Finite Group Databasebeta

← #25063067

Subgroups — #25063067

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063370C211yesmaximal, characteristic
2#19143709C211yesmaximal, characteristic, complemented
3#19143559C211yesmaximal, characteristic, complemented
4#19133038C211yesmaximal, characteristic, complemented
5#19133036C211yesmaximal, characteristic, complemented
6#19133032C211yesmaximal, characteristic, complemented
7#19133031C211yesmaximal, characteristic, complemented
8#19133030C211yesmaximal, characteristic, complemented
9#19133026C211yesmaximal, characteristic, complemented
10#19133018C211yesmaximal, characteristic, complemented
11#19132984C211yesmaximal, characteristic, complemented
12#19132979C211yesmaximal, characteristic, complemented
13#19132974C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1486C211yesmaximal, characteristic, complemented
16C2×#13063370C411yescharacteristic
17#14583380C411yescharacteristic
18#14583380C411yescharacteristic
19#14583378—21no—
20#14583378C411yescharacteristic
21#14583378C411yescharacteristic
22#14583374C411yescharacteristic
23#14583372—21no—
24#14583372—21no—
25#14583371—21no—
26#14583371C411yescharacteristic
27#14583371C411yescharacteristic
28C4×#10621898C2211yescharacteristic
29C4×#10621898C2211yescharacteristic
30C4×#10621900—21no—
31C4×#10621900C2211yescharacteristic
32C4×#10621900C2211yescharacteristic
33C2×C4×C22⋊D43—21no—
34C2×C4×C22⋊D43—21no—
35C4×D4×D43—21no—
36C4×D4×D43C2211yescharacteristic
37C4×D4×D43C2211yescharacteristic
38#14583028—21no—
39#14583028—21no—
40#14582975—21no—
41#14582974—21no—
42#14582973—21no—
43#14582969—21no—
44#14582969—21no—
45#14582968—21no—
46#14582956C2211yescharacteristic, complemented
47#14582955C2211yescharacteristic, complemented
48#14582951C2211yescharacteristic, complemented
49#14582950C2211yescharacteristic, complemented
50#14582950C2211yescharacteristic, complemented
51#14582921C2211yescharacteristic, complemented
52C4⋊C8×D43C2211yescharacteristic, complemented
53C4×#10621877C2211yescharacteristic, complemented
54C4×#10621872C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic, complemented
56#14582631C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58#14582629C2211yescharacteristic, complemented
59#14582629C2211yescharacteristic, complemented
60#14582628C2211yescharacteristic, complemented
61#14582628C2211yescharacteristic, complemented
62D4⋊(C43⋊C8)C2211yescharacteristic, complemented
63D4⋊(C43⋊C8)C2211yescharacteristic, complemented
64D4⋊(C43⋊C8)C2211yescharacteristic, complemented
65D4⋊(C43⋊C8)C2211yescharacteristic, complemented
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C2×C4×D4×C43C2211yescharacteristic
69C43×#431C2211yescharacteristic, complemented
70C43×#423C2211yescharacteristic, complemented
71C43×D4⋊C8C2211yescharacteristic, complemented
72C43×D4⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic, complemented
74C43×D4⋊C8C2211yescharacteristic, complemented
75#13063370—24no—
76#13063370—24no—
77C2×#10621898C2×C411yescharacteristic
78C2×#10621898C2×C411yescharacteristic
79C2×#10621900—21no—
80C2×#10621900C2×C411yescharacteristic
81C2×#10621900C2×C411yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C2×D4×D43—21no—
85C2×D4×D43C2×C411yescharacteristic
86C2×D4×D43C2×C411yescharacteristic
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C2×#10621877—21no—
90C2×#10621872—21no—
91C2×#10621872—21no—
92C2×C8×D43—21no—
93C2×C8×D43—21no—
94C4×Dic86C2×C411yescharacteristic
95C4×Dic86D411yescharacteristic
96C4×Dic86D411yescharacteristic
97C4×Dic86C2311yescharacteristic
98#13063290—21no—
99#13063290C2×C411yescharacteristic
100#13063290C2×C411yescharacteristic
101C4×D172C2×C411yescharacteristic
102C4×D172D411yescharacteristic
103C4×D172D411yescharacteristic
104C4×D172C2311yescharacteristic
105D4×Dic43—21no—
106D4×Dic43—21no—
107D4×Dic43C2×C411yescharacteristic
108D4×Dic43C2×C411yescharacteristic
109D4×Dic43C2×C411yescharacteristic
110D4×Dic43C2×C411yescharacteristic
111#13063287—21no—
112#13063287C2×C411yescharacteristic
113#13063287C2×C411yescharacteristic
114C4×C22⋊D43—21no—
115C4×C22⋊D43—21no—
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43D411yescharacteristic
129C4×C22⋊D43D411yescharacteristic
130C4×C22⋊D43D411yescharacteristic
131C4×C22⋊D43D411yescharacteristic
132(C22⋊D43)⋊C4—21no—
133(C22⋊D43)⋊C4—21no—
134(C22⋊D43)⋊C4—21no—
135(C22⋊D43)⋊C4—21no—
136(C22⋊D43)⋊C4—21no—
137(C22⋊D43)⋊C4—21no—
138(C22⋊D43)⋊C4—21no—
139(C22⋊D43)⋊C4—21no—
140#13063284C2×C411yescharacteristic
141#13063284C2×C411yescharacteristic
142#13063283—21no—
143#13063283C2×C411yescharacteristic
144#13063283C2×C411yescharacteristic
145#13063282—21no—
146#13063282C2×C411yescharacteristic
147#13063282C2×C411yescharacteristic
148#13063281—21no—
149#13063281—21no—
150#13063281—21no—
151#13063281—21no—
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C4⋊C4×D43—21no—
155C4⋊C4×D43C2×C411yescharacteristic
156C4⋊C4×D43C2×C411yescharacteristic
157C2×C22⋊Dic43—21no—
158C2×C22⋊Dic43—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C22⋊C4×D43—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43—21no—
167C42×D43—21no—
168C42×D43C2311yescharacteristic
169C42×D43C2311yescharacteristic
170C4⋊(C43⋊C8)C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063236—21no—
182#13063236—21no—
183#13063235—21no—
184#13063235—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C8×Dic43—21no—
189C22×D4×C43C2×C411yescharacteristic
190C23×C4×C43—21no—
191C2×M16×C43—21no—
192C4×D4×C43—21no—
193C4×D4×C43—21no—
194C4×D4×C43C2×C411yescharacteristic
195C4×D4×C43C2×C411yescharacteristic
196C4×D4×C43C2311yescharacteristic
197C4×D4×C43C2311yescharacteristic
198C2×C4⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43—21no—
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43—21no—
202C4⋊C8×C43—21no—
203C4⋊C8×C43C2311yescharacteristic
204C4⋊C8×C43C2311yescharacteristic
205C22⋊C8×C43—21no—
206C4×C8×C43C2311yescharacteristic
207C4×C8×C43C2311yescharacteristic
208C24×C43—21no—
209C23×D43—21no—
210C23×D43—21no—
211C2×D4×C43—22no—
212C2×D4×C43—22no—
213C2×D4×C43—21no—
214C2×D4×C43C22×C411yescharacteristic
215C2×D4×C43C22×C411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—81no—
222C22×C4×C43—81no—
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C2×C22⋊D43—28no—
227C2×C22⋊D43—28no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43C22⋊C411yescharacteristic
234C2×C22⋊D43C22⋊C411yescharacteristic
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241#10621900—28no—
242#10621900—22no—
243#10621900—22no—
244#10621900—22no—
245#10621900M1614yescomplemented
246D4×D43—28no—
247D4×D43—22no—
248D4×D43—22no—
249D4×D43—22no—
250D4×D43M1614yescomplemented
251#10621898—22no—
252#10621898—22no—
253#10621898—22no—
254#10621898—22no—
255C2×D172C22⋊C411yescharacteristic
256C2×D172C22×C411yescharacteristic
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—21no—
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—81no—
265C2×C4×D43—81no—
266C2×C4×D43—81no—
267C2×C4×D43—81no—
268C2×C4×D43C22×C411yescharacteristic
269C2×C4×D43C22×C411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×C4×D43C2×D411yescharacteristic
272C2×C4×D43C2×D411yescharacteristic
273C2×C4×D43C2×D411yescharacteristic
274C2×Dic86C22⋊C411yescharacteristic
275C2×Dic86C22×C411yescharacteristic
276M16×C43—81no—
277C2×C8×C43—21no—
278C2×C8×C43—21no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43C22×C411yescharacteristic
283C4⋊C4×C43C22×C411yescharacteristic
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C42×C43C22×C411yescharacteristic
289C42×C43C2×D411yescharacteristic
290C42×C43C2×D411yescharacteristic
291C42×C43C2411yescharacteristic
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43—21no—
297C22⋊Dic43C22⋊C411yescharacteristic
298C22⋊Dic43C22⋊C411yescharacteristic
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4C22⋊C411yescharacteristic
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309C4⋊Dic43C22⋊C411yescharacteristic
310C4⋊Dic43C22⋊C411yescharacteristic
311C4⋊Dic43C22×C411yescharacteristic
312C4⋊Dic43C22×C411yescharacteristic
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4C22⋊C411yescharacteristic
320Dic43⋊C4C22⋊C411yescharacteristic
321Dic43⋊C4C22⋊C411yescharacteristic
322Dic43⋊C4C22⋊C411yescharacteristic
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—21no—
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43C22×C411yescharacteristic
331C4×Dic43C22×C411yescharacteristic
332C4×Dic43C2×D411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C4×Dic43C2×D411yescharacteristic
336#10621877—42no—
337C2×C43⋊C8—21no—
338C2×C43⋊C8—21no—
339C2×C43⋊C8—21no—
340C2×C43⋊C8—21no—
341#10621872—42no—
342#10621872—81no—
343C8×D43—42no—
344C8×D43—81no—
345C23×C43—24no—
346C23×C43—21no—
347C23×C43—21no—
348C23×C43—81no—
349C23×C43—81no—
350C23×C43C2×C22⋊C411yescharacteristic
351C22×D43—21no—
352C22×D43—24no—
353C22×D43—24no—
354C22×D43—81no—
355C22×D43—81no—
356C22×D43—81no—
357C22×D43—81no—
358C22×D43C2×C22⋊C411yescharacteristic
359C22×D43C2×C22⋊C411yescharacteristic
360D4×C43—24no—
361D4×C43—21no—
362D4×C43—21no—
363D4×C43C2×M1612yes—
364D4×C43C2×M1612yes—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—81no—
377C2×C4×C43—81no—
378C2×C4×C43—81no—
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C23×C411yescharacteristic
383C2×C4×C43C22×D411yescharacteristic
384C2×C4×C43C22×D411yescharacteristic
385C22⋊D43—24no—
386C22⋊D43—24no—
387C22⋊D43—24no—
388C22⋊D43—22no—
389C22⋊D43—24no—
390C22⋊D43—22no—
391C22⋊D43—24no—
392C2×Dic43—24no—
393C2×Dic43—21no—
394C2×Dic43—24no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—81no—
398C2×Dic43—81no—
399C2×Dic43—81no—
400C2×Dic43—81no—
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43C2×C22⋊C411yescharacteristic
403C2×Dic43C2×C22⋊C411yescharacteristic
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407D172—22no—
408D172—21no—
409D172C2×M1612yes—
410C4×D43—24no—
411C4×D43—21no—
412C4×D43—21no—
413C4×D43—21no—
414C4×D43—21no—
415C4×D43—21no—
416C4×D43—21no—
417C4×D43—41no—
418C4×D43—41no—
419C4×D43—41no—
420C4×D43—41no—
421C4×D43—81no—
422C4×D43—81no—
423C4×D43—81no—
424C4×D43—81no—
425C4×D43—81no—
426C4×D43C2×M1612yes—
427C4×D43C2×M1612yes—
428Dic86—21no—
429Dic86—22no—
430Dic86C2×M1612yes—
431C8×C43—41no—
432C8×C43—41no—
433C8×C43—41no—
434C8×C43—41no—
435C43⋊C8—22no—
436C43⋊C8—41no—
437C43⋊C8—41no—
438C43⋊C8—41no—
439#17453—431nomaximal, Sylow
440C22×C43—22no—
441C22×C43—22no—
442C22×C43—21no—
443C22×C43—21no—
444C22×C43—21no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43—41no—
449C22×C43—84no—
450C22×C43C22×C22⋊C411yescharacteristic
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—22no—
454C2×D43—21no—
455C2×D43—21no—
456C2×D43—21no—
457C2×D43—41no—
458C2×D43—41no—
459C2×D43—84no—
460C2×D43—84no—
461C2×D43#40712yes—
462C4×C43—21no—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—41no—
467C4×C43—41no—
468C4×C43C22×M1611yescharacteristic
469C4×C43C22×M1611yescharacteristic
470C4×C43#57611yescharacteristic
471C4×C43#57711yescharacteristic
472Dic43—21no—
473Dic43—22no—
474Dic43—21no—
475Dic43—21no—
476Dic43—21no—
477Dic43—21no—
478Dic43—41no—
479Dic43—41no—
480Dic43#40712yes—
481C4×H(5,𝔽2)—431no—
482#2989—431no—
483#2965—431no—
484#1490—431no—
485#1490—431no—
486#1489—431no—
487#1489—431no—
488#1488—431no—
489#1488—431no—
490#1486—431no—
491#1486D4311yescharacteristic, complemented
492#1478—431no—
493#1477—431no—
494#1476—431no—
495C2×D4⋊C8—431no—
496C2×C43—42no—
497C2×C43—42no—
498C2×C43—41no—
499C2×C43C2×#40711yescharacteristic
500C2×C43#289711yescharacteristic
501C2×C43#290111yescharacteristic
502D43—22no—
503D43—41no—
504D43—42no—
505C2×H(5,𝔽2)—431no—
506#520—431no—
507#520—431no—
508#520—431no—
509#520—431no—
510#520—861no—
511#518—431no—
512#518—431no—
513#518—431no—
514#518—861no—
515#518—861no—
516#518—861no—
517C4×#41—431no—
518C4×#41—431no—
519C4×#41—431no—
520C4×#41—431no—
521C4×#41—861no—
522C2×C4×D4—431no—
523C2×C4×D4—431no—
524C2×C4×D4—861no—
525C2×C4×D4—861no—
526C2×C4×D4—861no—
527C2×C4×D4C2×D4311yescharacteristic
528#446—861no—
529#446—861no—
530#436—861no—
531#436—861no—
532#435—861no—
533#435—861no—
534#435—861no—
535#435—861no—
536#432—431no—
537#432—431no—
538#431—431no—
539#431—431no—
540#431—431no—
541#431C2×D4311yescharacteristic, complemented
542#423—431no—
543#423C2×D4311yescharacteristic, complemented
544C2×C4⋊C8—431no—
545C4×M16—431no—
546C4×M16—431no—
547C2×C4×C8—431no—
548Q8⋊C8—431no—
549Q8⋊C8—431no—
550Q8⋊C8—431no—
551Q8⋊C8—431no—
552D4⋊C8—431no—
553D4⋊C8—431no—
554D4⋊C8—431no—
555D4⋊C8—431no—
556D4⋊C8—431no—
557D4⋊C8—431no—
558D4⋊C8—431no—
559D4⋊C8—431no—
560D4⋊C8C2×D4311yescharacteristic, complemented
561D4⋊C8C2×D4311yescharacteristic, complemented
562D4⋊C8C2×D4311yescharacteristic, complemented
563D4⋊C8C2×D4311yescharacteristic, complemented
564C43#1745311yescharacteristic, complemented, Sylow
565H(5,𝔽2)—864no—
566H(5,𝔽2)—864no—
567C2×#41—431no—
568C2×#41—431no—
569C2×#41—431no—
570C2×#41—431no—
571C2×#41—861no—
572C22×D4—431no—
573C22×D4—431no—
574C22×D4—861no—
575C22×D4—861no—
576C22×D4—861no—
577C22×D4C4×D4311yescharacteristic
578C23×C4—21no—
579C23×C4—861no—
580C23×C4—861no—
581C2×M16—21no—
582C2×M16—861no—
583C2×M16—861no—
584C2×M16—861no—
585C22×C8—861no—
586C22×C8—861no—
587C4×Q8—431no—
588C4×Q8—431no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—431no—
592C4×Q8—431no—
593C4×Q8—861no—
594C4×D4—21no—
595C4×D4—21no—
596C4×D4—431no—
597C4×D4—431no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—431no—
603C4×D4—431no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4—861no—
631C4×D4—861no—
632C4×D4—861no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4C4×D4311yescharacteristic
636C4×D4C4×D4311yescharacteristic
637C4×D4C22×D4311yescharacteristic
638C4×D4C22×D4311yescharacteristic
639#117—431no—
640#117—431no—
641#117—431no—
642#117—431no—
643#117—431no—
644#117—431no—
645#117—861no—
646#117—861no—
647#117—861no—
648#117—861no—
649#117—861no—
650#117—861no—
651C2×C4⋊C4—431no—
652C2×C4⋊C4—431no—
653C2×C4⋊C4—861no—
654C2×C4⋊C4—861no—
655C2×C4⋊C4—861no—
656C2×C4⋊C4C4×D4311yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—861no—
659C2×C22⋊C4—861no—
660C2×C22⋊C4—861no—
661C2×C22⋊C4—861no—
662C2×C22⋊C4—861no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—861no—
666C2×C42—431no—
667C2×C42—431no—
668C2×C42—861no—
669C2×C42—861no—
670C2×C42—861no—
671C2×C42C22×D4311yescharacteristic
672C4⋊C8—21no—
673C4⋊C8—21no—
674C4⋊C8—431no—
675C4⋊C8—431no—
676C4⋊C8—861no—
677C4⋊C8—861no—
678C4⋊C8—861no—
679C4⋊C8—861no—
680C4⋊C8C22×D4311yescharacteristic
681C4⋊C8C22×D4311yescharacteristic
682C22⋊C8—21no—
683C22⋊C8—861no—
684C22⋊C8—861no—
685C22⋊C8—861no—
686C22⋊C8—861no—
687C22⋊C8—861no—
688#97—861no—
689#97—861no—
690#97—861no—
691#97—861no—
692C4×C8—431no—
693C4×C8—431no—
694C4×C8—861no—
695C4×C8—861no—
696C4×C8C22×D4311yescharacteristic
697C4×C8C22×D4311yescharacteristic
698C24—21no—
699C24—861no—
700C24—861no—
701#41—434no—
702#41—862no—
703#41—862no—
704#41—862no—
705#41—862no—
706#41—862no—
707#41—862no—
708#41—868no—
709#41—862no—
710C2×Q8—431no—
711C2×Q8—431no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—21no—
715C2×D4—434no—
716C2×D4—431no—
717C2×D4—431no—
718C2×D4—431no—
719C2×D4—431no—
720C2×D4—862no—
721C2×D4—861no—
722C2×D4—861no—
723C2×D4—862no—
724C2×D4—868no—
725C2×D4—861no—
726C2×D4—861no—
727C2×D4—868no—
728C2×D4—868no—
729C2×D4—861no—
730C2×D4—862no—
731C2×D4C2×C4×D4311yescharacteristic
732C2×D4C2×C4×D4311yescharacteristic
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—81no—
739C22×C4—81no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—431no—
743C22×C4—431no—
744C22×C4—431no—
745C22×C4—431no—
746C22×C4—861no—
747C22×C4—861no—
748C22×C4—861no—
749C22×C4—861no—
750C22×C4—861no—
751C22×C4—861no—
752C22×C4—861no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—861no—
758C22×C4—861no—
759C22×C4—3441no—
760C22×C4—3441no—
761C22×C4—3441no—
762C22×C4—3441no—
763C22×C4C2×C4×D4311yescharacteristic
764C22×C4D4×D4311yescharacteristic
765C22×C4D4×D4311yescharacteristic
766M16—81no—
767M16—3441no—
768M16—1722no—
769M16—1722no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—861no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—3441no—
779C2×C8—1722no—
780C4⋊C4—21no—
781C4⋊C4—431no—
782C4⋊C4—431no—
783C4⋊C4—431no—
784C4⋊C4—431no—
785C4⋊C4—431no—
786C4⋊C4—431no—
787C4⋊C4—431no—
788C4⋊C4—431no—
789C4⋊C4—861no—
790C4⋊C4—861no—
791C4⋊C4—861no—
792C4⋊C4—861no—
793C4⋊C4—861no—
794C4⋊C4—861no—
795C4⋊C4C2×C4×D4311yescharacteristic
796C4⋊C4C2×C4×D4311yescharacteristic
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—431no—
802C22⋊C4—431no—
803C22⋊C4—431no—
804C22⋊C4—431no—
805C22⋊C4—431no—
806C22⋊C4—431no—
807C22⋊C4—861no—
808C22⋊C4—861no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C22⋊C4—861no—
815C22⋊C4—861no—
816C22⋊C4—861no—
817C22⋊C4—861no—
818C42—431no—
819C42—431no—
820C42—431no—
821C42—431no—
822C42—431no—
823C42—431no—
824C42—861no—
825C42—861no—
826C42—861no—
827C42—861no—
828C42—861no—
829C42—861no—
830C42—861no—
831C42C2×C4×D4311yescharacteristic
832C42D4×D4311yescharacteristic
833C42D4×D4311yescharacteristic
834C42C23×D4311yescharacteristic
835C23—24no—
836C23—21no—
837C23—21no—
838C23—81no—
839C23—81no—
840C23—431no—
841C23—431no—
842C23—864no—
843C23—864no—
844C23—861no—
845C23—3441no—
846C23—3441no—
847C23—3441no—
848C23—3441no—
849C23C22⋊C4×D4311yescharacteristic
850Q8—432no—
851Q8—862no—
852Q8—861no—
853D4—24no—
854D4—21no—
855D4—21no—
856D4—432no—
857D4—862no—
858D4—862no—
859D4—864no—
860D4—862no—
861D4—864no—
862D4—864no—
863D4—864no—
864D4—864no—
865D4—861no—
866D4M16×D4312yes—
867D4M16×D4312yes—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—81no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—431no—
883C2×C4—432no—
884C2×C4—432no—
885C2×C4—431no—
886C2×C4—431no—
887C2×C4—431no—
888C2×C4—431no—
889C2×C4—431no—
890C2×C4—864no—
891C2×C4—864no—
892C2×C4—864no—
893C2×C4—861no—
894C2×C4—861no—
895C2×C4—861no—
896C2×C4—861no—
897C2×C4—861no—
898C2×C4—861no—
899C2×C4—861no—
900C2×C4—861no—
901C2×C4—861no—
902C2×C4—3441no—
903C2×C4—3441no—
904C2×C4—3441no—
905C2×C4—3441no—
906C2×C4—3441no—
907C2×C4—3441no—
908C2×C4—3441no—
909C2×C4—3441no—
910C2×C4—3441no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4—1721no—
915C2×C4C22⋊C4×D4311yescharacteristic
916C2×C4C22⋊C4×D4311yescharacteristic
917C2×C4C22⋊C4×D4311yescharacteristic
918C2×C4C22×C4×D4311yescharacteristic
919C2×C4C2×D4×D4311yescharacteristic
920C2×C4C2×D4×D4311yescharacteristic
921C8—41no—
922C8—41no—
923C8—41no—
924C8—41no—
925C8—862no—
926C8—1721no—
927C8—1721no—
928C8—1721no—
929C22—21no—
930C22—22no—
931C22—22no—
932C22—21no—
933C22—21no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—84no—
939C22—432no—
940C22—861no—
941C22—861no—
942C22—862no—
943C22—861no—
944C22—861no—
945C22—861no—
946C22—3444no—
947C22—3444no—
948C22—1721no—
949C22—1721no—
950C22C2×C22⋊C4×D4311yescharacteristic
951C4—21no—
952C4—21no—
953C4—21no—
954C4—21no—
955C4—41no—
956C4—41no—
957C4—432no—
958C4—861no—
959C4—862no—
960C4—861no—
961C4—861no—
962C4—861no—
963C4—861no—
964C4—1721no—
965C4—1721no—
966C4C2×M16×D4311yescharacteristic
967C4C2×M16×D4311yescharacteristic
968C4#1458370011yescharacteristic
969C4#1458370511yescharacteristic
970C2—41no—
971C2—42no—
972C2—42no—
973C2—862no—
974C2—1721no—
975C2—1722no—
976C2#407×D4311yescharacteristic
977C2#1914311611yescharacteristic
978C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1486C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#13063370C4
cosocleC42×C43C24
hypercenter#1486D43
hypocenterC43#17453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #19143709C2semidirect
3. #19143559C2semidirect
4. #19133038C2semidirect
5. #19133036C2semidirect
6. #19133032C2semidirect
7. #19133031C2semidirect
8. #19133030C2semidirect
9. #19133026C2semidirect
10. #19133018C2semidirect
11. #19132984C2semidirect
12. #19132979C2semidirect
13. #19132974C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1486C2semidirect
46. #14582956C22semidirect
47. #14582955C22semidirect
48. #14582951C22semidirect
49. #14582950C22semidirect
50. #14582950C22semidirect
51. #14582921C22semidirect
52. C4⋊C8×D43C22semidirect
53. C4×#10621877C22semidirect
54. C4×#10621872C22semidirect
55. C4×C8×D43C22semidirect
56. #14582631C22semidirect
57. #14582631C22semidirect
58. #14582629C22semidirect
59. #14582629C22semidirect
60. #14582628C22semidirect
61. #14582628C22semidirect
62. D4⋊(C43⋊C8)C22semidirect
63. D4⋊(C43⋊C8)C22semidirect
64. D4⋊(C43⋊C8)C22semidirect
65. D4⋊(C43⋊C8)C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#431C22semidirect
70. C43×#423C22semidirect
71. C43×D4⋊C8C22semidirect
72. C43×D4⋊C8C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
245. #10621900M16semidirect
250. D4×D43M16semidirect
491. #1486D43semidirect
541. #431C2×D43semidirect
543. #423C2×D43semidirect
560. D4⋊C8C2×D43semidirect
561. D4⋊C8C2×D43semidirect
562. D4⋊C8C2×D43semidirect
563. D4⋊C8C2×D43semidirect
564. C43#17453semidirect

Maximal subgroups

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

subgroupindex
C4×#130633702
#191437092
#191435592
#191330382
#191330362
#191330322
#191330312
#191330302
#191330262
#191330182
#191329842
#191329792
#191329742
D4⋊C8×D432
C43×#14862
#1745343