Finite Group Databasebeta

← #515700

Subgroups — #515700

Order 512.

4026 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2416C211yesmaximal, characteristic
2C2×#2324C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic, complemented
4C2×#2290C211yesmaximal, characteristic, complemented
5C2×#2274C211yesmaximal, characteristic, complemented
6#14222C212yesmaximal, complemented
7#14206C212yesmaximal, complemented
8#14195C212yesmaximal, complemented
9#14176C212yesmaximal, complemented
10#14136C211yesmaximal, characteristic, complemented
11#14100C212yesmaximal, complemented
12#14068C212yesmaximal, complemented
13#14045C211yesmaximal, characteristic, complemented
14#14022C211yesmaximal, characteristic, complemented
15#14012C212yesmaximal, complemented
16#13998C211yesmaximal, characteristic, complemented
17#13974C211yesmaximal, characteristic, complemented
18#13970C212yesmaximal, complemented
19#13907C211yesmaximal, characteristic, complemented
20#13871C211yesmaximal, characteristic, complemented
21#13785C211yesmaximal, characteristic, complemented
22#13783C211yesmaximal, characteristic, complemented
23C4×#380C211yesmaximal, characteristic, complemented
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2212yes—
30C22×#117C2211yescharacteristic
31C22×#117C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2416C4116yescomplemented
35C2×#396C2212yes—
36C2×#394C2212yes—
37#2324—28no—
38C4×#121—28no—
39C2×#390C2212yes—
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2212yes—
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49#2290—28no—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2211yescharacteristic
53C2×#388C2211yescharacteristic
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#387C2211yescharacteristic
57C2×#387C2211yescharacteristic
58C2×#386C2212yes—
59C2×#386C2211yescharacteristic
60C2×#386C2212yes—
61C2×#386C2211yescharacteristic
62C2×#386C2212yes—
63C2×#385C2212yes—
64C2×#385C2211yescharacteristic
65C2×#385C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×#380C2211yescharacteristic
69C2×#380C2212yes—
70C2×#380C2211yescharacteristic
71#2274—28no—
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C4⋊C4C2212yes—
74C2×C4×C4⋊C4C2212yes—
75C2×C4×C4⋊C4C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C4⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2212yes—
81C2×C4×C22⋊C4C2211yescharacteristic
82C2×C4×C22⋊C4C2212yes—
83C2×C4×C22⋊C4C2212yes—
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2212yes—
86C2×#376C2211yescharacteristic
87#1444C2212yes—
88#1443C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1437C2212yes—
102#1437C2212yes—
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2212yes—
120C4⋊#95C2212yes—
121#1434C2212yes—
122#1434C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C4×#95C2212yes—
128C23×D4C2311yescharacteristic
129C23×D4C2312yes—
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2312yes—
138C2×#121—24no—
139C2×#121—24no—
140C2×#121—24no—
141C2×#121—24no—
142C2×#121—44no—
143C2×#121—44no—
144C2×#121C2×C418yes—
145C2×#121C2×C418yescomplemented
146C2×#121C2×C4116yescomplemented
147C2×C4×D4—24no—
148C2×C4×D4—24no—
149C2×C4×D4—24no—
150C2×C4×D4—28no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—44no—
154C2×C4×D4—44no—
155C2×C4×D4C2×C418yescomplemented
156C2×#117—24no—
157C2×#117—24no—
158C2×#117—24no—
159C2×#117—24no—
160C2×#117—24no—
161C2×#117D418yescomplemented
162C22×C4⋊C4—24no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4C2×C418yescomplemented
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C42—24no—
207C22×C42—24no—
208C22×C42—24no—
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2312yes—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222#396C2×C4116yescomplemented
223#394C2×C4116yescomplemented
224#390—24no—
225#390—24no—
226#390—28no—
227#390—24no—
228#390—44no—
229#390C2×C418yescomplemented
230#389—24no—
231#389—24no—
232#389—24no—
233#389C2×C418yescomplemented
234#388—28no—
235#388—24no—
236#388—24no—
237#388—28no—
238#388—44no—
239#388—44no—
240#387—24no—
241#387—24no—
242#386—28no—
243#386—24no—
244#386—24no—
245#386—28no—
246#386C2×C4116yescomplemented
247#385—28no—
248#385—24no—
249#385—24no—
250#380—24no—
251#380—24no—
252#380—24no—
253#380—44no—
254#380C2×C418yescomplemented
255C4×C4⋊C4—24no—
256C4×C4⋊C4—24no—
257C4×C4⋊C4—24no—
258C4×C4⋊C4—28no—
259C4×C4⋊C4—24no—
260C4×C4⋊C4—24no—
261C4×C4⋊C4—28no—
262C4×C4⋊C4D418yescomplemented
263C4×C22⋊C4—24no—
264C4×C22⋊C4—28no—
265C4×C22⋊C4—24no—
266C4×C22⋊C4—28no—
267C4×C22⋊C4—28no—
268C4×C22⋊C4—44no—
269#376—24no—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
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—
305C25C2412yes—
306C25C2411yescharacteristic
307C25C2411yescharacteristic
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—24no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—24no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—42no—
325C22×D4—42no—
326C22×D4—41no—
327C22×D4—41no—
328C22×D4—42no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4C22×C414yes—
333C22×D4C22×C414yes—
334C22×D4C22×C418yes—
335C22×D4C22×C418yes—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4C22×C414yes—
374C23×C4C22×C414yes—
375C23×C4C22×C418yes—
376C23×C4C2×D414yes—
377C23×C4#4114yes—
378C23×C4C2411yescharacteristic
379C23×C4C2412yes—
380C23×C4C2411yescharacteristic
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2412yes—
387C23×C4C2411yescharacteristic
388C23×C4C2411yescharacteristic
389C23×C4C2412yes—
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398#121—232no—
399#121—232no—
400#121—432no—
401C4×D4—232no—
402C4×D4—432no—
403C4×D4—416no—
404#117—232no—
405#117—232no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—232no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—41no—
438C2×C4⋊C4—41no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4C22×C414yes—
447C2×C4⋊C4C22×C418yes—
448C2×C4⋊C4C22×C414yes—
449C2×C4⋊C4C22×C414yes—
450C2×C4⋊C4C22×C418yes—
451C2×C4⋊C4C22×C414yes—
452C2×C4⋊C4C2×D414yes—
453C2×C4⋊C4C2×D414yes—
454C2×C4⋊C4C2×D414yes—
455C2×C4⋊C4C2×D414yes—
456C2×C4⋊C4#4114yes—
457C2×C4⋊C4#4114yes—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4C22×C414yes—
522C2×C22⋊C4C22×C414yes—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C418yes—
528C2×C22⋊C4C2×D414yes—
529C2×C22⋊C4C2×D414yes—
530C2×C42—24no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—24no—
534C2×C42—24no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—24no—
550C2×C42—24no—
551C2×C42—24no—
552C2×C42—24no—
553C2×C42—42no—
554C2×C42—42no—
555C2×C42—416no—
556C2×C42—42no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42C22×C414yes—
565C2×C42C2×D414yes—
566C2×C42C2×D418yes—
567C2×C42C2×D414yes—
568C2×C42C2×D414yes—
569C2×C42#4114yes—
570#95—22no—
571#95—22no—
572#95—22no—
573#95—22no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—22no—
579#95—22no—
580#95—24no—
581#95—22no—
582#95—22no—
583#95—24no—
584#95—22no—
585#95—22no—
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#95—42no—
602#95C22×C418yes—
603#95C22×C418yes—
604#95C2×D418yes—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24C23×C414yes—
644C24C23×C412yes—
645C24C23×C412yes—
646C24C22×D412yes—
647C24C2×#4112yes—
648C24H(5,𝔽2)12yes—
649C24H(5,𝔽2)12yes—
650C24C2511yescharacteristic
651C2×D4—28no—
652C2×D4—28no—
653C2×D4—216no—
654C2×D4—216no—
655C2×D4—216no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—48no—
660C2×D4—44no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—48no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—84no—
676C2×D4—84no—
677C2×D4—84no—
678C2×D4—84no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—28no—
702C22×C4—28no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—22no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—216no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—44no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—48no—
822C22×C4—84no—
823C22×C4—84no—
824C22×C4—84no—
825C22×C4—84no—
826C22×C4—84no—
827C22×C4—84no—
828C22×C4—84no—
829C22×C4—84no—
830C22×C4C4×D4116yescomplemented
831C22×C4C23×C412yes—
832C22×C4C23×C412yes—
833C22×C4C23×C414yes—
834C22×C4C23×C414yes—
835C22×C4C23×C412yes—
836C22×C4C23×C414yes—
837C22×C4C23×C412yes—
838C22×C4C23×C412yes—
839C22×C4C22×D412yes—
840C22×C4C22×D414yes—
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C22×D414yes—
844C22×C4C22×D412yes—
845C22×C4C22×D412yes—
846C22×C4C22×D412yes—
847C22×C4C22×D412yes—
848C22×C4C22×D412yes—
849C22×C4C22×D412yes—
850C22×C4C2×#4114yes—
851C22×C4C2×#4114yes—
852C22×C4C2×#4112yes—
853C22×C4C2×#4112yes—
854C22×C4C2×#4112yes—
855C22×C4C2×#4112yes—
856C22×C4C2×#4112yes—
857C22×C4C2×#4112yes—
858C22×C4C2×#4112yes—
859C22×C4H(5,𝔽2)12yes—
860C22×C42−1+412yes—
861C4⋊C4—216no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—28no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—48no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—48no—
873C4⋊C4—44no—
874C4⋊C4—44no—
875C4⋊C4—84no—
876C4⋊C4—84no—
877C4⋊C4C4×D4116yes—
878C22⋊C4—216no—
879C22⋊C4—28no—
880C22⋊C4—216no—
881C22⋊C4—28no—
882C22⋊C4—216no—
883C22⋊C4—216no—
884C22⋊C4—28no—
885C22⋊C4—28no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—84no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C42—216no—
903C42—28no—
904C42—28no—
905C42—48no—
906C42—44no—
907C42—44no—
908C42—44no—
909C42—44no—
910C42—84no—
911C42—84no—
912C42—84no—
913C42—84no—
914C42#121116yescomplemented
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23C2×C4×D414yes—
1019C23#51814yes—
1020C23C24×C411yescharacteristic
1021C23C23×D411yescharacteristic
1022C23C23×D411yescharacteristic
1023C23C22×#4111yescharacteristic
1024C23C22×#4111yescharacteristic
1025C23C22×#4111yescharacteristic
1026C23C22×#4111yescharacteristic
1027C23C2×H(5,𝔽2)11yescharacteristic
1028C23C2×H(5,𝔽2)11yescharacteristic
1029C23C2×H(5,𝔽2)11yescharacteristic
1030C23C2×2−1+411yescharacteristic
1031C23#58511yescharacteristic
1032C23#58511yescharacteristic
1033C23#58511yescharacteristic
1034C23#58511yescharacteristic
1035D4—432no—
1036D4—416no—
1037D4—416no—
1038D4—816no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—232no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—416no—
1098C2×C4—416no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—416no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—816no—
1173C2×C4—816no—
1174C2×C4C2×C4×D414yes—
1175C2×C4C2×C4×D418yes—
1176C2×C4C2×C4×D414yes—
1177C2×C4C2×C4×D414yes—
1178C2×C4C4×#4114yes—
1179C2×C4C2×#12114yes—
1180C2×C4C2×#12114yes—
1181C2×C4C2×#12114yes—
1182C2×C4#52514yes—
1183C2×C4#52914yes—
1184C2×C4#53214yes—
1185C22—24no—
1186C22—24no—
1187C22—24no—
1188C22—24no—
1189C22—24no—
1190C22—24no—
1191C22—42no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—82no—
1223C22—82no—
1224C22—82no—
1225C22—82no—
1226C22—82no—
1227C22—82no—
1228C22—82no—
1229C22—82no—
1230C22C22×C4×D411yescharacteristic
1231C22C22×C4×D411yescharacteristic
1232C22C2×C4×#4111yescharacteristic
1233C22C2×#51811yescharacteristic
1234C22#342811yescharacteristic
1235C22C4×H(5,𝔽2)11yescharacteristic
1236C22C4×2−1+411yescharacteristic
1237C22C22×#12111yescharacteristic
1238C22C2×#52511yescharacteristic
1239C22C2×#52911yescharacteristic
1240C22C2×#53211yescharacteristic
1241C22#348411yescharacteristic
1242C22#348711yescharacteristic
1243C22#348811yescharacteristic
1244C22#348811yescharacteristic
1245C22#348811yescharacteristic
1246C22#348811yescharacteristic
1247C22#348911yescharacteristic
1248C22#348911yescharacteristic
1249C22#349211yescharacteristic
1250C22#349311yescharacteristic
1251C22#349411yescharacteristic
1252C22#349411yescharacteristic
1253C22#349411yescharacteristic
1254C22#349411yescharacteristic
1255C22#351111yescharacteristic
1256C22#351211yescharacteristic
1257C22#351311yescharacteristic
1258C22#351311yescharacteristic
1259C22#351711yescharacteristic
1260C22#351811yescharacteristic
1261C22#351911yescharacteristic
1262C22#352111yescharacteristic
1263C22#352211yescharacteristic
1264C22#352411yescharacteristic
1265C4—24no—
1266C4—24no—
1267C4—24no—
1268C4—28no—
1269C4—44no—
1270C4—42no—
1271C4—44no—
1272C4—42no—
1273C4—42no—
1274C4—44no—
1275C4—42no—
1276C4—42no—
1277C4—42no—
1278C4—42no—
1279C4—44no—
1280C4—82no—
1281C4—81no—
1282C4—82no—
1283C4—81no—
1284C4C4×#12118yes—
1285C2—44no—
1286C2—44no—
1287C2—84no—
1288C2C2×C4×#12111yescharacteristic
1289C2#3420411yescharacteristic
1290C2#3426711yescharacteristic
1291C2#3429011yescharacteristic
1292C2#3429311yescharacteristic
1293C2#3429811yescharacteristic
1294C2#3430111yescharacteristic
1295C2#3551811yescharacteristic
1296C2#3552511yescharacteristic
1297C2#3556311yescharacteristic
1298C2#3556711yescharacteristic
1299C2#3556911yescharacteristic
1300C2#3558811yescharacteristic
1301C2#3558911yescharacteristic
1302C2#3560011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2416C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2324C2semidirect
3. C2×C4×#121C2semidirect
4. C2×#2290C2semidirect
5. C2×#2274C2semidirect
6. #14222C2semidirect
7. #14206C2semidirect
8. #14195C2semidirect
9. #14176C2semidirect
10. #14136C2semidirect
11. #14100C2semidirect
12. #14068C2semidirect
13. #14045C2semidirect
14. #14022C2semidirect
15. #14012C2semidirect
16. #13998C2semidirect
17. #13974C2semidirect
18. #13970C2semidirect
19. #13907C2semidirect
20. #13871C2semidirect
21. #13785C2semidirect
22. #13783C2semidirect
23. C4×#380C2semidirect
34. #2416C4semidirect
145. C2×#121C2×C4semidirect
146. C2×#121C2×C4semidirect
155. C2×C4×D4C2×C4semidirect
161. C2×#117D4semidirect
164. C22×C4⋊C4C2×C4semidirect
222. #396C2×C4semidirect
223. #394C2×C4semidirect
229. #390C2×C4semidirect
233. #389C2×C4semidirect
246. #386C2×C4semidirect
254. #380C2×C4semidirect
262. C4×C4⋊C4D4semidirect
830. C22×C4C4×D4semidirect
914. C42#121semidirect

Maximal subgroups

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

subgroupindex
C2×#24162
C2×#23242
C2×C4×#1212
C2×#22902
C2×#22742
#142222
#142062
#141952
#141762
#141362
#141002
#140682
#140452
#140222
#140122
#139982
#139742
#139702
#139072
#138712
#137852
#137832
C4×#3802