Finite Group Databasebeta

← #362104

Subgroups — #362104

Order 512.

1506 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2351C211yesmaximal, characteristic
2C2×#1939C211yesmaximal, characteristic
3C2×#1805C211yesmaximal, characteristic
4C2×#1805C211yesmaximal, characteristic
5C2×#1803C211yesmaximal, characteristic
6C2×C4×#103C211yesmaximal, characteristic
7#13909C211yesmaximal, characteristic
8#11228C211yesmaximal, characteristic
9#11227C211yesmaximal, characteristic
10#11208C211yesmaximal, characteristic
11#11207C211yesmaximal, characteristic
12#10850C211yesmaximal, characteristic
13#10842C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×C4×Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4⋊C8C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×C4⋊C8C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2351—24no—
28#2351C418yescomplemented
29C2×#389—21no—
30C2×#389—21no—
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#384C2211yescharacteristic
34C2×#382—21no—
35C2×#382C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×#382C2211yescharacteristic
38C2×C4×C4⋊C4—21no—
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41#1939—24no—
42#1805—24no—
43#1805—24no—
44#1803—24no—
45C4×#103—24no—
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#340C2211yescharacteristic
57C2×#340C2211yescharacteristic
58C2×#336C2211yescharacteristic
59C2×#336C2211yescharacteristic
60#1441—21no—
61#1441—21no—
62#1436—21no—
63#1436—21no—
64C4⋊#95C2211yescharacteristic
65C4⋊#95C2211yescharacteristic
66C23×Q8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C23×C8C2311yescharacteristic
71C2×C4×Q8—22no—
72C2×C4×Q8—22no—
73C2×C4×Q8—22no—
74C2×C4×Q8—22no—
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—41no—
81C2×C4×Q8—41no—
82C2×C4×Q8—41no—
83C2×C4×Q8—41no—
84C2×C4×Q8C2×C414yes—
85C2×C4×Q8C2×C414yes—
86C2×C4×Q8C2×C414yes—
87C2×C4×Q8D414yes—
88C2×C4×Q8Q814yes—
89C22×C4⋊C4—21no—
90C22×C4⋊C4—21no—
91C22×C4⋊C4—21no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4—21no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—21no—
96C22×C4⋊C4D411yescharacteristic
97C22×C4⋊C4D411yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C42—21no—
106C22×C42—21no—
107C22×C42—21no—
108C22×C42—21no—
109C22×C42C2311yescharacteristic
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C2×C4⋊C8—22no—
113C2×C4⋊C8—22no—
114C2×C4⋊C8—22no—
115C2×C4⋊C8—22no—
116C2×C4⋊C8—22no—
117C2×C4⋊C8—22no—
118C2×C4⋊C8—22no—
119C2×C4⋊C8—41no—
120C2×C4⋊C8—41no—
121C2×#103—22no—
122C2×#103—22no—
123C2×#103—22no—
124C2×#103—22no—
125C2×#103—22no—
126C2×#103—22no—
127C2×#103—22no—
128C2×#103—22no—
129C2×#103—22no—
130C2×#103—22no—
131C2×#103D414yes—
132C2×#103Q814yes—
133C2×C4×C8—22no—
134C2×C4×C8—22no—
135C2×C4×C8—22no—
136#389—28no—
137#389—28no—
138#389—22no—
139#389—22no—
140#389C2×C414yes—
141#389C2×C414yes—
142#384—22no—
143#384—41no—
144#382—22no—
145#382—28no—
146#382—22no—
147#382—22no—
148#382—22no—
149#382—41no—
150#382C2×C414yes—
151C4×C4⋊C4—28no—
152C4×C4⋊C4—22no—
153C4×C4⋊C4—22no—
154C4×C4⋊C4C2×C414yes—
155C4×C4⋊C4D414yes—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95—21no—
165C2×#95—21no—
166C2×#95—21no—
167C2×#95—21no—
168C2×#95—21no—
169C2×#95D411yescharacteristic
170C2×#95D411yescharacteristic
171#340—22no—
172#340—22no—
173#340—22no—
174#340—22no—
175#340—22no—
176#340—22no—
177#340—22no—
178#340—22no—
179#340—41no—
180#340—41no—
181#340—41no—
182#340—41no—
183#336—22no—
184#336—22no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8C22×C412yes—
193C22×Q8C2×D412yes—
194C22×Q8C2×D412yes—
195C22×Q8C2×Q812yes—
196C22×Q8C2×Q812yes—
197C22×Q8#4112yes—
198C22×Q8#4112yes—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2411yescharacteristic
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8C2×D412yes—
241C22×C8C2×Q812yes—
242C4×Q8—28no—
243C4×Q8—28no—
244C4×Q8—28no—
245C4×Q8—28no—
246C4×Q8—28no—
247C4×Q8—44no—
248C4×Q8—44no—
249C4×Q8—44no—
250C4×Q8—44no—
251C4×Q8—44no—
252C4×Q8—44no—
253C4×Q8C4⋊C4116yescomplemented
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—81no—
313C2×C4⋊C4—81no—
314C2×C4⋊C4C22⋊C414yes—
315C2×C4⋊C4C22⋊C414yes—
316C2×C4⋊C4C22×C412yes—
317C2×C4⋊C4C22×C412yes—
318C2×C4⋊C4C22×C412yes—
319C2×C4⋊C4C2×D412yes—
320C2×C4⋊C4C2×D412yes—
321C2×C4⋊C4C2×Q812yes—
322C2×C4⋊C4C2×Q812yes—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—24no—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42—42no—
341C2×C42—81no—
342C2×C42—81no—
343C2×C42C22×C412yes—
344C2×C42C22×C412yes—
345C2×C42C22×C412yes—
346C2×C42C2×D412yes—
347C2×C42C2×D412yes—
348C2×C42C2×D412yes—
349C2×C42C2×D412yes—
350C2×C42C2×Q812yes—
351C2×C42#4112yes—
352C2×C42#4112yes—
353C4⋊C8—44no—
354C4⋊C8—44no—
355C4⋊C8—44no—
356#103—28no—
357#103—28no—
358#103—44no—
359#103—44no—
360C4×C8—44no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—42no—
366#95—42no—
367#95—42no—
368#95—42no—
369#95—42no—
370#95—42no—
371#95—42no—
372#95—81no—
373#95—81no—
374#95C22⋊C414yes—
375#95C22⋊C414yes—
376C24C22×D411yescharacteristic
377C2×Q8—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8C2×C4⋊C414yes—
399C2×Q8C4×D414yes—
400C2×Q8C4×Q814yes—
401C2×Q8#12114yes—
402C2×Q8C22⋊Q814yes—
403C2×Q8#12514yes—
404C2×Q8C4⋊Q814yes—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4C2×C22⋊C412yes—
492C22×C4C2×C22⋊C412yes—
493C22×C4C2×C22⋊C412yes—
494C22×C4C2×C22⋊C412yes—
495C22×C4C2×C22⋊C412yes—
496C22×C4C2×C22⋊C412yes—
497C22×C4#12112yes—
498C22×C4#12112yes—
499C22×C4C22⋊Q812yes—
500C22×C4C22⋊Q812yes—
501C22×C4#13512yes—
502C22×C4#13512yes—
503C22×C4C23×C411yescharacteristic
504C22×C4C22×D411yescharacteristic
505C22×C4C22×D411yescharacteristic
506C22×C4C22×D411yescharacteristic
507C22×C4C22×Q811yescharacteristic
508C22×C4C22×Q811yescharacteristic
509C22×C4C2×#4111yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4H(5,𝔽2)11yescharacteristic
514C22×C4H(5,𝔽2)11yescharacteristic
515C22×C42−1+411yescharacteristic
516C22×C42−1+411yescharacteristic
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—216no—
549C4⋊C4—28no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—44no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—48no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—84no—
580C4⋊C4—84no—
581C4⋊C4C2×C4⋊C414yes—
582C42—22no—
583C42—22no—
584C42—22no—
585C42—22no—
586C42—22no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—216no—
591C42—48no—
592C42—48no—
593C42—84no—
594C42C2×C4⋊C414yes—
595C42#11714yes—
596C42#12114yes—
597C42C22⋊Q814yes—
598C23C22×C22⋊C411yescharacteristic
599C23C2×#12111yescharacteristic
600C23C2×C22⋊Q811yescharacteristic
601C23D4211yescharacteristic
602C23#54611yescharacteristic
603C23#54811yescharacteristic
604C23D4×Q811yescharacteristic
605C23C2×#13511yescharacteristic
606C23C2×#13511yescharacteristic
607C23#57511yescharacteristic
608C23#57511yescharacteristic
609C23#57711yescharacteristic
610C23#57711yescharacteristic
611C23#57811yescharacteristic
612C23#57811yescharacteristic
613Q8—24no—
614Q8—24no—
615Q8—24no—
616Q8—24no—
617Q8—24no—
618Q8—24no—
619Q8—24no—
620Q8#38918yes—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4#38014yes—
717C2×C4#38014yes—
718C2×C4#41614yes—
719C2×C4C22×C4⋊C411yescharacteristic
720C2×C4C2×#11711yescharacteristic
721C2×C4C2×C4×D411yescharacteristic
722C2×C4C2×C4×Q811yescharacteristic
723C2×C4#51811yescharacteristic
724C2×C4#51911yescharacteristic
725C2×C4C2×#12111yescharacteristic
726C2×C4C2×#12111yescharacteristic
727C2×C4C2×C22⋊Q811yescharacteristic
728C2×C4C2×C22⋊Q811yescharacteristic
729C2×C4C2×#12511yescharacteristic
730C2×C4C2×C4⋊Q811yescharacteristic
731C2×C4#53711yescharacteristic
732C2×C4#53711yescharacteristic
733C2×C4#54411yescharacteristic
734C2×C4#54411yescharacteristic
735C2×C4D4211yescharacteristic
736C2×C4#54611yescharacteristic
737C2×C4#54711yescharacteristic
738C2×C4#54711yescharacteristic
739C2×C4#54811yescharacteristic
740C2×C4D4×Q811yescharacteristic
741C2×C4#55211yescharacteristic
742C2×C4#55211yescharacteristic
743C2×C4#55311yescharacteristic
744C2×C4#55311yescharacteristic
745C2×C4#55411yescharacteristic
746C2×C4#55411yescharacteristic
747C8—42no—
748C8—42no—
749C8—81no—
750C8—81no—
751C22C2×#38011yescharacteristic
752C22D4×C22⋊C411yescharacteristic
753C22Q8×C22⋊C411yescharacteristic
754C22#241611yescharacteristic
755C22#241711yescharacteristic
756C22#244011yescharacteristic
757C22#244211yescharacteristic
758C22C2×#41611yescharacteristic
759C22#289611yescharacteristic
760C22#289811yescharacteristic
761C22#289811yescharacteristic
762C22#303511yescharacteristic
763C22#303511yescharacteristic
764C22#304311yescharacteristic
765C22#304411yescharacteristic
766C22#307611yescharacteristic
767C22#307611yescharacteristic
768C22#308211yescharacteristic
769C22#308211yescharacteristic
770C22#327511yescharacteristic
771C22#327711yescharacteristic
772C22#328211yescharacteristic
773C22#328511yescharacteristic
774C22#330011yescharacteristic
775C22#330111yescharacteristic
776C22#332611yescharacteristic
777C22#332711yescharacteristic
778C22#336411yescharacteristic
779C22#336511yescharacteristic
780C22#337111yescharacteristic
781C22#337711yescharacteristic
782C22#338111yescharacteristic
783C22#338311yescharacteristic
784C22#338811yescharacteristic
785C22#339011yescharacteristic
786C4—28no—
787C4—24no—
788C4—24no—
789C4—24no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—44no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—161no—
799C4—161no—
800C4C2×#38911yescharacteristic
801C4#231611yescharacteristic
802C4#234411yescharacteristic
803C4#234511yescharacteristic
804C4#241611yescharacteristic
805C4#241711yescharacteristic
806C4#244011yescharacteristic
807C4#244211yescharacteristic
808C2#1390711yescharacteristic
809C2#2064511yescharacteristic
810C2#2065111yescharacteristic
811C2#2241611yescharacteristic
812C2#2242911yescharacteristic
813C2#2252111yescharacteristic
814C2#2252711yescharacteristic
815C2#2473411yescharacteristic
816C2#2473611yescharacteristic
817C2#2481911yescharacteristic
818C2#2482111yescharacteristic
819C2#2604811yescharacteristic
820C2#2605011yescharacteristic
821C2#2611411yescharacteristic
822C2#2611611yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
28. #2351C4semidirect
253. C4×Q8C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23512
C2×#19392
C2×#18052
C2×#18032
C2×C4×#1032
#139092
#112282
#112272
#112082
#112072
#108502
#108422
#107892