Finite Group Databasebeta

← #687084

Subgroups — #687084

Order 512.

4185 conjugacy classes of subgroups.

The subgroup lattice has 1338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2C2×#2412C211yesmaximal, characteristic, complemented
3C2×#2412C211yesmaximal, characteristic, complemented
4C2×#2424C211yesmaximal, characteristic
5C22×#396C211yesmaximal, characteristic, complemented
6C2×#2322C211yesmaximal, characteristic, complemented
7#16549C212yesmaximal, complemented
8#16467C212yesmaximal, complemented
9#15648C212yesmaximal, complemented
10#15439C212yesmaximal, complemented
11#15335C212yesmaximal, complemented
12#15316C212yesmaximal, complemented
13#15131C212yesmaximal, complemented
14#15073C211yesmaximal, characteristic, complemented
15#14911C211yesmaximal, characteristic, complemented
16#14911C211yesmaximal, characteristic, complemented
17#14754C212yesmaximal, complemented
18#14719C211yesmaximal, characteristic, complemented
19#14256C211yesmaximal, characteristic, complemented
20#14043C211yesmaximal, characteristic, complemented
21#13996C211yesmaximal, characteristic, complemented
22#13968C211yesmaximal, characteristic, complemented
23C22⋊C42C211yesmaximal, characteristic, complemented
24C22×#123C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×#120C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37C23×C22⋊C4C2211yescharacteristic
38C23×C22⋊C4C2211yescharacteristic
39C23×C22⋊C4C2211yescharacteristic
40#2501—28no—
41#2424—28no—
42#2412—28no—
43#2412—28no—
44C2×#399C2212yescomplemented
45C2×#399C2212yescomplemented
46C2×#397C2212yes—
47C2×#397C2212yes—
48C2×#396—28no—
49C2×#396C2211yescharacteristic
50C2×#396C2212yes—
51C2×#396C2212yes—
52C2×#396C2212yes—
53C2×#396C2212yes—
54C2×#394C2211yescharacteristic
55C2×#394C2212yes—
56C2×#394C2211yescharacteristic
57C2×#394C2212yes—
58C2×#394C2212yescomplemented
59C2×#392C2211yescharacteristic
60#2322—28no—
61C2×#390C2211yescharacteristic
62C2×#390C2212yescomplemented
63C2×#389C2212yescomplemented
64C2×#389C2212yescomplemented
65C2×#388C2211yescharacteristic
66C2×#388C2212yescomplemented
67C2×#387C2212yescomplemented
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2212yes—
71C2×#386C2211yescharacteristic
72C2×#386C2211yescharacteristic
73C2×#386C2211yescharacteristic
74C2×#386C2212yes—
75C2×#386C2211yescharacteristic
76C2×#385C2211yescharacteristic
77C2×#385C2211yescharacteristic
78C2×#385C2211yescharacteristic
79C2×#385C2212yescomplemented
80C2×#384C2212yescomplemented
81C2×#381C2211yescharacteristic
82C2×#381C2211yescharacteristic
83C2×#381C2211yescharacteristic
84C2×#381C2211yescharacteristic
85C2×#380C2212yes—
86C2×#380C2212yes—
87C2×#379C2211yescharacteristic
88C2×C4×C22⋊C4C2211yescharacteristic
89C2×C4×C22⋊C4C2211yescharacteristic
90C2×C4×C22⋊C4C2212yes—
91C22×#95C2211yescharacteristic
92#1445C2212yescomplemented
93#1444C2212yescomplemented
94#1442C2212yescomplemented
95#1442C2212yescomplemented
96#1441C2212yescomplemented
97#1441C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1441C2212yescomplemented
103#1440C2212yescomplemented
104#1439C2212yes—
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1437C2212yes—
118#1437C2212yes—
119#1437C2212yescomplemented
120#1436C2212yescomplemented
121#1436C2212yescomplemented
122C4⋊#95C2212yescomplemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2211yescharacteristic
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C2×#123—24no—
146C2×#123—24no—
147C2×#123—24no—
148C2×#123—24no—
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—24no—
152C2×#123—24no—
153C2×#123—24no—
154C2×#123—42no—
155C2×#123—42no—
156C2×#123D418yescomplemented
157C2×#121—24no—
158C2×#121—24no—
159C2×#121—24no—
160C2×#121—44no—
161C2×#121—42no—
162C2×#120—24no—
163C2×#120—24no—
164C2×#120—24no—
165C2×#120—24no—
166C2×#120—42no—
167C2×#120—42no—
168C2×C4×D4—24no—
169C2×C4×D4—24no—
170C2×C4×D4—42no—
171C22×C4⋊C4—24no—
172C22×C4⋊C4—24no—
173C22×C4⋊C4—24no—
174C22×C4⋊C4—24no—
175C22×C4⋊C4—24no—
176C22×C4⋊C4—44no—
177C22×C4⋊C4—42no—
178C22×C4⋊C4—42no—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2312yes—
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C22⋊C4—24no—
196C22×C22⋊C4—24no—
197C22×C22⋊C4—24no—
198C22×C22⋊C4—24no—
199C22×C22⋊C4—24no—
200C22×C22⋊C4—24no—
201C22×C22⋊C4—24no—
202C22×C22⋊C4—44no—
203C22×C22⋊C4—42no—
204C22×C22⋊C4—42no—
205C22×C22⋊C4D418yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2311yescharacteristic
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2311yescharacteristic
238C22×C22⋊C4C2311yescharacteristic
239C22×C22⋊C4C2311yescharacteristic
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2312yes—
243#399—28no—
244#399—28no—
245#397—28no—
246#397—28no—
247#396—28no—
248#396—28no—
249#396—28no—
250#396—28no—
251#396—24no—
252#394—28no—
253#394—28no—
254#394—24no—
255#394—24no—
256#394—44no—
257#392—24no—
258#390—24no—
259#390—28no—
260#389—28no—
261#389—44no—
262#388—24no—
263#388—28no—
264#387—28no—
265#386—24no—
266#386—24no—
267#386—24no—
268#386—24no—
269#386—28no—
270#386—24no—
271#386—28no—
272#386—42no—
273#385—24no—
274#385—28no—
275#385—24no—
276#385D418yescomplemented
277#384—28no—
278#381—24no—
279#381—24no—
280#381—24no—
281#381—42no—
282#380—28no—
283#380—28no—
284#379—24no—
285C4×C22⋊C4—24no—
286C4×C22⋊C4—24no—
287C4×C22⋊C4—44no—
288C2×#95—24no—
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C25—24no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25C2×D414yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—41no—
362C22×D4—41no—
363C22×D4—41no—
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×D4C2×D414yes—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—22no—
401C23×C4—24no—
402C23×C4—22no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—41no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4C2×D414yes—
417C23×C4C2×D414yes—
418C23×C4C2×D414yes—
419C23×C4C2×D414yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2412yes—
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438#123—232no—
439#123—416no—
440#123—416no—
441#123—416no—
442#121—416no—
443#121—416no—
444#120—416no—
445#120—416no—
446C4×D4—416no—
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—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
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—41no—
484C2×C4⋊C4—41no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—416no—
489C2×C4⋊C4—416no—
490C2×C4⋊C4—416no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4—42no—
493C2×C4⋊C4—42no—
494C2×C4⋊C4C2×D418yes—
495C2×C4⋊C4C2×D418yes—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
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—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—416no—
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—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—416no—
572C2×C22⋊C4—416no—
573C2×C22⋊C4—416no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4C2×D414yes—
587C2×C22⋊C4C2×D414yes—
588C2×C22⋊C4C2×D414yes—
589C2×C22⋊C4C2×D418yes—
590C2×C22⋊C4C2×D414yes—
591C2×C22⋊C4C2×D414yes—
592C2×C22⋊C4C2×D414yes—
593C2×C22⋊C4C2×D414yes—
594C2×C22⋊C4#4114yes—
595C2×C22⋊C4#4114yes—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—24no—
599C2×C42—24no—
600C2×C42—24no—
601C2×C42—41no—
602C2×C42—42no—
603C2×C42—42no—
604C2×C42—42no—
605#95—24no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—22no—
618#95—24no—
619#95—22no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—24no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95—42no—
628#95—42no—
629#95—42no—
630#95—42no—
631#95—42no—
632#95—42no—
633#95—42no—
634#95C2×D418yes—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—28no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—22no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—21no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—28no—
670C24—28no—
671C24—28no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24C22×D412yes—
703C24C22×D412yes—
704C24C22×D412yes—
705C24C22×D412yes—
706C24C22×D412yes—
707C24C22×D412yes—
708C24C2×#4112yes—
709C24C2×#4112yes—
710C24H(5,𝔽2)12yes—
711C24H(5,𝔽2)12yes—
712C242−1+414yes—
713C24C2511yescharacteristic
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—48no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—82no—
742C2×D4—84no—
743C2×D4—84no—
744C2×D4—82no—
745C2×D4—82no—
746C2×D4—84no—
747C2×D4—82no—
748C2×D4—82no—
749C2×D4—84no—
750C2×D4—84no—
751C2×D4—84no—
752C2×D4—84no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—44no—
857C22×C4—48no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—48no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—82no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D414yes—
900C22×C4C22×D414yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D414yes—
904C22×C4C22×D414yes—
905C22×C4C22×D412yes—
906C22×C4C2×#4114yes—
907C22×C4C2×#4114yes—
908C22×C4H(5,𝔽2)14yes—
909C4⋊C4—216no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C4⋊C4—84no—
924C4⋊C4—82no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—216no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—82no—
953C22⋊C4—84no—
954C22⋊C4—84no—
955C22⋊C4—84no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4#121116yescomplemented
959C42—48no—
960C42—44no—
961C42—84no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—24no—
1001C23—24no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—416no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
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—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—88no—
1074C23—88no—
1075C23—88no—
1076C23—816no—
1077C23—816no—
1078C23—816no—
1079C23—816no—
1080C23C2×#12114yes—
1081C23#53214yes—
1082C23#53614yes—
1083C23#54014yes—
1084C23D4214yes—
1085C23D4214yes—
1086C23#54614yes—
1087C23#55014yes—
1088C23C23×D411yescharacteristic
1089C23C23×D411yescharacteristic
1090C23C23×D411yescharacteristic
1091C23C22×#4111yescharacteristic
1092C23C22×#4111yescharacteristic
1093C23C2×H(5,𝔽2)12yes—
1094C23C2×H(5,𝔽2)11yescharacteristic
1095C23C2×H(5,𝔽2)11yescharacteristic
1096C23C2×2−1+412yes—
1097C23#58512yes—
1098C23#58512yes—
1099D4—416no—
1100D4—88no—
1101D4—88no—
1102D4—88no—
1103D4—88no—
1104D4—88no—
1105D4—88no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—416no—
1142C2×C4—416no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—416no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—816no—
1218C2×C4—88no—
1219C2×C4—88no—
1220C2×C4—88no—
1221C2×C4—88no—
1222C2×C4C2×#12118yes—
1223C2×C4#53414yes—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—28no—
1229C22—24no—
1230C22—24no—
1231C22—28no—
1232C22—28no—
1233C22—28no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—42no—
1238C22—44no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—44no—
1256C22—44no—
1257C22—832no—
1258C22—81no—
1259C22—81no—
1260C22—82no—
1261C22—82no—
1262C22—81no—
1263C22—81no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—82no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22#242818yes—
1280C22C22×#12111yescharacteristic
1281C22C2×#53211yescharacteristic
1282C22C2×#53411yescharacteristic
1283C22C2×#53611yescharacteristic
1284C22C2×#54011yescharacteristic
1285C22C2×D4211yescharacteristic
1286C22C2×D4211yescharacteristic
1287C22C2×#54611yescharacteristic
1288C22C2×#55011yescharacteristic
1289C22#348511yescharacteristic
1290C22#348511yescharacteristic
1291C22#348812yes—
1292C22#348912yes—
1293C22#348912yes—
1294C22#349612yes—
1295C22#352012yes—
1296C22#352012yes—
1297C22#352112yes—
1298C22#352112yes—
1299C22#353412yes—
1300C22#353512yes—
1301C22#353512yes—
1302C22#354212yes—
1303C4—24no—
1304C4—28no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C4—42no—
1309C4—44no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—44no—
1314C4—82no—
1315C4—81no—
1316C4—81no—
1317C4—82no—
1318C4—82no—
1319C4—81no—
1320C4—82no—
1321C2—28no—
1322C2—44no—
1323C2—82no—
1324C2—82no—
1325C2—161no—
1326C2C2×#242811yescharacteristic
1327C2#3508511yescharacteristic
1328C2#3546711yescharacteristic
1329C2#3582112yes—
1330C2#3764611yescharacteristic
1331C2#3764711yescharacteristic
1332C2#3764711yescharacteristic
1333C2#3933811yescharacteristic
1334C2#4088912yes—
1335C2#4302912yes—
1336C2#4397912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2424C2
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×#2501C2semidirect
2. C2×#2412C2semidirect
3. C2×#2412C2semidirect
5. C22×#396C2semidirect
6. C2×#2322C2semidirect
7. #16549C2semidirect
8. #16467C2semidirect
9. #15648C2semidirect
10. #15439C2semidirect
11. #15335C2semidirect
12. #15316C2semidirect
13. #15131C2semidirect
14. #15073C2semidirect
15. #14911C2semidirect
16. #14911C2semidirect
17. #14754C2semidirect
18. #14719C2semidirect
19. #14256C2semidirect
20. #14043C2semidirect
21. #13996C2semidirect
22. #13968C2semidirect
23. C22⋊C42C2semidirect
44. C2×#399C22semidirect
45. C2×#399C22semidirect
58. C2×#394C22semidirect
62. C2×#390C22semidirect
63. C2×#389C22semidirect
64. C2×#389C22semidirect
66. C2×#388C22semidirect
67. C2×#387C22semidirect
79. C2×#385C22semidirect
80. C2×#384C22semidirect
92. #1445C22semidirect
93. #1444C22semidirect
94. #1442C22semidirect
95. #1442C22semidirect
96. #1441C22semidirect
97. #1441C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
102. #1441C22semidirect
103. #1440C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
119. #1437C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. C4⋊#95C22semidirect
128. C22⋊#95C22semidirect
156. C2×#123D4semidirect
276. #385D4semidirect
958. C22⋊C4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24122
C2×#24242
C22×#3962
C2×#23222
#165492
#164672
#156482
#154392
#153352
#153162
#151312
#150732
#149112
#147542
#147192
#142562
#140432
#139962
#139682
C22⋊C422