Finite Group Databasebeta

← #25112798

Subgroups — #25112798

Order 11008.

1062 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583620C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic
3#19143327C211yesmaximal, characteristic
4#19135582C211yesmaximal, characteristic, complemented
5#19135582C211yesmaximal, characteristic, complemented
6#19135064C211yesmaximal, characteristic, complemented
7#19135060C211yesmaximal, characteristic, complemented
8#19135060C211yesmaximal, characteristic, complemented
9#19134677C211yesmaximal, characteristic, complemented
10#19134676C211yesmaximal, characteristic, complemented
11#19134589C211yesmaximal, characteristic, complemented
12#101×Dic43C211yesmaximal, characteristic, complemented
13#19134333C211yesmaximal, characteristic, complemented
14#19134332C211yesmaximal, characteristic, complemented
15C43×#1901C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C2×M16×D43C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19#14583620—21no—
20#14583620—21no—
21#14583620—21no—
22#14583620—21no—
23#14583620—21no—
24#14583620—21no—
25#14583620—21no—
26#14583620—21no—
27C2×#13063324C2211yescharacteristic
28C2×#13063320C412yes—
29C2×#13063318C412yes—
30C2×#13063311C412yes—
31C2×#13063301C2211yescharacteristic
32C2×Q8×Dic43C2211yescharacteristic
33C2×#13063290C412yes—
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×#13063284C2211yescharacteristic
36C2×#13063283C2211yescharacteristic
37#14582975—21no—
38#14582974—21no—
39#14582973—21no—
40#14582970—21no—
41#14582968—21no—
42#14582967—21no—
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582922C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×#13063244C2211yescharacteristic
48C2×#13063244C2211yescharacteristic
49#14582863C2211yescharacteristic
50#14582862C2211yescharacteristic
51#14582862C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582667C2211yescharacteristic
61#14582667C2211yescharacteristic
62#14582667C2211yescharacteristic
63#14582667C2211yescharacteristic
64C22×M16×C43C2211yescharacteristic
65C2×C22⋊Q8×C43C2211yescharacteristic
66C2×#101×C43C2211yescharacteristic
67C2×#101×C43C2211yescharacteristic
68C43×#407C2211yescharacteristic
69C43×#343C2211yescharacteristic
70C43×#343C2211yescharacteristic
71C22×Dic86C2×C412yes—
72C22×C22⋊D43C2×C411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C2×#10621877—21no—
75C2×#10621877—22no—
76C2×#10621877—41no—
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621872—21no—
82C2×#10621872—21no—
83M16×D43—22no—
84M16×D43—22no—
85M16×D43—41no—
86M16×D43—41no—
87C22×C43⋊C8—21no—
88C2×C8×D43—21no—
89C2×C8×D43—21no—
90#13063324—21no—
91#13063324—21no—
92#13063324—21no—
93#13063324—21no—
94#13063320—22no—
95#13063320—22no—
96#13063320—22no—
97#13063320—22no—
98#13063318—22no—
99#13063318—22no—
100#13063318—22no—
101#13063318—22no—
102#13063311—22no—
103#13063311—22no—
104#13063311—22no—
105#13063311—22no—
106#13063301—21no—
107#13063301—21no—
108#13063301—21no—
109#13063301—21no—
110Q8×Dic43—21no—
111Q8×Dic43—21no—
112Q8×Dic43—21no—
113Q8×Dic43—21no—
114#13063290—22no—
115#13063290—22no—
116#13063290—22no—
117#13063290—22no—
118C4×C22⋊D43D411yescharacteristic
119C4×C22⋊D43D411yescharacteristic
120C4×C22⋊D43D411yescharacteristic
121C4×C22⋊D43D411yescharacteristic
122C4×C22⋊D43D411yescharacteristic
123C4×C22⋊D43D411yescharacteristic
124C4×C22⋊D43D411yescharacteristic
125C4×C22⋊D43D411yescharacteristic
126#13063284—21no—
127#13063284—21no—
128#13063284—21no—
129#13063284—21no—
130#13063283—21no—
131#13063283—21no—
132#13063283—21no—
133#13063283—21no—
134C2×C4⋊Dic43C2×C412yes—
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4C2×C412yes—
138C2×Dic43⋊C4C2×C412yes—
139C2×Dic43⋊C4C2×C411yescharacteristic
140C2×C22⋊Dic43C2×C412yes—
141C2×C22⋊Dic43C2×C411yescharacteristic
142C2×(C2×D43)⋊C4C2×C412yes—
143C2×(C2×D43)⋊C4C2×C412yes—
144C2×(C2×D43)⋊C4C2×C411yescharacteristic
145C2×C4×Dic43C2×C412yes—
146C2×C4×Dic43C2×C412yes—
147C2×C4×Dic43C2×C412yes—
148C2×C4×Dic43C2311yescharacteristic
149Dic43⋊C8—21no—
150Dic43⋊C8—21no—
151Dic43⋊C8—21no—
152Dic43⋊C8—21no—
153#13063244—22no—
154#13063244—41no—
155C22⋊(C43⋊C8)—21no—
156C22⋊(C43⋊C8)—21no—
157(C2×D43)⋊C8—21no—
158(C2×D43)⋊C8—21no—
159(C2×D43)⋊C8—21no—
160(C2×D43)⋊C8—21no—
161#13063235—21no—
162#13063235—21no—
163C8×Dic43—21no—
164C8×Dic43—21no—
165C22×Q8×C43C2311yescharacteristic
166C23×C4×C43C2311yescharacteristic
167C2×M16×C43—21no—
168C2×M16×C43—22no—
169C2×M16×C43—41no—
170C2×M16×C43C2311yescharacteristic
171C2×M16×C43C2311yescharacteristic
172C2×M16×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C22×C8×C43—21no—
175C22⋊Q8×C43—21no—
176C22⋊Q8×C43—21no—
177C22⋊Q8×C43—21no—
178C22⋊Q8×C43—21no—
179C2×C4⋊C4×C43C2×C412yes—
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43C2×C412yes—
182#101×C43—22no—
183#101×C43—41no—
184C22⋊C8×C43—21no—
185C22⋊C8×C43—21no—
186C24×C43C22×C411yescharacteristic
187C23×D43C22×C411yescharacteristic
188C2×Q8×C43—21no—
189C2×Q8×C43—21no—
190C2×Q8×C43—21no—
191C2×Q8×C43—21no—
192C2×Q8×C43—21no—
193C2×Q8×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43C22×C412yes—
199C22×C4×C43C22×C411yescharacteristic
200C22×C4×C43C22×C412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C2×C22⋊D43—42no—
207C2×C22⋊D43C22⋊C411yescharacteristic
208C2×C22⋊D43C22⋊C411yescharacteristic
209C2×C22⋊D43C22⋊C411yescharacteristic
210C2×C22⋊D43C22⋊C411yescharacteristic
211C22×Dic43C22×C411yescharacteristic
212C22×Dic43C22×C411yescharacteristic
213C22×Dic43C22×C412yes—
214C22×Dic43C22×C412yes—
215C22×Dic43C22×C411yescharacteristic
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—44no—
227M16×C43—21no—
228M16×C43—21no—
229M16×C43—21no—
230M16×C43—21no—
231M16×C43—21no—
232M16×C43—21no—
233M16×C43—21no—
234M16×C43—42no—
235M16×C43#4112yes—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—42no—
241C4⋊C4×C43—22no—
242C4⋊C4×C43—22no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—22no—
247C22⋊Dic43—22no—
248C22⋊Dic43—22no—
249C22⋊Dic43C22⋊C411yescharacteristic
250C22⋊Dic43C22⋊C411yescharacteristic
251C22⋊Dic43C22⋊C411yescharacteristic
252C22⋊Dic43C22⋊C411yescharacteristic
253(C2×D43)⋊C4—22no—
254(C2×D43)⋊C4—22no—
255(C2×D43)⋊C4—22no—
256(C2×D43)⋊C4—22no—
257(C2×D43)⋊C4C22⋊C411yescharacteristic
258(C2×D43)⋊C4C22⋊C411yescharacteristic
259(C2×D43)⋊C4C22⋊C411yescharacteristic
260(C2×D43)⋊C4C22⋊C411yescharacteristic
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—22no—
266C4⋊Dic43—22no—
267Dic43⋊C4—22no—
268Dic43⋊C4—22no—
269Dic43⋊C4—22no—
270Dic43⋊C4—22no—
271Dic43⋊C4C22⋊C411yescharacteristic
272Dic43⋊C4C22⋊C411yescharacteristic
273Dic43⋊C4C22⋊C411yescharacteristic
274Dic43⋊C4C22⋊C411yescharacteristic
275C4×Dic43—22no—
276C4×Dic43—22no—
277C4×Dic43—22no—
278C4×Dic43—22no—
279C4×Dic43—22no—
280C4×Dic43—22no—
281C4×Dic43C2×D411yescharacteristic
282C4×Dic43C2×D411yescharacteristic
283C4×Dic43C2×D411yescharacteristic
284C4×Dic43C2×D411yescharacteristic
285#10621877—21no—
286#10621877—21no—
287#10621877—21no—
288#10621877—21no—
289#10621877—21no—
290#10621877—21no—
291#10621877—21no—
292#10621877—42no—
293#10621877#4112yes—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—42no—
299#10621872—42no—
300#10621872—42no—
301C8×D43—42no—
302C8×D43—42no—
303C23×C43—21no—
304C23×C43—21no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43C2×C22⋊C411yescharacteristic
308C23×C43C2×C22⋊C411yescharacteristic
309C23×C43C23×C411yescharacteristic
310C22×D43—21no—
311C22×D43—21no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43C2×C22⋊C411yescharacteristic
315C22×D43C2×C22⋊C411yescharacteristic
316Q8×C43—41no—
317Q8×C43—41no—
318Q8×C43—41no—
319Q8×C43—41no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—42no—
335C2×C4×C43C2×C22⋊C411yescharacteristic
336C2×C4×C43C2×C22⋊C411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C432−1+411yescharacteristic
343C22⋊D43—22no—
344C22⋊D43—22no—
345C22⋊D43—41no—
346C22⋊D43—41no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—41no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43C2×C22⋊C411yescharacteristic
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C4×D43—21no—
362C4×D43—21no—
363C4×D43—21no—
364C4×D43—21no—
365C4×D43—21no—
366C4×D43—21no—
367C4×D43—21no—
368C4×D43—21no—
369Dic86—44no—
370Dic86—44no—
371C8×C43—22no—
372C8×C43—41no—
373C8×C43—41no—
374C8×C43—41no—
375C43⋊C8—22no—
376C43⋊C8—41no—
377C43⋊C8—41no—
378C43⋊C8—41no—
379#22484—431nomaximal, Sylow
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43C22×C22⋊C411yescharacteristic
391C22×C43C4×#4111yescharacteristic
392C22×C43#52011yescharacteristic
393C2×D43—21no—
394C2×D43—21no—
395C2×D43—21no—
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C2×D43—81no—
400C2×D43—81no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43#54611yescharacteristic
406C4×C43#54611yescharacteristic
407C4×C43#54711yescharacteristic
408C4×C43#54711yescharacteristic
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—21no—
414Dic43—42no—
415Dic43—42no—
416Dic43#41312yes—
417C2×#556—431no—
418D4×M16—431no—
419D4×M16—431no—
420#1997—431no—
421#1997—431no—
422#1901—431no—
423#1901—431no—
424#1901—431no—
425#1901D4311yescharacteristic, complemented
426#1822—431no—
427#1822—431no—
428#1801—431no—
429C4×#101—431no—
430#1742—431no—
431#1742—431no—
432C2×C43—21no—
433C2×C43—21no—
434C2×C43—41no—
435C2×C43—41no—
436C2×C43#233911yescharacteristic
437C2×C43C2×#41311yescharacteristic
438C2×C43#288911yescharacteristic
439D43—41no—
440D43—41no—
441C22×M16—431no—
442C22×M16—431no—
443C22×M16—431no—
444C22×M16C2×D4311yescharacteristic
445#556—861no—
446#556—861no—
447#556—861no—
448#556—861no—
449#556—861no—
450#556—861no—
451#556—861no—
452#556—861no—
453C2×C4⋊Q8—431no—
454C2×#126—432no—
455C2×#126—432no—
456C2×#124—432no—
457C2×C22⋊Q8—431no—
458C2×C22⋊Q8C2×D4311yescharacteristic
459C2×C4×Q8—431no—
460C2×C4×Q8—432no—
461C2×C4×D4—431no—
462C2×#117—431no—
463C2×#117—431no—
464#436—861no—
465#436—861no—
466#435—861no—
467#435—861no—
468#435—861no—
469#435—861no—
470C8×D4—861no—
471C8×D4—861no—
472#423—431no—
473#423—431no—
474C2×#101—431no—
475C2×#101—431no—
476C2×#101C2×D4311yescharacteristic
477C2×#101C2×D4311yescharacteristic
478#407—431no—
479#407—431no—
480#407—431no—
481#407C2×D4311yescharacteristic
482C4×M16—431no—
483C4×M16—431no—
484#343—431no—
485#343—431no—
486#343—431no—
487#343—431no—
488#343—431no—
489#343—431no—
490#343—431no—
491#343—431no—
492#343—431no—
493#343—431no—
494#343C2×D4311yescharacteristic
495#343C2×D4311yescharacteristic
496C43#2248411yescharacteristic, complemented, Sylow
497C22×Q8—432no—
498C22×Q8C22×D4311yescharacteristic
499C22×D4—431no—
500C23×C4—431no—
501C23×C4C22×D4311yescharacteristic
502C2×M16—21no—
503C2×M16—22no—
504C2×M16—41no—
505C2×M16—431no—
506C2×M16—431no—
507C2×M16—431no—
508C2×M16—431no—
509C2×M16—861no—
510C2×M16—861no—
511C2×M16—861no—
512C2×M16—862no—
513C2×M16—862no—
514C2×M16—862no—
515C2×M16—1721no—
516C2×M16—1721no—
517C2×M16—1721no—
518C2×M16C22×D4311yescharacteristic
519C2×M16C22×D4311yescharacteristic
520C2×M16C22×D4311yescharacteristic
521C2×M16C22×D4311yescharacteristic
522C22×C8—21no—
523C22×C8—861no—
524C22×C8—861no—
525C22×C8—861no—
526C4⋊Q8—861no—
527C4⋊Q8—861no—
528C4⋊Q8—861no—
529C4⋊Q8—861no—
530#126—862no—
531#126—862no—
532#126—862no—
533#126—862no—
534#126—862no—
535#126—862no—
536#126—862no—
537#126—862no—
538#124—862no—
539#124—862no—
540#124—862no—
541#124—862no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—861no—
547C22⋊Q8—861no—
548C22⋊Q8—861no—
549C22⋊Q8—861no—
550C4×Q8—861no—
551C4×Q8—861no—
552C4×Q8—861no—
553C4×Q8—861no—
554C4×Q8—862no—
555C4×Q8—862no—
556C4×Q8—862no—
557C4×Q8—862no—
558C4×D4—431no—
559C4×D4—431no—
560C4×D4—431no—
561C4×D4—431no—
562C4×D4—431no—
563C4×D4—431no—
564C4×D4—431no—
565C4×D4—431no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117—861no—
572#117—861no—
573#117—861no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—432no—
576C2×C4⋊C4—432no—
577C2×C4⋊C4—432no—
578C2×C4⋊C4—431no—
579C2×C4⋊C4—431no—
580C2×C4⋊C4C4×D4312yes—
581C2×C4⋊C4C22×D4311yescharacteristic
582C2×C22⋊C4—431no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—432no—
585C2×C22⋊C4—432no—
586C2×C22⋊C4—432no—
587C2×C22⋊C4C4×D4312yes—
588C2×C42—431no—
589C2×C42—432no—
590C2×C42—432no—
591C2×C42—432no—
592C4⋊C8—861no—
593C4⋊C8—861no—
594C4⋊C8—861no—
595C4⋊C8—861no—
596#101—22no—
597#101—41no—
598#101—862no—
599#101—1721no—
600C22⋊C8—21no—
601C22⋊C8—21no—
602C22⋊C8—861no—
603C22⋊C8—861no—
604C22⋊C8—861no—
605C22⋊C8—861no—
606C22⋊C8—861no—
607C22⋊C8—861no—
608#97—861no—
609#97—861no—
610C4×C8—861no—
611C4×C8—861no—
612C24—431no—
613C24C2×C4×D4311yescharacteristic
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—862no—
621C2×Q8—862no—
622C2×Q8—1724no—
623C2×D4—431no—
624C2×D4—431no—
625C2×D4—431no—
626C2×D4—431no—
627C2×D4—1722no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4C2×C4×D4312yes—
646C22×C4C2×C4×D4311yescharacteristic
647C22×C4C2×C4×D4312yes—
648C22×C4D4×D4311yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4D4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4C23×D4311yescharacteristic
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—21no—
659M16—21no—
660M16—42no—
661M16—432no—
662M16—861no—
663M16—861no—
664M16—861no—
665M16—861no—
666M16—861no—
667M16—861no—
668M16—861no—
669M16—1722no—
670M16—1722no—
671M16—1722no—
672M16#1062190012yes—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—42no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—1722no—
683C2×C8—1722no—
684C2×C8—1722no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—431no—
690C4⋊C4—431no—
691C4⋊C4—431no—
692C4⋊C4—431no—
693C4⋊C4—862no—
694C4⋊C4—862no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—862no—
698C4⋊C4—862no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—431no—
706C22⋊C4—431no—
707C22⋊C4—431no—
708C22⋊C4—431no—
709C22⋊C4—431no—
710C22⋊C4—431no—
711C22⋊C4—431no—
712C22⋊C4—431no—
713C22⋊C4—862no—
714C22⋊C4—862no—
715C22⋊C4—862no—
716C22⋊C4—862no—
717C22⋊C4—862no—
718C22⋊C4—862no—
719C42—431no—
720C42—431no—
721C42—431no—
722C42—431no—
723C42—862no—
724C42—862no—
725C42—862no—
726C42—862no—
727C42—862no—
728C42—862no—
729C23—21no—
730C23—21no—
731C23—41no—
732C23—41no—
733C23—431no—
734C23—431no—
735C23—861no—
736C23—861no—
737C23—1721no—
738C23—1721no—
739C23C22⋊C4×D4311yescharacteristic
740C23C22⋊C4×D4311yescharacteristic
741C23C22×C4×D4311yescharacteristic
742Q8—41no—
743Q8—41no—
744Q8—41no—
745Q8—41no—
746Q8—1724no—
747Q8—1724no—
748D4—862no—
749D4—862no—
750D4—1721no—
751D4—1721no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—42no—
767C2×C4—431no—
768C2×C4—431no—
769C2×C4—431no—
770C2×C4—431no—
771C2×C4—431no—
772C2×C4—431no—
773C2×C4—862no—
774C2×C4—861no—
775C2×C4—861no—
776C2×C4—861no—
777C2×C4—861no—
778C2×C4—861no—
779C2×C4—861no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—1721no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4C22⋊C4×D4311yescharacteristic
790C2×C4C22⋊C4×D4311yescharacteristic
791C2×C4C2×D4×D4311yescharacteristic
792C2×C4C2×D4×D4311yescharacteristic
793C2×C4#41×D4311yescharacteristic
794C2×C4C2×#1062190011yescharacteristic
795C2×C4#1306337011yescharacteristic
796C2×C4#1306337211yescharacteristic
797C8—22no—
798C8—41no—
799C8—41no—
800C8—41no—
801C8—862no—
802C8—1721no—
803C8—1721no—
804C8—1721no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—81no—
814C22—81no—
815C22—861no—
816C22—861no—
817C22—861no—
818C22—861no—
819C22—861no—
820C22—861no—
821C22—3441no—
822C22—3441no—
823C22C2×C22⋊C4×D4311yescharacteristic
824C22C4×#1062190011yescharacteristic
825C22#1458337811yescharacteristic
826C4—21no—
827C4—21no—
828C4—42no—
829C4—42no—
830C4—432no—
831C4—861no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—1722no—
837C4—1722no—
838C4#1458353611yescharacteristic
839C4#1458353811yescharacteristic
840C4#1458354711yescharacteristic
841C4#1458354911yescharacteristic
842C2—21no—
843C2—21no—
844C2—41no—
845C2—41no—
846C2—1721no—
847C2—1721no—
848C2#1913742111yescharacteristic
849C2#413×D4311yescharacteristic
850C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1901C2
socleC22×C43C22×C22⋊C4
prime radicalC22×C22⋊D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1901D43
hypocenterC43#22484
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
4. #19135582C2semidirect
5. #19135582C2semidirect
6. #19135064C2semidirect
7. #19135060C2semidirect
8. #19135060C2semidirect
9. #19134677C2semidirect
10. #19134676C2semidirect
11. #19134589C2semidirect
12. #101×Dic43C2semidirect
13. #19134333C2semidirect
14. #19134332C2semidirect
15. C43×#1901C2semidirect
425. #1901D43semidirect
496. C43#22484semidirect

Maximal subgroups

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

subgroupindex
C2×#145836202
M16×C22⋊D432
#191433272
#191355822
#191350642
#191350602
#191346772
#191346762
#191345892
#101×Dic432
#191343332
#191343322
C43×#19012
#2248443