Finite Group Databasebeta

← #6555458

Subgroups — #6555458

Order 512.

1573 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37874C211yesmaximal, characteristic, complemented
2#34474C211yesmaximal, characteristic
3#29992C211yesmaximal, characteristic, complemented
4#29963C211yesmaximal, characteristic, complemented
5#29958C211yesmaximal, characteristic, complemented
6#29269C211yesmaximal, characteristic, complemented
7#29168C211yesmaximal, characteristic, complemented
8#29164C211yesmaximal, characteristic, complemented
9#28524C211yesmaximal, characteristic, complemented
10#27688C211yesmaximal, characteristic, complemented
11#27680C211yesmaximal, characteristic, complemented
12#26542C211yesmaximal, characteristic, complemented
13#26536C211yesmaximal, characteristic, complemented
14#26367C211yesmaximal, characteristic, complemented
15#26359C211yesmaximal, characteristic, complemented
16#26353C211yesmaximal, characteristic, complemented
17#26347C211yesmaximal, characteristic, complemented
18#26100C211yesmaximal, characteristic, complemented
19#26088C211yesmaximal, characteristic, complemented
20#25978C211yesmaximal, characteristic, complemented
21#25973C211yesmaximal, characteristic, complemented
22#25972C211yesmaximal, characteristic, complemented
23#25955C211yesmaximal, characteristic, complemented
24#23792C211yesmaximal, characteristic, complemented
25#23736C211yesmaximal, characteristic, complemented
26#23734C211yesmaximal, characteristic, complemented
27#22699C211yesmaximal, characteristic, complemented
28#22663C211yesmaximal, characteristic, complemented
29#22662C211yesmaximal, characteristic, complemented
30#22429C211yesmaximal, characteristic
31#22421C211yesmaximal, characteristic
32C2×#548C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#475C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#476C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#427C2211yescharacteristic
43C2×#417C2211yescharacteristic
44C2×#417C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C22×#103C2211yescharacteristic
47#2851C2211yescharacteristic
48#2792—21no—
49#2791—21no—
50#2790—21no—
51#2720—21no—
52#2660C2211yescharacteristic
53#2629C2211yescharacteristic
54#2583—21no—
55#2579—21no—
56#2570C2211yescharacteristic
57#2552C2211yescharacteristic
58#2473—21no—
59#2449—21no—
60#2442C2211yescharacteristic
61#2441C2211yescharacteristic
62#2440C2211yescharacteristic
63#2440C2211yescharacteristic
64#2379—21no—
65#2377—21no—
66#2368—21no—
67#2367C2211yescharacteristic
68#2363C2211yescharacteristic
69#2362C2211yescharacteristic
70#2357—21no—
71#2355C2211yescharacteristic
72#2354C2211yescharacteristic
73#2352C2211yescharacteristic
74D4×C4⋊C4C2211yescharacteristic
75Q8×C22⋊C4C2211yescharacteristic
76#2339C2211yescharacteristic
77#2337—21no—
78#2333—21no—
79#2332—21no—
80#2330C2211yescharacteristic
81#2326C2211yescharacteristic
82#2324C2211yescharacteristic
83#2320C2211yescharacteristic
84#2318—21no—
85#2317C2211yescharacteristic
86#2310C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88#2297C2211yescharacteristic
89#2290C2211yescharacteristic
90C2×#384C2211yescharacteristic
91#2101C2211yescharacteristic
92#2099C2211yescharacteristic
93#2099C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2097C2211yescharacteristic
97#2097C2211yescharacteristic
98#2096C2211yescharacteristic
99#2096C2211yescharacteristic
100#2096C2211yescharacteristic
101#2096C2211yescharacteristic
102#2096C2211yescharacteristic
103#2095C2211yescharacteristic
104#2095C2211yescharacteristic
105#2095C2211yescharacteristic
106#2094C2211yescharacteristic
107#2094C2211yescharacteristic
108#2093C2211yescharacteristic
109#2093C2211yescharacteristic
110#2092C2211yescharacteristic
111#2087C2211yescharacteristic
112#2086C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2068C2211yescharacteristic
116#2068C2211yescharacteristic
117#2067C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2065C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2057C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2025C2211yescharacteristic
130#2024C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1959C2211yescharacteristic
134#1958C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1948C2211yescharacteristic
138#1948C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1947C2211yescharacteristic
143#1940C2211yescharacteristic
144#1939C2211yescharacteristic
145#1921C2211yescharacteristic
146#1920C2211yescharacteristic
147#1919C2211yescharacteristic
148#1919C2211yescharacteristic
149#1895C2211yescharacteristic
150#1894C2211yescharacteristic
151#1894C2211yescharacteristic
152#1893C2211yescharacteristic
153#1875C2211yescharacteristic
154#1874C2211yescharacteristic
155#1872C2211yescharacteristic
156#1872C2211yescharacteristic
157#1865C2211yescharacteristic
158#1865C2211yescharacteristic
159#1865C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1864C2211yescharacteristic
163#1863C2211yescharacteristic
164#1862C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic
173#1851C2211yescharacteristic
174#1851C2211yescharacteristic
175#1851C2211yescharacteristic
176#1850C2211yescharacteristic
177#1847C2211yescharacteristic
178#1844C2211yescharacteristic
179#1832C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1807C2211yescharacteristic
184#1805C2211yescharacteristic
185#1804C2211yescharacteristic
186#1803C2211yescharacteristic
187#1803C2211yescharacteristic
188#1803C2211yescharacteristic
189#1802C2211yescharacteristic
190#1798C2211yescharacteristic
191#1797C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#107C2211yescharacteristic
198#1768C2211yescharacteristic
199#1763C2211yescharacteristic
200C4×#103C2211yescharacteristic
201#1729C2211yescharacteristic
202#1728C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#548—24no—
210#548Q818yescomplemented
211C2×C4⋊Q8C2311yescharacteristic
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121—21no—
222C2×#121C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C22×C4⋊C4—21no—
236C22×C4⋊C4—21no—
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C42C2311yescharacteristic
241#479—42no—
242#478—42no—
243#476—42no—
244#475—42no—
245#436—24no—
246#435—24no—
247#428—42no—
248#428—42no—
249#428—42no—
250#427—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279#419—42no—
280#417—42no—
281#417—42no—
282C2×#103—42no—
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313#400—21no—
314#400—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#395—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#390—21no—
344#390—21no—
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388D411yescharacteristic
375#388D411yescharacteristic
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387D411yescharacteristic
391#387D411yescharacteristic
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386D411yescharacteristic
400#386D411yescharacteristic
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385D411yescharacteristic
416#385D411yescharacteristic
417#384—21no—
418#384—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#383—21no—
427#382—21no—
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#381—21no—
435#380—21no—
436#380—21no—
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376C2311yescharacteristic
463C2×#95—21no—
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C2×Q814yes—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2×Q814yes—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C2×M16—22no—
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—22no—
529C2×M16—22no—
530C2×M16—22no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C4⋊Q8—41no—
546C4⋊Q8—41no—
547#125—41no—
548#125—41no—
549#125—41no—
550#125—41no—
551#125—82no—
552#124—28no—
553#124—22no—
554#124C2×Q814yes—
555C22⋊Q8—22no—
556C22⋊Q8—28no—
557C22⋊Q8—82no—
558C22⋊Q8—82no—
559C22⋊Q8C2×Q814yes—
560#121—28no—
561#121—22no—
562#121C2×Q814yes—
563C4×Q8—22no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8C2×Q814yes—
569C4×D4—28no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—82no—
575C4×D4C2×Q814yes—
576C4×D4#4114yes—
577#117—41no—
578#117—41no—
579#117—41no—
580#117—41no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—82no—
626C2×C4⋊C4—82no—
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—41no—
684C2×C42—41no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#107—22no—
693#107—22no—
694#107—22no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#106—22no—
701#106—22no—
702#106—22no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—22no—
713C4⋊C8—22no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720#103—22no—
721#103—22no—
722#103—22no—
723#103—22no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#102—22no—
737#102—22no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744C22⋊C8—22no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—22no—
748#97—22no—
749C4×C8—22no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24C22×D411yescharacteristic
799C24C22×D411yescharacteristic
800#41—44no—
801#41—44no—
802#41—82no—
803#41—82no—
804C2×Q8—24no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—44no—
816C2×Q8—44no—
817C2×Q8—81no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—82no—
823C2×Q8—82no—
824C2×Q8C22×Q812yes—
825C2×Q8C22×Q812yes—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4C22⋊Q814yes—
840C2×D4C22×Q812yes—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—24no—
853C22×C4—22no—
854C22×C4—24no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×Q812yes—
904C22×C4C22×Q812yes—
905C22×C4C2×#4112yes—
906C22×C4C2×#4112yes—
907C22×C4C2511yescharacteristic
908M16—44no—
909M16—44no—
910M16—44no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—44no—
934C2×C8H(5,𝔽2)12yes—
935C2×C8H(5,𝔽2)12yes—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4C22⋊Q814yes—
1000C4⋊C4C22×Q812yes—
1001C22⋊C4—24no—
1002C22⋊C4—24no—
1003C22⋊C4—24no—
1004C22⋊C4—24no—
1005C22⋊C4—22no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
1010C22⋊C4—41no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4C22⋊Q814yes—
1027C22⋊C4C22⋊Q814yes—
1028C42—24no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—41no—
1038C42—41no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42C22×Q812yes—
1050C42C2×#4112yes—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—22no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23C2×C22⋊Q812yes—
1071C23C2×C22⋊Q812yes—
1072C23C23×D411yescharacteristic
1073Q8—22no—
1074Q8—22no—
1075Q8—22no—
1076Q8—22no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081Q8—84no—
1082Q8—162no—
1083D4—22no—
1084D4—22no—
1085D4—44no—
1086D4—41no—
1087D4—41no—
1088D4—84no—
1089D4—84no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—44no—
1133C2×C4—44no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—84no—
1177C2×C4—84no—
1178C2×C4—162no—
1179C2×C4—162no—
1180C2×C4—162no—
1181C2×C4—162no—
1182C2×C4—162no—
1183C2×C4C2×C22⋊Q812yes—
1184C2×C4C2×C22⋊Q812yes—
1185C2×C4C2×C22⋊Q812yes—
1186C2×C4C2×C22⋊Q812yes—
1187C2×C4#57712yes—
1188C2×C4C23×Q811yescharacteristic
1189C2×C4C22×#4111yescharacteristic
1190C2×C4C2×H(5,𝔽2)11yescharacteristic
1191C2×C4C2×H(5,𝔽2)11yescharacteristic
1192C2×C4#58511yescharacteristic
1193C2×C4#58511yescharacteristic
1194C8—22no—
1195C8—22no—
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22C22×C22⋊Q811yescharacteristic
1224C22#348511yescharacteristic
1225C22#349811yescharacteristic
1226C22C2×#57711yescharacteristic
1227C22#358511yescharacteristic
1228C22#358611yescharacteristic
1229C22#358611yescharacteristic
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—42no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—41no—
1243C4—42no—
1244C4—42no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4—81no—
1255C4—81no—
1256C4—81no—
1257C4#350111yescharacteristic
1258C4#350111yescharacteristic
1259C4#351311yescharacteristic
1260C4#351311yescharacteristic
1261C2—42no—
1262C2—42no—
1263C2—82no—
1264C2#3583611yescharacteristic
1265C2#6049311yescharacteristic
1266C2#6049711yescharacteristic
1267C2#6174511yescharacteristic
1268C2#6177511yescharacteristic
1269C2#6244211yescharacteristic
1270C2#6246511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#548C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37874C2semidirect
3. #29992C2semidirect
4. #29963C2semidirect
5. #29958C2semidirect
6. #29269C2semidirect
7. #29168C2semidirect
8. #29164C2semidirect
9. #28524C2semidirect
10. #27688C2semidirect
11. #27680C2semidirect
12. #26542C2semidirect
13. #26536C2semidirect
14. #26367C2semidirect
15. #26359C2semidirect
16. #26353C2semidirect
17. #26347C2semidirect
18. #26100C2semidirect
19. #26088C2semidirect
20. #25978C2semidirect
21. #25973C2semidirect
22. #25972C2semidirect
23. #25955C2semidirect
24. #23792C2semidirect
25. #23736C2semidirect
26. #23734C2semidirect
27. #22699C2semidirect
28. #22663C2semidirect
29. #22662C2semidirect
210. #548Q8semidirect

Maximal subgroups

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

subgroupindex
#378742
#344742
#299922
#299632
#299582
#292692
#291682
#291642
#285242
#276882
#276802
#265422
#265362
#263672
#263592
#263532
#263472
#261002
#260882
#259782
#259732
#259722
#259552
#237922
#237362
#237342
#226992
#226632
#226622
#224292
#224212