Finite Group Databasebeta

← #154385

Subgroups — #154385

Order 512.

3442 conjugacy classes of subgroups.

The subgroup lattice has 1351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic
2C22×#389C211yesmaximal, characteristic
3C2×#1441C212yesmaximal
4C2×C4⋊#95C211yesmaximal, characteristic
5C2×C4⋊#95C211yesmaximal, characteristic
6C2×C4⋊#95C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8C2×C4×#95C211yesmaximal, characteristic
9#7557C212yesmaximal
10#7557C212yesmaximal
11#7556C212yesmaximal
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C4⋊C4C2212yes—
15C23×C4⋊C4C2212yes—
16C23×C4⋊C4C2211yescharacteristic
17C23×C4⋊C4C2211yescharacteristic
18C23×C42C2211yescharacteristic
19C23×C42C2211yescharacteristic
20C23×C42C2211yescharacteristic
21C2×#389—24no—
22C2×#389—24no—
23C2×#389—24no—
24C2×#389—24no—
25C2×#389—24no—
26C2×#389C418yescomplemented
27C22×#95C2212yes—
28C22×#95C2211yescharacteristic
29C22×#95C2211yescharacteristic
30C22×#95C2212yes—
31C22×#95C2212yes—
32C22×#95C2212yes—
33C22×#95C2212yes—
34C22×#95C2212yes—
35C22×#95C2212yes—
36C22×#95C2212yes—
37C22×#95C2212yes—
38C22×#95C2212yes—
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41#1441—28no—
42C4⋊#95—24no—
43C4⋊#95—24no—
44C4⋊#95—24no—
45C4⋊#95—24no—
46C4×#95—24no—
47C24×C4C2312yes—
48C24×C4C2312yes—
49C24×C4C2312yes—
50C24×C4C2312yes—
51C24×C4C2311yescharacteristic
52C24×C4C2311yescharacteristic
53C24×C4C2311yescharacteristic
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C24×C4C2311yescharacteristic
57C24×C4C2311yescharacteristic
58C22×C4⋊C4—22no—
59C22×C4⋊C4—22no—
60C22×C4⋊C4—22no—
61C22×C4⋊C4—22no—
62C22×C4⋊C4—22no—
63C22×C4⋊C4—22no—
64C22×C4⋊C4—22no—
65C22×C4⋊C4—22no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4—22no—
70C22×C4⋊C4—24no—
71C22×C4⋊C4—24no—
72C22×C4⋊C4—24no—
73C22×C4⋊C4—24no—
74C22×C4⋊C4—24no—
75C22×C4⋊C4—24no—
76C22×C4⋊C4—22no—
77C22×C4⋊C4—22no—
78C22×C4⋊C4—24no—
79C22×C4⋊C4—22no—
80C22×C4⋊C4—22no—
81C22×C4⋊C4—22no—
82C22×C4⋊C4—22no—
83C22×C4⋊C4—22no—
84C22×C4⋊C4—22no—
85C22×C4⋊C4—24no—
86C22×C4⋊C4—24no—
87C22×C4⋊C4—42no—
88C22×C4⋊C4—42no—
89C22×C4⋊C4—42no—
90C22×C4⋊C4—42no—
91C22×C4⋊C4C2×C418yes—
92C22×C4⋊C4C2×C414yes—
93C22×C4⋊C4C2×C414yes—
94C22×C4⋊C4D414yes—
95C22×C4⋊C4D414yes—
96C22×C4⋊C4D414yes—
97C22×C4⋊C4D414yes—
98C22×C4⋊C4Q814yes—
99C22×C4⋊C4Q814yes—
100C22×C42—22no—
101C22×C42—22no—
102C22×C42—22no—
103C22×C42—22no—
104C22×C42—22no—
105C22×C42—22no—
106C22×C42—22no—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42—22no—
110C22×C42—22no—
111C22×C42—22no—
112C22×C42—22no—
113C22×C42—22no—
114C22×C42—22no—
115C22×C42—22no—
116C22×C42—22no—
117C22×C42—22no—
118C22×C42C2×C414yes—
119C22×C42D414yes—
120C22×C42Q814yes—
121#389—232no—
122#389—232no—
123C2×#95—22no—
124C2×#95—22no—
125C2×#95—22no—
126C2×#95—22no—
127C2×#95—24no—
128C2×#95—24no—
129C2×#95—24no—
130C2×#95—24no—
131C2×#95—24no—
132C2×#95—22no—
133C2×#95—22no—
134C2×#95—22no—
135C2×#95—22no—
136C2×#95—22no—
137C2×#95—22no—
138C2×#95—24no—
139C2×#95—24no—
140C2×#95—24no—
141C2×#95—24no—
142C2×#95—24no—
143C2×#95—24no—
144C2×#95—24no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—24no—
152C2×#95—24no—
153C2×#95—24no—
154C2×#95—42no—
155C2×#95—42no—
156C2×#95—42no—
157C2×#95—42no—
158C2×#95—42no—
159C2×#95—42no—
160C2×#95—42no—
161C2×#95—42no—
162C2×#95C2×C418yes—
163C2×#95D414yes—
164C2×#95Q814yes—
165C25C2411yescharacteristic
166C23×C4—22no—
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—21no—
174C23×C4—21no—
175C23×C4—22no—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—21no—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—22no—
193C23×C4—22no—
194C23×C4—22no—
195C23×C4—22no—
196C23×C4—22no—
197C23×C4—22no—
198C23×C4—22no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—22no—
204C23×C4—22no—
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4—21no—
215C23×C4—21no—
216C23×C4—21no—
217C23×C4—21no—
218C23×C4—21no—
219C23×C4—21no—
220C23×C4—21no—
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—22no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—21no—
240C23×C4—22no—
241C23×C4—21no—
242C23×C4—21no—
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—21no—
246C23×C4—21no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4—21no—
250C23×C4—22no—
251C23×C4—21no—
252C23×C4—22no—
253C23×C4—21no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—21no—
257C23×C4—21no—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4C22×C414yes—
291C23×C4C22×C414yes—
292C23×C4C22×C412yes—
293C23×C4C22×C412yes—
294C23×C4C22×C412yes—
295C23×C4C2×D414yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D412yes—
300C23×C4C2×D412yes—
301C23×C4C2×D412yes—
302C23×C4C2×D412yes—
303C23×C4C2×D412yes—
304C23×C4C2×D412yes—
305C23×C4C2×D412yes—
306C23×C4C2×D412yes—
307C23×C4C2×D412yes—
308C23×C4C2×D412yes—
309C23×C4C2×Q814yes—
310C23×C4C2×Q814yes—
311C23×C4C2×Q812yes—
312C23×C4C2×Q812yes—
313C23×C4C2×Q812yes—
314C23×C4C2×Q812yes—
315C23×C4C2×Q812yes—
316C23×C4C2×Q812yes—
317C23×C4C2×Q812yes—
318C23×C4C2×Q812yes—
319C23×C4#4112yes—
320C23×C4#4112yes—
321C23×C4#4112yes—
322C23×C4#4112yes—
323C23×C4#4112yes—
324C23×C4#4112yes—
325C23×C4#4112yes—
326C23×C4#4112yes—
327C23×C4#4112yes—
328C23×C4#4112yes—
329C23×C4#4112yes—
330C23×C4#4112yes—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—216no—
344C2×C4⋊C4—216no—
345C2×C4⋊C4—216no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—48no—
353C2×C4⋊C4—48no—
354C2×C4⋊C4—48no—
355C2×C4⋊C4—48no—
356C2×C4⋊C4—48no—
357C2×C4⋊C4—48no—
358C2×C4⋊C4—48no—
359C2×C4⋊C4—48no—
360C2×C4⋊C4—48no—
361C2×C4⋊C4—48no—
362C2×C4⋊C4—48no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4C22⋊C4116yes—
372C2×C4⋊C4C4⋊C4116yescomplemented
373C2×C42—28no—
374C2×C42—28no—
375C2×C42—28no—
376C2×C42—28no—
377C2×C42—28no—
378C2×C42—28no—
379C2×C42—28no—
380C2×C42—28no—
381C2×C42—28no—
382C2×C42—44no—
383C2×C42—44no—
384C2×C42—44no—
385C2×C42—44no—
386C2×C42—44no—
387C2×C42—44no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42—44no—
391C2×C42—44no—
392C2×C42—44no—
393C2×C42—44no—
394#95—28no—
395#95—28no—
396#95—216no—
397#95—216no—
398#95—28no—
399#95—28no—
400#95—48no—
401#95—48no—
402#95—48no—
403#95—48no—
404#95—48no—
405#95—48no—
406#95—48no—
407#95—48no—
408C24C23×C411yescharacteristic
409C24C22×D411yescharacteristic
410C24C22×D411yescharacteristic
411C24C22×D411yescharacteristic
412C24C22×D411yescharacteristic
413C24C22×D411yescharacteristic
414C24C22×D411yescharacteristic
415C24C22×Q811yescharacteristic
416C24C22×Q811yescharacteristic
417C24C22×Q811yescharacteristic
418C24C22×Q811yescharacteristic
419C24C2×#4111yescharacteristic
420C24C2×#4111yescharacteristic
421C24C2×#4111yescharacteristic
422C24C2×#4111yescharacteristic
423C24C2×#4111yescharacteristic
424C24C2×#4111yescharacteristic
425C24C2×#4111yescharacteristic
426C24C2×#4111yescharacteristic
427C24C2×#4111yescharacteristic
428C24C2×#4111yescharacteristic
429C24C2×#4111yescharacteristic
430C24C2×#4111yescharacteristic
431C24H(5,𝔽2)11yescharacteristic
432C24H(5,𝔽2)11yescharacteristic
433C24H(5,𝔽2)11yescharacteristic
434C24H(5,𝔽2)11yescharacteristic
435C242−1+411yescharacteristic
436C242−1+411yescharacteristic
437C242−1+411yescharacteristic
438C242−1+411yescharacteristic
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—42no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—42no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—42no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—41no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4—41no—
673C22×C4—41no—
674C22×C4—41no—
675C22×C4—41no—
676C22×C4—41no—
677C22×C4—42no—
678C22×C4—41no—
679C22×C4—41no—
680C22×C4—41no—
681C22×C4—41no—
682C22×C4—41no—
683C22×C4—41no—
684C22×C4—41no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—41no—
688C22×C4—42no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—41no—
693C22×C4—41no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—41no—
701C22×C4—41no—
702C22×C4—41no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—41no—
713C22×C4—41no—
714C22×C4—41no—
715C22×C4—41no—
716C22×C4—42no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—41no—
724C22×C4—41no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—42no—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—42no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4—42no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—42no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4C2×C22⋊C418yes—
782C22×C4C2×C22⋊C414yes—
783C22×C4C2×C4⋊C418yes—
784C22×C4C2×C4⋊C414yes—
785C22×C4#11714yes—
786C22×C4C4×D414yes—
787C22×C4C4×D414yes—
788C22×C4C4×D414yes—
789C22×C4C4×Q814yes—
790C22×C4C4×Q814yes—
791C22×C4C4×Q814yes—
792C22×C4#12014yes—
793C22×C4#12114yes—
794C22×C4#12114yes—
795C22×C4#12114yes—
796C22×C4#12114yes—
797C22×C4#12114yes—
798C22×C4#12114yes—
799C22×C4#12114yes—
800C22×C4C22⋊Q814yes—
801C22×C4C22⋊Q814yes—
802C22×C4C22⋊Q814yes—
803C22×C4C22⋊Q814yes—
804C22×C4C22⋊Q814yes—
805C22×C4C22⋊Q814yes—
806C22×C4C22⋊Q814yes—
807C22×C4C22⋊Q814yes—
808C22×C4C22⋊Q814yes—
809C22×C4#12314yes—
810C22×C4#12314yes—
811C22×C4#12314yes—
812C22×C4#12414yes—
813C22×C4#12514yes—
814C22×C4#12514yes—
815C22×C4#12514yes—
816C22×C4#12514yes—
817C22×C4#12514yes—
818C22×C4#12614yes—
819C22×C4#12614yes—
820C22×C4C4⋊Q814yes—
821C22×C4C4⋊Q814yes—
822C22×C4C4⋊Q814yes—
823C22×C4C4⋊Q814yes—
824C4⋊C4—232no—
825C4⋊C4—232no—
826C4⋊C4—432no—
827C4⋊C4—432no—
828C4⋊C4—416no—
829C4⋊C4—416no—
830C42—416no—
831C42—416no—
832C42—416no—
833C23C22×C22⋊C411yescharacteristic
834C23C22×C4⋊C411yescharacteristic
835C23C2×#11711yescharacteristic
836C23C2×C4×D411yescharacteristic
837C23C2×C4×D411yescharacteristic
838C23C2×C4×D411yescharacteristic
839C23C2×C4×Q811yescharacteristic
840C23C2×C4×Q811yescharacteristic
841C23C2×C4×Q811yescharacteristic
842C23C4×#4111yescharacteristic
843C23C4×#4111yescharacteristic
844C23#51811yescharacteristic
845C23#51911yescharacteristic
846C23#52011yescharacteristic
847C23#52011yescharacteristic
848C23C2×#12011yescharacteristic
849C23C2×#12111yescharacteristic
850C23C2×#12111yescharacteristic
851C23C2×#12111yescharacteristic
852C23C2×#12111yescharacteristic
853C23C2×#12111yescharacteristic
854C23C2×#12111yescharacteristic
855C23C2×#12111yescharacteristic
856C23C2×C22⋊Q811yescharacteristic
857C23C2×C22⋊Q811yescharacteristic
858C23C2×C22⋊Q811yescharacteristic
859C23C2×C22⋊Q811yescharacteristic
860C23C2×C22⋊Q811yescharacteristic
861C23C2×C22⋊Q811yescharacteristic
862C23C2×C22⋊Q811yescharacteristic
863C23C2×C22⋊Q811yescharacteristic
864C23C2×C22⋊Q811yescharacteristic
865C23C2×#12311yescharacteristic
866C23C2×#12311yescharacteristic
867C23C2×#12311yescharacteristic
868C23#52511yescharacteristic
869C23#52511yescharacteristic
870C23C2×#12411yescharacteristic
871C23C2×#12511yescharacteristic
872C23C2×#12511yescharacteristic
873C23C2×#12511yescharacteristic
874C23C2×#12511yescharacteristic
875C23C2×#12511yescharacteristic
876C23C2×#12611yescharacteristic
877C23C2×#12611yescharacteristic
878C23#52911yescharacteristic
879C23#52911yescharacteristic
880C23#52911yescharacteristic
881C23#52911yescharacteristic
882C23#52911yescharacteristic
883C23#52911yescharacteristic
884C23#52911yescharacteristic
885C23#52911yescharacteristic
886C23C2×C4⋊Q811yescharacteristic
887C23C2×C4⋊Q811yescharacteristic
888C23C2×C4⋊Q811yescharacteristic
889C23C2×C4⋊Q811yescharacteristic
890C23#53211yescharacteristic
891C23#53211yescharacteristic
892C23#53211yescharacteristic
893C23#53211yescharacteristic
894C23#53311yescharacteristic
895C23#53311yescharacteristic
896C23#53311yescharacteristic
897C23#53311yescharacteristic
898C23#53311yescharacteristic
899C23#53311yescharacteristic
900C23#53511yescharacteristic
901C23#53611yescharacteristic
902C23#53711yescharacteristic
903C23#53711yescharacteristic
904C23#54011yescharacteristic
905C23#54011yescharacteristic
906C23#54011yescharacteristic
907C23#54011yescharacteristic
908C23#54111yescharacteristic
909C23#54111yescharacteristic
910C23#54111yescharacteristic
911C23#54111yescharacteristic
912C23#54211yescharacteristic
913C23#54211yescharacteristic
914C23#54211yescharacteristic
915C23#54211yescharacteristic
916C23#54211yescharacteristic
917C23#54211yescharacteristic
918C23#54211yescharacteristic
919C23#54211yescharacteristic
920C23#54411yescharacteristic
921C23#54411yescharacteristic
922C23#54411yescharacteristic
923C23#54411yescharacteristic
924C23D4211yescharacteristic
925C23D4211yescharacteristic
926C23D4211yescharacteristic
927C23D4211yescharacteristic
928C23#54611yescharacteristic
929C23#54611yescharacteristic
930C23#54611yescharacteristic
931C23#54611yescharacteristic
932C23#54611yescharacteristic
933C23#54611yescharacteristic
934C23#54611yescharacteristic
935C23#54611yescharacteristic
936C23#54711yescharacteristic
937C23#54711yescharacteristic
938C23#54711yescharacteristic
939C23#54711yescharacteristic
940C23#54711yescharacteristic
941C23#54711yescharacteristic
942C23#54811yescharacteristic
943C23#54811yescharacteristic
944C23#54811yescharacteristic
945C23#54811yescharacteristic
946C23#54811yescharacteristic
947C23#54811yescharacteristic
948C23#54811yescharacteristic
949C23#54811yescharacteristic
950C23D4×Q811yescharacteristic
951C23D4×Q811yescharacteristic
952C23D4×Q811yescharacteristic
953C23D4×Q811yescharacteristic
954C23D4×Q811yescharacteristic
955C23D4×Q811yescharacteristic
956C23#55011yescharacteristic
957C23#55011yescharacteristic
958C23#55011yescharacteristic
959C23#55011yescharacteristic
960C23#55211yescharacteristic
961C23#55211yescharacteristic
962C23#55211yescharacteristic
963C23#55211yescharacteristic
964C23#55311yescharacteristic
965C23#55311yescharacteristic
966C23#55311yescharacteristic
967C23#55311yescharacteristic
968C23#55411yescharacteristic
969C23#55411yescharacteristic
970C23#55411yescharacteristic
971C23#55411yescharacteristic
972C23#55411yescharacteristic
973C23#55411yescharacteristic
974C23#55411yescharacteristic
975C23#55411yescharacteristic
976C23#55511yescharacteristic
977C23#55511yescharacteristic
978C23#55611yescharacteristic
979C23#55611yescharacteristic
980C23#55711yescharacteristic
981C23#55711yescharacteristic
982C23#55711yescharacteristic
983C23#55711yescharacteristic
984C23#55711yescharacteristic
985C23#55711yescharacteristic
986C23Q8211yescharacteristic
987C23Q8211yescharacteristic
988C2×C4—24no—
989C2×C4—28no—
990C2×C4—28no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—24no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—24no—
1001C2×C4—24no—
1002C2×C4—24no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—28no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—44no—
1013C2×C4—42no—
1014C2×C4—42no—
1015C2×C4—44no—
1016C2×C4—44no—
1017C2×C4—42no—
1018C2×C4—44no—
1019C2×C4—42no—
1020C2×C4—44no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—44no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—42no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—42no—
1032C2×C4—42no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—44no—
1036C2×C4—42no—
1037C2×C4—44no—
1038C2×C4—42no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—42no—
1042C2×C4—42no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—44no—
1048C2×C4—42no—
1049C2×C4—42no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—44no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—42no—
1058C2×C4—42no—
1059C2×C4—42no—
1060C2×C4—42no—
1061C2×C4—42no—
1062C2×C4—44no—
1063C2×C4—44no—
1064C2×C4—42no—
1065C2×C4—44no—
1066C2×C4—42no—
1067C2×C4—42no—
1068C2×C4—42no—
1069C2×C4—42no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—42no—
1074C2×C4—42no—
1075C2×C4—42no—
1076C2×C4—42no—
1077C2×C4—42no—
1078C2×C4—42no—
1079C2×C4—42no—
1080C2×C4—42no—
1081C2×C4—42no—
1082C2×C4—44no—
1083C2×C4—44no—
1084C2×C4—44no—
1085C2×C4—44no—
1086C2×C4—42no—
1087C2×C4—42no—
1088C2×C4—42no—
1089C2×C4—42no—
1090C2×C4—42no—
1091C2×C4—42no—
1092C2×C4—42no—
1093C2×C4—42no—
1094C2×C4—42no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—44no—
1102C2×C4—42no—
1103C2×C4—42no—
1104C2×C4—42no—
1105C2×C4—42no—
1106C2×C4—44no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—44no—
1115C2×C4—44no—
1116C2×C4—44no—
1117C2×C4—44no—
1118C2×C4—44no—
1119C2×C4—44no—
1120C2×C4—44no—
1121C2×C4—44no—
1122C2×C4—82no—
1123C2×C4—82no—
1124C2×C4—82no—
1125C2×C4—82no—
1126C2×C4—82no—
1127C2×C4—82no—
1128C2×C4—82no—
1129C2×C4—82no—
1130C2×C4—82no—
1131C2×C4—82no—
1132C2×C4—82no—
1133C2×C4—82no—
1134C2×C4—82no—
1135C2×C4—82no—
1136C2×C4—82no—
1137C2×C4—82no—
1138C2×C4#38018yes—
1139C2×C4#38618yes—
1140C2×C4#38718yes—
1141C2×C4#38718yes—
1142C2×C4#38918yes—
1143C2×C4#38918yes—
1144C2×C4#39118yes—
1145C2×C4#39418yes—
1146C2×C4#39518yes—
1147C2×C4#39618yes—
1148C2×C4#39618yes—
1149C2×C4#39818yes—
1150C2×C4#39818yes—
1151C2×C4#39818yes—
1152C2×C4#40018yes—
1153C22C2×#38011yescharacteristic
1154C22C2×#38611yescharacteristic
1155C22C2×#38711yescharacteristic
1156C22C2×#38711yescharacteristic
1157C22C2×#38911yescharacteristic
1158C22C2×#38911yescharacteristic
1159C22#229311yescharacteristic
1160C22C2×#39111yescharacteristic
1161C22#229511yescharacteristic
1162C22C4×#12111yescharacteristic
1163C22C4×C22⋊Q811yescharacteristic
1164C22C4×#12511yescharacteristic
1165C22C4×C4⋊Q811yescharacteristic
1166C22#231911yescharacteristic
1167C22#232011yescharacteristic
1168C22#232311yescharacteristic
1169C22#232411yescharacteristic
1170C22#233011yescharacteristic
1171C22#233111yescharacteristic
1172C22D4×C22⋊C411yescharacteristic
1173C22#233911yescharacteristic
1174C22Q8×C22⋊C411yescharacteristic
1175C22#234111yescharacteristic
1176C22D4×C4⋊C411yescharacteristic
1177C22#234911yescharacteristic
1178C22Q8×C4⋊C411yescharacteristic
1179C22#235111yescharacteristic
1180C22#236011yescharacteristic
1181C22#236111yescharacteristic
1182C22#236211yescharacteristic
1183C22#236311yescharacteristic
1184C22#236511yescharacteristic
1185C22#236911yescharacteristic
1186C22#237011yescharacteristic
1187C22#237011yescharacteristic
1188C22C2×#39411yescharacteristic
1189C22C2×#39511yescharacteristic
1190C22C2×#39611yescharacteristic
1191C22C2×#39611yescharacteristic
1192C22C2×#39811yescharacteristic
1193C22C2×#39811yescharacteristic
1194C22C2×#39811yescharacteristic
1195C22C2×#40011yescharacteristic
1196C22#240711yescharacteristic
1197C22#240711yescharacteristic
1198C22#240811yescharacteristic
1199C22#240911yescharacteristic
1200C22#241411yescharacteristic
1201C22#241511yescharacteristic
1202C22#241611yescharacteristic
1203C22#241711yescharacteristic
1204C22#242011yescharacteristic
1205C22#242011yescharacteristic
1206C22#242111yescharacteristic
1207C22#242111yescharacteristic
1208C22#242211yescharacteristic
1209C22#242211yescharacteristic
1210C22#242311yescharacteristic
1211C22#242311yescharacteristic
1212C22#242611yescharacteristic
1213C22#242611yescharacteristic
1214C22#242611yescharacteristic
1215C22#242611yescharacteristic
1216C22#242711yescharacteristic
1217C22#242711yescharacteristic
1218C22#242711yescharacteristic
1219C22#242711yescharacteristic
1220C22#242811yescharacteristic
1221C22#242811yescharacteristic
1222C22#242811yescharacteristic
1223C22#242811yescharacteristic
1224C22#242911yescharacteristic
1225C22#242911yescharacteristic
1226C22#242911yescharacteristic
1227C22#242911yescharacteristic
1228C22#243911yescharacteristic
1229C22#243911yescharacteristic
1230C22#244011yescharacteristic
1231C22#244011yescharacteristic
1232C22#244111yescharacteristic
1233C22#244111yescharacteristic
1234C22#244211yescharacteristic
1235C22#244211yescharacteristic
1236C22#245111yescharacteristic
1237C22#245111yescharacteristic
1238C22#245111yescharacteristic
1239C22#245111yescharacteristic
1240C22#245111yescharacteristic
1241C22#245211yescharacteristic
1242C22#245211yescharacteristic
1243C22#245211yescharacteristic
1244C22#245211yescharacteristic
1245C22#245211yescharacteristic
1246C22#245311yescharacteristic
1247C22#245311yescharacteristic
1248C22#245311yescharacteristic
1249C22#245311yescharacteristic
1250C22#245311yescharacteristic
1251C22#245411yescharacteristic
1252C22#245411yescharacteristic
1253C22#245411yescharacteristic
1254C22#245411yescharacteristic
1255C22#245411yescharacteristic
1256C22#248911yescharacteristic
1257C22#249011yescharacteristic
1258C22#249111yescharacteristic
1259C22#249211yescharacteristic
1260C22#249411yescharacteristic
1261C22#249511yescharacteristic
1262C22#249611yescharacteristic
1263C22#249711yescharacteristic
1264C22#250611yescharacteristic
1265C22#250611yescharacteristic
1266C22#250611yescharacteristic
1267C22#250711yescharacteristic
1268C22#250711yescharacteristic
1269C22#250711yescharacteristic
1270C22#250811yescharacteristic
1271C22#250811yescharacteristic
1272C22#250811yescharacteristic
1273C22#250911yescharacteristic
1274C22#250911yescharacteristic
1275C22#250911yescharacteristic
1276C22#253511yescharacteristic
1277C22#253611yescharacteristic
1278C22#253711yescharacteristic
1279C22#253811yescharacteristic
1280C22#254611yescharacteristic
1281C22#255011yescharacteristic
1282C22#255011yescharacteristic
1283C22#255011yescharacteristic
1284C22#255011yescharacteristic
1285C22#255111yescharacteristic
1286C22#255111yescharacteristic
1287C22#255211yescharacteristic
1288C22#255211yescharacteristic
1289C22#256711yescharacteristic
1290C22#258411yescharacteristic
1291C22#258411yescharacteristic
1292C22#262411yescharacteristic
1293C22#262511yescharacteristic
1294C22#262811yescharacteristic
1295C22#262911yescharacteristic
1296C22#264411yescharacteristic
1297C22#264511yescharacteristic
1298C22#264711yescharacteristic
1299C22#264711yescharacteristic
1300C22#285111yescharacteristic
1301C22#285411yescharacteristic
1302C22#285511yescharacteristic
1303C22#285711yescharacteristic
1304C22#285911yescharacteristic
1305C22#286011yescharacteristic
1306C22#286311yescharacteristic
1307C22#286411yescharacteristic
1308C4—44no—
1309C4—44no—
1310C4—44no—
1311C4—48no—
1312C4—44no—
1313C4—44no—
1314C4—44no—
1315C4—48no—
1316C4—84no—
1317C4—84no—
1318C4#1441116yescomplemented
1319C2C2×#144111yescharacteristic
1320C2#1392011yescharacteristic
1321C2#1393511yescharacteristic
1322C2#1396911yescharacteristic
1323C2#1397011yescharacteristic
1324C2#1400511yescharacteristic
1325C2#1400611yescharacteristic
1326C2#1404511yescharacteristic
1327C2#1404611yescharacteristic
1328C2#1405311yescharacteristic
1329C2#1405411yescharacteristic
1330C2#1413211yescharacteristic
1331C2#1413311yescharacteristic
1332C2#1426611yescharacteristic
1333C2#1469911yescharacteristic
1334C2#1512611yescharacteristic
1335C2#1512811yescharacteristic
1336C2#1513111yescharacteristic
1337C2#1513711yescharacteristic
1338C2#1513711yescharacteristic
1339C2#1513911yescharacteristic
1340C2#1514111yescharacteristic
1341C2#1514911yescharacteristic
1342C2#1517911yescharacteristic
1343C2#1518711yescharacteristic
1344C2#1518911yescharacteristic
1345C2#1519411yescharacteristic
1346C2#1521811yescharacteristic
1347C2#1522011yescharacteristic
1348C2#1522511yescharacteristic
1349C2#1522511yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC25C24
commutatorC24C23×C4
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C1

Complements

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

NH ≅ G/Ntype
26. C2×#389C4semidirect
372. C2×C4⋊C4C4⋊C4semidirect
1318. C4#1441semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C2×#14412
C2×C4⋊#952
C2×C4×#952
#75572
#75562