Finite Group Databasebeta

← C2×#19138485 #25264108

Subgroups — C2×#19138485 #25264108

Order 11008.

4282 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063310C211yesmaximal, characteristic, complemented
2C22×#13063300C211yesmaximal, characteristic, complemented
3C22×C4×D172C211yesmaximal, characteristic, complemented
4C22×#13063287C211yesmaximal, characteristic, complemented
5#19138485C2116yesmaximal, direct product factor
6C2×#14582821C211yesmaximal, characteristic, complemented
7C2×#14582809C211yesmaximal, characteristic, complemented
8C2×#14582809C211yesmaximal, characteristic, complemented
9C2×#14582809C211yesmaximal, characteristic, complemented
10C2×#14582801C211yesmaximal, characteristic, complemented
11C2×#14582791C211yesmaximal, characteristic, complemented
12C2×#14582791C211yesmaximal, characteristic, complemented
13C2×#14582777C211yesmaximal, characteristic, complemented
14C2×#14582777C211yesmaximal, characteristic, complemented
15C2×#14582773C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×D172C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×D172C2211yescharacteristic
20C23×D172C2211yescharacteristic
21C23×D172C2211yescharacteristic
22C23×D172C2211yescharacteristic
23C23×C4×D43C2211yescharacteristic
24C23×C4×D43C2211yescharacteristic
25C23×C4×D43C2211yescharacteristic
26C2×#13063310—28no—
27C2×#13063310C2218yescomplemented
28C2×#13063300—28no—
29C2×#13063300C2218yescomplemented
30C2×C4×D172—28no—
31C2×C4×D172C2218yescomplemented
32C2×#13063287—28no—
33C2×#13063287C2218yescomplemented
34C22×C4⋊Dic43C2211yescharacteristic
35C22×C4⋊Dic43C2211yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C22×(C2×D43)⋊C4C2211yescharacteristic
38C22×(C2×D43)⋊C4C2211yescharacteristic
39C22×(C2×D43)⋊C4C2211yescharacteristic
40C22×(C2×D43)⋊C4C2211yescharacteristic
41C22×(C2×D43)⋊C4C2211yescharacteristic
42C22×(C2×D43)⋊C4C2211yescharacteristic
43C22×(C2×D43)⋊C4C2211yescharacteristic
44C22×(C2×D43)⋊C4C2211yescharacteristic
45C22×(C2×D43)⋊C4C2211yescharacteristic
46C22×(C2×D43)⋊C4C2211yescharacteristic
47C22×(C2×D43)⋊C4C2211yescharacteristic
48C22×(C2×D43)⋊C4C2211yescharacteristic
49C22×(C2×D43)⋊C4C2211yescharacteristic
50C22×C4×Dic43C2211yescharacteristic
51#14582821C2218yescomplemented
52#14582809C2218yescomplemented
53#14582809C2218yescomplemented
54#14582809C2218yescomplemented
55#14582801C2218yescomplemented
56#14582791C2218yescomplemented
57#14582791C2218yescomplemented
58#14582777C2218yescomplemented
59#14582777C2218yescomplemented
60#14582773C2218yescomplemented
61C2×C43⋊#95C2211yescharacteristic
62C2×C43⋊#95C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C43×#387C2218yescomplemented
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C2×#95×C43C2211yescharacteristic
71C24×D43C2311yescharacteristic
72C24×D43C2311yescharacteristic
73C24×D43C2311yescharacteristic
74C24×D43C2311yescharacteristic
75C22×D172—24no—
76C22×D172—24no—
77C22×D172—24no—
78C22×D172—24no—
79C22×D172—24no—
80C22×D172—24no—
81C22×D172—24no—
82C22×D172—24no—
83C22×D172—24no—
84C22×D172—24no—
85C22×D172—24no—
86C22×D172—24no—
87C22×D172—24no—
88C22×D172—42no—
89C22×D172—42no—
90C22×D172—42no—
91C22×D172—42no—
92C22×D172—42no—
93C22×D172C2314yes—
94C22×D172C2314yes—
95C22×D172C2314yes—
96C22×D172C2314yes—
97C22×D172C2314yes—
98C22×D172C2314yes—
99C23×Dic43C2311yescharacteristic
100C23×Dic43C2311yescharacteristic
101C23×Dic43C2311yescharacteristic
102C23×Dic43C2311yescharacteristic
103C22×C4×D43—24no—
104C22×C4×D43—24no—
105C22×C4×D43—24no—
106C22×C4×D43—24no—
107C22×C4×D43—24no—
108C22×C4×D43—24no—
109C22×C4×D43—42no—
110C22×C4×D43—42no—
111C22×C4×D43—42no—
112C22×C4×D43C2314yes—
113C22×C4×D43C2314yes—
114C22×C4×D43C2314yes—
115#13063310—232no—
116#13063300—232no—
117C4×D172—232no—
118#13063287—232no—
119C2×C4⋊Dic43—24no—
120C2×C4⋊Dic43—42no—
121C2×C4⋊Dic43C2314yes—
122C2×C4⋊Dic43C2314yes—
123C2×Dic43⋊C4—24no—
124C2×Dic43⋊C4C2314yes—
125C2×(C2×D43)⋊C4—24no—
126C2×(C2×D43)⋊C4—24no—
127C2×(C2×D43)⋊C4—24no—
128C2×(C2×D43)⋊C4—24no—
129C2×(C2×D43)⋊C4—24no—
130C2×(C2×D43)⋊C4—24no—
131C2×(C2×D43)⋊C4—24no—
132C2×(C2×D43)⋊C4—24no—
133C2×(C2×D43)⋊C4—24no—
134C2×(C2×D43)⋊C4—42no—
135C2×(C2×D43)⋊C4—42no—
136C2×(C2×D43)⋊C4—42no—
137C2×(C2×D43)⋊C4D418yescomplemented
138C2×(C2×D43)⋊C4C2314yes—
139C2×(C2×D43)⋊C4C2314yes—
140C2×(C2×D43)⋊C4C2314yes—
141C2×(C2×D43)⋊C4C2314yes—
142C2×(C2×D43)⋊C4C2314yes—
143C2×(C2×D43)⋊C4C2314yes—
144C2×(C2×D43)⋊C4C2314yes—
145C2×(C2×D43)⋊C4C2314yes—
146C2×(C2×D43)⋊C4C2314yes—
147C2×(C2×D43)⋊C4C2314yes—
148C2×(C2×D43)⋊C4C2314yes—
149C2×(C2×D43)⋊C4C2314yes—
150C2×(C2×D43)⋊C4C2314yes—
151C2×C4×Dic43—24no—
152C2×C4×Dic43C2314yes—
153C43⋊#95C2314yes—
154C43⋊#95C2314yes—
155C23×C4×C43C2311yescharacteristic
156C23×C4×C43C2311yescharacteristic
157C23×C4×C43C2311yescharacteristic
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C23×C4×C43C2311yescharacteristic
161C23×C4×C43C2311yescharacteristic
162C2×C4⋊C4×C43—24no—
163C2×C4⋊C4×C43D418yescomplemented
164C2×C4⋊C4×C43C2314yes—
165C2×C4⋊C4×C43C2314yes—
166C2×C42×C43—24no—
167C2×C42×C43C2314yes—
168#95×C43C2314yes—
169#95×C43C2314yes—
170#95×C43C2314yes—
171#95×C43C2314yes—
172C24×C43C2411yescharacteristic
173C23×D43—22no—
174C23×D43—22no—
175C23×D43—22no—
176C23×D43—22no—
177C23×D43—22no—
178C23×D43—22no—
179C23×D43—22no—
180C23×D43—22no—
181C23×D43—22no—
182C23×D43—22no—
183C23×D43—22no—
184C23×D43—22no—
185C23×D43—22no—
186C23×D43—22no—
187C23×D43—22no—
188C23×D43—22no—
189C23×D43—22no—
190C23×D43—22no—
191C23×D43—22no—
192C23×D43—22no—
193C23×D43—22no—
194C23×D43—22no—
195C23×D43—22no—
196C23×D43—22no—
197C23×D43—22no—
198C23×D43C2×D414yes—
199C23×D43#4114yes—
200C23×D43#4114yes—
201C23×D43C2412yes—
202C23×D43C2412yes—
203C23×D43C2412yes—
204C23×D43C2412yes—
205C22×C4×C43—22no—
206C22×C4×C43—22no—
207C22×C4×C43—22no—
208C22×C4×C43—22no—
209C22×C4×C43—22no—
210C22×C4×C43—22no—
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—22no—
221C22×C4×C43C2×D414yes—
222C22×C4×C43C2×D414yes—
223C22×C4×C43C2×D414yes—
224C22×C4×C43C2×D414yes—
225C22×C4×C43#4114yes—
226C22×C4×C43C2412yes—
227C22×C4×C43C2412yes—
228C22×C4×C43C2412yes—
229C22×C4×C43C2412yes—
230C22×C4×C43C2412yes—
231C22×C4×C43C2412yes—
232C22×C4×C43C2412yes—
233C22×Dic43—22no—
234C22×Dic43—22no—
235C22×Dic43—22no—
236C22×Dic43—22no—
237C22×Dic43—22no—
238C22×Dic43—22no—
239C22×Dic43—22no—
240C22×Dic43—22no—
241C22×Dic43—22no—
242C22×Dic43—22no—
243C22×Dic43—22no—
244C22×Dic43C2×D414yes—
245C22×Dic43C2412yes—
246C22×Dic43C2412yes—
247C22×Dic43C2412yes—
248C22×Dic43C2412yes—
249C2×D172—232no—
250C2×D172—232no—
251C2×D172—28no—
252C2×D172—28no—
253C2×D172—28no—
254C2×D172—28no—
255C2×D172—28no—
256C2×D172—28no—
257C2×D172—28no—
258C2×D172—28no—
259C2×D172—28no—
260C2×D172—28no—
261C2×D172—28no—
262C2×D172—28no—
263C2×D172—28no—
264C2×D172—44no—
265C2×D172—44no—
266C2×D172—44no—
267C2×D172—44no—
268C2×D172—44no—
269C2×D172—416no—
270C2×D172—416no—
271C2×D172—416no—
272C2×D172—416no—
273C2×C4×D43—28no—
274C2×C4×D43—28no—
275C2×C4×D43—28no—
276C2×C4×D43—28no—
277C2×C4×D43—28no—
278C2×C4×D43—28no—
279C2×C4×D43—44no—
280C2×C4×D43—44no—
281C2×C4×D43—44no—
282C2×C4×D43—416no—
283C2×C4×D43—416no—
284C2×C4×D43—416no—
285C4⋊C4×C43—28no—
286C4⋊C4×C43C2×D4116yescomplemented
287C42×C43—28no—
288(C2×D43)⋊C4—28no—
289(C2×D43)⋊C4—28no—
290(C2×D43)⋊C4—28no—
291(C2×D43)⋊C4—28no—
292(C2×D43)⋊C4—28no—
293(C2×D43)⋊C4—28no—
294(C2×D43)⋊C4—28no—
295(C2×D43)⋊C4—28no—
296(C2×D43)⋊C4—28no—
297(C2×D43)⋊C4—44no—
298(C2×D43)⋊C4—44no—
299(C2×D43)⋊C4—44no—
300(C2×D43)⋊C4C2×D4116yescomplemented
301C4⋊Dic43—28no—
302C4⋊Dic43—44no—
303Dic43⋊C4—28no—
304C4×Dic43—28no—
305C23×C43C22×D412yes—
306C23×C43C22×D412yes—
307C23×C43C2×#4112yes—
308C23×C43C2×#4112yes—
309C23×C43C2×#4112yes—
310C23×C43H(5,𝔽2)12yes—
311C23×C43H(5,𝔽2)12yes—
312C23×C43C2511yescharacteristic
313C22×D43—28no—
314C22×D43—28no—
315C22×D43—28no—
316C22×D43—28no—
317C22×D43—28no—
318C22×D43—28no—
319C22×D43—28no—
320C22×D43—28no—
321C22×D43—28no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—22no—
325C22×D43—22no—
326C22×D43—22no—
327C22×D43—22no—
328C22×D43—22no—
329C22×D43—22no—
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—22no—
345C22×D43—22no—
346C22×D43—22no—
347C22×D43—44no—
348C22×D43—44no—
349C22×D43—44no—
350C22×D43—44no—
351C22×D43—44no—
352C22×D43—44no—
353C22×D43—44no—
354C22×D43—44no—
355C22×D43—44no—
356C22×D43—44no—
357C22×D43—44no—
358C22×D43—44no—
359C22×D43—44no—
360C22×D43—44no—
361C22×D43—44no—
362C22×D43—44no—
363C22×D43—44no—
364C22×D43—44no—
365C22×D43—44no—
366C22×D43C22×D414yes—
367C22×D43C2×#4114yes—
368C22×D43C2×#4114yes—
369C2×C4×C43—28no—
370C2×C4×C43—28no—
371C2×C4×C43—28no—
372C2×C4×C43—28no—
373C2×C4×C43—28no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—22no—
386C2×C4×C43—22no—
387C2×C4×C43—22no—
388C2×C4×C43—22no—
389C2×C4×C43—22no—
390C2×C4×C43—44no—
391C2×C4×C43—44no—
392C2×C4×C43C22×D414yes—
393C2×C4×C43C22×D414yes—
394C2×C4×C43C22×D414yes—
395C2×C4×C43C22×D414yes—
396C2×C4×C43C2×#4114yes—
397C2×Dic43—28no—
398C2×Dic43—22no—
399C2×Dic43—22no—
400C2×Dic43—22no—
401C2×Dic43—22no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—22no—
406C2×Dic43—22no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—44no—
410C2×Dic43—44no—
411C2×Dic43—44no—
412C2×Dic43C22×D414yes—
413D172—232no—
414D172—232no—
415D172—416no—
416D172—416no—
417D172—416no—
418D172—416no—
419C4×D43—416no—
420C4×D43—416no—
421C4×D43—416no—
422C2×#2456—431nomaximal, Sylow
423C22×C43#52514yes—
424C22×C43#52514yes—
425C22×C43#53814yes—
426C22×C43D4214yes—
427C22×C43#54614yes—
428C22×C43#55014yes—
429C22×C43#55314yes—
430C22×C43C23×D411yescharacteristic
431C22×C43C23×D411yescharacteristic
432C22×C43C22×#4111yescharacteristic
433C22×C43C22×#4111yescharacteristic
434C22×C43C22×#4111yescharacteristic
435C22×C43C2×H(5,𝔽2)11yescharacteristic
436C22×C43C2×H(5,𝔽2)11yescharacteristic
437C2×D43—24no—
438C2×D43—24no—
439C2×D43—24no—
440C2×D43—24no—
441C2×D43—24no—
442C2×D43—24no—
443C2×D43—24no—
444C2×D43—24no—
445C2×D43—24no—
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—42no—
455C2×D43—42no—
456C2×D43—42no—
457C2×D43—42no—
458C2×D43—416no—
459C2×D43—416no—
460C2×D43—416no—
461C2×D43—42no—
462C2×D43—42no—
463C2×D43—42no—
464C2×D43—42no—
465C2×D43—42no—
466C2×D43—42no—
467C2×D43—42no—
468C2×D43—88no—
469C4×C43—24no—
470C4×C43—24no—
471C4×C43—24no—
472C4×C43—24no—
473C4×C43—24no—
474C4×C43—42no—
475C4×C43—42no—
476Dic43—24no—
477Dic43—42no—
478Dic43—42no—
479Dic43—42no—
480C22×#123—431no—
481C22×#121—431no—
482C22×C4×D4—431no—
483C22×C4×D4—431no—
484#2456—4316no—
485C2×#396—431no—
486C2×#392—431no—
487C2×#392—431no—
488C2×#392—431no—
489C2×#390—431no—
490C2×#388—431no—
491C2×#388—431no—
492C2×#387D4311yescharacteristic, complemented
493C2×#386—431no—
494C2×#386—431no—
495C2×#385—431no—
496C2×C43#245618yescomplemented
497C2×C43C2×#52511yescharacteristic
498C2×C43C2×#52511yescharacteristic
499C2×C43C2×#53811yescharacteristic
500C2×C43C2×D4211yescharacteristic
501C2×C43C2×#54611yescharacteristic
502C2×C43C2×#55011yescharacteristic
503C2×C43C2×#55311yescharacteristic
504D43—44no—
505D43—44no—
506D43—44no—
507D43—82no—
508C23×D4—431no—
509C23×D4—431no—
510C23×D4—431no—
511C23×D4—431no—
512C23×D4—431no—
513C23×D4—431no—
514C24×C4—431no—
515C24×C4—431no—
516C24×C4—431no—
517C2×#123—438no—
518C2×#123—868no—
519C2×#121—438no—
520C2×#121—868no—
521C2×C4×D4—438no—
522C2×C4×D4—438no—
523C2×C4×D4—868no—
524C2×C4×D4—868no—
525C22×C4⋊C4—431no—
526C22×C4⋊C4—431no—
527C22×C4⋊C4—431no—
528C22×C4⋊C4C2×D4311yescharacteristic
529C22×C4⋊C4C2×D4311yescharacteristic
530C22×C22⋊C4—431no—
531C22×C22⋊C4—431no—
532C22×C22⋊C4—431no—
533C22×C22⋊C4—431no—
534C22×C22⋊C4—431no—
535C22×C22⋊C4—431no—
536C22×C22⋊C4—431no—
537C22×C22⋊C4—431no—
538C22×C22⋊C4—431no—
539C22×C22⋊C4—431no—
540C22×C22⋊C4—431no—
541C22×C22⋊C4—431no—
542C22×C22⋊C4—431no—
543C22×C42—431no—
544C22×C42C2×D4311yescharacteristic
545#396—438no—
546#392—438no—
547#392—438no—
548#392—438no—
549#390—438no—
550#388—438no—
551#388—438no—
552#387C2×D4318yescomplemented
553#386—438no—
554#386—438no—
555#385—438no—
556C2×#95—431no—
557C2×#95—431no—
558C2×#95C2×D4311yescharacteristic
559C2×#95C2×D4311yescharacteristic
560C2×#95C2×D4311yescharacteristic
561C2×#95C2×D4311yescharacteristic
562C43C2×#245611yescharacteristic, complemented, Sylow
563C25—431no—
564C25—431no—
565C25—431no—
566C25—431no—
567C22×D4—434no—
568C22×D4—434no—
569C22×D4—434no—
570C22×D4—434no—
571C22×D4—434no—
572C22×D4—434no—
573C22×D4—864no—
574C22×D4—864no—
575C22×D4—864no—
576C22×D4—864no—
577C22×D4—864no—
578C22×D4—864no—
579C22×D4—864no—
580C22×D4—864no—
581C22×D4—864no—
582C22×D4—864no—
583C22×D4—864no—
584C22×D4—864no—
585C22×D4—864no—
586C22×D4—1722no—
587C22×D4—1722no—
588C22×D4—1722no—
589C22×D4—1722no—
590C22×D4—1722no—
591C23×C4—431no—
592C23×C4—431no—
593C23×C4—431no—
594C23×C4—431no—
595C23×C4—434no—
596C23×C4—434no—
597C23×C4—434no—
598C23×C4—864no—
599C23×C4—864no—
600C23×C4—864no—
601C23×C4—864no—
602C23×C4—864no—
603C23×C4—864no—
604C23×C4—1722no—
605C23×C4—1722no—
606C23×C4—1722no—
607C23×C4C22×D4311yescharacteristic
608C23×C4C22×D4311yescharacteristic
609C23×C4C22×D4311yescharacteristic
610C23×C4C22×D4311yescharacteristic
611C23×C4C22×D4311yescharacteristic
612C23×C4C22×D4311yescharacteristic
613C23×C4C22×D4311yescharacteristic
614#123—8632no—
615#121—8632no—
616C4×D4—8632no—
617C4×D4—8632no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—434no—
620C2×C4⋊C4—434no—
621C2×C4⋊C4—434no—
622C2×C4⋊C4—864no—
623C2×C4⋊C4—864no—
624C2×C4⋊C4—1722no—
625C2×C4⋊C4D17218yescomplemented
626C2×C4⋊C4C22×D4314yes—
627C2×C4⋊C4C22×D4314yes—
628C2×C22⋊C4—438no—
629C2×C22⋊C4—434no—
630C2×C22⋊C4—434no—
631C2×C22⋊C4—434no—
632C2×C22⋊C4—434no—
633C2×C22⋊C4—434no—
634C2×C22⋊C4—434no—
635C2×C22⋊C4—434no—
636C2×C22⋊C4—434no—
637C2×C22⋊C4—434no—
638C2×C22⋊C4—434no—
639C2×C22⋊C4—434no—
640C2×C22⋊C4—434no—
641C2×C22⋊C4—434no—
642C2×C22⋊C4—864no—
643C2×C22⋊C4—864no—
644C2×C22⋊C4—864no—
645C2×C22⋊C4—864no—
646C2×C22⋊C4—864no—
647C2×C22⋊C4—864no—
648C2×C22⋊C4—864no—
649C2×C22⋊C4—864no—
650C2×C22⋊C4—864no—
651C2×C22⋊C4—1722no—
652C2×C22⋊C4—1722no—
653C2×C22⋊C4—1722no—
654C2×C42—24no—
655C2×C42—434no—
656C2×C42—864no—
657C2×C42C22×D4314yes—
658#95—434no—
659#95—434no—
660#95C22×D4314yes—
661#95C22×D4314yes—
662#95C22×D4314yes—
663#95C22×D4314yes—
664C24—434no—
665C24—434no—
666C24—434no—
667C24—432no—
668C24—432no—
669C24—432no—
670C24—432no—
671C24—862no—
672C24—862no—
673C24—862no—
674C24—862no—
675C24—862no—
676C24—862no—
677C24—862no—
678C24—862no—
679C24—862no—
680C24—862no—
681C24—862no—
682C24—862no—
683C24—862no—
684C24—862no—
685C24—862no—
686C24—862no—
687C24—862no—
688C24—862no—
689C24—862no—
690C24—862no—
691C24—862no—
692C24—862no—
693C24—862no—
694C24—862no—
695C24—862no—
696C24C23×D4311yescharacteristic
697C2×D4—868no—
698C2×D4—868no—
699C2×D4—868no—
700C2×D4—868no—
701C2×D4—8632no—
702C2×D4—8632no—
703C2×D4—868no—
704C2×D4—868no—
705C2×D4—868no—
706C2×D4—868no—
707C2×D4—868no—
708C2×D4—868no—
709C2×D4—868no—
710C2×D4—868no—
711C2×D4—868no—
712C2×D4—1724no—
713C2×D4—1724no—
714C2×D4—1724no—
715C2×D4—1724no—
716C2×D4—1724no—
717C2×D4—17216no—
718C2×D4—17216no—
719C2×D4—17216no—
720C2×D4—17216no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—434no—
738C22×C4—432no—
739C22×C4—432no—
740C22×C4—432no—
741C22×C4—432no—
742C22×C4—868no—
743C22×C4—868no—
744C22×C4—868no—
745C22×C4—862no—
746C22×C4—862no—
747C22×C4—862no—
748C22×C4—862no—
749C22×C4—862no—
750C22×C4—862no—
751C22×C4—862no—
752C22×C4—862no—
753C22×C4—862no—
754C22×C4—862no—
755C22×C4—862no—
756C22×C4—868no—
757C22×C4—868no—
758C22×C4—868no—
759C22×C4—1724no—
760C22×C4—1724no—
761C22×C4—1724no—
762C22×C4—17216no—
763C22×C4—17216no—
764C22×C4—17216no—
765C22×C4C2×D17214yes—
766C22×C4C2×D17214yes—
767C22×C4C2×D17214yes—
768C22×C4D4×D4314yes—
769C22×C4#1062190214yes—
770C22×C4C23×D4312yes—
771C22×C4C23×D4312yes—
772C22×C4C23×D4312yes—
773C22×C4C23×D4312yes—
774C22×C4C23×D4312yes—
775C22×C4C23×D4312yes—
776C22×C4C23×D4312yes—
777C4⋊C4—28no—
778C4⋊C4—868no—
779C4⋊C4—868no—
780C4⋊C4—1724no—
781C4⋊C4C2×D172116yescomplemented
782C22⋊C4—4316no—
783C22⋊C4—868no—
784C22⋊C4—868no—
785C22⋊C4—868no—
786C22⋊C4—868no—
787C22⋊C4—868no—
788C22⋊C4—868no—
789C22⋊C4—868no—
790C22⋊C4—868no—
791C22⋊C4—868no—
792C22⋊C4—1724no—
793C22⋊C4—1724no—
794C22⋊C4—1724no—
795C42—28no—
796C42—868no—
797C23—434no—
798C23—434no—
799C23—434no—
800C23—868no—
801C23—868no—
802C23—868no—
803C23—868no—
804C23—868no—
805C23—862no—
806C23—862no—
807C23—862no—
808C23—862no—
809C23—862no—
810C23—862no—
811C23—862no—
812C23—862no—
813C23—862no—
814C23—862no—
815C23—862no—
816C23—862no—
817C23—862no—
818C23—862no—
819C23—862no—
820C23—862no—
821C23—862no—
822C23—862no—
823C23—868no—
824C23—868no—
825C23—868no—
826C23—868no—
827C23—862no—
828C23—862no—
829C23—862no—
830C23—862no—
831C23—862no—
832C23—862no—
833C23—862no—
834C23—1724no—
835C23—1724no—
836C23—1724no—
837C23—1724no—
838C23—1724no—
839C23—1724no—
840C23—1724no—
841C23—1724no—
842C23—1724no—
843C23—1724no—
844C23—1724no—
845C23—1724no—
846C23—1724no—
847C23—1724no—
848C23—1724no—
849C23—1724no—
850C23—1724no—
851C23—1724no—
852C23—1724no—
853C23C2×D4×D4312yes—
854C23C22×D17212yes—
855C23#41×D4312yes—
856C23#41×D4312yes—
857C23C2×#1062190212yes—
858C23#1306337112yes—
859C23#1306337112yes—
860C23C24×D4311yescharacteristic
861D4—8632no—
862D4—8632no—
863D4—17216no—
864D4—17216no—
865D4—17216no—
866D4—17216no—
867C2×C4—28no—
868C2×C4—28no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—28no—
880C2×C4—28no—
881C2×C4—28no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—434no—
891C2×C4—862no—
892C2×C4—862no—
893C2×C4—868no—
894C2×C4—862no—
895C2×C4—862no—
896C2×C4—862no—
897C2×C4—862no—
898C2×C4—862no—
899C2×C4—862no—
900C2×C4—862no—
901C2×C4—862no—
902C2×C4—862no—
903C2×C4—17216no—
904C2×C4—17216no—
905C2×C4—17216no—
906C2×C4—1724no—
907C2×C4—1724no—
908C2×C4—1724no—
909C2×C4C2×D4×D4314yes—
910C2×C4C22×D17214yes—
911C2×C4C22×D17214yes—
912C2×C4C22×D17214yes—
913C2×C4C2×#1062190214yes—
914C22—864no—
915C22—864no—
916C22—864no—
917C22—864no—
918C22—864no—
919C22—864no—
920C22—864no—
921C22—864no—
922C22—864no—
923C22—3448no—
924C22—1722no—
925C22—1722no—
926C22—1722no—
927C22—1722no—
928C22—1722no—
929C22—1722no—
930C22—1722no—
931C22—1722no—
932C22—1722no—
933C22—1722no—
934C22—1722no—
935C22—1722no—
936C22—1722no—
937C22—1722no—
938C22—1722no—
939C22—1722no—
940C22—1722no—
941C22—1722no—
942C22—1722no—
943C22—17216no—
944C22—17216no—
945C22—17216no—
946C22#1458341114yes—
947C22#1458341214yes—
948C22#1458348814yes—
949C22D4×D17214yes—
950C22#1458354114yes—
951C22#1458357114yes—
952C22#1458360214yes—
953C22C22×D4×D4311yescharacteristic
954C22C23×D17211yescharacteristic
955C22C2×#41×D4311yescharacteristic
956C22C2×#41×D4311yescharacteristic
957C22C22×#1062190211yescharacteristic
958C22C2×#1306337111yescharacteristic
959C22C2×#1306337111yescharacteristic
960C4—24no—
961C4—24no—
962C4—24no—
963C4—24no—
964C4—24no—
965C4—42no—
966C4—42no—
967C4—864no—
968C4—1722no—
969C4—1722no—
970C4—1722no—
971C2—3442no—
972C2—1724no—
973C2—1724no—
974C2—1724no—
975C2#1913848518yesdirect product factor
976C2C2×#1458341111yescharacteristic
977C2C2×#1458341211yescharacteristic
978C2C2×#1458348811yescharacteristic
979C2C2×D4×D17211yescharacteristic
980C2C2×#1458354111yescharacteristic
981C2C2×#1458357111yescharacteristic
982C2C2×#1458360211yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
hypercenterC2×#387D43
hypocenterC43C2×#2456
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#13063310C2semidirect
2. C22×#13063300C2semidirect
3. C22×C4×D172C2semidirect
4. C22×#13063287C2semidirect
5. #19138485C2direct (N × H)
6. C2×#14582821C2semidirect
7. C2×#14582809C2semidirect
8. C2×#14582809C2semidirect
9. C2×#14582809C2semidirect
10. C2×#14582801C2semidirect
11. C2×#14582791C2semidirect
12. C2×#14582791C2semidirect
13. C2×#14582777C2semidirect
14. C2×#14582777C2semidirect
15. C2×#14582773C2semidirect
16. C2×C43×#387C2semidirect
27. C2×#13063310C22semidirect
29. C2×#13063300C22semidirect
31. C2×C4×D172C22semidirect
33. C2×#13063287C22semidirect
51. #14582821C22semidirect
52. #14582809C22semidirect
53. #14582809C22semidirect
54. #14582809C22semidirect
55. #14582801C22semidirect
56. #14582791C22semidirect
57. #14582791C22semidirect
58. #14582777C22semidirect
59. #14582777C22semidirect
60. #14582773C22semidirect
66. C43×#387C22semidirect
137. C2×(C2×D43)⋊C4D4semidirect
163. C2×C4⋊C4×C43D4semidirect
286. C4⋊C4×C43C2×D4semidirect
300. (C2×D43)⋊C4C2×D4semidirect
492. C2×#387D43semidirect
496. C2×C43#2456semidirect
552. #387C2×D43semidirect
562. C43C2×#2456semidirect
625. C2×C4⋊C4D172semidirect
781. C4⋊C4C2×D172semidirect
975. C2#19138485direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633102
C22×#130633002
C22×C4×D1722
C22×#130632872
#191384852
C2×#145828212
C2×#145828092
C2×#145828012
C2×#145827912
C2×#145827772
C2×#145827732
C2×C43×#3872
C2×#245643