Finite Group Databasebeta

← #6410540

Subgroups — #6410540

Order 512.

1390 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36638C211yesmaximal, characteristic
2#23377C212yesmaximal, complemented
3#23376C212yesmaximal, complemented
4#23257C211yesmaximal, characteristic, complemented
5#23253C211yesmaximal, characteristic, complemented
6#23208C211yesmaximal, characteristic, complemented
7#23204C211yesmaximal, characteristic, complemented
8#22836C211yesmaximal, characteristic, complemented
9#22829C211yesmaximal, characteristic, complemented
10#22735C211yesmaximal, characteristic, complemented
11#22701C211yesmaximal, characteristic, complemented
12#22637C212yesmaximal, complemented
13#22593C212yesmaximal, complemented
14#22365C212yesmaximal, complemented
15#22361C212yesmaximal, complemented
16#22139C211yesmaximal, characteristic
17#22133C211yesmaximal, characteristic
18#22104C211yesmaximal, characteristic, complemented
19#22098C211yesmaximal, characteristic, complemented
20#22016C212yesmaximal, complemented
21#22004C212yesmaximal, complemented
22#20808C211yesmaximal, characteristic, complemented
23#20777C211yesmaximal, characteristic, complemented
24C2×#446C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×#436C2211yescharacteristic
27C2×C8×D4C2211yescharacteristic
28C2×#431C2211yescharacteristic
29C2×#431C2211yescharacteristic
30#2866C412yes—
31#2865C412yes—
32#2864C411yescharacteristic
33#2863C411yescharacteristic
34#2861C411yescharacteristic
35#2860C411yescharacteristic
36#2855C411yescharacteristic
37#2854C411yescharacteristic
38#2853C412yes—
39#2852C412yes—
40#2851C411yescharacteristic
41#2850C411yescharacteristic
42C4×#125C2211yescharacteristic
43C4×#126C2212yes—
44C4×#124C2211yescharacteristic
45C4×C22⋊Q8C2211yescharacteristic
46C4×#123C2212yes—
47C4×#121C2211yescharacteristic
48#2298C2212yes—
49#2295C2211yescharacteristic
50#2293C2211yescharacteristic
51#2290C2212yes—
52C2×C43C2211yescharacteristic
53#1984C2211yescharacteristic
54#1984C2211yescharacteristic
55#1955C2212yes—
56#1954C2212yes—
57#1954C2211yescharacteristic
58#1954C2211yescharacteristic
59#1940C2212yes—
60#1940C2212yes—
61#1940C2212yes—
62#1939C2212yes—
63#1939C2212yes—
64#1939C2212yes—
65#1939C2211yescharacteristic
66#1939C2211yescharacteristic
67#1939C2211yescharacteristic
68#1939C2211yescharacteristic
69#1924C2212yes—
70#1924C2212yes—
71#1924C2212yes—
72#1924C2212yes—
73#1924C2212yes—
74#1923C2212yes—
75#1923C2212yes—
76#1923C2212yes—
77#1923C2212yes—
78#1923C2212yes—
79#1923C2212yes—
80#1923C2212yes—
81#1917C2212yes—
82#1917C2212yes—
83#1917C2212yes—
84#1916C2212yes—
85#1916C2212yes—
86#1916C2212yes—
87#1916C2212yes—
88#1916C2212yes—
89#1870C2212yes—
90#1869C2212yes—
91#1851C2212yes—
92#1851C2212yes—
93#1851C2212yes—
94#1850C2212yes—
95#1850C2212yes—
96#1850C2212yes—
97#1842C2211yescharacteristic
98#1842C2211yescharacteristic
99#1840C2212yes—
100#1839C2212yes—
101#1832C2212yes—
102#1831C2211yescharacteristic
103#1831C2211yescharacteristic
104#1831C2211yescharacteristic
105#1831C2211yescharacteristic
106#1818C2212yes—
107#1817C2212yes—
108#1798C2212yes—
109#1797C2211yescharacteristic
110#1797C2211yescharacteristic
111#1797C2211yescharacteristic
112#1797C2211yescharacteristic
113#1797C2211yescharacteristic
114#1797C2211yescharacteristic
115#1771C2212yes—
116#1770C2211yescharacteristic
117#1770C2211yescharacteristic
118C8×C4⋊C4C2211yescharacteristic
119C8×C4⋊C4C2211yescharacteristic
120C8×C4⋊C4C2212yes—
121#1768C2212yes—
122C4×C4⋊C8C2211yescharacteristic
123C4×C4⋊C8C2211yescharacteristic
124C4×C4⋊C8C2211yescharacteristic
125C4×C4⋊C8C2211yescharacteristic
126C4×C4⋊C8C2211yescharacteristic
127C4×C4⋊C8C2211yescharacteristic
128#1753C2212yes—
129C8×C22⋊C4C2212yes—
130#1750C2212yes—
131C4×C22⋊C8C2212yes—
132#1746C2212yes—
133#1744C2212yes—
134#1729C2212yes—
135C22×M16C2312yes—
136C23×C8C2312yes—
137C2×#126C2×C412yes—
138C2×#125C2×C411yescharacteristic
139C2×#124C2×C411yescharacteristic
140C2×#123C2×C412yes—
141C2×C22⋊Q8C2×C411yescharacteristic
142C2×#121C2×C411yescharacteristic
143C2×C4×Q8C2311yescharacteristic
144C2×C4×D4C2311yescharacteristic
145C2×C4×D4C2312yes—
146C2×#117C2312yes—
147C22×C42C2×C411yescharacteristic
148C22×C42C2×C411yescharacteristic
149C22×C42C2×C411yescharacteristic
150C22×C42C2×C411yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#446—42no—
155C8×Q8—42no—
156#436—42no—
157C8×D4—42no—
158#431—42no—
159#431—42no—
160C2×C4⋊C8C2311yescharacteristic
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2311yescharacteristic
164C2×C4⋊C8C2311yescharacteristic
165C2×C4⋊C8C2311yescharacteristic
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2311yescharacteristic
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2311yescharacteristic
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2311yescharacteristic
176C2×C4⋊C8C2311yescharacteristic
177C2×C4⋊C8C2311yescharacteristic
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C22⋊C8C2311yescharacteristic
183C2×C22⋊C8C2311yescharacteristic
184C2×C22⋊C8C2311yescharacteristic
185C2×C22⋊C8C2311yescharacteristic
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2312yes—
188C2×C22⋊C8C2312yes—
189C2×C22⋊C8C2312yes—
190C2×C22⋊C8C2312yes—
191C2×C22⋊C8C2312yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×#97C2312yes—
195C2×#97C2312yes—
196C2×#97C2312yes—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203C2×C4×C8C2312yes—
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206#391C2×C411yescharacteristic
207#391C2×C411yescharacteristic
208#391C2×C411yescharacteristic
209#391C2×C411yescharacteristic
210#390C2×C411yescharacteristic
211#390C2×C411yescharacteristic
212#390C2×C411yescharacteristic
213#390C2×C411yescharacteristic
214#389C2×C411yescharacteristic
215#389C2×C411yescharacteristic
216#389C2×C411yescharacteristic
217#389C2×C411yescharacteristic
218#389C2×C411yescharacteristic
219#389C2×C411yescharacteristic
220#389C2×C411yescharacteristic
221#389C2×C411yescharacteristic
222#388C2×C412yes—
223#388C2×C412yes—
224#388C2×C412yes—
225#388C2×C412yes—
226#388C2×C412yes—
227#388C2×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#387C2×C412yes—
247#387C2×C412yes—
248#387C2×C412yes—
249#387C2×C412yes—
250#387C2×C412yes—
251#387C2×C412yes—
252#387C2×C412yes—
253#387C2×C412yes—
254#386C2×C412yes—
255#386C2×C412yes—
256#386C2×C412yes—
257#386C2×C412yes—
258#385C2×C412yes—
259#385C2×C412yes—
260#385C2×C412yes—
261#385C2×C412yes—
262#383C2×C412yes—
263#382C2×C411yescharacteristic
264#382C2×C411yescharacteristic
265#381C2×C412yes—
266#380C2×C411yescharacteristic
267#380C2×C411yescharacteristic
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2312yes—
270C4×C4⋊C4C2312yes—
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
274C4×C22⋊C4C2312yes—
275C4×C22⋊C4C2312yes—
276C4×C22⋊C4C2312yes—
277C4×C22⋊C4C2312yes—
278C4×C22⋊C4C2312yes—
279#376C2312yes—
280C43C2×C411yescharacteristic
281C43C2×C411yescharacteristic
282C43C2×C411yescharacteristic
283C43C2×C411yescharacteristic
284C43C2311yescharacteristic
285C43C2311yescharacteristic
286C43C2311yescharacteristic
287C43C2311yescharacteristic
288#336C2311yescharacteristic
289#336C2311yescharacteristic
290#336C2311yescharacteristic
291#336C2311yescharacteristic
292#336C2311yescharacteristic
293#336C2311yescharacteristic
294#336C2311yescharacteristic
295#336C2311yescharacteristic
296#336C2312yes—
297#336C2312yes—
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303#336C2312yes—
304#336C2312yes—
305#336C2312yes—
306#336C2312yes—
307#336C2312yes—
308#336C2312yes—
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315#336C2312yes—
316C22×Q8C22×C411yescharacteristic
317C22×D4C22×C411yescharacteristic
318C22×D4C22×C412yes—
319C23×C4C22×C411yescharacteristic
320C23×C4C22×C411yescharacteristic
321C23×C4C22×C411yescharacteristic
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C411yescharacteristic
324C23×C4C22×C411yescharacteristic
325C23×C4C2412yes—
326C23×C4C2411yescharacteristic
327C2×M16—42no—
328C2×M16—42no—
329C2×M16—42no—
330C22×C8—42no—
331C22×C8—42no—
332C22×C8—42no—
333C22×C8C2411yescharacteristic
334C22×C8C2412yes—
335C22×C8C2411yescharacteristic
336C22×C8C2412yes—
337C22×C8C2412yes—
338C22×C8C2412yes—
339C22×C8C2411yescharacteristic
340C22×C8C2411yescharacteristic
341C22×C8C2411yescharacteristic
342C22×C8C2411yescharacteristic
343C22×C8C2411yescharacteristic
344C22×C8C2411yescharacteristic
345#126—44no—
346#125—24no—
347#124—24no—
348#123—44no—
349C22⋊Q8—24no—
350#121—24no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—42no—
356C4×D4—42no—
357#117—42no—
358#117—42no—
359C2×C4⋊C4C22×C411yescharacteristic
360C2×C4⋊C4C22×C411yescharacteristic
361C2×C4⋊C4C22×C412yes—
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×C412yes—
371C2×C4⋊C4C22×C412yes—
372C2×C4⋊C4C22×C412yes—
373C2×C4⋊C4C22×C412yes—
374C2×C4⋊C4C22×C412yes—
375C2×C4⋊C4C22×C412yes—
376C2×C4⋊C4C22×C412yes—
377C2×C22⋊C4C22×C412yes—
378C2×C22⋊C4C22×C412yes—
379C2×C22⋊C4C22×C412yes—
380C2×C22⋊C4C22×C412yes—
381C2×C22⋊C4C22×C412yes—
382C2×C22⋊C4C22×C412yes—
383C2×C22⋊C4C22×C412yes—
384C2×C22⋊C4C22×C412yes—
385C2×C22⋊C4C22×C412yes—
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×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—41no—
399C2×C42—41no—
400C2×C42—41no—
401C2×C42—41no—
402C2×C42C22×C411yescharacteristic
403C2×C42C22×C411yescharacteristic
404C2×C42C22×C411yescharacteristic
405C2×C42C22×C411yescharacteristic
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C411yescharacteristic
408C2×C42C22×C411yescharacteristic
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×C411yescharacteristic
418C2×C42C22×C411yescharacteristic
419C2×C42C22×C411yescharacteristic
420C2×C42C22×C411yescharacteristic
421C2×C42C22×C411yescharacteristic
422C2×C42C22×C411yescharacteristic
423C2×C42C22×C411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2412yes—
426C2×C42C2412yes—
427C2×C42C2412yes—
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C4⋊C8—22no—
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—22no—
437C4⋊C8—42no—
438C4⋊C8—42no—
439C4⋊C8—42no—
440C4⋊C8—42no—
441C4⋊C8—41no—
442C4⋊C8—41no—
443C4⋊C8—41no—
444C4⋊C8—41no—
445C4⋊C8—41no—
446C4⋊C8—41no—
447C4⋊C8—41no—
448C4⋊C8—41no—
449C4⋊C8—41no—
450C4⋊C8—41no—
451C4⋊C8—41no—
452C4⋊C8—41no—
453C4⋊C8—42no—
454C4⋊C8—42no—
455C22⋊C8—42no—
456C22⋊C8—42no—
457C22⋊C8—42no—
458C22⋊C8—42no—
459C22⋊C8—42no—
460C22⋊C8—42no—
461C22⋊C8—41no—
462C22⋊C8—41no—
463C22⋊C8—41no—
464C22⋊C8—41no—
465C22⋊C8—42no—
466C22⋊C8—42no—
467#97—42no—
468#97—42no—
469#97—42no—
470C4×C8—22no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—42no—
475C4×C8—42no—
476C4×C8—42no—
477C4×C8—42no—
478C4×C8—42no—
479#95C22×C412yes—
480#95C22×C412yes—
481#95C22×C412yes—
482#95C22×C412yes—
483#95C22×C412yes—
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×C412yes—
504C24C23×C411yescharacteristic
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×D4—24no—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—22no—
512C2×D4—42no—
513C2×D4—42no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4#13114yes—
544C22×C4C23×C412yes—
545C22×C4C23×C412yes—
546C22×C4C23×C412yes—
547C22×C4C23×C412yes—
548C22×C4C23×C412yes—
549C22×C4C23×C412yes—
550C22×C4C23×C412yes—
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C411yescharacteristic
553C22×C4C23×C411yescharacteristic
554C22×C4C23×C411yescharacteristic
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C23×C411yescharacteristic
560C22×C4C23×C411yescharacteristic
561C22×C4C23×C411yescharacteristic
562C22×C4C23×C411yescharacteristic
563C22×C4C23×C411yescharacteristic
564C22×C4C2511yescharacteristic
565M16—84no—
566C2×C8—21no—
567C2×C8—21no—
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—22no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—22no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—22no—
593C2×C8—22no—
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—84no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C42—22no—
637C42—22no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—22no—
647C42—22no—
648C42—22no—
649C42—22no—
650C42—21no—
651C42—21no—
652C42—22no—
653C42—21no—
654C42—21no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—41no—
666C42—41no—
667C42—41no—
668C42—41no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42#13114yes—
674C42H(5,𝔽2)12yes—
675C422−1+412yes—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23C2×#13112yes—
690C23C24×C411yescharacteristic
691Q8—44no—
692D4—44no—
693D4—84no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—28no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
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—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4#52012yes—
760C2×C4#52012yes—
761C2×C4C2×#13112yes—
762C2×C4C2×#13112yes—
763C2×C4C2×#13112yes—
764C2×C4C2×#13112yes—
765C2×C4C2×#13112yes—
766C2×C4#56812yes—
767C2×C4#56812yes—
768C2×C4C2×H(5,𝔽2)11yescharacteristic
769C2×C4C2×2−1+411yescharacteristic
770C2×C4#58511yescharacteristic
771C2×C4#58511yescharacteristic
772C2×C4#58511yescharacteristic
773C2×C4#58511yescharacteristic
774C8—41no—
775C8—41no—
776C8—41no—
777C8—41no—
778C8—41no—
779C8—41no—
780C8—42no—
781C8—41no—
782C8—42no—
783C8—41no—
784C8—42no—
785C8—42no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22C2×#52011yescharacteristic
801C22#342811yescharacteristic
802C22#342811yescharacteristic
803C22C22×#13111yescharacteristic
804C22C22×#13111yescharacteristic
805C22C2×#56811yescharacteristic
806C22C2×#56811yescharacteristic
807C4—22no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—22no—
813C4—41no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—41no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4#299414yes—
827C4#355111yescharacteristic
828C4#355111yescharacteristic
829C4#355711yescharacteristic
830C4#355711yescharacteristic
831C2—42no—
832C2—82no—
833C2#3439711yescharacteristic
834C2C2×#299411yescharacteristic
835C2#6026611yescharacteristic
836C2#6027911yescharacteristic
837C2#6029011yescharacteristic
838C2#6029211yescharacteristic
839C2#6029411yescharacteristic
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. #23377C2semidirect
3. #23376C2semidirect
4. #23257C2semidirect
5. #23253C2semidirect
6. #23208C2semidirect
7. #23204C2semidirect
8. #22836C2semidirect
9. #22829C2semidirect
10. #22735C2semidirect
11. #22701C2semidirect
12. #22637C2semidirect
13. #22593C2semidirect
14. #22365C2semidirect
15. #22361C2semidirect
18. #22104C2semidirect
19. #22098C2semidirect
20. #22016C2semidirect
21. #22004C2semidirect
22. #20808C2semidirect
23. #20777C2semidirect

Maximal subgroups

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

subgroupindex
#366382
#233772
#233762
#232572
#232532
#232082
#232042
#228362
#228292
#227352
#227012
#226372
#225932
#223652
#223612
#221392
#221332
#221042
#220982
#220162
#220042
#208082
#207772