Finite Group Databasebeta

← #651343

Subgroups — #651343

Order 512.

5158 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#532C211yesmaximal, characteristic
2C2×#2550C211yesmaximal, characteristic, complemented
3C2×#2490C211yesmaximal, characteristic, complemented
4C2×#2454C211yesmaximal, characteristic, complemented
5#15785C212yesmaximal, complemented
6#15340C212yesmaximal, complemented
7#15321C212yesmaximal, complemented
8#15316C212yesmaximal, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15140C211yesmaximal, characteristic, complemented
11#15127C211yesmaximal, characteristic, complemented
12#15126C211yesmaximal, characteristic, complemented
13#14889C212yesmaximal, complemented
14#14824C212yesmaximal, complemented
15#14697C211yesmaximal, characteristic, complemented
16#14185C212yesmaximal, complemented
17#14053C211yesmaximal, characteristic, complemented
18#14018C211yesmaximal, characteristic, complemented
19#13998C211yesmaximal, characteristic, complemented
20#13979C211yesmaximal, characteristic, complemented
21#13937C212yesmaximal, complemented
22#13820C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C23×#41C2212yes—
25C2×#532—28no—
26C2×#532—28no—
27C2×#532—28no—
28C22×C4⋊Q8C2211yescharacteristic
29C22×#127C2211yescharacteristic
30C22×#125C2211yescharacteristic
31C22×#124C2212yes—
32C22×#121C2211yescharacteristic
33C22×#121C2212yes—
34C22×#121C2211yescharacteristic
35C22×C4×D4C2212yes—
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2550—28no—
40#2490—28no—
41#2454—28no—
42C2×#399C2212yes—
43C2×#398C2212yes—
44C2×#397C2212yes—
45C2×#396C2212yes—
46C2×#395C2212yes—
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2212yes—
50C2×#394C2212yes—
51C2×#394C2212yes—
52C2×#394C2212yes—
53C2×#391C2212yes—
54C2×#391C2212yes—
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#390C2211yescharacteristic
63C2×#390C2212yes—
64C2×#390C2212yes—
65C2×#389C2211yescharacteristic
66C2×#389C2211yescharacteristic
67C2×#389C2212yes—
68C2×#389C2211yescharacteristic
69C2×#389C2211yescharacteristic
70C2×#388C2212yes—
71C2×#385C2211yescharacteristic
72C2×#385C2212yes—
73C2×#385C2211yescharacteristic
74C2×#385C2212yes—
75C2×#385C2212yes—
76C2×#382C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#380C2212yes—
80C2×C4×C4⋊C4C2211yescharacteristic
81C2×C4×C4⋊C4C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2212yes—
87#1446C2212yes—
88#1441C2212yes—
89#1440C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1437C2212yes—
109#1436C2211yescharacteristic
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2211yescharacteristic
114#1436C2211yescharacteristic
115#1436C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117C4⋊#95C2211yescharacteristic
118C4⋊#95C2211yescharacteristic
119C4⋊#95C2211yescharacteristic
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2211yescharacteristic
127C4×#95C2211yescharacteristic
128C4×#95C2211yescharacteristic
129C22×#41—28no—
130C22×#41—28no—
131C22×#41—28no—
132C22×#41—28no—
133C22×#41—44no—
134C22×#41—44no—
135C22×#41—44no—
136C23×Q8C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148#532—2128no—
149C2×C4⋊Q8—24no—
150C2×C4⋊Q8—24no—
151C2×C4⋊Q8D418yes—
152C2×#127—24no—
153C2×#127—24no—
154C2×#127—24no—
155C2×#125—24no—
156C2×#125—24no—
157C2×#125—24no—
158C2×#124—28no—
159C2×#124—28no—
160C2×#124—28no—
161C2×#121—24no—
162C2×#121—28no—
163C2×#121—24no—
164C2×#121—24no—
165C2×#121—28no—
166C2×#121—24no—
167C2×#121—24no—
168C2×#121—28no—
169C2×#121D418yes—
170C2×C4×D4—24no—
171C2×C4×D4—28no—
172C2×C4×D4—24no—
173C2×C4×D4—28no—
174C2×C4×D4—24no—
175C2×C4×D4—24no—
176C2×C4×D4—28no—
177C2×C4×D4—24no—
178C2×C4×D4D418yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C42—24no—
223C22×C42—24no—
224C22×C42—24no—
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2311yescharacteristic
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2312yes—
234C22×C42C2312yes—
235#399—28no—
236#398—28no—
237#397—28no—
238#396—28no—
239#395—28no—
240#394—28no—
241#394—28no—
242#394—44no—
243#394—44no—
244#394—44no—
245#394—44no—
246#391—28no—
247#391—44no—
248#390—24no—
249#390—24no—
250#390—24no—
251#390—24no—
252#390—28no—
253#390—24no—
254#390—24no—
255#390—24no—
256#390—24no—
257#390—44no—
258#389—24no—
259#389—28no—
260#389—24no—
261#389—24no—
262#389—24no—
263#388—28no—
264#385—28no—
265#385—24no—
266#385—24no—
267#385—44no—
268#385—44no—
269#382—24no—
270#380—28no—
271#380—24no—
272#380—24no—
273C4×C4⋊C4—24no—
274C4×C4⋊C4—24no—
275C4×C4⋊C4—24no—
276C4×C4⋊C4—24no—
277C4×C22⋊C4—24no—
278C4×C22⋊C4—24no—
279C4×C22⋊C4—44no—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2311yescharacteristic
314C25C2412yes—
315C25C2412yes—
316C25C2411yescharacteristic
317C2×#41—264no—
318C2×#41—432no—
319C2×#41—432no—
320C2×#41—432no—
321C2×#41—432no—
322C2×#41—432no—
323C2×#41—432no—
324C22×Q8—24no—
325C22×Q8—24no—
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—42no—
329C22×Q8—42no—
330C22×Q8C2×D418yes—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4C2×D414yes—
371C22×D4C2×D414yes—
372C22×D4C2×D418yes—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—41no—
400C23×C4—41no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4C2×D414yes—
406C23×C4C2×D418yes—
407C23×C4#4114yes—
408C23×C4C2411yescharacteristic
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C4⋊Q8—232no—
429#127—232no—
430#125—416no—
431#124—264no—
432#121—232no—
433#121—264no—
434#121—232no—
435C4×D4—264no—
436C4×D4—232no—
437C4×D4—232no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—41no—
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⋊C4C2×D414yes—
484C2×C4⋊C4C2×D418yes—
485C2×C4⋊C4C2×D414yes—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D414yes—
488C2×C4⋊C4#4114yescomplemented
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
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—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
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—42no—
565C2×C22⋊C4C2×D418yes—
566C2×C22⋊C4C2×D418yes—
567C2×C42—232no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—22no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—22no—
581C2×C42—22no—
582C2×C42—22no—
583C2×C42—22no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—24no—
590C2×C42—24no—
591C2×C42—42no—
592C2×C42—42no—
593C2×C42—42no—
594C2×C42—42no—
595C2×C42C2×D414yes—
596C2×C42C2×D414yes—
597C2×C42#4114yescomplemented
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—22no—
614#95—22no—
615#95—24no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—24no—
621#95—24no—
622#95—22no—
623#95—24no—
624#95—22no—
625#95—41no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95#4114yescomplemented
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24C22×D414yes—
673C24C22×D414yes—
674C24C22×D412yes—
675C24C2×#4112yes—
676C24H(5,𝔽2)12yes—
677C24C2511yescharacteristic
678#41—4256no—
679C2×Q8—216no—
680C2×Q8—216no—
681C2×Q8—48no—
682C2×Q8—48no—
683C2×Q8—48no—
684C2×Q8—48no—
685C2×Q8—48no—
686C2×D4—216no—
687C2×D4—216no—
688C2×D4—216no—
689C2×D4—216no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—216no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—28no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—48no—
706C2×D4—48no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—48no—
711C2×D4—48no—
712C2×D4—48no—
713C2×D4—48no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—48no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—28no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—216no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—216no—
803C22×C4—216no—
804C22×C4—28no—
805C22×C4—28no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—48no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4C22×D412yes—
877C22×C4C22×D414yes—
878C22×C4C22×D412yes—
879C22×C4C22×D414yes—
880C22×C4C22×D414yes—
881C22×C4C22×D414yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C2×#4112yes—
889C22×C4C2×#4112yes—
890C22×C4C2×#4112yes—
891C22×C4C2×#4114yes—
892C22×C4C2×#4112yes—
893C22×C4C2×#4112yes—
894C22×C4C2×#4112yes—
895C22×C4C2×#4112yes—
896C22×C4C2×#4112yes—
897C22×C4C2×#4112yes—
898C22×C4H(5,𝔽2)12yes—
899C22×C4H(5,𝔽2)12yes—
900C22×C4H(5,𝔽2)12yes—
901C22×C42−1+412yes—
902C22×C42−1+412yes—
903C4⋊C4—216no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—84no—
917C4⋊C4—84no—
918C4⋊C4—84no—
919C4⋊C4#120116yes—
920C22⋊C4—28no—
921C22⋊C4—216no—
922C22⋊C4—216no—
923C22⋊C4—216no—
924C22⋊C4—216no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—44no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C42—28no—
947C42—28no—
948C42—28no—
949C42—28no—
950C42—28no—
951C42—44no—
952C42—44no—
953C42—44no—
954C42—84no—
955C42—84no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
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—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23#54614yes—
1061C23C23×D411yescharacteristic
1062C23C23×D411yescharacteristic
1063C23C23×D411yescharacteristic
1064C23C22×#4111yescharacteristic
1065C23C22×#4111yescharacteristic
1066C23C22×#4111yescharacteristic
1067C23C22×#4111yescharacteristic
1068C23C2×H(5,𝔽2)11yescharacteristic
1069C23C2×H(5,𝔽2)11yescharacteristic
1070C23C2×H(5,𝔽2)11yescharacteristic
1071C23C2×H(5,𝔽2)11yescharacteristic
1072C23C2×2−1+411yescharacteristic
1073C23C2×2−1+411yescharacteristic
1074C23#58511yescharacteristic
1075C23#58511yescharacteristic
1076Q8—432no—
1077D4—432no—
1078D4—432no—
1079D4—432no—
1080D4—432no—
1081D4—416no—
1082D4—416no—
1083C2×C4—232no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
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—24no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—24no—
1132C2×C4—432no—
1133C2×C4—416no—
1134C2×C4—432no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—416no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—41no—
1217C2×C4C2×#12018yes—
1218C2×C4C2×#12014yes—
1219C2×C4#53214yes—
1220C2×C4#53614yes—
1221C2×C4#54614yes—
1222C2×C4#54614yes—
1223C2×C4#54714yes—
1224C2×C4#54714yes—
1225C2×C4#54814yes—
1226C2×C4#54814yes—
1227C2×C4#55014yes—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22C22×#12011yescharacteristic
1274C22C2×#53211yescharacteristic
1275C22#344411yescharacteristic
1276C22C2×#53611yescharacteristic
1277C22#346011yescharacteristic
1278C22C2×#54611yescharacteristic
1279C22C2×#54611yescharacteristic
1280C22C2×#54611yescharacteristic
1281C22C2×#54711yescharacteristic
1282C22C2×#54711yescharacteristic
1283C22C2×#54811yescharacteristic
1284C22C2×#54811yescharacteristic
1285C22C2×#55011yescharacteristic
1286C22D4×#4111yescharacteristic
1287C22D4×#4111yescharacteristic
1288C22#348011yescharacteristic
1289C22#348111yescharacteristic
1290C22#348411yescharacteristic
1291C22#348411yescharacteristic
1292C22#348411yescharacteristic
1293C22#348711yescharacteristic
1294C22#348811yescharacteristic
1295C22#348811yescharacteristic
1296C22#349411yescharacteristic
1297C22#350711yescharacteristic
1298C22#350811yescharacteristic
1299C22#351111yescharacteristic
1300C22#351111yescharacteristic
1301C22#351711yescharacteristic
1302C22#351911yescharacteristic
1303C22#352211yescharacteristic
1304C22#354711yescharacteristic
1305C22#354811yescharacteristic
1306C22#355411yescharacteristic
1307C22#355911yescharacteristic
1308C4—24no—
1309C4—24no—
1310C4—28no—
1311C4—24no—
1312C4—42no—
1313C4—44no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—44no—
1319C4—42no—
1320C4—81no—
1321C4—81no—
1322C4—82no—
1323C4—82no—
1324C4—81no—
1325C4—81no—
1326C4—82no—
1327C4#243218yes—
1328C2—44no—
1329C2—84no—
1330C2—84no—
1331C2C2×#243211yescharacteristic
1332C2#3488911yescharacteristic
1333C2#3557111yescharacteristic
1334C2#3613911yescharacteristic
1335C2#3615011yescharacteristic
1336C2#3615211yescharacteristic
1337C2#3642911yescharacteristic
1338C2#3775611yescharacteristic
1339C2#3779211yescharacteristic
1340C2#3947011yescharacteristic
1341C2#3987711yescharacteristic
1342C2#5905711yescharacteristic
1343C2#5907811yescharacteristic
1344C2#5911011yescharacteristic
1345C2#5911711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#532C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2550C2semidirect
3. C2×#2490C2semidirect
4. C2×#2454C2semidirect
5. #15785C2semidirect
6. #15340C2semidirect
7. #15321C2semidirect
8. #15316C2semidirect
9. #15219C2semidirect
10. #15140C2semidirect
11. #15127C2semidirect
12. #15126C2semidirect
13. #14889C2semidirect
14. #14824C2semidirect
15. #14697C2semidirect
16. #14185C2semidirect
17. #14053C2semidirect
18. #14018C2semidirect
19. #13998C2semidirect
20. #13979C2semidirect
21. #13937C2semidirect
22. #13820C2semidirect
23. C4×#385C2semidirect
488. C2×C4⋊C4#41semidirect
597. C2×C42#41semidirect
631. #95#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5322
C2×#25502
C2×#24902
C2×#24542
#157852
#153402
#153212
#153162
#152192
#151402
#151272
#151262
#148892
#148242
#146972
#141852
#140532
#140182
#139982
#139792
#139372
#138202
C4×#3852