Finite Group Databasebeta

← #6383762

Subgroups — #6383762

Order 512.

1765 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34876C211yesmaximal, characteristic
2#23277C211yesmaximal, characteristic, complemented
3#23275C211yesmaximal, characteristic, complemented
4#23275C212yesmaximal, complemented
5#23251C212yesmaximal, complemented
6#23178C211yesmaximal, characteristic, complemented
7#23177C211yesmaximal, characteristic, complemented
8#23088C212yesmaximal, complemented
9#23086C212yesmaximal, complemented
10#23085C212yesmaximal, complemented
11#23083C212yesmaximal, complemented
12#21381C212yesmaximal, complemented
13#21380C211yesmaximal, characteristic, complemented
14#21373C211yesmaximal, characteristic, complemented
15#21273C212yesmaximal, complemented
16#21272C212yesmaximal, complemented
17#20490C212yesmaximal, complemented
18#20484C212yesmaximal, complemented
19#20469C212yesmaximal, complemented
20C2×#529C2211yescharacteristic
21C2×C4×#41C2211yescharacteristic
22C2×#436C2212yes—
23C2×#435C2212yes—
24C2×#435C2212yes—
25C2×C8×D4C2212yes—
26C2×#433C2212yes—
27C2×#432C2212yes—
28C2×#432C2211yescharacteristic
29C2×#431C2212yes—
30C2×#431C2211yescharacteristic
31C2×#405C2212yes—
32C2×C4×M16C2211yescharacteristic
33C22×C4×C8C2211yescharacteristic
34#2611C411yescharacteristic
35#2611C411yescharacteristic
36#2610C411yescharacteristic
37#2610C411yescharacteristic
38#2604C412yes—
39#2603C412yes—
40#2564C411yescharacteristic
41#2564C411yescharacteristic
42#2543C411yescharacteristic
43#2543C411yescharacteristic
44#2498C412yes—
45#2430C412yes—
46#2399C2211yescharacteristic
47#2398C2211yescharacteristic
48#2398C2211yescharacteristic
49#2397C2211yescharacteristic
50C4×#121C2212yes—
51C4×#121C2212yes—
52#2290C2212yes—
53#2290C2212yes—
54C2×#376C2211yescharacteristic
55#1985C2212yes—
56#1984C2212yes—
57#1984C2212yes—
58#1984C2212yes—
59#1955C2212yes—
60#1955C2212yes—
61#1955C2212yes—
62#1954C2212yes—
63#1954C2212yes—
64#1954C2212yes—
65#1954C2212yes—
66#1954C2212yes—
67#1940C2212yes—
68#1940C2212yes—
69#1939C2212yes—
70#1939C2212yes—
71#1924C2212yes—
72#1924C2212yes—
73#1924C2212yes—
74#1924C2212yes—
75#1923C2212yes—
76#1923C2212yes—
77#1923C2212yes—
78#1923C2212yes—
79#1870C2211yescharacteristic
80#1870C2212yes—
81#1870C2211yescharacteristic
82#1870C2211yescharacteristic
83#1870C2211yescharacteristic
84#1870C2212yes—
85#1869C2211yescharacteristic
86#1869C2212yes—
87#1869C2211yescharacteristic
88#1869C2211yescharacteristic
89#1869C2211yescharacteristic
90#1869C2212yes—
91#1771C2212yes—
92#1771C2212yes—
93C8×C4⋊C4C2212yes—
94C8×C4⋊C4C2212yes—
95#1768C2212yes—
96#1768C2212yes—
97#1768C2212yes—
98#1768C2212yes—
99#1753C2212yes—
100#1753C2212yes—
101#1753C2212yes—
102#1753C2212yes—
103#1752C2212yes—
104C8×C22⋊C4C2212yes—
105C8×C22⋊C4C2212yes—
106C8×C22⋊C4C2212yes—
107#1750C2212yes—
108#1750C2212yes—
109#1749C2212yes—
110#1749C2212yes—
111#1749C2212yes—
112C4×C22⋊C8C2212yes—
113C4×C22⋊C8C2212yes—
114C4×C22⋊C8C2212yes—
115#1746C2212yes—
116#1746C2212yes—
117#1726C2212yes—
118#1726C2212yes—
119C22×#41C2×C411yescharacteristic
120C22×M16C2311yescharacteristic
121C22×M16C2311yescharacteristic
122C22×M16C2312yes—
123C23×C8C2311yescharacteristic
124C23×C8C2311yescharacteristic
125C23×C8C2312yes—
126#529—42no—
127#529—42no—
128C2×#126C2×C412yes—
129C2×#125C2×C411yescharacteristic
130C2×#124C2×C411yescharacteristic
131C2×#123C2×C412yes—
132C2×C22⋊Q8C2×C411yescharacteristic
133C2×#121C2×C412yes—
134C2×#121C2×C411yescharacteristic
135C2×#121C2×C412yes—
136C4×#41—42no—
137C4×#41—42no—
138C2×C4×Q8C2×C411yescharacteristic
139C2×C4×Q8C2311yescharacteristic
140C2×C4×Q8C2311yescharacteristic
141C2×C4×D4C2×C411yescharacteristic
142C2×C4×D4C2×C411yescharacteristic
143C2×C4×D4C2×C411yescharacteristic
144C2×C4×D4C2312yes—
145C2×C4×D4C2312yes—
146C2×C4×D4C2311yescharacteristic
147C2×C4×D4C2311yescharacteristic
148C2×C4×D4C2311yescharacteristic
149C2×C4×D4C2312yes—
150C2×C4×D4C2311yescharacteristic
151C2×#117C2×C411yescharacteristic
152C2×#117C2×C411yescharacteristic
153C2×#117C2×C411yescharacteristic
154C2×#117C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159#436—28no—
160#435—28no—
161#435—28no—
162C8×D4—28no—
163#433—44no—
164#432—28no—
165#432—42no—
166#431—28no—
167#431—42no—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C22⋊C8C2312yes—
179C2×C22⋊C8C2312yes—
180C2×C22⋊C8C2312yes—
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2312yes—
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2311yescharacteristic
189C2×C22⋊C8C2311yescharacteristic
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2311yescharacteristic
193C2×C22⋊C8C2311yescharacteristic
194#405—44no—
195C4×M16—42no—
196C2×#97C2312yes—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×#97C2312yes—
200C2×#97C2312yes—
201C2×#97C2312yes—
202C2×#97C2312yes—
203C2×C4×C8—42no—
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207C2×C4×C8C2312yes—
208C2×C4×C8C2312yes—
209C2×C4×C8C2312yes—
210C2×C4×C8C2312yes—
211C2×C4×C8C2312yes—
212C2×C4×C8C2312yes—
213#400C2×C411yescharacteristic
214#400C2×C411yescharacteristic
215#400C2×C412yes—
216#399C2×C411yescharacteristic
217#399C2×C411yescharacteristic
218#399C2×C412yes—
219#398C2×C412yes—
220#398C2×C411yescharacteristic
221#398C2×C411yescharacteristic
222#397C2×C412yes—
223#397C2×C411yescharacteristic
224#397C2×C411yescharacteristic
225#395C2×C411yescharacteristic
226#395C2×C411yescharacteristic
227#395C2×C412yes—
228#394C2×C412yes—
229#394C2×C411yescharacteristic
230#394C2×C411yescharacteristic
231#393C2×C411yescharacteristic
232#393C2×C411yescharacteristic
233#393C2×C412yes—
234#392C2×C412yes—
235#392C2×C411yescharacteristic
236#392C2×C411yescharacteristic
237#390C2×C412yes—
238#390C2×C412yes—
239#389C2×C412yes—
240#389C2×C412yes—
241#388C2×C412yes—
242#388C2×C412yes—
243#388C2×C412yes—
244#388C2×C412yes—
245#388C2×C412yes—
246#388C2×C412yes—
247#388C2×C412yes—
248#388C2×C412yes—
249#387C2×C412yes—
250#387C2×C412yes—
251#387C2×C412yes—
252#387C2×C412yes—
253#386C2×C412yes—
254#386C2×C412yes—
255#386C2×C412yes—
256#386C2×C412yes—
257#386C2×C412yes—
258#386C2×C412yes—
259#386C2×C412yes—
260#386C2×C412yes—
261#385C2×C412yes—
262#385C2×C412yes—
263#385C2×C412yes—
264#385C2×C412yes—
265#380C2×C412yes—
266#380C2×C412yes—
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2312yes—
269C4×C22⋊C4C2312yes—
270C4×C22⋊C4C2312yes—
271C4×C22⋊C4C2312yes—
272C4×C22⋊C4C2312yes—
273#376C2×C412yes—
274#376C2×C411yescharacteristic
275#376C2×C411yescharacteristic
276#376C2311yescharacteristic
277#376C2311yescharacteristic
278#376C2312yes—
279C2×#95C2×C411yescharacteristic
280C2×#95C2×C411yescharacteristic
281C2×#95C2×C412yes—
282#336C2312yes—
283#336C2312yes—
284#336C2312yes—
285#336C2312yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298C2×#41—24no—
299C2×#41—42no—
300C2×#41—42no—
301C22×Q8C22×C411yescharacteristic
302C22×Q8C22×C411yescharacteristic
303C22×D4C22×C411yescharacteristic
304C22×D4C22×C412yes—
305C22×D4C22×C411yescharacteristic
306C22×D4C22×C412yes—
307C22×D4C22×C412yes—
308C22×D4C22×C411yescharacteristic
309C22×D4C22×C411yescharacteristic
310C23×C4C22×C411yescharacteristic
311C23×C4C22×C411yescharacteristic
312C23×C4C22×C411yescharacteristic
313C23×C4C22×C412yes—
314C23×C4C22×C411yescharacteristic
315C23×C4C22×C411yescharacteristic
316C23×C4C22×C411yescharacteristic
317C23×C4C22×C412yes—
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C2×M16—24no—
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—24no—
326C2×M16—41no—
327C2×M16—41no—
328C2×M16—42no—
329C22×C8—24no—
330C22×C8—24no—
331C22×C8—24no—
332C22×C8—24no—
333C22×C8—41no—
334C22×C8—41no—
335C22×C8—42no—
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2412yes—
340C22×C8C2412yes—
341C22×C8C2412yes—
342C22×C8C2412yes—
343C22×C8C2412yes—
344#126—44no—
345#125—42no—
346#124—42no—
347#123—44no—
348C22⋊Q8—42no—
349#121—28no—
350#121—42no—
351#121—44no—
352C4×Q8—42no—
353C4×Q8—41no—
354C4×Q8—41no—
355C4×Q8—41no—
356C4×Q8—41no—
357C4×D4—24no—
358C4×D4—24no—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4—42no—
362C4×D4—42no—
363C4×D4—42no—
364C4×D4—41no—
365C4×D4—41no—
366C4×D4—41no—
367C4×D4—41no—
368C4×D4—41no—
369C4×D4—41no—
370C4×D4—42no—
371C4×D4—42no—
372C4×D4—41no—
373C4×D4—41no—
374#117—24no—
375#117—24no—
376#117—42no—
377#117—42no—
378#117—42no—
379C2×C4⋊C4C22×C412yes—
380C2×C4⋊C4C22×C412yes—
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C22×C412yes—
385C2×C4⋊C4C22×C411yescharacteristic
386C2×C4⋊C4C22×C411yescharacteristic
387C2×C4⋊C4C22×C411yescharacteristic
388C2×C4⋊C4C22×C411yescharacteristic
389C2×C4⋊C4C22×C411yescharacteristic
390C2×C4⋊C4C22×C411yescharacteristic
391C2×C4⋊C4C22×C411yescharacteristic
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C4⋊C4C22×C412yes—
395C2×C4⋊C4C22×C412yes—
396C2×C4⋊C4C22×C412yes—
397C2×C22⋊C4C22×C412yes—
398C2×C22⋊C4C22×C412yes—
399C2×C22⋊C4C22×C412yes—
400C2×C22⋊C4C22×C412yes—
401C2×C22⋊C4C22×C412yes—
402C2×C22⋊C4C22×C412yes—
403C2×C22⋊C4C22×C412yes—
404C2×C22⋊C4C22×C412yes—
405C2×C22⋊C4C22×C412yes—
406C2×C22⋊C4C22×C411yescharacteristic
407C2×C22⋊C4C22×C411yescharacteristic
408C2×C22⋊C4C22×C411yescharacteristic
409C2×C22⋊C4C22×C411yescharacteristic
410C2×C22⋊C4C22×C411yescharacteristic
411C2×C22⋊C4C22×C411yescharacteristic
412C2×C22⋊C4C22×C412yes—
413C2×C22⋊C4C22×C412yes—
414C2×C22⋊C4C22×C412yes—
415C2×C22⋊C4C22×C412yes—
416C2×C22⋊C4C22×C412yes—
417C2×C22⋊C4C22×C412yes—
418C2×C22⋊C4C22×C412yes—
419C2×C22⋊C4C22×C412yes—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42C22×C411yescharacteristic
429C2×C42C22×C411yescharacteristic
430C2×C42C22×C411yescharacteristic
431C2×C42C22×C411yescharacteristic
432C2×C42C22×C411yescharacteristic
433C2×C42C22×C411yescharacteristic
434C2×C42C22×C412yes—
435C2×C42C22×C412yes—
436C2×C42C2412yes—
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C2×C42C2411yescharacteristic
440C2×C42C2412yes—
441C2×C42C2412yes—
442C2×C42C2411yescharacteristic
443C4⋊C8—24no—
444C4⋊C8—24no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448C4⋊C8—42no—
449C4⋊C8#4118yescomplemented
450C4⋊C8#4118yescomplemented
451C22⋊C8—24no—
452C22⋊C8—24no—
453C22⋊C8—24no—
454C22⋊C8—24no—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C22⋊C8—24no—
460C22⋊C8—24no—
461C22⋊C8—24no—
462C22⋊C8—24no—
463C22⋊C8—41no—
464C22⋊C8—41no—
465C22⋊C8—41no—
466C22⋊C8—41no—
467C22⋊C8—42no—
468C22⋊C8—42no—
469#97—24no—
470#97—24no—
471#97—24no—
472#97—24no—
473#97—24no—
474#97—24no—
475#97—42no—
476C4×C8—24no—
477C4×C8—24no—
478C4×C8—24no—
479C4×C8—24no—
480C4×C8—24no—
481C4×C8—24no—
482C4×C8—42no—
483C4×C8—42no—
484C4×C8—42no—
485#95C22×C412yes—
486#95C22×C412yes—
487#95C22×C412yes—
488#95C22×C412yes—
489#95C22×C411yescharacteristic
490#95C22×C411yescharacteristic
491#95C22×C412yes—
492#95C22×C411yescharacteristic
493#95C22×C411yescharacteristic
494#95C22×C412yes—
495#95C22×C412yes—
496#95C22×C412yes—
497#95C22×C412yes—
498#95C22×C412yes—
499#95C22×C412yes—
500#95C22×C412yes—
501#95C22×C412yes—
502#95C22×C412yes—
503#95C22×C412yes—
504#95C22×C412yes—
505#95C22×C412yes—
506#95C22×C412yes—
507C24C23×C412yes—
508C24C23×C411yescharacteristic
509C24C23×C411yescharacteristic
510C24C23×C411yescharacteristic
511#41—416no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×Q8—41no—
515C2×Q8—41no—
516C2×Q8—42no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—22no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—42no—
531C2×D4—41no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4#13114yes—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
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—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4C23×C412yes—
577C22×C4C23×C412yes—
578C22×C4C23×C411yescharacteristic
579C22×C4C23×C411yescharacteristic
580C22×C4C23×C411yescharacteristic
581C22×C4C23×C411yescharacteristic
582C22×C4C23×C411yescharacteristic
583C22×C4C23×C411yescharacteristic
584C22×C4C23×C412yes—
585C22×C4C23×C412yes—
586C22×C4C23×C412yes—
587C22×C4C23×C411yescharacteristic
588C22×C4C23×C412yes—
589C22×C4C23×C412yes—
590C22×C4C23×C411yescharacteristic
591C22×C4C23×C411yescharacteristic
592C22×C4C23×C411yescharacteristic
593C22×C4C23×C411yescharacteristic
594C22×C4C2511yescharacteristic
595M16—44no—
596M16—48no—
597M16—44no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—44no—
619C2×C8—48no—
620C2×C8—44no—
621C2×C8C2×#4114yes—
622C2×C8C2×#4114yes—
623C2×C8C2×#4114yes—
624C2×C8C2×#4114yes—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—24no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—42no—
641C4⋊C4—41no—
642C4⋊C4—42no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—41no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C42—24no—
667C42—24no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—22no—
675C42—22no—
676C42—21no—
677C42—21no—
678C42—22no—
679C42—21no—
680C42—21no—
681C42—22no—
682C42—21no—
683C42—21no—
684C42C2×#4114yes—
685C42C2×#4114yes—
686C42H(5,𝔽2)12yes—
687C42H(5,𝔽2)12yes—
688C23—22no—
689C23—22no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23C2×#13112yes—
709C23C2×#13112yes—
710C23C24×C411yescharacteristic
711Q8—44no—
712Q8—82no—
713D4—44no—
714D4—48no—
715D4—44no—
716D4—44no—
717D4—84no—
718D4—84no—
719D4—82no—
720C2×C4—28no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—44no—
763C2×C4—48no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—84no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4C4×#4114yes—
783C2×C4C4×#4114yes—
784C2×C4#51812yes—
785C2×C4#51812yes—
786C2×C4C2×#13112yes—
787C2×C4#56812yes—
788C2×C4C22×#4112yes—
789C2×C4C22×#4112yes—
790C2×C4C2×H(5,𝔽2)11yescharacteristic
791C2×C4C2×H(5,𝔽2)11yescharacteristic
792C8—24no—
793C8—24no—
794C8—24no—
795C8—24no—
796C8—42no—
797C8—42no—
798C8—42no—
799C8—42no—
800C22—24no—
801C22—24no—
802C22—22no—
803C22—22no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—41no—
822C22C2×C4×#4112yes—
823C22C2×#51811yescharacteristic
824C22C22×#13111yescharacteristic
825C22C2×#56811yescharacteristic
826C22#357312yes—
827C4—24no—
828C4—24no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—42no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—42no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—42no—
845C4#348111yescharacteristic
846C4#348111yescharacteristic
847C4#348312yes—
848C2—42no—
849C2—42no—
850C2—82no—
851C2—81no—
852C2#3415511yescharacteristic
853C2#6021512yes—
854C2#6021712yes—
855C2#6023311yescharacteristic
856C2#6023511yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radical#34876C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #23277C2semidirect
3. #23275C2semidirect
4. #23275C2semidirect
5. #23251C2semidirect
6. #23178C2semidirect
7. #23177C2semidirect
8. #23088C2semidirect
9. #23086C2semidirect
10. #23085C2semidirect
11. #23083C2semidirect
12. #21381C2semidirect
13. #21380C2semidirect
14. #21373C2semidirect
15. #21273C2semidirect
16. #21272C2semidirect
17. #20490C2semidirect
18. #20484C2semidirect
19. #20469C2semidirect
449. C4⋊C8#41semidirect
450. C4⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#348762
#232772
#232752
#232512
#231782
#231772
#230882
#230862
#230852
#230832
#213812
#213802
#213732
#212732
#212722
#204902
#204842
#204692