Finite Group Databasebeta

← #649475

Subgroups — #649475

Order 512.

5350 conjugacy classes of subgroups.

The subgroup lattice has 1374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#532C211yesmaximal, characteristic
2C2×#2447C211yesmaximal, characteristic, complemented
3C2×#2445C211yesmaximal, characteristic, complemented
4C2×#2339C211yesmaximal, characteristic, complemented
5#15984C212yesmaximal, complemented
6#15950C212yesmaximal, complemented
7#15277C212yesmaximal, complemented
8#15277C212yesmaximal, complemented
9#15226C211yesmaximal, characteristic, complemented
10#15217C211yesmaximal, characteristic, complemented
11#15188C211yesmaximal, characteristic, complemented
12#15180C211yesmaximal, characteristic, complemented
13#14823C212yesmaximal, complemented
14#14823C212yesmaximal, complemented
15#14697C211yesmaximal, characteristic, complemented
16#14027C211yesmaximal, characteristic, complemented
17#14025C211yesmaximal, characteristic, complemented
18#14016C212yesmaximal, complemented
19#13968C212yesmaximal, complemented
20#13937C211yesmaximal, characteristic, complemented
21#13937C211yesmaximal, characteristic, complemented
22#13937C211yesmaximal, characteristic, complemented
23C4×#385C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C23×#41C2211yescharacteristic
26C2×#532—28no—
27C2×#532—28no—
28C2×#532—28no—
29C22×C4⋊Q8C2211yescharacteristic
30C22×#127C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×#124C2211yescharacteristic
33C22×#123C2212yes—
34C22×#121C2212yes—
35C22×#121C2212yes—
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2212yes—
38C22×C4×D4C2212yes—
39C22×C4×D4C2211yescharacteristic
40C23×C42C2211yescharacteristic
41#2447—28no—
42#2445—28no—
43C2×#397C2212yes—
44C2×#397C2212yes—
45C2×#394C2212yes—
46C2×#394C2212yes—
47#2339—28no—
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic
62C2×#389C2211yescharacteristic
63C2×#389C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#385C2211yescharacteristic
70C2×#385C2212yes—
71C2×#385C2211yescharacteristic
72C2×#385C2212yes—
73C2×#381C2212yes—
74C2×#381C2212yes—
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C4⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2212yes—
82#1442C2212yes—
83#1442C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1441C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yes—
95#1440C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yes—
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2211yescharacteristic
111#1436C2211yescharacteristic
112#1436C2211yescharacteristic
113#1436C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C22⋊#95C2212yes—
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2212yes—
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yes—
127C4×#95C2211yescharacteristic
128C4×#95C2211yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—24no—
134C22×#41—24no—
135C22×#41—24no—
136C22×#41—24no—
137C22×#41—24no—
138C22×#41—42no—
139C22×#41—42no—
140C22×#41—42no—
141C22×#41—42no—
142C22×#41D418yes—
143C23×Q8C2311yescharacteristic
144C23×Q8C2311yescharacteristic
145C23×D4C2311yescharacteristic
146C23×D4C2312yes—
147C23×D4C2312yes—
148C23×D4C2312yes—
149C23×D4C2312yes—
150C23×D4C2311yescharacteristic
151C24×C4C2312yes—
152C24×C4C2311yescharacteristic
153C24×C4C2311yescharacteristic
154C24×C4C2312yes—
155C24×C4C2312yes—
156C24×C4C2311yescharacteristic
157C24×C4C2312yes—
158#532—2128no—
159C2×C4⋊Q8—24no—
160C2×C4⋊Q8—24no—
161C2×C4⋊Q8—24no—
162C2×#127—24no—
163C2×#127—24no—
164C2×#127D418yes—
165C2×#124—24no—
166C2×#124—24no—
167C2×#124—24no—
168C2×#124—24no—
169C2×#124—24no—
170C2×#124D418yes—
171C2×#123—28no—
172C2×#123—28no—
173C2×#123—44no—
174C2×#121—28no—
175C2×#121—28no—
176C2×#121—28no—
177C2×#121—28no—
178C2×#121—28no—
179C2×#121—28no—
180C2×C4×D4—28no—
181C2×C4×D4—28no—
182C2×C4×D4—28no—
183C2×C4×D4—28no—
184C2×C4×D4—24no—
185C2×C4×D4—24no—
186C2×C4×D4—24no—
187C2×C4×D4—24no—
188C2×C4×D4—28no—
189C2×C4×D4—28no—
190C2×C4×D4—42no—
191C2×C4×D4—42no—
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2311yescharacteristic
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C42—24no—
229C22×C42—24no—
230C22×C42—24no—
231C22×C42C2311yescharacteristic
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2311yescharacteristic
235C22×C42C2311yescharacteristic
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239#397—28no—
240#397—28no—
241#394—28no—
242#394—28no—
243#391—24no—
244#391—24no—
245#391—24no—
246#391—24no—
247#391—42no—
248#391—42no—
249#391—42no—
250#391—42no—
251#390—24no—
252#390—24no—
253#390—24no—
254#390—24no—
255#390—42no—
256#390—42no—
257#389—24no—
258#389—24no—
259#386—28no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—44no—
264#385—24no—
265#385—28no—
266#385—24no—
267#385—44no—
268#381—28no—
269#381—28no—
270#380—24no—
271#380—24no—
272C4×C4⋊C4—24no—
273C4×C4⋊C4—24no—
274C4×C22⋊C4—24no—
275C4×C22⋊C4—24no—
276C2×#95—28no—
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2312yes—
294C2×#95C2311yescharacteristic
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2311yescharacteristic
317C25C2412yes—
318C25C2412yes—
319C25C2411yescharacteristic
320C2×#41—232no—
321C2×#41—232no—
322C2×#41—232no—
323C2×#41—416no—
324C2×#41—416no—
325C2×#41—416no—
326C2×#41—416no—
327C2×#41—416no—
328C2×#41—416no—
329C2×#41—416no—
330C2×#41—416no—
331C2×#41—416no—
332C2×#41—416no—
333C2×#41—416no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—22no—
346C22×Q8C2×D414yes—
347C22×Q8C2×D414yes—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—22no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—24no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—24no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4C2×D414yes—
384C22×D4C2×D418yes—
385C22×D4C2×D418yes—
386C22×D4C2×D418yes—
387C22×D4C2×D414yes—
388C22×D4C2×D414yes—
389C22×D4C2×D414yes—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
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—22no—
415C23×C4—22no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—24no—
419C23×C4—41no—
420C23×C4—41no—
421C23×C4—41no—
422C23×C4—41no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4C2×D418yes—
436C23×C4C2×D414yes—
437C23×C4#4114yes—
438C23×C4#4114yes—
439C23×C4C2412yes—
440C23×C4C2412yes—
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2412yes—
451C23×C4C2411yescharacteristic
452C23×C4C2411yescharacteristic
453C23×C4C2411yescharacteristic
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C4⋊Q8—232no—
460#127—232no—
461#124—232no—
462#124—232no—
463#123—432no—
464#121—264no—
465#121—264no—
466C4×D4—264no—
467C4×D4—264no—
468C4×D4—416no—
469C4×D4—416no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—42no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4#4114yescomplemented
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
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—22no—
518C2×C22⋊C4—22no—
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—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
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⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4C2×D418yes—
577C2×C22⋊C4C2×D418yes—
578C2×C42—232no—
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—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—22no—
594C2×C42—22no—
595C2×C42—22no—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42C2×D414yes—
602C2×C42C2×D414yes—
603#95—22no—
604#95—24no—
605#95—24no—
606#95—24no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—22no—
622#95—24no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—24no—
627#95—24no—
628#95—22no—
629#95—22no—
630#95—42no—
631#95—41no—
632#95—41no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95—42no—
642#95#4114yescomplemented
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—22no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24C22×D414yes—
682C24C22×D414yes—
683C24C22×D414yes—
684C24C22×D414yes—
685C24C22×D412yes—
686C24C2×#4112yes—
687C24C2×#4112yes—
688C24C2511yescharacteristic
689#41—4128no—
690#41—4128no—
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—28no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—28no—
697C2×Q8—44no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×Q8—44no—
704C2×Q8—44no—
705C2×D4—216no—
706C2×D4—216no—
707C2×D4—216no—
708C2×D4—216no—
709C2×D4—216no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—216no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
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#120116yes—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—28no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—216no—
768C22×C4—216no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—216no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—21no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—48no—
880C22×C4—48no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—48no—
890C22×C4—48no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4—84no—
904C22×C4—84no—
905C22×C4—84no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4—84no—
909C22×C4—84no—
910C22×C4—84no—
911C22×C4#123116yescomplemented
912C22×C4C22×D414yes—
913C22×C4C22×D414yes—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C22×D412yes—
921C22×C4C22×D412yes—
922C22×C4C2×#4112yes—
923C22×C4C2×#4112yes—
924C22×C4C2×#4112yes—
925C22×C4C2×#4112yes—
926C22×C4C2×#4112yes—
927C22×C4C2×#4112yes—
928C22×C4C2×#4112yes—
929C22×C4C2×#4112yes—
930C22×C4C2×#4112yes—
931C22×C4C2×#4112yes—
932C22×C4H(5,𝔽2)12yes—
933C22×C4H(5,𝔽2)12yes—
934C22×C4H(5,𝔽2)12yes—
935C22×C42−1+412yes—
936C4⋊C4—216no—
937C4⋊C4—216no—
938C4⋊C4—28no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—44no—
942C4⋊C4—44no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—48no—
946C4⋊C4—44no—
947C4⋊C4—84no—
948C22⋊C4—28no—
949C22⋊C4—216no—
950C22⋊C4—216no—
951C22⋊C4—216no—
952C22⋊C4—216no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C22⋊C4—84no—
968C22⋊C4—84no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C42—28no—
973C42—28no—
974C42—28no—
975C42—28no—
976C42—44no—
977C42—44no—
978C42—44no—
979C42—44no—
980C23—22no—
981C23—24no—
982C23—22no—
983C23—24no—
984C23—22no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—22no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—22no—
1007C23—24no—
1008C23—24no—
1009C23—22no—
1010C23—24no—
1011C23—24no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—42no—
1024C23—42no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—42no—
1030C23—42no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—41no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—41no—
1045C23—41no—
1046C23—42no—
1047C23—42no—
1048C23—41no—
1049C23—42no—
1050C23—41no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—41no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
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—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23C2×#12018yes—
1084C23C2×#12314yes—
1085C23C23×D411yescharacteristic
1086C23C23×D411yescharacteristic
1087C23C23×D411yescharacteristic
1088C23C22×#4111yescharacteristic
1089C23C22×#4111yescharacteristic
1090C23C22×#4111yescharacteristic
1091C23C22×#4111yescharacteristic
1092C23C2×H(5,𝔽2)11yescharacteristic
1093C23C2×H(5,𝔽2)11yescharacteristic
1094C23C2×H(5,𝔽2)11yescharacteristic
1095C23C2×2−1+411yescharacteristic
1096C23#58511yescharacteristic
1097C23#58511yescharacteristic
1098C23#58511yescharacteristic
1099C23#58511yescharacteristic
1100Q8—416no—
1101Q8—416no—
1102D4—232no—
1103D4—432no—
1104D4—432no—
1105D4—432no—
1106D4—432no—
1107D4—416no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
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—232no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—432no—
1152C2×C4—416no—
1153C2×C4—416no—
1154C2×C4—432no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—42no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—42no—
1243C2×C4—816no—
1244C2×C4—816no—
1245C2×C4C2×#12014yes—
1246C2×C4C2×#12314yes—
1247C2×C4C2×#12314yes—
1248C2×C4#53414yes—
1249C2×C4#54614yes—
1250C2×C4#54614yes—
1251C2×C4#54614yes—
1252C2×C4#54614yes—
1253C2×C4#54614yes—
1254C2×C4#54714yes—
1255C22—24no—
1256C22—28no—
1257C22—28no—
1258C22—28no—
1259C22—24no—
1260C22—24no—
1261C22—42no—
1262C22—44no—
1263C22—42no—
1264C22—44no—
1265C22—42no—
1266C22—44no—
1267C22—42no—
1268C22—44no—
1269C22—42no—
1270C22—44no—
1271C22—42no—
1272C22—44no—
1273C22—42no—
1274C22—42no—
1275C22—44no—
1276C22—42no—
1277C22—44no—
1278C22—42no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—44no—
1284C22—42no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22—44no—
1289C22—44no—
1290C22—44no—
1291C22—44no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—82no—
1299C22—82no—
1300C22C22×#12011yescharacteristic
1301C22C22×#12311yescharacteristic
1302C22#344411yescharacteristic
1303C22C2×#53411yescharacteristic
1304C22#345511yescharacteristic
1305C22C2×#54611yescharacteristic
1306C22C2×#54611yescharacteristic
1307C22C2×#54611yescharacteristic
1308C22C2×#54611yescharacteristic
1309C22C2×#54611yescharacteristic
1310C22C2×#54711yescharacteristic
1311C22D4×#4111yescharacteristic
1312C22D4×#4111yescharacteristic
1313C22D4×#4111yescharacteristic
1314C22D4×#4111yescharacteristic
1315C22#348011yescharacteristic
1316C22#348011yescharacteristic
1317C22#348511yescharacteristic
1318C22#348511yescharacteristic
1319C22#348811yescharacteristic
1320C22#348811yescharacteristic
1321C22#348911yescharacteristic
1322C22#348911yescharacteristic
1323C22#350611yescharacteristic
1324C22#350711yescharacteristic
1325C22#350811yescharacteristic
1326C22#351111yescharacteristic
1327C22#351111yescharacteristic
1328C22#351211yescharacteristic
1329C22#351411yescharacteristic
1330C22#351711yescharacteristic
1331C22#354611yescharacteristic
1332C22#355411yescharacteristic
1333C22#356211yescharacteristic
1334C22#356211yescharacteristic
1335C4—24no—
1336C4—24no—
1337C4—24no—
1338C4—42no—
1339C4—42no—
1340C4—44no—
1341C4—44no—
1342C4—42no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—82no—
1347C4—81no—
1348C4—81no—
1349C4—82no—
1350C4—81no—
1351C4—82no—
1352C4—82no—
1353C4—81no—
1354C4#240518yes—
1355C2—44no—
1356C2—48no—
1357C2—84no—
1358C2C2×#240511yescharacteristic
1359C2#3474411yescharacteristic
1360C2#3551711yescharacteristic
1361C2#3614111yescharacteristic
1362C2#3614911yescharacteristic
1363C2#3621211yescharacteristic
1364C2#3621311yescharacteristic
1365C2#3769911yescharacteristic
1366C2#3770011yescharacteristic
1367C2#3988811yescharacteristic
1368C2#3988911yescharacteristic
1369C2#5903311yescharacteristic
1370C2#5906411yescharacteristic
1371C2#5914511yescharacteristic
1372C2#5914611yescharacteristic
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×#2447C2semidirect
3. C2×#2445C2semidirect
4. C2×#2339C2semidirect
5. #15984C2semidirect
6. #15950C2semidirect
7. #15277C2semidirect
8. #15277C2semidirect
9. #15226C2semidirect
10. #15217C2semidirect
11. #15188C2semidirect
12. #15180C2semidirect
13. #14823C2semidirect
14. #14823C2semidirect
15. #14697C2semidirect
16. #14027C2semidirect
17. #14025C2semidirect
18. #14016C2semidirect
19. #13968C2semidirect
20. #13937C2semidirect
21. #13937C2semidirect
22. #13937C2semidirect
23. C4×#385C2semidirect
505. C2×C4⋊C4#41semidirect
642. #95#41semidirect
911. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C22×#5322
C2×#24472
C2×#24452
C2×#23392
#159842
#159502
#152772
#152262
#152172
#151882
#151802
#148232
#146972
#140272
#140252
#140162
#139682
#139372
C4×#3852