Finite Group Databasebeta

← #6409593

Subgroups — #6409593

Order 512.

1434 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#34913C211yesmaximal, characteristic
2#23382C212yesmaximal, complemented
3#23381C212yesmaximal, complemented
4#22990C211yesmaximal, characteristic
5#22989C211yesmaximal, characteristic
6#22957C211yesmaximal, characteristic, complemented
7#22952C211yesmaximal, characteristic, complemented
8#22822C211yesmaximal, characteristic, complemented
9#22795C211yesmaximal, characteristic, complemented
10#22752C212yesmaximal, complemented
11#22721C211yesmaximal, characteristic, complemented
12#22650C211yesmaximal, characteristic, complemented
13#22649C212yesmaximal, complemented
14#22301C211yesmaximal, characteristic, complemented
15#22299C211yesmaximal, characteristic, complemented
16#22214C211yesmaximal, characteristic, complemented
17#22210C211yesmaximal, characteristic, complemented
18#22074C212yesmaximal, complemented
19#22068C212yesmaximal, complemented
20#21975C212yesmaximal, complemented
21#21928C212yesmaximal, complemented
22#20793C211yesmaximal, characteristic, complemented
23#20782C211yesmaximal, characteristic, complemented
24C2×#446C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×#436C2212yes—
27C2×#436C2211yescharacteristic
28C2×#436C2211yescharacteristic
29C2×#435C2212yes—
30C2×#431C2212yes—
31C2×#424C2212yes—
32C2×#424C2212yes—
33C2×#423C2211yescharacteristic
34C2×#423C2212yes—
35C22×C4⋊C8C2211yescharacteristic
36#2578C412yes—
37#2577C412yes—
38#2576C412yes—
39#2575C412yes—
40#2514C411yescharacteristic
41#2508C411yescharacteristic
42#2495C411yescharacteristic
43#2489C411yescharacteristic
44#2454C411yescharacteristic
45#2447C411yescharacteristic
46#2427C411yescharacteristic
47#2420C411yescharacteristic
48#2401C2212yes—
49#2395C2212yes—
50C4×#125C2211yescharacteristic
51C4×#124C2211yescharacteristic
52C4×C22⋊Q8C2211yescharacteristic
53C4×#121C2211yescharacteristic
54#2295C2211yescharacteristic
55#2290C2212yes—
56#2283C2212yes—
57C42×D4C2211yescharacteristic
58C4×#117C2211yescharacteristic
59#1984C2211yescharacteristic
60#1984C2211yescharacteristic
61#1954C2211yescharacteristic
62#1954C2211yescharacteristic
63#1940C2212yes—
64#1940C2212yes—
65#1939C2212yes—
66#1939C2212yes—
67#1939C2211yescharacteristic
68#1939C2211yescharacteristic
69#1939C2212yes—
70#1939C2211yescharacteristic
71#1939C2211yescharacteristic
72#1939C2212yes—
73#1939C2212yes—
74#1939C2212yes—
75#1924C2212yes—
76#1924C2212yes—
77#1924C2212yes—
78#1923C2212yes—
79#1923C2212yes—
80#1923C2212yes—
81#1923C2212yes—
82#1923C2212yes—
83#1917C2212yes—
84#1917C2212yes—
85#1917C2212yes—
86#1916C2212yes—
87#1916C2212yes—
88#1916C2212yes—
89#1916C2212yes—
90#1916C2212yes—
91#1870C2212yes—
92#1869C2212yes—
93#1851C2212yes—
94#1851C2212yes—
95#1851C2212yes—
96#1851C2212yes—
97#1851C2212yes—
98#1851C2212yes—
99#1851C2212yes—
100#1851C2212yes—
101#1851C2212yes—
102#1850C2212yes—
103#1843C2212yes—
104#1843C2212yes—
105#1843C2212yes—
106#1842C2211yescharacteristic
107#1842C2211yescharacteristic
108#1842C2211yescharacteristic
109#1842C2211yescharacteristic
110#1840C2211yescharacteristic
111#1840C2211yescharacteristic
112#1832C2212yes—
113#1832C2211yescharacteristic
114#1832C2211yescharacteristic
115#1818C2211yescharacteristic
116#1818C2211yescharacteristic
117#1798C2211yescharacteristic
118#1798C2211yescharacteristic
119#1797C2212yes—
120#1797C2212yes—
121#1770C2211yescharacteristic
122C8×C4⋊C4C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124C8×C4⋊C4C2211yescharacteristic
125#1768C2212yes—
126#1768C2212yes—
127C4×C4⋊C8C2211yescharacteristic
128C4×C4⋊C8C2211yescharacteristic
129#1753C2212yes—
130C8×C22⋊C4C2212yes—
131C4×C22⋊C8C2211yescharacteristic
132C4×C22⋊C8C2211yescharacteristic
133#1744C2211yescharacteristic
134#1744C2211yescharacteristic
135C22×M16C2312yes—
136C22×M16C2312yes—
137C22×M16C2312yes—
138C23×C8C2312yes—
139C2×#125C2×C411yescharacteristic
140C2×#124C2×C411yescharacteristic
141C2×C22⋊Q8C2×C411yescharacteristic
142C2×#121C2×C411yescharacteristic
143C2×C4×Q8C2311yescharacteristic
144C2×C4×D4C2×C411yescharacteristic
145C2×C4×D4C2×C411yescharacteristic
146C2×C4×D4C2312yes—
147C2×C4×D4C2311yescharacteristic
148C2×#117C2311yescharacteristic
149C2×#117C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152#446—42no—
153C8×Q8—42no—
154#436—42no—
155#436—42no—
156#436—44no—
157#435—44no—
158#431—44no—
159#424—44no—
160#424—44no—
161#423—44no—
162#423—42no—
163C2×C4⋊C8—42no—
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2312yes—
167C2×C4⋊C8C2312yes—
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2311yescharacteristic
174C2×C4⋊C8C2312yes—
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×C22⋊C8C2311yescharacteristic
189C2×C22⋊C8C2311yescharacteristic
190C2×C22⋊C8C2311yescharacteristic
191C2×C22⋊C8C2311yescharacteristic
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C22⋊C8C2312yes—
197C2×C22⋊C8C2312yes—
198C2×#97C2312yes—
199C2×#97C2312yes—
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207C2×C4×C8C2312yes—
208#401C2×C412yes—
209#400C2×C412yes—
210#400C2×C412yes—
211#400C2×C412yes—
212#400C2×C412yes—
213#399C2×C412yes—
214#398C2×C412yes—
215#397C2×C412yes—
216#397C2×C412yes—
217#397C2×C412yes—
218#397C2×C412yes—
219#397C2×C412yes—
220#397C2×C412yes—
221#396C2×C412yes—
222#394C2×C412yes—
223#394C2×C412yes—
224#391C2×C411yescharacteristic
225#391C2×C411yescharacteristic
226#391C2×C411yescharacteristic
227#391C2×C411yescharacteristic
228#390C2×C411yescharacteristic
229#390C2×C411yescharacteristic
230#389C2×C411yescharacteristic
231#389C2×C411yescharacteristic
232#389C2×C411yescharacteristic
233#389C2×C411yescharacteristic
234#389C2×C411yescharacteristic
235#389C2×C411yescharacteristic
236#388C2×C412yes—
237#388C2×C412yes—
238#388C2×C412yes—
239#388C2×C412yes—
240#388C2×C412yes—
241#387C2×C412yes—
242#387C2×C412yes—
243#387C2×C412yes—
244#387C2×C412yes—
245#387C2×C412yes—
246#387C2×C412yes—
247#387C2×C412yes—
248#386C2×C412yes—
249#386C2×C412yes—
250#386C2×C412yes—
251#385C2×C412yes—
252#385C2×C412yes—
253#385C2×C412yes—
254#383C2×C412yes—
255#383C2×C412yes—
256#382C2×C411yescharacteristic
257#382C2×C412yes—
258#382C2×C412yes—
259#382C2×C411yescharacteristic
260#381C2×C412yes—
261#381C2×C412yes—
262#380C2×C412yes—
263#380C2×C412yes—
264#380C2×C411yescharacteristic
265#380C2×C411yescharacteristic
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2×C411yescharacteristic
268C4×C4⋊C4C2×C411yescharacteristic
269C4×C4⋊C4C2×C411yescharacteristic
270C4×C4⋊C4C2×C411yescharacteristic
271C4×C4⋊C4C2×C411yescharacteristic
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C22⋊C4C2×C412yes—
279C4×C22⋊C4C2×C411yescharacteristic
280C4×C22⋊C4C2×C412yes—
281C4×C22⋊C4C2×C411yescharacteristic
282C4×C22⋊C4C2×C411yescharacteristic
283C4×C22⋊C4C2×C411yescharacteristic
284C4×C22⋊C4C2312yes—
285C4×C22⋊C4C2312yes—
286C4×C22⋊C4C2312yes—
287C4×C22⋊C4C2312yes—
288C4×C22⋊C4C2312yes—
289#376C2311yescharacteristic
290#376C2312yes—
291#376C2311yescharacteristic
292C43C2311yescharacteristic
293C43C2311yescharacteristic
294#336C2312yes—
295#336C2312yes—
296#336C2312yes—
297#336C2312yes—
298#336C2311yescharacteristic
299#336C2311yescharacteristic
300#336C2311yescharacteristic
301#336C2311yescharacteristic
302#336C2311yescharacteristic
303#336C2311yescharacteristic
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2311yescharacteristic
307#336C2311yescharacteristic
308#336C2311yescharacteristic
309#336C2311yescharacteristic
310#336C2311yescharacteristic
311#336C2311yescharacteristic
312#336C2311yescharacteristic
313#336C2311yescharacteristic
314#336C2312yes—
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318#336C2312yes—
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322C22×Q8C22×C411yescharacteristic
323C22×D4C22×C411yescharacteristic
324C22×D4C22×C412yes—
325C23×C4C22×C411yescharacteristic
326C23×C4C22×C412yes—
327C23×C4C22×C412yes—
328C23×C4C22×C411yescharacteristic
329C23×C4C2412yes—
330C23×C4C2411yescharacteristic
331C2×M16—24no—
332C2×M16—42no—
333C2×M16—42no—
334C2×M16—42no—
335C2×M16—42no—
336C2×M16—42no—
337C2×M16—42no—
338C2×M16—42no—
339C2×M16—42no—
340C22×C8—24no—
341C22×C8—42no—
342C22×C8—42no—
343C22×C8C2412yes—
344C22×C8C2412yes—
345C22×C8C2411yescharacteristic
346C22×C8C2411yescharacteristic
347C22×C8C2412yes—
348C22×C8C2412yes—
349C22×C8C2411yescharacteristic
350C22×C8C2411yescharacteristic
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353C22×C8C2411yescharacteristic
354C22×C8C2411yescharacteristic
355#125—24no—
356#124—42no—
357C22⋊Q8—24no—
358#121—42no—
359C4×Q8—22no—
360C4×Q8—22no—
361C4×D4—24no—
362C4×D4—24no—
363C4×D4—24no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—42no—
367#117—22no—
368#117—22no—
369#117—22no—
370#117—22no—
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C411yescharacteristic
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C4⋊C4C22×C411yescharacteristic
377C2×C4⋊C4C22×C412yes—
378C2×C4⋊C4C22×C411yescharacteristic
379C2×C4⋊C4C22×C412yes—
380C2×C4⋊C4C22×C411yescharacteristic
381C2×C4⋊C4C22×C412yes—
382C2×C4⋊C4C22×C412yes—
383C2×C4⋊C4C22×C411yescharacteristic
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×C22⋊C4C22×C411yescharacteristic
392C2×C22⋊C4C22×C411yescharacteristic
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×C22⋊C4C22×C412yes—
404C2×C22⋊C4C22×C412yes—
405C2×C22⋊C4C22×C412yes—
406C2×C22⋊C4C22×C412yes—
407C2×C22⋊C4C22×C412yes—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C411yescharacteristic
414C2×C42C22×C411yescharacteristic
415C2×C42C22×C411yescharacteristic
416C2×C42C22×C412yes—
417C2×C42C22×C412yes—
418C2×C42C22×C411yescharacteristic
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C411yescharacteristic
423C2×C42C22×C411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2412yes—
428C2×C42C2412yes—
429C2×C42C2411yescharacteristic
430C2×C42C2412yes—
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C4⋊C8—22no—
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—24no—
437C4⋊C8—22no—
438C4⋊C8—22no—
439C4⋊C8—24no—
440C4⋊C8—22no—
441C4⋊C8—22no—
442C4⋊C8—22no—
443C4⋊C8—42no—
444C4⋊C8—42no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448C4⋊C8—42no—
449C4⋊C8—42no—
450C4⋊C8—42no—
451C4⋊C8—42no—
452C4⋊C8—42no—
453C4⋊C8—42no—
454C4⋊C8—42no—
455C4⋊C8—42no—
456C4⋊C8—42no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461C22⋊C8—42no—
462C22⋊C8—42no—
463C22⋊C8—42no—
464C22⋊C8—42no—
465C22⋊C8—42no—
466C22⋊C8—42no—
467#97—42no—
468#97—42no—
469C4×C8—22no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—42no—
474C4×C8—42no—
475C4×C8—42no—
476C4×C8—42no—
477#95C22×C411yescharacteristic
478#95C22×C411yescharacteristic
479#95C22×C411yescharacteristic
480#95C22×C411yescharacteristic
481#95C22×C411yescharacteristic
482#95C22×C411yescharacteristic
483#95C22×C411yescharacteristic
484#95C22×C411yescharacteristic
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—
503#95C22×C412yes—
504#95C22×C412yes—
505#95C22×C412yes—
506#95C22×C412yes—
507#95C22×C412yes—
508#95C22×C412yes—
509C24C23×C412yes—
510C24C23×C411yescharacteristic
511C2×Q8—22no—
512C2×Q8—22no—
513C2×Q8—22no—
514C2×D4—24no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—42no—
519C2×D4—42no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—42no—
542C22×C4C23×C412yes—
543C22×C4C23×C411yescharacteristic
544C22×C4C23×C412yes—
545C22×C4C23×C411yescharacteristic
546C22×C4C23×C412yes—
547C22×C4C23×C412yes—
548C22×C4C23×C411yescharacteristic
549C22×C4C23×C411yescharacteristic
550C22×C4C23×C411yescharacteristic
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C412yes—
555C22×C4C23×C412yes—
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C23×C411yescharacteristic
560C22×C4C23×C412yes—
561C22×C4C23×C411yescharacteristic
562C22×C4H(5,𝔽2)12yes—
563C22×C42−1+412yes—
564C22×C4C2511yescharacteristic
565M16—84no—
566M16—84no—
567M16—84no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—21no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—22no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—84no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—24no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4#13114yes—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—24no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C42—24no—
643C42—22no—
644C42—22no—
645C42—24no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—22no—
651C42—22no—
652C42—22no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—22no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—22no—
663C42—22no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42H(5,𝔽2)12yes—
669C42H(5,𝔽2)12yes—
670C422−1+412yes—
671C422−1+412yes—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23#52012yes—
686C23C24×C411yescharacteristic
687Q8—44no—
688D4—44no—
689D4—84no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—82no—
753C2×C4—84no—
754C2×C4#52012yes—
755C2×C4#52012yes—
756C2×C4#52012yes—
757C2×C4#52012yes—
758C2×C4#52012yes—
759C2×C4C2×#13114yes—
760C2×C4C2×#13112yes—
761C2×C4#56812yes—
762C2×C4C2×H(5,𝔽2)11yescharacteristic
763C2×C4C2×H(5,𝔽2)11yescharacteristic
764C2×C4C2×H(5,𝔽2)11yescharacteristic
765C2×C4C2×2−1+411yescharacteristic
766C2×C4C2×2−1+411yescharacteristic
767C2×C4C2×2−1+411yescharacteristic
768C8—42no—
769C8—42no—
770C8—42no—
771C8—41no—
772C8—41no—
773C8—42no—
774C8—41no—
775C8—41no—
776C8—41no—
777C8—41no—
778C8—41no—
779C8—41no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22C2×#52011yescharacteristic
795C22C2×#52011yescharacteristic
796C22C2×#52011yescharacteristic
797C22C22×#13111yescharacteristic
798C22C2×#56811yescharacteristic
799C22#357311yescharacteristic
800C22#357311yescharacteristic
801C4—22no—
802C4—22no—
803C4—22no—
804C4—24no—
805C4—22no—
806C4—42no—
807C4—41no—
808C4—42no—
809C4—42no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—42no—
816C4—42no—
817C4—42no—
818C4—41no—
819C4—41no—
820C4#299314yes—
821C4#354311yescharacteristic
822C4#354411yescharacteristic
823C4#355211yescharacteristic
824C4#355211yescharacteristic
825C2—42no—
826C2—82no—
827C2#3438411yescharacteristic
828C2C2×#299311yescharacteristic
829C2#6027011yescharacteristic
830C2#6027111yescharacteristic
831C2#6027311yescharacteristic
832C2#6027311yescharacteristic
833C2#6027411yescharacteristic
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. #23382C2semidirect
3. #23381C2semidirect
6. #22957C2semidirect
7. #22952C2semidirect
8. #22822C2semidirect
9. #22795C2semidirect
10. #22752C2semidirect
11. #22721C2semidirect
12. #22650C2semidirect
13. #22649C2semidirect
14. #22301C2semidirect
15. #22299C2semidirect
16. #22214C2semidirect
17. #22210C2semidirect
18. #22074C2semidirect
19. #22068C2semidirect
20. #21975C2semidirect
21. #21928C2semidirect
22. #20793C2semidirect
23. #20782C2semidirect

Maximal subgroups

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

subgroupindex
#349132
#233822
#233812
#229902
#229892
#229572
#229522
#228222
#227952
#227522
#227212
#226502
#226492
#223012
#222992
#222142
#222102
#220742
#220682
#219752
#219282
#207932
#207822