Finite Group Databasebeta

← #25112282

Subgroups — #25112282

Order 11008.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#10621877C211yesmaximal, characteristic, complemented
2C2×#14582916C211yesmaximal, characteristic, complemented
3C22×#13063252C211yesmaximal, characteristic, complemented
4#19137040C211yesmaximal, characteristic, complemented
5#19135515C211yesmaximal, characteristic, complemented
6#19135428C211yesmaximal, characteristic, complemented
7#19135044C211yesmaximal, characteristic, complemented
8#19135039C211yesmaximal, characteristic, complemented
9#19134898C211yesmaximal, characteristic, complemented
10#19134898C211yesmaximal, characteristic, complemented
11#19134615C211yesmaximal, characteristic, complemented
12#19134539C211yesmaximal, characteristic, complemented
13#19134539C211yesmaximal, characteristic, complemented
14#19134405C211yesmaximal, characteristic, complemented
15D4×#41×C43C211yesmaximal, characteristic
16C22×#10621877C2211yescharacteristic, complemented
17C22×#10621877C2211yescharacteristic, complemented
18C2×#13063284C2211yescharacteristic, complemented
19C22×C4×Dic43C2211yescharacteristic, complemented
20#14582977—21no—
21#14582971—21no—
22#14582971—21no—
23D4×C43⋊C8—21no—
24#14582923C2211yescharacteristic, complemented
25#14582916—24no—
26C2×#13063252—24no—
27C2×#13063252C2211yescharacteristic
28C2×#13063252C2211yescharacteristic
29C2×#13063252C2211yescharacteristic
30C2×#13063252C2211yescharacteristic
31C2×#13063252C2211yescharacteristic, complemented
32C2×#13063252C2211yescharacteristic, complemented
33C2×#13063252C2211yescharacteristic, complemented
34C2×#13063252C2211yescharacteristic, complemented
35C2×#13063252C2211yescharacteristic, complemented
36C2×#13063252C2211yescharacteristic, complemented
37C2×#13063252C2211yescharacteristic, complemented
38C2×#13063252C2211yescharacteristic, complemented
39#14582863C2211yescharacteristic, complemented
40#14582863C2211yescharacteristic, complemented
41C4×#10621877C2211yescharacteristic, complemented
42#14582792—21no—
43#14582785—21no—
44#14582779—21no—
45#14582774—21no—
46C4×C4⋊Dic43C2211yescharacteristic, complemented
47C4×C22⋊Dic43C2211yescharacteristic, complemented
48C4×C22⋊Dic43C2211yescharacteristic, complemented
49#14582745C2211yescharacteristic, complemented
50#14582658C2211yescharacteristic, complemented
51#14582658C2211yescharacteristic, complemented
52#14582658C2211yescharacteristic, complemented
53#14582658C2211yescharacteristic, complemented
54C22×#41×C43C2211yescharacteristic
55C22×#41×C43C2211yescharacteristic
56C43×#550C411yescharacteristic, complemented
57D4×Q8×C43C411yescharacteristic, complemented
58C43×#548C411yescharacteristic, complemented
59C43×#548C411yescharacteristic, complemented
60C43×#547—21no—
61C43×#547C411yescharacteristic, complemented
62C43×#546—21no—
63C43×#546—21no—
64C43×#546C411yescharacteristic, complemented
65C43×#546C411yescharacteristic, complemented
66D42×C43—21no—
67D42×C43C411yescharacteristic, complemented
68C43×#532—21no—
69C43×#532C2211yescharacteristic
70C43×#525—21no—
71C43×#525—21no—
72C43×#525C2211yescharacteristic
73C43×#525C2211yescharacteristic
74C4×#41×C43C2211yescharacteristic
75C2×C4×D4×C43—21no—
76C2×C4×D4×C43C2211yescharacteristic
77C23×Dic43—21no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—22no—
81C2×#10621877—22no—
82C2×#10621877—41no—
83C2×#10621877—41no—
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C22×C43⋊C8—21no—
89C22×C43⋊C8—21no—
90#13063284—22no—
91#13063284—41no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×C4×Dic43—22no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—41no—
100C2×C4×Dic43C2311yescharacteristic
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)—21no—
106#13063252—22no—
107#13063252—22no—
108#13063252—22no—
109#13063252—22no—
110#13063252—22no—
111#13063252—22no—
112#13063252—22no—
113#13063252—41no—
114#13063252—41no—
115#13063252—41no—
116#13063252—41no—
117#13063252D414yescomplemented
118C22⋊(C43⋊C8)—21no—
119C22⋊(C43⋊C8)—21no—
120C22⋊(C43⋊C8)—21no—
121C22⋊(C43⋊C8)—21no—
122#13063236—21no—
123C4×C43⋊C8—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C2×#41×C43—21no—
130C2×#41×C43—21no—
131C2×#41×C43—21no—
132C2×#41×C43—21no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—22no—
137C2×#41×C43—41no—
138C2×#41×C43—41no—
139C2×#41×C43—41no—
140C2×#41×C43—41no—
141C2×#41×C43C2×C411yescharacteristic
142C2×#41×C43C2×C411yescharacteristic
143C2×#41×C43C2×C411yescharacteristic, complemented
144C2×#41×C43C2×C411yescharacteristic, complemented
145C2×#41×C43C2311yescharacteristic
146C2×#41×C43C2311yescharacteristic
147C2×#41×C43C2311yescharacteristic
148C22×Q8×C43C2×C411yescharacteristic
149C22×Q8×C43C2×C411yescharacteristic, complemented
150C22×D4×C43—21no—
151C22×D4×C43—21no—
152C22×D4×C43—21no—
153C22×D4×C43C2×C411yescharacteristic
154C22×D4×C43C2×C411yescharacteristic, complemented
155C22×D4×C43D411yescharacteristic
156C23×C4×C43—21no—
157C23×C4×C43—21no—
158C23×C4×C43C2311yescharacteristic
159C23×C4×C43C2311yescharacteristic
160C4⋊Q8×C43—21no—
161C4⋊Q8×C43C2×C411yescharacteristic, complemented
162#127×C43—21no—
163#127×C43C2×C411yescharacteristic, complemented
164#124×C43—21no—
165#124×C43—21no—
166#124×C43C2×C411yescharacteristic, complemented
167#124×C43C2×C411yescharacteristic, complemented
168#123×C43—21no—
169#123×C43—21no—
170#123×C43—21no—
171#123×C43—21no—
172#123×C43—21no—
173#123×C43—21no—
174C22⋊Q8×C43—21no—
175C22⋊Q8×C43—21no—
176C22⋊Q8×C43—21no—
177C22⋊Q8×C43—21no—
178C22⋊Q8×C43C2×C411yescharacteristic
179C22⋊Q8×C43C2×C411yescharacteristic
180C22⋊Q8×C43C2×C411yescharacteristic, complemented
181C22⋊Q8×C43C2×C411yescharacteristic, complemented
182#121×C43—21no—
183#121×C43—21no—
184#121×C43—21no—
185#121×C43—21no—
186#121×C43—21no—
187#121×C43—21no—
188#121×C43—21no—
189#121×C43—21no—
190#121×C43—21no—
191#121×C43—21no—
192#121×C43C2×C411yescharacteristic
193#121×C43C2×C411yescharacteristic
194#121×C43C2×C411yescharacteristic, complemented
195#121×C43C2×C411yescharacteristic, complemented
196#120×C43—21no—
197#120×C43—21no—
198#120×C43—21no—
199#120×C43—21no—
200#120×C43—21no—
201#120×C43—21no—
202C4×Q8×C43C2×C411yescharacteristic, complemented
203C4×Q8×C43C2×C411yescharacteristic, complemented
204C4×D4×C43—21no—
205C4×D4×C43—21no—
206C4×D4×C43—21no—
207C4×D4×C43—21no—
208C4×D4×C43—21no—
209C4×D4×C43—21no—
210C4×D4×C43—21no—
211C4×D4×C43—21no—
212C4×D4×C43—21no—
213C4×D4×C43—21no—
214C4×D4×C43—21no—
215C4×D4×C43—21no—
216C4×D4×C43C2×C411yescharacteristic
217C4×D4×C43C2×C411yescharacteristic
218C4×D4×C43C2×C411yescharacteristic
219C4×D4×C43C2×C411yescharacteristic
220C4×D4×C43C2×C411yescharacteristic, complemented
221C4×D4×C43C2×C411yescharacteristic, complemented
222C4×D4×C43D411yescharacteristic
223C4×D4×C43D411yescharacteristic
224C4×D4×C43D411yescharacteristic
225C4×D4×C43D411yescharacteristic
226#117×C43—21no—
227#117×C43C2311yescharacteristic
228C2×C4⋊C4×C43—21no—
229C2×C4⋊C4×C43D411yescharacteristic
230C2×C22⋊C4×C43—21no—
231C2×C22⋊C4×C43—21no—
232C2×C22⋊C4×C43D411yescharacteristic
233C2×C22⋊C4×C43D411yescharacteristic
234C2×C42×C43—21no—
235C2×C42×C43C2311yescharacteristic
236C24×C43—21no—
237C24×C43—21no—
238C24×C43C2×D411yescharacteristic
239C24×C43C2×D411yescharacteristic
240#41×C43—21no—
241#41×C43—21no—
242#41×C43—22no—
243#41×C43—22no—
244#41×C43—22no—
245#41×C43—22no—
246#41×C43—21no—
247#41×C43—21no—
248#41×C43—21no—
249#41×C43—21no—
250#41×C43—21no—
251#41×C43—21no—
252#41×C43—21no—
253#41×C43—21no—
254#41×C43—42no—
255#41×C43—42no—
256#41×C43—42no—
257#41×C43—42no—
258#41×C43—41no—
259#41×C43—41no—
260#41×C43—41no—
261#41×C43—41no—
262#41×C43—42no—
263#41×C43—42no—
264#41×C43—42no—
265#41×C43—42no—
266#41×C43C2×D412yes—
267#41×C43#4112yes—
268C2×Q8×C43—21no—
269C2×Q8×C43—21no—
270C2×Q8×C43—22no—
271C2×Q8×C43—22no—
272C2×Q8×C43—41no—
273C2×Q8×C43—41no—
274C2×Q8×C43C22×C411yescharacteristic
275C2×Q8×C43C22×C411yescharacteristic
276C2×Q8×C43C22×C411yescharacteristic
277C2×D4×C43—21no—
278C2×D4×C43—21no—
279C2×D4×C43—21no—
280C2×D4×C43—21no—
281C2×D4×C43—21no—
282C2×D4×C43—21no—
283C2×D4×C43—21no—
284C2×D4×C43—21no—
285C2×D4×C43—21no—
286C2×D4×C43—21no—
287C2×D4×C43—21no—
288C2×D4×C43—21no—
289C2×D4×C43—21no—
290C2×D4×C43—21no—
291C2×D4×C43—21no—
292C2×D4×C43—22no—
293C2×D4×C43—22no—
294C2×D4×C43—42no—
295C2×D4×C43—42no—
296C2×D4×C43—42no—
297C2×D4×C43—42no—
298C2×D4×C43—42no—
299C2×D4×C43—41no—
300C2×D4×C43—41no—
301C2×D4×C43—44no—
302C2×D4×C43C22⋊C411yescharacteristic
303C2×D4×C43C22⋊C411yescharacteristic
304C2×D4×C43C22⋊C411yescharacteristic
305C2×D4×C43C22⋊C411yescharacteristic
306C2×D4×C43C22×C411yescharacteristic
307C2×D4×C43C22×C411yescharacteristic
308C2×D4×C43C22×C411yescharacteristic
309C22×C4×C43—21no—
310C22×C4×C43—21no—
311C22×C4×C43—21no—
312C22×C4×C43—21no—
313C22×C4×C43—21no—
314C22×C4×C43—21no—
315C22×C4×C43—21no—
316C22×C4×C43—21no—
317C22×C4×C43—21no—
318C22×C4×C43—21no—
319C22×C4×C43—21no—
320C22×C4×C43—21no—
321C22×C4×C43—21no—
322C22×C4×C43—21no—
323C22×C4×C43—21no—
324C22×C4×C43—21no—
325C22×C4×C43—21no—
326C22×C4×C43—21no—
327C22×C4×C43—21no—
328C22×C4×C43—42no—
329C22×C4×C43—42no—
330C22×C4×C43—42no—
331C22×C4×C43—42no—
332C22×C4×C43C22×C411yescharacteristic
333C22×C4×C43C22×C411yescharacteristic
334C22×C4×C43C22×C411yescharacteristic
335C22×C4×C43C22×C411yescharacteristic
336C22×C4×C43C2×D411yescharacteristic
337C22×C4×C43C2×D411yescharacteristic
338C22×C4×C43C2×D411yescharacteristic
339C22×C4×C43C2×D411yescharacteristic
340C22×C4×C43C2×D411yescharacteristic
341C22×C4×C43C2×D411yescharacteristic
342C22×C4×C43C2×D411yescharacteristic
343C22×C4×C43C2×D411yescharacteristic
344C22×C4×C43C2411yescharacteristic
345C22×Dic43—21no—
346C22×Dic43—21no—
347C22×Dic43—21no—
348C22×Dic43—21no—
349C22×Dic43—42no—
350C22×Dic43—42no—
351C22×Dic43—42no—
352C4⋊C4×C43—21no—
353C4⋊C4×C43—21no—
354C4⋊C4×C43—21no—
355C4⋊C4×C43—21no—
356C4⋊C4×C43—21no—
357C4⋊C4×C43—21no—
358C4⋊C4×C43—21no—
359C4⋊C4×C43—21no—
360C4⋊C4×C43C22⋊C411yescharacteristic
361C4⋊C4×C43C22⋊C411yescharacteristic
362C4⋊C4×C43C22⋊C411yescharacteristic
363C4⋊C4×C43C22⋊C411yescharacteristic
364C4⋊C4×C43C22×C411yescharacteristic
365C4⋊C4×C43C22×C411yescharacteristic
366C22⋊C4×C43—21no—
367C22⋊C4×C43—21no—
368C22⋊C4×C43—21no—
369C22⋊C4×C43—21no—
370C22⋊C4×C43—21no—
371C22⋊C4×C43—21no—
372C22⋊C4×C43—21no—
373C22⋊C4×C43—21no—
374C22⋊C4×C43—21no—
375C22⋊C4×C43—21no—
376C22⋊C4×C43—21no—
377C22⋊C4×C43—21no—
378C22⋊C4×C43—21no—
379C22⋊C4×C43—21no—
380C22⋊C4×C43—21no—
381C22⋊C4×C43C22⋊C411yescharacteristic
382C22⋊C4×C43C22⋊C411yescharacteristic
383C22⋊C4×C43C22⋊C411yescharacteristic
384C22⋊C4×C43C22⋊C411yescharacteristic
385C22⋊C4×C43C22⋊C411yescharacteristic
386C22⋊C4×C43C22⋊C411yescharacteristic
387C22⋊C4×C43C22⋊C411yescharacteristic
388C22⋊C4×C43C22⋊C411yescharacteristic
389C42×C43—21no—
390C42×C43—21no—
391C42×C43—21no—
392C42×C43C22×C411yescharacteristic
393C42×C43C22×C411yescharacteristic
394C42×C43C2×D411yescharacteristic
395C42×C43C2×D411yescharacteristic
396C22⋊Dic43—42no—
397C22⋊Dic43—42no—
398C22⋊Dic43—42no—
399C4⋊Dic43—42no—
400C4⋊Dic43—42no—
401C4×Dic43—21no—
402C4×Dic43—21no—
403C4×Dic43—21no—
404C4×Dic43—21no—
405C4×Dic43—21no—
406C4×Dic43—21no—
407C4×Dic43—21no—
408C4×Dic43—42no—
409C4×Dic43C2×D412yescomplemented
410#10621877—21no—
411#10621877—21no—
412#10621877—21no—
413#10621877—21no—
414#10621877—21no—
415#10621877—21no—
416#10621877—21no—
417#10621877—42no—
418#10621877—42no—
419#10621877C2×D412yescomplemented
420C2×C43⋊C8—21no—
421C2×C43⋊C8—21no—
422C2×C43⋊C8—21no—
423C2×C43⋊C8—21no—
424C2×C43⋊C8—42no—
425C2×C43⋊C8—42no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43—21no—
429C23×C43—22no—
430C23×C43—21no—
431C23×C43—21no—
432C23×C43—21no—
433C23×C43—21no—
434C23×C43—41no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—42no—
438C23×C43—42no—
439C23×C43—42no—
440C23×C43—42no—
441C23×C43—81no—
442C23×C43—81no—
443C23×C43C2×C22⋊C411yescharacteristic
444C23×C43C2×C22⋊C411yescharacteristic
445C23×C43C2×C22⋊C411yescharacteristic
446C23×C43C2×C22⋊C411yescharacteristic
447C23×C43C22×D411yescharacteristic
448Q8×C43—21no—
449Q8×C43—21no—
450Q8×C43—21no—
451Q8×C43—21no—
452Q8×C43—21no—
453Q8×C43—42no—
454Q8×C43—42no—
455Q8×C43C4×D412yes—
456D4×C43—22no—
457D4×C43—22no—
458D4×C43—22no—
459D4×C43—22no—
460D4×C43—21no—
461D4×C43—21no—
462D4×C43—21no—
463D4×C43—21no—
464D4×C43—21no—
465D4×C43—41no—
466D4×C43—41no—
467D4×C43—42no—
468D4×C43—42no—
469D4×C43—42no—
470D4×C43—42no—
471D4×C43—42no—
472D4×C43—42no—
473D4×C43—42no—
474D4×C43—42no—
475D4×C43—41no—
476D4×C43—41no—
477D4×C43—41no—
478D4×C43—41no—
479D4×C43—42no—
480D4×C43—81no—
481D4×C43—81no—
482D4×C43—81no—
483D4×C43C4×D412yes—
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—21no—
491C2×C4×C43—21no—
492C2×C4×C43—21no—
493C2×C4×C43—21no—
494C2×C4×C43—21no—
495C2×C4×C43—21no—
496C2×C4×C43—21no—
497C2×C4×C43—21no—
498C2×C4×C43—21no—
499C2×C4×C43—21no—
500C2×C4×C43—21no—
501C2×C4×C43—22no—
502C2×C4×C43—21no—
503C2×C4×C43—21no—
504C2×C4×C43—21no—
505C2×C4×C43—21no—
506C2×C4×C43—22no—
507C2×C4×C43—21no—
508C2×C4×C43—21no—
509C2×C4×C43—21no—
510C2×C4×C43—21no—
511C2×C4×C43—41no—
512C2×C4×C43—41no—
513C2×C4×C43—42no—
514C2×C4×C43—42no—
515C2×C4×C43—42no—
516C2×C4×C43—42no—
517C2×C4×C43—42no—
518C2×C4×C43—42no—
519C2×C4×C43—42no—
520C2×C4×C43—41no—
521C2×C4×C43—41no—
522C2×C4×C43—41no—
523C2×C4×C43—41no—
524C2×C4×C43—81no—
525C2×C4×C43C2×C22⋊C411yescharacteristic
526C2×C4×C43C2×C22⋊C411yescharacteristic
527C2×C4×C43C2×C22⋊C411yescharacteristic
528C2×C4×C43C2×C22⋊C411yescharacteristic
529C2×C4×C43C2×C22⋊C411yescharacteristic
530C2×C4×C43C2×C22⋊C411yescharacteristic
531C2×C4×C43C2×C22⋊C411yescharacteristic
532C2×C4×C43C2×C22⋊C411yescharacteristic
533C2×C4×C43C23×C411yescharacteristic
534C2×C4×C43C22×D411yescharacteristic
535C2×C4×C43C22×D411yescharacteristic
536C2×C4×C43C2×#4111yescharacteristic
537C2×C4×C43H(5,𝔽2)11yescharacteristic
538C2×C4×C43H(5,𝔽2)11yescharacteristic
539C2×Dic43—22no—
540C2×Dic43—22no—
541C2×Dic43—41no—
542C2×Dic43—41no—
543C2×Dic43—41no—
544C2×Dic43—48no—
545C2×Dic43—41no—
546C2×Dic43—41no—
547C2×Dic43—41no—
548C2×Dic43—41no—
549C2×Dic43—41no—
550C2×Dic43—41no—
551C2×Dic43—41no—
552C43⋊C8—22no—
553C43⋊C8—41no—
554C43⋊C8—41no—
555C43⋊C8—41no—
556#22434—431nomaximal, Sylow
557C22×C43—21no—
558C22×C43—21no—
559C22×C43—21no—
560C22×C43—21no—
561C22×C43—21no—
562C22×C43—21no—
563C22×C43—21no—
564C22×C43—22no—
565C22×C43—21no—
566C22×C43—21no—
567C22×C43—21no—
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—21no—
571C22×C43—42no—
572C22×C43—42no—
573C22×C43—41no—
574C22×C43—41no—
575C22×C43—41no—
576C22×C43—41no—
577C22×C43—41no—
578C22×C43—41no—
579C22×C43—41no—
580C22×C43—41no—
581C22×C43—81no—
582C22×C43—81no—
583C22×C43—84no—
584C22×C43—84no—
585C22×C43#42112yescomplemented
586C22×C43C22×C22⋊C411yescharacteristic
587C22×C43D4211yescharacteristic
588C22×C43#54611yescharacteristic
589C4×C43—21no—
590C4×C43—21no—
591C4×C43—21no—
592C4×C43—21no—
593C4×C43—22no—
594C4×C43—21no—
595C4×C43—21no—
596C4×C43—21no—
597C4×C43—21no—
598C4×C43—41no—
599C4×C43—41no—
600C4×C43—41no—
601C4×C43—41no—
602C4×C43C2×C4×D411yescharacteristic
603C4×C43#51811yescharacteristic
604C4×C43D4211yescharacteristic
605C4×C43#54611yescharacteristic
606Dic43—42no—
607Dic43—42no—
608Dic43—81no—
609Dic43—81no—
610D4×#41D4311yescharacteristic
611D4×M16—431no—
612C2×#421—431no—
613C22×#104—431no—
614#2290—431no—
615#1980—431no—
616#1963—431no—
617#1897—431no—
618#1896—431no—
619#1871—431no—
620#1871—431no—
621#1806—431no—
622#1789—431no—
623#1789—431no—
624#1759—431no—
625C2×C43—21no—
626C2×C43—21no—
627C2×C43—22no—
628C2×C43—41no—
629C2×C43—41no—
630C2×C43—41no—
631C2×C43—42no—
632C2×C43—81no—
633C2×C43—81no—
634C2×C43D4×C22⋊C411yescharacteristic
635C2×C43C2×#42111yescharacteristic
636C2×C43#290111yescharacteristic
637C22×#41C2×D4311yescharacteristic
638C22×#41C2×D4311yescharacteristic
639C22×M16—431no—
640C22×M16—431no—
641#550Dic4311yescharacteristic, complemented
642D4×Q8Dic4311yescharacteristic, complemented
643#548Dic4311yescharacteristic, complemented
644#548Dic4311yescharacteristic, complemented
645#547—21no—
646#547Dic4311yescharacteristic, complemented
647#546—21no—
648#546—21no—
649#546Dic4311yescharacteristic, complemented
650#546Dic4311yescharacteristic, complemented
651D42—21no—
652D42Dic4311yescharacteristic, complemented
653#532—21no—
654#532C2×D4311yescharacteristic
655#525—21no—
656#525—21no—
657#525C2×D4311yescharacteristic
658#525C2×D4311yescharacteristic
659C4×#41C2×D4311yescharacteristic
660C2×C4×D4—21no—
661C2×C4×D4C2×D4311yescharacteristic
662C2×#117—431no—
663C22×C42—431no—
664#436—861no—
665#435—861no—
666#435—861no—
667C8×D4—861no—
668#423—431no—
669#421—864no—
670C2×#104—431no—
671C2×#104—431no—
672C2×#104—431no—
673C2×#104—431no—
674C2×#104—431no—
675C2×#104—431no—
676C2×#104—431no—
677C2×#104—431no—
678C2×#104—431no—
679C2×#104—431no—
680C2×#104—431no—
681C2×#104—431no—
682C2×#104—864no—
683#407—431no—
684#407—431no—
685C4×M16—431no—
686#388—861no—
687#387—861no—
688#386—861no—
689#385—861no—
690C4×C4⋊C4—431no—
691C4×C22⋊C4—431no—
692C4×C22⋊C4—431no—
693#376—431no—
694#339—431no—
695#339—431no—
696#339—431no—
697#339—431no—
698C43#2243411yescharacteristic, complemented, Sylow
699C2×#41—21no—
700C2×#41—21no—
701C2×#41—21no—
702C2×#41—21no—
703C2×#41—22no—
704C2×#41—22no—
705C2×#41—22no—
706C2×#41—22no—
707C2×#41—41no—
708C2×#41—41no—
709C2×#41—41no—
710C2×#41—41no—
711C2×#41C2×Dic4311yescharacteristic
712C2×#41C2×Dic4311yescharacteristic
713C2×#41C2×Dic4311yescharacteristic, complemented
714C2×#41C2×Dic4311yescharacteristic, complemented
715C2×#41C22×D4311yescharacteristic
716C2×#41C22×D4311yescharacteristic
717C2×#41C22×D4311yescharacteristic
718C22×Q8C2×Dic4311yescharacteristic
719C22×Q8C2×Dic4311yescharacteristic, complemented
720C22×D4—21no—
721C22×D4—21no—
722C22×D4—21no—
723C22×D4C2×Dic4311yescharacteristic
724C22×D4C2×Dic4311yescharacteristic, complemented
725C22×D4C22⋊D4311yescharacteristic
726C23×C4—21no—
727C23×C4—21no—
728C23×C4—861no—
729C23×C4C22×D4311yescharacteristic
730C23×C4C22×D4311yescharacteristic
731C2×M16—431no—
732C2×M16—431no—
733C2×M16—431no—
734C2×M16—431no—
735C2×M16—861no—
736C2×M16—861no—
737C2×M16—862no—
738C2×M16—862no—
739C2×M16—1721no—
740C2×M16—1721no—
741C22×C8—861no—
742C22×C8—861no—
743C4⋊Q8—21no—
744C4⋊Q8C2×Dic4311yescharacteristic, complemented
745#127—21no—
746#127C2×Dic4311yescharacteristic, complemented
747#124—21no—
748#124—21no—
749#124C2×Dic4311yescharacteristic, complemented
750#124C2×Dic4311yescharacteristic, complemented
751#123—21no—
752#123—21no—
753#123—21no—
754#123—21no—
755#123—21no—
756#123—21no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—21no—
760C22⋊Q8—21no—
761C22⋊Q8C2×Dic4311yescharacteristic
762C22⋊Q8C2×Dic4311yescharacteristic
763C22⋊Q8C2×Dic4311yescharacteristic, complemented
764C22⋊Q8C2×Dic4311yescharacteristic, complemented
765#121—21no—
766#121—21no—
767#121—21no—
768#121—21no—
769#121—21no—
770#121—21no—
771#121—21no—
772#121—21no—
773#121—21no—
774#121—21no—
775#121C2×Dic4311yescharacteristic
776#121C2×Dic4311yescharacteristic
777#121C2×Dic4311yescharacteristic, complemented
778#121C2×Dic4311yescharacteristic, complemented
779#120—21no—
780#120—21no—
781#120—21no—
782#120—21no—
783#120—21no—
784#120—21no—
785C4×Q8C2×Dic4311yescharacteristic, complemented
786C4×Q8C2×Dic4311yescharacteristic, complemented
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—21no—
790C4×D4—21no—
791C4×D4—21no—
792C4×D4—21no—
793C4×D4—21no—
794C4×D4—21no—
795C4×D4—21no—
796C4×D4—21no—
797C4×D4—21no—
798C4×D4—21no—
799C4×D4C2×Dic4311yescharacteristic
800C4×D4C2×Dic4311yescharacteristic
801C4×D4C2×Dic4311yescharacteristic
802C4×D4C2×Dic4311yescharacteristic
803C4×D4C2×Dic4311yescharacteristic, complemented
804C4×D4C2×Dic4311yescharacteristic, complemented
805C4×D4C22⋊D4311yescharacteristic
806C4×D4C22⋊D4311yescharacteristic
807C4×D4C22⋊D4311yescharacteristic
808C4×D4C22⋊D4311yescharacteristic
809#117—21no—
810#117—862no—
811#117—1721no—
812#117C22×D4311yescharacteristic
813C2×C4⋊C4—21no—
814C2×C4⋊C4—861no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4C22⋊D4311yescharacteristic
817C2×C22⋊C4—21no—
818C2×C22⋊C4—21no—
819C2×C22⋊C4—861no—
820C2×C22⋊C4—861no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4C22⋊D4311yescharacteristic
823C2×C22⋊C4C22⋊D4311yescharacteristic
824C2×C42—21no—
825C2×C42—431no—
826C2×C42—431no—
827C2×C42—431no—
828C2×C42—431no—
829C2×C42—862no—
830C2×C42—861no—
831C2×C42—1721no—
832C2×C42C22×D4311yescharacteristic
833C4⋊C8—861no—
834C4⋊C8—861no—
835#104—434no—
836#104—862no—
837#104—862no—
838#104—862no—
839#104—862no—
840#104—862no—
841#104—862no—
842#104—862no—
843#104—1721no—
844#104—1721no—
845#104—1721no—
846#104—1721no—
847C22⋊C8—861no—
848C22⋊C8—861no—
849C22⋊C8—861no—
850C22⋊C8—861no—
851#97—861no—
852C4×C8—861no—
853#95—861no—
854#95—861no—
855#95—861no—
856#95—861no—
857#95—861no—
858C24—21no—
859C24—21no—
860C24C2×C22⋊D4311yescharacteristic
861C24C2×C22⋊D4311yescharacteristic
862#41—21no—
863#41—21no—
864#41—22no—
865#41—22no—
866#41—22no—
867#41—22no—
868#41—21no—
869#41—21no—
870#41—21no—
871#41—21no—
872#41—21no—
873#41—21no—
874#41—21no—
875#41—21no—
876#41—42no—
877#41—42no—
878#41—42no—
879#41—42no—
880#41—41no—
881#41—41no—
882#41—41no—
883#41—41no—
884#41—42no—
885#41—42no—
886#41—42no—
887#41—42no—
888#41D4×D4312yes—
889#41#1062190012yes—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—22no—
893C2×Q8—22no—
894C2×Q8—41no—
895C2×Q8—41no—
896C2×Q8C22×Dic4311yescharacteristic
897C2×Q8C22×Dic4311yescharacteristic
898C2×Q8C22×Dic4311yescharacteristic
899C2×D4—21no—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—41no—
917C2×D4—41no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—42no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4C22⋊Dic4311yescharacteristic
925C2×D4C22⋊Dic4311yescharacteristic
926C2×D4C22⋊Dic4311yescharacteristic
927C2×D4C22⋊Dic4311yescharacteristic
928C2×D4C22×Dic4311yescharacteristic
929C2×D4C22×Dic4311yescharacteristic
930C2×D4C22×Dic4311yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—861no—
955C22×C4—861no—
956C22×C4—861no—
957C22×C4—861no—
958C22×C4—1722no—
959C22×C4—1722no—
960C22×C4—1722no—
961C22×C4C22×Dic4311yescharacteristic
962C22×C4C22×Dic4311yescharacteristic
963C22×C4C22×Dic4311yescharacteristic
964C22×C4C22×Dic4311yescharacteristic
965C22×C4C2×C22⋊D4311yescharacteristic
966C22×C4C2×C22⋊D4311yescharacteristic
967C22×C4C2×C22⋊D4311yescharacteristic
968C22×C4C2×C22⋊D4311yescharacteristic
969C22×C4C2×C22⋊D4311yescharacteristic
970C22×C4C2×C22⋊D4311yescharacteristic
971C22×C4C2×C22⋊D4311yescharacteristic
972C22×C4C2×C22⋊D4311yescharacteristic
973C22×C4C23×D4311yescharacteristic
974M16—432no—
975M16—861no—
976M16—861no—
977M16—861no—
978M16—861no—
979M16—861no—
980M16—861no—
981M16—861no—
982M16—1722no—
983M16—1722no—
984C2×C8—861no—
985C2×C8—861no—
986C2×C8—861no—
987C2×C8—861no—
988C2×C8—1722no—
989C2×C8—1722no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—1722no—
999C4⋊C4—1722no—
1000C4⋊C4C22⋊Dic4311yescharacteristic
1001C4⋊C4C22⋊Dic4311yescharacteristic
1002C4⋊C4C22⋊Dic4311yescharacteristic
1003C4⋊C4C22⋊Dic4311yescharacteristic
1004C4⋊C4C22×Dic4311yescharacteristic
1005C4⋊C4C22×Dic4311yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—21no—
1011C22⋊C4—21no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—21no—
1015C22⋊C4—21no—
1016C22⋊C4—21no—
1017C22⋊C4—21no—
1018C22⋊C4—21no—
1019C22⋊C4—21no—
1020C22⋊C4—21no—
1021C22⋊C4—1722no—
1022C22⋊C4—1722no—
1023C22⋊C4—1722no—
1024C22⋊C4C22⋊Dic4311yescharacteristic
1025C22⋊C4C22⋊Dic4311yescharacteristic
1026C22⋊C4C22⋊Dic4311yescharacteristic
1027C22⋊C4C22⋊Dic4311yescharacteristic
1028C22⋊C4C22⋊Dic4311yescharacteristic
1029C22⋊C4C22⋊Dic4311yescharacteristic
1030C22⋊C4C22⋊Dic4311yescharacteristic
1031C22⋊C4C22⋊Dic4311yescharacteristic
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—432no—
1036C42—861no—
1037C42—861no—
1038C42—861no—
1039C42—861no—
1040C42—861no—
1041C42—861no—
1042C42—861no—
1043C42—1722no—
1044C42C22×Dic4311yescharacteristic
1045C42C22×Dic4311yescharacteristic
1046C42C2×C22⋊D4311yescharacteristic
1047C42C2×C22⋊D4311yescharacteristic
1048C23—21no—
1049C23—22no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—81no—
1064C23—81no—
1065C23C2×C22⋊Dic4311yescharacteristic
1066C23C2×C22⋊Dic4311yescharacteristic
1067C23C2×C22⋊Dic4311yescharacteristic
1068C23C2×C22⋊Dic4311yescharacteristic
1069C23C22×C22⋊D4311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—21no—
1075Q8—42no—
1076Q8—42no—
1077Q8D4×Dic4312yes—
1078D4—22no—
1079D4—22no—
1080D4—22no—
1081D4—22no—
1082D4—21no—
1083D4—21no—
1084D4—21no—
1085D4—21no—
1086D4—21no—
1087D4—41no—
1088D4—41no—
1089D4—42no—
1090D4—42no—
1091D4—42no—
1092D4—42no—
1093D4—42no—
1094D4—42no—
1095D4—42no—
1096D4—42no—
1097D4—42no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—81no—
1103D4—81no—
1104D4—81no—
1105D4D4×Dic4312yes—
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—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—81no—
1147C2×C4—862no—
1148C2×C4—862no—
1149C2×C4—1721no—
1150C2×C4—1721no—
1151C2×C4—1721no—
1152C2×C4—1721no—
1153C2×C4—1721no—
1154C2×C4—1721no—
1155C2×C4—1721no—
1156C2×C4—1721no—
1157C2×C4—1721no—
1158C2×C4—1728no—
1159C2×C4—1721no—
1160C2×C4C2×C22⋊Dic4311yescharacteristic
1161C2×C4C2×C22⋊Dic4311yescharacteristic
1162C2×C4C2×C22⋊Dic4311yescharacteristic
1163C2×C4C2×C22⋊Dic4311yescharacteristic
1164C2×C4C2×C22⋊Dic4311yescharacteristic
1165C2×C4C2×C22⋊Dic4311yescharacteristic
1166C2×C4C2×C22⋊Dic4311yescharacteristic
1167C2×C4C2×C22⋊Dic4311yescharacteristic
1168C2×C4C23×Dic4311yescharacteristic
1169C2×C4C2×D4×D4311yescharacteristic
1170C2×C4C22×C22⋊D4311yescharacteristic
1171C2×C4C2×#1062190011yescharacteristic
1172C2×C4#1306337011yescharacteristic
1173C2×C4#1306337011yescharacteristic
1174C8—862no—
1175C8—1721no—
1176C8—1721no—
1177C8—1721no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—22no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—21no—
1191C22—21no—
1192C22—42no—
1193C22—42no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—81no—
1203C22—81no—
1204C22—84no—
1205C22—84no—
1206C22#1458291612yescomplemented
1207C22C22×C22⋊Dic4311yescharacteristic
1208C22D4×C22⋊D4311yescharacteristic
1209C22#1458354311yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—22no—
1215C4—21no—
1216C4—21no—
1217C4—21no—
1218C4—21no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—3441no—
1224C4—3441no—
1225C4—1722no—
1226C4—1722no—
1227C4C2×D4×Dic4311yescharacteristic
1228C4#1458337411yescharacteristic
1229C4D4×C22⋊D4311yescharacteristic
1230C4#1458354311yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—22no—
1234C2—41no—
1235C2—41no—
1236C2—41no—
1237C2—42no—
1238C2—81no—
1239C2—81no—
1240C2D4×C22⋊Dic4311yescharacteristic
1241C2C2×#1458291611yescharacteristic
1242C2#1914314211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalD4×#41×C43C2
socleC22×C43C22×C22⋊C4
cosocleC22×C4×C43C24
hypercenterD4×#41D43
hypocenterC43#22434
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. D4×#10621877C2semidirect
2. C2×#14582916C2semidirect
3. C22×#13063252C2semidirect
4. #19137040C2semidirect
5. #19135515C2semidirect
6. #19135428C2semidirect
7. #19135044C2semidirect
8. #19135039C2semidirect
9. #19134898C2semidirect
10. #19134898C2semidirect
11. #19134615C2semidirect
12. #19134539C2semidirect
13. #19134539C2semidirect
14. #19134405C2semidirect
16. C22×#10621877C22semidirect
17. C22×#10621877C22semidirect
18. C2×#13063284C22semidirect
19. C22×C4×Dic43C22semidirect
24. #14582923C22semidirect
31. C2×#13063252C22semidirect
32. C2×#13063252C22semidirect
33. C2×#13063252C22semidirect
34. C2×#13063252C22semidirect
35. C2×#13063252C22semidirect
36. C2×#13063252C22semidirect
37. C2×#13063252C22semidirect
38. C2×#13063252C22semidirect
39. #14582863C22semidirect
40. #14582863C22semidirect
41. C4×#10621877C22semidirect
46. C4×C4⋊Dic43C22semidirect
47. C4×C22⋊Dic43C22semidirect
48. C4×C22⋊Dic43C22semidirect
49. #14582745C22semidirect
50. #14582658C22semidirect
51. #14582658C22semidirect
52. #14582658C22semidirect
53. #14582658C22semidirect
56. C43×#550C4semidirect
57. D4×Q8×C43C4semidirect
58. C43×#548C4semidirect
59. C43×#548C4semidirect
61. C43×#547C4semidirect
64. C43×#546C4semidirect
65. C43×#546C4semidirect
67. D42×C43C4semidirect
117. #13063252D4semidirect
143. C2×#41×C43C2×C4semidirect
144. C2×#41×C43C2×C4semidirect
149. C22×Q8×C43C2×C4semidirect
154. C22×D4×C43C2×C4semidirect
161. C4⋊Q8×C43C2×C4semidirect
163. #127×C43C2×C4semidirect
166. #124×C43C2×C4semidirect
167. #124×C43C2×C4semidirect
180. C22⋊Q8×C43C2×C4semidirect
181. C22⋊Q8×C43C2×C4semidirect
194. #121×C43C2×C4semidirect
195. #121×C43C2×C4semidirect
202. C4×Q8×C43C2×C4semidirect
203. C4×Q8×C43C2×C4semidirect
220. C4×D4×C43C2×C4semidirect
221. C4×D4×C43C2×C4semidirect
409. C4×Dic43C2×D4semidirect
419. #10621877C2×D4semidirect
585. C22×C43#421semidirect
641. #550Dic43semidirect
642. D4×Q8Dic43semidirect
643. #548Dic43semidirect
644. #548Dic43semidirect
646. #547Dic43semidirect
649. #546Dic43semidirect
650. #546Dic43semidirect
652. D42Dic43semidirect
698. C43#22434semidirect
713. C2×#41C2×Dic43semidirect
714. C2×#41C2×Dic43semidirect
719. C22×Q8C2×Dic43semidirect
724. C22×D4C2×Dic43semidirect
744. C4⋊Q8C2×Dic43semidirect
746. #127C2×Dic43semidirect
749. #124C2×Dic43semidirect
750. #124C2×Dic43semidirect
763. C22⋊Q8C2×Dic43semidirect
764. C22⋊Q8C2×Dic43semidirect
777. #121C2×Dic43semidirect
778. #121C2×Dic43semidirect
785. C4×Q8C2×Dic43semidirect
786. C4×Q8C2×Dic43semidirect
803. C4×D4C2×Dic43semidirect
804. C4×D4C2×Dic43semidirect
1206. C22#14582916semidirect

Maximal subgroups

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

subgroupindex
D4×#106218772
C2×#145829162
C22×#130632522
#191370402
#191355152
#191354282
#191350442
#191350392
#191348982
#191346152
#191345392
#191344052
D4×#41×C432
#2243443