Finite Group Databasebeta

← #534287

Subgroups — #534287

Order 512.

4734 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C22⋊C4C211yesmaximal, characteristic
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C2×#2293C211yesmaximal, characteristic, complemented
4#14427C212yesmaximal, complemented
5#14365C212yesmaximal, complemented
6#14068C212yesmaximal, complemented
7#14064C212yesmaximal, complemented
8#14018C211yesmaximal, characteristic, complemented
9#13993C211yesmaximal, characteristic, complemented
10#13991C212yesmaximal, complemented
11#13984C212yesmaximal, complemented
12#13979C211yesmaximal, characteristic, complemented
13#13973C211yesmaximal, characteristic, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13916C211yesmaximal, characteristic, complemented
16#13902C211yesmaximal, characteristic
17#13875C211yesmaximal, characteristic, complemented
18#13868C212yesmaximal, complemented
19#13820C211yesmaximal, characteristic, complemented
20#13820C211yesmaximal, characteristic, complemented
21C22⋊C42C212yesmaximal, complemented
22C4×#390C211yesmaximal, characteristic, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2212yescomplemented
30C23×C22⋊C4C2212yes—
31C23×C22⋊C4C2212yes—
32D4×C22⋊C4—28no—
33D4×C22⋊C4C4116yescomplemented
34#2293—28no—
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic, complemented
44C2×#389C2211yescharacteristic, complemented
45C2×#388C2211yescharacteristic
46C2×#388C2211yescharacteristic
47C2×#388C2212yescomplemented
48C2×#388C2212yescomplemented
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#385C2212yescomplemented
54C2×#382C2211yescharacteristic, complemented
55C2×#381C2212yescomplemented
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#379C2212yes—
60C2×#379C2212yes—
61C2×#379C2212yes—
62C2×#379C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic, complemented
64C2×C4×C4⋊C4C2211yescharacteristic, complemented
65C2×C4×C4⋊C4C2211yescharacteristic, complemented
66C2×C4×C4⋊C4C2211yescharacteristic, complemented
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2212yescomplemented
71C2×C4×C22⋊C4C2212yescomplemented
72C2×C4×C22⋊C4C2212yescomplemented
73C2×C4×C22⋊C4C2212yescomplemented
74C2×C4×C22⋊C4C2212yescomplemented
75C2×C43C2211yescharacteristic, complemented
76#1443C2212yescomplemented
77#1443C2212yescomplemented
78#1442C2212yescomplemented
79#1440C2212yes—
80#1440C2212yescomplemented
81#1440C2212yescomplemented
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1439C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1438C2212yes—
91#1438C2212yes—
92#1437C2212yes—
93#1437C2211yescharacteristic
94#1437C2212yes—
95#1437C2212yes—
96#1437C2211yescharacteristic
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1436C2211yescharacteristic, complemented
104#1436C2212yescomplemented
105#1436C2211yescharacteristic, complemented
106C4⋊#95C2211yescharacteristic, complemented
107C4⋊#95C2211yescharacteristic, complemented
108C4⋊#95C2211yescharacteristic, complemented
109C4⋊#95C2211yescharacteristic, complemented
110C4⋊#95C2211yescharacteristic, complemented
111C4⋊#95C2211yescharacteristic, complemented
112#1434C2212yescomplemented
113#1434C2211yescharacteristic, complemented
114#1434C2212yescomplemented
115#1434C2211yescharacteristic, complemented
116C22⋊#95C2212yescomplemented
117C22⋊#95C2212yescomplemented
118C22⋊#95C2212yescomplemented
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C4×#95C2211yescharacteristic, complemented
125C4×#95C2211yescharacteristic, complemented
126C26C2312yes—
127C23×D4—24no—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—42no—
132C23×D4—42no—
133C23×D4C2×C418yes—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2312yes—
139C24×C4C2312yes—
140C24×C4C2312yes—
141C24×C4C2312yes—
142C2×C4×D4—24no—
143C2×C4×D4—24no—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×C4×D4—24no—
147C2×C4×D4—24no—
148C2×C4×D4—42no—
149C2×C4×D4—42no—
150C2×C4×D4—42no—
151C2×C4×D4—42no—
152C2×C4×D4C2×C418yescomplemented
153C2×C4×D4C2×C418yescomplemented
154C2×#117—28no—
155C2×#117—44no—
156C2×#117—44no—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C22⋊C4—28no—
168C22×C22⋊C4—28no—
169C22×C22⋊C4—44no—
170C22×C22⋊C4—44no—
171C22×C22⋊C4—44no—
172C22×C22⋊C4C2×C4116yescomplemented
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⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2312yes—
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2311yescharacteristic
213C22×C42C2312yes—
214C22×C42C2312yes—
215#390—24no—
216#390—24no—
217#390—24no—
218#390—24no—
219#390—24no—
220#390C2×C418yes—
221#390C2×C418yes—
222#390D418yes—
223#389—24no—
224#389—24no—
225#388—28no—
226#388—28no—
227#388—24no—
228#388—24no—
229#386—28no—
230#386—28no—
231#386C2×C4116yescomplemented
232#386C2×C4116yescomplemented
233#385—44no—
234#382—42no—
235#381—44no—
236#380—24no—
237#380—42no—
238#380C2×C418yescomplemented
239#379—28no—
240#379—28no—
241#379—44no—
242#379C2×C4116yescomplemented
243C4×C4⋊C4—24no—
244C4×C4⋊C4—42no—
245C4×C4⋊C4—42no—
246C4×C4⋊C4—42no—
247C4×C22⋊C4—28no—
248C4×C22⋊C4—24no—
249C4×C22⋊C4—44no—
250C4×C22⋊C4—44no—
251C4×C22⋊C4—44no—
252C4×C22⋊C4—42no—
253C4×C22⋊C4—44no—
254C4×C22⋊C4C2×C418yescomplemented
255C2×#95C2311yescharacteristic
256C2×#95C2311yescharacteristic
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2312yes—
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C43—24no—
294C25—24no—
295C25—24no—
296C25—24no—
297C25—24no—
298C25—24no—
299C25—24no—
300C25—42no—
301C25—42no—
302C25—42no—
303C25—42no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25C22×C418yes—
309C25C2412yes—
310C25C2411yescharacteristic
311C25C2412yes—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—232no—
317C22×D4—232no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—416no—
327C22×D4—42no—
328C22×D4—42no—
329C22×D4—416no—
330C22×D4—416no—
331C22×D4—416no—
332C22×D4—416no—
333C22×D4C22×C418yes—
334C22×D4C22×C414yes—
335C22×D4C22×C414yes—
336C22×D4C2×D414yes—
337C22×D4#4114yes—
338C22×D4#4114yes—
339C22×D4#4114yes—
340C23×C4—24no—
341C23×C4—24no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—22no—
346C23×C4—24no—
347C23×C4—24no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
371C23×C4—42no—
372C23×C4C22×C414yes—
373C23×C4C22×C418yes—
374C23×C4C22×C418yes—
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377C23×C4C2412yes—
378C23×C4C2411yescharacteristic
379C23×C4C2412yes—
380C23×C4C2411yescharacteristic
381C23×C4C2411yescharacteristic
382C23×C4C2412yes—
383C23×C4C2412yes—
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2411yescharacteristic
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C4×D4—232no—
396C4×D4—416no—
397C4×D4—416no—
398C4×D4—416no—
399#117—432no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—24no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—41no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4C22×C414yes—
428C2×C4⋊C4C22×C414yes—
429C2×C4⋊C4C2×D414yes—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—24no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—432no—
471C2×C22⋊C4—432no—
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—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—41no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—41no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4C22×C414yes—
507C2×C22⋊C4C22×C418yes—
508C2×C22⋊C4C22×C418yes—
509C2×C22⋊C4C22×C414yes—
510C2×C22⋊C4C22×C418yes—
511C2×C22⋊C4C22×C418yes—
512C2×C22⋊C4C22×C418yes—
513C2×C22⋊C4C22×C418yes—
514C2×C22⋊C4C22×C418yes—
515C2×C22⋊C4C2×D418yes—
516C2×C22⋊C4C2×D418yes—
517C2×C22⋊C4#4114yes—
518C2×C22⋊C4#4114yes—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—24no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—24no—
541C2×C42—22no—
542C2×C42—22no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—24no—
547C2×C42—42no—
548C2×C42—41no—
549C2×C42—41no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42—42no—
553C2×C42—42no—
554C2×C42—42no—
555C2×C42C22×C414yes—
556C2×C42C22×C414yes—
557C2×C42C2×D414yes—
558#95—22no—
559#95—22no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—24no—
571#95—22no—
572#95—42no—
573#95—41no—
574#95—42no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95—41no—
581#95—41no—
582#95—42no—
583#95—41no—
584#95—41no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95C22×C414yes—
594#95C22×C414yes—
595#95C22×C418yes—
596C24—21no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—216no—
633C24—216no—
634C24—216no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—84no—
652C24—84no—
653C24—84no—
654C24—84no—
655C24—84no—
656C24—84no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24C23×C414yes—
668C24C23×C414yes—
669C24C23×C412yes—
670C24C22×D414yes—
671C24C2×#4114yes—
672C24C2×#4114yes—
673C24C2×#4114yes—
674C24C2×#4112yes—
675C24C2×#4112yes—
676C24C2511yescharacteristic
677C2×D4—216no—
678C2×D4—216no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—48no—
692C2×D4—4128no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4#117116yescomplemented
698C2×D4C4×D4116yes—
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—216no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—22no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
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—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—28no—
781C22×C4—28no—
782C22×C4—216no—
783C22×C4—28no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
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—21no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4C23×C412yes—
850C22×C4C23×C412yes—
851C22×C4C23×C412yes—
852C22×C4C23×C412yes—
853C22×C4C23×C414yes—
854C22×C4C23×C414yes—
855C22×C4C23×C412yes—
856C22×C4C23×C412yes—
857C22×C4C22×D414yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C22×D412yes—
861C22×C4C2×#4112yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4112yes—
865C22×C4C2×#4112yes—
866C22×C4C2×#4112yes—
867C22×C4C2×#4112yes—
868C22×C4H(5,𝔽2)12yes—
869C22×C4H(5,𝔽2)12yes—
870C22×C4H(5,𝔽2)12yes—
871C22×C4H(5,𝔽2)12yes—
872C22×C4H(5,𝔽2)12yes—
873C22×C4H(5,𝔽2)12yes—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—44no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C22⋊C4—216no—
885C22⋊C4—28no—
886C22⋊C4—28no—
887C22⋊C4—216no—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—48no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—48no—
896C22⋊C4—44no—
897C22⋊C4—48no—
898C22⋊C4—44no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—48no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—48no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—84no—
910C22⋊C4—84no—
911C22⋊C4—84no—
912C22⋊C4—84no—
913C42—28no—
914C42—28no—
915C42—28no—
916C42—28no—
917C42—44no—
918C42—44no—
919C42—48no—
920C42—44no—
921C42—44no—
922C42—44no—
923C42—44no—
924C42—84no—
925C42—84no—
926C23—22no—
927C23—24no—
928C23—22no—
929C23—24no—
930C23—24no—
931C23—24no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—22no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—24no—
969C23—24no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—24no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—432no—
981C23—432no—
982C23—432no—
983C23—42no—
984C23—41no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—41no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—41no—
997C23—42no—
998C23—41no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—41no—
1006C23—41no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—41no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—41no—
1016C23—41no—
1017C23—42no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—41no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—816no—
1032C23—816no—
1033C23—816no—
1034C23—816no—
1035C23—816no—
1036C23—816no—
1037C23—816no—
1038C23—816no—
1039C23—816no—
1040C23—816no—
1041C23—816no—
1042C23—816no—
1043C23C2×#11718yes—
1044C23C2×C4×D418yes—
1045C23C4×#4114yes—
1046C23C24×C411yescharacteristic
1047C23C23×D411yescharacteristic
1048C23C22×#4111yescharacteristic
1049C23C22×#4111yescharacteristic
1050C23C22×#4111yescharacteristic
1051C23C22×#4111yescharacteristic
1052C23C22×#4111yescharacteristic
1053C23C2×H(5,𝔽2)11yescharacteristic
1054C23C2×H(5,𝔽2)11yescharacteristic
1055C23C2×H(5,𝔽2)11yescharacteristic
1056C23C2×H(5,𝔽2)11yescharacteristic
1057C23C2×H(5,𝔽2)11yescharacteristic
1058C23C2×H(5,𝔽2)11yescharacteristic
1059C23#58511yescharacteristic
1060C23#58511yescharacteristic
1061D4—232no—
1062D4—232no—
1063D4—432no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—432no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—416no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—41no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—41no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—816no—
1198C2×C4—816no—
1199C2×C4—816no—
1200C2×C4C2×#11714yes—
1201C2×C4C2×C4×D414yes—
1202C2×C4#51814yes—
1203C2×C4#51814yes—
1204C2×C4#54614yes—
1205C2×C4#54614yes—
1206C2×C4#54614yes—
1207C2×C4#55114yes—
1208C2×C4#55114yes—
1209C22—24no—
1210C22—28no—
1211C22—28no—
1212C22—24no—
1213C22—28no—
1214C22—24no—
1215C22—28no—
1216C22—28no—
1217C22—28no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—42no—
1223C22—42no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—42no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—42no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—44no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—44no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—42no—
1249C22—44no—
1250C22—44no—
1251C22—42no—
1252C22—44no—
1253C22—42no—
1254C22—864no—
1255C22C22×#11711yescharacteristic
1256C22C22×C4×D411yescharacteristic
1257C22C2×C4×#4111yescharacteristic
1258C22C2×#51811yescharacteristic
1259C22C2×#51811yescharacteristic
1260C22C4×H(5,𝔽2)11yescharacteristic
1261C22C4×H(5,𝔽2)11yescharacteristic
1262C22C2×#54611yescharacteristic
1263C22C2×#54611yescharacteristic
1264C22C2×#54611yescharacteristic
1265C22D4×#4111yescharacteristic
1266C22C2×#55111yescharacteristic
1267C22C2×#55111yescharacteristic
1268C22#347511yescharacteristic
1269C22#348111yescharacteristic
1270C22#348111yescharacteristic
1271C22#348111yescharacteristic
1272C22#348111yescharacteristic
1273C22#348111yescharacteristic
1274C22#348411yescharacteristic
1275C22#348811yescharacteristic
1276C22#350511yescharacteristic
1277C22#350811yescharacteristic
1278C22#351311yescharacteristic
1279C22#351311yescharacteristic
1280C22#351411yescharacteristic
1281C22#351411yescharacteristic
1282C22#351911yescharacteristic
1283C22#351911yescharacteristic
1284C22#351911yescharacteristic
1285C22#352111yescharacteristic
1286C22#354311yescharacteristic
1287C22#354611yescharacteristic
1288C22#354611yescharacteristic
1289C22#354911yescharacteristic
1290C4—24no—
1291C4—24no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—44no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—44no—
1304C4—82no—
1305C4—82no—
1306C4—81no—
1307C4—81no—
1308C4—82no—
1309C4#234218yes—
1310C2—48no—
1311C2—48no—
1312C2—44no—
1313C2C2×#234211yescharacteristic
1314C2#3412611yescharacteristic
1315C2C4×#54611yescharacteristic
1316C2#3426111yescharacteristic
1317C2#3429011yescharacteristic
1318C2#3432011yescharacteristic
1319C2#3449311yescharacteristic
1320C2#5903011yescharacteristic
1321C2#5903811yescharacteristic
1322C2#5904111yescharacteristic
1323C2#5909911yescharacteristic
1324C2#5948011yescharacteristic
1325C2#5948811yescharacteristic
1326C2#5956211yescharacteristic
1327C2#5994511yescharacteristic
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
3. C2×#2293C2semidirect
4. #14427C2semidirect
5. #14365C2semidirect
6. #14068C2semidirect
7. #14064C2semidirect
8. #14018C2semidirect
9. #13993C2semidirect
10. #13991C2semidirect
11. #13984C2semidirect
12. #13979C2semidirect
13. #13973C2semidirect
14. #13941C2semidirect
15. #13916C2semidirect
17. #13875C2semidirect
18. #13868C2semidirect
19. #13820C2semidirect
20. #13820C2semidirect
21. C22⋊C42C2semidirect
22. C4×#390C2semidirect
23. C4×#388C2semidirect
29. C22×#117C22semidirect
33. D4×C22⋊C4C4semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
47. C2×#388C22semidirect
48. C2×#388C22semidirect
53. C2×#385C22semidirect
54. C2×#382C22semidirect
55. C2×#381C22semidirect
63. C2×C4×C4⋊C4C22semidirect
64. C2×C4×C4⋊C4C22semidirect
65. C2×C4×C4⋊C4C22semidirect
66. C2×C4×C4⋊C4C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C2×C4×C22⋊C4C22semidirect
75. C2×C43C22semidirect
76. #1443C22semidirect
77. #1443C22semidirect
78. #1442C22semidirect
80. #1440C22semidirect
81. #1440C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. C4⋊#95C22semidirect
107. C4⋊#95C22semidirect
108. C4⋊#95C22semidirect
109. C4⋊#95C22semidirect
110. C4⋊#95C22semidirect
111. C4⋊#95C22semidirect
112. #1434C22semidirect
113. #1434C22semidirect
114. #1434C22semidirect
115. #1434C22semidirect
116. C22⋊#95C22semidirect
117. C22⋊#95C22semidirect
118. C22⋊#95C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C4×#95C22semidirect
125. C4×#95C22semidirect
152. C2×C4×D4C2×C4semidirect
153. C2×C4×D4C2×C4semidirect
172. C22×C22⋊C4C2×C4semidirect
231. #386C2×C4semidirect
232. #386C2×C4semidirect
238. #380C2×C4semidirect
242. #379C2×C4semidirect
254. C4×C22⋊C4C2×C4semidirect
697. C2×D4#117semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C22⋊C42
C2×#22932
#144272
#143652
#140682
#140642
#140182
#139932
#139912
#139842
#139792
#139732
#139412
#139162
#139022
#138752
#138682
#138202
C22⋊C422
C4×#3902
C4×#3882