Finite Group Databasebeta

← #612452

Subgroups — #612452

Order 512.

6379 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2849C211yesmaximal, characteristic, complemented
2C2×#2849C211yesmaximal, characteristic, complemented
3C2×#2847C211yesmaximal, characteristic
4C2×#2425C211yesmaximal, characteristic, complemented
5C2×C4×#120C211yesmaximal, characteristic, complemented
6C23×#95C211yesmaximal, characteristic, complemented
7#14935C211yesmaximal, characteristic, complemented
8#14926C211yesmaximal, characteristic, complemented
9#14912C211yesmaximal, characteristic, complemented
10#14912C211yesmaximal, characteristic, complemented
11#14748C212yesmaximal, complemented
12#14747C212yesmaximal, complemented
13#14737C212yesmaximal, complemented
14#14736C212yesmaximal, complemented
15#14694C211yesmaximal, characteristic, complemented
16#14693C211yesmaximal, characteristic, complemented
17#14140C212yesmaximal, complemented
18#14023C212yesmaximal, complemented
19#14004C212yesmaximal, complemented
20#13996C211yesmaximal, characteristic, complemented
21#13968C211yesmaximal, characteristic, complemented
22#13899C212yesmaximal, complemented
23#13874C211yesmaximal, characteristic, complemented
24C25×C4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C25×C4C2211yescharacteristic
27C22×#123C2211yescharacteristic
28C22×#123C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×#121C2212yes—
33C22×#120C2211yescharacteristic
34C22×#120C2211yescharacteristic
35C22×C4×D4C2212yes—
36C22×C4×D4C2211yescharacteristic
37#2849—28no—
38#2849—28no—
39#2847—28no—
40#2425—28no—
41C2×#398C2211yescharacteristic, complemented
42C2×#397C2211yescharacteristic, complemented
43C2×#396C2211yescharacteristic, complemented
44C2×#394C2211yescharacteristic, complemented
45C4×#120—28no—
46C2×#389C2211yescharacteristic, complemented
47C2×#388C2211yescharacteristic, complemented
48C2×#386C2212yes—
49C2×#386C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic, complemented
63C2×#385C2212yes—
64C2×#385C2212yes—
65C2×#385C2212yes—
66C2×#385C2212yes—
67C2×#385C2211yescharacteristic
68C2×#385C2211yescharacteristic
69C2×#385C2212yes—
70C2×#385C2212yes—
71C2×#385C2211yescharacteristic
72C2×#385C2212yes—
73C2×#381C2211yescharacteristic
74C2×#381C2211yescharacteristic
75C2×#381C2211yescharacteristic
76C2×#381C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#380C2212yes—
79C2×#380C2211yescharacteristic, complemented
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2212yes—
84C22×#95—28no—
85C22×#95C2212yes—
86C22×#95C2211yescharacteristic
87C22×#95C2211yescharacteristic
88C22×#95C2211yescharacteristic
89C22×#95C2212yes—
90C22×#95C2212yes—
91C22×#95C2212yes—
92C22×#95C2211yescharacteristic
93#1445C2212yescomplemented
94#1444C2212yescomplemented
95#1443C2212yescomplemented
96#1443C2212yescomplemented
97#1442C2212yescomplemented
98#1442C2212yescomplemented
99#1442C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1441C2212yescomplemented
103#1441C2212yescomplemented
104#1441C2212yescomplemented
105#1441C2212yescomplemented
106#1440C2212yescomplemented
107#1440C2212yescomplemented
108#1440C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1438C2212yescomplemented
115#1437C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118C4⋊#95C2212yescomplemented
119#1434C2212yescomplemented
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yes—
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2311yescharacteristic
133C23×D4C2312yes—
134C23×D4C2311yescharacteristic
135C24×C4—24no—
136C24×C4—24no—
137C24×C4—24no—
138C24×C4—24no—
139C24×C4—24no—
140C24×C4—28no—
141C24×C4—28no—
142C24×C4—24no—
143C24×C4—24no—
144C24×C4—24no—
145C24×C4—24no—
146C24×C4—42no—
147C24×C4—44no—
148C24×C4—42no—
149C24×C4—44no—
150C24×C4—42no—
151C24×C4—42no—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2312yes—
157C24×C4C2312yes—
158C24×C4C2312yes—
159C24×C4C2312yes—
160C24×C4C2311yescharacteristic
161C24×C4C2311yescharacteristic
162C24×C4C2311yescharacteristic
163C24×C4C2312yes—
164C24×C4C2312yes—
165C2×#123—24no—
166C2×#123—24no—
167C2×#123—24no—
168C2×#123—24no—
169C2×#123—24no—
170C2×#123—24no—
171C2×#123—24no—
172C2×#123—24no—
173C2×#123—42no—
174C2×#123—42no—
175C2×#123—42no—
176C2×#123—42no—
177C2×#121—24no—
178C2×#121—28no—
179C2×#121—24no—
180C2×#121—28no—
181C2×#121—44no—
182C2×#121—42no—
183C2×#120—24no—
184C2×#120—24no—
185C2×#120—24no—
186C2×#120—24no—
187C2×#120—24no—
188C2×#120D418yes—
189C2×C4×D4—24no—
190C2×C4×D4—28no—
191C2×C4×D4—24no—
192C2×C4×D4—28no—
193C2×C4×D4—42no—
194C2×C4×D4—44no—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2312yes—
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2312yes—
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2312yes—
235C22×C42C2312yes—
236C22×C42C2311yescharacteristic
237#398—24no—
238#397—24no—
239#396—24no—
240#394—24no—
241#389—24no—
242#388—24no—
243#386—24no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—24no—
248#386—28no—
249#386—24no—
250#386—28no—
251#386—28no—
252#386—28no—
253#386—24no—
254#386—28no—
255#386—24no—
256#386—42no—
257#386—44no—
258#385—24no—
259#385—28no—
260#385—28no—
261#385—28no—
262#385—28no—
263#385—28no—
264#385—24no—
265#385—28no—
266#385—44no—
267#385—42no—
268#381—24no—
269#381—24no—
270#381—24no—
271#381—24no—
272#380—24no—
273#380—28no—
274#380—24no—
275#379—24no—
276#379D418yescomplemented
277C4×C22⋊C4—24no—
278C4×C22⋊C4—28no—
279C2×#95—24no—
280C2×#95—24no—
281C2×#95—24no—
282C2×#95—28no—
283C2×#95—28no—
284C2×#95—28no—
285C2×#95—28no—
286C2×#95D418yescomplemented
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
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—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2311yescharacteristic
322C2×#95C2311yescharacteristic
323C2×#95C2311yescharacteristic
324C2×#95C2311yescharacteristic
325C25—22no—
326C25—24no—
327C25—24no—
328C25—22no—
329C25—24no—
330C25—22no—
331C25—22no—
332C25—24no—
333C25C2×D414yes—
334C25C2×D414yes—
335C25#4114yes—
336C25C2411yescharacteristic
337C25C2411yescharacteristic
338C25C2411yescharacteristic
339C25C2412yes—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—22no—
366C22×D4—24no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—41no—
370C22×D4—42no—
371C22×D4C2×D414yes—
372C22×D4C2×D418yes—
373C23×C4—232no—
374C23×C4—232no—
375C23×C4—232no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4—24no—
414C23×C4—24no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—24no—
418C23×C4—24no—
419C23×C4—24no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—22no—
423C23×C4—24no—
424C23×C4—22no—
425C23×C4—24no—
426C23×C4—22no—
427C23×C4—24no—
428C23×C4—22no—
429C23×C4—24no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—24no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—42no—
443C23×C4—42no—
444C23×C4—42no—
445C23×C4—42no—
446C23×C4—42no—
447C23×C4—42no—
448C23×C4—42no—
449C23×C4—42no—
450C23×C4—41no—
451C23×C4—416no—
452C23×C4—416no—
453C23×C4—416no—
454C23×C4—416no—
455C23×C4—432no—
456C23×C4—432no—
457C23×C4—416no—
458C23×C4—416no—
459C23×C4—416no—
460C23×C4—416no—
461C23×C4—432no—
462C23×C4—432no—
463C23×C4—416no—
464C23×C4—416no—
465C23×C4C2×D414yes—
466C23×C4C2×D414yes—
467C23×C4C2×D414yes—
468C23×C4#4114yes—
469C23×C4#4118yes—
470C23×C4#4118yes—
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473C23×C4C2412yes—
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2411yescharacteristic
480C23×C4C2412yes—
481C23×C4C2411yescharacteristic
482C23×C4C2411yescharacteristic
483C23×C4C2411yescharacteristic
484C23×C4C2411yescharacteristic
485C23×C4C2412yes—
486C23×C4C2412yes—
487C23×C4C2412yes—
488C23×C4C2411yescharacteristic
489C23×C4C2411yescharacteristic
490#123—416no—
491#123—416no—
492#123—416no—
493#123—416no—
494#121—416no—
495#121—432no—
496#120—232no—
497#120—416no—
498C4×D4—416no—
499C4×D4—432no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—22no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—24no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—42no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—42no—
527C2×C4⋊C4—41no—
528C2×C4⋊C4—42no—
529C2×C4⋊C4—41no—
530C2×C4⋊C4—42no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4—42no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—22no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—24no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4C2×D414yes—
611C2×C22⋊C4C2×D418yes—
612C2×C22⋊C4C2×D414yes—
613C2×C22⋊C4C2×D418yes—
614C2×C22⋊C4C2×D414yes—
615C2×C22⋊C4C2×D418yes—
616C2×C42—24no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—24no—
620C2×C42—42no—
621C2×C42—41no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—24no—
633#95—24no—
634#95—22no—
635#95—24no—
636#95—24no—
637#95—24no—
638#95—24no—
639#95—24no—
640#95—24no—
641#95—24no—
642#95—24no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—24no—
647#95—24no—
648#95—24no—
649#95—24no—
650#95—42no—
651#95—42no—
652#95—42no—
653#95—42no—
654#95—42no—
655#95—42no—
656#95C2×D414yes—
657#95C2×D414yes—
658#95C2×D414yes—
659#95C2×D414yes—
660C24—28no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—216no—
666C24—28no—
667C24—216no—
668C24—216no—
669C24—216no—
670C24—28no—
671C24—216no—
672C24—28no—
673C24—216no—
674C24—28no—
675C24—28no—
676C24—216no—
677C24—216no—
678C24—28no—
679C24—28no—
680C24—216no—
681C24—216no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—22no—
698C24—22no—
699C24—21no—
700C24—21no—
701C24—21no—
702C24—22no—
703C24—22no—
704C24—21no—
705C24—21no—
706C24—21no—
707C24—22no—
708C24—21no—
709C24—22no—
710C24—21no—
711C24—21no—
712C24—21no—
713C24—22no—
714C24—22no—
715C24#121116yes—
716C24C22×D412yes—
717C24C22×D412yes—
718C24C22×D412yes—
719C24C22×D414yes—
720C24C22×D414yes—
721C24C22×D412yes—
722C24C2×#4112yes—
723C24C2×#4114yes—
724C24C2×#4112yes—
725C24C2×#4114yes—
726C24C2×#4114yes—
727C24H(5,𝔽2)12yes—
728C24H(5,𝔽2)12yes—
729C24H(5,𝔽2)14yes—
730C242−1+414yes—
731C24C2511yescharacteristic
732C2×D4—28no—
733C2×D4—216no—
734C2×D4—28no—
735C2×D4—216no—
736C2×D4—28no—
737C2×D4—216no—
738C2×D4—44no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—48no—
748C2×D4—44no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—44no—
753C2×D4—48no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—44no—
763C2×D4—82no—
764C2×D4—84no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—216no—
772C22×C4—216no—
773C22×C4—216no—
774C22×C4—216no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—28no—
783C22×C4—216no—
784C22×C4—216no—
785C22×C4—28no—
786C22×C4—28no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—216no—
854C22×C4—216no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—22no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—21no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—44no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—48no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—48no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4—48no—
924C22×C4—4128no—
925C22×C4—4128no—
926C22×C4—4128no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—44no—
930C22×C4—44no—
931C22×C4—48no—
932C22×C4—48no—
933C22×C4—48no—
934C22×C4—48no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—44no—
940C22×C4—44no—
941C22×C4—44no—
942C22×C4—44no—
943C22×C4—48no—
944C22×C4—48no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—82no—
949C22×C4—84no—
950C22×C4C22×D414yes—
951C22×C4C22×D412yes—
952C22×C4C22×D414yes—
953C22×C4C22×D412yes—
954C22×C4C22×D412yes—
955C22×C4C22×D412yes—
956C22×C4C22×D412yes—
957C22×C4C22×D412yes—
958C22×C4C22×D412yes—
959C22×C4C22×D412yes—
960C22×C4C22×D412yes—
961C22×C4C2×#4114yes—
962C22×C4C2×#4114yes—
963C22×C4C2×#4114yes—
964C22×C4C2×#4114yes—
965C22×C4C2×#4114yes—
966C4⋊C4—44no—
967C4⋊C4—48no—
968C4⋊C4—44no—
969C4⋊C4—48no—
970C4⋊C4—44no—
971C4⋊C4—44no—
972C4⋊C4—44no—
973C4⋊C4—44no—
974C4⋊C4—48no—
975C4⋊C4—48no—
976C4⋊C4—44no—
977C4⋊C4—82no—
978C4⋊C4—84no—
979C22⋊C4—28no—
980C22⋊C4—216no—
981C22⋊C4—28no—
982C22⋊C4—216no—
983C22⋊C4—28no—
984C22⋊C4—216no—
985C22⋊C4—44no—
986C22⋊C4—48no—
987C22⋊C4—44no—
988C22⋊C4—48no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—48no—
992C22⋊C4—44no—
993C22⋊C4—48no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—48no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—44no—
1002C22⋊C4—48no—
1003C22⋊C4—44no—
1004C22⋊C4—82no—
1005C22⋊C4—84no—
1006C42—44no—
1007C42—48no—
1008C23—232no—
1009C23—232no—
1010C23—232no—
1011C23—232no—
1012C23—232no—
1013C23—264no—
1014C23—264no—
1015C23—232no—
1016C23—264no—
1017C23—22no—
1018C23—22no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—232no—
1028C23—264no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23—22no—
1045C23—24no—
1046C23—22no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—24no—
1057C23—24no—
1058C23—24no—
1059C23—24no—
1060C23—24no—
1061C23—24no—
1062C23—24no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—24no—
1067C23—24no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—42no—
1072C23—42no—
1073C23—41no—
1074C23—42no—
1075C23—41no—
1076C23—42no—
1077C23—41no—
1078C23—42no—
1079C23—41no—
1080C23—41no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—42no—
1091C23—42no—
1092C23—41no—
1093C23—42no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—42no—
1098C23—42no—
1099C23—41no—
1100C23—42no—
1101C23—42no—
1102C23—41no—
1103C23—41no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23C2×#12114yes—
1110C23C2×#12118yes—
1111C23#52514yes—
1112C23#52918yes—
1113C23#53814yes—
1114C23#53918yes—
1115C23D4214yes—
1116C23D4214yes—
1117C23#54614yes—
1118C23#54614yes—
1119C23#54618yes—
1120C23#54618yes—
1121C23#54718yes—
1122C23#54718yes—
1123C23C23×D411yescharacteristic
1124C23C23×D411yescharacteristic
1125C23C23×D411yescharacteristic
1126C23C22×#4111yescharacteristic
1127C23C22×#4112yes—
1128C23C22×#4112yes—
1129C23C22×#4111yescharacteristic
1130C23C2×H(5,𝔽2)11yescharacteristic
1131C23C2×H(5,𝔽2)11yescharacteristic
1132C23C2×H(5,𝔽2)12yes—
1133C23C2×2−1+412yes—
1134D4—416no—
1135D4—432no—
1136D4—88no—
1137D4—88no—
1138D4—816no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—24no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—22no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—416no—
1182C2×C4—432no—
1183C2×C4—416no—
1184C2×C4—432no—
1185C2×C4—416no—
1186C2×C4—416no—
1187C2×C4—432no—
1188C2×C4—432no—
1189C2×C4—432no—
1190C2×C4—432no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—416no—
1200C2×C4—416no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—42no—
1206C2×C4—41no—
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—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—41no—
1226C2×C4—42no—
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—41no—
1236C2×C4—42no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—41no—
1243C2×C4—42no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—42no—
1264C2×C4—42no—
1265C2×C4—42no—
1266C2×C4—88no—
1267C2×C4#52514yes—
1268C2×C4#52514yes—
1269C22—2128no—
1270C22—24no—
1271C22—24no—
1272C22—28no—
1273C22—28no—
1274C22—24no—
1275C22—24no—
1276C22—28no—
1277C22—28no—
1278C22—24no—
1279C22—28no—
1280C22—28no—
1281C22—28no—
1282C22—28no—
1283C22—28no—
1284C22—28no—
1285C22—28no—
1286C22—28no—
1287C22—28no—
1288C22—28no—
1289C22—24no—
1290C22—28no—
1291C22—28no—
1292C22—28no—
1293C22—28no—
1294C22—42no—
1295C22—42no—
1296C22—44no—
1297C22—42no—
1298C22—44no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—82no—
1303C22—81no—
1304C22—82no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—82no—
1311C22—82no—
1312C22—81no—
1313C22—82no—
1314C22—81no—
1315C22—82no—
1316C22#242418yes—
1317C22#2425116yescomplemented
1318C22C22×#12111yescharacteristic
1319C22C2×#52511yescharacteristic
1320C22C2×#52511yescharacteristic
1321C22C2×#52511yescharacteristic
1322C22C2×#52912yes—
1323C22#344412yes—
1324C22C2×#53811yescharacteristic
1325C22C2×#53912yes—
1326C22C2×D4211yescharacteristic
1327C22C2×D4211yescharacteristic
1328C22C2×#54612yes—
1329C22C2×#54612yes—
1330C22C2×#54611yescharacteristic
1331C22C2×#54611yescharacteristic
1332C22C2×#54712yes—
1333C22C2×#54712yes—
1334C22#348411yescharacteristic
1335C22#348611yescharacteristic
1336C22#349012yes—
1337C22#349012yes—
1338C22#349212yes—
1339C22#349212yes—
1340C22#349212yes—
1341C4—24no—
1342C4—24no—
1343C4—42no—
1344C4—44no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C4—44no—
1350C4—42no—
1351C4—42no—
1352C4—44no—
1353C4—42no—
1354C4—44no—
1355C4—81no—
1356C4—81no—
1357C4—82no—
1358C4—81no—
1359C4—82no—
1360C2—28no—
1361C2—216no—
1362C2—82no—
1363C2—161no—
1364C2C2×#242411yescharacteristic
1365C2C2×#242512yes—
1366C2#3498911yescharacteristic
1367C2#3499712yes—
1368C2#3609811yescharacteristic
1369C2#3609811yescharacteristic
1370C2#3610311yescharacteristic
1371C2#3610311yescharacteristic
1372C2#3614612yes—
1373C2#3614612yes—
1374C2#3662111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2847C2
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
2. C2×#2849C2semidirect
4. C2×#2425C2semidirect
5. C2×C4×#120C2semidirect
6. C23×#95C2semidirect
7. #14935C2semidirect
8. #14926C2semidirect
9. #14912C2semidirect
10. #14912C2semidirect
11. #14748C2semidirect
12. #14747C2semidirect
13. #14737C2semidirect
14. #14736C2semidirect
15. #14694C2semidirect
16. #14693C2semidirect
17. #14140C2semidirect
18. #14023C2semidirect
19. #14004C2semidirect
20. #13996C2semidirect
21. #13968C2semidirect
22. #13899C2semidirect
23. #13874C2semidirect
41. C2×#398C22semidirect
42. C2×#397C22semidirect
43. C2×#396C22semidirect
44. C2×#394C22semidirect
46. C2×#389C22semidirect
47. C2×#388C22semidirect
62. C2×#386C22semidirect
79. C2×#380C22semidirect
93. #1445C22semidirect
94. #1444C22semidirect
95. #1443C22semidirect
96. #1443C22semidirect
97. #1442C22semidirect
98. #1442C22semidirect
99. #1442C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
102. #1441C22semidirect
103. #1441C22semidirect
104. #1441C22semidirect
105. #1441C22semidirect
106. #1440C22semidirect
107. #1440C22semidirect
108. #1440C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1438C22semidirect
115. #1437C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. C4⋊#95C22semidirect
119. #1434C22semidirect
128. C22⋊#95C22semidirect
276. #379D4semidirect
286. C2×#95D4semidirect
1317. C22#2425semidirect

Maximal subgroups

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

subgroupindex
C2×#28492
C2×#28472
C2×#24252
C2×C4×#1202
C23×#952
#149352
#149262
#149122
#147482
#147472
#147372
#147362
#146942
#146932
#141402
#140232
#140042
#139962
#139682
#138992
#138742