Finite Group Databasebeta

← #6401727

Subgroups — #6401727

Order 512.

1427 conjugacy classes of subgroups.

The subgroup lattice has 835 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34941C211yesmaximal, characteristic
2#23264C212yesmaximal, complemented
3#23246C212yesmaximal, complemented
4#23149C211yesmaximal, characteristic, complemented
5#23056C212yesmaximal, complemented
6#23055C211yesmaximal, characteristic, complemented
7#22957C211yesmaximal, characteristic, complemented
8#22828C211yesmaximal, characteristic, complemented
9#22790C212yesmaximal
10#22751C211yesmaximal, characteristic
11#22626C211yesmaximal, characteristic, complemented
12#22600C211yesmaximal, characteristic, complemented
13#22379C212yesmaximal, complemented
14#22324C212yesmaximal, complemented
15#22311C211yesmaximal, characteristic, complemented
16#22104C211yesmaximal, characteristic, complemented
17#21602C212yesmaximal, complemented
18#21597C211yesmaximal, characteristic, complemented
19#21110C212yesmaximal
20#21101C211yesmaximal, characteristic
21#20570C211yesmaximal, characteristic, complemented
22#20537C211yesmaximal, characteristic, complemented
23#20437C211yesmaximal, characteristic, complemented
24C2×#446C2211yescharacteristic
25C2×#446C2211yescharacteristic
26C2×C8×Q8C2212yes—
27C2×#433C2212yes—
28C2×#432C2211yescharacteristic
29C2×#431C2211yescharacteristic
30C2×#423C2211yescharacteristic
31C2×#405C2212yes—
32C22×C4×C8C2211yescharacteristic
33#2574C412yes—
34#2574C412yes—
35#2567C411yescharacteristic
36#2563C411yescharacteristic
37#2552C411yescharacteristic
38#2538C411yescharacteristic
39#2508C412yes—
40#2497C411yescharacteristic
41#2497C411yescharacteristic
42#2454C412yes—
43#2423C411yescharacteristic
44#2423C411yescharacteristic
45#2396C2212yes—
46#2396C2212yes—
47C4×C4⋊Q8C2211yescharacteristic
48C4×#125C2212yes—
49C4×C22⋊Q8C2211yescharacteristic
50C4×C22⋊Q8C2211yescharacteristic
51#2293C2212yes—
52#2285C2211yescharacteristic
53#2285C2211yescharacteristic
54C42×Q8C2211yescharacteristic
55C42×D4C2211yescharacteristic
56#1985C2212yes—
57#1985C2212yes—
58#1984C2211yescharacteristic
59#1984C2211yescharacteristic
60#1984C2212yes—
61#1940C2212yes—
62#1939C2211yescharacteristic
63#1939C2212yes—
64#1939C2211yescharacteristic
65#1939C2211yescharacteristic
66#1939C2211yescharacteristic
67#1924C2212yes—
68#1924C2212yes—
69#1924C2212yes—
70#1923C2212yes—
71#1923C2211yescharacteristic
72#1923C2212yes—
73#1923C2211yescharacteristic
74#1917C2212yes—
75#1917C2212yes—
76#1917C2212yes—
77#1917C2212yes—
78#1917C2212yes—
79#1917C2212yes—
80#1917C2212yes—
81#1917C2212yes—
82#1916C2212yes—
83#1916C2212yes—
84#1916C2212yes—
85#1916C2212yes—
86#1916C2212yes—
87#1916C2212yes—
88#1916C2211yescharacteristic
89#1916C2211yescharacteristic
90#1916C2212yes—
91#1870C2212yes—
92#1869C2211yescharacteristic
93#1869C2211yescharacteristic
94#1851C2212yes—
95#1850C2212yes—
96#1850C2211yescharacteristic
97#1850C2211yescharacteristic
98#1839C2212yes—
99#1831C2211yescharacteristic
100#1818C2212yes—
101#1798C2212yes—
102#1797C2211yescharacteristic
103#1797C2211yescharacteristic
104#1771C2212yes—
105#1771C2212yes—
106#1771C2212yes—
107#1771C2212yes—
108#1771C2212yes—
109#1770C2212yes—
110#1770C2211yescharacteristic
111#1770C2211yescharacteristic
112#1770C2212yes—
113#1770C2211yescharacteristic
114#1770C2211yescharacteristic
115C8×C4⋊C4C2211yescharacteristic
116C8×C4⋊C4C2212yes—
117C8×C4⋊C4C2211yescharacteristic
118C8×C4⋊C4C2211yescharacteristic
119C8×C4⋊C4C2211yescharacteristic
120#1767C2212yes—
121C4×C4⋊C8C2211yescharacteristic
122C4×C4⋊C8C2211yescharacteristic
123#1753C2212yes—
124#1753C2212yes—
125#1752C2212yes—
126#1750C2212yes—
127#1750C2212yes—
128#1750C2212yes—
129C4×C22⋊C8C2211yescharacteristic
130C4×C22⋊C8C2211yescharacteristic
131#1745C2212yes—
132#1744C2211yescharacteristic
133#1744C2212yes—
134#1729C2212yes—
135C22×M16C2312yes—
136C23×C8C2311yescharacteristic
137C23×C8C2311yescharacteristic
138C2×C4⋊Q8C2×C411yescharacteristic
139C2×#125C2×C412yes—
140C2×C22⋊Q8C2×C411yescharacteristic
141C2×C22⋊Q8C2×C411yescharacteristic
142C2×C4×Q8C2×C411yescharacteristic
143C2×C4×Q8C2×C411yescharacteristic
144C2×C4×Q8C2311yescharacteristic
145C2×C4×Q8C2312yes—
146C2×C4×D4C2×C411yescharacteristic
147C2×C4×D4C2×C411yescharacteristic
148C2×C4×D4C2311yescharacteristic
149C2×#117C2312yes—
150C2×#117C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#446—24no—
154#446—24no—
155C8×Q8—44no—
156#433—44no—
157#432—24no—
158#431—24no—
159#423—24no—
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2311yescharacteristic
177C2×C22⋊C8C2311yescharacteristic
178C2×C22⋊C8C2311yescharacteristic
179C2×C22⋊C8C2311yescharacteristic
180C2×C22⋊C8C2311yescharacteristic
181C2×C22⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2311yescharacteristic
184#405—44no—
185C2×#97C2312yes—
186C2×#97C2312yes—
187C2×#97C2312yes—
188C2×#97C2312yes—
189C2×#97C2312yes—
190C2×#97C2312yes—
191C2×#97C2312yes—
192C2×C4×C8—24no—
193C2×C4×C8C2311yescharacteristic
194C2×C4×C8C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2312yes—
197C2×C4×C8C2312yes—
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2312yes—
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203C2×C4×C8C2311yescharacteristic
204#400C2×C412yes—
205#400C2×C412yes—
206#399C2×C412yes—
207#399C2×C412yes—
208#398C2×C412yes—
209#398C2×C412yes—
210#398C2×C412yes—
211#398C2×C412yes—
212#396C2×C412yes—
213#396C2×C412yes—
214#396C2×C412yes—
215#396C2×C412yes—
216#395C2×C412yes—
217#395C2×C412yes—
218#393C2×C412yes—
219#393C2×C412yes—
220#391C2×C412yes—
221#391C2×C411yescharacteristic
222#391C2×C411yescharacteristic
223#390C2×C412yes—
224#390C2×C412yes—
225#389C2×C412yes—
226#389C2×C412yes—
227#389C2×C411yescharacteristic
228#389C2×C411yescharacteristic
229#389C2×C412yes—
230#389C2×C412yes—
231#389C2×C411yescharacteristic
232#389C2×C411yescharacteristic
233#389C2×C412yes—
234#388C2×C412yes—
235#388C2×C412yes—
236#388C2×C412yes—
237#388C2×C412yes—
238#387C2×C412yes—
239#387C2×C412yes—
240#387C2×C412yes—
241#387C2×C412yes—
242#387C2×C412yes—
243#387C2×C412yes—
244#385C2×C412yes—
245#385C2×C412yes—
246#384C2×C411yescharacteristic
247#384C2×C411yescharacteristic
248#384C2×C411yescharacteristic
249#384C2×C411yescharacteristic
250#384C2×C411yescharacteristic
251#382C2×C412yes—
252#382C2×C412yes—
253#382C2×C412yes—
254#380C2×C411yescharacteristic
255#380C2×C411yescharacteristic
256#380C2×C411yescharacteristic
257#380C2×C411yescharacteristic
258#380C2×C412yes—
259#380C2×C412yes—
260#380C2×C411yescharacteristic
261#380C2×C411yescharacteristic
262C4×C4⋊C4C2×C411yescharacteristic
263C4×C4⋊C4C2×C411yescharacteristic
264C4×C4⋊C4C2×C412yes—
265C4×C4⋊C4C2×C412yes—
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2×C411yescharacteristic
268C4×C4⋊C4C2311yescharacteristic
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2311yescharacteristic
278C4×C22⋊C4C2×C411yescharacteristic
279C4×C22⋊C4C2×C411yescharacteristic
280C4×C22⋊C4C2×C411yescharacteristic
281C4×C22⋊C4C2×C411yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C4×C22⋊C4C2312yes—
284C4×C22⋊C4C2311yescharacteristic
285C4×C22⋊C4C2312yes—
286C43C2312yes—
287C43C2311yescharacteristic
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2311yescharacteristic
298#336C2312yes—
299#336C2312yes—
300#336C2311yescharacteristic
301#336C2311yescharacteristic
302#336C2312yes—
303#336C2312yes—
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2312yes—
307#336C2312yes—
308#336C2311yescharacteristic
309#336C2311yescharacteristic
310#336C2311yescharacteristic
311#336C2312yes—
312#336C2311yescharacteristic
313#336C2312yes—
314#336C2311yescharacteristic
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319C22×Q8C22×C411yescharacteristic
320C22×Q8C22×C412yes—
321C22×D4C22×C411yescharacteristic
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C411yescharacteristic
324C23×C4C22×C411yescharacteristic
325C23×C4C22×C411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—42no—
331C22×C8—22no—
332C22×C8—22no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—22no—
336C22×C8—41no—
337C22×C8C2411yescharacteristic
338C22×C8C2412yes—
339C22×C8C2411yescharacteristic
340C22×C8C2411yescharacteristic
341C22×C8C2412yes—
342C22×C8C2411yescharacteristic
343C22×C8C2411yescharacteristic
344C22×C8C2412yes—
345C22×C8C2411yescharacteristic
346C22×C8C2411yescharacteristic
347C22×C8C2412yes—
348C22×C8C2411yescharacteristic
349C4⋊Q8—24no—
350#125—44no—
351C22⋊Q8—42no—
352C22⋊Q8—42no—
353C4×Q8—24no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×Q8—42no—
357C4×Q8—42no—
358C4×Q8—42no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—24no—
362C4×D4—42no—
363#117—42no—
364#117—42no—
365#117—42no—
366#117—42no—
367C2×C4⋊C4C22×C411yescharacteristic
368C2×C4⋊C4C22×C411yescharacteristic
369C2×C4⋊C4C22×C411yescharacteristic
370C2×C4⋊C4C22×C411yescharacteristic
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C412yes—
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C412yes—
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C4⋊C4C22×C411yescharacteristic
377C2×C4⋊C4C22×C412yes—
378C2×C4⋊C4C22×C412yes—
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C411yescharacteristic
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
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×C412yes—
391C2×C4⋊C4C22×C412yes—
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C412yes—
394C2×C4⋊C4C22×C412yes—
395C2×C4⋊C4C22×C412yes—
396C2×C4⋊C4C22×C412yes—
397C2×C22⋊C4C22×C411yescharacteristic
398C2×C22⋊C4C22×C411yescharacteristic
399C2×C22⋊C4C22×C411yescharacteristic
400C2×C22⋊C4C22×C411yescharacteristic
401C2×C22⋊C4C22×C411yescharacteristic
402C2×C22⋊C4C22×C412yes—
403C2×C22⋊C4C22×C412yes—
404C2×C22⋊C4C22×C412yes—
405C2×C22⋊C4C22×C412yes—
406C2×C22⋊C4C22×C411yescharacteristic
407C2×C22⋊C4C22×C412yes—
408C2×C22⋊C4C22×C412yes—
409C2×C22⋊C4C22×C412yes—
410C2×C22⋊C4C22×C412yes—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42C22×C411yescharacteristic
416C2×C42C22×C412yes—
417C2×C42C22×C411yescharacteristic
418C2×C42C22×C411yescharacteristic
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C412yes—
423C2×C42C22×C412yes—
424C2×C42C22×C411yescharacteristic
425C2×C42C22×C412yes—
426C2×C42C22×C411yescharacteristic
427C2×C42C2412yes—
428C2×C42C2412yes—
429C2×C42C2412yes—
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2412yes—
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C4⋊C8—24no—
437C4⋊C8—22no—
438C4⋊C8—22no—
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—24no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—22no—
445C4⋊C8—22no—
446C4⋊C8—42no—
447C4⋊C8—41no—
448C4⋊C8—42no—
449C4⋊C8—42no—
450C4⋊C8#4114yes—
451C22⋊C8—24no—
452C22⋊C8—22no—
453C22⋊C8—22no—
454C22⋊C8—22no—
455C22⋊C8—22no—
456C22⋊C8—24no—
457C22⋊C8—22no—
458C22⋊C8—41no—
459C22⋊C8—42no—
460#97—24no—
461#97—24no—
462#97—24no—
463#97—42no—
464#97—42no—
465#97—42no—
466#97—42no—
467C4×C8—22no—
468C4×C8—22no—
469C4×C8—24no—
470C4×C8—24no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—42no—
475C4×C8—42no—
476C4×C8—42no—
477C4×C8#4114yes—
478#95C22×C411yescharacteristic
479#95C22×C411yescharacteristic
480#95C22×C411yescharacteristic
481#95C22×C411yescharacteristic
482#95C22×C411yescharacteristic
483#95C22×C411yescharacteristic
484#95C22×C412yes—
485#95C22×C412yes—
486#95C22×C412yes—
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—
503C24C23×C411yescharacteristic
504C24C23×C411yescharacteristic
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—24no—
508C2×Q8—22no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—41no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4C23×C411yescharacteristic
537C22×C4C23×C411yescharacteristic
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C412yes—
540C22×C4C23×C411yescharacteristic
541C22×C4C23×C412yes—
542C22×C4C23×C412yes—
543C22×C4C23×C412yes—
544C22×C4C23×C412yes—
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C412yes—
547C22×C4C23×C411yescharacteristic
548C22×C4C23×C412yes—
549C22×C4C23×C412yes—
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C411yescharacteristic
555C22×C4C23×C411yescharacteristic
556C22×C42−1+412yes—
557C22×C42−1+412yes—
558C22×C4C2511yescharacteristic
559M16—48no—
560C2×C8—28no—
561C2×C8—21no—
562C2×C8—22no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—22no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—21no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—22no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—22no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—22no—
589C2×C8—21no—
590C2×C8—22no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—44no—
594C2×C8C2×#4112yes—
595C2×C8C2×#4112yes—
596C2×C8C2×#4114yes—
597C2×C8H(5,𝔽2)12yes—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—41no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—24no—
647C42—22no—
648C42—21no—
649C42—21no—
650C42—22no—
651C42—22no—
652C42—21no—
653C42—21no—
654C42—22no—
655C42—22no—
656C42—21no—
657C42—22no—
658C42—21no—
659C42—21no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—21no—
664C42—41no—
665C42—42no—
666C42—41no—
667C42—42no—
668C42—42no—
669C42#13114yes—
670C42C2×#4112yes—
671C42C2×#4112yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23#51912yes—
686C23C24×C411yescharacteristic
687Q8—48no—
688Q8—44no—
689D4—44no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—21no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—82no—
754C2×C4C4×#4112yes—
755C2×C4C4×#4112yes—
756C2×C4#51912yes—
757C2×C4C2×#13112yes—
758C2×C4C2×#13112yes—
759C2×C4C2×#13112yes—
760C2×C4#56812yes—
761C2×C4#56812yes—
762C2×C4C22×#4111yescharacteristic
763C2×C4C22×#4111yescharacteristic
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C2×C4C2×2−1+411yescharacteristic
766C2×C4C2×2−1+411yescharacteristic
767C2×C4#58511yescharacteristic
768C8—22no—
769C8—22no—
770C8—22no—
771C8—24no—
772C8—41no—
773C8—42no—
774C8—41no—
775C8—41no—
776C8—41no—
777C8—42no—
778C8—41no—
779C8—42no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22C2×C4×#4111yescharacteristic
795C22C2×#51911yescharacteristic
796C22C4×H(5,𝔽2)11yescharacteristic
797C22C22×#13111yescharacteristic
798C22C2×#56811yescharacteristic
799C22C2×#56811yescharacteristic
800C22#357311yescharacteristic
801C4—22no—
802C4—22no—
803C4—22no—
804C4—22no—
805C4—22no—
806C4—41no—
807C4—41no—
808C4—42no—
809C4—42no—
810C4—41no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—41no—
819C4—41no—
820C4#296914yes—
821C4#349211yescharacteristic
822C4#349511yescharacteristic
823C4#351611yescharacteristic
824C4#352011yescharacteristic
825C2—42no—
826C2—81no—
827C2#3429911yescharacteristic
828C2C2×#296911yescharacteristic
829C2#6021611yescharacteristic
830C2#6025011yescharacteristic
831C2#6025411yescharacteristic
832C2#6030611yescharacteristic
833C2#6032011yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC22×D4C22×C4
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. #23264C2semidirect
3. #23246C2semidirect
4. #23149C2semidirect
5. #23056C2semidirect
6. #23055C2semidirect
7. #22957C2semidirect
8. #22828C2semidirect
11. #22626C2semidirect
12. #22600C2semidirect
13. #22379C2semidirect
14. #22324C2semidirect
15. #22311C2semidirect
16. #22104C2semidirect
17. #21602C2semidirect
18. #21597C2semidirect
21. #20570C2semidirect
22. #20537C2semidirect
23. #20437C2semidirect

Maximal subgroups

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

subgroupindex
#349412
#232642
#232462
#231492
#230562
#230552
#229572
#228282
#227902
#227512
#226262
#226002
#223792
#223242
#223112
#221042
#216022
#215972
#211102
#211012
#205702
#205372
#204372