Finite Group Databasebeta

← #25019391

Subgroups — #25019391

Order 11008.

2266 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
1C22×#13063304C211yesmaximal, characteristic
2C22×C4×Dic86C211yesmaximal, characteristic, complemented
3C2×#14582805C211yesmaximal, characteristic, complemented
4C2×#14582759C211yesmaximal, characteristic
5#19132846C212yesmaximal, complemented
6#19132838C212yesmaximal
7#19132832C212yesmaximal
8#19132826C212yesmaximal, complemented
9#19132825C211yesmaximal, characteristic, complemented
10#19132825C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C43C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C2×#13063304—24no—
14C2×#13063304—24no—
15C2×#13063304C418yescomplemented
16C2×C4×Dic86—24no—
17C2×C4×Dic86—24no—
18C2×C4×Dic86—24no—
19C22×C4⋊Dic43C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C22×C4⋊Dic43C2211yescharacteristic
22C22×Dic43⋊C4C2212yes—
23C22×Dic43⋊C4C2212yes—
24C22×C22⋊Dic43C2212yes—
25C22×C22⋊Dic43C2212yes—
26C22×C4×Dic43C2212yes—
27#14582805—24no—
28#14582759—24no—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C24×C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C22×C42×C43C2211yescharacteristic
41C4×C22⋊C4×C43—24no—
42C2×#95×C43C2211yescharacteristic
43C2×#95×C43C2211yescharacteristic
44C22×Dic86—22no—
45C22×Dic86—22no—
46C22×Dic86—22no—
47C22×Dic86—22no—
48C22×Dic86C2×C414yes—
49C22×Dic86D414yes—
50C22×Dic86D414yes—
51C23×Dic43C2312yes—
52C23×Dic43C2312yes—
53C23×Dic43C2312yes—
54C23×Dic43C2312yes—
55#13063304—232no—
56C4×Dic86—232no—
57C2×C4⋊Dic43—22no—
58C2×C4⋊Dic43—22no—
59C2×C4⋊Dic43—22no—
60C2×C4⋊Dic43—22no—
61C2×C4⋊Dic43—22no—
62C2×C4⋊Dic43—22no—
63C2×C4⋊Dic43—22no—
64C2×C4⋊Dic43C2×C414yes—
65C2×C4⋊Dic43D414yes—
66C2×Dic43⋊C4—24no—
67C2×Dic43⋊C4—24no—
68C2×Dic43⋊C4—24no—
69C2×Dic43⋊C4—24no—
70C2×Dic43⋊C4—24no—
71C2×Dic43⋊C4C2×C418yes—
72C2×C22⋊Dic43—24no—
73C2×C22⋊Dic43—24no—
74C2×C22⋊Dic43—24no—
75C2×C22⋊Dic43—24no—
76C2×C22⋊Dic43—42no—
77C2×C22⋊Dic43C2×C418yes—
78C2×C4×Dic43—24no—
79C2×C4×Dic43—24no—
80C2×C4×Dic43—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—24no—
85C43⋊#95—24no—
86C43⋊#95—42no—
87C43⋊#95—42no—
88C25×C43C2311yescharacteristic
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—22no—
92C23×C4×C43—22no—
93C23×C4×C43—22no—
94C23×C4×C43—22no—
95C23×C4×C43C2×C414yes—
96C23×C4×C43C2311yescharacteristic
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C23×C4×C43C2311yescharacteristic
100C23×C4×C43C2311yescharacteristic
101C23×C4×C43C2311yescharacteristic
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43—22no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43Q814yescomplemented
108C2×C42×C43—22no—
109C2×C42×C43—22no—
110C2×C42×C43—22no—
111C2×C42×C43—22no—
112C2×C42×C43—22no—
113C2×C42×C43D414yes—
114#95×C43—22no—
115#95×C43—22no—
116C24×C43—21no—
117C24×C43—21no—
118C24×C43—21no—
119C24×C43—21no—
120C24×C43—21no—
121C24×C43—21no—
122C24×C43—21no—
123C24×C43—21no—
124C24×C43—21no—
125C24×C43—21no—
126C24×C43—21no—
127C24×C43—21no—
128C24×C43C22×C412yes—
129C24×C43C2×Q812yes—
130C24×C43#4112yes—
131C24×C43C2411yescharacteristic
132C22×C4×C43—28no—
133C22×C4×C43—28no—
134C22×C4×C43—28no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—44no—
164C22×C4×C43—44no—
165C22×C4×C43—44no—
166C22×C4×C43—44no—
167C22×C4×C43C22×C412yes—
168C22×C4×C43C22×C412yes—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D412yes—
171C22×C4×C43C2×D412yes—
172C22×C4×C43C2×D412yes—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×Q812yes—
176C22×C4×C43C2×Q812yes—
177C22×C4×C43#4112yes—
178C22×C4×C43#4112yes—
179C22×C4×C43#4112yes—
180C22×C4×C43#4112yes—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43C22×C414yes—
205C22×Dic43C22×C414yes—
206C22×Dic43C2×D414yes—
207C22×Dic43C2×D414yes—
208C22×Dic43C2×D414yes—
209C2×Dic86—28no—
210C2×Dic86—28no—
211C2×Dic86—28no—
212C2×Dic86—28no—
213C2×Dic86—28no—
214C2×Dic86—28no—
215C2×Dic86C22⋊C4116yescomplemented
216C22⋊C4×C43—28no—
217C22⋊C4×C43—28no—
218C42×C43—28no—
219C42×C43—44no—
220C22⋊Dic43—216no—
221C22⋊Dic43—48no—
222C4⋊Dic43—28no—
223C4⋊Dic43—28no—
224C4⋊Dic43—44no—
225Dic43⋊C4—216no—
226Dic43⋊C4—216no—
227C4×Dic43—216no—
228C23×C43—22no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—22no—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—41no—
247C23×C43—41no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C4×Q814yescomplemented
263C23×C43C23×C411yescharacteristic
264C23×C43C22×D411yescharacteristic
265C23×C43C22×D411yescharacteristic
266C23×C43C22×D411yescharacteristic
267C23×C43C22×D411yescharacteristic
268C23×C43C22×Q811yescharacteristic
269C23×C43C2×#4111yescharacteristic
270C23×C43C2×#4111yescharacteristic
271C23×C43C2×#4111yescharacteristic
272C23×C43C2×#4111yescharacteristic
273C23×C43C2×#4111yescharacteristic
274C23×C43H(5,𝔽2)11yescharacteristic
275C23×C432−1+411yescharacteristic
276C23×C432−1+411yescharacteristic
277C23×C432−1+411yescharacteristic
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—416no—
313C2×C4×C43C2×C22⋊C414yes—
314C2×C4×C43C4×D414yes—
315C2×C4×C43C4×D414yes—
316C2×C4×C43#12014yes—
317C2×C4×C43#12114yes—
318C2×C4×C43#12114yes—
319C2×C4×C43C22⋊Q814yescomplemented
320C2×C4×C43#12314yes—
321C2×Dic43—24no—
322C2×Dic43—24no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—24no—
329C2×Dic43—24no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43—24no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43C2×C22⋊C418yes—
349Dic86—232no—
350#13969—431nomaximal, Sylow
351C22×C43—24no—
352C22×C43—24no—
353C22×C43—24no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43C22×C22⋊C411yescharacteristic
367C22×C43C2×C4×D411yescharacteristic
368C22×C43C2×C4×D411yescharacteristic
369C22×C43C2×C4×Q811yescharacteristic
370C22×C43C4×#4111yescharacteristic
371C22×C43#51911yescharacteristic
372C22×C43#52011yescharacteristic
373C22×C43C2×#12011yescharacteristic
374C22×C43C2×#12111yescharacteristic
375C22×C43C2×#12111yescharacteristic
376C22×C43C2×C22⋊Q811yescharacteristic
377C22×C43C2×#12311yescharacteristic
378C22×C43#52511yescharacteristic
379C22×C43#52911yescharacteristic
380C22×C43#53311yescharacteristic
381C22×C43#53611yescharacteristic
382C22×C43#53711yescharacteristic
383C22×C43#54111yescharacteristic
384C22×C43#54211yescharacteristic
385C22×C43#54611yescharacteristic
386C22×C43#54711yescharacteristic
387C22×C43#54811yescharacteristic
388C22×C43#54811yescharacteristic
389C22×C43#54811yescharacteristic
390C22×C43#54811yescharacteristic
391C22×C43#54811yescharacteristic
392C22×C43D4×Q811yescharacteristic
393C22×C43D4×Q811yescharacteristic
394C22×C43D4×Q811yescharacteristic
395C22×C43#55011yescharacteristic
396C22×C43#55011yescharacteristic
397C22×C43#55211yescharacteristic
398C22×C43#55211yescharacteristic
399C22×C43#55411yescharacteristic
400C22×C43#55611yescharacteristic
401C4×C43—24no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—42no—
406C4×C43#38618yes—
407Dic43—28no—
408Dic43—44no—
409Dic43—44no—
410Dic43—82no—
411C22×C22⋊Q8—431no—
412C22×C4×Q8—431no—
413C2×#391—431no—
414C2×#380—431no—
415C2×C4×C22⋊C4D4311yescharacteristic
416#1441—432no—
417#1439—432no—
418#1437—432no—
419#1436—432no—
420C4⋊#95—431no—
421C4⋊#95—431no—
422C2×C43—44no—
423C2×C43C2×#38611yescharacteristic
424C2×C43C4×C22⋊Q811yescharacteristic
425C2×C43#232311yescharacteristic
426C2×C43Q8×C22⋊C411yescharacteristic
427C2×C43#234111yescharacteristic
428C2×C43#236011yescharacteristic
429C2×C43#236211yescharacteristic
430C2×C43#240711yescharacteristic
431C2×C43#240911yescharacteristic
432C2×C43#242111yescharacteristic
433C2×C43#242311yescharacteristic
434C2×C43#242611yescharacteristic
435C2×C43#242911yescharacteristic
436C2×C43#253611yescharacteristic
437C2×C43#253811yescharacteristic
438C23×Q8—431no—
439C24×C4C2×D4311yescharacteristic
440C2×C22⋊Q8—438no—
441C2×C22⋊Q8—864no—
442C2×C22⋊Q8—864no—
443C2×C4×Q8—864no—
444C2×C4×Q8—864no—
445C2×C4×Q8—864no—
446C22×C4⋊C4—432no—
447C22×C4⋊C4—431no—
448C22×C4⋊C4—431no—
449C22×C4⋊C4—432no—
450C22×C4⋊C4—431no—
451C22×C22⋊C4—432no—
452C22×C22⋊C4—432no—
453C22×C22⋊C4C2×D4311yescharacteristic
454C22×C22⋊C4C2×D4311yescharacteristic
455C22×C42—432no—
456C22×C42C2×D4311yescharacteristic
457C22×C42C2×D4311yescharacteristic
458#391—864no—
459#380—864no—
460C4×C22⋊C4—24no—
461C2×#95—432no—
462C2×#95—432no—
463C2×#95—432no—
464C2×#95—432no—
465C2×#95—432no—
466C2×#95—432no—
467C2×#95—432no—
468C2×#95C2×D4311yescharacteristic
469C2×#95C2×D4311yescharacteristic
470C43#1396911yescharacteristic, complemented, Sylow
471C25C22×D4311yescharacteristic
472C22×Q8—434no—
473C22×Q8—434no—
474C22×Q8—434no—
475C22×Q8—862no—
476C22×Q8—862no—
477C22×Q8—862no—
478C22×Q8—862no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—432no—
486C23×C4—432no—
487C23×C4—432no—
488C23×C4—432no—
489C23×C4C4×D4314yes—
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C23×C4C22×D4311yescharacteristic
493C23×C4C22×D4311yescharacteristic
494C23×C4C22×D4311yescharacteristic
495C23×C4C22×D4311yescharacteristic
496C22⋊Q8—8632no—
497C4×Q8—8632no—
498C2×C4⋊C4—438no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—434no—
501C2×C4⋊C4—864no—
502C2×C4⋊C4—864no—
503C2×C4⋊C4—864no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—862no—
506C2×C4⋊C4—862no—
507C2×C4⋊C4—862no—
508C2×C4⋊C4—864no—
509C2×C4⋊C4—862no—
510C2×C4⋊C4—862no—
511C2×C4⋊C4—862no—
512C2×C4⋊C4—862no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—438no—
519C2×C22⋊C4—864no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—864no—
523C2×C22⋊C4—1722no—
524C2×C22⋊C4Dic8614yescomplemented
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—864no—
531C2×C42—864no—
532C2×C42—864no—
533C2×C42C22⋊D4314yes—
534#95—22no—
535#95—22no—
536#95—864no—
537#95—864no—
538#95—864no—
539#95—864no—
540#95—864no—
541#95—1722no—
542#95—1722no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24C2×Dic8612yes—
556C24C2×C4×D4312yes—
557C24#1062189812yes—
558C24C23×D4311yescharacteristic
559C2×Q8—4316no—
560C2×Q8—868no—
561C2×Q8—868no—
562C2×Q8—868no—
563C2×Q8—868no—
564C2×Q8—868no—
565C2×Q8—868no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—434no—
602C22×C4—434no—
603C22×C4—434no—
604C22×C4—434no—
605C22×C4—434no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4C2×Dic8612yes—
630C22×C4C2×Dic8612yes—
631C22×C4C2×C4×D4312yes—
632C22×C4C2×C4×D4312yes—
633C22×C4#1062189812yes—
634C22×C4#1062189812yes—
635C22×C4#1062189812yes—
636C22×C4D4×D4312yes—
637C22×C4D4×D4312yes—
638C22×C4D4×D4312yes—
639C22×C4#1062190012yes—
640C22×C4C2×C22⋊D4312yes—
641C22×C4C2×C22⋊D4312yes—
642C22×C4C2×C22⋊D4312yes—
643C4⋊C4—8616no—
644C4⋊C4—8616no—
645C4⋊C4—868no—
646C4⋊C4—868no—
647C4⋊C4—1724no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—8616no—
651C22⋊C4—1728no—
652C42—28no—
653C42—44no—
654C42—8616no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C4×Dic8614yescomplemented
690C23C22×C4×D4311yescharacteristic
691C23C2×D4×D4311yescharacteristic
692C23C2×D4×D4311yescharacteristic
693C23C2×D4×D4311yescharacteristic
694C23C22×C22⋊D4311yescharacteristic
695C23C22×Dic8611yescharacteristic
696C23C2×#1062190011yescharacteristic
697C23C2×#1062189811yescharacteristic
698C23C2×#1062189811yescharacteristic
699C23C2×#1062189811yescharacteristic
700C23C2×#1062189811yescharacteristic
701C23#1306337111yescharacteristic
702C23#1306337211yescharacteristic
703C23#1306337211yescharacteristic
704C23#1306337211yescharacteristic
705Q8—8632no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—416no—
741C2×C4—438no—
742C2×C4—864no—
743C2×C4—864no—
744C2×C4—864no—
745C2×C4—864no—
746C2×C4—864no—
747C2×C4—864no—
748C2×C4—864no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—864no—
752C2×C4—864no—
753C2×C4—864no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4C22⋊C4×D4314yes—
770C2×C4(C22⋊D43)⋊C414yes—
771C2×C4C4×C22⋊D4314yes—
772C2×C4#1306329314yes—
773C2×C4#1306329614yes—
774C2×C4#1306329814yes—
775C2×C4#1306330414yescomplemented
776C2×C4#1306330714yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C2×C22⋊C4×D4311yescharacteristic
793C22C2×(C22⋊D43)⋊C411yescharacteristic
794C22C2×C4×C22⋊D4311yescharacteristic
795C22C2×C4×Dic8611yescharacteristic
796C22C4×#1062189811yescharacteristic
797C22#1458337611yescharacteristic
798C22#1458337911yescharacteristic
799C22C2×#1306329311yescharacteristic
800C22C2×#1306329611yescharacteristic
801C22C2×#1306329811yescharacteristic
802C22C2×#1306330411yescharacteristic
803C22C2×#1306330711yescharacteristic
804C22#1458341011yescharacteristic
805C22#1458343311yescharacteristic
806C22#1458345611yescharacteristic
807C22#1458347011yescharacteristic
808C22#1458347711yescharacteristic
809C22#1458351111yescharacteristic
810C22#1458352011yescharacteristic
811C22#1458354511yescharacteristic
812C22#1458355411yescharacteristic
813C22#1458355811yescharacteristic
814C22#1458355811yescharacteristic
815C22#1458355811yescharacteristic
816C22#1458355811yescharacteristic
817C22#1458355811yescharacteristic
818C22D4×Dic8611yescharacteristic
819C22D4×Dic8611yescharacteristic
820C22D4×Dic8611yescharacteristic
821C22#1458357011yescharacteristic
822C22#1458357011yescharacteristic
823C22#1458358911yescharacteristic
824C22#1458358911yescharacteristic
825C22#1458360611yescharacteristic
826C22#1458361911yescharacteristic
827C4—24no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—868no—
833C4—3442no—
834C4—1724no—
835C4—1724no—
836C4#1458277518yes—
837C2—44no—
838C2C2×#1458277511yescharacteristic
839C2C4×#1306330411yescharacteristic
840C2#1913727711yescharacteristic
841C2C22⋊C4×Dic8611yescharacteristic
842C2#1913743511yescharacteristic
843C2#1913759811yescharacteristic
844C2#1913762011yescharacteristic
845C2#1913794011yescharacteristic
846C2#1913796011yescharacteristic
847C2#1913809811yescharacteristic
848C2#1913812011yescharacteristic
849C2#1913816111yescharacteristic
850C2#1913819411yescharacteristic
851C2#1913950411yescharacteristic
852C2#1913951711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#13969
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic86C2semidirect
3. C2×#14582805C2semidirect
5. #19132846C2semidirect
8. #19132826C2semidirect
9. #19132825C2semidirect
10. #19132825C2semidirect
15. C2×#13063304C4semidirect
107. C2×C22⋊C4×C43Q8semidirect
215. C2×Dic86C22⋊C4semidirect
262. C23×C43C4×Q8semidirect
319. C2×C4×C43C22⋊Q8semidirect
470. C43#13969semidirect
524. C2×C22⋊C4Dic86semidirect
689. C23C4×Dic86semidirect
775. C2×C4#13063304semidirect

Maximal subgroups

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

subgroupindex
C22×#130633042
C22×C4×Dic862
C2×#145828052
C2×#145827592
#191328462
#191328382
#191328322
#191328262
#191328252
C2×C4×C22⋊C4×C432
#1396943