Finite Group Databasebeta

← #525044

Subgroups — #525044

Order 512.

3998 conjugacy classes of subgroups.

The subgroup lattice has 1289 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊C4C211yesmaximal, characteristic
2#14700C211yesmaximal, characteristic, complemented
3#14516C212yesmaximal, complemented
4#14415C212yesmaximal, complemented
5#14366C212yesmaximal, complemented
6#14365C212yesmaximal, complemented
7#14267C212yesmaximal, complemented
8#14145C212yesmaximal, complemented
9#14141C211yesmaximal, characteristic, complemented
10#14022C211yesmaximal, characteristic, complemented
11#14002C211yesmaximal, characteristic, complemented
12#13993C211yesmaximal, characteristic, complemented
13#13973C211yesmaximal, characteristic, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13920C211yesmaximal, characteristic, complemented
16#13902C211yesmaximal, characteristic
17#13902C211yesmaximal, characteristic
18#13875C211yesmaximal, characteristic, complemented
19#13873C212yesmaximal, complemented
20#13820C211yesmaximal, characteristic, complemented
21#13775C212yesmaximal, complemented
22C4×#390C211yesmaximal, characteristic, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C23×C22⋊C4C2212yes—
28D4×C22⋊C4C4116yescomplemented
29C2×#390C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#390C2211yescharacteristic
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#389C2211yescharacteristic, complemented
40C2×#389C2211yescharacteristic, complemented
41C2×#388C2211yescharacteristic
42C2×#388C2211yescharacteristic
43C2×#388C2212yescomplemented
44C2×#388C2212yescomplemented
45C2×#388C2212yescomplemented
46C2×#388C2212yescomplemented
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#382C2211yescharacteristic, complemented
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2212yescomplemented
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×#379C2212yes—
57C2×#379C2212yes—
58C2×#379C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic, complemented
60C2×C4×C4⋊C4C2211yescharacteristic, complemented
61C2×C4×C4⋊C4C2211yescharacteristic, complemented
62C2×C4×C4⋊C4C2211yescharacteristic, complemented
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yescomplemented
67C2×C4×C22⋊C4C2212yescomplemented
68C2×C4×C22⋊C4C2212yescomplemented
69C2×C43C2211yescharacteristic, complemented
70#1443C2212yescomplemented
71#1443C2212yescomplemented
72#1442C2212yescomplemented
73#1440C2212yes—
74#1440C2212yescomplemented
75#1440C2212yescomplemented
76#1440C2212yescomplemented
77#1440C2212yescomplemented
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1438C2212yes—
87#1438C2212yes—
88#1438C2212yes—
89#1438C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1437C2211yescharacteristic
93#1437C2212yes—
94#1437C2211yescharacteristic
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1437C2212yescomplemented
104#1437C2212yescomplemented
105#1436C2211yescharacteristic, complemented
106#1436C2212yescomplemented
107#1436C2211yescharacteristic, complemented
108C4⋊#95C2211yescharacteristic, complemented
109C4⋊#95C2211yescharacteristic, complemented
110C4⋊#95C2211yescharacteristic, complemented
111C4⋊#95C2211yescharacteristic, complemented
112C4⋊#95C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114#1434C2212yescomplemented
115#1434C2212yescomplemented
116#1434C2211yescharacteristic, complemented
117#1434C2211yescharacteristic, complemented
118C22⋊#95C2212yescomplemented
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C4×#95C2211yescharacteristic, complemented
123C4×#95C2211yescharacteristic, complemented
124C26C2312yes—
125C23×D4—24no—
126C23×D4—24no—
127C23×D4—42no—
128C23×D4—42no—
129C23×D4—42no—
130C23×D4—42no—
131C23×D4C2×C418yes—
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C24×C4C2311yescharacteristic
136C24×C4C2312yes—
137C24×C4C2312yes—
138C2×C4×D4—42no—
139C2×C4×D4—42no—
140C2×C4×D4—42no—
141C2×C4×D4—42no—
142C2×C4×D4C2×C418yes—
143C2×C4×D4C2×C418yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C22⋊C4—44no—
155C22×C22⋊C4—44no—
156C22×C22⋊C4C2×C4116yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C42C2311yescharacteristic
189C22×C42C2311yescharacteristic
190C22×C42C2311yescharacteristic
191C22×C42C2311yescharacteristic
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2311yescharacteristic
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198C22×C42C2311yescharacteristic
199C22×C42C2312yes—
200C22×C42C2312yes—
201#390—24no—
202#390—24no—
203#390—24no—
204#390—24no—
205#390—42no—
206#390—42no—
207#390—42no—
208#390—42no—
209#390C2×C418yes—
210#390C2×C418yes—
211#389—42no—
212#389—42no—
213#388—24no—
214#388—24no—
215#388—44no—
216#388—44no—
217#388—44no—
218#388—44no—
219#386C2×C4116yes—
220#386C2×C4116yes—
221#382—42no—
222#380—44no—
223#380—42no—
224#380—42no—
225#380C2×C418yes—
226#379—28no—
227#379—28no—
228#379—44no—
229#379—44no—
230#379C2×C4116yes—
231C4×C4⋊C4—42no—
232C4×C4⋊C4—42no—
233C4×C4⋊C4—42no—
234C4×C4⋊C4—42no—
235C4×C22⋊C4—44no—
236C4×C22⋊C4—44no—
237C4×C22⋊C4—42no—
238C4×C22⋊C4—42no—
239C4×C22⋊C4—44no—
240C4×C22⋊C4C2×C418yes—
241C2×#95C2311yescharacteristic
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2311yescharacteristic
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C43—42no—
280C25—24no—
281C25—24no—
282C25—24no—
283C25—24no—
284C25—42no—
285C25—42no—
286C25—42no—
287C25—42no—
288C25—42no—
289C25—42no—
290C25—42no—
291C25—42no—
292C25—42no—
293C25—42no—
294C25C22×C418yes—
295C25C2412yes—
296C25C2411yescharacteristic
297C25C2412yes—
298C22×D4—24no—
299C22×D4—24no—
300C22×D4—232no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4—416no—
312C22×D4—416no—
313C22×D4—42no—
314C22×D4—42no—
315C22×D4—42no—
316C22×D4—42no—
317C22×D4—416no—
318C22×D4—416no—
319C22×D4—416no—
320C22×D4—416no—
321C22×D4C22×C414yes—
322C22×D4C22×C414yes—
323C22×D4C22×C418yes—
324C22×D4#4114yes—
325C22×D4#4114yes—
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—24no—
333C23×C4—24no—
334C23×C4—42no—
335C23×C4—42no—
336C23×C4—42no—
337C23×C4—42no—
338C23×C4—42no—
339C23×C4—42no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4—42no—
344C23×C4C22×C414yes—
345C23×C4C22×C418yes—
346C23×C4C22×C418yes—
347C23×C4C2411yescharacteristic
348C23×C4C2412yes—
349C23×C4C2412yes—
350C23×C4C2411yescharacteristic
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2411yescharacteristic
354C23×C4C2411yescharacteristic
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2411yescharacteristic
358C23×C4C2411yescharacteristic
359C23×C4C2411yescharacteristic
360C23×C4C2411yescharacteristic
361C23×C4C2411yescharacteristic
362C23×C4C2411yescharacteristic
363C23×C4C2411yescharacteristic
364C23×C4C2411yescharacteristic
365C23×C4C2411yescharacteristic
366C23×C4C2411yescharacteristic
367C4×D4—416no—
368C4×D4—416no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4C22×C414yes—
398C2×C4⋊C4C22×C414yes—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—24no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—432no—
432C2×C22⋊C4—42no—
433C2×C22⋊C4—42no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—41no—
439C2×C22⋊C4—41no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—42no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—41no—
446C2×C22⋊C4—41no—
447C2×C22⋊C4—42no—
448C2×C22⋊C4—42no—
449C2×C22⋊C4—42no—
450C2×C22⋊C4—42no—
451C2×C22⋊C4—42no—
452C2×C22⋊C4—41no—
453C2×C22⋊C4—41no—
454C2×C22⋊C4—42no—
455C2×C22⋊C4—42no—
456C2×C22⋊C4—42no—
457C2×C22⋊C4—42no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—42no—
461C2×C22⋊C4—42no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—42no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—42no—
482C2×C22⋊C4C22×C414yes—
483C2×C22⋊C4C22×C418yes—
484C2×C22⋊C4C22×C414yes—
485C2×C22⋊C4C22×C418yes—
486C2×C22⋊C4C22×C418yes—
487C2×C22⋊C4C22×C418yes—
488C2×C22⋊C4C22×C418yes—
489C2×C22⋊C4C22×C418yes—
490C2×C22⋊C4C22×C418yes—
491C2×C22⋊C4#4114yes—
492C2×C22⋊C4#4114yes—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—24no—
516C2×C42—41no—
517C2×C42—41no—
518C2×C42—41no—
519C2×C42—41no—
520C2×C42—41no—
521C2×C42—41no—
522C2×C42—42no—
523C2×C42—42no—
524C2×C42—42no—
525C2×C42—42no—
526C2×C42—42no—
527C2×C42—42no—
528C2×C42—42no—
529C2×C42—42no—
530C2×C42C22×C414yes—
531C2×C42C22×C414yes—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—24no—
538#95—24no—
539#95—22no—
540#95—22no—
541#95—42no—
542#95—41no—
543#95—42no—
544#95—41no—
545#95—42no—
546#95—42no—
547#95—41no—
548#95—41no—
549#95—41no—
550#95—42no—
551#95—41no—
552#95—41no—
553#95—42no—
554#95—42no—
555#95—42no—
556#95—42no—
557#95—42no—
558#95—42no—
559#95—42no—
560#95—42no—
561#95—42no—
562#95—42no—
563#95—42no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95C22×C414yes—
568#95C22×C414yes—
569#95C22×C418yes—
570C24—22no—
571C24—22no—
572C24—21no—
573C24—21no—
574C24—22no—
575C24—22no—
576C24—21no—
577C24—21no—
578C24—21no—
579C24—21no—
580C24—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—21no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—21no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—216no—
609C24—216no—
610C24—48no—
611C24—48no—
612C24—48no—
613C24—48no—
614C24—48no—
615C24—48no—
616C24—48no—
617C24—48no—
618C24—48no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—84no—
624C24—84no—
625C24—84no—
626C24—84no—
627C24—84no—
628C24—84no—
629C24—84no—
630C24—84no—
631C24—84no—
632C24—84no—
633C24—84no—
634C24—84no—
635C24—84no—
636C24—84no—
637C24—84no—
638C24—84no—
639C24—84no—
640C24—84no—
641C24—84no—
642C24—84no—
643C24C23×C414yes—
644C24C23×C414yes—
645C24C23×C412yes—
646C24C2×#4114yes—
647C24C2×#4114yes—
648C24C2×#4112yes—
649C24C2×#4112yes—
650C24C2511yescharacteristic
651C2×D4—216no—
652C2×D4—28no—
653C2×D4—28no—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—48no—
662C2×D4—48no—
663C2×D4—4128no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4#117116yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—28no—
752C22×C4—216no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—48no—
796C22×C4—48no—
797C22×C4—48no—
798C22×C4—48no—
799C22×C4—48no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4—84no—
805C22×C4—84no—
806C22×C4—84no—
807C22×C4—84no—
808C22×C4—84no—
809C22×C4—84no—
810C22×C4—84no—
811C22×C4—84no—
812C22×C4C23×C412yes—
813C22×C4C23×C412yes—
814C22×C4C23×C412yes—
815C22×C4C23×C412yes—
816C22×C4C23×C414yes—
817C22×C4C23×C414yes—
818C22×C4C23×C412yes—
819C22×C4C23×C412yes—
820C22×C4C2×#4112yes—
821C22×C4C2×#4112yes—
822C22×C4C2×#4112yes—
823C22×C4C2×#4112yes—
824C22×C4C2×#4112yes—
825C22×C4C2×#4112yes—
826C22×C4H(5,𝔽2)12yes—
827C22×C4H(5,𝔽2)12yes—
828C22×C4H(5,𝔽2)12yes—
829C22×C4H(5,𝔽2)12yes—
830C22×C4H(5,𝔽2)12yes—
831C22×C4H(5,𝔽2)12yes—
832C22×C4H(5,𝔽2)12yes—
833C22×C4H(5,𝔽2)12yes—
834C4⋊C4—28no—
835C4⋊C4—28no—
836C4⋊C4—44no—
837C4⋊C4—44no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—84no—
843C4⋊C4—84no—
844C22⋊C4—28no—
845C22⋊C4—28no—
846C22⋊C4—216no—
847C22⋊C4—48no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—48no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—44no—
854C22⋊C4—44no—
855C22⋊C4—48no—
856C22⋊C4—48no—
857C22⋊C4—48no—
858C22⋊C4—48no—
859C22⋊C4—48no—
860C22⋊C4—44no—
861C22⋊C4—48no—
862C22⋊C4—44no—
863C22⋊C4—84no—
864C22⋊C4—84no—
865C22⋊C4—84no—
866C22⋊C4—84no—
867C22⋊C4—84no—
868C22⋊C4—84no—
869C22⋊C4—84no—
870C22⋊C4—84no—
871C22⋊C4—84no—
872C22⋊C4—84no—
873C22⋊C4—84no—
874C22⋊C4—84no—
875C42—28no—
876C42—28no—
877C42—44no—
878C42—44no—
879C42—44no—
880C42—44no—
881C42—44no—
882C42—44no—
883C42—44no—
884C42—44no—
885C42—84no—
886C42—84no—
887C42—84no—
888C23—22no—
889C23—24no—
890C23—22no—
891C23—24no—
892C23—24no—
893C23—24no—
894C23—22no—
895C23—22no—
896C23—24no—
897C23—24no—
898C23—22no—
899C23—22no—
900C23—24no—
901C23—24no—
902C23—24no—
903C23—24no—
904C23—24no—
905C23—24no—
906C23—24no—
907C23—24no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—24no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—24no—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—24no—
930C23—24no—
931C23—432no—
932C23—432no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—42no—
938C23—42no—
939C23—42no—
940C23—42no—
941C23—41no—
942C23—42no—
943C23—42no—
944C23—41no—
945C23—42no—
946C23—42no—
947C23—41no—
948C23—41no—
949C23—42no—
950C23—41no—
951C23—42no—
952C23—41no—
953C23—42no—
954C23—42no—
955C23—41no—
956C23—41no—
957C23—42no—
958C23—42no—
959C23—41no—
960C23—41no—
961C23—42no—
962C23—41no—
963C23—42no—
964C23—41no—
965C23—42no—
966C23—42no—
967C23—42no—
968C23—42no—
969C23—42no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—42no—
978C23—42no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—816no—
994C23—816no—
995C23—816no—
996C23—816no—
997C23—816no—
998C23—816no—
999C23—816no—
1000C23—816no—
1001C23—816no—
1002C23—816no—
1003C23—816no—
1004C23—816no—
1005C23—816no—
1006C23C2×#11718yes—
1007C23C4×#4114yes—
1008C23C24×C411yescharacteristic
1009C23C22×#4111yescharacteristic
1010C23C22×#4111yescharacteristic
1011C23C22×#4111yescharacteristic
1012C23C22×#4111yescharacteristic
1013C23C2×H(5,𝔽2)11yescharacteristic
1014C23C2×H(5,𝔽2)11yescharacteristic
1015C23C2×H(5,𝔽2)11yescharacteristic
1016C23C2×H(5,𝔽2)11yescharacteristic
1017C23C2×H(5,𝔽2)11yescharacteristic
1018C23C2×H(5,𝔽2)11yescharacteristic
1019C23C2×H(5,𝔽2)11yescharacteristic
1020C23C2×H(5,𝔽2)11yescharacteristic
1021C23#58511yescharacteristic
1022C23#58511yescharacteristic
1023D4—232no—
1024D4—432no—
1025D4—416no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—42no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—42no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—42no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—416no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—816no—
1160C2×C4—816no—
1161C2×C4C2×#11714yes—
1162C2×C4#51814yes—
1163C2×C4#51814yes—
1164C2×C4#51814yes—
1165C2×C4#53814yes—
1166C2×C4#53814yes—
1167C2×C4#53814yes—
1168C2×C4#53814yes—
1169C22—24no—
1170C22—24no—
1171C22—24no—
1172C22—28no—
1173C22—28no—
1174C22—28no—
1175C22—44no—
1176C22—44no—
1177C22—44no—
1178C22—42no—
1179C22—44no—
1180C22—42no—
1181C22—44no—
1182C22—42no—
1183C22—44no—
1184C22—42no—
1185C22—44no—
1186C22—42no—
1187C22—44no—
1188C22—42no—
1189C22—42no—
1190C22—44no—
1191C22—42no—
1192C22—44no—
1193C22—42no—
1194C22—44no—
1195C22—42no—
1196C22—44no—
1197C22—42no—
1198C22—42no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—864no—
1207C22—82no—
1208C22—82no—
1209C22—82no—
1210C22—82no—
1211C22—82no—
1212C22—82no—
1213C22—82no—
1214C22—82no—
1215C22C22×#11711yescharacteristic
1216C22C2×C4×#4111yescharacteristic
1217C22C2×#51811yescharacteristic
1218C22C2×#51811yescharacteristic
1219C22C2×#51811yescharacteristic
1220C22C4×H(5,𝔽2)11yescharacteristic
1221C22C4×H(5,𝔽2)11yescharacteristic
1222C22C2×#53811yescharacteristic
1223C22C2×#53811yescharacteristic
1224C22C2×#53811yescharacteristic
1225C22C2×#53811yescharacteristic
1226C22#348111yescharacteristic
1227C22#348111yescharacteristic
1228C22#348111yescharacteristic
1229C22#348111yescharacteristic
1230C22#350511yescharacteristic
1231C22#350511yescharacteristic
1232C22#350811yescharacteristic
1233C22#350811yescharacteristic
1234C22#351311yescharacteristic
1235C22#351411yescharacteristic
1236C22#351411yescharacteristic
1237C22#351411yescharacteristic
1238C22#351911yescharacteristic
1239C22#351911yescharacteristic
1240C22#351911yescharacteristic
1241C22#352111yescharacteristic
1242C22#353711yescharacteristic
1243C22#354211yescharacteristic
1244C22#354311yescharacteristic
1245C22#354311yescharacteristic
1246C22#354611yescharacteristic
1247C22#354611yescharacteristic
1248C22#354911yescharacteristic
1249C22#355811yescharacteristic
1250C4—24no—
1251C4—42no—
1252C4—42no—
1253C4—42no—
1254C4—42no—
1255C4—42no—
1256C4—42no—
1257C4—44no—
1258C4—44no—
1259C4—42no—
1260C4—42no—
1261C4—42no—
1262C4—42no—
1263C4—82no—
1264C4—82no—
1265C4—81no—
1266C4—82no—
1267C4—81no—
1268C4—82no—
1269C4#231218yes—
1270C2—48no—
1271C2—44no—
1272C2—84no—
1273C2C2×#231211yescharacteristic
1274C2#3412611yescharacteristic
1275C2#3426111yescharacteristic
1276C2#3432011yescharacteristic
1277C2#3432011yescharacteristic
1278C2#3447111yescharacteristic
1279C2#3449311yescharacteristic
1280C2#4004411yescharacteristic
1281C2#4004911yescharacteristic
1282C2#4005311yescharacteristic
1283C2#4005611yescharacteristic
1284C2#4016411yescharacteristic
1285C2#4016911yescharacteristic
1286C2#4017311yescharacteristic
1287C2#4017611yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14700C2semidirect
3. #14516C2semidirect
4. #14415C2semidirect
5. #14366C2semidirect
6. #14365C2semidirect
7. #14267C2semidirect
8. #14145C2semidirect
9. #14141C2semidirect
10. #14022C2semidirect
11. #14002C2semidirect
12. #13993C2semidirect
13. #13973C2semidirect
14. #13941C2semidirect
15. #13920C2semidirect
18. #13875C2semidirect
19. #13873C2semidirect
20. #13820C2semidirect
21. #13775C2semidirect
22. C4×#390C2semidirect
23. C4×#388C2semidirect
28. D4×C22⋊C4C4semidirect
39. C2×#389C22semidirect
40. C2×#389C22semidirect
43. C2×#388C22semidirect
44. C2×#388C22semidirect
45. C2×#388C22semidirect
46. C2×#388C22semidirect
49. C2×#382C22semidirect
53. C2×#380C22semidirect
59. C2×C4×C4⋊C4C22semidirect
60. C2×C4×C4⋊C4C22semidirect
61. C2×C4×C4⋊C4C22semidirect
62. C2×C4×C4⋊C4C22semidirect
66. C2×C4×C22⋊C4C22semidirect
67. C2×C4×C22⋊C4C22semidirect
68. C2×C4×C22⋊C4C22semidirect
69. C2×C43C22semidirect
70. #1443C22semidirect
71. #1443C22semidirect
72. #1442C22semidirect
74. #1440C22semidirect
75. #1440C22semidirect
76. #1440C22semidirect
77. #1440C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1437C22semidirect
104. #1437C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. #1436C22semidirect
108. C4⋊#95C22semidirect
109. C4⋊#95C22semidirect
110. C4⋊#95C22semidirect
111. C4⋊#95C22semidirect
112. C4⋊#95C22semidirect
113. C4⋊#95C22semidirect
114. #1434C22semidirect
115. #1434C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
118. C22⋊#95C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C4×#95C22semidirect
123. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊C42
#147002
#145162
#144152
#143662
#143652
#142672
#141452
#141412
#140222
#140022
#139932
#139732
#139412
#139202
#139022
#138752
#138732
#138202
#137752
C4×#3902
C4×#3882