Finite Group Databasebeta

← #612494

Subgroups — #612494

Order 512.

5142 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic, complemented
2C2×#2404C211yesmaximal, characteristic
3C2×#2297C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊C4C211yesmaximal, characteristic, complemented
5#14946C211yesmaximal, characteristic, complemented
6#14945C211yesmaximal, characteristic, complemented
7#14797C212yesmaximal, complemented
8#14768C212yesmaximal, complemented
9#14760C212yesmaximal, complemented
10#14751C212yesmaximal, complemented
11#14718C211yesmaximal, characteristic, complemented
12#14718C211yesmaximal, characteristic, complemented
13#14705C211yesmaximal, characteristic, complemented
14#14696C211yesmaximal, characteristic, complemented
15#14696C211yesmaximal, characteristic, complemented
16#14694C211yesmaximal, characteristic, complemented
17#14182C212yesmaximal, complemented
18#14181C212yesmaximal, complemented
19#14096C212yesmaximal, complemented
20#13984C212yesmaximal, complemented
21#13962C211yesmaximal, characteristic, complemented
22#13956C211yesmaximal, characteristic, complemented
23#13868C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2212yes—
27C22×#120C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C42C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2849—28no—
35#2404—28no—
36C2×#394C2212yes—
37C2×#394C2212yes—
38C2×#393C2211yescharacteristic
39C2×#393C2211yescharacteristic
40C2×#392C2211yescharacteristic
41C2×#392C2211yescharacteristic
42#2297—28no—
43C2×#391C2212yescomplemented
44C2×#390C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#388C2212yescomplemented
47C2×#386C2211yescharacteristic
48C2×#386C2212yes—
49C2×#386C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#386C2211yescharacteristic
52C2×#386C2211yescharacteristic
53C2×#386C2211yescharacteristic
54C2×#386C2211yescharacteristic
55C2×#386C2211yescharacteristic
56C2×#386C2211yescharacteristic
57C2×#386C2212yes—
58C2×#386C2211yescharacteristic
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#385C2211yescharacteristic
65C2×#385C2212yes—
66C2×#385C2211yescharacteristic
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#381C2212yes—
70C2×#381C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#379C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×C4×C22⋊C4—28no—
75C2×C4×C22⋊C4C2212yes—
76C2×C4×C22⋊C4C2212yes—
77C2×C4×C22⋊C4C2212yes—
78C2×C4×C22⋊C4C2212yes—
79C2×C4×C22⋊C4C2212yescomplemented
80C2×C4×C22⋊C4C2212yescomplemented
81C22×#95C2211yescharacteristic
82C22×#95C2211yescharacteristic
83#1446C2212yescomplemented
84#1445C2212yescomplemented
85#1445C2212yescomplemented
86#1443C2212yescomplemented
87#1443C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yescomplemented
103#1437C2212yes—
104#1437C2212yes—
105#1437C2212yescomplemented
106#1437C2212yescomplemented
107#1436C2212yescomplemented
108#1436C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113C4⋊#95C2212yescomplemented
114#1434C2212yescomplemented
115#1434C2212yescomplemented
116#1434C2212yescomplemented
117C22⋊#95C2212yes—
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C22×#41—24no—
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—42no—
134C22×#41—42no—
135C23×Q8C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C23×D4C2311yescharacteristic
142C23×D4C2311yescharacteristic
143C24×C4—24no—
144C24×C4—28no—
145C24×C4—24no—
146C24×C4—44no—
147C24×C4—42no—
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2312yes—
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C2×#123—28no—
159C2×#123—28no—
160C2×#123—44no—
161C2×#120—24no—
162C2×#120—24no—
163C2×#120—24no—
164C2×#120—24no—
165C2×#120—42no—
166C2×#120—42no—
167C2×#117—24no—
168C2×#117—24no—
169C2×#117—42no—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4D418yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C42—24no—
213C22×C42—24no—
214C22×C42—24no—
215C22×C42—44no—
216C22×C42—42no—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2312yes—
221C22×C42C2312yes—
222#394—28no—
223#394—28no—
224#393—24no—
225#393—24no—
226#392—24no—
227#392—24no—
228#391—28no—
229#390—28no—
230#388—44no—
231#388—44no—
232#386—24no—
233#386—24no—
234#386—24no—
235#386—24no—
236#386—24no—
237#386—24no—
238#386—28no—
239#386—28no—
240#386—24no—
241#386—24no—
242#386—24no—
243#386—24no—
244#386—24no—
245#386—44no—
246#386—42no—
247#386—42no—
248#386D418yescomplemented
249#385—24no—
250#385—24no—
251#385—28no—
252#385—42no—
253#385—42no—
254#381—24no—
255#381—24no—
256#381—28no—
257#379—24no—
258#379—42no—
259C4×C22⋊C4—28no—
260C4×C22⋊C4—28no—
261C4×C22⋊C4—28no—
262C4×C22⋊C4—28no—
263C4×C22⋊C4—28no—
264C4×C22⋊C4—28no—
265C2×#95—24no—
266C2×#95—24no—
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
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—
305C25—24no—
306C25—22no—
307C25—22no—
308C25—24no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—42no—
314C25—42no—
315C25C2×D414yes—
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C25C2411yescharacteristic
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C2×#41—232no—
322C2×#41—416no—
323C2×#41—416no—
324C2×#41—416no—
325C2×#41—416no—
326C2×#41—416no—
327C2×#41—416no—
328C22×Q8—22no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—41no—
334C22×Q8—41no—
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—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—41no—
365C22×D4—41no—
366C22×D4—41no—
367C22×D4—41no—
368C22×D4—41no—
369C22×D4—41no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4C2×D414yes—
375C22×D4#4114yes—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—232no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—24no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—24no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—24no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—41no—
426C23×C4—41no—
427C23×C4—41no—
428C23×C4—41no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—432no—
432C23×C4—416no—
433C23×C4—416no—
434C23×C4—432no—
435C23×C4C2×D414yes—
436C23×C4C2×D414yes—
437C23×C4C2×D414yes—
438C23×C4#4114yes—
439C23×C4#4114yes—
440C23×C4#4118yescomplemented
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2411yescharacteristic
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2412yes—
459#123—432no—
460#120—416no—
461#120—416no—
462#117—416no—
463C2×C4⋊C4—24no—
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—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C22⋊C4—232no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—232no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
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—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
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×D414yes—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4C2×D418yes—
571C2×C22⋊C4#4118yescomplemented
572C2×C42—24no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—24no—
576C2×C42—24no—
577C2×C42—24no—
578C2×C42—24no—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—24no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—416no—
588C2×C42—416no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—24no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
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—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95C2×D418yes—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—216no—
632C24—216no—
633C24—28no—
634C24—28no—
635C24—28no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—22no—
669C24—22no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—22no—
675C24—22no—
676C24—44no—
677C24—44no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—44no—
689C24—44no—
690C24—44no—
691C24—44no—
692C24C22×D412yes—
693C24C22×D412yes—
694C24C22×D412yes—
695C24C22×D412yes—
696C24C22×D412yes—
697C24C2×#4112yes—
698C24C2×#4114yes—
699C24C2×#4114yes—
700C24C2×#4112yes—
701C24C2×#4112yes—
702C24C2×#4112yes—
703C24H(5,𝔽2)12yes—
704C24H(5,𝔽2)12yes—
705C24C2511yescharacteristic
706#41—4128no—
707C2×Q8—28no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—44no—
711C2×Q8—44no—
712C2×Q8—44no—
713C2×Q8—44no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
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—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—82no—
748C2×D4—82no—
749C2×D4—82no—
750C2×D4—82no—
751C2×D4—84no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—216no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—216no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—216no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—216no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—216no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—44no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—4128no—
898C22×C4—48no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—48no—
903C22×C4—44no—
904C22×C4—48no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—48no—
912C22×C4#123116yescomplemented
913C22×C4C22×D412yes—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D414yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D414yes—
920C22×C4C2×#4112yes—
921C22×C4C2×#4114yes—
922C22×C4C2×#4114yes—
923C22×C4C2×#4114yes—
924C22×C4C2×#4112yes—
925C22×C4C2×#4112yes—
926C22×C4C2×#4112yes—
927C22×C4C2×#4112yes—
928C22×C4C2×#4114yes—
929C22×C4H(5,𝔽2)14yes—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—84no—
934C4⋊C4—84no—
935C22⋊C4—216no—
936C22⋊C4—216no—
937C22⋊C4—28no—
938C22⋊C4—28no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—216no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—82no—
960C22⋊C4—82no—
961C22⋊C4—82no—
962C22⋊C4—82no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C42—48no—
968C42—48no—
969C42—48no—
970C42—48no—
971C42—48no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—232no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—22no—
1001C23—22no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—22no—
1021C23—24no—
1022C23—24no—
1023C23—416no—
1024C23—416no—
1025C23—416no—
1026C23—416no—
1027C23—432no—
1028C23—416no—
1029C23—432no—
1030C23—432no—
1031C23—432no—
1032C23—41no—
1033C23—41no—
1034C23—416no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23—41no—
1044C23—41no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—41no—
1068C23—42no—
1069C23—41no—
1070C23—41no—
1071C23—42no—
1072C23—41no—
1073C23—42no—
1074C23—42no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23C2×#12314yes—
1090C23#52514yes—
1091C23#52514yes—
1092C23#52514yes—
1093C23#53814yes—
1094C23D4214yes—
1095C23#54614yes—
1096C23#54614yes—
1097C23#55114yes—
1098C23C23×D411yescharacteristic
1099C23C23×D411yescharacteristic
1100C23C22×#4111yescharacteristic
1101C23C22×#4111yescharacteristic
1102C23C22×#4112yes—
1103C23C22×#4112yes—
1104C23C22×#4111yescharacteristic
1105C23C2×H(5,𝔽2)11yescharacteristic
1106C23C2×H(5,𝔽2)11yescharacteristic
1107C23C2×H(5,𝔽2)12yes—
1108C23#58512yes—
1109Q8—416no—
1110D4—416no—
1111D4—416no—
1112D4—416no—
1113D4—88no—
1114D4—88no—
1115D4—88no—
1116D4—88no—
1117C2×C4—232no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—232no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—432no—
1162C2×C4—432no—
1163C2×C4—416no—
1164C2×C4—416no—
1165C2×C4—416no—
1166C2×C4—416no—
1167C2×C4—416no—
1168C2×C4—416no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4C2×#12314yes—
1239C2×C4C2×#12314yes—
1240C2×C4#54618yes—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—28no—
1245C22—24no—
1246C22—28no—
1247C22—24no—
1248C22—28no—
1249C22—28no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—464no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—44no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—44no—
1268C22—42no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—44no—
1277C22—42no—
1278C22—42no—
1279C22—44no—
1280C22—44no—
1281C22—42no—
1282C22—44no—
1283C22—42no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—82no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—81no—
1296C22#241818yes—
1297C22C22×#12311yescharacteristic
1298C22C2×#52511yescharacteristic
1299C22C2×#52511yescharacteristic
1300C22C2×#52511yescharacteristic
1301C22#344412yes—
1302C22#344412yes—
1303C22C2×#53811yescharacteristic
1304C22#346012yes—
1305C22C2×D4211yescharacteristic
1306C22C2×#54612yes—
1307C22C2×#54611yescharacteristic
1308C22C2×#54611yescharacteristic
1309C22D4×#4112yes—
1310C22C2×#55111yescharacteristic
1311C22#347512yes—
1312C22#348112yes—
1313C22#348411yescharacteristic
1314C22#348511yescharacteristic
1315C22#349012yes—
1316C22#349412yes—
1317C22#350612yes—
1318C22#351312yes—
1319C22#351912yes—
1320C4—28no—
1321C4—24no—
1322C4—24no—
1323C4—44no—
1324C4—44no—
1325C4—44no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—42no—
1330C4—44no—
1331C4—81no—
1332C4—81no—
1333C4—82no—
1334C4—82no—
1335C4—81no—
1336C4—82no—
1337C4—81no—
1338C2—28no—
1339C2—44no—
1340C2—44no—
1341C2—82no—
1342C2—82no—
1343C2C2×#241811yescharacteristic
1344C2#3473212yes—
1345C2#3505312yes—
1346C2#3515211yescharacteristic
1347C2#3609811yescharacteristic
1348C2#3609911yescharacteristic
1349C2#3614712yes—
1350C2#3631611yescharacteristic
1351C2#3633012yes—
1352C2#3634011yescharacteristic
1353C2#3662611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2404C2
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×#2849C2semidirect
3. C2×#2297C2semidirect
4. C22×C4×C22⋊C4C2semidirect
5. #14946C2semidirect
6. #14945C2semidirect
7. #14797C2semidirect
8. #14768C2semidirect
9. #14760C2semidirect
10. #14751C2semidirect
11. #14718C2semidirect
12. #14718C2semidirect
13. #14705C2semidirect
14. #14696C2semidirect
15. #14696C2semidirect
16. #14694C2semidirect
17. #14182C2semidirect
18. #14181C2semidirect
19. #14096C2semidirect
20. #13984C2semidirect
21. #13962C2semidirect
22. #13956C2semidirect
23. #13868C2semidirect
43. C2×#391C22semidirect
44. C2×#390C22semidirect
45. C2×#388C22semidirect
46. C2×#388C22semidirect
79. C2×C4×C22⋊C4C22semidirect
80. C2×C4×C22⋊C4C22semidirect
83. #1446C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1443C22semidirect
87. #1443C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
102. #1438C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1436C22semidirect
108. #1436C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. C4⋊#95C22semidirect
114. #1434C22semidirect
115. #1434C22semidirect
116. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
248. #386D4semidirect
440. C23×C4#41semidirect
571. C2×C22⋊C4#41semidirect
912. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#24042
C2×#22972
C22×C4×C22⋊C42
#149462
#149452
#147972
#147682
#147602
#147512
#147182
#147052
#146962
#146942
#141822
#141812
#140962
#139842
#139622
#139562
#138682