Finite Group Databasebeta

← #6687219

Subgroups — #6687219

Order 512.

1923 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3210C211yesmaximal, characteristic, complemented
2C2×#3170C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4#36134C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#30602C214yesmaximal, complemented
7#30409C214yesmaximal, complemented
8#30276C211yesmaximal, characteristic, complemented
9#29876C211yesmaximal, characteristic, complemented
10#28717C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#26169C214yesmaximal, complemented
13#25857C211yesmaximal, characteristic, complemented
14#25674C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#24904C214yesmaximal, complemented
18#22270C211yesmaximal, characteristic, complemented
19#21101C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24#3210—28no—
25#3170—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#494C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#467C2214yes—
36C2×#464C2214yes—
37C2×#452C2214yes—
38C2×C4×Q16C2214yes—
39C2×#431C2211yescharacteristic
40C22×C4×C8C2211yescharacteristic
41#2868C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2552—21no—
48#2542—21no—
49#2540—21no—
50#2538C2212yes—
51#2490—21no—
52#2454—21no—
53#2448C2212yes—
54#2441—21no—
55#2441—21no—
56#2429—21no—
57#2429—21no—
58#2427—21no—
59#2426—21no—
60#2426C2212yes—
61#2423C2212yes—
62#2423C2212yes—
63#2414—21no—
64#2407C2212yes—
65#2367—21no—
66#2365—21no—
67#2363—21no—
68#2354—21no—
69Q8×C4⋊C4C2212yes—
70#2341C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2093C2214yes—
75#2093C2214yes—
76#2086C2214yes—
77#2075C2214yes—
78#2072C2214yes—
79#2055C2214yes—
80#2042C2214yes—
81#2036C2214yes—
82#2036C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1957C2211yescharacteristic
88#1956C2211yescharacteristic
89#1956C2211yescharacteristic
90#1934C2214yes—
91#1923C2212yes—
92#1916C2212yes—
93#1893C2214yes—
94#1880C2214yes—
95#1880C2214yes—
96#1878C2214yes—
97#1878C2214yes—
98#1869C2212yes—
99#1863C2214yes—
100#1863C2214yes—
101#1850C2212yes—
102#1834C2211yescharacteristic
103#1803C2214yes—
104#1788C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41C2312yes—
110C22×Q16C2314yes—
111C22×SD16C2314yes—
112C23×C8C2312yes—
113#533—24no—
114#533—24no—
115#533—24no—
116#533—42no—
117#533—42no—
118#533—42no—
119#532—24no—
120#532—42no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×#127C2311yescharacteristic
129C2×#125—21no—
130C2×#125—21no—
131C2×#125—21no—
132C2×#124—21no—
133C2×#124—21no—
134C2×#124C2312yes—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—21no—
137C2×C22⋊Q8—21no—
138C2×C22⋊Q8—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8C2312yes—
142C2×C22⋊Q8C2312yes—
143C2×C22⋊Q8C2312yes—
144C2×#121—21no—
145C2×#121—21no—
146C2×#121—21no—
147C2×#121—21no—
148C2×#121C2312yes—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8—21no—
152C2×C4×Q8C2312yes—
153C2×C4×Q8C2312yes—
154C2×C4×Q8C2312yes—
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×C4×D4D411yescharacteristic
160C2×C4×D4D411yescharacteristic
161C2×C4×D4C2311yescharacteristic
162C2×#117—21no—
163C2×#117—21no—
164C2×#117—21no—
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#500—24no—
168#500—42no—
169#494D418yescomplemented
170#492—24no—
171#487—24no—
172#487—24no—
173#487—24no—
174#486—24no—
175#486—42no—
176#467—216no—
177#464—216no—
178#452—216no—
179C4×Q16—216no—
180#431—24no—
181C2×#107C2314yes—
182C2×#107C2314yes—
183C2×C4⋊C8C2312yes—
184C2×C4⋊C8C2312yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×C4×C8—24no—
197C2×C4×C8C2311yescharacteristic
198C2×C4×C8C2312yes—
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202#399—22no—
203#399—22no—
204#399—22no—
205#398—22no—
206#398—22no—
207#397—22no—
208#396—22no—
209#396—22no—
210#396—22no—
211#394—22no—
212#394—22no—
213#392—22no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391C2312yes—
218#391C2312yes—
219#390—22no—
220#390—22no—
221#390—22no—
222#390—22no—
223#390—21no—
224#390—21no—
225#390—21no—
226#390—21no—
227#390C2312yes—
228#390C2312yes—
229#390C2312yes—
230#389—22no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—22no—
239#389—22no—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#388—22no—
244#388—22no—
245#388—22no—
246#388—22no—
247#388—22no—
248#387—22no—
249#387—22no—
250#386—22no—
251#385—22no—
252#384—22no—
253#384—21no—
254#384—21no—
255#384C2311yescharacteristic
256#384C2311yescharacteristic
257#384C2312yes—
258#384C2312yes—
259#380—21no—
260#380—21no—
261#380—21no—
262#380—22no—
263#380C2312yes—
264#380C2312yes—
265#380C2312yes—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—21no—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2311yescharacteristic
274C4×C22⋊C4—22no—
275C4×C22⋊C4D411yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4C2311yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C43C2311yescharacteristic
282#340C2314yes—
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#336C2312yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291C2×#41—24no—
292C2×#41—42no—
293C2×#41—44no—
294C2×#41—44no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8C2412yes—
299C22×Q8C2412yes—
300C22×D4—22no—
301C22×D4—22no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C2×D411yescharacteristic
305C22×D4C2412yes—
306C23×C4—22no—
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C2×Q16—44no—
314C2×Q16—44no—
315C2×Q16C2×D4116yes—
316C2×SD16—28no—
317C2×SD16—44no—
318C2×SD16—44no—
319C22×C8—24no—
320C22×C8—42no—
321C22×C8—42no—
322C22×C8C2412yes—
323C22×C8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—44no—
335C4⋊Q8—82no—
336C4⋊Q8C2×D414yes—
337C4⋊Q8C2×D414yes—
338#127—22no—
339#127—22no—
340#125—44no—
341#125—44no—
342#125—44no—
343#124—24no—
344#124—42no—
345#124—44no—
346#124—82no—
347C22⋊Q8—24no—
348C22⋊Q8—24no—
349C22⋊Q8—24no—
350C22⋊Q8—42no—
351C22⋊Q8—42no—
352C22⋊Q8—42no—
353C22⋊Q8—44no—
354C22⋊Q8—44no—
355C22⋊Q8—44no—
356C22⋊Q8—82no—
357C22⋊Q8—82no—
358C22⋊Q8—82no—
359#121—44no—
360#121—44no—
361#121—44no—
362#121—44no—
363#121—82no—
364C4×Q8—24no—
365C4×Q8—24no—
366C4×Q8—24no—
367C4×Q8—44no—
368C4×Q8—42no—
369C4×Q8—42no—
370C4×Q8—42no—
371C4×Q8—44no—
372C4×Q8—44no—
373C4×Q8—44no—
374C4×Q8—44no—
375C4×D4—24no—
376C4×D4—24no—
377C4×D4—44no—
378C4×D4—44no—
379C4×D4—42no—
380#117—44no—
381#117—44no—
382#117—44no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4C2×D411yescharacteristic
410C2×C4⋊C4C2×D411yescharacteristic
411C2×C4⋊C4C2×D411yescharacteristic
412C2×C4⋊C4C2412yes—
413C2×C4⋊C4C2412yes—
414C2×C4⋊C4C2412yes—
415C2×C4⋊C4C2412yes—
416C2×C4⋊C4C2412yes—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457C2×C42C2411yescharacteristic
458C2×C42C2411yescharacteristic
459C2×C42C2411yescharacteristic
460#107—28no—
461#107—44no—
462C4⋊C8—24no—
463C4⋊C8—42no—
464#103—28no—
465#103—28no—
466#103—28no—
467#103—44no—
468#103—44no—
469#102—28no—
470#102—44no—
471#102—44no—
472C22⋊C8—24no—
473C22⋊C8—42no—
474C22⋊C8—42no—
475C4×C8—24no—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8C2×D414yes—
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#95C2×D411yescharacteristic
491#95C2×D411yescharacteristic
492#95C2×D411yescharacteristic
493#95C2×D411yescharacteristic
494#95C2×D411yescharacteristic
495#95C2×D411yescharacteristic
496C24—22no—
497C24C22×D411yescharacteristic
498C24C22×D411yescharacteristic
499#41—88no—
500#41—88no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—24no—
504C2×Q8—24no—
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8C22×D414yes—
517C2×Q8C22×D414yes—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4—41no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—82no—
535C2×D4—82no—
536C2×D4—82no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—82no—
566C22×C4#13714yes—
567C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
580Q16—416no—
581SD16—88no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—48no—
594C2×C8C22×D414yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—41no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—82no—
627C4⋊C4—82no—
628C4⋊C4—82no—
629C4⋊C4—82no—
630C4⋊C4—82no—
631C4⋊C4—82no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—82no—
647C22⋊C4—82no—
648C22⋊C4—82no—
649C22⋊C4—82no—
650C22⋊C4—82no—
651C22⋊C4—82no—
652C22⋊C4—82no—
653C42—22no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—22no—
665C42—22no—
666C42—44no—
667C42—44no—
668C42—44no—
669C42—44no—
670C42—82no—
671C42#13514yes—
672C42C22×D412yes—
673C42H(5,𝔽2)12yes—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23C2×#13712yes—
695C23C23×D411yescharacteristic
696Q8—28no—
697Q8—28no—
698Q8—44no—
699Q8—44no—
700Q8—84no—
701Q8—84no—
702Q8—84no—
703D4—44no—
704D4—44no—
705D4—44no—
706D4—88no—
707D4—84no—
708D4—84no—
709D4—164no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—28no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—88no—
767C2×C4D4212yes—
768C2×C4D4212yes—
769C2×C4C2×#13512yes—
770C2×C4C2×#13512yes—
771C2×C4C2×#13512yes—
772C2×C4C2×#13712yes—
773C2×C4C2×#13712yes—
774C2×C4#57612yes—
775C2×C4#57812yes—
776C2×C4C23×D411yescharacteristic
777C2×C4C2×H(5,𝔽2)11yescharacteristic
778C2×C4#58512yes—
779C2×C4#58512yes—
780C8—24no—
781C8—42no—
782C8—42no—
783C8—42no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22#344911yescharacteristic
806C22C2×D4211yescharacteristic
807C22#350011yescharacteristic
808C22C22×#13511yescharacteristic
809C22C22×#13711yescharacteristic
810C22C2×#57611yescharacteristic
811C22C2×#57811yescharacteristic
812C4—22no—
813C4—22no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—44no—
818C4—44no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4#327014yes—
830C4#328714yes—
831C4#348512yes—
832C4#356212yes—
833C2—42no—
834C2—81no—
835C2—162no—
836C2#3768211yescharacteristic
837C2#6094711yescharacteristic
838C2#6101411yescharacteristic
839C2C2×#327011yescharacteristic
840C2C2×#328711yescharacteristic
841C2#6252811yescharacteristic
842C2#6253711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36150C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3210C2semidirect
2. C2×#3170C2semidirect
4. #36134C2semidirect
5. #33042C2semidirect
6. #30602C2semidirect
7. #30409C2semidirect
8. #30276C2semidirect
9. #29876C2semidirect
10. #28717C2semidirect
11. #28614C2semidirect
12. #26169C2semidirect
13. #25857C2semidirect
14. #25674C2semidirect
15. #25674C2semidirect
16. #25598C2semidirect
17. #24904C2semidirect
18. #22270C2semidirect
19. #21101C2semidirect
169. #494D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32102
C2×#31702
#361502
#361342
#330422
#306022
#304092
#302762
#298762
#287172
#286142
#261692
#258572
#256742
#255982
#249042
#222702
#211012