Finite Group Databasebeta

← #25112001

Subgroups — #25112001

Order 11008.

2014 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583533C211yesmaximal, characteristic
2C2×(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
3C22×#13063245C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5C4⋊C4×C22⋊D43C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135399C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19135022C211yesmaximal, characteristic, complemented
10#19134911C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic, complemented
12#19134527C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C22×D4×D43—21no—
18C22×D4×D43C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic, complemented
20C22×C8×D43C2211yescharacteristic, complemented
21#14583533—24no—
22#14583533C418yescomplemented
23C2×#13063321C2211yescharacteristic
24C2×#13063300C2211yescharacteristic
25C2×#13063298—21no—
26C2×#13063295—21no—
27C2×#13063293—21no—
28C2×#13063287C2211yescharacteristic
29C2×C4×C22⋊D43—21no—
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic, complemented
32(C22⋊D43)⋊C8—24no—
33C2×Dic43⋊C8C2211yescharacteristic, complemented
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic, complemented
38C2×#13063246C2211yescharacteristic, complemented
39C2×#13063246C2211yescharacteristic, complemented
40C2×#13063245—24no—
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic, complemented
44C2×#13063245C2211yescharacteristic, complemented
45#102×D43—24no—
46C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
47C2×C8×Dic43C2211yescharacteristic, complemented
48#14582794—21no—
49#14582772—21no—
50#14582770—21no—
51#14582768C2211yescharacteristic, complemented
52#14582759C2211yescharacteristic, complemented
53#14582756C2211yescharacteristic, complemented
54C4⋊C4×Dic43C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×#121×C43C2211yescharacteristic
58C22×C4⋊C4×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C24×D43—21no—
66C22×D172—22no—
67C22×D172—22no—
68C22×D172—21no—
69C22×D172—21no—
70C22×D172—22no—
71C22×D172—41no—
72C22×D172—41no—
73C22×D172C2×C414yescomplemented
74C22×D172C2311yescharacteristic
75C22×D172C2311yescharacteristic
76C22×C22⋊D43—21no—
77C22×C22⋊D43—21no—
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—28no—
81C2×D4×D43—22no—
82C2×D4×D43—22no—
83C2×D4×D43—22no—
84C2×D4×D43—41no—
85C2×D4×D43—41no—
86C2×D4×D43—44no—
87C2×D4×D43—44no—
88C2×D4×D43C2×C414yescomplemented
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92C22×C43⋊C8—22no—
93C22×C43⋊C8—22no—
94C22×C43⋊C8—41no—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97C2×C8×D43—22no—
98C2×C8×D43—22no—
99C2×C8×D43—41no—
100#13063321—22no—
101#13063321C2×C414yescomplemented
102#13063300—22no—
103#13063300C2×C414yescomplemented
104#13063298—28no—
105#13063295—28no—
106#13063293—28no—
107#13063287—22no—
108#13063287C2×C414yescomplemented
109C4×C22⋊D43—44no—
110C4×C22⋊D43C2×C414yes—
111C4×C22⋊D43D414yes—
112C2×C4⋊Dic43C2311yescharacteristic
113C2×C4⋊Dic43C2311yescharacteristic
114C2×Dic43⋊C4—21no—
115C2×Dic43⋊C4—21no—
116C2×Dic43⋊C4—21no—
117C2×Dic43⋊C4D411yescharacteristic
118C4⋊C4×D43—22no—
119C4⋊C4×D43—41no—
120C2×C22⋊Dic43—21no—
121C2×C22⋊Dic43D411yescharacteristic
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4—21no—
125C2×(C2×D43)⋊C4D411yescharacteristic
126C2×C4×Dic43—21no—
127C2×C4×Dic43C2311yescharacteristic
128Dic43⋊C8—22no—
129#13063247—22no—
130#13063247—22no—
131#13063247—41no—
132#13063247—41no—
133#13063246—22no—
134#13063246—41no—
135#13063245—22no—
136#13063245—22no—
137#13063245—22no—
138#13063245D414yescomplemented
139(C2×D43)⋊C8—22no—
140C8×Dic43—22no—
141C43⋊#95—21no—
142C43⋊#95—21no—
143C43⋊#95—21no—
144C22×D4×C43—21no—
145C22×D4×C43C2311yescharacteristic
146C23×C4×C43—21no—
147C23×C4×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150#121×C43—22no—
151#121×C43C2×C414yescomplemented
152C2×C4⋊C4×C43—22no—
153C2×C4⋊C4×C43—21no—
154C2×C4⋊C4×C43—41no—
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C4⋊C4×C43C2311yescharacteristic
157C2×C4⋊C4×C43C2311yescharacteristic
158C2×C22⋊C4×C43—21no—
159#102×C43—22no—
160#102×C43—41no—
161C22⋊C8×C43—22no—
162C24×C43—21no—
163C24×C43C2×D411yescharacteristic
164C23×D43—21no—
165C23×D43—21no—
166C23×D43—24no—
167C23×D43—24no—
168C23×D43—42no—
169C23×D43—42no—
170C23×D43—42no—
171C23×D43—42no—
172C23×D43—42no—
173C23×D43—42no—
174C23×D43—42no—
175C23×D43—42no—
176C23×D43—81no—
177C23×D43—81no—
178C23×D43—81no—
179C23×D43—81no—
180C23×D43C2×D411yescharacteristic
181C2×D4×C43—21no—
182C2×D4×C43—24no—
183C2×D4×C43—21no—
184C2×D4×C43—21no—
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—42no—
188C2×D4×C43—42no—
189C2×D4×C43C22×C412yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43—81no—
200C22×C4×C43C22×C412yes—
201C22×C4×C43C2×D412yes—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—42no—
210C2×C22⋊D43—42no—
211C2×C22⋊D43—81no—
212C2×C22⋊D43—81no—
213C2×C22⋊D43C22⋊C414yes—
214C2×C22⋊D43D814yes—
215C2×C22⋊D43SD1614yes—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221D4×D43—28no—
222D4×D43—44no—
223D4×D43—44no—
224D4×D43—44no—
225D4×D43—432no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—24no—
230C2×D172—21no—
231C2×D172—24no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—28no—
237C2×D172—42no—
238C2×D172—42no—
239C2×D172—44no—
240C2×D172—44no—
241C2×D172—44no—
242C2×D172—42no—
243C2×D172—42no—
244C2×D172C22×C412yes—
245C2×D172C22×C412yes—
246C2×D172C2×D412yes—
247C2×D172#4112yes—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—24no—
253C2×C4×D43—42no—
254C2×C4×D43—42no—
255C2×C4×D43—42no—
256C2×C4×D43—42no—
257C2×C4×D43—81no—
258C2×C4×D43C22×C412yes—
259C2×C4×D43C2×D412yes—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—42no—
271C4⋊C4×C43C22×C412yes—
272C4⋊C4×C43C2×D412yescomplemented
273C22⋊C4×C43—24no—
274C22⋊Dic43—42no—
275C22⋊Dic43C22⋊C414yes—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4—24no—
278(C2×D43)⋊C4—42no—
279(C2×D43)⋊C4C22⋊C414yes—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284Dic43⋊C4—42no—
285Dic43⋊C4—42no—
286Dic43⋊C4—81no—
287Dic43⋊C4C22⋊C414yes—
288C4×Dic43—42no—
289C4×Dic43C22×C412yes—
290C4×Dic43C2×D412yes—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—44no—
297C2×C43⋊C8C2×D412yescomplemented
298C8×D43—44no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43—41no—
308C23×C43—41no—
309C23×C43—41no—
310C23×C43C2×C22⋊C412yes—
311C23×C43C2×D812yes—
312C23×C43C2×SD1612yes—
313C23×C43C22×D411yescharacteristic
314C22×D43—21no—
315C22×D43—21no—
316C22×D43—21no—
317C22×D43—21no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—48no—
323C22×D43—48no—
324C22×D43—41no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—41no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—41no—
331C22×D43—41no—
332C22×D43—41no—
333C22×D43—41no—
334C22×D43—48no—
335C22×D43—48no—
336C22×D43—84no—
337C22×D43—84no—
338C22×D43—84no—
339C22×D43—84no—
340C22×D43—84no—
341C22×D43—84no—
342C22×D43—84no—
343C22×D43—84no—
344C22×D43—84no—
345C22×D43—84no—
346C22×D43C2×C22⋊C412yes—
347C22×D43C2×D812yes—
348C22×D43C2×SD1612yes—
349D4×C43—22no—
350D4×C43—22no—
351D4×C43—48no—
352D4×C43—41no—
353D4×C43—41no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—84no—
370C2×C4×C43C2×C22⋊C412yes—
371C2×C4×C43C23×C411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D411yescharacteristic
374C2×C4×C43C2×#4111yescharacteristic
375C2×C4×C43H(5,𝔽2)11yescharacteristic
376C2×C4×C43H(5,𝔽2)11yescharacteristic
377C22⋊D43—48no—
378C22⋊D43—48no—
379C22⋊D43—84no—
380C22⋊D43#102116yescomplemented
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43C2×C22⋊C412yes—
392C2×Dic43C2×C22⋊C412yes—
393C2×Dic43C2×C22⋊C412yes—
394C2×Dic43C2×D812yes—
395C2×Dic43C2×SD1612yes—
396D172—22no—
397D172—22no—
398D172—22no—
399D172—22no—
400D172—22no—
401D172—48no—
402D172—48no—
403D172—41no—
404D172—41no—
405D172C4×D414yescomplemented
406C4×D43—22no—
407C4×D43—22no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—48no—
411C4×D43—84no—
412C8×C43—41no—
413C8×C43—41no—
414C43⋊C8—22no—
415C43⋊C8—41no—
416D4×#102—431nomaximal, Sylow
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—22no—
421C22×C43—22no—
422C22×C43—22no—
423C22×C43—42no—
424C22×C43—42no—
425C22×C43—42no—
426C22×C43—81no—
427C22×C43—81no—
428C22×C43—81no—
429C22×C43—81no—
430C22×C43C2×#10214yescomplemented
431C22×C43C22×C22⋊C411yescharacteristic
432C22×C43D4211yescharacteristic
433C22×C43#54611yescharacteristic
434C22×C43C22×D811yescharacteristic
435C22×C43C22×SD1611yescharacteristic
436C22×C43#57611yescharacteristic
437C22×C43#57711yescharacteristic
438C2×D43—22no—
439C2×D43—22no—
440C2×D43—22no—
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—24no—
445C2×D43—42no—
446C2×D43—42no—
447C2×D43—42no—
448C2×D43—42no—
449C2×D43—42no—
450C2×D43—42no—
451C2×D43—42no—
452C2×D43—42no—
453C2×D43—42no—
454C2×D43—816no—
455C2×D43—816no—
456C2×D43—81no—
457C2×D43—81no—
458C2×D43—81no—
459C2×D43—81no—
460C2×D43C2×#10214yescomplemented
461C4×C43—22no—
462C4×C43—42no—
463C4×C43—42no—
464C4×C43—81no—
465C4×C43C2×C4×D411yescharacteristic
466C4×C43#51811yescharacteristic
467C4×C43D4211yescharacteristic
468C4×C43#54611yescharacteristic
469Dic43—22no—
470Dic43—22no—
471Dic43—81no—
472Dic43—81no—
473Dic43C2×#10214yescomplemented
474C2×D42—431no—
475C2×C8×D4—431no—
476C22×#102—431no—
477C22×#102—431no—
478D4×C4⋊C4—431no—
479#1982—431no—
480#1957—431no—
481#1893—431no—
482#1893—431no—
483#1874—431no—
484#1874D4311yescharacteristic, complemented
485#1802—431no—
486#1786—431no—
487#1786—431no—
488C4×#102—431no—
489C2×C43—24no—
490C2×C43—82no—
491C2×C43D4×C22⋊C411yescharacteristic
492C2×C43C22×#10211yescharacteristic
493C2×C43#289711yescharacteristic
494C2×C43D4×D811yescharacteristic
495C2×C43D4×SD1611yescharacteristic
496C2×C43#329411yescharacteristic
497C2×C43#329511yescharacteristic
498D43—24no—
499D43—44no—
500D43—82no—
501C23×D4—431no—
502C23×D4—431no—
503C23×D4—861no—
504C23×C8—431no—
505C23×C8—431no—
506D42—438no—
507D42—864no—
508C2×#127—431no—
509C2×#121—431no—
510C2×#121—861no—
511C2×#121C2×D4311yescharacteristic
512C2×#120—861no—
513C2×#120—861no—
514C2×C4×D4—431no—
515C2×C4×D4—431no—
516C2×C4×D4—861no—
517C22×C4⋊C4—431no—
518C22×C4⋊C4C2×D4311yescharacteristic, complemented
519C8×D4—864no—
520C2×C4⋊C8—431no—
521C2×#102—431no—
522C2×#102—431no—
523C2×#102—431no—
524C2×#102—431no—
525C2×#102—431no—
526C2×#102—431no—
527C2×#102—431no—
528C2×#102—431no—
529C2×#102—431no—
530C2×#102—431no—
531C2×#102—864no—
532C2×#102—864no—
533C2×#102C2×D4311yescharacteristic, complemented
534C2×#102C2×D4311yescharacteristic, complemented
535C2×C22⋊C8—431no—
536C2×C22⋊C8C2×D4311yescharacteristic, complemented
537C2×C4×C8—431no—
538#389—861no—
539#385—861no—
540#385—861no—
541#384—431no—
542#380—431no—
543#380—431no—
544C4×C4⋊C4—431no—
545#340—431no—
546#340—431no—
547#340C2×D4311yescharacteristic, complemented
548#340C2×D4311yescharacteristic, complemented
549C43D4×#10211yescharacteristic, complemented, Sylow
550C25—861no—
551C25—861no—
552C22×D4—21no—
553C22×D4—431no—
554C22×D4—434no—
555C22×D4—434no—
556C22×D4—431no—
557C22×D4—431no—
558C22×D4—862no—
559C22×D4—862no—
560C22×D4—861no—
561C22×D4—862no—
562C22×D4—861no—
563C22×D4—861no—
564C22×D4—861no—
565C22×D4—862no—
566C22×D4—862no—
567C22×D4—868no—
568C22×D4—861no—
569C22×D4—862no—
570C22×D4—1721no—
571C22×D4—1721no—
572C22×D4—1721no—
573C22×D4—1721no—
574C22×D4—1724no—
575C22×D4—1724no—
576C22×D4C22×D4311yescharacteristic
577C23×C4—21no—
578C23×C4—431no—
579C23×C4—861no—
580C23×C4—861no—
581C23×C4C22×D4311yescharacteristic
582C22×C8—431no—
583C22×C8—431no—
584C22×C8—862no—
585C22×C8—862no—
586C22×C8—862no—
587C22×C8—862no—
588C22×C8—1721no—
589C22×C8—1721no—
590C22×C8C22×D4311yescharacteristic
591C22×C8C22×D4311yescharacteristic
592#127—434no—
593#127—862no—
594#121—22no—
595#121—434no—
596#121—868no—
597#121—862no—
598#121C4×D4314yescomplemented
599#120—868no—
600#120—868no—
601C4×D4—434no—
602C4×D4—434no—
603C4×D4—434no—
604C4×D4—862no—
605C4×D4—1724no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—1721no—
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C4⋊C4C22×D4311yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—431no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C42—431no—
628C2×C42—861no—
629C4⋊C8—862no—
630#102—22no—
631#102—41no—
632#102—434no—
633#102—862no—
634#102—862no—
635#102—862no—
636#102—862no—
637#102—862no—
638#102—862no—
639#102—1721no—
640#102—1721no—
641#102—1721no—
642C22⋊C8—22no—
643C22⋊C8—862no—
644C4×C8—862no—
645#95—861no—
646#95—861no—
647#95—861no—
648C24—21no—
649C24—431no—
650C24—864no—
651C24—861no—
652C24—864no—
653C24—861no—
654C24—3441no—
655C24—3441no—
656C24—3441no—
657C24—3441no—
658C24—1722no—
659C24—1722no—
660C24—1722no—
661C24—1722no—
662C24—1722no—
663C24—1722no—
664C24—1722no—
665C24—1722no—
666C24D4×D4311yescharacteristic
667C2×D4—24no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—434no—
676C2×D4—434no—
677C2×D4—434no—
678C2×D4—432no—
679C2×D4—432no—
680C2×D4—432no—
681C2×D4—432no—
682C2×D4—868no—
683C2×D4—864no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—864no—
687C2×D4—868no—
688C2×D4—864no—
689C2×D4—861no—
690C2×D4—861no—
691C2×D4—861no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—3441no—
698C2×D4—3441no—
699C2×D4—1724no—
700C2×D4—1724no—
701C2×D4—1724no—
702C2×D4—1722no—
703C2×D4—1722no—
704C2×D4—1722no—
705C2×D4—1722no—
706C2×D4—1722no—
707C2×D4—1722no—
708C2×D4—1724no—
709C2×D4—1724no—
710C2×D4—1724no—
711C2×D4—1722no—
712C2×D4—1722no—
713C2×D4—17232no—
714C2×D4C2×C4×D4312yes—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—81no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—432no—
729C22×C4—432no—
730C22×C4—864no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—3441no—
738C22×C4—1722no—
739C22×C4—1722no—
740C22×C4—1722no—
741C22×C4—1722no—
742C22×C4C2×C4×D4312yes—
743C22×C4D4×D4311yescharacteristic
744C22×C4D4×D4312yes—
745C22×C4C23×D4311yescharacteristic
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—432no—
753C2×C8—861no—
754C2×C8—861no—
755C2×C8—861no—
756C2×C8—861no—
757C2×C8—861no—
758C2×C8—1724no—
759C2×C8—1724no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—42no—
765C4⋊C4—434no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—3441no—
771C4⋊C4—1722no—
772C4⋊C4—1722no—
773C4⋊C4C2×C4×D4312yes—
774C4⋊C4D4×D4312yescomplemented
775C22⋊C4—24no—
776C22⋊C4—434no—
777C22⋊C4—434no—
778C22⋊C4—864no—
779C22⋊C4—864no—
780C22⋊C4—1722no—
781C22⋊C4—1722no—
782C42—432no—
783C42—432no—
784C42—1722no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—432no—
797C23—432no—
798C23—432no—
799C23—861no—
800C23—861no—
801C23—861no—
802C23—861no—
803C23—862no—
804C23—862no—
805C23—862no—
806C23—862no—
807C23—3444no—
808C23—3444no—
809C23—3444no—
810C23—3444no—
811C23—3444no—
812C23—3444no—
813C23—3444no—
814C23—3444no—
815C23—3444no—
816C23—3444no—
817C23—1728no—
818C23—1728no—
819C23—1728no—
820C23—1728no—
821C23—1721no—
822C23—1721no—
823C23—1721no—
824C23—1721no—
825C23—1721no—
826C23—1721no—
827C23—1721no—
828C23—1721no—
829C23—1721no—
830C23—1721no—
831C23C22⋊C4×D4312yes—
832C23D8×D4312yes—
833C23SD16×D4312yes—
834C23C2×D4×D4311yescharacteristic
835D4—22no—
836D4—22no—
837D4—48no—
838D4—41no—
839D4—41no—
840D4—4316no—
841D4—434no—
842D4—862no—
843D4—862no—
844D4—862no—
845D4—862no—
846D4—862no—
847D4—3444no—
848D4—1728no—
849D4—1728no—
850D4—1728no—
851D4—1728no—
852D4—1721no—
853D4—1721no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—84no—
870C2×C4—432no—
871C2×C4—432no—
872C2×C4—432no—
873C2×C4—432no—
874C2×C4—432no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—862no—
882C2×C4—862no—
883C2×C4—3444no—
884C2×C4—1728no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4—1721no—
888C2×C4—1721no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4C22⋊C4×D4312yes—
892C2×C4C22×C4×D4311yescharacteristic
893C2×C4C2×D4×D4311yescharacteristic
894C2×C4C2×D4×D4311yescharacteristic
895C2×C4#41×D4311yescharacteristic
896C2×C4#1306337011yescharacteristic
897C2×C4#1306337111yescharacteristic
898C8—41no—
899C8—41no—
900C8—862no—
901C8—1721no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—434no—
916C22—862no—
917C22—862no—
918C22—862no—
919C22—862no—
920C22—862no—
921C22—862no—
922C22—864no—
923C22—34416no—
924C22—34416no—
925C22—3441no—
926C22—3441no—
927C22—3441no—
928C22—3441no—
929C22—1722no—
930C22—1722no—
931C22—1722no—
932C22—1722no—
933C22—1722no—
934C22—1722no—
935C22—1722no—
936C22—1722no—
937C22—1722no—
938C22#102×D4314yescomplemented
939C22C2×C22⋊C4×D4311yescharacteristic
940C22#1458353111yescharacteristic
941C22#1458354111yescharacteristic
942C22C2×D8×D4311yescharacteristic
943C22C2×SD16×D4311yescharacteristic
944C22#1458370311yescharacteristic
945C22#1458370811yescharacteristic
946C4—22no—
947C4—42no—
948C4—42no—
949C4—81no—
950C4—434no—
951C4—862no—
952C4—862no—
953C4—3441no—
954C4—3441no—
955C4C4×D4×D4311yescharacteristic
956C4#1458337111yescharacteristic
957C4#1458353311yescharacteristic
958C4#1458353811yescharacteristic
959C2—24no—
960C2—82no—
961C2—864no—
962C2—3442no—
963C2—1724no—
964C2#1913741311yescharacteristic
965C2C2×#102×D4311yescharacteristic
966C2#1914311911yescharacteristic
967C2#1914626511yescharacteristic
968C2#1914628411yescharacteristic
969C2#1914640611yescharacteristic
970C2#1914641711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583533C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43D4×#102
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D43)⋊C8C2semidirect
3. C22×#13063245C2semidirect
4. C2×#102×D43C2semidirect
5. C4⋊C4×C22⋊D43C2semidirect
6. #19135520C2semidirect
7. #19135399C2semidirect
8. #19135024C2semidirect
9. #19135022C2semidirect
10. #19134911C2semidirect
11. #19134594C2semidirect
12. #19134527C2semidirect
13. #19134524C2semidirect
14. #19134409C2semidirect
15. C43×#1874C2semidirect
19. C23×C43⋊C8C22semidirect
20. C22×C8×D43C22semidirect
22. #14583533C4semidirect
31. C2×C4⋊C4×D43C22semidirect
33. C2×Dic43⋊C8C22semidirect
36. C2×#13063247C22semidirect
37. C2×#13063247C22semidirect
38. C2×#13063246C22semidirect
39. C2×#13063246C22semidirect
43. C2×#13063245C22semidirect
44. C2×#13063245C22semidirect
46. C2×(C2×D43)⋊C8C22semidirect
47. C2×C8×Dic43C22semidirect
51. #14582768C22semidirect
52. #14582759C22semidirect
53. #14582756C22semidirect
54. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C22×C4⋊C4×C43C22semidirect
59. C2×#102×C43C22semidirect
60. C2×#102×C43C22semidirect
61. C2×C22⋊C8×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
73. C22×D172C2×C4semidirect
88. C2×D4×D43C2×C4semidirect
101. #13063321C2×C4semidirect
103. #13063300C2×C4semidirect
108. #13063287C2×C4semidirect
138. #13063245D4semidirect
151. #121×C43C2×C4semidirect
272. C4⋊C4×C43C2×D4semidirect
297. C2×C43⋊C8C2×D4semidirect
380. C22⋊D43#102semidirect
405. D172C4×D4semidirect
430. C22×C43C2×#102semidirect
460. C2×D43C2×#102semidirect
473. Dic43C2×#102semidirect
484. #1874D43semidirect
518. C22×C4⋊C4C2×D43semidirect
533. C2×#102C2×D43semidirect
534. C2×#102C2×D43semidirect
536. C2×C22⋊C8C2×D43semidirect
547. #340C2×D43semidirect
548. #340C2×D43semidirect
549. C43D4×#102semidirect
598. #121C4×D43semidirect
774. C4⋊C4D4×D43semidirect
938. C22#102×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835332
C2×(C22⋊D43)⋊C82
C22×#130632452
C2×#102×D432
C4⋊C4×C22⋊D432
#191355202
#191353992
#191350242
#191350222
#191349112
#191345942
#191345272
#191345242
#191344092
C43×#18742
D4×#10243