Finite Group Databasebeta

← #774057

Subgroups — #774057

Order 512.

3636 conjugacy classes of subgroups.

The subgroup lattice has 1315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2417C211yesmaximal, characteristic, complemented
4C2×#2417C211yesmaximal, characteristic, complemented
5C2×#2417C211yesmaximal, characteristic, complemented
6C2×#2360C211yesmaximal, characteristic, complemented
7#16550C212yesmaximal, complemented
8#15629C212yesmaximal, complemented
9#15439C212yesmaximal, complemented
10#15335C212yesmaximal, complemented
11#15309C212yesmaximal, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15179C211yesmaximal, characteristic, complemented
14#15178C211yesmaximal, characteristic, complemented
15#15131C212yesmaximal, complemented
16#14771C212yesmaximal, complemented
17#14207C212yesmaximal
18#14024C211yesmaximal, characteristic, complemented
19#14005C211yesmaximal, characteristic, complemented
20#13997C211yesmaximal, characteristic, complemented
21#13872C211yesmaximal, characteristic, complemented
22C4×#392C211yesmaximal, characteristic
23C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37#2542—28no—
38#2538—28no—
39#2417—28no—
40#2417—28no—
41#2417—28no—
42C2×#399C2212yes—
43C2×#399C2212yes—
44C2×#398C2212yes—
45C2×#398C2212yes—
46C2×#398C2212yes—
47C2×#396C2212yes—
48C2×#396C2212yes—
49C2×#396C2212yes—
50C2×#396C2212yes—
51C2×#396C2212yes—
52C2×#392C2211yescharacteristic
53#2360—28no—
54C2×#391C2211yescharacteristic
55C2×#391C2211yescharacteristic
56C2×#391C2211yescharacteristic
57C2×#391C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#390C2212yes—
60C2×#390C2212yes—
61C2×#389C2212yes—
62C2×#389C2212yes—
63C2×#389C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#389C2212yes—
66C2×#389C2211yescharacteristic
67C2×#387C2212yes—
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#386C2212yes—
71C2×#386C2212yes—
72C2×#385C2212yes—
73C2×#384C2212yes—
74C2×#384C2211yescharacteristic
75C2×#380C2212yes—
76C2×#380C2212yes—
77C2×#380C2211yescharacteristic
78C2×#380C2211yescharacteristic
79C2×#380C2211yescharacteristic
80C2×#380C2212yes—
81C2×#380C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83C2×C4×C4⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2212yes—
87C2×C4×C22⋊C4C2212yes—
88C2×C4×C22⋊C4C2211yescharacteristic
89#1445C2212yes—
90#1444C2211yescharacteristic
91#1444C2212yes—
92#1444C2212yes—
93#1444C2212yes—
94#1442C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1440C2212yes—
103#1439C2211yescharacteristic
104#1439C2212yes—
105#1439C2211yescharacteristic
106#1439C2211yescharacteristic
107#1439C2212yes—
108#1439C2212yes—
109#1439C2212yes—
110#1439C2212yes—
111#1439C2212yes—
112#1439C2212yes—
113#1438C2211yescharacteristic
114#1438C2211yescharacteristic
115#1438C2211yescharacteristic
116#1437C2212yes—
117#1436C2212yes—
118#1436C2212yes—
119#1436C2212yes—
120#1436C2212yes—
121#1436C2212yes—
122C4⋊#95C2212yes—
123C4⋊#95C2211yescharacteristic
124C4⋊#95C2211yescharacteristic
125C4⋊#95C2211yescharacteristic
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C4×#95C2211yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×C4⋊Q8—24no—
140C2×C4⋊Q8—24no—
141C2×C4⋊Q8—42no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—24no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—24no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—42no—
156C2×C22⋊Q8—42no—
157C2×C22⋊Q8—42no—
158C2×C22⋊Q8—42no—
159C2×C22⋊Q8D418yescomplemented
160C2×C4×Q8—24no—
161C2×C4×Q8—24no—
162C2×C4×Q8—42no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—24no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—24no—
169C2×C4×D4—42no—
170C2×C4×D4—42no—
171C2×C4×D4—42no—
172C22×C4⋊C4—24no—
173C22×C4⋊C4—24no—
174C22×C4⋊C4—24no—
175C22×C4⋊C4—24no—
176C22×C4⋊C4—24no—
177C22×C4⋊C4—42no—
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2311yescharacteristic
190C22×C4⋊C4C2312yes—
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2312yes—
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2311yescharacteristic
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2312yes—
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2312yes—
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2312yes—
224C22×C22⋊C4C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2312yes—
228C22×C42C2312yes—
229C22×C42C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232#399—28no—
233#399—28no—
234#398—28no—
235#398—28no—
236#398—28no—
237#396—28no—
238#396—28no—
239#396—28no—
240#396—28no—
241#396—28no—
242#392Q818yescomplemented
243#391—24no—
244#391—24no—
245#391—24no—
246#391—24no—
247#391—42no—
248#390—28no—
249#390—28no—
250#389—28no—
251#389—24no—
252#389—24no—
253#389—28no—
254#389—44no—
255#389D418yescomplemented
256#387—28no—
257#386—28no—
258#386—28no—
259#386—28no—
260#386—44no—
261#385—28no—
262#384—24no—
263#384—28no—
264#380—24no—
265#380—24no—
266#380—28no—
267#380—28no—
268#380—24no—
269#380—28no—
270#380D418yescomplemented
271C4×C4⋊C4—24no—
272C4×C4⋊C4—24no—
273C4×C22⋊C4—24no—
274C4×C22⋊C4—24no—
275C4×C22⋊C4—28no—
276C4×C22⋊C4—44no—
277C4×C22⋊C4—42no—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2311yescharacteristic
313C25C2411yescharacteristic
314C25C2411yescharacteristic
315C25C2411yescharacteristic
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—22no—
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—22no—
329C22×Q8C2×D414yes—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4—41no—
346C22×D4—41no—
347C22×D4—41no—
348C22×D4C2×Q814yes—
349C22×D4C2×Q814yes—
350C22×D4C2×Q814yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4C2×D414yes—
385C23×C4C2×D414yes—
386C23×C4C2412yes—
387C23×C4C2412yes—
388C23×C4C2411yescharacteristic
389C23×C4C2411yescharacteristic
390C23×C4C2411yescharacteristic
391C23×C4C2412yes—
392C23×C4C2412yes—
393C23×C4C2412yes—
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2411yescharacteristic
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C4⋊Q8—416no—
407C22⋊Q8—232no—
408C22⋊Q8—416no—
409C22⋊Q8—416no—
410C22⋊Q8—416no—
411C22⋊Q8—416no—
412C22⋊Q8—416no—
413C4×Q8—416no—
414C4×D4—416no—
415C4×D4—416no—
416C4×D4—416no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—416no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—41no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—416no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D414yes—
488C2×C4⋊C4C2×D414yes—
489C2×C4⋊C4C2×D418yes—
490C2×C4⋊C4C2×D418yes—
491C2×C4⋊C4C2×D414yes—
492C2×C4⋊C4C2×D414yes—
493C2×C4⋊C4#4114yes—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—41no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—41no—
540C2×C22⋊C4—41no—
541C2×C22⋊C4—41no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
556C2×C22⋊C4C2×D418yes—
557C2×C22⋊C4C2×Q814yes—
558C2×C22⋊C4C2×Q814yes—
559C2×C22⋊C4C2×Q814yes—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—24no—
567C2×C42—24no—
568C2×C42—22no—
569C2×C42—24no—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—24no—
573C2×C42—22no—
574C2×C42—24no—
575C2×C42—42no—
576C2×C42—42no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42C2×D414yes—
580C2×C42#4114yes—
581#95—22no—
582#95—22no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—22no—
599#95—22no—
600#95—24no—
601#95—24no—
602#95—22no—
603#95—22no—
604#95—42no—
605#95—41no—
606#95—42no—
607#95—42no—
608#95—41no—
609#95—42no—
610#95—41no—
611#95—42no—
612#95—42no—
613#95C2×D418yes—
614#95C2×D418yes—
615#95C2×Q814yes—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24C22×D412yes—
655C24C22×D412yes—
656C24C22×Q812yes—
657C24C22×Q812yes—
658C24C22×Q812yes—
659C242−1+412yes—
660C242−1+412yes—
661C24C2511yescharacteristic
662C2×Q8—28no—
663C2×Q8—28no—
664C2×Q8—28no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—44no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—28no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—21no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—28no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—48no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4C22×D414yes—
847C22×C4C22×D414yes—
848C22×C4C22×D412yes—
849C22×C4C22×D414yes—
850C22×C4C22×D412yes—
851C22×C4C22×D414yes—
852C22×C4C22×D412yes—
853C22×C4C22×D414yes—
854C22×C4C22×D414yes—
855C22×C4C22×D412yes—
856C22×C4C22×D412yes—
857C22×C4C22×D412yes—
858C22×C4C22×D412yes—
859C22×C4C22×Q812yes—
860C22×C4C22×Q812yes—
861C22×C4C22×Q812yes—
862C22×C4C22×Q812yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4114yes—
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×C42−1+412yes—
872C4⋊C4—216no—
873C4⋊C4—28no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—44no—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—48no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—84no—
894C4⋊C4—84no—
895C4⋊C4—84no—
896C4⋊C4#121116yes—
897C22⋊C4—216no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—48no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—44no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—44no—
915C22⋊C4—48no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C42—28no—
920C42—28no—
921C42—48no—
922C42—48no—
923C42—44no—
924C42—44no—
925C42—84no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23D4×Q814yes—
1030C23D4×Q814yes—
1031C23C23×D411yescharacteristic
1032C23C23×D411yescharacteristic
1033C23C23×D411yescharacteristic
1034C23C23×Q811yescharacteristic
1035C23C22×#4111yescharacteristic
1036C23C22×#4111yescharacteristic
1037C23C2×H(5,𝔽2)11yescharacteristic
1038C23C2×H(5,𝔽2)11yescharacteristic
1039C23C2×H(5,𝔽2)11yescharacteristic
1040C23C2×2−1+411yescharacteristic
1041C23C2×2−1+411yescharacteristic
1042C23C2×2−1+411yescharacteristic
1043C23#58511yescharacteristic
1044C23#58511yescharacteristic
1045C23#58511yescharacteristic
1046Q8—416no—
1047Q8—88no—
1048D4—416no—
1049D4—416no—
1050D4—416no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—42no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—42no—
1105C2×C4—41no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—42no—
1122C2×C4—41no—
1123C2×C4—42no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—41no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—41no—
1183C2×C4—816no—
1184C2×C4—816no—
1185C2×C4—88no—
1186C2×C4C2×#12118yes—
1187C2×C4C2×#12114yes—
1188C2×C4#53214yes—
1189C2×C4#54014yes—
1190C2×C4D4214yes—
1191C2×C4D4214yes—
1192C2×C4#54614yes—
1193C2×C4D4×Q814yes—
1194C2×C4#55014yes—
1195C2×C4#55414yes—
1196C22—24no—
1197C22—24no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22C22×#12111yescharacteristic
1242C22C2×#53211yescharacteristic
1243C22C2×#54011yescharacteristic
1244C22C2×D4211yescharacteristic
1245C22C2×D4211yescharacteristic
1246C22C2×#54611yescharacteristic
1247C22C2×D4×Q811yescharacteristic
1248C22C2×D4×Q811yescharacteristic
1249C22C2×D4×Q811yescharacteristic
1250C22C2×#55011yescharacteristic
1251C22C2×#55411yescharacteristic
1252C22Q8×#4111yescharacteristic
1253C22#348811yescharacteristic
1254C22#348911yescharacteristic
1255C22#348911yescharacteristic
1256C22#348911yescharacteristic
1257C22#348911yescharacteristic
1258C22#348911yescharacteristic
1259C22#349511yescharacteristic
1260C22#349511yescharacteristic
1261C22#349611yescharacteristic
1262C22#349611yescharacteristic
1263C22#349711yescharacteristic
1264C22#350111yescharacteristic
1265C22#350111yescharacteristic
1266C22#350711yescharacteristic
1267C22#352011yescharacteristic
1268C22#352111yescharacteristic
1269C22#352311yescharacteristic
1270C22#353611yescharacteristic
1271C22#353811yescharacteristic
1272C22#353811yescharacteristic
1273C22#353911yescharacteristic
1274C22#354811yescharacteristic
1275C22#355111yescharacteristic
1276C4—24no—
1277C4—24no—
1278C4—28no—
1279C4—42no—
1280C4—44no—
1281C4—44no—
1282C4—42no—
1283C4—44no—
1284C4—42no—
1285C4—42no—
1286C4—44no—
1287C4—42no—
1288C4—42no—
1289C4—81no—
1290C4—82no—
1291C4—81no—
1292C4—82no—
1293C4—81no—
1294C4—82no—
1295C4#242818yes—
1296C2—44no—
1297C2—44no—
1298C2—82no—
1299C2C2×#242811yescharacteristic
1300C2#3582111yescharacteristic
1301C2#3583411yescharacteristic
1302C2Q8×#12111yescharacteristic
1303C2#3656111yescharacteristic
1304C2#3966411yescharacteristic
1305C2#4263311yescharacteristic
1306C2#4488411yescharacteristic
1307C2#4510311yescharacteristic
1308C2#4511311yescharacteristic
1309C2#4543211yescharacteristic
1310C2#5899811yescharacteristic
1311C2#5899811yescharacteristic
1312C2#5901611yescharacteristic
1313C2#5982311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
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×#2542C2semidirect
2. C2×#2538C2semidirect
3. C2×#2417C2semidirect
4. C2×#2417C2semidirect
5. C2×#2417C2semidirect
6. C2×#2360C2semidirect
7. #16550C2semidirect
8. #15629C2semidirect
9. #15439C2semidirect
10. #15335C2semidirect
11. #15309C2semidirect
12. #15182C2semidirect
13. #15179C2semidirect
14. #15178C2semidirect
15. #15131C2semidirect
16. #14771C2semidirect
18. #14024C2semidirect
19. #14005C2semidirect
20. #13997C2semidirect
21. #13872C2semidirect
23. C22⋊C4×C4⋊C4C2semidirect
159. C2×C22⋊Q8D4semidirect
242. #392Q8semidirect
255. #389D4semidirect
270. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#25382
C2×#24172
C2×#23602
#165502
#156292
#154392
#153352
#153092
#151822
#151792
#151782
#151312
#147712
#142072
#140242
#140052
#139972
#138722
C4×#3922
C22⋊C4×C4⋊C42