Finite Group Databasebeta

← #6421542

Subgroups — #6421542

Order 512.

1414 conjugacy classes of subgroups.

The subgroup lattice has 829 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34780C211yesmaximal, characteristic
2#23379C212yesmaximal, complemented
3#23373C212yesmaximal, complemented
4#23257C211yesmaximal, characteristic, complemented
5#22956C211yesmaximal, characteristic, complemented
6#22952C211yesmaximal, characteristic, complemented
7#22908C212yesmaximal
8#22721C211yesmaximal, characteristic, complemented
9D4×C4⋊C8C211yesmaximal, characteristic
10#22633C211yesmaximal, characteristic, complemented
11#22603C211yesmaximal, characteristic, complemented
12#22595C212yesmaximal, complemented
13#22352C212yesmaximal, complemented
14#22306C212yesmaximal, complemented
15#22301C211yesmaximal, characteristic, complemented
16#22100C211yesmaximal, characteristic, complemented
17#22063C212yesmaximal
18#22019C211yesmaximal, characteristic, complemented
19#21977C212yesmaximal, complemented
20#21973C211yesmaximal, characteristic, complemented
21#21597C211yesmaximal, characteristic, complemented
22C2×#1939C211yesmaximal, characteristic, complemented
23#21101C211yesmaximal, characteristic
24C2×#446C2211yescharacteristic
25C2×C8×Q8C2211yescharacteristic
26C2×C8×D4C2212yes—
27C2×#432C2212yes—
28C2×#431C2211yescharacteristic
29C22×C4⋊C8C2212yes—
30C22×C4⋊C8C2211yescharacteristic
31C22×C4⋊C8C2211yescharacteristic
32C22×C4×C8C2211yescharacteristic
33#2524C412yes—
34#2515C412yes—
35#2514C411yescharacteristic
36#2508C411yescharacteristic
37#2503C411yescharacteristic
38#2495C411yescharacteristic
39#2493C412yes—
40#2489C411yescharacteristic
41#2486C411yescharacteristic
42#2442C411yescharacteristic
43#2419C412yes—
44#2417C411yescharacteristic
45#2402C2212yes—
46#2401C2212yes—
47C4×#125C2211yescharacteristic
48C4×C22⋊Q8C2211yescharacteristic
49C4×C22⋊Q8C2211yescharacteristic
50C4×#123C2212yes—
51#2295C2211yescharacteristic
52#2283C2212yes—
53#2283C2211yescharacteristic
54C42×D4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56#1984C2211yescharacteristic
57#1984C2211yescharacteristic
58#1940C2212yes—
59#1940C2212yes—
60#1940C2212yes—
61#1940C2212yes—
62#1940C2212yes—
63#1939C2211yescharacteristic
64#1939C2211yescharacteristic
65#1939C2212yes—
66#1939C2211yescharacteristic
67#1939C2211yescharacteristic
68#1939C2212yes—
69#1939C2212yes—
70#1939C2212yes—
71#1939C2212yes—
72#1939C2211yescharacteristic
73#1939C2212yes—
74#1939C2211yescharacteristic
75#1939C2211yescharacteristic
76#1939C2211yescharacteristic
77#1924C2212yes—
78#1924C2212yes—
79#1923C2212yes—
80#1923C2212yes—
81#1923C2211yescharacteristic
82#1923C2211yescharacteristic
83#1917C2212yes—
84#1917C2212yes—
85#1917C2212yes—
86#1917C2212yes—
87#1917C2212yes—
88#1916C2212yes—
89#1916C2212yes—
90#1916C2212yes—
91#1916C2211yescharacteristic
92#1916C2212yes—
93#1916C2212yes—
94#1916C2211yescharacteristic
95#1916C2212yes—
96#1916C2212yes—
97#1869C2211yescharacteristic
98#1869C2211yescharacteristic
99#1850C2212yes—
100#1850C2212yes—
101#1850C2212yes—
102#1850C2211yescharacteristic
103#1850C2212yes—
104#1850C2212yes—
105#1850C2212yes—
106#1850C2211yescharacteristic
107#1850C2212yes—
108#1843C2212yes—
109#1843C2212yes—
110#1842C2211yescharacteristic
111#1840C2212yes—
112#1832C2212yes—
113#1832C2212yes—
114#1832C2212yes—
115#1817C2212yes—
116#1797C2211yescharacteristic
117#1797C2211yescharacteristic
118#1771C2212yes—
119#1771C2212yes—
120#1770C2211yescharacteristic
121#1770C2211yescharacteristic
122#1770C2211yescharacteristic
123C8×C4⋊C4C2211yescharacteristic
124#1768C2212yes—
125C4×C4⋊C8C2211yescharacteristic
126C4×C4⋊C8C2211yescharacteristic
127#1752C2212yes—
128#1752C2212yes—
129C8×C22⋊C4C2212yes—
130C4×C22⋊C8C2211yescharacteristic
131C4×C22⋊C8C2211yescharacteristic
132#1746C2212yes—
133#1744C2211yescharacteristic
134C2×#336C2212yes—
135C23×C8C2311yescharacteristic
136C23×C8C2311yescharacteristic
137C23×C8C2312yes—
138C23×C8C2312yes—
139C2×#125C2×C411yescharacteristic
140C2×#123C2×C412yes—
141C2×C22⋊Q8C2×C411yescharacteristic
142C2×C22⋊Q8C2×C411yescharacteristic
143C2×C4×Q8C2311yescharacteristic
144C2×C4×D4C2×C411yescharacteristic
145C2×C4×D4C2×C411yescharacteristic
146C2×C4×D4C2311yescharacteristic
147C22×C4⋊C4C2×C411yescharacteristic
148C22×C4⋊C4C2×C411yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152#446—42no—
153C8×Q8—42no—
154C8×D4—44no—
155#432—44no—
156#431—42no—
157C2×C4⋊C8—42no—
158C2×C4⋊C8—42no—
159C2×C4⋊C8—44no—
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⋊C8C2312yes—
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2312yes—
171C2×C4⋊C8C2312yes—
172C2×C4⋊C8C2311yescharacteristic
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×C4⋊C8C2312yes—
179C2×C4⋊C8C2312yes—
180C2×C4⋊C8C2312yes—
181C2×C4⋊C8C2312yes—
182C2×C22⋊C8C2312yes—
183C2×C22⋊C8C2311yescharacteristic
184C2×C22⋊C8C2311yescharacteristic
185C2×C22⋊C8C2311yescharacteristic
186C2×C22⋊C8C2312yes—
187C2×C22⋊C8C2311yescharacteristic
188C2×C22⋊C8C2311yescharacteristic
189C2×C22⋊C8C2311yescharacteristic
190C2×#97C2312yes—
191C2×#97C2312yes—
192C2×#97C2312yes—
193C2×#97C2312yes—
194C2×C4×C8—42no—
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2312yes—
202C2×C4×C8C2312yes—
203C2×C4×C8C2312yes—
204#401C2×C412yes—
205#400C2×C412yes—
206#400C2×C412yes—
207#400C2×C412yes—
208#400C2×C412yes—
209#400C2×C412yes—
210#400C2×C412yes—
211#400C2×C412yes—
212#398C2×C412yes—
213#398C2×C412yes—
214#398C2×C412yes—
215#398C2×C412yes—
216#397C2×C412yes—
217#397C2×C412yes—
218#397C2×C412yes—
219#396C2×C412yes—
220#391C2×C411yescharacteristic
221#391C2×C411yescharacteristic
222#391C2×C411yescharacteristic
223#391C2×C411yescharacteristic
224#389C2×C411yescharacteristic
225#389C2×C411yescharacteristic
226#389C2×C411yescharacteristic
227#389C2×C411yescharacteristic
228#389C2×C411yescharacteristic
229#389C2×C411yescharacteristic
230#388C2×C412yes—
231#388C2×C412yes—
232#387C2×C412yes—
233#387C2×C412yes—
234#387C2×C412yes—
235#387C2×C412yes—
236#387C2×C412yes—
237#387C2×C412yes—
238#387C2×C412yes—
239#387C2×C412yes—
240#386C2×C412yes—
241#385C2×C412yes—
242#385C2×C412yes—
243#385C2×C412yes—
244#383C2×C412yes—
245#383C2×C412yes—
246#383C2×C412yes—
247#382C2×C411yescharacteristic
248#382C2×C411yescharacteristic
249#382C2×C412yes—
250#382C2×C411yescharacteristic
251#382C2×C412yes—
252#381C2×C412yes—
253#381C2×C412yes—
254#381C2×C412yes—
255#381C2×C412yes—
256#380C2×C412yes—
257#380C2×C411yescharacteristic
258#380C2×C412yes—
259#380C2×C411yescharacteristic
260#380C2×C411yescharacteristic
261#380C2×C411yescharacteristic
262C4×C4⋊C4C2×C411yescharacteristic
263C4×C4⋊C4C2×C411yescharacteristic
264C4×C4⋊C4C2×C411yescharacteristic
265C4×C4⋊C4C2×C412yes—
266C4×C4⋊C4C2×C411yescharacteristic
267C4×C4⋊C4C2312yes—
268C4×C4⋊C4C2312yes—
269C4×C4⋊C4C2311yescharacteristic
270C4×C4⋊C4C2311yescharacteristic
271C4×C4⋊C4C2312yes—
272C4×C4⋊C4C2312yes—
273C4×C4⋊C4C2311yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2311yescharacteristic
277C4×C22⋊C4C2×C411yescharacteristic
278C4×C22⋊C4C2×C411yescharacteristic
279C4×C22⋊C4C2×C411yescharacteristic
280C4×C22⋊C4C2×C411yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C4×C22⋊C4C2312yes—
284C4×C22⋊C4C2312yes—
285C4×C22⋊C4C2312yes—
286#376C2312yes—
287#376C2312yes—
288C2×#95C2×C412yes—
289C43C2311yescharacteristic
290#336C2312yes—
291#336C2312yes—
292#336C2312yes—
293#336C2312yes—
294#336C2312yes—
295#336C2312yes—
296#336C2311yescharacteristic
297#336C2311yescharacteristic
298#336C2312yes—
299#336C2312yes—
300#336C2312yes—
301#336C2312yes—
302#336C2312yes—
303#336C2312yes—
304#336C2312yes—
305#336C2312yes—
306#336C2311yescharacteristic
307#336C2312yes—
308#336C2312yes—
309#336C2311yescharacteristic
310#336C2311yescharacteristic
311#336C2311yescharacteristic
312#336C2311yescharacteristic
313#336C2311yescharacteristic
314#336C2311yescharacteristic
315#336C2312yes—
316#336C2311yescharacteristic
317#336C2312yes—
318#336C2312yes—
319C22×Q8C22×C411yescharacteristic
320C22×D4C22×C411yescharacteristic
321C23×C4C22×C412yes—
322C23×C4C22×C411yescharacteristic
323C23×C4C22×C411yescharacteristic
324C23×C4C22×C411yescharacteristic
325C23×C4C22×C411yescharacteristic
326C23×C4C22×C412yes—
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C22×C8—22no—
330C22×C8—22no—
331C22×C8—24no—
332C22×C8—22no—
333C22×C8—41no—
334C22×C8—41no—
335C22×C8—41no—
336C22×C8—42no—
337C22×C8—42no—
338C22×C8—42no—
339C22×C8—42no—
340C22×C8—42no—
341C22×C8C2412yes—
342C22×C8C2411yescharacteristic
343C22×C8C2411yescharacteristic
344C22×C8C2411yescharacteristic
345C22×C8C2412yes—
346C22×C8C2412yes—
347C22×C8C2411yescharacteristic
348C22×C8C2411yescharacteristic
349C22×C8C2412yes—
350C22×C8C2411yescharacteristic
351C22×C8C2411yescharacteristic
352C22×C8C2411yescharacteristic
353#125—42no—
354#123—28no—
355C22⋊Q8—24no—
356C22⋊Q8—42no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×D4—24no—
360C4×D4—24no—
361C4×D4—22no—
362C4×D4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4C22×C411yescharacteristic
366C2×C4⋊C4C22×C411yescharacteristic
367C2×C4⋊C4C22×C411yescharacteristic
368C2×C4⋊C4C22×C411yescharacteristic
369C2×C4⋊C4C22×C412yes—
370C2×C4⋊C4C22×C411yescharacteristic
371C2×C4⋊C4C22×C411yescharacteristic
372C2×C4⋊C4C22×C411yescharacteristic
373C2×C4⋊C4C22×C411yescharacteristic
374C2×C4⋊C4C22×C412yes—
375C2×C4⋊C4C22×C411yescharacteristic
376C2×C4⋊C4C22×C412yes—
377C2×C4⋊C4C22×C412yes—
378C2×C4⋊C4C22×C412yes—
379C2×C4⋊C4C22×C411yescharacteristic
380C2×C4⋊C4C22×C412yes—
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×C22⋊C4C22×C411yescharacteristic
389C2×C22⋊C4C22×C411yescharacteristic
390C2×C22⋊C4C22×C411yescharacteristic
391C2×C22⋊C4C22×C411yescharacteristic
392C2×C22⋊C4C22×C411yescharacteristic
393C2×C22⋊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×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42C22×C411yescharacteristic
407C2×C42C22×C411yescharacteristic
408C2×C42C22×C411yescharacteristic
409C2×C42C22×C411yescharacteristic
410C2×C42C22×C411yescharacteristic
411C2×C42C22×C411yescharacteristic
412C2×C42C22×C411yescharacteristic
413C2×C42C22×C412yes—
414C2×C42C22×C412yes—
415C2×C42C22×C411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2412yes—
418C2×C42C2411yescharacteristic
419C2×C42C2411yescharacteristic
420C2×C42C2412yes—
421C2×C42C2412yes—
422C2×C42C2411yescharacteristic
423C2×C42C2412yes—
424C2×C42C2411yescharacteristic
425C4⋊C8—22no—
426C4⋊C8—22no—
427C4⋊C8—22no—
428C4⋊C8—22no—
429C4⋊C8—22no—
430C4⋊C8—42no—
431C4⋊C8—42no—
432C4⋊C8—42no—
433C4⋊C8—42no—
434C4⋊C8—42no—
435C4⋊C8—42no—
436C4⋊C8—42no—
437C4⋊C8—42no—
438C4⋊C8—42no—
439C4⋊C8—41no—
440C4⋊C8—41no—
441C4⋊C8—41no—
442C4⋊C8—42no—
443C4⋊C8—42no—
444C4⋊C8—42no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447C22⋊C8—22no—
448C22⋊C8—24no—
449C22⋊C8—22no—
450C22⋊C8—22no—
451C22⋊C8—41no—
452C22⋊C8—41no—
453C22⋊C8—41no—
454C22⋊C8—42no—
455#97—24no—
456#97—42no—
457#97—42no—
458#97—42no—
459C4×C8—22no—
460C4×C8—22no—
461C4×C8—22no—
462C4×C8—22no—
463C4×C8—41no—
464C4×C8—41no—
465C4×C8—42no—
466C4×C8—42no—
467C4×C8—42no—
468#95C22×C412yes—
469#95C22×C412yes—
470#95C22×C412yes—
471#95C22×C412yes—
472#95C22×C412yes—
473#95C22×C412yes—
474#95C22×C412yes—
475#95C22×C412yes—
476#95C22×C412yes—
477#95C22×C412yes—
478#95C22×C412yes—
479#95C22×C412yes—
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—
503C24C23×C411yescharacteristic
504C24C23×C411yescharacteristic
505C2×Q8—22no—
506C2×Q8—22no—
507C2×Q8—22no—
508C2×D4—22no—
509C2×D4—22no—
510C2×D4#13114yes—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4#13114yes—
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×C412yes—
549C22×C4C23×C412yes—
550C22×C4C23×C412yes—
551C22×C4C23×C411yescharacteristic
552C22×C4C23×C412yes—
553C22×C4C23×C412yes—
554C22×C4C23×C411yescharacteristic
555C22×C4C23×C411yescharacteristic
556C22×C4C23×C411yescharacteristic
557C22×C4C23×C411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4H(5,𝔽2)12yes—
560C22×C42−1+412yes—
561C22×C4C2511yescharacteristic
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—22no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—22no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—22no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—22no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—44no—
598C2×C8—44no—
599C2×C8—84no—
600C2×C8—84no—
601C2×C82−1+412yes—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C42—22no—
638C42—22no—
639C42—24no—
640C42—24no—
641C42—22no—
642C42—22no—
643C42—22no—
644C42—22no—
645C42—22no—
646C42—21no—
647C42—21no—
648C42—22no—
649C42—22no—
650C42—21no—
651C42—22no—
652C42—22no—
653C42—21no—
654C42—21no—
655C42—22no—
656C42—22no—
657C42—21no—
658C42—21no—
659C42—22no—
660C42—22no—
661C42—21no—
662C42—41no—
663C42H(5,𝔽2)12yes—
664C422−1+412yes—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23#52012yes—
676C23C2×#13112yes—
677C23C2×#13112yes—
678C23C2×#13112yes—
679C23C24×C411yescharacteristic
680Q8—44no—
681D4—28no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—48no—
743C2×C4—44no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—84no—
749C2×C4#52012yes—
750C2×C4#52012yes—
751C2×C4#52012yes—
752C2×C4C2×#13112yes—
753C2×C4C2×#13112yes—
754C2×C4C2×#13112yes—
755C2×C4#56812yes—
756C2×C4C2×H(5,𝔽2)11yescharacteristic
757C2×C4C2×H(5,𝔽2)11yescharacteristic
758C2×C4C2×2−1+411yescharacteristic
759C2×C4C2×2−1+411yescharacteristic
760C2×C4C2×2−1+411yescharacteristic
761C2×C4#58511yescharacteristic
762C8—22no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C8—42no—
769C8—42no—
770C8—42no—
771C8—42no—
772C8—41no—
773C8—41no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22#299414yes—
788C22C2×#52011yescharacteristic
789C22C2×#52011yescharacteristic
790C22C4×2−1+411yescharacteristic
791C22C22×#13111yescharacteristic
792C22C22×#13111yescharacteristic
793C22C2×#56811yescharacteristic
794C22#357311yescharacteristic
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—42no—
808C4—42no—
809C4—41no—
810C4—41no—
811C4—42no—
812C4—41no—
813C4—42no—
814C4#299214yes—
815C4#353811yescharacteristic
816C4#354211yescharacteristic
817C4#354411yescharacteristic
818C4#356311yescharacteristic
819C2—24no—
820C2—42no—
821C2#3446511yescharacteristic
822C2C2×#299211yescharacteristic
823C2C2×#299411yescharacteristic
824C2#6027111yescharacteristic
825C2#6027311yescharacteristic
826C2#6033411yescharacteristic
827C2#6034111yescharacteristic
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. #23379C2semidirect
3. #23373C2semidirect
4. #23257C2semidirect
5. #22956C2semidirect
6. #22952C2semidirect
8. #22721C2semidirect
10. #22633C2semidirect
11. #22603C2semidirect
12. #22595C2semidirect
13. #22352C2semidirect
14. #22306C2semidirect
15. #22301C2semidirect
16. #22100C2semidirect
18. #22019C2semidirect
19. #21977C2semidirect
20. #21973C2semidirect
21. #21597C2semidirect
22. C2×#1939C2semidirect

Maximal subgroups

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

subgroupindex
#347802
#233792
#233732
#232572
#229562
#229522
#229082
#227212
D4×C4⋊C82
#226332
#226032
#225952
#223522
#223062
#223012
#221002
#220632
#220192
#219772
#219732
#215972
C2×#19392
#211012