Finite Group Databasebeta

← #6594639

Subgroups — #6594639

Order 512.

1602 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37858C212yesmaximal, complemented
2#33215C211yesmaximal, characteristic, complemented
3#33138C211yesmaximal, characteristic, complemented
4#32930C211yesmaximal, characteristic
5#29174C212yesmaximal, complemented
6#28850C212yesmaximal, complemented
7#28080C212yesmaximal, complemented
8#27928C211yesmaximal, characteristic, complemented
9#27871C212yesmaximal, complemented
10#27839C211yesmaximal, characteristic, complemented
11#27838C211yesmaximal, characteristic, complemented
12#27791C211yesmaximal, characteristic, complemented
13#27712C212yesmaximal, complemented
14#26064C211yesmaximal, characteristic, complemented
15#25032C211yesmaximal, characteristic, complemented
16#24560C212yesmaximal, complemented
17#23027C211yesmaximal, characteristic, complemented
18#22933C212yesmaximal, complemented
19#22614C211yesmaximal, characteristic, complemented
20#21524C211yesmaximal, characteristic, complemented
21#20821C211yesmaximal, characteristic, complemented
22#20658C211yesmaximal, characteristic, complemented
23#20385C211yesmaximal, characteristic, complemented
24C24×C8C2211yescharacteristic
25C2×#500C2211yescharacteristic, complemented
26C2×#482C2212yes—
27C2×#466C2211yescharacteristic
28C2×#466C2211yescharacteristic
29C2×#466C2211yescharacteristic
30C2×C4×D8C2211yescharacteristic, complemented
31C2×#427C2211yescharacteristic
32C2×#427C2211yescharacteristic
33C2×#407C2211yescharacteristic
34C2×#405C2211yescharacteristic
35C2×#405C2211yescharacteristic
36#2847C2212yes—
37#2743—22no—
38#2737—22no—
39#2685—22no—
40#2684—22no—
41#2628C2212yes—
42#2624C2212yes—
43#2578—22no—
44#2572—22no—
45#2521—22no—
46#2516—22no—
47#2500C2212yes—
48#2496C2212yes—
49#2495C2212yes—
50#2491C2212yes—
51#2439C2212yes—
52#2420C2212yes—
53#2363C2212yes—
54#2347C2212yes—
55#2324C2212yes—
56#2314C2212yes—
57#2280C2212yes—
58#2280C2211yescharacteristic
59#2101C2212yescomplemented
60#2099C2212yescomplemented
61#2094C2212yescomplemented
62#2092C2212yescomplemented
63#2085C2212yescomplemented
64#2077C2212yes—
65#2075C2212yes—
66#2073C2212yescomplemented
67#2058C2212yescomplemented
68#2034C2212yes—
69#2033C2212yes—
70#2023C2212yescomplemented
71#1993C2212yescomplemented
72#1970C2211yescharacteristic, complemented
73#1970C2211yescharacteristic, complemented
74#1970C2211yescharacteristic, complemented
75#1944C2212yescomplemented
76#1942C2211yescharacteristic, complemented
77#1942C2211yescharacteristic, complemented
78#1942C2211yescharacteristic, complemented
79#1942C2211yescharacteristic, complemented
80#1942C2211yescharacteristic, complemented
81#1936C2212yescomplemented
82#1936C2212yescomplemented
83#1936C2212yescomplemented
84#1926C2212yescomplemented
85#1925C2212yescomplemented
86#1920C2212yescomplemented
87#1919C2212yescomplemented
88#1919C2212yescomplemented
89#1918C2212yescomplemented
90#1895C2212yes—
91#1895C2212yes—
92#1893C2212yes—
93#1893C2212yes—
94#1893C2212yes—
95#1875C2212yes—
96#1864C2212yescomplemented
97#1864C2212yescomplemented
98#1854C2212yes—
99#1846C2211yescharacteristic, complemented
100#1846C2211yescharacteristic, complemented
101#1845C2211yescharacteristic, complemented
102#1836C2212yescomplemented
103#1825C2212yes—
104#1809C2212yes—
105#1809C2212yes—
106#1808C2211yescharacteristic
107#1808C2211yescharacteristic
108#1808C2211yescharacteristic
109#1808C2211yescharacteristic
110#1808C2211yescharacteristic
111#1808C2211yescharacteristic
112#1808C2211yescharacteristic
113#1807C2212yes—
114#1807C2212yes—
115#1776C2212yescomplemented
116C4×#107C2211yescharacteristic, complemented
117C4×#107C2211yescharacteristic, complemented
118C4×#107C2211yescharacteristic, complemented
119#1762C2212yescomplemented
120#1752C2211yescharacteristic
121#1752C2211yescharacteristic
122#1752C2211yescharacteristic
123#1752C2211yescharacteristic
124C8×C22⋊C4C2211yescharacteristic
125C8×C22⋊C4C2211yescharacteristic
126C8×C22⋊C4C2211yescharacteristic
127C8×C22⋊C4C2211yescharacteristic
128#1735C2212yes—
129#1729C2211yescharacteristic
130#1729C2211yescharacteristic
131C24×C4C2311yescharacteristic
132C22×D8C2311yescharacteristic
133C22×M16C2311yescharacteristic
134C22×M16C2311yescharacteristic
135C23×C8—24no—
136C23×C8—24no—
137C23×C8—42no—
138C23×C8C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141C23×C8C2311yescharacteristic
142C23×C8C2311yescharacteristic
143C23×C8C2311yescharacteristic
144C2×C4⋊Q8C2312yes—
145C2×#126—22no—
146C2×#124—22no—
147C2×#121C2312yes—
148C2×#121C2312yes—
149C2×#121C2312yes—
150C2×#120—22no—
151C2×C4×D4C2312yes—
152C2×#117C2312yes—
153C2×#117C2312yes—
154C2×#117C2311yescharacteristic
155C2×#117C2311yescharacteristic
156#500—42no—
157#482—28no—
158#466—24no—
159#466—24no—
160#466—42no—
161C4×D8—42no—
162#427—24no—
163#427—42no—
164C2×#107C2312yes—
165C2×#107C2311yescharacteristic
166C2×#107C2311yescharacteristic
167C2×#107C2311yescharacteristic
168C2×#107C2311yescharacteristic
169C2×#107C2311yescharacteristic
170C2×#107C2311yescharacteristic
171C2×#107C2311yescharacteristic
172C2×#107C2312yes—
173C2×#106C2312yes—
174C2×#106C2312yes—
175C2×#106C2312yes—
176C2×#106C2312yes—
177C2×#102C2312yes—
178C2×#102C2312yes—
179C2×#102C2312yes—
180C2×#102C2312yes—
181C2×#102C2312yes—
182C2×#102C2312yes—
183C2×#102C2312yes—
184#407—24no—
185C2×C22⋊C8C2311yescharacteristic
186C2×C22⋊C8C2311yescharacteristic
187C2×C22⋊C8C2311yescharacteristic
188C2×C22⋊C8C2311yescharacteristic
189#405—24no—
190#405—42no—
191C2×#97C2311yescharacteristic
192C2×#97C2311yescharacteristic
193C2×#97C2311yescharacteristic
194C2×#97C2311yescharacteristic
195C2×C4×C8C2311yescharacteristic
196C2×C4×C8C2311yescharacteristic
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2311yescharacteristic
199#400—22no—
200#400—22no—
201#400—22no—
202#399—22no—
203#399—22no—
204#397—22no—
205#397—22no—
206#397—22no—
207#397—22no—
208#396—22no—
209#395—22no—
210#394—22no—
211#394—22no—
212#394—22no—
213#394—22no—
214#394—22no—
215#394—22no—
216#393—22no—
217#393—22no—
218#393—22no—
219#391—22no—
220#390—22no—
221#390—22no—
222#390C2312yes—
223#390C2312yes—
224#390C2312yes—
225#389C2312yes—
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#388—22no—
231#388—22no—
232#388—22no—
233#388—22no—
234#388—22no—
235#388—22no—
236#388—22no—
237#388—22no—
238#388—22no—
239#388—22no—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#386—22no—
245#386—22no—
246#386—22no—
247#386—22no—
248#386—22no—
249#386—22no—
250#385—22no—
251#384C2312yes—
252#383—22no—
253#383—22no—
254#382C2312yes—
255#382C2312yes—
256#381—22no—
257#381—22no—
258#381D411yescharacteristic
259#381D411yescharacteristic
260#380D411yescharacteristic
261#380D411yescharacteristic
262#380D411yescharacteristic
263#380D411yescharacteristic
264#380C2312yes—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268#380C2312yes—
269#380C2312yes—
270#380C2312yes—
271#379—22no—
272#379D411yescharacteristic
273#379D411yescharacteristic
274C4×C4⋊C4—22no—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C22⋊C4—22no—
279C4×C22⋊C4—22no—
280C4×C22⋊C4—22no—
281C4×C22⋊C4C2311yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C4×C22⋊C4C2311yescharacteristic
284C4×C22⋊C4C2311yescharacteristic
285#340C2312yes—
286#340C2312yes—
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#336C2311yescharacteristic
301#336C2311yescharacteristic
302#336C2311yescharacteristic
303#336C2311yescharacteristic
304#336C2311yescharacteristic
305#336C2311yescharacteristic
306#336C2311yescharacteristic
307#336C2311yescharacteristic
308C25C2×D411yescharacteristic
309C22×Q8—22no—
310C22×D4—22no—
311C22×D4—22no—
312C22×D4—22no—
313C22×D4C2412yes—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—41no—
320C23×C4—41no—
321C23×C4C2×D411yescharacteristic
322C23×C4C2×D411yescharacteristic
323C23×C4C2×D411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C2×D8—22no—
328C2×D8—22no—
329C2×D8—22no—
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—22no—
334C2×M16—41no—
335C2×M16—41no—
336C22×C8—22no—
337C22×C8—22no—
338C22×C8—22no—
339C22×C8—22no—
340C22×C8—22no—
341C22×C8—22no—
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—22no—
346C22×C8—22no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—41no—
350C22×C8—41no—
351C22×C8—41no—
352C22×C8—416no—
353C22×C8#4114yes—
354C22×C8#4114yes—
355C22×C8C2411yescharacteristic
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C4⋊Q8—42no—
364C4⋊Q8—42no—
365#126—84no—
366#124—84no—
367#121—24no—
368#121—24no—
369#121—24no—
370#121—24no—
371#121—42no—
372#121—42no—
373#120—84no—
374C4×D4—42no—
375C4×D4—42no—
376#117—22no—
377#117—22no—
378#117—24no—
379#117—24no—
380#117—41no—
381#117—41no—
382#117—42no—
383#117—42no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4C2×D411yescharacteristic
393C2×C4⋊C4C2×D411yescharacteristic
394C2×C4⋊C4C2×D411yescharacteristic
395C2×C4⋊C4C2×D411yescharacteristic
396C2×C4⋊C4C2412yes—
397C2×C4⋊C4C2412yes—
398C2×C4⋊C4C2412yes—
399C2×C4⋊C4C2412yes—
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2412yes—
402C2×C4⋊C4C2412yes—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4C2×D411yescharacteristic
423C2×C22⋊C4C2×D411yescharacteristic
424C2×C22⋊C4C2×D411yescharacteristic
425C2×C22⋊C4C2×D411yescharacteristic
426C2×C22⋊C4C2×D411yescharacteristic
427C2×C22⋊C4C2×D411yescharacteristic
428C2×C22⋊C4C2×D411yescharacteristic
429C2×C22⋊C4C2×D411yescharacteristic
430C2×C22⋊C4C2×D411yescharacteristic
431C2×C22⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42C2411yescharacteristic
440C2×C42C2411yescharacteristic
441C2×C42C2411yescharacteristic
442C2×C42C2411yescharacteristic
443#107—22no—
444#107—22no—
445#107—22no—
446#107—22no—
447#107—24no—
448#107—22no—
449#107—22no—
450#107—22no—
451#107—42no—
452#106—24no—
453#106—24no—
454#106—42no—
455#106—42no—
456#102—24no—
457#102—24no—
458#102—24no—
459#102—24no—
460#102—42no—
461#102—42no—
462#102—42no—
463C22⋊C8—22no—
464C22⋊C8—22no—
465C22⋊C8—22no—
466C22⋊C8#4114yes—
467#97—22no—
468#97—22no—
469#97—41no—
470#97—41no—
471C4×C8—22no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—22no—
475#95—22no—
476#95—22no—
477#95—22no—
478#95—22no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95—22no—
486#95—22no—
487#95—22no—
488#95—22no—
489#95—22no—
490#95—22no—
491#95—22no—
492#95—22no—
493#95—22no—
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499#95C2×D411yescharacteristic
500#95C2×D411yescharacteristic
501#95C2×D411yescharacteristic
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—41no—
507C24—41no—
508C24—41no—
509C24—41no—
510C24C22×D411yescharacteristic
511C24C22×D411yescharacteristic
512C24C22×D411yescharacteristic
513C2×Q8—82no—
514C2×Q8—82no—
515C2×Q8—82no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—82no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4—82no—
530C2×D4—82no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—82no—
566C22×C4—82no—
567C22×C4—82no—
568C22×C4C22×D411yescharacteristic
569C22×C4C22×D411yescharacteristic
570C22×C4C22×D411yescharacteristic
571C22×C4C22×D411yescharacteristic
572C22×C4C22×D411yescharacteristic
573C22×C4C22×D411yescharacteristic
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C42−1+412yes—
583C22×C4C2511yescharacteristic
584D8—44no—
585M16—44no—
586M16—44no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—28no—
596C2×C8—28no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—44no—
607C2×C8—44no—
608C2×C8—44no—
609C2×C8—44no—
610C2×C8C2×#4112yes—
611C2×C8C2×#4112yes—
612C2×C8C2×#4112yes—
613C2×C8C2×#4112yes—
614C2×C8C2×#4112yes—
615C2×C8C2×#4112yes—
616C2×C8H(5,𝔽2)12yes—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—82no—
636C4⋊C4—82no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4—82no—
640C4⋊C4—82no—
641C4⋊C4—82no—
642C4⋊C4—82no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—41no—
648C22⋊C4—41no—
649C22⋊C4—41no—
650C22⋊C4—41no—
651C22⋊C4—41no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—41no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—44no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C22⋊C4—82no—
665C22⋊C4—82no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C22⋊C4—82no—
670C22⋊C4—82no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—82no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—44no—
683C42—82no—
684C42—82no—
685C42—82no—
686C42—82no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23#53212yes—
720C23#54712yes—
721C23#57612yes—
722C23C23×D411yescharacteristic
723Q8—164no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—42no—
728D4—164no—
729D4—164no—
730D4—164no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
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—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—164no—
799C2×C4#53212yes—
800C2×C4#54712yes—
801C2×C4C22×#4111yescharacteristic
802C2×C4C22×#4111yescharacteristic
803C2×C4C22×#4111yescharacteristic
804C2×C4C2×H(5,𝔽2)11yescharacteristic
805C2×C4C2×2−1+411yescharacteristic
806C2×C4#58511yescharacteristic
807C8—22no—
808C8—22no—
809C8—22no—
810C8—22no—
811C8—41no—
812C8—41no—
813C8—41no—
814C8#55114yes—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—416no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22C2×#53211yescharacteristic
845C22C2×#54711yescharacteristic
846C22#349611yescharacteristic
847C22C2×#57611yescharacteristic
848C22#358411yescharacteristic
849C22#358411yescharacteristic
850C22#358411yescharacteristic
851C4—22no—
852C4—22no—
853C4—41no—
854C4—41no—
855C4—41no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—82no—
868C4—82no—
869C4C2×#55111yescharacteristic
870C4#347511yescharacteristic
871C4#349511yescharacteristic
872C4#352011yescharacteristic
873C2—42no—
874C2—42no—
875C2—42no—
876C2—162no—
877C2#3618311yescharacteristic
878C2#6068211yescharacteristic
879C2#6070711yescharacteristic
880C2#6126111yescharacteristic
881C2#6126211yescharacteristic
882C2#6226611yescharacteristic
883C2#6227511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#32930C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37858C2semidirect
2. #33215C2semidirect
3. #33138C2semidirect
5. #29174C2semidirect
6. #28850C2semidirect
7. #28080C2semidirect
8. #27928C2semidirect
9. #27871C2semidirect
10. #27839C2semidirect
11. #27838C2semidirect
12. #27791C2semidirect
13. #27712C2semidirect
14. #26064C2semidirect
15. #25032C2semidirect
16. #24560C2semidirect
17. #23027C2semidirect
18. #22933C2semidirect
19. #22614C2semidirect
20. #21524C2semidirect
21. #20821C2semidirect
22. #20658C2semidirect
23. #20385C2semidirect
25. C2×#500C22semidirect
30. C2×C4×D8C22semidirect
59. #2101C22semidirect
60. #2099C22semidirect
61. #2094C22semidirect
62. #2092C22semidirect
63. #2085C22semidirect
66. #2073C22semidirect
67. #2058C22semidirect
70. #2023C22semidirect
71. #1993C22semidirect
72. #1970C22semidirect
73. #1970C22semidirect
74. #1970C22semidirect
75. #1944C22semidirect
76. #1942C22semidirect
77. #1942C22semidirect
78. #1942C22semidirect
79. #1942C22semidirect
80. #1942C22semidirect
81. #1936C22semidirect
82. #1936C22semidirect
83. #1936C22semidirect
84. #1926C22semidirect
85. #1925C22semidirect
86. #1920C22semidirect
87. #1919C22semidirect
88. #1919C22semidirect
89. #1918C22semidirect
96. #1864C22semidirect
97. #1864C22semidirect
99. #1846C22semidirect
100. #1846C22semidirect
101. #1845C22semidirect
102. #1836C22semidirect
115. #1776C22semidirect
116. C4×#107C22semidirect
117. C4×#107C22semidirect
118. C4×#107C22semidirect
119. #1762C22semidirect

Maximal subgroups

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

subgroupindex
#378582
#332152
#331382
#329302
#291742
#288502
#280802
#279282
#278712
#278392
#278382
#277912
#277122
#260642
#250322
#245602
#230272
#229332
#226142
#215242
#208212
#206582
#203852