Finite Group Databasebeta

← #989816

Subgroups — #989816

Order 512.

3886 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2C2×#2545C211yesmaximal, characteristic, complemented
3C2×#2432C211yesmaximal, characteristic, complemented
4C2×#2432C211yesmaximal, characteristic, complemented
5C2×#2407C211yesmaximal, characteristic
6C2×#2429C211yesmaximal, characteristic, complemented
7#17103C212yesmaximal, complemented
8#16323C212yesmaximal, complemented
9#16312C212yesmaximal, complemented
10#16290C212yesmaximal, complemented
11#15651C212yesmaximal, complemented
12#15392C212yesmaximal, complemented
13#15345C212yesmaximal, complemented
14#15215C211yesmaximal, characteristic, complemented
15#15215C211yesmaximal, characteristic, complemented
16#15190C211yesmaximal, characteristic, complemented
17#15179C211yesmaximal, characteristic, complemented
18#15178C211yesmaximal, characteristic, complemented
19#14405C212yesmaximal, complemented
20#14141C211yesmaximal, characteristic, complemented
21#14021C211yesmaximal, characteristic, complemented
22#13969C211yesmaximal, characteristic, complemented
23C4×#394C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4⋊Q8C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38#2545—28no—
39#2542—28no—
40#2432—28no—
41#2432—28no—
42#2429—28no—
43#2407—28no—
44C2×#399C2212yes—
45C2×#399C2212yes—
46C2×#398C2212yes—
47C2×#396C2212yes—
48C2×#396C2212yes—
49C2×#396C2212yes—
50C2×#394C2211yescharacteristic
51C2×#394C2212yes—
52C2×#394C2212yes—
53C2×#394C2212yes—
54C2×#394C2212yes—
55C2×#394C2212yes—
56C2×#392C2212yes—
57C2×#391C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#391C2211yescharacteristic
60C2×#391C2211yescharacteristic
61C2×#391C2211yescharacteristic
62C2×#391C2211yescharacteristic
63C2×#390C2212yes—
64C2×#390C2211yescharacteristic
65C2×#390C2211yescharacteristic
66C2×#390C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#389C2212yes—
69C2×#388C2212yes—
70C2×#388C2212yes—
71C2×#388C2212yes—
72C2×#388C2212yes—
73C2×#386C2212yes—
74C2×#385C2212yes—
75C2×#385C2212yes—
76C2×#385C2212yes—
77C2×#385C2212yes—
78C2×#385C2212yes—
79C2×#384C2212yes—
80C2×#380C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic
87#1444C2212yes—
88#1444C2212yes—
89#1444C2212yes—
90#1444C2212yes—
91#1444C2212yes—
92#1444C2212yes—
93#1443C2212yes—
94#1442C2212yes—
95#1442C2211yescharacteristic
96#1442C2212yes—
97#1441C2211yescharacteristic
98#1441C2212yes—
99#1441C2212yes—
100#1440C2211yescharacteristic
101#1440C2211yescharacteristic
102#1440C2212yes—
103#1440C2212yes—
104#1439C2212yes—
105#1439C2212yes—
106#1439C2211yescharacteristic
107#1439C2211yescharacteristic
108#1439C2212yes—
109#1439C2212yes—
110#1439C2212yes—
111#1439C2212yes—
112#1439C2212yes—
113#1439C2212yes—
114#1439C2212yes—
115#1438C2211yescharacteristic
116#1438C2212yes—
117#1438C2212yes—
118#1438C2212yes—
119#1438C2212yes—
120#1437C2212yes—
121#1437C2212yes—
122#1436C2212yes—
123#1436C2212yes—
124C4⋊#95C2211yescharacteristic
125C4⋊#95C2211yescharacteristic
126C4⋊#95C2211yescharacteristic
127#1434C2212yes—
128C4×#95C2211yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—42no—
133C22×#41—42no—
134C22×#41—42no—
135C22×#41—42no—
136C23×Q8C2311yescharacteristic
137C23×Q8C2311yescharacteristic
138C23×Q8C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C23×D4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C2×C4⋊Q8—24no—
147C2×C4⋊Q8—24no—
148C2×C4⋊Q8—24no—
149C2×C4⋊Q8—24no—
150C2×C4⋊Q8—24no—
151C2×C4⋊Q8—42no—
152C2×C4⋊Q8—42no—
153C2×C4⋊Q8—42no—
154C2×C4⋊Q8—42no—
155C2×#124—24no—
156C2×#124—24no—
157C2×#124—24no—
158C2×#124—24no—
159C2×#124—42no—
160C2×#124—42no—
161C2×C22⋊Q8—24no—
162C2×C22⋊Q8—24no—
163C2×C22⋊Q8—24no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—24no—
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—24no—
168C2×C22⋊Q8—42no—
169C2×C22⋊Q8—42no—
170C2×C22⋊Q8—42no—
171C2×C22⋊Q8—42no—
172C2×C22⋊Q8—42no—
173C2×C22⋊Q8—42no—
174C2×C22⋊Q8—42no—
175C2×C22⋊Q8D418yescomplemented
176C2×#121—24no—
177C2×#121—42no—
178C2×#121—42no—
179C2×C4×Q8—24no—
180C2×C4×Q8—24no—
181C2×C4×Q8—42no—
182C2×C4×D4—24no—
183C2×C4×D4—24no—
184C2×C4×D4—42no—
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2312yes—
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239#399—28no—
240#399—28no—
241#398—28no—
242#396—28no—
243#396—28no—
244#396—28no—
245#394—28no—
246#394—28no—
247#394—28no—
248#394—28no—
249#394—28no—
250#394—24no—
251#392—28no—
252#391—24no—
253#391—24no—
254#391—24no—
255#391—42no—
256#391—42no—
257#391D418yescomplemented
258#390—24no—
259#390—24no—
260#390—28no—
261#390D418yes—
262#389—24no—
263#389—28no—
264#388—28no—
265#388—28no—
266#388—28no—
267#388—28no—
268#386—28no—
269#385—28no—
270#385—28no—
271#385—28no—
272#385—28no—
273#385—28no—
274#384—28no—
275#380—24no—
276C4×C4⋊C4—24no—
277C4×C4⋊C4—24no—
278C4×C22⋊C4—24no—
279C4×C22⋊C4—24no—
280C4×C22⋊C4—24no—
281C4×C22⋊C4—42no—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2311yescharacteristic
313C2×#95C2311yescharacteristic
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2311yescharacteristic
317C25C2412yes—
318C25C2411yescharacteristic
319C25C2411yescharacteristic
320C2×#41—416no—
321C2×#41—416no—
322C2×#41—416no—
323C2×#41—416no—
324C2×#41—416no—
325C2×#41—416no—
326C2×#41—416no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8C2×D414yes—
347C22×Q8C2×D414yes—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4C2×D414yes—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4C2×D414yes—
397C23×C4C2412yes—
398C23×C4C2411yescharacteristic
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C23×C4C2412yes—
403C23×C4C2412yes—
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C4⋊Q8—416no—
418C4⋊Q8—416no—
419C4⋊Q8—416no—
420#124—416no—
421#124—416no—
422C22⋊Q8—416no—
423C22⋊Q8—416no—
424C22⋊Q8—416no—
425C22⋊Q8—416no—
426C22⋊Q8—416no—
427#121—416no—
428C4×Q8—416no—
429C4×D4—416no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—41no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D414yes—
488C2×C4⋊C4C2×D414yes—
489C2×C4⋊C4C2×D418yes—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4C2×D418yes—
569C2×C22⋊C4C2×D418yes—
570C2×C22⋊C4C2×D418yes—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—24no—
583C2×C42—24no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—42no—
589C2×C42—42no—
590C2×C42C2×D414yes—
591C2×C42C2×D414yes—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—42no—
614#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—41no—
619#95—41no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95C2×D418yes—
625#95C2×D418yes—
626#95#4114yescomplemented
627C24—21no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—22no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24C22×D414yes—
670C24C22×D412yes—
671C242−1+412yes—
672C24C2511yescharacteristic
673#41—4128no—
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—28no—
679C2×Q8—28no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—28no—
698C2×D4—28no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—44no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—84no—
719C2×D4—84no—
720C2×D4—84no—
721C2×D4—84no—
722C2×D4—84no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—21no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4C22×D414yes—
862C22×C4C22×D414yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×D412yes—
867C22×C4C22×D414yes—
868C22×C4C22×D414yes—
869C22×C4C22×D414yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C22×D412yes—
873C22×C4C22×D412yes—
874C22×C4C2×#4112yes—
875C22×C4C2×#4112yes—
876C22×C4C2×#4112yes—
877C22×C4H(5,𝔽2)12yes—
878C22×C4H(5,𝔽2)12yes—
879C22×C4H(5,𝔽2)12yes—
880C22×C4H(5,𝔽2)12yes—
881C22×C42−1+412yes—
882C22×C42−1+412yes—
883C22×C42−1+412yes—
884C4⋊C4—28no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C22⋊C4—28no—
905C22⋊C4—216no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—48no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—44no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—84no—
931C42—28no—
932C42—28no—
933C42—48no—
934C42—48no—
935C42—44no—
936C42—44no—
937C42—44no—
938C23—22no—
939C23—24no—
940C23—22no—
941C23—24no—
942C23—24no—
943C23—22no—
944C23—24no—
945C23—22no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—24no—
953C23—22no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—41no—
960C23—42no—
961C23—42no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—42no—
971C23—41no—
972C23—41no—
973C23—42no—
974C23—41no—
975C23—42no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—42no—
981C23—42no—
982C23—41no—
983C23—42no—
984C23—42no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—42no—
991C23—42no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—41no—
1005C23—41no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—42no—
1014C23—41no—
1015C23—42no—
1016C23—42no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—42no—
1029C23—41no—
1030C23—41no—
1031C23—42no—
1032C23—41no—
1033C23—42no—
1034C23—42no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—42no—
1040C23—42no—
1041C23—41no—
1042C23—41no—
1043C23C23×D411yescharacteristic
1044C23C23×D411yescharacteristic
1045C23C23×D411yescharacteristic
1046C23C22×#4111yescharacteristic
1047C23C2×H(5,𝔽2)11yescharacteristic
1048C23C2×H(5,𝔽2)11yescharacteristic
1049C23C2×H(5,𝔽2)11yescharacteristic
1050C23C2×H(5,𝔽2)11yescharacteristic
1051C23C2×2−1+411yescharacteristic
1052C23C2×2−1+411yescharacteristic
1053C23C2×2−1+411yescharacteristic
1054C23C2×2−1+411yescharacteristic
1055C23#58511yescharacteristic
1056C23#58511yescharacteristic
1057C23#58511yescharacteristic
1058Q8—416no—
1059Q8—416no—
1060Q8—88no—
1061D4—416no—
1062D4—432no—
1063D4—416no—
1064D4—816no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—432no—
1111C2×C4—42no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—42no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—416no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—88no—
1200C2×C4#53414yes—
1201C2×C4#53514yes—
1202C2×C4#53514yes—
1203C2×C4D4214yes—
1204C2×C4D4214yes—
1205C2×C4D4214yes—
1206C2×C4#54714yes—
1207C2×C4#56014yes—
1208C22—44no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—44no—
1221C22—42no—
1222C22—42no—
1223C22—44no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—81no—
1230C22—82no—
1231C22—81no—
1232C22—81no—
1233C22—82no—
1234C22—81no—
1235C22—81no—
1236C22—82no—
1237C22—81no—
1238C22—81no—
1239C22—82no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—82no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—82no—
1249C22—81no—
1250C22—82no—
1251C22—81no—
1252C22—82no—
1253C22C2×#53411yescharacteristic
1254C22C2×#53511yescharacteristic
1255C22C2×#53511yescharacteristic
1256C22C2×D4211yescharacteristic
1257C22C2×D4211yescharacteristic
1258C22C2×D4211yescharacteristic
1259C22C2×#54711yescharacteristic
1260C22D4×#4111yescharacteristic
1261C22D4×#4111yescharacteristic
1262C22#348511yescharacteristic
1263C22#348611yescharacteristic
1264C22#348611yescharacteristic
1265C22#348911yescharacteristic
1266C22#348911yescharacteristic
1267C22#348911yescharacteristic
1268C22#349711yescharacteristic
1269C22#349711yescharacteristic
1270C22#349911yescharacteristic
1271C22#351111yescharacteristic
1272C22#351111yescharacteristic
1273C22#351711yescharacteristic
1274C22#352011yescharacteristic
1275C22C2×#56011yescharacteristic
1276C22#354111yescharacteristic
1277C22#354111yescharacteristic
1278C22#354711yescharacteristic
1279C22#355211yescharacteristic
1280C22#355211yescharacteristic
1281C22#355211yescharacteristic
1282C22#355411yescharacteristic
1283C22#355411yescharacteristic
1284C22#356111yescharacteristic
1285C22#356111yescharacteristic
1286C22#356211yescharacteristic
1287C22#356211yescharacteristic
1288C4—24no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—44no—
1294C4—44no—
1295C4—42no—
1296C4—42no—
1297C4—44no—
1298C4—42no—
1299C4—44no—
1300C4—44no—
1301C4—42no—
1302C4—81no—
1303C4—81no—
1304C4—82no—
1305C4—81no—
1306C4—82no—
1307C4#266918yes—
1308C2—82no—
1309C2—84no—
1310C2—82no—
1311C2#3948811yescharacteristic
1312C2#3985411yescharacteristic
1313C2#3988911yescharacteristic
1314C2#4268011yescharacteristic
1315C2#4278711yescharacteristic
1316C2#4280011yescharacteristic
1317C2#4509111yescharacteristic
1318C2#4524811yescharacteristic
1319C2#4533211yescharacteristic
1320C2#4562811yescharacteristic
1321C2C2×#266911yescharacteristic
1322C2#5304711yescharacteristic
1323C2#5900211yescharacteristic
1324C2#5906611yescharacteristic
1325C2#5912811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2542C2semidirect
2. C2×#2545C2semidirect
3. C2×#2432C2semidirect
4. C2×#2432C2semidirect
6. C2×#2429C2semidirect
7. #17103C2semidirect
8. #16323C2semidirect
9. #16312C2semidirect
10. #16290C2semidirect
11. #15651C2semidirect
12. #15392C2semidirect
13. #15345C2semidirect
14. #15215C2semidirect
15. #15215C2semidirect
16. #15190C2semidirect
17. #15179C2semidirect
18. #15178C2semidirect
19. #14405C2semidirect
20. #14141C2semidirect
21. #14021C2semidirect
22. #13969C2semidirect
23. C4×#394C2semidirect
175. C2×C22⋊Q8D4semidirect
257. #391D4semidirect
626. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#25452
C2×#24322
C2×#24072
C2×#24292
#171032
#163232
#163122
#162902
#156512
#153922
#153452
#152152
#151902
#151792
#151782
#144052
#141412
#140212
#139692
C4×#3942