Finite Group Databasebeta

← #6385704

Subgroups — #6385704

Order 512.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#556C211yesmaximal, characteristic
2#23284C212yesmaximal, complemented
3#23280C212yesmaximal, complemented
4#23208C211yesmaximal, characteristic
5#23205C211yesmaximal, characteristic
6#23150C211yesmaximal, characteristic, complemented
7#23052C212yesmaximal, complemented
8#22828C211yesmaximal, characteristic, complemented
9#22828C211yesmaximal, characteristic, complemented
10#22823C211yesmaximal, characteristic, complemented
11#22795C211yesmaximal, characteristic
12#22641C212yesmaximal, complemented
13#21714C211yesmaximal, characteristic, complemented
14#21667C212yesmaximal, complemented
15#21666C212yesmaximal, complemented
16#21634C211yesmaximal, characteristic
17#21631C211yesmaximal, characteristic
18#21600C212yesmaximal, complemented
19#20520C211yesmaximal, characteristic, complemented
20C4×#446C211yesmaximal, characteristic, complemented
21C4×C8×Q8C211yesmaximal, characteristic, complemented
22#20494C211yesmaximal, characteristic
23#20472C212yesmaximal, complemented
24C2×#556C411yescharacteristic
25C2×#446C2211yescharacteristic
26C2×#446C2211yescharacteristic
27C2×#446C2211yescharacteristic
28C2×#446C2211yescharacteristic
29C2×C8×Q8C2211yescharacteristic
30C2×C8×Q8C2211yescharacteristic
31C2×#436C2211yescharacteristic
32C2×#436C2211yescharacteristic
33C2×#431C2212yes—
34C2×C4×M16C2212yes—
35#2373C412yes—
36#2373C412yes—
37#2367C411yescharacteristic
38#2367C411yescharacteristic
39#2365C411yescharacteristic
40#2362C412yes—
41#2356C411yescharacteristic
42#2356C411yescharacteristic
43#2355C411yescharacteristic
44#2354C411yescharacteristic
45#2347C412yes—
46C4×C4⋊Q8C2211yescharacteristic
47C4×#126C2212yes—
48C4×#126C2212yes—
49C4×#124C2211yescharacteristic
50C4×#124C2211yescharacteristic
51C4×C22⋊Q8C2212yes—
52C42×Q8C2211yescharacteristic
53C42×Q8C2211yescharacteristic
54C42×Q8C2211yescharacteristic
55C42×D4C2211yescharacteristic
56C4×#117C2212yes—
57#1985C2212yes—
58#1984C2211yescharacteristic
59#1984C2211yescharacteristic
60#1984C2211yescharacteristic
61#1984C2211yescharacteristic
62#1954C2211yescharacteristic
63#1954C2211yescharacteristic
64#1940C2212yes—
65#1940C2212yes—
66#1940C2212yes—
67#1924C2212yes—
68#1924C2212yes—
69#1924C2212yes—
70#1924C2212yes—
71#1923C2212yes—
72#1923C2212yes—
73#1923C2212yes—
74#1923C2212yes—
75#1923C2212yes—
76#1923C2212yes—
77#1917C2212yes—
78#1917C2212yes—
79#1916C2212yes—
80#1916C2212yes—
81#1916C2212yes—
82#1916C2212yes—
83#1916C2212yes—
84#1916C2212yes—
85#1851C2212yes—
86#1851C2212yes—
87#1842C2211yescharacteristic
88#1839C2212yes—
89#1839C2212yes—
90#1831C2211yescharacteristic
91#1831C2211yescharacteristic
92#1797C2212yes—
93#1771C2212yes—
94#1771C2212yes—
95#1771C2211yescharacteristic
96#1771C2211yescharacteristic
97#1771C2211yescharacteristic
98#1771C2211yescharacteristic
99#1771C2212yes—
100#1771C2212yes—
101#1771C2212yes—
102#1771C2212yes—
103#1770C2211yescharacteristic
104#1770C2211yescharacteristic
105C8×C4⋊C4C2211yescharacteristic
106C8×C4⋊C4C2211yescharacteristic
107C8×C4⋊C4C2212yes—
108C8×C4⋊C4C2211yescharacteristic
109C8×C4⋊C4C2211yescharacteristic
110C8×C4⋊C4C2212yes—
111#1767C2211yescharacteristic
112#1767C2211yescharacteristic
113#1767C2212yes—
114C4×C4⋊C8C2211yescharacteristic
115C4×C4⋊C8C2211yescharacteristic
116C4×C4⋊C8C2212yes—
117C4×C4⋊C8C2211yescharacteristic
118C4×C4⋊C8C2211yescharacteristic
119#1753C2212yes—
120#1753C2212yes—
121#1753C2212yes—
122#1753C2212yes—
123#1753C2212yes—
124#1753C2212yes—
125#1753C2212yes—
126#1753C2212yes—
127#1749C2212yes—
128#1744C2212yes—
129#1744C2212yes—
130C4×#97C2211yescharacteristic
131C4×#97C2211yescharacteristic
132C4×#97C2212yes—
133C42×C8C2211yescharacteristic
134C42×C8C2212yes—
135C22×M16C2312yes—
136C22×M16C2312yes—
137#556—28no—
138C2×C4⋊Q8C2×C411yescharacteristic
139C2×#126C2×C412yes—
140C2×#126C2×C412yes—
141C2×#124C2×C411yescharacteristic
142C2×#124C2×C411yescharacteristic
143C2×C22⋊Q8C2×C412yes—
144C2×C4×Q8C2×C411yescharacteristic
145C2×C4×Q8C2×C411yescharacteristic
146C2×C4×Q8C2×C411yescharacteristic
147C2×C4×Q8C2×C411yescharacteristic
148C2×C4×Q8C2×C411yescharacteristic
149C2×C4×Q8C2×C411yescharacteristic
150C2×C4×Q8C2311yescharacteristic
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×D4C2×C411yescharacteristic
154C2×C4×D4C2×C411yescharacteristic
155C2×C4×D4C2311yescharacteristic
156C2×#117C2×C412yes—
157C2×#117C2×C412yes—
158C22×C42C2312yes—
159#446—24no—
160#446—24no—
161#446—24no—
162#446—24no—
163C8×Q8—24no—
164C8×Q8—24no—
165#436—24no—
166#436—24no—
167#431—28no—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2311yescharacteristic
183C2×C4⋊C8C2311yescharacteristic
184C2×C22⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C4×M16—28no—
191C2×#97C2312yes—
192C2×#97C2312yes—
193C2×#97C2311yescharacteristic
194C2×#97C2311yescharacteristic
195C2×#97C2311yescharacteristic
196C2×#97C2312yes—
197C2×#97C2311yescharacteristic
198C2×#97C2311yescharacteristic
199C2×#97C2312yes—
200C2×#97C2311yescharacteristic
201C2×#97C2311yescharacteristic
202C2×#97C2311yescharacteristic
203C2×C4×C8C2312yes—
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207C2×C4×C8C2311yescharacteristic
208C2×C4×C8C2312yes—
209C2×C4×C8C2311yescharacteristic
210C2×C4×C8C2311yescharacteristic
211C2×C4×C8C2312yes—
212C2×C4×C8C2311yescharacteristic
213C2×C4×C8C2311yescharacteristic
214C2×C4×C8C2311yescharacteristic
215C2×C4×C8C2312yes—
216C2×C4×C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218#391C2×C411yescharacteristic
219#391C2×C411yescharacteristic
220#391C2×C412yes—
221#391C2×C411yescharacteristic
222#391C2×C411yescharacteristic
223#390C2×C411yescharacteristic
224#390C2×C411yescharacteristic
225#389C2×C412yes—
226#389C2×C412yes—
227#389C2×C412yes—
228#388C2×C412yes—
229#388C2×C412yes—
230#388C2×C412yes—
231#388C2×C412yes—
232#388C2×C412yes—
233#388C2×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#387C2×C412yes—
245#387C2×C412yes—
246#385C2×C412yes—
247#385C2×C412yes—
248#384C2×C411yescharacteristic
249#383C2×C412yes—
250#383C2×C412yes—
251#382C2×C411yescharacteristic
252#382C2×C411yescharacteristic
253#380C2×C412yes—
254C4×C4⋊C4C2×C411yescharacteristic
255C4×C4⋊C4C2×C412yes—
256C4×C4⋊C4C2×C412yes—
257C4×C4⋊C4C2×C412yes—
258C4×C4⋊C4C2×C411yescharacteristic
259C4×C4⋊C4C2×C411yescharacteristic
260C4×C4⋊C4C2×C411yescharacteristic
261C4×C4⋊C4C2×C411yescharacteristic
262C4×C4⋊C4C2×C411yescharacteristic
263C4×C4⋊C4C2×C411yescharacteristic
264C4×C4⋊C4C2×C411yescharacteristic
265C4×C4⋊C4C2×C411yescharacteristic
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2×C412yes—
268C4×C4⋊C4C2×C412yes—
269C4×C4⋊C4C2×C412yes—
270C4×C4⋊C4C2×C411yescharacteristic
271C4×C4⋊C4C2×C411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2311yescharacteristic
280C4×C22⋊C4C2×C412yes—
281C4×C22⋊C4C2×C412yes—
282C4×C22⋊C4C2×C412yes—
283C4×C22⋊C4C2×C412yes—
284C4×C22⋊C4C2312yes—
285C4×C22⋊C4C2312yes—
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2312yes—
288C4×C22⋊C4C2312yes—
289#376C2×C412yes—
290#376C2×C412yes—
291C43C2312yes—
292C43C2312yes—
293C43C2311yescharacteristic
294C43C2311yescharacteristic
295C43C2311yescharacteristic
296#336C2312yes—
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303#336C2311yescharacteristic
304#336C2311yescharacteristic
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2311yescharacteristic
315#336C2312yes—
316#336C2312yes—
317#336C2311yescharacteristic
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320#336C2312yes—
321C22×Q8C22×C411yescharacteristic
322C22×Q8C22×C411yescharacteristic
323C22×Q8C22×C411yescharacteristic
324C22×D4C22×C411yescharacteristic
325C23×C4C22×C412yes—
326C23×C4C22×C412yes—
327C23×C4C2412yes—
328C2×M16—24no—
329C2×M16—24no—
330C2×M16—24no—
331C2×M16—24no—
332C2×M16—24no—
333C2×M16—42no—
334C22×C8C2412yes—
335C22×C8C2411yescharacteristic
336C22×C8C2412yes—
337C22×C8C2411yescharacteristic
338C22×C8C2412yes—
339C22×C8C2411yescharacteristic
340C22×C8C2411yescharacteristic
341C22×C8C2412yes—
342C22×C8C2411yescharacteristic
343C22×C8C2411yescharacteristic
344C22×C8C2411yescharacteristic
345C22×C8C2411yescharacteristic
346C4⋊Q8—24no—
347#126—28no—
348#126—28no—
349#124—24no—
350#124—24no—
351C22⋊Q8—28no—
352C4×Q8—24no—
353C4×Q8—24no—
354C4×Q8—24no—
355C4×Q8—24no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—42no—
363C4×Q8M1618yescomplemented
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—22no—
367C4×D4—22no—
368#117—28no—
369#117—44no—
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×C411yescharacteristic
382C2×C4⋊C4C22×C411yescharacteristic
383C2×C4⋊C4C22×C411yescharacteristic
384C2×C4⋊C4C22×C411yescharacteristic
385C2×C4⋊C4C22×C412yes—
386C2×C4⋊C4C22×C412yes—
387C2×C4⋊C4C22×C412yes—
388C2×C4⋊C4C22×C412yes—
389C2×C4⋊C4C22×C411yescharacteristic
390C2×C4⋊C4C22×C412yes—
391C2×C4⋊C4C22×C411yescharacteristic
392C2×C4⋊C4C22×C412yes—
393C2×C4⋊C4C22×C411yescharacteristic
394C2×C22⋊C4C22×C412yes—
395C2×C22⋊C4C22×C412yes—
396C2×C22⋊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×C42—24no—
406C2×C42—24no—
407C2×C42C22×C412yes—
408C2×C42C22×C412yes—
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C22×C411yescharacteristic
412C2×C42C22×C412yes—
413C2×C42C22×C412yes—
414C2×C42C22×C411yescharacteristic
415C2×C42C22×C411yescharacteristic
416C2×C42C22×C411yescharacteristic
417C2×C42C22×C412yes—
418C2×C42C22×C412yes—
419C2×C42C22×C412yes—
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C411yescharacteristic
423C2×C42C22×C412yes—
424C2×C42C22×C412yes—
425C2×C42C22×C411yescharacteristic
426C2×C42C22×C411yescharacteristic
427C2×C42C22×C412yes—
428C2×C42C22×C411yescharacteristic
429C2×C42C2412yes—
430C2×C42C2411yescharacteristic
431C2×C42C2412yes—
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2412yes—
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438C2×C42C2411yescharacteristic
439C4⋊C8—24no—
440C4⋊C8—24no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—22no—
444C4⋊C8—24no—
445C4⋊C8—22no—
446C4⋊C8—24no—
447C4⋊C8—24no—
448C4⋊C8—22no—
449C4⋊C8—22no—
450C4⋊C8—22no—
451C4⋊C8—22no—
452C4⋊C8—42no—
453C4⋊C8#4114yes—
454C4⋊C8#4114yes—
455C22⋊C8—24no—
456C22⋊C8—24no—
457C22⋊C8—24no—
458C22⋊C8—24no—
459C22⋊C8—42no—
460C22⋊C8—42no—
461#97—22no—
462#97—24no—
463#97—22no—
464#97—24no—
465#97—22no—
466#97—22no—
467#97—24no—
468#97—22no—
469#97—41no—
470#97—42no—
471#97—41no—
472#97#4114yes—
473C4×C8—24no—
474C4×C8—24no—
475C4×C8—24no—
476C4×C8—24no—
477C4×C8—24no—
478C4×C8—24no—
479C4×C8—22no—
480C4×C8—22no—
481C4×C8—22no—
482C4×C8—22no—
483C4×C8—22no—
484C4×C8—22no—
485C4×C8—41no—
486C4×C8—42no—
487C4×C8#4114yes—
488#95C22×C411yescharacteristic
489#95C22×C411yescharacteristic
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—
503#95C22×C412yes—
504#95C22×C412yes—
505#95C22×C411yescharacteristic
506#95C22×C411yescharacteristic
507#95C22×C412yes—
508#95C22×C412yes—
509#95C22×C411yescharacteristic
510#95C22×C411yescharacteristic
511#95C22×C412yes—
512#95C22×C412yes—
513C24C23×C412yes—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—41no—
522C2×Q8C2×M1614yes—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4C23×C412yes—
539C22×C4C23×C411yescharacteristic
540C22×C4C23×C411yescharacteristic
541C22×C4C23×C411yescharacteristic
542C22×C4C23×C412yes—
543C22×C4C23×C412yes—
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C411yescharacteristic
547C22×C4C23×C412yes—
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C412yes—
554C22×C4C23×C412yes—
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C412yes—
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C2511yescharacteristic
560M16—48no—
561M16—48no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—22no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—22no—
571C2×C8—21no—
572C2×C8—22no—
573C2×C8—21no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—22no—
580C2×C8—21no—
581C2×C8—22no—
582C2×C8—21no—
583C2×C8—22no—
584C2×C8—21no—
585C2×C8—22no—
586C2×C8—21no—
587C2×C8—22no—
588C2×C8—21no—
589C2×C8—22no—
590C2×C8C2×#4112yes—
591C2×C8C2×#4112yes—
592C2×C8C2×#4112yes—
593C2×C8C2×#4114yes—
594C2×C8C2×#4112yes—
595C2×C8C2×#4112yes—
596C2×C8C2×#4112yes—
597C2×C82−1+412yes—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—24no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—41no—
619C4⋊C4C2×M1614yes—
620C4⋊C4C2×M1618yes—
621C4⋊C4#13114yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C42—24no—
634C42—24no—
635C42—24no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—24no—
640C42—22no—
641C42—22no—
642C42—24no—
643C42—24no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—21no—
648C42—22no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—22no—
653C42—22no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—41no—
662C42—42no—
663C42—41no—
664C42—41no—
665C42—42no—
666C42—42no—
667C42—41no—
668C42—41no—
669C42C2×M1618yes—
670C42C2×M1614yes—
671C42C2×#4112yes—
672C42C2×#4112yes—
673C42C2×#4112yes—
674C42C2×#4112yes—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23C24×C411yescharacteristic
683Q8—28no—
684Q8—44no—
685Q8—44no—
686D4—44no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—48no—
739C2×C4—48no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4C4×#4112yes—
745C2×C4C4×#4112yes—
746C2×C4C4×#4112yes—
747C2×C4C4×#4112yes—
748C2×C4C22×M1614yes—
749C2×C4C22×M1612yes—
750C2×C4C22×M1614yes—
751C2×C4C22×M1612yes—
752C2×C4C22×M1612yes—
753C2×C4C2×#13114yes—
754C2×C4C2×#13112yes—
755C2×C4#56812yes—
756C2×C4C22×#4111yescharacteristic
757C2×C4C22×#4111yescharacteristic
758C2×C4C22×#4111yescharacteristic
759C2×C4C22×#4111yescharacteristic
760C2×C4C2×2−1+411yescharacteristic
761C2×C4#58511yescharacteristic
762C8—24no—
763C8—22no—
764C8—22no—
765C8—22no—
766C8—22no—
767C8—42no—
768C8—41no—
769C8—41no—
770C8—42no—
771C8—42no—
772C8—41no—
773C8#55614yescomplemented
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22C2×C4×#4111yescharacteristic
782C22C2×C4×#4111yescharacteristic
783C22C4×2−1+411yescharacteristic
784C22C23×M1611yescharacteristic
785C22C22×#13111yescharacteristic
786C22C2×#56811yescharacteristic
787C22#357311yescharacteristic
788C4—24no—
789C4—22no—
790C4—24no—
791C4—22no—
792C4—22no—
793C4—24no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—42no—
798C4—41no—
799C4—41no—
800C4—41no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4#296514yes—
809C4C2×#55611yescharacteristic
810C4#347511yescharacteristic
811C4#348011yescharacteristic
812C4#348211yescharacteristic
813C2—82no—
814C2C4×#55611yescharacteristic
815C2C2×#296511yescharacteristic
816C2M16×#4111yescharacteristic
817C2#6021511yescharacteristic
818C2#6021911yescharacteristic
819C2#6033311yescharacteristic
820C2#6033511yescharacteristic
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. #23284C2semidirect
3. #23280C2semidirect
6. #23150C2semidirect
7. #23052C2semidirect
8. #22828C2semidirect
9. #22828C2semidirect
10. #22823C2semidirect
12. #22641C2semidirect
13. #21714C2semidirect
14. #21667C2semidirect
15. #21666C2semidirect
18. #21600C2semidirect
19. #20520C2semidirect
20. C4×#446C2semidirect
21. C4×C8×Q8C2semidirect
23. #20472C2semidirect
363. C4×Q8M16semidirect
773. C8#556semidirect

Maximal subgroups

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

subgroupindex
C4×#5562
#232842
#232802
#232082
#232052
#231502
#230522
#228282
#228232
#227952
#226412
#217142
#216672
#216662
#216342
#216312
#216002
#205202
C4×#4462
C4×C8×Q82
#204942
#204722