Finite Group Databasebeta

← #6387964

Subgroups — #6387964

Order 512.

2060 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2993C211yesmaximal, characteristic, complemented
2C2×#2905C211yesmaximal, characteristic, complemented
3#34877C211yesmaximal, characteristic
4#22994C212yesmaximal, complemented
5#22991C212yesmaximal, complemented
6#22961C212yesmaximal, complemented
7#22958C212yesmaximal, complemented
8#22757C212yesmaximal, complemented
9#22756C212yesmaximal, complemented
10#22652C212yesmaximal, complemented
11#22651C212yesmaximal, complemented
12#22073C212yesmaximal, complemented
13#22071C212yesmaximal, complemented
14#21974C211yesmaximal, characteristic, complemented
15#21854C211yesmaximal, characteristic, complemented
16#21441C212yesmaximal, complemented
17#21439C212yesmaximal, complemented
18#20717C211yesmaximal, characteristic, complemented
19#20549C211yesmaximal, characteristic, complemented
20C23×M16C2212yes—
21C2×#529C2211yescharacteristic
22C22×#117C2211yescharacteristic
23#2993—28no—
24C2×#446C2211yescharacteristic, complemented
25C2×C8×Q8C2211yescharacteristic, complemented
26C2×#436C2212yes—
27C2×#436C2212yes—
28C2×#436C2211yescharacteristic, complemented
29C2×#435C2212yes—
30C2×#435C2212yes—
31C2×#435C2212yes—
32C2×C8×D4C2212yes—
33C2×C8×D4C2211yescharacteristic, complemented
34C2×#433C2212yescomplemented
35C2×#432C2211yescharacteristic
36C2×#431C2211yescharacteristic
37#2905—28no—
38C2×#424C2212yes—
39C2×#424C2212yes—
40C2×#424C2212yes—
41C2×#424C2212yes—
42C2×#424C2212yescomplemented
43C2×#423C2212yes—
44C2×#423C2211yescharacteristic
45C2×#423C2211yescharacteristic
46#2611C412yes—
47#2610C412yes—
48#2601C412yes—
49#2601C412yes—
50#2591C411yescharacteristic
51#2583C411yescharacteristic
52#2561C411yescharacteristic
53#2539C411yescharacteristic
54#2413C412yes—
55#2411C412yes—
56#2396C2212yes—
57#2392C2212yes—
58C4×#123C2212yes—
59C4×#120C2212yes—
60#2293C2212yes—
61#2293C2212yes—
62C4×#117C2211yescharacteristic
63#1985C2212yescomplemented
64#1955C2212yescomplemented
65#1940C2212yescomplemented
66#1940C2212yescomplemented
67#1939C2212yescomplemented
68#1939C2212yescomplemented
69#1939C2212yescomplemented
70#1939C2212yescomplemented
71#1924C2212yescomplemented
72#1924C2212yescomplemented
73#1923C2212yescomplemented
74#1923C2212yescomplemented
75#1917C2212yescomplemented
76#1917C2212yescomplemented
77#1916C2212yescomplemented
78#1916C2212yescomplemented
79#1870C2212yes—
80#1870C2212yes—
81#1870C2212yes—
82#1870C2212yes—
83#1869C2212yes—
84#1869C2212yes—
85#1851C2212yes—
86#1851C2212yes—
87#1851C2212yes—
88#1851C2212yes—
89#1851C2212yescomplemented
90#1851C2212yescomplemented
91#1850C2212yes—
92#1850C2212yes—
93#1850C2212yescomplemented
94#1850C2212yescomplemented
95#1842C2211yescharacteristic, complemented
96#1842C2211yescharacteristic, complemented
97#1831C2211yescharacteristic, complemented
98#1831C2211yescharacteristic, complemented
99#1817C2211yescharacteristic
100#1817C2211yescharacteristic
101#1798C2212yes—
102#1798C2212yes—
103#1798C2212yescomplemented
104#1798C2212yescomplemented
105#1779C2211yescharacteristic
106#1779C2211yescharacteristic
107#1771C2212yescomplemented
108#1771C2212yescomplemented
109#1767C2212yescomplemented
110C4×C4⋊C8C2212yescomplemented
111#1753C2212yes—
112#1753C2212yes—
113#1753C2212yes—
114#1753C2212yes—
115#1752C2212yes—
116C8×C22⋊C4C2212yes—
117#1750C2212yes—
118#1750C2212yes—
119C24×C4C2311yescharacteristic
120C22×M16—28no—
121C22×M16—44no—
122C22×M16—44no—
123C22×M16C2312yes—
124C22×M16C2312yes—
125C22×M16C2312yes—
126C22×M16C2312yes—
127C22×M16C2312yes—
128C23×C8C2312yes—
129C23×C8C2312yes—
130C23×C8C2312yes—
131#529—24no—
132#529—24no—
133C2×#126C2×C412yes—
134C2×#125C2×C411yescharacteristic
135C2×#124C2×C411yescharacteristic
136C2×#123C2×C412yes—
137C2×#123C2×C412yes—
138C2×C22⋊Q8C2×C411yescharacteristic
139C2×#121C2×C411yescharacteristic
140C2×#120C2×C412yes—
141C2×C4×Q8C2311yescharacteristic
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×C4×D4C2311yescharacteristic
146C2×#117—24no—
147C2×#117—24no—
148C2×#117C2×C412yes—
149C2×#117C2×C412yes—
150C2×#117C2×C412yes—
151C2×#117C2312yes—
152C2×#117C2312yes—
153C2×#117C2312yes—
154C22×C4⋊C4C2×C411yescharacteristic
155C22×C4⋊C4C2×C411yescharacteristic
156C22×C22⋊C4C2×C411yescharacteristic
157C22×C22⋊C4C2×C411yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#446—24no—
161C8×Q8—24no—
162#436—28no—
163#436—24no—
164#436—44no—
165#435—28no—
166#435—44no—
167#435—44no—
168C8×D4—24no—
169C8×D4—44no—
170#433—28no—
171#432—24no—
172#431—24no—
173#424—28no—
174#424—28no—
175#424—28no—
176#424—28no—
177#424—28no—
178#423—28no—
179#423—24no—
180#423D418yescomplemented
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2311yescharacteristic
184C2×C4⋊C8C2311yescharacteristic
185C2×C4⋊C8C2311yescharacteristic
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192C2×C4⋊C8C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C4⋊C8C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×C22⋊C8C2312yes—
201C2×C22⋊C8C2312yes—
202C2×C22⋊C8C2312yes—
203C2×C22⋊C8C2312yes—
204C2×C22⋊C8C2311yescharacteristic
205C2×C22⋊C8C2311yescharacteristic
206C2×C22⋊C8C2311yescharacteristic
207C2×C22⋊C8C2311yescharacteristic
208C2×C22⋊C8C2312yes—
209C2×C22⋊C8C2312yes—
210C2×C22⋊C8C2312yes—
211C2×C22⋊C8C2312yes—
212C2×C22⋊C8C2312yes—
213C2×C22⋊C8C2312yes—
214C2×#97C2312yes—
215C2×#97C2312yes—
216C2×#97C2312yes—
217C2×#97C2312yes—
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2311yescharacteristic
220C2×C4×C8C2312yes—
221C2×C4×C8C2312yes—
222C2×C4×C8C2312yes—
223#400C2×C412yes—
224#399C2×C412yes—
225#398C2×C412yes—
226#398C2×C412yes—
227#398C2×C412yes—
228#397C2×C412yes—
229#396C2×C412yes—
230#396C2×C412yes—
231#396C2×C412yes—
232#396C2×C412yes—
233#395C2×C412yes—
234#394C2×C412yes—
235#394C2×C412yes—
236#394C2×C412yes—
237#393C2×C412yes—
238#392C2×C412yes—
239#390C2×C412yes—
240#390C2×C412yes—
241#390C2×C412yes—
242#390C2×C412yes—
243#389C2×C412yes—
244#389C2×C412yes—
245#389C2×C412yes—
246#389C2×C412yes—
247#388C2×C412yes—
248#388C2×C412yes—
249#388C2×C412yes—
250#388C2×C412yes—
251#388C2×C412yes—
252#388C2×C412yes—
253#388C2×C412yes—
254#388C2×C412yes—
255#388C2×C412yes—
256#388C2×C412yes—
257#387C2×C412yes—
258#387C2×C412yes—
259#386C2×C412yes—
260#386C2×C412yes—
261#386C2×C412yes—
262#386C2×C412yes—
263#385C2×C412yes—
264#385C2×C412yes—
265#385C2×C412yes—
266#385C2×C412yes—
267#381C2×C412yes—
268#379C2×C412yes—
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C411yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C22⋊C4C2×C411yescharacteristic
275C4×C22⋊C4C2×C411yescharacteristic
276C4×C22⋊C4C2312yes—
277C4×C22⋊C4C2312yes—
278C4×C22⋊C4C2312yes—
279C4×C22⋊C4C2312yes—
280C4×C22⋊C4C2312yes—
281#376C2×C412yes—
282C43C2311yescharacteristic
283C43C2311yescharacteristic
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—
298#336C2312yes—
299#336C2312yes—
300C25C22×C411yescharacteristic
301C22×Q8C22×C411yescharacteristic
302C22×D4C22×C412yes—
303C22×D4C22×C412yes—
304C22×D4C22×C412yes—
305C22×D4C22×C411yescharacteristic
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—24no—
309C23×C4—24no—
310C23×C4C22×C411yescharacteristic
311C23×C4C22×C412yes—
312C23×C4C22×C411yescharacteristic
313C23×C4C22×C411yescharacteristic
314C23×C4C22×C411yescharacteristic
315C23×C4C22×C411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C2×M16—24no—
320C2×M16—24no—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—24no—
324C2×M16—24no—
325C2×M16—42no—
326C2×M16—42no—
327C2×M16—42no—
328C2×M16—42no—
329C2×M16—42no—
330C2×M16—42no—
331C2×M16—42no—
332C2×M16—42no—
333C2×M16—432no—
334C2×M16C2×D418yes—
335C22×C8—24no—
336C22×C8—24no—
337C22×C8—24no—
338C22×C8—24no—
339C22×C8—24no—
340C22×C8—42no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8—42no—
344C22×C8C2411yescharacteristic
345C22×C8C2412yes—
346C22×C8C2412yes—
347C22×C8C2411yescharacteristic
348C22×C8C2411yescharacteristic
349C22×C8C2411yescharacteristic
350C22×C8C2412yes—
351C22×C8C2412yes—
352C22×C8C2412yes—
353C22×C8C2412yes—
354#126—28no—
355#125—24no—
356#124—24no—
357#123—28no—
358#123—44no—
359C22⋊Q8—24no—
360#121—24no—
361#120—44no—
362C4×Q8—22no—
363C4×Q8—22no—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—24no—
367C4×D4—24no—
368C4×D4—24no—
369C4×D4—24no—
370C4×D4—22no—
371C4×D4—22no—
372#117—28no—
373#117—28no—
374#117—24no—
375#117—24no—
376#117—24no—
377#117—24no—
378#117—24no—
379#117—24no—
380#117—44no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4C22×C412yes—
384C2×C4⋊C4C22×C412yes—
385C2×C4⋊C4C22×C412yes—
386C2×C4⋊C4C22×C412yes—
387C2×C4⋊C4C22×C412yes—
388C2×C4⋊C4C22×C412yes—
389C2×C4⋊C4C22×C412yes—
390C2×C4⋊C4C22×C411yescharacteristic
391C2×C4⋊C4C22×C412yes—
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C412yes—
394C2×C4⋊C4C22×C411yescharacteristic
395C2×C4⋊C4C22×C412yes—
396C2×C4⋊C4C22×C412yes—
397C2×C4⋊C4C22×C412yes—
398C2×C4⋊C4C22×C412yes—
399C2×C4⋊C4C22×C412yes—
400C2×C4⋊C4C22×C412yes—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4C22×C412yes—
404C2×C22⋊C4C22×C412yes—
405C2×C22⋊C4C22×C412yes—
406C2×C22⋊C4C22×C412yes—
407C2×C22⋊C4C22×C412yes—
408C2×C22⋊C4C22×C412yes—
409C2×C22⋊C4C22×C412yes—
410C2×C22⋊C4C22×C412yes—
411C2×C22⋊C4C22×C412yes—
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×C22⋊C4C22×C412yes—
421C2×C22⋊C4C22×C412yes—
422C2×C22⋊C4C22×C412yes—
423C2×C22⋊C4C22×C412yes—
424C2×C22⋊C4C22×C412yes—
425C2×C22⋊C4C22×C412yes—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42C22×C412yes—
429C2×C42C22×C412yes—
430C2×C42C22×C412yes—
431C2×C42C22×C411yescharacteristic
432C2×C42C22×C411yescharacteristic
433C2×C42C22×C411yescharacteristic
434C2×C42C22×C411yescharacteristic
435C2×C42C22×C411yescharacteristic
436C2×C42C22×C411yescharacteristic
437C2×C42C2×D414yes—
438C2×C42#4114yes—
439C2×C42C2412yes—
440C2×C42C2412yes—
441C2×C42C2412yes—
442C2×C42C2412yes—
443C2×C42C2411yescharacteristic
444C2×C42C2411yescharacteristic
445C4⋊C8—24no—
446C4⋊C8—24no—
447C4⋊C8—24no—
448C4⋊C8—24no—
449C4⋊C8—24no—
450C4⋊C8—24no—
451C4⋊C8—24no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454C4⋊C8—22no—
455C4⋊C8—22no—
456C4⋊C8—24no—
457C4⋊C8—42no—
458C4⋊C8—42no—
459C4⋊C8—42no—
460C4⋊C8—42no—
461C4⋊C8C2×D418yes—
462C4⋊C8C2×D414yes—
463C4⋊C8C2×D414yes—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8—22no—
467C22⋊C8—22no—
468C22⋊C8—24no—
469C22⋊C8—24no—
470C22⋊C8—24no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C22⋊C8—24no—
474C22⋊C8—42no—
475C22⋊C8—42no—
476C22⋊C8—42no—
477C22⋊C8—42no—
478#97—24no—
479#97—24no—
480#97—42no—
481#97—42no—
482C4×C8—24no—
483C4×C8—22no—
484C4×C8—22no—
485C4×C8—42no—
486C4×C8—42no—
487#95C22×C412yes—
488#95C22×C412yes—
489#95C22×C412yes—
490#95C22×C412yes—
491#95C22×C412yes—
492#95C22×C412yes—
493#95C22×C412yes—
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—
503C24—22no—
504C24—24no—
505C24—42no—
506C24—41no—
507C24—41no—
508C24C23×C412yes—
509C24C23×C411yescharacteristic
510C24C23×C412yes—
511C2×Q8—22no—
512C2×Q8—41no—
513C2×Q8—41no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—22no—
518C2×D4—24no—
519C2×D4—42no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—42no—
525C2×D4—42no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—216no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—42no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—42no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4C4×D414yes—
555C22×C4C4×D414yes—
556C22×C4C23×C412yes—
557C22×C4C23×C412yes—
558C22×C4C23×C412yes—
559C22×C4C23×C412yes—
560C22×C4C23×C412yes—
561C22×C4C23×C412yes—
562C22×C4C23×C412yes—
563C22×C4C23×C412yes—
564C22×C4C23×C411yescharacteristic
565C22×C4C23×C411yescharacteristic
566C22×C4C23×C411yescharacteristic
567C22×C4C23×C411yescharacteristic
568C22×C4C23×C411yescharacteristic
569C22×C4C23×C412yes—
570C22×C4C23×C412yes—
571C22×C4C22×D412yes—
572C22×C4C2×#4112yes—
573C22×C4H(5,𝔽2)14yes—
574C22×C42−1+414yes—
575C22×C4C2511yescharacteristic
576M16—48no—
577M16—48no—
578M16—48no—
579M16—48no—
580M16—84no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—48no—
606C2×C8—48no—
607C2×C8—84no—
608C2×C8C22×D414yes—
609C2×C8C22×D414yes—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—24no—
618C4⋊C4—22no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C42—24no—
652C42—24no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—41no—
662C42—41no—
663C42—41no—
664C42—41no—
665C42—42no—
666C42C4×D414yes—
667C42C4×D414yes—
668C42C22×D412yes—
669C42C22×D412yes—
670C42C2×#4112yes—
671C42C2×#4112yes—
672C23—28no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—84no—
691C23—84no—
692C23—82no—
693C23—82no—
694C23C2×C4×D412yes—
695C23#52014yes—
696C23C24×C411yescharacteristic
697Q8—44no—
698D4—48no—
699D4—44no—
700D4—84no—
701D4—84no—
702C2×C4—216no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
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—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—82no—
753C2×C4—82no—
754C2×C4C2×C4×D412yes—
755C2×C4C2×C4×D412yes—
756C2×C4C2×C4×D412yes—
757C2×C4C2×C4×D412yes—
758C2×C4C2×C4×D412yes—
759C2×C4#52014yes—
760C2×C4#56814yes—
761C2×C4C23×D411yescharacteristic
762C2×C4C22×#4111yescharacteristic
763C2×C4C2×H(5,𝔽2)12yes—
764C2×C4C2×2−1+412yes—
765C8—24no—
766C8—24no—
767C8—42no—
768C8—42no—
769C8—41no—
770C8—41no—
771C8—41no—
772C8—41no—
773C8—42no—
774C8—42no—
775C22—24no—
776C22—24no—
777C22—22no—
778C22—24no—
779C22—22no—
780C22—22no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—88no—
795C22C22×C4×D411yescharacteristic
796C22C2×#52012yes—
797C22C2×#56812yes—
798C22#357311yescharacteristic
799C22#357311yescharacteristic
800C4—24no—
801C4—22no—
802C4—24no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4#348411yescharacteristic
816C4#348611yescharacteristic
817C4#349212yes—
818C2—44no—
819C2—42no—
820C2—82no—
821C2#3420011yescharacteristic
822C2#6014211yescharacteristic
823C2#6014411yescharacteristic
824C2#6027212yes—
825C2#6027312yes—
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radical#2539C4
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
1. C2×#2993C2semidirect
2. C2×#2905C2semidirect
4. #22994C2semidirect
5. #22991C2semidirect
6. #22961C2semidirect
7. #22958C2semidirect
8. #22757C2semidirect
9. #22756C2semidirect
10. #22652C2semidirect
11. #22651C2semidirect
12. #22073C2semidirect
13. #22071C2semidirect
14. #21974C2semidirect
15. #21854C2semidirect
16. #21441C2semidirect
17. #21439C2semidirect
18. #20717C2semidirect
19. #20549C2semidirect
24. C2×#446C22semidirect
25. C2×C8×Q8C22semidirect
28. C2×#436C22semidirect
33. C2×C8×D4C22semidirect
34. C2×#433C22semidirect
42. C2×#424C22semidirect
63. #1985C22semidirect
64. #1955C22semidirect
65. #1940C22semidirect
66. #1940C22semidirect
67. #1939C22semidirect
68. #1939C22semidirect
69. #1939C22semidirect
70. #1939C22semidirect
71. #1924C22semidirect
72. #1924C22semidirect
73. #1923C22semidirect
74. #1923C22semidirect
75. #1917C22semidirect
76. #1917C22semidirect
77. #1916C22semidirect
78. #1916C22semidirect
89. #1851C22semidirect
90. #1851C22semidirect
93. #1850C22semidirect
94. #1850C22semidirect
95. #1842C22semidirect
96. #1842C22semidirect
97. #1831C22semidirect
98. #1831C22semidirect
103. #1798C22semidirect
104. #1798C22semidirect
107. #1771C22semidirect
108. #1771C22semidirect
109. #1767C22semidirect
110. C4×C4⋊C8C22semidirect
180. #423D4semidirect

Maximal subgroups

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

subgroupindex
C2×#29932
C2×#29052
#348772
#229942
#229912
#229612
#229582
#227572
#227562
#226522
#226512
#220732
#220712
#219742
#218542
#214412
#214392
#207172
#205492