×M16—861no—
641C2×M16—861no—
642C22×C8—21no—
643C22×C8—861no—
644C22×C8—861no—
645C22×C8—861no—
646C22×C8—861no—
647C22×C8—861no—
648C4⋊Q8—861no—
649C4⋊Q8—861no—
650C4⋊Q8—861no—
651C4⋊Q8—861no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—861no—
657#123—861no—
658#123—861no—
659#123—861no—
660#123—861no—
661#123—861no—
662#123—861no—
663#123—861no—
664#123—861no—
665#123—861no—
666#123—861no—
667#123—861no—
668C22⋊Q8—861no—
669C22⋊Q8—861no—
670C22⋊Q8—861no—
671C22⋊Q8—861no—
672C22⋊Q8—861no—
673C22⋊Q8—861no—
674C22⋊Q8—861no—
675C22⋊Q8—861no—
676#121—861no—
677#121—861no—
678#121—861no—
679#121—861no—
680#121—861no—
681#121—861no—
682#121—861no—
683#121—861no—
684C4×D4—861no—
685C4×D4—861no—
686C4×D4—861no—
687C4×D4—861no—
688C4×D4—861no—
689C4×D4—861no—
690C4×D4—861no—
691C4×D4—861no—
692C2×C4⋊C4—431no—
693C2×C4⋊C4—431no—
694C2×C4⋊C4—431no—
695C2×C4⋊C4—431no—
696C2×C4⋊C4—431no—
697C2×C4⋊C4—431no—
698C2×C4⋊C4—431no—
699C2×C4⋊C4—431no—
700C2×C4⋊C4—861no—
701C2×C4⋊C4—861no—
702C2×C4⋊C4—861no—
703C2×C4⋊C4—861no—
704C2×C4⋊C4—861no—
705C2×C4⋊C4—861no—
706C2×C4⋊C4—861no—
707C2×C4⋊C4—861no—
708C2×C4⋊C4C4×D4311yescharacteristic
709C2×C4⋊C4C22×D4311yescharacteristic
710C2×C22⋊C4—431no—
711C2×C22⋊C4—431no—
712C2×C22⋊C4—431no—
713C2×C22⋊C4—431no—
714C2×C22⋊C4—431no—
715C2×C22⋊C4C4×D4311yescharacteristic
716C2×C22⋊C4C4×D4311yescharacteristic
717C2×C22⋊C4C22×D4311yescharacteristic
718C2×C42—431no—
719C22⋊C8—21no—
720C22⋊C8—21no—
721C22⋊C8—431no—
722C22⋊C8—431no—
723C22⋊C8—431no—
724C22⋊C8—431no—
725C22⋊C8—861no—
726C22⋊C8—861no—
727C22⋊C8—861no—
728C22⋊C8—861no—
729C22⋊C8—861no—
730C22⋊C8—861no—
731C22⋊C8—861no—
732C22⋊C8—861no—
733C22⋊C8—861no—
734C22⋊C8—861no—
735C22⋊C8C22×D4311yescharacteristic
736C22⋊C8C22×D4311yescharacteristic
737C22⋊C8C22×D4311yescharacteristic
738C22⋊C8C22×D4311yescharacteristic
739C24—431no—
740C24—431no—
741C24C2×C4×D4311yescharacteristic
742C24C2×C4×D4311yescharacteristic
743#41—864no—
744#41—864no—
745#41—1722no—
746#41—1722no—
747#41—1722no—
748#41—1722no—
749#41—1722no—
750#41—1722no—
751#41—1724no—
752#41—1724no—
753#41—1724no—
754#41—1724no—
755C2×Q8—431no—
756C2×Q8—431no—
757C2×Q8—431no—
758C2×Q8—431no—
759C2×Q8—861no—
760C2×Q8—861no—
761C2×Q8—1722no—
762C2×Q8—1722no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—42no—
766C2×D4—431no—
767C2×D4—431no—
768C2×D4—431no—
769C2×D4—431no—
770C2×D4—431no—
771C2×D4—431no—
772C2×D4—431no—
773C2×D4—431no—
774C2×D4—431no—
775C2×D4—431no—
776C2×D4—431no—
777C2×D4—431no—
778C2×D4—862no—
779C2×D4—864no—
780C2×D4—861no—
781C2×D4—861no—
782C2×D4—861no—
783C2×D4—861no—
784C2×D4—1722no—
785C2×D4—1721no—
786C2×D4—1722no—
787C2×D4—1722no—
788C22×C4—42no—
789C22×C4—431no—
790C22×C4—431no—
791C22×C4—431no—
792C22×C4—431no—
793C22×C4—431no—
794C22×C4—431no—
795C22×C4—431no—
796C22×C4—431no—
797C22×C4—431no—
798C22×C4—431no—
799C22×C4—431no—
800C22×C4—431no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—862no—
804C22×C4—861no—
805C22×C4—861no—
806C22×C4—861no—
807C22×C4—861no—
808C22×C4—861no—
809C22×C4—861no—
810C22×C4—862no—
811C22×C4—861no—
812C22×C4—861no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—1721no—
816C22×C4—1722no—
817C22×C4—1722no—
818C22×C4—1722no—
819C22×C4—1721no—
820C22×C4—1722no—
821C22×C4—1722no—
822C22×C4C2×C4×D4311yescharacteristic
823C22×C4C2×C4×D4311yescharacteristic
824C22×C4C2×C4×D4311yescharacteristic
825C22×C4C2×C4×D4311yescharacteristic
826C22×C4D4×D4311yescharacteristic
827C22×C4D4×D4311yescharacteristic
828C22×C4D4×D4311yescharacteristic
829C22×C4D4×D4311yescharacteristic
830C22×C4C23×D4311yescharacteristic
831M16—42no—
832M16—1722no—
833M16—1722no—
834M16—1722no—
835M16—1722no—
836M16—1722no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—42no—
842C2×C8—861no—
843C2×C8—861no—
844C2×C8—861no—
845C2×C8—861no—
846C2×C8—1722no—
847C2×C8—1722no—
848C2×C8—1722no—
849C2×C8—1722no—
850C2×C8—1722no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—861no—
856C4⋊C4—861no—
857C4⋊C4—861no—
858C4⋊C4—861no—
859C4⋊C4—861no—
860C4⋊C4—861no—
861C4⋊C4—861no—
862C4⋊C4—861no—
863C4⋊C4—861no—
864C4⋊C4—861no—
865C4⋊C4—861no—
866C4⋊C4—861no—
867C4⋊C4—861no—
868C4⋊C4—861no—
869C4⋊C4—861no—
870C4⋊C4—861no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—861no—
878C22⋊C4—861no—
879C22⋊C4—861no—
880C22⋊C4—861no—
881C22⋊C4—861no—
882C22⋊C4—861no—
883C22⋊C4—861no—
884C22⋊C4—861no—
885C22⋊C4—861no—
886C22⋊C4—861no—
887C42—861no—
888C42—861no—
889C23—22no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—431no—
899C23—431no—
900C23—431no—
901C23—431no—
902C23—862no—
903C23—861no—
904C23—861no—
905C23—861no—
906C23—861no—
907C23—1721no—
908C23—1721no—
909C23—1721no—
910C23C22⋊C4×D4311yescharacteristic
911C23C22⋊C4×D4311yescharacteristic
912C23C22×C4×D4311yescharacteristic
913Q8—862no—
914Q8—862no—
915Q8—1721no—
916Q8—1721no—
917Q8—1722no—
918Q8—1722no—
919D4—42no—
920D4—42no—
921D4—434no—
922D4—862no—
923D4—862no—
924D4—862no—
925D4—862no—
926D4—862no—
927D4—862no—
928D4—862no—
929D4—1721no—
930D4—1721no—
931D4—1721no—
932D4—1721no—
933D4—1722no—
934D4—1722no—
935D4—1722no—
936D4—1722no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—431no—
951C2×C4—431no—
952C2×C4—431no—
953C2×C4—431no—
954C2×C4—432no—
955C2×C4—862no—
956C2×C4—862no—
957C2×C4—862no—
958C2×C4—862no—
959C2×C4—862no—
960C2×C4—861no—
961C2×C4—861no—
962C2×C4—861no—
963C2×C4—861no—
964C2×C4—861no—
965C2×C4—861no—
966C2×C4—861no—
967C2×C4—1721no—
968C2×C4—1721no—
969C2×C4—1721no—
970C2×C4—1721no—
971C2×C4—1722no—
972C2×C4—1722no—
973C2×C4—1722no—
974C2×C4—1722no—
975C2×C4—1722no—
976C2×C4—1721no—
977C2×C4—1722no—
978C2×C4—1722no—
979C2×C4—1722no—
980C2×C4—1722no—
981C2×C4—1722no—
982C2×C4—1721no—
983C2×C4—1721no—
984C2×C4C22⋊C4×D4311yescharacteristic
985C2×C4C22⋊C4×D4311yescharacteristic
986C2×C4C2×D4×D4311yescharacteristic
987C2×C4C2×D4×D4311yescharacteristic
988C8—41no—
989C8—41no—
990C8—41no—
991C8—41no—
992C8—1721no—
993C8—1721no—
994C8—1721no—
995C8—1721no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22—432no—
1011C22—861no—
1012C22—861no—
1013C22—861no—
1014C22—861no—
1015C22—861no—
1016C22—861no—
1017C22—861no—
1018C22—861no—
1019C22—861no—
1020C22—861no—
1021C22—861no—
1022C22—3441no—
1023C22—3441no—
1024C22—1722no—
1025C22—1722no—
1026C22#99×D4312yes—
1027C22C2×C22⋊C4×D4311yescharacteristic
1028C22#131×D4311yescharacteristic
1029C22#1458366411yescharacteristic
1030C4—21no—
1031C4—21no—
1032C4—21no—
1033C4—21no—
1034C4—41no—
1035C4—41no—
1036C4—41no—
1037C4—432no—
1038C4—862no—
1039C4—861no—
1040C4—861no—
1041C4—861no—
1042C4—1721no—
1043C4—1721no—
1044C4—1721no—
1045C2—21no—
1046C2—21no—
1047C2—22no—
1048C2—41no—
1049C2—81no—
1050C2—862no—
1051C2—1721no—
1052C2—1721no—
1053C2—1721no—
1054C2#1914304311yescharacteristic
1055C2C2×#99×D4311yescharacteristic
1056C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1468C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583547C2
cosocleC22×C4×C43C24
hypercenter#1468D43
hypocenterC43#17416
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #19143045C2semidirect
3. #19143041C2semidirect
4. #19132957C2semidirect
5. #19132957C2semidirect
6. #19132943C2semidirect
7. #19132940C2semidirect
8. #19132940C2semidirect
9. #19132930C2semidirect
10. #19132924C2semidirect
11. #19132923C2semidirect
12. #19132910C2semidirect
13. C2×#14582624C2semidirect
14. #324×D43C2semidirect
15. C43×#1468C2semidirect
436. C2×Dic43#131semidirect
525. #1468D43semidirect
603. C43#17416semidirect

Maximal subgroups

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

subgroupindex
C2×#145835472
#191430452
#191430412
#191329572
#191329432
#191329402
#191329302
#191329242
#191329232
#191329102
C2×#145826242
#324×D432
C43×#14682
#1741643