Finite Group Databasebeta

← #519716

Subgroups — #519716

Order 512.

5204 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2412C211yesmaximal, characteristic
2C2×#2358C211yesmaximal, characteristic
3C2×C4×#123C211yesmaximal, characteristic, complemented
4C22×#385C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
6#14705C211yesmaximal, characteristic, complemented
7#14696C211yesmaximal, characteristic, complemented
8#14694C211yesmaximal, characteristic
9#14195C212yesmaximal, complemented
10#14183C212yesmaximal, complemented
11#14182C212yesmaximal, complemented
12#14177C212yesmaximal, complemented
13#14044C211yesmaximal, characteristic, complemented
14#14028C212yesmaximal, complemented
15#14019C212yesmaximal, complemented
16#14016C211yesmaximal, characteristic, complemented
17#13996C211yesmaximal, characteristic, complemented
18#13992C211yesmaximal, characteristic, complemented
19#13869C211yesmaximal, characteristic, complemented
20#13813C212yesmaximal, complemented
21C22⋊C4×C4⋊C4C212yesmaximal, complemented
22C22⋊C42C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#120C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2212yes—
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35C23×C42C2211yescharacteristic
36#2412C4116yescomplemented
37C2×#397C2212yes—
38C2×#394C2212yes—
39#2358—28no—
40C4×#123—28no—
41C2×#390C2211yescharacteristic
42C2×#388C2211yescharacteristic
43C2×#388C2211yescharacteristic
44C2×#388C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#387C2212yescomplemented
47C2×#386C2211yescharacteristic
48C2×#386C2211yescharacteristic
49C2×#386C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2211yescharacteristic
54C2×#386C2211yescharacteristic
55C2×#386C2212yes—
56C2×#385—28no—
57C2×#385C2211yescharacteristic
58C2×#385C2211yescharacteristic
59C2×#385C2212yes—
60C2×#385C2212yes—
61C2×#385C2211yescharacteristic
62C2×#385C2211yescharacteristic
63C2×#385C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#385C2211yescharacteristic
66C2×#381C2211yescharacteristic
67C2×#381C2211yescharacteristic
68C2×#381C2211yescharacteristic
69C2×#380C2212yes—
70C2×#379C2211yescharacteristic
71C2×C4×C4⋊C4C2212yescomplemented
72C2×C4×C4⋊C4C2212yescomplemented
73C2×C4×C22⋊C4—28no—
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2212yes—
77C2×C4×C22⋊C4C2212yes—
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2212yes—
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2212yescomplemented
84C22×#95C2211yescharacteristic
85C22×#95C2211yescharacteristic
86C22×#95C2212yes—
87#1445C2212yescomplemented
88#1443C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1441C2212yescomplemented
93#1440C2212yes—
94#1440C2212yes—
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1437C2212yes—
98#1437C2212yes—
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107#1436C2212yescomplemented
108#1436C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111C4⋊#95C2212yescomplemented
112C4⋊#95C2212yescomplemented
113#1434C2212yescomplemented
114#1434C2212yescomplemented
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2212yes—
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2212yescomplemented
127C4×#95C2212yescomplemented
128C26C2311yescharacteristic
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C24×C4—24no—
133C24×C4—28no—
134C24×C4—24no—
135C24×C4—44no—
136C24×C4—42no—
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2312yes—
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2311yescharacteristic
149C2×#123—24no—
150C2×#123—24no—
151C2×#123C2×C418yescomplemented
152C2×#120—24no—
153C2×#120—24no—
154C2×#120C2×C418yes—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—28no—
159C2×C4×D4—42no—
160C22×C4⋊C4—28no—
161C22×C4⋊C4—28no—
162C22×C4⋊C4—44no—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—28no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4C2×C418yescomplemented
181C22×C22⋊C4C2×C418yescomplemented
182C22×C22⋊C4D418yes—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C42—24no—
211C22×C42—24no—
212C22×C42—24no—
213C22×C42—44no—
214C22×C42—42no—
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224#397C2×C4116yescomplemented
225#394C2×C4116yescomplemented
226#390—24no—
227#388—28no—
228#388—24no—
229#388—24no—
230#388—44no—
231#387—28no—
232#386—24no—
233#386—24no—
234#386—28no—
235#386—24no—
236#386—24no—
237#386—44no—
238#386—42no—
239#386C2×C418yescomplemented
240#386C2×C4116yescomplemented
241#385—24no—
242#385—24no—
243#385—28no—
244#385—24no—
245#385—24no—
246#385—24no—
247#385—28no—
248#385C2×C418yescomplemented
249#385D418yescomplemented
250#381—24no—
251#381—42no—
252#381C2×C418yescomplemented
253#380C2×C4116yescomplemented
254#379—24no—
255C4×C4⋊C4—28no—
256C4×C4⋊C4—44no—
257C4×C22⋊C4—24no—
258C4×C22⋊C4—24no—
259C4×C22⋊C4—28no—
260C4×C22⋊C4—28no—
261C4×C22⋊C4—28no—
262C4×C22⋊C4—28no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4—28no—
266C4×C22⋊C4—28no—
267C2×#95—24no—
268C2×#95—24no—
269C2×#95—28no—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C25—22no—
309C25—22no—
310C25—24no—
311C25—24no—
312C25—22no—
313C25—22no—
314C25—42no—
315C25—42no—
316C25C22×C414yes—
317C25C2×D414yes—
318C25#4114yes—
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4C22×C414yes—
338C22×D4C22×C414yes—
339C22×D4C22×C414yes—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—232no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—24no—
355C23×C4—22no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—432no—
397C23×C4—41no—
398C23×C4—41no—
399C23×C4—42no—
400C23×C4—41no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—416no—
404C23×C4—416no—
405C23×C4—432no—
406C23×C4C22×C414yes—
407C23×C4C22×C418yes—
408C23×C4C22×C414yes—
409C23×C4C2×D414yes—
410C23×C4C2×D414yes—
411C23×C4C2×D414yes—
412C23×C4#4118yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432#123—232no—
433#120—232no—
434C4×D4—416no—
435C4×D4—416no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—432no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4C22×C418yescomplemented
460C2×C4⋊C4C22×C418yescomplemented
461C2×C4⋊C4C2×D418yes—
462C2×C22⋊C4—232no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—232no—
485C2×C22⋊C4—232no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—416no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—41no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—41no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C414yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C414yes—
528C2×C22⋊C4C22×C414yes—
529C2×C22⋊C4C22×C414yes—
530C2×C22⋊C4C22×C414yes—
531C2×C22⋊C4C22×C418yescomplemented
532C2×C22⋊C4C22×C418yescomplemented
533C2×C22⋊C4C2×D414yes—
534C2×C22⋊C4C2×D414yes—
535C2×C22⋊C4C2×D414yes—
536C2×C22⋊C4C2×D414yes—
537C2×C22⋊C4C2×D414yes—
538C2×C22⋊C4C2×D414yes—
539C2×C22⋊C4#4114yes—
540C2×C22⋊C4#4118yes—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—24no—
545C2×C42—24no—
546C2×C42—24no—
547C2×C42—24no—
548C2×C42—24no—
549C2×C42—24no—
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—24no—
554C2×C42—24no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—22no—
558C2×C42—41no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42—416no—
566C2×C42—416no—
567C2×C42—42no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—22no—
584#95—22no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95C22×C418yescomplemented
602#95C22×C418yescomplemented
603#95C22×C418yescomplemented
604#95C22×C418yescomplemented
605#95C2×D418yes—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—22no—
616C24—28no—
617C24—216no—
618C24—28no—
619C24—28no—
620C24—28no—
621C24—216no—
622C24—28no—
623C24—28no—
624C24—28no—
625C24—28no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—21no—
631C24—22no—
632C24—21no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—44no—
645C24—48no—
646C24—44no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24C4×D4116yes—
657C24C23×C412yes—
658C24C23×C412yes—
659C24C23×C412yes—
660C24C23×C412yes—
661C24C22×D412yes—
662C24C22×D412yes—
663C24C22×D412yes—
664C24C22×D412yes—
665C24C2×#4112yes—
666C24C2×#4112yes—
667C24C2×#4112yes—
668C24C2×#4112yes—
669C24C2×#4114yes—
670C24C2×#4114yes—
671C24H(5,𝔽2)12yes—
672C242−1+412yes—
673C24C2511yescharacteristic
674C2×D4—28no—
675C2×D4—28no—
676C2×D4—28no—
677C2×D4—216no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—48no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—48no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—84no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—216no—
694C22×C4—28no—
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—216no—
710C22×C4—216no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—216no—
716C22×C4—28no—
717C22×C4—216no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—216no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—216no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—44no—
803C22×C4—48no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—44no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—44no—
810C22×C4—48no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—4128no—
828C22×C4—48no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—48no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—48no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—82no—
847C22×C4—84no—
848C22×C4—82no—
849C22×C4—82no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4C23×C412yes—
853C22×C4C23×C414yes—
854C22×C4C23×C414yes—
855C22×C4C23×C414yes—
856C22×C4C23×C412yes—
857C22×C4C23×C412yes—
858C22×C4C23×C414yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C22×D412yes—
863C22×C4C22×D414yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×D414yes—
867C22×C4C2×#4114yes—
868C22×C4C2×#4114yes—
869C22×C4C2×#4114yes—
870C22×C4C2×#4114yes—
871C22×C4C2×#4114yes—
872C22×C4H(5,𝔽2)14yes—
873C4⋊C4—216no—
874C4⋊C4—216no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—44no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—82no—
882C22⋊C4—216no—
883C22⋊C4—28no—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—216no—
891C22⋊C4—216no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—82no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4C4×D4116yescomplemented
908C22⋊C4#123116yescomplemented
909C42—48no—
910C42—48no—
911C42—48no—
912C42—48no—
913C42—48no—
914C42—48no—
915C42—44no—
916C42—44no—
917C42—82no—
918C23—22no—
919C23—24no—
920C23—22no—
921C23—24no—
922C23—24no—
923C23—22no—
924C23—22no—
925C23—24no—
926C23—22no—
927C23—24no—
928C23—24no—
929C23—22no—
930C23—22no—
931C23—24no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—24no—
943C23—24no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—232no—
953C23—22no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—22no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—232no—
968C23—22no—
969C23—22no—
970C23—24no—
971C23—22no—
972C23—24no—
973C23—416no—
974C23—416no—
975C23—432no—
976C23—432no—
977C23—416no—
978C23—432no—
979C23—416no—
980C23—432no—
981C23—416no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—41no—
991C23—41no—
992C23—42no—
993C23—41no—
994C23—42no—
995C23—41no—
996C23—41no—
997C23—42no—
998C23—41no—
999C23—42no—
1000C23—42no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23C2×C4×D414yes—
1009C23C2×C4×D414yes—
1010C23C2×C4×D414yes—
1011C23C2×C4×D414yes—
1012C23C4×#4118yes—
1013C23#52014yes—
1014C23C2×#12314yes—
1015C23#52514yes—
1016C23#52918yes—
1017C23D4214yes—
1018C23#54714yes—
1019C23#54814yes—
1020C23#55314yes—
1021C23C24×C411yescharacteristic
1022C23C23×D411yescharacteristic
1023C23C23×D411yescharacteristic
1024C23C22×#4111yescharacteristic
1025C23C22×#4111yescharacteristic
1026C23C22×#4112yes—
1027C23C22×#4112yes—
1028C23C2×H(5,𝔽2)11yescharacteristic
1029C23C2×H(5,𝔽2)12yes—
1030C23C2×2−1+411yescharacteristic
1031C23#58512yes—
1032D4—416no—
1033D4—416no—
1034D4—88no—
1035C2×C4—232no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—432no—
1086C2×C4—416no—
1087C2×C4—416no—
1088C2×C4—432no—
1089C2×C4—432no—
1090C2×C4—416no—
1091C2×C4—416no—
1092C2×C4—416no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—41no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—41no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—42no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—41no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
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—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—88no—
1154C2×C4—88no—
1155C2×C4—88no—
1156C2×C4C2×C4×D418yes—
1157C2×C4C2×#12314yes—
1158C2×C4C2×#12314yes—
1159C2×C4#54618yes—
1160C22—24no—
1161C22—24no—
1162C22—28no—
1163C22—28no—
1164C22—24no—
1165C22—28no—
1166C22—28no—
1167C22—24no—
1168C22—24no—
1169C22—28no—
1170C22—28no—
1171C22—24no—
1172C22—24no—
1173C22—24no—
1174C22—24no—
1175C22—24no—
1176C22—28no—
1177C22—28no—
1178C22—24no—
1179C22—24no—
1180C22—24no—
1181C22—24no—
1182C22—24no—
1183C22—464no—
1184C22—42no—
1185C22—44no—
1186C22—44no—
1187C22—42no—
1188C22—44no—
1189C22—42no—
1190C22—44no—
1191C22—42no—
1192C22—42no—
1193C22—44no—
1194C22—42no—
1195C22—42no—
1196C22—44no—
1197C22—81no—
1198C22—82no—
1199C22—81no—
1200C22—82no—
1201C22—81no—
1202C22—81no—
1203C22C4×#12318yescomplemented
1204C22#236118yes—
1205C22C22×C4×D411yescharacteristic
1206C22C22×C4×D411yescharacteristic
1207C22C2×C4×#4112yes—
1208C22C2×#52011yescharacteristic
1209C22C4×H(5,𝔽2)12yes—
1210C22C22×#12311yescharacteristic
1211C22C2×#52511yescharacteristic
1212C22C2×#52912yes—
1213C22C2×D4211yescharacteristic
1214C22C2×#54612yes—
1215C22C2×#54711yescharacteristic
1216C22C2×#54811yescharacteristic
1217C22D4×#4112yes—
1218C22C2×#55311yescharacteristic
1219C22#347512yes—
1220C22#348112yes—
1221C22#348411yescharacteristic
1222C22#348511yescharacteristic
1223C22#349012yes—
1224C22#349512yes—
1225C22#350512yes—
1226C22#351312yes—
1227C22#352012yes—
1228C4—28no—
1229C4—28no—
1230C4—24no—
1231C4—24no—
1232C4—44no—
1233C4—42no—
1234C4—44no—
1235C4—42no—
1236C4—44no—
1237C4—42no—
1238C4—44no—
1239C4—42no—
1240C4—42no—
1241C4—42no—
1242C4—42no—
1243C4—81no—
1244C4—82no—
1245C4—82no—
1246C4—81no—
1247C2—28no—
1248C2—28no—
1249C2—44no—
1250C2—82no—
1251C2C2×C4×#12311yescharacteristic
1252C2C2×#236111yescharacteristic
1253C2C4×#54612yes—
1254C2#3426411yescharacteristic
1255C2#3429612yes—
1256C2D4×#12311yescharacteristic
1257C2#3609811yescharacteristic
1258C2#3610812yes—
1259C2#3623711yescharacteristic
1260C2#3624312yes—
1261C2#3634111yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#120C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×C4×#123C2semidirect
4. C22×#385C2semidirect
5. C22×C4×C22⋊C4C2semidirect
6. #14705C2semidirect
7. #14696C2semidirect
9. #14195C2semidirect
10. #14183C2semidirect
11. #14182C2semidirect
12. #14177C2semidirect
13. #14044C2semidirect
14. #14028C2semidirect
15. #14019C2semidirect
16. #14016C2semidirect
17. #13996C2semidirect
18. #13992C2semidirect
19. #13869C2semidirect
20. #13813C2semidirect
21. C22⋊C4×C4⋊C4C2semidirect
22. C22⋊C42C2semidirect
23. C4×#385C2semidirect
36. #2412C4semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
46. C2×#387C22semidirect
71. C2×C4×C4⋊C4C22semidirect
72. C2×C4×C4⋊C4C22semidirect
83. C2×C4×C22⋊C4C22semidirect
87. #1445C22semidirect
88. #1443C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
92. #1441C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. #1436C22semidirect
108. #1436C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. C4⋊#95C22semidirect
112. C4⋊#95C22semidirect
113. #1434C22semidirect
114. #1434C22semidirect
126. C22⋊#95C22semidirect
127. C4×#95C22semidirect
151. C2×#123C2×C4semidirect
180. C22×C22⋊C4C2×C4semidirect
181. C22×C22⋊C4C2×C4semidirect
224. #397C2×C4semidirect
225. #394C2×C4semidirect
239. #386C2×C4semidirect
240. #386C2×C4semidirect
248. #385C2×C4semidirect
249. #385D4semidirect
252. #381C2×C4semidirect
253. #380C2×C4semidirect
459. C2×C4⋊C4C22×C4semidirect
460. C2×C4⋊C4C22×C4semidirect
531. C2×C22⋊C4C22×C4semidirect
532. C2×C22⋊C4C22×C4semidirect
601. #95C22×C4semidirect
602. #95C22×C4semidirect
603. #95C22×C4semidirect
604. #95C22×C4semidirect
907. C22⋊C4C4×D4semidirect
908. C22⋊C4#123semidirect
1203. C22C4×#123semidirect

Maximal subgroups

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

subgroupindex
C2×#24122
C2×#23582
C2×C4×#1232
C22×#3852
C22×C4×C22⋊C42
#147052
#146962
#146942
#141952
#141832
#141822
#141772
#140442
#140282
#140192
#140162
#139962
#139922
#138692
#138132
C22⋊C4×C4⋊C42
C22⋊C422
C4×#3852