Finite Group Databasebeta

← #25134248

Subgroups — #25134248

Order 11008.

1448 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583138C211yesmaximal, characteristic, complemented
2C2×#14583061C211yesmaximal, characteristic, complemented
3C2×#14583061C211yesmaximal, characteristic, complemented
4C2×#14582895C211yesmaximal, characteristic, complemented
5#19138024C211yesmaximal, characteristic, complemented
6#19135838C211yesmaximal, characteristic, complemented
7#19135795C211yesmaximal, characteristic, complemented
8#19135695C211yesmaximal, characteristic, complemented
9#19135603C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134908C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134842C211yesmaximal, characteristic, complemented
14#19134535C211yesmaximal, characteristic, complemented
15C2×C43×#547C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063304C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23#14583138—24no—
24#14583061—24no—
25#14583061—24no—
26C2×#13063258C2211yescharacteristic
27#14582895—24no—
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41#14582827—21no—
42#14582813—21no—
43#14582805C2211yescharacteristic
44#14582797C2211yescharacteristic
45#14582794—21no—
46#14582793—21no—
47#14582759C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C22×#41×C43C2211yescharacteristic
54C43×#547—24no—
55C43×#547—24no—
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#123×C43—21no—
58C2×#123×C43—21no—
59C2×C22⋊Q8×C43C2211yescharacteristic
60C2×C22⋊Q8×C43C2211yescharacteristic
61C2×#121×C43—21no—
62C2×C4×D4×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic
64C22×C4⋊C4×C43—21no—
65C22×Dic86C2311yescharacteristic
66C2×#10621885—22no—
67C2×#10621885—22no—
68C2×#10621885—22no—
69C2×#10621885—41no—
70C2×#10621885—41no—
71C2×#10621885—41no—
72C2×#10621883—22no—
73C2×#10621883—22no—
74C2×#10621883—22no—
75C22×C43⋊C8—22no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85#13063304—41no—
86#13063284—22no—
87#13063284—41no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C4×Dic43—21no—
99#13063258—22no—
100#13063249—22no—
101#13063249—22no—
102#13063249—22no—
103#13063249—22no—
104#13063249—22no—
105#13063249—41no—
106#13063248—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246D414yescomplemented
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C2×#41×C43—22no—
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—41no—
125C2×#41×C43—41no—
126C2×#41×C43—41no—
127C2×#41×C43—41no—
128C2×#41×C43D414yes—
129C22×Q8×C43C2311yescharacteristic
130C22×Q8×C43C2311yescharacteristic
131C22×D4×C43—21no—
132C22×D4×C43—21no—
133C22×D4×C43D411yescharacteristic
134C22×D4×C43C2311yescharacteristic
135C23×C4×C43—21no—
136C23×C4×C43—21no—
137C23×C4×C43—21no—
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C4⋊Q8×C43—22no—
141C4⋊Q8×C43—22no—
142#123×C43—28no—
143#123×C43—28no—
144C22⋊Q8×C43—22no—
145C22⋊Q8×C43—22no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43D414yes—
148#121×C43—28no—
149C4×D4×C43—22no—
150C4×D4×C43—22no—
151C4×D4×C43—22no—
152C4×D4×C43—22no—
153C2×C4⋊C4×C43—28no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43—21no—
156C2×C4⋊C4×C43—21no—
157C2×C4⋊C4×C43—21no—
158C2×C4⋊C4×C43D411yescharacteristic
159C2×C4⋊C4×C43C2311yescharacteristic
160C2×C22⋊C4×C43—21no—
161C2×C22⋊C4×C43—21no—
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43D411yescharacteristic
164C2×C22⋊C4×C43D411yescharacteristic
165C2×C42×C43C2311yescharacteristic
166C24×C43—21no—
167C24×C43C2×D411yescharacteristic
168C24×C43C2×D411yescharacteristic
169#41×C43—28no—
170#41×C43—44no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174#41×C43—44no—
175#41×C43—44no—
176#41×C43—44no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43—21no—
180C2×Q8×C43—21no—
181C2×Q8×C43—21no—
182C2×Q8×C43—21no—
183C2×Q8×C43—21no—
184C2×Q8×C43—21no—
185C2×Q8×C43—21no—
186C2×Q8×C43—21no—
187C2×Q8×C43C2×D412yes—
188C2×Q8×C43C2×D412yes—
189C2×D4×C43—24no—
190C2×D4×C43—22no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—22no—
195C2×D4×C43—24no—
196C2×D4×C43—41no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43—42no—
200C2×D4×C43—42no—
201C2×D4×C43C2×D412yes—
202C2×D4×C43C2×D412yes—
203C2×D4×C43#4112yes—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—24no—
209C22×C4×C43—24no—
210C22×C4×C43—24no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—42no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43—42no—
224C22×C4×C43—42no—
225C22×C4×C43—42no—
226C22×C4×C43C2×D412yes—
227C22×C4×C43C2×D412yes—
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—21no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—22no—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43C2×D412yes—
250C22⋊C4×C43—24no—
251C22⋊C4×C43—24no—
252C22⋊C4×C43—22no—
253C22⋊C4×C43—24no—
254C22⋊C4×C43—22no—
255C42×C43—21no—
256C42×C43—21no—
257C22⋊Dic43—42no—
258C22⋊Dic43—42no—
259C22⋊Dic43—42no—
260C22⋊Dic43—42no—
261#10621885—44no—
262#10621885—44no—
263#10621883—44no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43C2×D412yes—
270Dic43⋊C4—42no—
271Dic43⋊C4—42no—
272Dic43⋊C4—42no—
273C4×Dic43—42no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C2×C43⋊C8—44no—
286C2×C43⋊C8C2×D412yes—
287C23×C43—22no—
288C23×C43—21no—
289C23×C43—22no—
290C23×C43—21no—
291C23×C43—22no—
292C23×C43—21no—
293C23×C43—21no—
294C23×C43—21no—
295C23×C43—21no—
296C23×C43—21no—
297C23×C43—21no—
298C23×C43—21no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—41no—
307C23×C43#12012yes—
308C23×C43C22×D411yescharacteristic
309Q8×C43—22no—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43—41no—
314Q8×C43—41no—
315Q8×C43—41no—
316Q8×C43—41no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—44no—
321D4×C43—48no—
322D4×C43—48no—
323D4×C43#12114yes—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—22no—
334C2×C4×C43—21no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—48no—
342C2×C4×C43—48no—
343C2×C4×C43—48no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—41no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43#12012yes—
355C2×C4×C43#13512yes—
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C2×#4111yescharacteristic
360C2×C4×C43H(5,𝔽2)11yescharacteristic
361C2×C4×C43H(5,𝔽2)11yescharacteristic
362C2×Dic43—22no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—41no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374Dic86—41no—
375Dic86—41no—
376Dic86—41no—
377Dic86—41no—
378C43⋊C8—22no—
379C43⋊C8—41no—
380C43⋊C8—41no—
381C43⋊C8—41no—
382#24430—431nomaximal, Sylow
383C22×C43—24no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—41no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43C2×#12011yescharacteristic
405C22×C43D4211yescharacteristic
406C22×C43#54611yescharacteristic
407C22×C43C2×#13511yescharacteristic
408C22×C43#57511yescharacteristic
409C22×C43#57811yescharacteristic
410C22×C43#57811yescharacteristic
411C4×C43—22no—
412C4×C43—22no—
413C4×C43—41no—
414C4×C43—42no—
415C4×C43—42no—
416C4×C43—42no—
417C4×C43—41no—
418C4×C43C2×#12111yescharacteristic
419C4×C43#53411yescharacteristic
420C4×C43D4211yescharacteristic
421C4×C43#54611yescharacteristic
422Dic43—42no—
423Dic43—81no—
424Dic43—81no—
425Dic43—81no—
426C2×#547D4311yescharacteristic
427C2×#467—431no—
428C2×#452—431no—
429C2×#452—431no—
430C2×#416—431no—
431#2415—431no—
432#2043—431no—
433#2036—431no—
434#2016—431no—
435#2001—431no—
436#1877—431no—
437#1873—431no—
438#1869—431no—
439#1862—431no—
440#1788—431no—
441C2×C43—42no—
442C2×C43—44no—
443C2×C43—81no—
444C2×C43#241011yescharacteristic
445C2×C43#300211yescharacteristic
446C2×C43#301111yescharacteristic
447C2×C43#326911yescharacteristic
448C2×C43#328311yescharacteristic
449C2×C43#330211yescharacteristic
450C2×C43#331511yescharacteristic
451C22×#41C2×D4311yescharacteristic
452C22×#41C2×D4311yescharacteristic
453C22×Q16—431no—
454C22×Q16—431no—
455C22×SD16—431no—
456C23×C8—431no—
457#547—24no—
458#547—24no—
459C2×C4⋊Q8C2×D4311yescharacteristic
460C2×#123—21no—
461C2×#123—21no—
462C2×C22⋊Q8—431no—
463C2×C22⋊Q8—431no—
464C2×C22⋊Q8C2×D4311yescharacteristic
465C2×C22⋊Q8C2×D4311yescharacteristic
466C2×#121—21no—
467C2×C4×D4C2×D4311yescharacteristic
468C2×C4×D4C2×D4311yescharacteristic
469C2×#117—431no—
470C22×C4⋊C4—21no—
471#467—864no—
472#452—864no—
473#452—864no—
474C2×#107—431no—
475#416—864no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#103—431no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×C22⋊C8—431no—
487C2×C22⋊C8—431no—
488C2×C22⋊C8—431no—
489#397—861no—
490#394—861no—
491#391—431no—
492#389—431no—
493#389—861no—
494#388—861no—
495#380—431no—
496#340—431no—
497#340—431no—
498#336—431no—
499#336—431no—
500C43#2443011yescharacteristic, complemented, Sylow
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41C22⋊D4314yes—
513C22×Q8—431no—
514C22×Q8C22×D4311yescharacteristic
515C22×Q8C22×D4311yescharacteristic
516C22×D4—21no—
517C22×D4—21no—
518C22×D4C22⋊D4311yescharacteristic
519C22×D4C22×D4311yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C22×D4311yescharacteristic
524C23×C4C22×D4311yescharacteristic
525C2×Q16—862no—
526C2×Q16—862no—
527C2×Q16—862no—
528C2×Q16—1721no—
529C2×Q16—1721no—
530C2×Q16—1721no—
531C2×SD16—862no—
532C2×SD16—862no—
533C2×SD16—862no—
534C22×C8—431no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—1721no—
541C4⋊Q8—22no—
542C4⋊Q8—22no—
543#123—28no—
544#123—28no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—862no—
549C22⋊Q8—862no—
550C22⋊Q8—862no—
551C22⋊Q8—1721no—
552C22⋊Q8C22⋊D4314yes—
553#121—28no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—28no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—861no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4C22⋊D4311yescharacteristic
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4C22⋊D4311yescharacteristic
581C2×C22⋊C4C22⋊D4311yescharacteristic
582C2×C42—861no—
583C2×C42C22×D4311yescharacteristic
584#107—862no—
585#103—862no—
586#103—862no—
587#103—862no—
588#103—862no—
589#103—862no—
590#103—862no—
591#103—1721no—
592#102—434no—
593#102—862no—
594#102—862no—
595C22⋊C8—862no—
596C22⋊C8—862no—
597C22⋊C8—1721no—
598#95—861no—
599#95—861no—
600#95—861no—
601#95—861no—
602C24—21no—
603C24C2×C22⋊D4311yescharacteristic
604C24C2×C22⋊D4311yescharacteristic
605#41—28no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611#41—44no—
612#41—44no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×Q8—861no—
627C2×Q8—861no—
628C2×Q8—861no—
629C2×Q8C2×C22⋊D4312yes—
630C2×Q8C2×C22⋊D4312yes—
631C2×D4—24no—
632C2×D4—22no—
633C2×D4—24no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—41no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4D4×D4312yes—
644C2×D4#1062190012yes—
645C2×D4C2×C22⋊D4312yes—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—24no—
651C22×C4—24no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4C2×C22⋊D4311yescharacteristic
673C22×C4C2×C22⋊D4311yescharacteristic
674C22×C4C2×C22⋊D4311yescharacteristic
675C22×C4C2×C22⋊D4312yes—
676C22×C4C2×C22⋊D4312yes—
677C22×C4C2×C22⋊D4311yescharacteristic
678C22×C4C23×D4311yescharacteristic
679Q16—1724no—
680Q16—1724no—
681SD16—1724no—
682C2×C8—432no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—861no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—1724no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—432no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—1722no—
708C4⋊C4—1722no—
709C4⋊C4—1722no—
710C4⋊C4C2×C22⋊D4312yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—1722no—
717C22⋊C4—1722no—
718C22⋊C4—1722no—
719C22⋊C4—1722no—
720C42—21no—
721C42—21no—
722C42—1722no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23#1306329412yes—
744C23C22×C22⋊D4311yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—22no—
748Q8—22no—
749Q8—41no—
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—1721no—
754Q8—1721no—
755Q8—1721no—
756Q8—1721no—
757D4—22no—
758D4—22no—
759D4—22no—
760D4—44no—
761D4—48no—
762D4—48no—
763D4#1306329714yes—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—862no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4#1306329412yes—
807C2×C4#1306334512yes—
808C2×C4C2×D4×D4311yescharacteristic
809C2×C4C22×C22⋊D4311yescharacteristic
810C2×C4C22×C22⋊D4311yescharacteristic
811C2×C4C2×#1062190011yescharacteristic
812C2×C4#1306337011yescharacteristic
813C2×C4#1306337011yescharacteristic
814C8—862no—
815C8—1721no—
816C8—1721no—
817C8—1721no—
818C22—22no—
819C22—22no—
820C22—24no—
821C22—22no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—41no—
828C22—42no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22C2×#1306329411yescharacteristic
840C22D4×C22⋊D4311yescharacteristic
841C22#1458354311yescharacteristic
842C22C2×#1306334511yescharacteristic
843C22#1458369711yescharacteristic
844C22#1458371411yescharacteristic
845C22#1458371411yescharacteristic
846C4—22no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—41no—
853C4—3441no—
854C4—3441no—
855C4—3441no—
856C4—1722no—
857C4C2×#1306329711yescharacteristic
858C4#1458345811yescharacteristic
859C4D4×C22⋊D4311yescharacteristic
860C4#1458354311yescharacteristic
861C2—42no—
862C2—44no—
863C2—81no—
864C2#1913796911yescharacteristic
865C2#1914381311yescharacteristic
866C2#1914389011yescharacteristic
867C2#1914614611yescharacteristic
868C2#1914631311yescharacteristic
869C2#1914651211yescharacteristic
870C2#1914669111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#547C2
socleC23×C43C22×D4
hypercenterC2×#547D43
hypocenterC43#24430
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#14583138C2semidirect
2. C2×#14583061C2semidirect
3. C2×#14583061C2semidirect
4. C2×#14582895C2semidirect
5. #19138024C2semidirect
6. #19135838C2semidirect
7. #19135795C2semidirect
8. #19135695C2semidirect
9. #19135603C2semidirect
10. #19134929C2semidirect
11. #19134908C2semidirect
12. #19134888C2semidirect
13. #19134842C2semidirect
14. #19134535C2semidirect
109. #13063246D4semidirect
500. C43#24430semidirect

Maximal subgroups

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

subgroupindex
C2×#145831382
C2×#145830612
C2×#145828952
#191380242
#191358382
#191357952
#191356952
#191356032
#191349292
#191349082
#191348882
#191348422
#191345352
C2×C43×#5472
#2443043