Finite Group Databasebeta

← #6409515

Subgroups — #6409515

Order 512.

1385 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34915C211yesmaximal, characteristic
2#23319C212yesmaximal, complemented
3#23317C212yesmaximal, complemented
4#23258C211yesmaximal, characteristic, complemented
5#23253C211yesmaximal, characteristic, complemented
6#23205C211yesmaximal, characteristic, complemented
7#23204C211yesmaximal, characteristic, complemented
8#22821C211yesmaximal, characteristic, complemented
9#22796C212yesmaximal, complemented
10#22796C211yesmaximal, characteristic, complemented
11#22756C212yesmaximal, complemented
12Q8×C4⋊C8C211yesmaximal, characteristic, complemented
13#22651C211yesmaximal, characteristic, complemented
14#22348C212yesmaximal, complemented
15#22342C212yesmaximal, complemented
16#22137C211yesmaximal, characteristic
17#22133C211yesmaximal, characteristic
18#22100C211yesmaximal, characteristic, complemented
19#22098C211yesmaximal, characteristic, complemented
20#21980C212yesmaximal, complemented
21#21923C212yesmaximal, complemented
22#20812C211yesmaximal, characteristic, complemented
23#20809C211yesmaximal, characteristic, complemented
24C2×C8×Q8C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×#436C2211yescharacteristic
27C2×C8×D4C2211yescharacteristic
28C2×#433C2212yes—
29C2×#433C2212yes—
30C2×#431C2211yescharacteristic
31C2×#431C2211yescharacteristic
32C2×#424C2212yes—
33#2597C412yes—
34#2596C412yes—
35#2595C412yes—
36#2594C412yes—
37#2513C411yescharacteristic
38#2509C411yescharacteristic
39#2494C411yescharacteristic
40#2490C411yescharacteristic
41#2453C411yescharacteristic
42#2448C411yescharacteristic
43#2426C411yescharacteristic
44#2421C411yescharacteristic
45#2401C2212yes—
46#2395C2212yes—
47C4×#125C2211yescharacteristic
48C4×#124C2211yescharacteristic
49C4×C22⋊Q8C2211yescharacteristic
50C4×#121C2211yescharacteristic
51#2298C2212yes—
52#2293C2211yescharacteristic
53#2293C2212yes—
54C42×Q8C2211yescharacteristic
55C4×#117C2211yescharacteristic
56#1984C2211yescharacteristic
57#1984C2211yescharacteristic
58#1954C2212yes—
59#1954C2212yes—
60#1954C2211yescharacteristic
61#1954C2211yescharacteristic
62#1940C2212yes—
63#1940C2212yes—
64#1939C2212yes—
65#1939C2212yes—
66#1939C2212yes—
67#1939C2212yes—
68#1939C2211yescharacteristic
69#1939C2211yescharacteristic
70#1939C2211yescharacteristic
71#1939C2211yescharacteristic
72#1924C2212yes—
73#1924C2212yes—
74#1924C2212yes—
75#1923C2212yes—
76#1923C2212yes—
77#1923C2212yes—
78#1923C2212yes—
79#1923C2212yes—
80#1923C2212yes—
81#1923C2212yes—
82#1923C2212yes—
83#1923C2212yes—
84#1917C2212yes—
85#1916C2212yes—
86#1916C2212yes—
87#1916C2212yes—
88#1916C2212yes—
89#1916C2212yes—
90#1916C2212yes—
91#1916C2212yes—
92#1870C2212yes—
93#1869C2212yes—
94#1851C2212yes—
95#1851C2212yes—
96#1851C2212yes—
97#1850C2212yes—
98#1850C2212yes—
99#1850C2212yes—
100#1843C2211yescharacteristic
101#1843C2211yescharacteristic
102#1842C2211yescharacteristic
103#1842C2212yes—
104#1842C2211yescharacteristic
105#1832C2211yescharacteristic
106#1832C2211yescharacteristic
107#1832C2212yes—
108#1831C2212yes—
109#1798C2211yescharacteristic
110#1798C2212yes—
111#1798C2212yes—
112#1798C2211yescharacteristic
113#1798C2212yes—
114#1798C2211yescharacteristic
115#1798C2211yescharacteristic
116#1797C2211yescharacteristic
117#1797C2211yescharacteristic
118#1770C2212yes—
119#1770C2211yescharacteristic
120C8×C4⋊C4C2212yes—
121C8×C4⋊C4C2211yescharacteristic
122C8×C4⋊C4C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124#1768C2212yes—
125#1767C2211yescharacteristic
126C4×C4⋊C8C2212yes—
127C4×C4⋊C8C2211yescharacteristic
128C4×C4⋊C8C2211yescharacteristic
129C4×C4⋊C8C2211yescharacteristic
130C4×C4⋊C8C2211yescharacteristic
131C4×C4⋊C8C2211yescharacteristic
132C4×C4⋊C8C2212yes—
133#1753C2212yes—
134C8×C22⋊C4C2212yes—
135C22×M16C2312yes—
136C23×C8C2312yes—
137C2×#125C2×C411yescharacteristic
138C2×#124C2×C411yescharacteristic
139C2×C22⋊Q8C2×C411yescharacteristic
140C2×#121C2×C411yescharacteristic
141C2×C4×Q8C2×C411yescharacteristic
142C2×C4×Q8C2×C411yescharacteristic
143C2×C4×Q8C2311yescharacteristic
144C2×C4×D4C2311yescharacteristic
145C2×C4×D4C2312yes—
146C2×#117C2312yes—
147C2×#117C2311yescharacteristic
148C2×#117C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C8×Q8—42no—
151C8×Q8—42no—
152#436—42no—
153C8×D4—42no—
154#433—44no—
155#433—44no—
156#431—42no—
157#431—42no—
158#424—44no—
159C2×C4⋊C8C2311yescharacteristic
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2311yescharacteristic
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C22⋊C8C2312yes—
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2311yescharacteristic
188C2×C22⋊C8C2311yescharacteristic
189C2×C22⋊C8C2311yescharacteristic
190C2×C22⋊C8C2311yescharacteristic
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2312yes—
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207C2×C4×C8C2312yes—
208C2×C4×C8C2312yes—
209#401C2×C412yes—
210#400C2×C412yes—
211#400C2×C412yes—
212#400C2×C412yes—
213#400C2×C412yes—
214#399C2×C412yes—
215#398C2×C412yes—
216#397C2×C412yes—
217#397C2×C412yes—
218#397C2×C412yes—
219#397C2×C412yes—
220#397C2×C412yes—
221#397C2×C412yes—
222#396C2×C412yes—
223#394C2×C412yes—
224#394C2×C412yes—
225#391C2×C411yescharacteristic
226#391C2×C411yescharacteristic
227#390C2×C412yes—
228#390C2×C412yes—
229#390C2×C411yescharacteristic
230#390C2×C411yescharacteristic
231#390C2×C411yescharacteristic
232#390C2×C411yescharacteristic
233#389C2×C411yescharacteristic
234#389C2×C411yescharacteristic
235#389C2×C412yes—
236#389C2×C412yes—
237#389C2×C411yescharacteristic
238#389C2×C411yescharacteristic
239#389C2×C411yescharacteristic
240#389C2×C411yescharacteristic
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#388C2×C412yes—
250#388C2×C412yes—
251#388C2×C412yes—
252#388C2×C412yes—
253#388C2×C412yes—
254#387C2×C412yes—
255#387C2×C412yes—
256#387C2×C412yes—
257#387C2×C412yes—
258#387C2×C412yes—
259#387C2×C412yes—
260#387C2×C412yes—
261#386C2×C412yes—
262#385C2×C412yes—
263#382C2×C411yescharacteristic
264#382C2×C411yescharacteristic
265#380C2×C411yescharacteristic
266#380C2×C411yescharacteristic
267C4×C4⋊C4C2×C411yescharacteristic
268C4×C4⋊C4C2×C412yes—
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C412yes—
271C4×C4⋊C4C2×C411yescharacteristic
272C4×C4⋊C4C2×C411yescharacteristic
273C4×C4⋊C4C2×C411yescharacteristic
274C4×C4⋊C4C2×C411yescharacteristic
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2311yescharacteristic
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2312yes—
281C4×C22⋊C4C2×C411yescharacteristic
282C4×C22⋊C4C2×C411yescharacteristic
283C4×C22⋊C4C2×C411yescharacteristic
284C4×C22⋊C4C2×C411yescharacteristic
285C4×C22⋊C4C2312yes—
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2312yes—
288C4×C22⋊C4C2312yes—
289C4×C22⋊C4C2312yes—
290#376C2311yescharacteristic
291#376C2311yescharacteristic
292C43C2311yescharacteristic
293C43C2312yes—
294C43C2311yescharacteristic
295#336C2312yes—
296#336C2312yes—
297#336C2311yescharacteristic
298#336C2312yes—
299#336C2311yescharacteristic
300#336C2312yes—
301#336C2311yescharacteristic
302#336C2311yescharacteristic
303#336C2311yescharacteristic
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2311yescharacteristic
307#336C2312yes—
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319C22×Q8C22×C411yescharacteristic
320C22×D4C22×C411yescharacteristic
321C22×D4C22×C412yes—
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2412yes—
326C2×M16—42no—
327C2×M16—42no—
328C2×M16—42no—
329C22×C8—42no—
330C22×C8—42no—
331C22×C8—42no—
332C22×C8C2411yescharacteristic
333C22×C8C2412yes—
334C22×C8C2411yescharacteristic
335C22×C8C2412yes—
336C22×C8C2411yescharacteristic
337C22×C8C2411yescharacteristic
338C22×C8C2411yescharacteristic
339C22×C8C2411yescharacteristic
340C22×C8C2412yes—
341C22×C8C2412yes—
342C22×C8C2411yescharacteristic
343C22×C8C2411yescharacteristic
344#125—24no—
345#124—24no—
346C22⋊Q8—24no—
347#121—24no—
348C4×Q8—24no—
349C4×Q8—24no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—42no—
355C4×D4—42no—
356#117—24no—
357#117—22no—
358#117—24no—
359#117—22no—
360#117—41no—
361#117—41no—
362C2×C4⋊C4C22×C411yescharacteristic
363C2×C4⋊C4C22×C411yescharacteristic
364C2×C4⋊C4C22×C412yes—
365C2×C4⋊C4C22×C412yes—
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C4⋊C4C22×C411yescharacteristic
368C2×C4⋊C4C22×C412yes—
369C2×C4⋊C4C22×C412yes—
370C2×C4⋊C4C22×C411yescharacteristic
371C2×C4⋊C4C22×C412yes—
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C412yes—
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C411yescharacteristic
378C2×C4⋊C4C22×C411yescharacteristic
379C2×C4⋊C4C22×C412yes—
380C2×C4⋊C4C22×C412yes—
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C411yescharacteristic
384C2×C22⋊C4C22×C411yescharacteristic
385C2×C22⋊C4C22×C411yescharacteristic
386C2×C22⋊C4C22×C412yes—
387C2×C22⋊C4C22×C412yes—
388C2×C22⋊C4C22×C412yes—
389C2×C22⋊C4C22×C412yes—
390C2×C22⋊C4C22×C412yes—
391C2×C22⋊C4C22×C412yes—
392C2×C22⋊C4C22×C412yes—
393C2×C22⋊C4C22×C411yescharacteristic
394C2×C22⋊C4C22×C411yescharacteristic
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×C42—22no—
404C2×C42—22no—
405C2×C42C22×C411yescharacteristic
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C412yes—
408C2×C42C22×C412yes—
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C22×C411yescharacteristic
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C411yescharacteristic
415C2×C42C22×C411yescharacteristic
416C2×C42C22×C411yescharacteristic
417C2×C42C22×C412yes—
418C2×C42C22×C412yes—
419C2×C42C2411yescharacteristic
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2412yes—
423C2×C42C2412yes—
424C2×C42C2412yes—
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C4⋊C8—22no—
429C4⋊C8—24no—
430C4⋊C8—24no—
431C4⋊C8—22no—
432C4⋊C8—22no—
433C4⋊C8—22no—
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C4⋊C8—22no—
438C4⋊C8—41no—
439C4⋊C8—41no—
440C4⋊C8—42no—
441C4⋊C8—41no—
442C4⋊C8—41no—
443C4⋊C8—42no—
444C4⋊C8—42no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448C4⋊C8—41no—
449C4⋊C8—41no—
450C4⋊C8—41no—
451C4⋊C8—41no—
452C4⋊C8—42no—
453C4⋊C8—42no—
454C22⋊C8—42no—
455C22⋊C8—42no—
456C22⋊C8—41no—
457C22⋊C8—41no—
458C22⋊C8—41no—
459C22⋊C8—41no—
460C22⋊C8—42no—
461C22⋊C8—42no—
462C22⋊C8—42no—
463C22⋊C8—42no—
464C22⋊C8—42no—
465C22⋊C8—42no—
466#97—42no—
467#97—42no—
468C4×C8—22no—
469C4×C8—22no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—42no—
473C4×C8—42no—
474C4×C8—42no—
475C4×C8—42no—
476C4×C8—42no—
477C4×C8—42no—
478#95C22×C411yescharacteristic
479#95C22×C411yescharacteristic
480#95C22×C411yescharacteristic
481#95C22×C411yescharacteristic
482#95C22×C411yescharacteristic
483#95C22×C411yescharacteristic
484#95C22×C411yescharacteristic
485#95C22×C411yescharacteristic
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—
503#95C22×C412yes—
504#95C22×C412yes—
505#95C22×C412yes—
506C24C23×C412yes—
507C24C23×C411yescharacteristic
508C2×Q8—22no—
509C2×Q8—22no—
510C2×Q8#13114yes—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—24no—
515C2×D4—42no—
516C2×D4—42no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4C23×C411yescharacteristic
536C22×C4C23×C411yescharacteristic
537C22×C4C23×C412yes—
538C22×C4C23×C411yescharacteristic
539C22×C4C23×C411yescharacteristic
540C22×C4C23×C412yes—
541C22×C4C23×C412yes—
542C22×C4C23×C411yescharacteristic
543C22×C4C23×C411yescharacteristic
544C22×C4C23×C411yescharacteristic
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C412yes—
547C22×C4C23×C412yes—
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C412yes—
553C22×C4C23×C412yes—
554C22×C4C23×C411yescharacteristic
555C22×C4C2511yescharacteristic
556M16—84no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—21no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—21no—
582C2×C8—21no—
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—21no—
592C2×C8—21no—
593C2×C8—84no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—22no—
599C4⋊C4—24no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—22no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—42no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—42no—
615C4⋊C4#13114yes—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—41no—
632C22⋊C4—41no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C42—22no—
636C42—22no—
637C42—24no—
638C42—24no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—21no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—21no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—22no—
657C42—41no—
658C42—41no—
659C42—42no—
660C42—42no—
661C42—41no—
662C42—41no—
663C42H(5,𝔽2)12yes—
664C42H(5,𝔽2)12yes—
665C422−1+412yes—
666C422−1+412yes—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—22no—
675C23—22no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—22no—
680C23—21no—
681C23C24×C411yescharacteristic
682Q8—28no—
683D4—44no—
684D4—84no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
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—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4#52012yes—
748C2×C4#52012yes—
749C2×C4#52012yes—
750C2×C4#52012yes—
751C2×C4C2×#13114yes—
752C2×C4C2×#13114yes—
753C2×C4C2×#13112yes—
754C2×C4C2×#13112yes—
755C2×C4C2×H(5,𝔽2)11yescharacteristic
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C2×C4C2×2−1+411yescharacteristic
758C2×C4C2×2−1+411yescharacteristic
759C2×C4#58511yescharacteristic
760C2×C4#58511yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C8—41no—
765C8—42no—
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—42no—
772C8—42no—
773C22—42no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—41no—
786C22—42no—
787C22C2×#52011yescharacteristic
788C22C2×#52011yescharacteristic
789C22#342811yescharacteristic
790C22C22×#13111yescharacteristic
791C22C22×#13111yescharacteristic
792C22#357311yescharacteristic
793C22#357311yescharacteristic
794C4—24no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—24no—
799C4—41no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—42no—
808C4—41no—
809C4—41no—
810C4—42no—
811C4—41no—
812C4—41no—
813C4#299414yes—
814C4#354611yescharacteristic
815C4#354711yescharacteristic
816C4#355411yescharacteristic
817C4#355511yescharacteristic
818C2—81no—
819C2—82no—
820C2#3438311yescharacteristic
821C2C2×#299411yescharacteristic
822C2#6026711yescharacteristic
823C2#6027411yescharacteristic
824C2#6027411yescharacteristic
825C2#6029811yescharacteristic
826C2#6030111yescharacteristic
subgroupG/H
center, Frattini, cosocleC22×C4C25
commutator, socleC23C24×C4
prime radicalC2×#121C2×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. #23319C2semidirect
3. #23317C2semidirect
4. #23258C2semidirect
5. #23253C2semidirect
6. #23205C2semidirect
7. #23204C2semidirect
8. #22821C2semidirect
9. #22796C2semidirect
10. #22796C2semidirect
11. #22756C2semidirect
12. Q8×C4⋊C8C2semidirect
13. #22651C2semidirect
14. #22348C2semidirect
15. #22342C2semidirect
18. #22100C2semidirect
19. #22098C2semidirect
20. #21980C2semidirect
21. #21923C2semidirect
22. #20812C2semidirect
23. #20809C2semidirect

Maximal subgroups

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

subgroupindex
#349152
#233192
#233172
#232582
#232532
#232052
#232042
#228212
#227962
#227562
Q8×C4⋊C82
#226512
#223482
#223422
#221372
#221332
#221002
#220982
#219802
#219232
#208122
#208092