Finite Group Databasebeta

← #2104⋊C4 #391182

Subgroups — #2104⋊C4 #391182

Order 512.

843 conjugacy classes of subgroups.

The subgroup lattice has 699 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2104C211yesmaximal, characteristic
2#11344C211yesmaximal, characteristic
3#11318C211yesmaximal, characteristic
4#11287C211yesmaximal, characteristic
5#11279C211yesmaximal, characteristic
6#11279C211yesmaximal, characteristic
7#10918C211yesmaximal, characteristic
8#10918C211yesmaximal, characteristic
9#10915C211yesmaximal, characteristic
10#10915C211yesmaximal, characteristic
11#10912C211yesmaximal, characteristic
12#10912C211yesmaximal, characteristic
13#10829C211yesmaximal, characteristic
14#10829C211yesmaximal, characteristic
15#10801C211yesmaximal, characteristic
16#2315C2211yescharacteristic
17#2315C2211yescharacteristic
18C2×#385C2211yescharacteristic
19C2×#385C2211yescharacteristic
20#2273C2211yescharacteristic
21#2273C2211yescharacteristic
22C2×C4×C22⋊C4C2211yescharacteristic
23#2104C418yescomplemented
24C2×#342C2211yescharacteristic
25C2×#342C2211yescharacteristic
26C2×#342C2211yescharacteristic
27C2×#342C2211yescharacteristic
28C2×#342C2211yescharacteristic
29C2×#342C2211yescharacteristic
30C2×#342C2211yescharacteristic
31C2×#342C2211yescharacteristic
32C2×#342C2211yescharacteristic
33C2×#342C2211yescharacteristic
34C2×#342C2211yescharacteristic
35C2×#342C2211yescharacteristic
36C2×#342C2211yescharacteristic
37C2×#342C2211yescharacteristic
38C2×#342C2211yescharacteristic
39C2×#342C2211yescharacteristic
40C2×#342C2211yescharacteristic
41C2×#342C2211yescharacteristic
42C2×#342C2211yescharacteristic
43C2×#342C2211yescharacteristic
44C2×#342C2211yescharacteristic
45C2×#342C2211yescharacteristic
46C2×#342C2211yescharacteristic
47C2×#342C2211yescharacteristic
48C22⋊#95C2211yescharacteristic
49C22⋊#95C2211yescharacteristic
50C22⋊#95C2211yescharacteristic
51C22⋊#95C2211yescharacteristic
52C24×C4C2311yescharacteristic
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C22⋊C4C2311yescharacteristic
56C22×C22⋊C4C2311yescharacteristic
57C22×C22⋊C4C2311yescharacteristic
58C22×C22⋊C4C2311yescharacteristic
59C22×C22⋊C4C2311yescharacteristic
60C22×C22⋊C4C2311yescharacteristic
61C22×C22⋊C4C2311yescharacteristic
62C22×C22⋊C4C2311yescharacteristic
63C22×C22⋊C4C2311yescharacteristic
64C22×C22⋊C4C2311yescharacteristic
65C22×C22⋊C4C2311yescharacteristic
66C22×C22⋊C4C2311yescharacteristic
67C22×C22⋊C4C2311yescharacteristic
68C22×C22⋊C4C2311yescharacteristic
69C22×C42—21no—
70#385—21no—
71#385—21no—
72#385—21no—
73#385—21no—
74#385—21no—
75#385—21no—
76#385—21no—
77#385—21no—
78#385—41no—
79#385—41no—
80#385—41no—
81#385—41no—
82#380—41no—
83#380—41no—
84C4×C22⋊C4—21no—
85C4×C22⋊C4—21no—
86C4×C22⋊C4—21no—
87C4×C22⋊C4—21no—
88C4×C22⋊C4—41no—
89C4×C22⋊C4—41no—
90C4×C22⋊C4—41no—
91C4×C22⋊C4—41no—
92C4×C22⋊C4—41no—
93C4×C22⋊C4—41no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—21no—
97C2×#95—41no—
98C2×#95—41no—
99C2×#95—41no—
100C2×#95—41no—
101#342—22no—
102#342—22no—
103#342—22no—
104#342—22no—
105#342—22no—
106#342—22no—
107#342—22no—
108#342—22no—
109#342—22no—
110#342—41no—
111#342—41no—
112#342—41no—
113#342—41no—
114#342—41no—
115#342—41no—
116#342—41no—
117#342—41no—
118#342C2×C414yes—
119#342C2×C414yes—
120#342C2×C414yes—
121#342C2×C414yes—
122#342C2×C414yes—
123#342C2×C414yes—
124#342C2×C414yes—
125C25C2411yescharacteristic
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—21no—
129C23×C4—21no—
130C23×C4—21no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4—21no—
134C23×C4—21no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—21no—
139C23×C4—21no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4—21no—
143C23×C4—21no—
144C23×C4—82no—
145C23×C4#4111yescharacteristic
146C23×C4#4111yescharacteristic
147C23×C4#4111yescharacteristic
148C23×C4#4111yescharacteristic
149C23×C4#4111yescharacteristic
150C23×C4#4111yescharacteristic
151C2×C4⋊C4—41no—
152C2×C4⋊C4—41no—
153C2×C4⋊C4—41no—
154C2×C4⋊C4—41no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—82no—
160C2×C4⋊C4—82no—
161C2×C22⋊C4—21no—
162C2×C22⋊C4—21no—
163C2×C22⋊C4—21no—
164C2×C22⋊C4—21no—
165C2×C22⋊C4—21no—
166C2×C22⋊C4—21no—
167C2×C22⋊C4—21no—
168C2×C22⋊C4—21no—
169C2×C22⋊C4—21no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—21no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—21no—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—21no—
179C2×C22⋊C4—21no—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—21no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C22⋊C4—21no—
199C2×C22⋊C4—21no—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4C22×C412yes—
236C2×C22⋊C4C22×C412yes—
237C2×C22⋊C4C22×C412yes—
238C2×C22⋊C4C22×C412yes—
239C2×C22⋊C4C22×C412yes—
240C2×C22⋊C4C22×C412yes—
241C2×C22⋊C4C22×C412yes—
242C2×C22⋊C4#4112yes—
243C2×C22⋊C4#4112yes—
244C2×C22⋊C4#4112yes—
245C2×C42—41no—
246C2×C42—41no—
247C2×C42—41no—
248C2×C42—41no—
249C2×C42—41no—
250C2×C42—41no—
251C2×C42—82no—
252#95—41no—
253#95—41no—
254#95—41no—
255#95—41no—
256#95—41no—
257#95—41no—
258#95—42no—
259#95—41no—
260#95—41no—
261#95—41no—
262#95—41no—
263#95—42no—
264#95—82no—
265#95—82no—
266#95—82no—
267#95—82no—
268C24—81no—
269C24—81no—
270C24C23×C411yescharacteristic
271C24C2×#4111yescharacteristic
272C24C2×#4111yescharacteristic
273C24C2×#4111yescharacteristic
274C24C2×#4111yescharacteristic
275C24C2×#4111yescharacteristic
276C24C2×#4111yescharacteristic
277C24H(5,𝔽2)11yescharacteristic
278C24H(5,𝔽2)11yescharacteristic
279C24H(5,𝔽2)11yescharacteristic
280C24H(5,𝔽2)11yescharacteristic
281C242−1+411yescharacteristic
282C242−1+411yescharacteristic
283C242−1+411yescharacteristic
284C242−1+411yescharacteristic
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—42no—
314C22×C4—42no—
315C22×C4—42no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—81no—
351C22×C4—81no—
352C22×C4—81no—
353C22×C4—81no—
354C22×C4—81no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4—81no—
358C22×C4—81no—
359C22×C4—81no—
360C22×C4—81no—
361C22×C4—81no—
362C22×C4—81no—
363C22×C4—81no—
364C22×C4—81no—
365C22×C4—81no—
366C22×C4—81no—
367C22×C4—81no—
368C22×C4—81no—
369C22×C4—81no—
370C22×C4—81no—
371C22×C4—81no—
372C22×C4—81no—
373C22×C4—81no—
374C22×C4—81no—
375C22×C4—81no—
376C22×C4—81no—
377C22×C4—81no—
378C22×C4—81no—
379C22×C4—81no—
380C22×C4—81no—
381C22×C4—81no—
382C22×C4—81no—
383C22×C4—81no—
384C22×C4—81no—
385C4⋊C4—82no—
386C4⋊C4—82no—
387C4⋊C4—82no—
388C4⋊C4—82no—
389C4⋊C4—161no—
390C4⋊C4—161no—
391C4⋊C4—161no—
392C4⋊C4—161no—
393C22⋊C4—22no—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—22no—
403C22⋊C4—22no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—22no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C42—82no—
450C42—82no—
451C42—161no—
452C42—161no—
453C42—161no—
454C42—161no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—81no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23—81no—
477C23C4×#4111yescharacteristic
478C23C4×#4111yescharacteristic
479C23C4×#4111yescharacteristic
480C23#52011yescharacteristic
481C23#52011yescharacteristic
482C23#52011yescharacteristic
483C23#52011yescharacteristic
484C23#53811yescharacteristic
485C23#53811yescharacteristic
486C23#53811yescharacteristic
487C23#53911yescharacteristic
488C23#53911yescharacteristic
489C23#53911yescharacteristic
490C23#54111yescharacteristic
491C23#54111yescharacteristic
492C23#54111yescharacteristic
493C23#54211yescharacteristic
494C23#54211yescharacteristic
495C23#54211yescharacteristic
496C23#55111yescharacteristic
497C23#55111yescharacteristic
498C23#55111yescharacteristic
499C23#55211yescharacteristic
500C23#55211yescharacteristic
501C23#55211yescharacteristic
502C23#55311yescharacteristic
503C23#55311yescharacteristic
504C23#55311yescharacteristic
505C23#55611yescharacteristic
506C23#55611yescharacteristic
507C23#55611yescharacteristic
508C23#56011yescharacteristic
509C23#56311yescharacteristic
510C23#56311yescharacteristic
511C23#56311yescharacteristic
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4—81no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—81no—
577C2×C4—81no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—82no—
581C2×C4—82no—
582C2×C4—82no—
583C2×C4—82no—
584C2×C4—82no—
585C2×C4—82no—
586C2×C4—82no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—82no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—82no—
595C2×C4—82no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—161no—
599C2×C4—161no—
600C2×C4—161no—
601C2×C4—161no—
602C2×C4—161no—
603C2×C4—161no—
604C2×C4—161no—
605C2×C4—161no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22#233411yescharacteristic
649C22#233411yescharacteristic
650C22#233411yescharacteristic
651C22#237311yescharacteristic
652C22#237311yescharacteristic
653C22#237311yescharacteristic
654C22#238311yescharacteristic
655C22#276011yescharacteristic
656C22#276211yescharacteristic
657C22#276211yescharacteristic
658C22#276211yescharacteristic
659C22#278711yescharacteristic
660C22#278711yescharacteristic
661C22#278711yescharacteristic
662C22#280111yescharacteristic
663C4—42no—
664C4—82no—
665C4—82no—
666C4—82no—
667C4—82no—
668C4—82no—
669C4—82no—
670C4—82no—
671C4—82no—
672C4—82no—
673C4—82no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—161no—
680C4—161no—
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2—21no—
690C2—21no—
691C2—21no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2#1462011yescharacteristic
696C2#3270011yescharacteristic
697C2#3270111yescharacteristic
subgroupG/H
center, socleC22#2760
commutatorC24C23×C4
Frattini, prime radical, cosocleC25C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C25 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
23. #2104C4semidirect

Maximal subgroups

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

subgroupindex
C2×#21042
#113442
#113182
#112872
#112792
#109182
#109152
#109122
#108292
#108012