Finite Group Databasebeta

← #6458369

Subgroups — #6458369

Order 512.

1722 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35640C211yesmaximal, characteristic, complemented
2#35529C211yesmaximal, characteristic
3#27830C212yesmaximal, complemented
4#27829C212yesmaximal, complemented
5#27829C212yesmaximal, complemented
6#27826C212yesmaximal, complemented
7#27822C212yesmaximal, complemented
8#27819C212yesmaximal, complemented
9#27817C212yesmaximal, complemented
10#27814C212yesmaximal, complemented
11#23748C211yesmaximal, characteristic, complemented
12#23744C211yesmaximal, characteristic, complemented
13#23456C211yesmaximal, characteristic
14C2×#2025C211yesmaximal, characteristic
15#21326C211yesmaximal, characteristic, complemented
16#21326C211yesmaximal, characteristic, complemented
17#21325C211yesmaximal, characteristic, complemented
18#21315C211yesmaximal, characteristic, complemented
19#21095C211yesmaximal, characteristic
20#21091C211yesmaximal, characteristic
21#20650C211yesmaximal, characteristic
22#20439C211yesmaximal, characteristic, complemented
23#20416C211yesmaximal, characteristic
24C2×#544C2211yescharacteristic
25C2×#544C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C2×#518C2211yescharacteristic
28C2×#424C2211yescharacteristic
29C2×#418C2211yescharacteristic
30C2×#418C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C2×#405C2211yescharacteristic
34C2×#405C2211yescharacteristic
35C2×C4×M16C2211yescharacteristic
36#2583—22no—
37#2566C2212yes—
38#2566C2212yes—
39#2563C2212yes—
40#2552—21no—
41#2552—21no—
42#2552C2212yescomplemented
43#2552C2212yescomplemented
44#2550—21no—
45#2550—21no—
46#2550C2212yescomplemented
47#2550C2212yescomplemented
48#2542C2212yes—
49#2502—22no—
50#2454—21no—
51#2454—21no—
52#2452—21no—
53#2452—21no—
54#2437—22no—
55#2437—22no—
56#2317C2211yescharacteristic
57#2317C2211yescharacteristic
58#2317C2211yescharacteristic
59#2309C2211yescharacteristic
60#2296C2211yescharacteristic
61#2296C2211yescharacteristic
62C2×#390C2211yescharacteristic
63#2285C2211yescharacteristic
64#2274C2211yescharacteristic
65#2101C2211yescharacteristic, complemented
66#2101C2212yescomplemented
67#2101C2211yescharacteristic, complemented
68#2101C2211yescharacteristic, complemented
69#2101C2212yescomplemented
70#2101C2211yescharacteristic, complemented
71#2100C2212yescomplemented
72#2100C2211yescharacteristic, complemented
73#2100C2211yescharacteristic, complemented
74#2099C2211yescharacteristic, complemented
75#2099C2211yescharacteristic, complemented
76#2099C2212yescomplemented
77#2025C2212yes—
78#2025C2212yes—
79#2025C2212yes—
80#2025C2212yes—
81#2025C2212yes—
82#2025C2212yes—
83#2023C2212yes—
84#2023C2212yes—
85#1993C2212yescomplemented
86#1993C2212yescomplemented
87#1992C2212yescomplemented
88#1992C2212yescomplemented
89#1992C2212yescomplemented
90#1992C2212yescomplemented
91#1991C2212yescomplemented
92#1991C2212yescomplemented
93#1991C2212yescomplemented
94#1991C2212yescomplemented
95#1990C2212yescomplemented
96#1990C2212yescomplemented
97#1989C2212yescomplemented
98#1989C2212yescomplemented
99#1988C2212yescomplemented
100#1987C2212yescomplemented
101#1936C2212yes—
102#1936C2212yes—
103#1936C2212yes—
104#1936C2212yes—
105#1934C2212yes—
106#1934C2212yes—
107#1934C2212yes—
108#1934C2212yes—
109#1804C2212yes—
110#1804C2212yes—
111#1802C2212yes—
112#1802C2212yes—
113#1771C2212yescomplemented
114#1771C2212yescomplemented
115#1770C2212yescomplemented
116C8×C4⋊C4C2212yescomplemented
117#1762C2212yes—
118#1762C2212yes—
119C4×#102C2212yes—
120C4×#102C2212yes—
121#1736C2211yescharacteristic
122#1736C2211yescharacteristic
123#1736C2211yescharacteristic
124#1736C2211yescharacteristic
125#1736C2211yescharacteristic
126#1736C2211yescharacteristic
127#1735C2211yescharacteristic
128#1735C2211yescharacteristic
129#1735C2211yescharacteristic
130#1735C2211yescharacteristic
131C2×#340C2211yescharacteristic
132C2×#340C2211yescharacteristic
133#1729C2211yescharacteristic
134C2×#336C2211yescharacteristic
135C23×D4C2311yescharacteristic
136C22×M16C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140#544—24no—
141#544—24no—
142#544—24no—
143#544—42no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8C2312yes—
147C2×C4⋊Q8C2312yes—
148C2×#125—21no—
149C2×#125—21no—
150C2×#125—24no—
151C2×#125—21no—
152C2×#125—21no—
153C2×#125—42no—
154C2×#125C2312yes—
155C2×#125C2312yes—
156C2×#125C2312yes—
157C2×#125C2312yes—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8—22no—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8—22no—
162#518—24no—
163#518—24no—
164C2×C4×D4—21no—
165C2×C4×D4—21no—
166C2×C4×D4C2312yes—
167C2×C4×D4C2312yes—
168C2×#117C2311yescharacteristic
169C2×#117C2311yescharacteristic
170C2×#117C2311yescharacteristic
171C2×#117C2311yescharacteristic
172C2×#117C2311yescharacteristic
173C2×#117C2311yescharacteristic
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C22⋊C4—21no—
180C22×C22⋊C4—21no—
181C22×C22⋊C4—22no—
182C22×C42C2311yescharacteristic
183#424—24no—
184C2×C4⋊C8C2312yes—
185C2×C4⋊C8C2312yes—
186#418—42no—
187#418Q818yescomplemented
188C2×#102—24no—
189C2×#102—42no—
190C2×#102C2312yes—
191C2×#102C2312yes—
192C2×#102C2312yes—
193C2×#102C2312yes—
194C2×#102C2312yes—
195C2×#102C2312yes—
196C2×#102C2312yes—
197C2×#102C2312yes—
198#405—24no—
199#405—42no—
200C4×M16—42no—
201C2×#97C2312yes—
202C2×#97C2312yes—
203C2×#97C2312yes—
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2312yes—
207#399—22no—
208#399—22no—
209#398—22no—
210#398—22no—
211#398—22no—
212#398—22no—
213#398—22no—
214#398—22no—
215#396—22no—
216#396—22no—
217#396—22no—
218#396—22no—
219#395—22no—
220#395—22no—
221#393—22no—
222#393—22no—
223#391—22no—
224#391—22no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390C2312yes—
230#390C2312yes—
231#390C2312yes—
232#390C2312yes—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—22no—
238#389—22no—
239#389—22no—
240#389—22no—
241#389D411yescharacteristic
242#389D411yescharacteristic
243#389D411yescharacteristic
244#389D411yescharacteristic
245#389C2312yes—
246#389C2312yes—
247#389C2311yescharacteristic
248#389C2311yescharacteristic
249#389C2311yescharacteristic
250#389C2311yescharacteristic
251#385—21no—
252#385—21no—
253#385—22no—
254#385—22no—
255#385—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#385—22no—
260#385D412yes—
261#385D412yes—
262#384—21no—
263#384—22no—
264#384—22no—
265#384C2311yescharacteristic
266#384C2312yes—
267#384C2312yes—
268#384C2311yescharacteristic
269#382—21no—
270#382C2311yescharacteristic
271#382C2312yes—
272#382C2311yescharacteristic
273#382C2312yes—
274#380—21no—
275#380—21no—
276#380—22no—
277#380—22no—
278#379—22no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4—21no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—21no—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2312yes—
288C4×C4⋊C4C2312yes—
289C4×C22⋊C4—22no—
290#340C2311yescharacteristic
291#340C2311yescharacteristic
292#340C2312yes—
293#340C2312yes—
294#340C2311yescharacteristic
295#340C2311yescharacteristic
296#340C2311yescharacteristic
297#340C2311yescharacteristic
298#340C2311yescharacteristic
299#340C2311yescharacteristic
300#340C2312yes—
301#340C2311yescharacteristic
302#340C2312yes—
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2312yes—
310#340C2311yescharacteristic
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2312yes—
315#340C2312yes—
316#340C2312yes—
317#340C2312yes—
318#340C2312yes—
319#340C2312yes—
320#340C2312yes—
321#340C2312yes—
322#336C2311yescharacteristic
323#336C2311yescharacteristic
324#336C2312yes—
325#336C2312yes—
326#336C2311yescharacteristic
327#336C2311yescharacteristic
328C25—21no—
329C22×Q8—22no—
330C22×Q8—22no—
331C22×D4—21no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4C2×Q814yes—
338C22×D4C2412yes—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D411yescharacteristic
346C23×C4C2411yescharacteristic
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—22no—
350C2×M16—22no—
351C2×M16—22no—
352C2×M16C2×Q814yes—
353C22×C8—22no—
354C22×C8—22no—
355C22×C8—22no—
356C22×C8—22no—
357C22×C8—22no—
358C22×C8—22no—
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C22×C8C2412yes—
364C22×C8C2412yes—
365C4⋊Q8—24no—
366C4⋊Q8—24no—
367C4⋊Q8—24no—
368C4⋊Q8—42no—
369C4⋊Q8—44no—
370C4⋊Q8—44no—
371#125—24no—
372#125—24no—
373#125—24no—
374#125—24no—
375#125—24no—
376#125—42no—
377#125—42no—
378#125—42no—
379#125—44no—
380#125—44no—
381#125—44no—
382#125—44no—
383C22⋊Q8—48no—
384C22⋊Q8—48no—
385C22⋊Q8—84no—
386C22⋊Q8—84no—
387C4×D4—24no—
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—44no—
392C4×D4—44no—
393#117—22no—
394#117—22no—
395#117—22no—
396#117—22no—
397#117—22no—
398#117—22no—
399#117—22no—
400#117—22no—
401#117—22no—
402#117C2×Q814yes—
403#117#4114yes—
404#117#4114yes—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—44no—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D412yes—
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2×D412yes—
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4#4114yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
458C2×C4⋊C4C2412yes—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—48no—
474C2×C22⋊C4—82no—
475C2×C22⋊C4—82no—
476C2×C22⋊C4C2×D412yes—
477C2×C22⋊C4C2×D412yes—
478C2×C42—21no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2412yes—
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2412yes—
492C4⋊C8—24no—
493C4⋊C8—24no—
494#102—24no—
495#102—24no—
496#102—42no—
497#102—42no—
498#102—42no—
499#102—42no—
500#102C2×Q818yes—
501#102C2×Q818yes—
502#97—24no—
503#97—42no—
504#97—42no—
505C4×C8—24no—
506C4×C8—42no—
507C4×C8—42no—
508#95—22no—
509#95—22no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—22no—
519#95—22no—
520#95—22no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95C2×D412yes—
525#95C2×D412yes—
526#95C2×D412yes—
527#95C2×D412yes—
528C24—22no—
529C24—24no—
530C24—42no—
531C24—42no—
532C24—81no—
533C24—81no—
534C24—81no—
535C24—81no—
536C24C22×D411yescharacteristic
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—82no—
540C2×Q8—82no—
541C2×Q8—82no—
542C2×Q8—82no—
543C2×D4—28no—
544C2×D4—24no—
545C2×D4—28no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—42no—
554C2×D4—44no—
555C2×D4C22×Q814yes—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D412yes—
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D411yescharacteristic
597C22×C4C22×Q812yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4112yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C42−1+412yes—
603C22×C4C2511yescharacteristic
604M16—28no—
605M16—44no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—22no—
615C2×C8—21no—
616C2×C8—22no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—22no—
623C2×C8—44no—
624C2×C8—44no—
625C2×C8C22×Q814yes—
626C4⋊C4—24no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—44no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—82no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—81no—
670C4⋊C4—81no—
671C4⋊C4—81no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C4⋊C4—82no—
677C4⋊C4—82no—
678C4⋊C4#12414yes—
679C4⋊C4#12414yes—
680C4⋊C4C22×Q812yes—
681C4⋊C4C22×Q812yes—
682C4⋊C4C2×#4114yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—82no—
697C22⋊C4—82no—
698C22⋊C4#12418yes—
699C42—22no—
700C42—22no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—22no—
705C42—21no—
706C42—22no—
707C42—21no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42—82no—
712C42—82no—
713C42C2×#4114yes—
714C42C2×#4114yes—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—48no—
727C23—84no—
728C23—84no—
729C23—162no—
730C23—162no—
731C23—162no—
732C23—162no—
733C23C2×#12412yes—
734C23#54612yes—
735C23D4×Q812yes—
736C23C23×D411yescharacteristic
737Q8—164no—
738Q8—164no—
739D4—24no—
740D4—24no—
741D4—42no—
742D4—42no—
743D4—48no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—82no—
800C2×C4—82no—
801C2×C4—84no—
802C2×C4—84no—
803C2×C4—164no—
804C2×C4—164no—
805C2×C4—162no—
806C2×C4C2×#12414yes—
807C2×C4C2×#12414yes—
808C2×C4C2×#12412yes—
809C2×C4#53314yes—
810C2×C4#54214yes—
811C2×C4#54612yes—
812C2×C4D4×Q812yes—
813C2×C4#55414yes—
814C2×C4#55614yes—
815C2×C4C23×Q811yescharacteristic
816C2×C4C22×#4111yescharacteristic
817C2×C4C22×#4111yescharacteristic
818C2×C4C22×#4111yescharacteristic
819C2×C4C2×H(5,𝔽2)11yescharacteristic
820C2×C4C2×2−1+411yescharacteristic
821C8—24no—
822C8—41no—
823C8—41no—
824C8—42no—
825C8—41no—
826C8—41no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—168no—
841C22#249214yes—
842C22C22×#12411yescharacteristic
843C22C2×#54611yescharacteristic
844C22C2×D4×Q811yescharacteristic
845C22#358411yescharacteristic
846C22#358411yescharacteristic
847C22#358511yescharacteristic
848C22#358511yescharacteristic
849C4—24no—
850C4—24no—
851C4—41no—
852C4—41no—
853C4—42no—
854C4—44no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—82no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—82no—
867C4—81no—
868C4#249214yes—
869C4C2×#53311yescharacteristic
870C4C2×#54211yescharacteristic
871C4C2×#55411yescharacteristic
872C4C2×#55611yescharacteristic
873C2—24no—
874C2—84no—
875C2C2×#249211yescharacteristic
876C2#6062411yescharacteristic
877C2#6062611yescharacteristic
878C2#6118711yescharacteristic
879C2#6118911yescharacteristic
880C2#6138511yescharacteristic
881C2#6138511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #35640C2semidirect
3. #27830C2semidirect
4. #27829C2semidirect
5. #27829C2semidirect
6. #27826C2semidirect
7. #27822C2semidirect
8. #27819C2semidirect
9. #27817C2semidirect
10. #27814C2semidirect
11. #23748C2semidirect
12. #23744C2semidirect
15. #21326C2semidirect
16. #21326C2semidirect
17. #21325C2semidirect
18. #21315C2semidirect
22. #20439C2semidirect
42. #2552C22semidirect
43. #2552C22semidirect
46. #2550C22semidirect
47. #2550C22semidirect
65. #2101C22semidirect
66. #2101C22semidirect
67. #2101C22semidirect
68. #2101C22semidirect
69. #2101C22semidirect
70. #2101C22semidirect
71. #2100C22semidirect
72. #2100C22semidirect
73. #2100C22semidirect
74. #2099C22semidirect
75. #2099C22semidirect
76. #2099C22semidirect
85. #1993C22semidirect
86. #1993C22semidirect
87. #1992C22semidirect
88. #1992C22semidirect
89. #1992C22semidirect
90. #1992C22semidirect
91. #1991C22semidirect
92. #1991C22semidirect
93. #1991C22semidirect
94. #1991C22semidirect
95. #1990C22semidirect
96. #1990C22semidirect
97. #1989C22semidirect
98. #1989C22semidirect
99. #1988C22semidirect
100. #1987C22semidirect
113. #1771C22semidirect
114. #1771C22semidirect
115. #1770C22semidirect
116. C8×C4⋊C4C22semidirect
187. #418Q8semidirect

Maximal subgroups

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

subgroupindex
#356402
#355292
#278302
#278292
#278262
#278222
#278192
#278172
#278142
#237482
#237442
#234562
C2×#20252
#213262
#213252
#213152
#210952
#210912
#206502
#204392
#204162