Finite Group Databasebeta

← #25269555

Subgroups — #25269555

Order 11008.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583482C212yesmaximal, complemented
2#19142962C211yesmaximal, characteristic, complemented
3#19142952C211yesmaximal, characteristic, complemented
4#19142940C211yesmaximal, characteristic, complemented
5#19142926C211yesmaximal, characteristic, complemented
6#19140732C212yesmaximal, complemented
7#19140721C212yesmaximal, complemented
8#19139664C212yesmaximal, complemented
9#19139649C212yesmaximal, complemented
10#19139181C211yesmaximal, characteristic, complemented
11#19138958C211yesmaximal, characteristic, complemented
12#19138721C212yesmaximal, complemented
13#19138360C211yesmaximal, characteristic, complemented
14#19138297C211yesmaximal, characteristic, complemented
15#19138232C211yesmaximal, characteristic, complemented
16#19138183C211yesmaximal, characteristic, complemented
17#19138125C212yesmaximal, complemented
18#19138035C211yesmaximal, characteristic, complemented
19#19137951C211yesmaximal, characteristic, complemented
20#19137255C212yesmaximal, complemented
21C4×#13063299C211yesmaximal, characteristic, complemented
22C2×#14582801C211yesmaximal, characteristic, complemented
23C42×D4×C43C211yesmaximal, characteristic, complemented
24C23×D172C2211yescharacteristic
25#14583482—216no—
26C2×#13063325C2211yescharacteristic, complemented
27C2×#13063322C2211yescharacteristic
28C2×#13063322C2211yescharacteristic
29C2×#13063320C2212yescomplemented
30C2×#13063319C2212yescomplemented
31C2×#13063313C2212yescomplemented
32C2×#13063313C2212yescomplemented
33C2×#13063311C2212yescomplemented
34C2×#13063310C2212yescomplemented
35C2×#13063308C2212yescomplemented
36C2×#13063302C2212yes—
37C2×#13063299C2211yescharacteristic
38C2×#13063299C2211yescharacteristic
39C2×#13063299C2211yescharacteristic
40C2×#13063299C2212yescomplemented
41C2×#13063299C2212yescomplemented
42C2×#13063299C2211yescharacteristic, complemented
43C2×#13063298C2212yescomplemented
44C2×#13063297C2212yes—
45C2×#13063295C2212yes—
46C2×#13063295C2212yes—
47C2×#13063293C2212yes—
48C2×C4×D172C2211yescharacteristic, complemented
49C2×C4×C22⋊D43C2212yes—
50C22×C4⋊Dic43C2211yescharacteristic
51C22×(C2×D43)⋊C4C2212yes—
52C22×(C2×D43)⋊C4C2212yes—
53#14582831C2212yescomplemented
54#14582826C2212yescomplemented
55#14582821C2212yescomplemented
56#14582821C2212yescomplemented
57#14582820C2212yescomplemented
58#14582817C2212yescomplemented
59#14582817C2212yescomplemented
60#14582816C2212yes—
61#14582816C2212yescomplemented
62#14582815C2212yescomplemented
63#14582815C2212yescomplemented
64#14582812C2212yescomplemented
65#14582809C2212yes—
66#14582809C2212yes—
67#14582808C2212yes—
68#14582808C2212yescomplemented
69#14582801C2211yescharacteristic
70#14582801C2211yescharacteristic
71#14582801C2211yescharacteristic
72#14582801C2211yescharacteristic
73#14582801C2212yes—
74#14582801C2211yescharacteristic
75#14582801C2212yes—
76#14582801C2211yescharacteristic
77#14582801C2211yescharacteristic
78#14582801C2211yescharacteristic
79#14582801C2211yescharacteristic, complemented
80#14582801C2212yescomplemented
81#14582801C2212yescomplemented
82#14582801C2211yescharacteristic, complemented
83#14582801C2212yescomplemented
84#14582801C2212yescomplemented
85#14582797C2211yescharacteristic, complemented
86#14582797C2211yescharacteristic, complemented
87#14582797C2211yescharacteristic, complemented
88#14582797C2211yescharacteristic, complemented
89#14582791C2212yescomplemented
90#14582791C2212yescomplemented
91#14582790C2212yescomplemented
92#14582790C2212yescomplemented
93#14582790C2212yescomplemented
94#14582790C2212yescomplemented
95#14582790C2212yescomplemented
96#14582790C2212yescomplemented
97#14582778C2212yes—
98#14582778C2212yescomplemented
99#14582777C2212yescomplemented
100#14582777C2212yescomplemented
101#14582776C2212yes—
102#14582774C2212yes—
103#14582769C2211yescharacteristic, complemented
104#14582759C2211yescharacteristic
105#14582759C2211yescharacteristic, complemented
106#14582754C2212yes—
107C4×C4⋊Dic43C2211yescharacteristic, complemented
108C4×(C2×D43)⋊C4C2212yescomplemented
109C2×C4×D4×C43C2211yescharacteristic
110C2×C4×D4×C43C2211yescharacteristic
111C2×C4×D4×C43C2211yescharacteristic
112C22×C42×C43C2211yescharacteristic
113C22×C42×C43C2211yescharacteristic, complemented
114C4×C4⋊C4×C43C2211yescharacteristic, complemented
115C4×C4⋊C4×C43C2211yescharacteristic, complemented
116C4×C4⋊C4×C43C2211yescharacteristic, complemented
117C4×C22⋊C4×C43C2211yescharacteristic
118C4×C22⋊C4×C43C2211yescharacteristic
119C4×C22⋊C4×C43C2211yescharacteristic
120C4×C22⋊C4×C43C2211yescharacteristic, complemented
121C4×C22⋊C4×C43C2211yescharacteristic, complemented
122C4×C22⋊C4×C43C2211yescharacteristic, complemented
123C43×C43C2211yescharacteristic, complemented
124C24×D43C2312yes—
125C22×Dic86C2312yes—
126C22×D172—24no—
127C22×D172—42no—
128C22×D172—42no—
129C22×D172C2311yescharacteristic
130C22×D172C2311yescharacteristic
131C22×D172C2311yescharacteristic
132C22×D172C2312yes—
133C22×D172C2312yes—
134C22×D172C2312yes—
135C22×D172C2312yes—
136C22×D172C2312yes—
137C22×C22⋊D43C2312yes—
138C22×C22⋊D43C2312yes—
139C22×C22⋊D43C2312yes—
140C22×C22⋊D43C2312yes—
141C23×Dic43C2312yes—
142C22×C4×D43C2312yes—
143#13063325—42no—
144#13063322—42no—
145#13063322—42no—
146#13063320—28no—
147#13063319—28no—
148#13063313—28no—
149#13063313—44no—
150#13063311—28no—
151#13063310—28no—
152#13063308—28no—
153#13063302—28no—
154#13063299—28no—
155#13063299—24no—
156#13063299—42no—
157#13063299—42no—
158#13063299—42no—
159#13063299—44no—
160#13063298—28no—
161#13063297—28no—
162#13063295—28no—
163#13063295—28no—
164#13063293—28no—
165C4×D172—42no—
166C4×C22⋊D43—28no—
167C2×C4⋊Dic43—42no—
168C2×C4⋊Dic43C2311yescharacteristic
169C2×C4⋊Dic43C2311yescharacteristic
170C2×C4⋊Dic43C2311yescharacteristic
171C2×C4⋊Dic43C2311yescharacteristic
172C2×C4⋊Dic43C2311yescharacteristic
173C2×C4⋊Dic43C2312yes—
174C2×C4⋊Dic43C2312yes—
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2312yes—
177C2×Dic43⋊C4C2312yes—
178C2×Dic43⋊C4C2312yes—
179C2×Dic43⋊C4C2312yes—
180C2×Dic43⋊C4C2312yes—
181C2×C22⋊Dic43C2312yes—
182C2×C22⋊Dic43C2312yes—
183C2×(C2×D43)⋊C4—28no—
184C2×(C2×D43)⋊C4—44no—
185C2×(C2×D43)⋊C4C2312yes—
186C2×(C2×D43)⋊C4C2312yes—
187C2×(C2×D43)⋊C4C2312yes—
188C2×(C2×D43)⋊C4C2312yes—
189C2×(C2×D43)⋊C4C2312yes—
190C2×(C2×D43)⋊C4C2312yes—
191C2×(C2×D43)⋊C4C2312yes—
192C2×(C2×D43)⋊C4C2312yes—
193C2×(C2×D43)⋊C4C2312yes—
194C2×(C2×D43)⋊C4C2312yes—
195C2×(C2×D43)⋊C4C2312yes—
196C2×(C2×D43)⋊C4C2312yes—
197C2×(C2×D43)⋊C4C2312yes—
198C2×(C2×D43)⋊C4C2312yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2312yes—
204C2×(C2×D43)⋊C4C2312yes—
205C2×(C2×D43)⋊C4C2312yes—
206C2×(C2×D43)⋊C4C2312yes—
207C2×(C2×D43)⋊C4C2312yes—
208C2×(C2×D43)⋊C4C2312yes—
209C2×(C2×D43)⋊C4C2312yes—
210C2×C4×Dic43C2312yes—
211C43⋊#95C2312yes—
212C43⋊#95C2312yes—
213C43⋊#95C2312yes—
214C43⋊#95C2312yes—
215C43⋊#95C2312yes—
216C43⋊#95C2312yes—
217C43⋊#95C2312yes—
218C22×D4×C43C2311yescharacteristic
219C23×C4×C43C2311yescharacteristic
220C23×C4×C43C2311yescharacteristic
221C23×C4×C43C2311yescharacteristic
222C23×C4×C43C2311yescharacteristic
223C23×C4×C43C2311yescharacteristic
224C23×C4×C43C2311yescharacteristic
225C4×D4×C43—24no—
226C4×D4×C43—24no—
227C4×D4×C43D418yescomplemented
228C2×C4⋊C4×C43C2311yescharacteristic
229C2×C4⋊C4×C43C2311yescharacteristic
230C2×C4⋊C4×C43C2311yescharacteristic
231C2×C22⋊C4×C43C2311yescharacteristic
232C2×C22⋊C4×C43C2311yescharacteristic
233C2×C22⋊C4×C43C2311yescharacteristic
234C2×C22⋊C4×C43C2311yescharacteristic
235C2×C22⋊C4×C43C2311yescharacteristic
236C2×C22⋊C4×C43C2311yescharacteristic
237C2×C42×C43—42no—
238C2×C42×C43—42no—
239C2×C42×C43C2311yescharacteristic
240C2×C42×C43C2311yescharacteristic
241C2×C42×C43C2311yescharacteristic
242C2×C42×C43C2311yescharacteristic
243C2×C42×C43C2311yescharacteristic
244C2×C42×C43C2311yescharacteristic
245C2×C42×C43C2311yescharacteristic
246C2×C42×C43C2311yescharacteristic
247C2×C42×C43C2311yescharacteristic
248C2×C42×C43C2311yescharacteristic
249C2×C42×C43C2311yescharacteristic
250C2×C42×C43C2311yescharacteristic
251C2×C42×C43C2311yescharacteristic
252#95×C43C2311yescharacteristic
253#95×C43C2311yescharacteristic
254#95×C43C2311yescharacteristic
255#95×C43C2311yescharacteristic
256#95×C43C2311yescharacteristic
257#95×C43C2311yescharacteristic
258C24×C43C2411yescharacteristic
259C24×C43C2411yescharacteristic
260C23×D43—24no—
261C23×D43—24no—
262C23×D43—24no—
263C23×D43—42no—
264C23×D43—42no—
265C23×D43—42no—
266C23×D43—42no—
267C23×D43C2412yes—
268C23×D43C2412yes—
269C23×D43C2412yes—
270C2×D4×C43—22no—
271C2×D4×C43—22no—
272C2×D4×C43C2×D414yes—
273C22×C4×C43—22no—
274C22×C4×C43—22no—
275C22×C4×C43—22no—
276C22×C4×C43—22no—
277C22×C4×C43—22no—
278C22×C4×C43—22no—
279C22×C4×C43—22no—
280C22×C4×C43—22no—
281C22×C4×C43—22no—
282C22×C4×C43—41no—
283C22×C4×C43—41no—
284C22×C4×C43—41no—
285C22×C4×C43—41no—
286C22×C4×C43—41no—
287C22×C4×C43—41no—
288C22×C4×C43C2×D414yes—
289C22×C4×C43C2×D414yescomplemented
290C22×C4×C43#4114yes—
291C22×C4×C43C2411yescharacteristic
292C22×C4×C43C2411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2411yescharacteristic
295C22×C4×C43C2411yescharacteristic
296C22×C4×C43C2411yescharacteristic
297C22×C4×C43C2411yescharacteristic
298C22×C4×C43C2411yescharacteristic
299C22×C4×C43C2411yescharacteristic
300C22×C4×C43C2411yescharacteristic
301C22×C4×C43C2411yescharacteristic
302C22×C4×C43C2411yescharacteristic
303C22×C4×C43C2411yescharacteristic
304C2×C22⋊D43—24no—
305C2×C22⋊D43—24no—
306C2×C22⋊D43—24no—
307C2×C22⋊D43—24no—
308C2×C22⋊D43—24no—
309C2×C22⋊D43—24no—
310C2×C22⋊D43—42no—
311C2×C22⋊D43—42no—
312C2×C22⋊D43—42no—
313C2×C22⋊D43—42no—
314C2×C22⋊D43—42no—
315C2×C22⋊D43—42no—
316C22×Dic43—24no—
317C22×Dic43—42no—
318C22×Dic43—42no—
319C22×Dic43C2412yes—
320C22×Dic43C2412yes—
321C22×Dic43C2412yes—
322C22×Dic43C2412yes—
323C22×Dic43C2412yes—
324C2×D172—22no—
325C2×D172—24no—
326C2×D172—22no—
327C2×D172—22no—
328C2×D172—22no—
329C2×D172—22no—
330C2×D172—22no—
331C2×D172—22no—
332C2×D172—22no—
333C2×D172—22no—
334C2×D172—24no—
335C2×D172—24no—
336C2×D172—24no—
337C2×D172—24no—
338C2×D172—42no—
339C2×D172—42no—
340C2×D172—42no—
341C2×D172—42no—
342C2×D172—42no—
343C2×D172—42no—
344C2×D172—42no—
345C2×D172—42no—
346C2×D172—42no—
347C2×D172—42no—
348C2×D172—416no—
349C2×C4×D43—24no—
350C2×C4×D43—42no—
351C2×C4×D43—42no—
352C2×Dic86—24no—
353C2×Dic86—42no—
354C2×Dic86—42no—
355C4⋊C4×C43—22no—
356C4⋊C4×C43—22no—
357C4⋊C4×C43C2×D414yescomplemented
358C22⋊C4×C43—22no—
359C22⋊C4×C43—22no—
360C22⋊C4×C43—22no—
361C22⋊C4×C43C2×D414yes—
362C22⋊C4×C43C2×D414yescomplemented
363C22⋊C4×C43#4114yes—
364C42×C43—22no—
365C42×C43—22no—
366C42×C43—22no—
367C42×C43—22no—
368C42×C43—22no—
369C42×C43—22no—
370C42×C43—22no—
371C42×C43—41no—
372C42×C43—41no—
373C42×C43—41no—
374C42×C43—41no—
375C42×C43—41no—
376C42×C43C2×D414yescomplemented
377C22⋊Dic43—24no—
378C22⋊Dic43—24no—
379(C2×D43)⋊C4—24no—
380(C2×D43)⋊C4—24no—
381(C2×D43)⋊C4—24no—
382(C2×D43)⋊C4—24no—
383(C2×D43)⋊C4—24no—
384(C2×D43)⋊C4—24no—
385(C2×D43)⋊C4—24no—
386(C2×D43)⋊C4—24no—
387(C2×D43)⋊C4—24no—
388(C2×D43)⋊C4—24no—
389(C2×D43)⋊C4—24no—
390(C2×D43)⋊C4—24no—
391(C2×D43)⋊C4—24no—
392(C2×D43)⋊C4—24no—
393(C2×D43)⋊C4—24no—
394(C2×D43)⋊C4—24no—
395(C2×D43)⋊C4—42no—
396(C2×D43)⋊C4—42no—
397(C2×D43)⋊C4—42no—
398(C2×D43)⋊C4—42no—
399(C2×D43)⋊C4—42no—
400(C2×D43)⋊C4—42no—
401(C2×D43)⋊C4—42no—
402(C2×D43)⋊C4—42no—
403(C2×D43)⋊C4—42no—
404C4⋊Dic43—24no—
405C4⋊Dic43—22no—
406C4⋊Dic43—22no—
407C4⋊Dic43—22no—
408C4⋊Dic43—22no—
409C4⋊Dic43—22no—
410C4⋊Dic43—42no—
411C4⋊Dic43—42no—
412C4⋊Dic43—42no—
413Dic43⋊C4—24no—
414Dic43⋊C4—24no—
415Dic43⋊C4—24no—
416Dic43⋊C4—24no—
417C4×Dic43—24no—
418C23×C43—21no—
419C23×C43—21no—
420C23×C43—21no—
421C23×C43—21no—
422C23×C43—21no—
423C23×C43—21no—
424C23×C43—21no—
425C23×C43—21no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43C22×D412yes—
429C23×C43C22×D412yes—
430C23×C43C2×#4112yes—
431C23×C43C2×#4112yes—
432C23×C43C2511yescharacteristic
433C22×D43—22no—
434C22×D43—22no—
435C22×D43—22no—
436C22×D43—22no—
437C22×D43—22no—
438C22×D43—22no—
439C22×D43—22no—
440C22×D43—22no—
441C22×D43—22no—
442C22×D43—22no—
443C22×D43—22no—
444C22×D43—22no—
445C22×D43—22no—
446C22×D43—22no—
447C22×D43—22no—
448C22×D43—22no—
449C22×D43—22no—
450C22×D43—22no—
451C22×D43—22no—
452C22×D43—22no—
453C22×D43—22no—
454C22×D43—48no—
455C22×D43—48no—
456C22×D43—48no—
457C22×D43—84no—
458C22×D43—84no—
459C22×D43—84no—
460C22×D43—84no—
461D4×C43—28no—
462C2×C4×C43—21no—
463C2×C4×C43—21no—
464C2×C4×C43—21no—
465C2×C4×C43—21no—
466C2×C4×C43—21no—
467C2×C4×C43—21no—
468C2×C4×C43—21no—
469C2×C4×C43—21no—
470C2×C4×C43—21no—
471C2×C4×C43—21no—
472C2×C4×C43—21no—
473C2×C4×C43—21no—
474C2×C4×C43—21no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—21no—
479C2×C4×C43—21no—
480C2×C4×C43—28no—
481C2×C4×C43—21no—
482C2×C4×C43—21no—
483C2×C4×C43—21no—
484C2×C4×C43—21no—
485C2×C4×C43—21no—
486C2×C4×C43—21no—
487C2×C4×C43—21no—
488C2×C4×C43—21no—
489C2×C4×C43—21no—
490C2×C4×C43—44no—
491C2×C4×C43—44no—
492C2×C4×C43—44no—
493C2×C4×C43—44no—
494C2×C4×C43—44no—
495C2×C4×C43C22×D412yes—
496C2×C4×C43C22×D412yes—
497C2×C4×C43C22×D412yes—
498C2×C4×C43C22×D412yes—
499C2×C4×C43C22×D412yes—
500C2×C4×C43C2×#4112yes—
501C2×C4×C43C2×#4112yes—
502C2×C4×C43C2×#4112yes—
503C2×C4×C43C2×#4112yes—
504C2×C4×C43H(5,𝔽2)12yes—
505C2×C4×C43H(5,𝔽2)12yes—
506C2×C4×C43H(5,𝔽2)12yes—
507C22⋊D43—48no—
508C22⋊D43—84no—
509C22⋊D43—84no—
510C22⋊D43—84no—
511C2×Dic43—22no—
512C2×Dic43—22no—
513C2×Dic43—22no—
514C2×Dic43—22no—
515C2×Dic43—22no—
516C2×Dic43—22no—
517C2×Dic43—22no—
518C2×Dic43—22no—
519C2×Dic43—22no—
520C2×Dic43—22no—
521C2×Dic43—22no—
522C2×Dic43—22no—
523C2×Dic43—22no—
524C2×Dic43—22no—
525C2×Dic43—22no—
526C2×Dic43—84no—
527D172—48no—
528D172—44no—
529D172—44no—
530D172—44no—
531D172—84no—
532D172—84no—
533D172—84no—
534D172—84no—
535C4×D43—84no—
536Dic86—84no—
537#35007—431nomaximal, Sylow
538C22×C43—22no—
539C22×C43—22no—
540C22×C43—22no—
541C22×C43—22no—
542C22×C43—22no—
543C22×C43—22no—
544C22×C43—22no—
545C22×C43—22no—
546C22×C43—22no—
547C22×C43—41no—
548C22×C43—41no—
549C22×C43—41no—
550C22×C43—41no—
551C22×C43#53214yes—
552C22×C43C23×D411yescharacteristic
553C22×C43C22×#4111yescharacteristic
554C22×C43C22×#4111yescharacteristic
555C22×C43C2×H(5,𝔽2)11yescharacteristic
556C22×C43C2×H(5,𝔽2)11yescharacteristic
557C22×C43C2×H(5,𝔽2)11yescharacteristic
558C22×C43#58511yescharacteristic
559C2×D43—42no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C2×D43—42no—
564C2×D43—42no—
565C2×D43—42no—
566C2×D43—42no—
567C2×D43—42no—
568C2×D43—42no—
569C2×D43—42no—
570C2×D43—42no—
571C2×D43—42no—
572C2×D43—42no—
573C2×D43—42no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—42no—
579C2×D43—42no—
580C2×D43—816no—
581C4×C43—22no—
582C4×C43—22no—
583C4×C43—22no—
584C4×C43—22no—
585C4×C43—22no—
586C4×C43—22no—
587C4×C43—22no—
588C4×C43—22no—
589C4×C43—22no—
590C4×C43—41no—
591C4×C43—41no—
592C4×C43—41no—
593C4×C43#53814yescomplemented
594Dic43—42no—
595Dic43—42no—
596Dic43—42no—
597Dic43—42no—
598Dic43—42no—
599C2×#538—432no—
600#2860—431no—
601#2858—431no—
602#2856—431no—
603#2854—431no—
604#2662—432no—
605#2661—432no—
606#2555—432no—
607#2554—432no—
608#2512—431no—
609#2491—431no—
610#2472—432no—
611#2445—431no—
612#2440—431no—
613#2433—431no—
614#2428—431no—
615#2424—432no—
616#2416—431no—
617#2408—431no—
618#2321—432no—
619C4×#121—431no—
620C2×#390—431no—
621C42×D4D4311yescharacteristic, complemented
622C2×C43—24no—
623C2×C43—42no—
624C2×C43C2×#53211yescharacteristic
625C2×C43C2×#53811yescharacteristic
626C2×C43#346011yescharacteristic
627C2×C43#349611yescharacteristic
628C2×C43#349811yescharacteristic
629C2×C43#351411yescharacteristic
630C2×C43#351911yescharacteristic
631D43—82no—
632D43—82no—
633D43—82no—
634C23×D4—431no—
635#538—8616no—
636C2×C4⋊Q8—431no—
637C2×#127—431no—
638C2×#127—431no—
639C2×#126—432no—
640C2×#126—432no—
641C2×#124—432no—
642C2×#124—432no—
643C2×#124—432no—
644C2×#123—432no—
645C2×#123—432no—
646C2×C22⋊Q8—432no—
647C2×#121—432no—
648C2×#121—432no—
649C2×#121—431no—
650C2×#121—431no—
651C2×#121—431no—
652C2×#121—431no—
653C2×#121—432no—
654C2×#121—432no—
655C2×#120—432no—
656C2×#120—432no—
657C2×#120—432no—
658C2×C4×D4—432no—
659C2×C4×D4—431no—
660C2×C4×D4C2×D4311yescharacteristic
661C2×C4×D4C2×D4311yescharacteristic
662C2×C4×D4C2×D4311yescharacteristic
663C22×C4⋊C4—431no—
664C22×C22⋊C4—432no—
665C22×C22⋊C4—432no—
666C22×C42C2×D4311yescharacteristic
667C22×C42C2×D4311yescharacteristic, complemented
668#398—432no—
669#397—432no—
670#396—432no—
671#396—432no—
672#395—432no—
673#394—432no—
674#394—432no—
675#394—432no—
676#394—432no—
677#394—432no—
678#394—432no—
679#393—432no—
680#392—432no—
681#392—432no—
682#392—432no—
683#392—432no—
684#390—432no—
685#390—432no—
686#390—431no—
687#390—431no—
688#390—431no—
689#390—431no—
690#390—431no—
691#390—431no—
692#390—432no—
693#390—431no—
694#390—431no—
695#390—432no—
696#390—431no—
697#390—432no—
698#390—431no—
699#390—432no—
700#389—431no—
701#389—431no—
702#389—431no—
703#389—431no—
704#388—432no—
705#388—432no—
706#388—432no—
707#388—432no—
708#388—432no—
709#388—432no—
710#388—432no—
711#388—432no—
712#386—432no—
713#386—432no—
714#386—432no—
715#386—432no—
716#386—432no—
717#385—432no—
718#384—431no—
719#380—431no—
720#380—431no—
721#379—432no—
722C4×C4⋊C4—431no—
723C4×C4⋊C4C2×D4311yescharacteristic, complemented
724C4×C4⋊C4C2×D4311yescharacteristic, complemented
725C4×C4⋊C4C2×D4311yescharacteristic, complemented
726C4×C22⋊C4—432no—
727C4×C22⋊C4C2×D4311yescharacteristic
728C4×C22⋊C4C2×D4311yescharacteristic
729C4×C22⋊C4C2×D4311yescharacteristic
730C4×C22⋊C4C2×D4311yescharacteristic, complemented
731C4×C22⋊C4C2×D4311yescharacteristic, complemented
732C4×C22⋊C4C2×D4311yescharacteristic, complemented
733C43C2×D4311yescharacteristic, complemented
734C43#3500711yescharacteristic, complemented, Sylow
735C25—432no—
736C22×Q8—432no—
737C22×D4—432no—
738C22×D4—432no—
739C22×D4—432no—
740C22×D4—432no—
741C22×D4—431no—
742C22×D4—431no—
743C22×D4—431no—
744C22×D4—432no—
745C22×D4—432no—
746C22×D4—432no—
747C22×D4—432no—
748C22×D4—432no—
749C22×D4—864no—
750C22×D4—1722no—
751C22×D4—1722no—
752C22×D4C22×D4311yescharacteristic
753C23×C4—432no—
754C23×C4—432no—
755C23×C4C22×D4311yescharacteristic
756C23×C4C22×D4311yescharacteristic
757C23×C4C22×D4311yescharacteristic
758C23×C4C22×D4311yescharacteristic
759C23×C4C22×D4311yescharacteristic
760C23×C4C22×D4311yescharacteristic
761C4⋊Q8—1722no—
762#127—1722no—
763#127—1722no—
764#126—868no—
765#126—868no—
766#124—868no—
767#124—868no—
768#124—1724no—
769#123—868no—
770#123—868no—
771C22⋊Q8—868no—
772#121—868no—
773#121—868no—
774#121—864no—
775#121—868no—
776#121—1724no—
777#121—1722no—
778#121—1722no—
779#121—1722no—
780#120—868no—
781#120—868no—
782#120—868no—
783C4×D4—24no—
784C4×D4—24no—
785C4×D4—868no—
786C4×D4—1722no—
787C4×D4D17218yescomplemented
788C2×C4⋊C4—431no—
789C2×C4⋊C4—431no—
790C2×C4⋊C4—431no—
791C2×C4⋊C4—432no—
792C2×C4⋊C4—432no—
793C2×C4⋊C4—432no—
794C2×C4⋊C4—432no—
795C2×C4⋊C4—431no—
796C2×C4⋊C4—431no—
797C2×C4⋊C4—432no—
798C2×C4⋊C4—432no—
799C2×C4⋊C4—432no—
800C2×C4⋊C4—432no—
801C2×C4⋊C4—1722no—
802C2×C4⋊C4C22×D4311yescharacteristic
803C2×C4⋊C4C22×D4311yescharacteristic
804C2×C4⋊C4C22×D4311yescharacteristic
805C2×C22⋊C4—432no—
806C2×C22⋊C4—432no—
807C2×C22⋊C4—432no—
808C2×C22⋊C4—432no—
809C2×C22⋊C4—432no—
810C2×C22⋊C4—432no—
811C2×C22⋊C4—432no—
812C2×C22⋊C4—432no—
813C2×C22⋊C4—432no—
814C2×C22⋊C4—432no—
815C2×C22⋊C4—432no—
816C2×C22⋊C4—432no—
817C2×C22⋊C4—432no—
818C2×C22⋊C4—432no—
819C2×C22⋊C4—432no—
820C2×C22⋊C4—432no—
821C2×C22⋊C4—432no—
822C2×C22⋊C4—432no—
823C2×C22⋊C4—432no—
824C2×C22⋊C4—432no—
825C2×C22⋊C4—432no—
826C2×C22⋊C4—432no—
827C2×C22⋊C4—432no—
828C2×C22⋊C4—432no—
829C2×C22⋊C4—432no—
830C2×C22⋊C4—432no—
831C2×C22⋊C4—432no—
832C2×C22⋊C4—868no—
833C2×C22⋊C4—1724no—
834C2×C22⋊C4C22×D4311yescharacteristic
835C2×C22⋊C4C22×D4311yescharacteristic
836C2×C22⋊C4C22×D4311yescharacteristic
837C2×C22⋊C4C22×D4311yescharacteristic
838C2×C22⋊C4C22×D4311yescharacteristic
839C2×C22⋊C4C22×D4311yescharacteristic
840C2×C42—42no—
841C2×C42—42no—
842C2×C42—432no—
843C2×C42C22×D4311yescharacteristic
844C2×C42C22×D4311yescharacteristic
845C2×C42C22×D4311yescharacteristic
846C2×C42C22×D4311yescharacteristic
847C2×C42C22×D4311yescharacteristic
848C2×C42C22×D4311yescharacteristic
849C2×C42C22×D4311yescharacteristic
850C2×C42C22×D4311yescharacteristic
851C2×C42C22×D4311yescharacteristic
852C2×C42C22×D4311yescharacteristic
853C2×C42C22×D4311yescharacteristic
854C2×C42C22×D4311yescharacteristic
855C2×C42C22×D4311yescharacteristic
856#95—432no—
857#95—432no—
858#95—432no—
859#95—432no—
860#95—432no—
861#95—432no—
862#95—432no—
863#95C22×D4311yescharacteristic
864#95C22×D4311yescharacteristic
865#95C22×D4311yescharacteristic
866#95C22×D4311yescharacteristic
867#95C22×D4311yescharacteristic
868#95C22×D4311yescharacteristic
869C24—432no—
870C24—432no—
871C24—432no—
872C24—864no—
873C24—864no—
874C24—864no—
875C24—1722no—
876C24—1722no—
877C24—1722no—
878C24—1722no—
879C24C23×D4311yescharacteristic
880C24C23×D4311yescharacteristic
881C2×Q8—864no—
882C2×Q8—1722no—
883C2×Q8—1722no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—864no—
887C2×D4—864no—
888C2×D4—864no—
889C2×D4—864no—
890C2×D4—864no—
891C2×D4—864no—
892C2×D4—864no—
893C2×D4—864no—
894C2×D4—864no—
895C2×D4—864no—
896C2×D4—862no—
897C2×D4—864no—
898C2×D4—862no—
899C2×D4—862no—
900C2×D4—862no—
901C2×D4—862no—
902C2×D4—862no—
903C2×D4—862no—
904C2×D4—862no—
905C2×D4—862no—
906C2×D4—1722no—
907C2×D4—1722no—
908C2×D4—1722no—
909C2×D4—1722no—
910C2×D4—1722no—
911C2×D4—1722no—
912C2×D4—1722no—
913C2×D4—1722no—
914C2×D4—1722no—
915C2×D4—1722no—
916C2×D4—17216no—
917C2×D4—1722no—
918C2×D4—1722no—
919C2×D4—1722no—
920C2×D4—1722no—
921C2×D4—1722no—
922C2×D4—1722no—
923C2×D4C2×D17214yes—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—432no—
940C22×C4—432no—
941C22×C4—432no—
942C22×C4—432no—
943C22×C4—432no—
944C22×C4—864no—
945C22×C4—864no—
946C22×C4—1722no—
947C22×C4—1722no—
948C22×C4—1722no—
949C22×C4—1722no—
950C22×C4C2×D17214yes—
951C22×C4C2×D17214yescomplemented
952C22×C4#1062189814yes—
953C22×C4C23×D4311yescharacteristic
954C22×C4C23×D4311yescharacteristic
955C22×C4C23×D4311yescharacteristic
956C22×C4C23×D4311yescharacteristic
957C22×C4C23×D4311yescharacteristic
958C22×C4C23×D4311yescharacteristic
959C22×C4C23×D4311yescharacteristic
960C22×C4C23×D4311yescharacteristic
961C22×C4C23×D4311yescharacteristic
962C22×C4C23×D4311yescharacteristic
963C22×C4C23×D4311yescharacteristic
964C22×C4C23×D4311yescharacteristic
965C22×C4C23×D4311yescharacteristic
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—864no—
969C4⋊C4—864no—
970C4⋊C4—864no—
971C4⋊C4—864no—
972C4⋊C4—864no—
973C4⋊C4—862no—
974C4⋊C4—862no—
975C4⋊C4—862no—
976C4⋊C4—862no—
977C4⋊C4—862no—
978C4⋊C4—1722no—
979C4⋊C4—1722no—
980C4⋊C4—1722no—
981C4⋊C4C2×D17214yescomplemented
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—864no—
986C22⋊C4—864no—
987C22⋊C4—864no—
988C22⋊C4—864no—
989C22⋊C4—864no—
990C22⋊C4—864no—
991C22⋊C4—864no—
992C22⋊C4—864no—
993C22⋊C4—864no—
994C22⋊C4—864no—
995C22⋊C4—864no—
996C22⋊C4—864no—
997C22⋊C4—864no—
998C22⋊C4—864no—
999C22⋊C4—864no—
1000C22⋊C4—864no—
1001C22⋊C4—864no—
1002C22⋊C4—864no—
1003C22⋊C4—1722no—
1004C22⋊C4—1722no—
1005C22⋊C4—1722no—
1006C22⋊C4—1722no—
1007C22⋊C4—1722no—
1008C22⋊C4—1722no—
1009C22⋊C4—1722no—
1010C22⋊C4—1722no—
1011C22⋊C4—1722no—
1012C22⋊C4C2×D17214yes—
1013C22⋊C4C2×D17214yescomplemented
1014C22⋊C4#1062189814yes—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—22no—
1020C42—22no—
1021C42—22no—
1022C42—41no—
1023C42—41no—
1024C42—41no—
1025C42—41no—
1026C42—41no—
1027C42—864no—
1028C42C2×D17214yescomplemented
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—862no—
1040C23—862no—
1041C23—862no—
1042C23—862no—
1043C23—862no—
1044C23—862no—
1045C23—862no—
1046C23—862no—
1047C23—862no—
1048C23—862no—
1049C23—862no—
1050C23—862no—
1051C23—862no—
1052C23—862no—
1053C23—862no—
1054C23—862no—
1055C23—862no—
1056C23—862no—
1057C23—862no—
1058C23—862no—
1059C23—862no—
1060C23—3444no—
1061C23—3444no—
1062C23—3444no—
1063C23—3444no—
1064C23—1728no—
1065C23—1728no—
1066C23—1728no—
1067C23C22×D17212yes—
1068C23C22×D17212yes—
1069C23C2×#1062189812yes—
1070C23C2×#1062189812yes—
1071C23C24×D4311yescharacteristic
1072Q8—3444no—
1073D4—28no—
1074D4—3444no—
1075D4—3444no—
1076D4—3444no—
1077D4—3444no—
1078D4—3444no—
1079D4—3444no—
1080D4—3444no—
1081D4—1728no—
1082D4—1728no—
1083D4—1724no—
1084D4—1724no—
1085D4—1724no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—28no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—862no—
1120C2×C4—862no—
1121C2×C4—862no—
1122C2×C4—862no—
1123C2×C4—862no—
1124C2×C4—862no—
1125C2×C4—862no—
1126C2×C4—862no—
1127C2×C4—862no—
1128C2×C4—862no—
1129C2×C4—862no—
1130C2×C4—862no—
1131C2×C4—862no—
1132C2×C4—862no—
1133C2×C4—862no—
1134C2×C4—3444no—
1135C2×C4—3444no—
1136C2×C4C22×D17212yes—
1137C2×C4C22×D17212yes—
1138C2×C4C22×D17212yes—
1139C2×C4C22×D17212yes—
1140C2×C4C22×D17212yes—
1141C2×C4C2×#1062189812yes—
1142C2×C4C2×#1062189812yes—
1143C2×C4C2×#1062189812yes—
1144C2×C4C2×#1062189812yes—
1145C2×C4#1306337012yes—
1146C2×C4#1306337112yes—
1147C2×C4#1306337112yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—34416no—
1162C22—1722no—
1163C22—1722no—
1164C22—1722no—
1165C22—1722no—
1166C22—1722no—
1167C22—1722no—
1168C22—1722no—
1169C22—1722no—
1170C22—1722no—
1171C22—1722no—
1172C22—1722no—
1173C22—1722no—
1174C22—1722no—
1175C22—1722no—
1176C22—1722no—
1177C22—1722no—
1178C22—1722no—
1179C22—1722no—
1180C22—1722no—
1181C22—1722no—
1182C22—1722no—
1183C22#1458344914yes—
1184C22C23×D17211yescharacteristic
1185C22C22×#1062189811yescharacteristic
1186C22C22×#1062189811yescharacteristic
1187C22C2×#1306337011yescharacteristic
1188C22C2×#1306337111yescharacteristic
1189C22C2×#1306337111yescharacteristic
1190C22#1458373511yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—22no—
1197C4—22no—
1198C4—22no—
1199C4—22no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—1722no—
1204C4—1722no—
1205C4—1722no—
1206C4—1722no—
1207C4—1722no—
1208C4#1458348214yescomplemented
1209C2—24no—
1210C2—42no—
1211C2—3442no—
1212C2—3442no—
1213C2—3442no—
1214C2C2×#1458344911yescharacteristic
1215C2C2×#1458348211yescharacteristic
1216C2#1914801111yescharacteristic
1217C2#1914835911yescharacteristic
1218C2#1914837311yescharacteristic
1219C2#1914855611yescharacteristic
1220C2#1914862711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC42×D4×C43C2
hypercenterC42×D4D43
hypocenterC43#35007
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C42×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14583482C2semidirect
2. #19142962C2semidirect
3. #19142952C2semidirect
4. #19142940C2semidirect
5. #19142926C2semidirect
6. #19140732C2semidirect
7. #19140721C2semidirect
8. #19139664C2semidirect
9. #19139649C2semidirect
10. #19139181C2semidirect
11. #19138958C2semidirect
12. #19138721C2semidirect
13. #19138360C2semidirect
14. #19138297C2semidirect
15. #19138232C2semidirect
16. #19138183C2semidirect
17. #19138125C2semidirect
18. #19138035C2semidirect
19. #19137951C2semidirect
20. #19137255C2semidirect
21. C4×#13063299C2semidirect
22. C2×#14582801C2semidirect
23. C42×D4×C43C2semidirect
26. C2×#13063325C22semidirect
29. C2×#13063320C22semidirect
30. C2×#13063319C22semidirect
31. C2×#13063313C22semidirect
32. C2×#13063313C22semidirect
33. C2×#13063311C22semidirect
34. C2×#13063310C22semidirect
35. C2×#13063308C22semidirect
40. C2×#13063299C22semidirect
41. C2×#13063299C22semidirect
42. C2×#13063299C22semidirect
43. C2×#13063298C22semidirect
48. C2×C4×D172C22semidirect
53. #14582831C22semidirect
54. #14582826C22semidirect
55. #14582821C22semidirect
56. #14582821C22semidirect
57. #14582820C22semidirect
58. #14582817C22semidirect
59. #14582817C22semidirect
61. #14582816C22semidirect
62. #14582815C22semidirect
63. #14582815C22semidirect
64. #14582812C22semidirect
68. #14582808C22semidirect
79. #14582801C22semidirect
80. #14582801C22semidirect
81. #14582801C22semidirect
82. #14582801C22semidirect
83. #14582801C22semidirect
84. #14582801C22semidirect
85. #14582797C22semidirect
86. #14582797C22semidirect
87. #14582797C22semidirect
88. #14582797C22semidirect
89. #14582791C22semidirect
90. #14582791C22semidirect
91. #14582790C22semidirect
92. #14582790C22semidirect
93. #14582790C22semidirect
94. #14582790C22semidirect
95. #14582790C22semidirect
96. #14582790C22semidirect
98. #14582778C22semidirect
99. #14582777C22semidirect
100. #14582777C22semidirect
103. #14582769C22semidirect
105. #14582759C22semidirect
107. C4×C4⋊Dic43C22semidirect
108. C4×(C2×D43)⋊C4C22semidirect
113. C22×C42×C43C22semidirect
114. C4×C4⋊C4×C43C22semidirect
115. C4×C4⋊C4×C43C22semidirect
116. C4×C4⋊C4×C43C22semidirect
120. C4×C22⋊C4×C43C22semidirect
121. C4×C22⋊C4×C43C22semidirect
122. C4×C22⋊C4×C43C22semidirect
123. C43×C43C22semidirect
227. C4×D4×C43D4semidirect
289. C22×C4×C43C2×D4semidirect
357. C4⋊C4×C43C2×D4semidirect
362. C22⋊C4×C43C2×D4semidirect
376. C42×C43C2×D4semidirect
593. C4×C43#538semidirect
621. C42×D4D43semidirect
667. C22×C42C2×D43semidirect
723. C4×C4⋊C4C2×D43semidirect
724. C4×C4⋊C4C2×D43semidirect
725. C4×C4⋊C4C2×D43semidirect
730. C4×C22⋊C4C2×D43semidirect
731. C4×C22⋊C4C2×D43semidirect
732. C4×C22⋊C4C2×D43semidirect
733. C43C2×D43semidirect
734. C43#35007semidirect
787. C4×D4D172semidirect
951. C22×C4C2×D172semidirect
981. C4⋊C4C2×D172semidirect
1013. C22⋊C4C2×D172semidirect
1028. C42C2×D172semidirect
1208. C4#14583482semidirect

Maximal subgroups

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

subgroupindex
C2×#145834822
#191429622
#191429522
#191429402
#191429262
#191407322
#191407212
#191396642
#191396492
#191391812
#191389582
#191387212
#191383602
#191382972
#191382322
#191381832
#191381252
#191380352
#191379512
#191372552
C4×#130632992
C2×#145828012
C42×D4×C432
#3500743