Finite Group Databasebeta

← #25112107

Subgroups — #25112107

Order 11008.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582971C211yesmaximal, characteristic, complemented
2C2×#14582900C211yesmaximal, characteristic, complemented
3C22×#13063249C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic43C211yesmaximal, characteristic, complemented
5#19135528C211yesmaximal, characteristic, complemented
6#19135412C211yesmaximal, characteristic, complemented
7#19135029C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134913C211yesmaximal, characteristic, complemented
10#19134903C211yesmaximal, characteristic, complemented
11#19134600C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134530C211yesmaximal, characteristic, complemented
14#19134425C211yesmaximal, characteristic, complemented
15C2×C43×#548C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18C2×D4×Dic43—21no—
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21#14582971—24no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23#14582900—24no—
24C2×#13063249—24no—
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063249C2211yescharacteristic
32C2×#13063249C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063246C2211yescharacteristic
36C2×#13063246C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×#13063236C2211yescharacteristic
40#14582798—21no—
41#14582774—21no—
42#14582774—21no—
43#14582769C2211yescharacteristic
44#14582759C2211yescharacteristic
45#14582759C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C23×Q8×C43C2211yescharacteristic
53C43×#548—24no—
54C43×#548C418yescomplemented
55C2×#124×C43—21no—
56C2×#124×C43C2211yescharacteristic
57C2×C22⋊Q8×C43—21no—
58C2×C22⋊Q8×C43C2211yescharacteristic
59C2×#121×C43—21no—
60C2×#121×C43C2211yescharacteristic
61C2×C4×Q8×C43C2211yescharacteristic
62C2×C4×D4×C43—21no—
63C2×C4×D4×C43C2211yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C2×#10621877—22no—
67C2×#10621877—22no—
68C2×#10621877—41no—
69C22×C43⋊C8—22no—
70C22×C43⋊C8—22no—
71C22×C43⋊C8—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76D4×Dic43—44no—
77C2×C4⋊Dic43—22no—
78C2×C4⋊Dic43—22no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—41no—
84C2×C4⋊Dic43—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C4×Dic43—21no—
92C4⋊(C43⋊C8)—22no—
93#13063249—22no—
94#13063249—22no—
95#13063249—22no—
96#13063249—22no—
97#13063249—22no—
98#13063249—41no—
99#13063249—41no—
100#13063249D414yescomplemented
101#13063246—22no—
102#13063246—22no—
103#13063246—41no—
104#13063246—41no—
105C22⋊(C43⋊C8)—22no—
106C22⋊(C43⋊C8)—22no—
107#13063236—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43—22no—
114C2×#41×C43—41no—
115C2×#41×C43—41no—
116C2×#41×C43C2×C414yescomplemented
117C22×Q8×C43—21no—
118C22×Q8×C43—22no—
119C22×Q8×C43—22no—
120C22×Q8×C43—22no—
121C22×Q8×C43—41no—
122C22×Q8×C43—41no—
123C22×Q8×C43C2×C414yescomplemented
124C22×Q8×C43C2311yescharacteristic
125C22×Q8×C43C2311yescharacteristic
126C22×D4×C43—21no—
127C22×D4×C43—21no—
128C22×D4×C43D411yescharacteristic
129C22×D4×C43C2311yescharacteristic
130C23×C4×C43—21no—
131C23×C4×C43—21no—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134#124×C43—28no—
135#124×C43—22no—
136#124×C43C2×C414yescomplemented
137C22⋊Q8×C43—22no—
138C22⋊Q8×C43—28no—
139C22⋊Q8×C43C2×C414yescomplemented
140#121×C43—28no—
141#121×C43—22no—
142#121×C43C2×C414yescomplemented
143C4×Q8×C43—22no—
144C4×Q8×C43C2×C414yescomplemented
145C4×D4×C43—28no—
146C4×D4×C43C2×C414yes—
147C4×D4×C43D414yes—
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43—21no—
150C2×C4⋊C4×C43D411yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155C2×C22⋊C4×C43—21no—
156C2×C22⋊C4×C43D411yescharacteristic
157C2×C22⋊C4×C43D411yescharacteristic
158C2×C42×C43—21no—
159C2×C42×C43C2311yescharacteristic
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162C24×C43C2×D411yescharacteristic
163#41×C43—28no—
164#41×C43—44no—
165#41×C43—44no—
166#41×C43—44no—
167C2×Q8×C43—24no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—28no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—42no—
178C2×Q8×C43—42no—
179C2×Q8×C43—44no—
180C2×Q8×C43—44no—
181C2×Q8×C43—44no—
182C2×Q8×C43C22×C412yes—
183C2×Q8×C43C22×C412yes—
184C2×Q8×C43C2×D412yes—
185C2×Q8×C43#4112yes—
186C2×D4×C43—21no—
187C2×D4×C43—24no—
188C2×D4×C43—24no—
189C2×D4×C43—22no—
190C2×D4×C43—22no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—42no—
199C2×D4×C43C22⋊C414yes—
200C2×D4×C43C22×C412yes—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—24no—
210C22×C4×C43—24no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—42no—
215C22×C4×C43—42no—
216C22×C4×C43—42no—
217C22×C4×C43—42no—
218C22×C4×C43C22×C412yes—
219C22×C4×C43C22×C412yes—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2×D412yes—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43—42no—
232C22×Dic43—42no—
233C22×Dic43—42no—
234C22×Dic43—42no—
235C22×Dic43—81no—
236C22×Dic43—81no—
237C4⋊C4×C43—24no—
238C4⋊C4×C43—24no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43C22⋊C414yes—
241C4⋊C4×C43C22×C412yes—
242C22⋊C4×C43—24no—
243C22⋊C4×C43—24no—
244C22⋊C4×C43—24no—
245C22⋊C4×C43—24no—
246C22⋊C4×C43C22⋊C414yes—
247C22⋊C4×C43C22⋊C414yes—
248C42×C43—24no—
249C42×C43C22×C412yes—
250C42×C43C2×D412yes—
251C22⋊Dic43—42no—
252C22⋊Dic43—42no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—42no—
261C4⋊Dic43—42no—
262C4⋊Dic43—42no—
263C4⋊Dic43—81no—
264C4⋊Dic43C2×D412yes—
265C4×Dic43—42no—
266#10621877—44no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—44no—
279C2×C43⋊C8C2×D412yes—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—22no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43C2×C22⋊C412yes—
298C23×C43C2×C22⋊C412yes—
299C23×C43AGL(1,ℤ/8)12yes—
300C23×C43#13712yes—
301C23×C43C22×D411yescharacteristic
302Q8×C43—22no—
303Q8×C43—22no—
304Q8×C43—22no—
305Q8×C43—22no—
306Q8×C43—22no—
307Q8×C43—48no—
308Q8×C43—41no—
309Q8×C43—41no—
310Q8×C43C4×D414yescomplemented
311D4×C43—28no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—48no—
315D4×C43—48no—
316D4×C43—41no—
317D4×C43—41no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—21no—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—48no—
340C2×C4×C43—48no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43C2×C22⋊C412yes—
346C2×C4×C43C2×C22⋊C412yes—
347C2×C4×C43C2×C22⋊C412yes—
348C2×C4×C43C2×C22⋊C412yes—
349C2×C4×C43C23×C411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C2×Dic43—22no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—84no—
368C2×Dic43—84no—
369C43⋊C8—22no—
370C43⋊C8—41no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373#22421—431nomaximal, Sylow
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43#41714yescomplemented
395C22×C43C22×C22⋊C411yescharacteristic
396C22×C43D4211yescharacteristic
397C22×C43#54611yescharacteristic
398C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C43C2×#13711yescharacteristic
400C22×C43#57711yescharacteristic
401C22×C43#57811yescharacteristic
402C4×C43—22no—
403C4×C43—22no—
404C4×C43—24no—
405C4×C43—22no—
406C4×C43—22no—
407C4×C43—42no—
408C4×C43—42no—
409C4×C43C2×C4×D411yescharacteristic
410C4×C43#51811yescharacteristic
411C4×C43D4211yescharacteristic
412C4×C43#54611yescharacteristic
413Dic43—42no—
414Dic43—81no—
415Dic43—81no—
416Dic43—81no—
417C2×#548D4311yescharacteristic
418C2×#435—431no—
419C2×#417—431no—
420C22×#103—431no—
421D4×C4⋊C4—431no—
422#1983—431no—
423#1959—431no—
424#1894—431no—
425#1893—431no—
426#1874—431no—
427#1872—431no—
428#1803—431no—
429#1788—431no—
430#1787—431no—
431#1763—431no—
432C2×C43—24no—
433C2×C43—42no—
434C2×C43—82no—
435C2×C43D4×C22⋊C411yescharacteristic
436C2×C43C2×#41711yescharacteristic
437C2×C43#289811yescharacteristic
438C2×C43#326511yescharacteristic
439C2×C43#327011yescharacteristic
440C2×C43#330811yescharacteristic
441C2×C43#331611yescharacteristic
442C22×#41C2×D4311yescharacteristic
443C23×Q8C2×D4311yescharacteristic
444C22×M16—431no—
445C23×C8—431no—
446#548—24no—
447#548Dic4318yescomplemented
448C2×#124—21no—
449C2×#124C2×D4311yescharacteristic
450C2×C22⋊Q8—21no—
451C2×C22⋊Q8C2×D4311yescharacteristic
452C2×#121—21no—
453C2×#121C2×D4311yescharacteristic
454C2×C4×Q8C2×D4311yescharacteristic
455C2×C4×D4—21no—
456C2×C4×D4—861no—
457C2×C4×D4C2×D4311yescharacteristic
458C22×C4⋊C4—431no—
459C22×C4⋊C4—431no—
460#435—864no—
461C2×C4⋊C8—431no—
462#417—864no—
463C2×#103—431no—
464C2×#103—431no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—864no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×C22⋊C8—431no—
477C2×C22⋊C8—431no—
478C2×#97—431no—
479#389—861no—
480#385—861no—
481#385—861no—
482#384—431no—
483#380—431no—
484#380—431no—
485C4×C4⋊C4—431no—
486#340—431no—
487#340—431no—
488#340—431no—
489#340—431no—
490C43#2242111yescharacteristic, complemented, Sylow
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41C2×Dic4314yescomplemented
497C22×Q8—21no—
498C22×Q8—22no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—41no—
502C22×Q8—41no—
503C22×Q8C2×Dic4314yescomplemented
504C22×Q8C22×D4311yescharacteristic
505C22×Q8C22×D4311yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4C22⋊D4311yescharacteristic
509C22×D4C22×D4311yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4C22×D4311yescharacteristic
515C23×C4C22×D4311yescharacteristic
516C2×M16—862no—
517C2×M16—862no—
518C2×M16—1721no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8—431no—
522C22×C8—431no—
523C22×C8—862no—
524C22×C8—862no—
525C22×C8—1721no—
526#124—28no—
527#124—22no—
528#124C2×Dic4314yescomplemented
529C22⋊Q8—22no—
530C22⋊Q8—28no—
531C22⋊Q8C2×Dic4314yescomplemented
532#121—28no—
533#121—22no—
534#121C2×Dic4314yescomplemented
535C4×Q8—22no—
536C4×Q8C2×Dic4314yescomplemented
537C4×D4—28no—
538C4×D4—1724no—
539C4×D4C2×Dic4314yes—
540C4×D4C22⋊D4314yes—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—862no—
548C2×C4⋊C4—862no—
549C2×C4⋊C4—861no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—1721no—
554C2×C4⋊C4—1721no—
555C2×C4⋊C4C22⋊D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4C22⋊D4311yescharacteristic
564C2×C22⋊C4C22⋊D4311yescharacteristic
565C2×C42—21no—
566C2×C42—861no—
567C2×C42C22×D4311yescharacteristic
568C4⋊C8—862no—
569#103—434no—
570#103—862no—
571#103—862no—
572#103—862no—
573#103—862no—
574#103—862no—
575#103—1721no—
576#103—1721no—
577#102—862no—
578#102—862no—
579#102—1721no—
580#102—1721no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583#97—862no—
584#95—861no—
585#95—861no—
586#95—861no—
587C24—21no—
588C24C2×C22⋊D4311yescharacteristic
589C24C2×C22⋊D4311yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594C2×Q8—24no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—28no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—44no—
607C2×Q8—44no—
608C2×Q8—44no—
609C2×Q8D4×D4312yes—
610C2×Q8#1062190012yes—
611C2×Q8C22×Dic4312yes—
612C2×Q8C22×Dic4312yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4C22⋊Dic4314yes—
627C2×D4C22×Dic4312yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—3441no—
650C22×C4—3441no—
651C22×C4—1722no—
652C22×C4—1722no—
653C22×C4—1722no—
654C22×C4—1722no—
655C22×C4C22×Dic4312yes—
656C22×C4C22×Dic4312yes—
657C22×C4C2×C22⋊D4311yescharacteristic
658C22×C4C2×C22⋊D4311yescharacteristic
659C22×C4C2×C22⋊D4311yescharacteristic
660C22×C4C2×C22⋊D4311yescharacteristic
661C22×C4C2×C22⋊D4312yes—
662C22×C4C2×C22⋊D4312yes—
663C22×C4C23×D4311yescharacteristic
664M16—1724no—
665C2×C8—432no—
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—861no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—1724no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—21no—
681C4⋊C4—432no—
682C4⋊C4—861no—
683C4⋊C4—861no—
684C4⋊C4—861no—
685C4⋊C4—861no—
686C4⋊C4—861no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—3441no—
690C4⋊C4—1722no—
691C4⋊C4—1722no—
692C4⋊C4—1722no—
693C4⋊C4C22⋊Dic4314yes—
694C4⋊C4C22×Dic4312yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—1722no—
700C22⋊C4—1722no—
701C22⋊C4C22⋊Dic4314yes—
702C22⋊C4C22⋊Dic4314yes—
703C42—24no—
704C42—1722no—
705C42C22×Dic4312yes—
706C42C2×C22⋊D4312yes—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23C2×C22⋊Dic4312yes—
725C23C2×C22⋊Dic4312yes—
726C23#1306335012yes—
727C23#1306335512yes—
728C23C22×C22⋊D4311yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—48no—
735Q8—41no—
736Q8—41no—
737Q8D4×Dic4314yescomplemented
738D4—28no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—48no—
743D4—41no—
744D4—41no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—862no—
773C2×C4—3444no—
774C2×C4—3444no—
775C2×C4—1721no—
776C2×C4—1721no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4C2×C22⋊Dic4312yes—
787C2×C4C2×C22⋊Dic4312yes—
788C2×C4C2×C22⋊Dic4312yes—
789C2×C4C2×C22⋊Dic4312yes—
790C2×C4C23×Dic4311yescharacteristic
791C2×C4C2×D4×D4311yescharacteristic
792C2×C4C22×C22⋊D4311yescharacteristic
793C2×C4C2×#1062190011yescharacteristic
794C2×C4#1306337011yescharacteristic
795C2×C4#1306337011yescharacteristic
796C8—862no—
797C8—1721no—
798C8—1721no—
799C8—1721no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22#1458290014yescomplemented
821C22C22×C22⋊Dic4311yescharacteristic
822C22D4×C22⋊D4311yescharacteristic
823C22#1458354311yescharacteristic
824C22C2×#1306335011yescharacteristic
825C22C2×#1306335511yescharacteristic
826C22#1458370711yescharacteristic
827C22#1458371411yescharacteristic
828C4—22no—
829C4—22no—
830C4—24no—
831C4—22no—
832C4—22no—
833C4—42no—
834C4—42no—
835C4—3441no—
836C4—3441no—
837C4—3441no—
838C4—1722no—
839C4C2×D4×Dic4311yescharacteristic
840C4#1458337411yescharacteristic
841C4D4×C22⋊D4311yescharacteristic
842C4#1458354311yescharacteristic
843C2—24no—
844C2—42no—
845C2—82no—
846C2D4×C22⋊Dic4311yescharacteristic
847C2C2×#1458290011yescharacteristic
848C2#1914312811yescharacteristic
849C2#1914609111yescharacteristic
850C2#1914616111yescharacteristic
851C2#1914658611yescharacteristic
852C2#1914670611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#548C2
socleC23×C43C22×D4
cosocleC22×C4×C43C24
hypercenterC2×#548D43
hypocenterC43#22421
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#14582971C2semidirect
2. C2×#14582900C2semidirect
3. C22×#13063249C2semidirect
4. D4×C4⋊Dic43C2semidirect
5. #19135528C2semidirect
6. #19135412C2semidirect
7. #19135029C2semidirect
8. #19135024C2semidirect
9. #19134913C2semidirect
10. #19134903C2semidirect
11. #19134600C2semidirect
12. #19134535C2semidirect
13. #19134530C2semidirect
14. #19134425C2semidirect
54. C43×#548C4semidirect
100. #13063249D4semidirect
116. C2×#41×C43C2×C4semidirect
123. C22×Q8×C43C2×C4semidirect
136. #124×C43C2×C4semidirect
139. C22⋊Q8×C43C2×C4semidirect
142. #121×C43C2×C4semidirect
144. C4×Q8×C43C2×C4semidirect
310. Q8×C43C4×D4semidirect
394. C22×C43#417semidirect
447. #548Dic43semidirect
490. C43#22421semidirect
496. C2×#41C2×Dic43semidirect
503. C22×Q8C2×Dic43semidirect
528. #124C2×Dic43semidirect
531. C22⋊Q8C2×Dic43semidirect
534. #121C2×Dic43semidirect
536. C4×Q8C2×Dic43semidirect
737. Q8D4×Dic43semidirect
820. C22#14582900semidirect

Maximal subgroups

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

subgroupindex
C2×#145829712
C2×#145829002
C22×#130632492
D4×C4⋊Dic432
#191355282
#191354122
#191350292
#191350242
#191349132
#191349032
#191346002
#191345352
#191345302
#191344252
C2×C43×#5482
#2242143