Finite Group Databasebeta

← #6815596

Subgroups — #6815596

Order 512.

1927 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3230C211yesmaximal, characteristic, complemented
2C2×#3210C211yesmaximal, characteristic, complemented
3#36150C211yesmaximal, characteristic
4#36129C211yesmaximal, characteristic, complemented
5#33252C211yesmaximal, characteristic, complemented
6#31169C214yesmaximal, complemented
7#31041C214yesmaximal, complemented
8#29876C211yesmaximal, characteristic, complemented
9#29807C211yesmaximal, characteristic, complemented
10#28655C211yesmaximal, characteristic, complemented
11#28616C211yesmaximal, characteristic, complemented
12#27252C214yesmaximal, complemented
13#26948C214yesmaximal, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25857C211yesmaximal, characteristic, complemented
16#25674C211yesmaximal, characteristic, complemented
17#25600C211yesmaximal, characteristic, complemented
18#21647C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24#3230—28no—
25#3210—28no—
26C2×#500C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#494C2211yescharacteristic
29C2×#492C2211yescharacteristic
30C2×#487C2211yescharacteristic
31C2×#487C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#484C2214yes—
36C2×#477C2214yes—
37C2×#464C2214yes—
38C2×#452C2214yes—
39C2×#431C2211yescharacteristic
40C2×#431C2211yescharacteristic
41#2862C2211yescharacteristic
42#2858C2211yescharacteristic
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2856C2211yescharacteristic
47#2550—21no—
48#2540—21no—
49#2492C2212yes—
50#2490—21no—
51#2454—21no—
52#2451C2212yes—
53#2448C2212yes—
54#2446—21no—
55#2442—21no—
56#2439—21no—
57#2429—21no—
58#2427—21no—
59#2426—21no—
60#2426C2212yes—
61#2417C2212yes—
62#2414—21no—
63#2409—21no—
64#2407C2212yes—
65#2367—21no—
66#2363—21no—
67#2360C2212yes—
68#2352—21no—
69#2341C2212yes—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2086C2214yes—
75#2075C2214yes—
76#2067C2214yes—
77#2056C2214yes—
78#2055C2214yes—
79#2042C2214yes—
80#2036C2214yes—
81#2023C2214yes—
82#2001C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1973C2214yes—
88#1973C2214yes—
89#1957C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1955C2212yes—
93#1940C2212yes—
94#1935C2214yes—
95#1925C2214yes—
96#1924C2212yes—
97#1924C2212yes—
98#1878C2214yes—
99#1878C2214yes—
100#1874C2214yes—
101#1863C2214yes—
102#1834C2211yescharacteristic
103#1788C2214yes—
104C4×C4⋊C8C2211yescharacteristic
105#1763C2214yes—
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C4×#97C2211yescharacteristic
109C22×#41C2312yes—
110C23×Q8—21no—
111C22×Q16C2314yes—
112C22×SD16C2314yes—
113#533—24no—
114#533—24no—
115#533—42no—
116#533—42no—
117#532—24no—
118#532—42no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8C2311yescharacteristic
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2311yescharacteristic
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2312yes—
128C2×C4⋊Q8C2311yescharacteristic
129C2×#127C2311yescharacteristic
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⋊Q8C2312yes—
140C2×C22⋊Q8C2312yes—
141C2×C22⋊Q8C2312yes—
142C2×#121—21no—
143C2×#121—21no—
144C2×#121—21no—
145C2×#121—21no—
146C2×#121C2312yes—
147C2×C4×Q8—21no—
148C2×C4×Q8—21no—
149C2×C4×Q8—21no—
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2312yes—
153C2×C4×D4—21no—
154C2×C4×D4—21no—
155C2×C4×D4D411yescharacteristic
156C2×C4×D4D411yescharacteristic
157C2×C4×D4C2311yescharacteristic
158C2×#117—21no—
159C2×#117—21no—
160C22×C4⋊C4—21no—
161C22×C4⋊C4C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164#500—24no—
165#500—24no—
166#494—24no—
167#492—24no—
168#487—24no—
169#487—42no—
170#487D418yescomplemented
171#486—24no—
172#486—42no—
173#484—216no—
174#477—216no—
175#464—216no—
176#452—216no—
177#431—24no—
178#431—24no—
179C2×#107C2314yes—
180C2×#107C2314yes—
181C2×C4⋊C8C2312yes—
182C2×C4⋊C8C2312yes—
183C2×C4⋊C8C2312yes—
184C2×#103C2314yes—
185C2×#103C2314yes—
186C2×#103C2314yes—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#102C2314yes—
190C2×#102C2314yes—
191C2×#102C2314yes—
192C2×C22⋊C8C2312yes—
193C2×C22⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×#97C2312yes—
197C2×#97C2312yes—
198C2×C4×C8C2311yescharacteristic
199C2×C4×C8C2311yescharacteristic
200C2×C4×C8C2311yescharacteristic
201C2×C4×C8C2311yescharacteristic
202#400—22no—
203#399—22no—
204#398—22no—
205#398—22no—
206#397—22no—
207#396—22no—
208#396—22no—
209#395—22no—
210#394—22no—
211#394—22no—
212#393—22no—
213#392—22no—
214#391—21no—
215#391—21no—
216#391—21no—
217#391—21no—
218#391—21no—
219#391—22no—
220#391—22no—
221#391C2312yes—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#390—22no—
226#390—22no—
227#390—22no—
228#390—21no—
229#390—21no—
230#390—21no—
231#390—21no—
232#390C2312yes—
233#390C2312yes—
234#390C2312yes—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—22no—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#388—22no—
247#388—22no—
248#388—22no—
249#388—22no—
250#387—22no—
251#387—22no—
252#386—22no—
253#386—22no—
254#385—22no—
255#385—22no—
256#384C2311yescharacteristic
257#384C2311yescharacteristic
258#382—21no—
259#382—21no—
260#380—21no—
261#380—21no—
262#380—21no—
263#380—21no—
264#380—22no—
265#380—22no—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—21no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C22⋊C4—22no—
276C4×C22⋊C4—22no—
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C43C2311yescharacteristic
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
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×Q8—22no—
299C22×Q8—44no—
300C22×Q8—44no—
301C22×Q8—82no—
302C22×Q8C2412yes—
303C22×Q8C2412yes—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4C2×D411yescharacteristic
309C22×D4C2412yes—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2×D411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×Q16—28no—
319C2×Q16—44no—
320C2×Q16—44no—
321C2×SD16—28no—
322C2×SD16—44no—
323C2×SD16—44no—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C4⋊Q8—24no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—42no—
338C4⋊Q8—44no—
339C4⋊Q8—44no—
340C4⋊Q8C2×D414yes—
341C4⋊Q8C2×D414yes—
342#127—22no—
343#127—22no—
344#125—44no—
345#125—44no—
346#124—24no—
347#124—42no—
348#124—44no—
349#124—82no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352C22⋊Q8—44no—
353C22⋊Q8—42no—
354C22⋊Q8—42no—
355C22⋊Q8—44no—
356C22⋊Q8—44no—
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—42no—
367C4×Q8—42no—
368C4×Q8—44no—
369C4×Q8—44no—
370C4×Q8—44no—
371C4×Q8—82no—
372C4×D4—24no—
373C4×D4—44no—
374C4×D4—44no—
375C4×D4—42no—
376C4×D4—42no—
377#117—44no—
378#117—44no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
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—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4C2×D411yescharacteristic
405C2×C4⋊C4C2×D411yescharacteristic
406C2×C4⋊C4C2×D411yescharacteristic
407C2×C4⋊C4C2412yes—
408C2×C4⋊C4C2412yes—
409C2×C4⋊C4C2412yes—
410C2×C4⋊C4C2412yes—
411C2×C4⋊C4C2412yes—
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⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
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×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42C2×D411yescharacteristic
441C2×C42C2×D411yescharacteristic
442C2×C42C2×D411yescharacteristic
443C2×C42C2×D411yescharacteristic
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2411yescharacteristic
449C2×C42C2411yescharacteristic
450C2×C42C2411yescharacteristic
451C2×C42C2411yescharacteristic
452C2×C42C2411yescharacteristic
453#107—28no—
454#107—28no—
455C4⋊C8—24no—
456C4⋊C8—24no—
457C4⋊C8—42no—
458#103—28no—
459#103—44no—
460#103—44no—
461#103—44no—
462#103C2×D4116yes—
463#102—28no—
464#102—44no—
465#102—44no—
466C22⋊C8—24no—
467C22⋊C8—24no—
468C22⋊C8—42no—
469C22⋊C8—42no—
470#97—42no—
471#97—42no—
472C4×C8—22no—
473C4×C8—22no—
474C4×C8—22no—
475C4×C8C2×D414yes—
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#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—24no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—24no—
506C2×Q8—24no—
507C2×Q8—24no—
508C2×Q8—24no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—42no—
512C2×Q8—42no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—42no—
518C2×Q8—42no—
519C2×Q8—82no—
520C2×Q8—816no—
521C2×Q8C22×D414yes—
522C2×D4—22no—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—24no—
526C2×D4—24no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4—42no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—82no—
539C2×D4—82no—
540C2×D4—82no—
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—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—82no—
572C22×C4—82no—
573C22×C4#13714yes—
574C22×C4C22×D411yescharacteristic
575C22×C4C22×D411yescharacteristic
576C22×C4C22×D411yescharacteristic
577C22×C4C22×D411yescharacteristic
578C22×C4C22×D411yescharacteristic
579C22×C4C22×D411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C2511yescharacteristic
587Q16—88no—
588SD16—88no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—22no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8C22×D414yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—82no—
630C4⋊C4—82no—
631C4⋊C4—82no—
632C4⋊C4—82no—
633C4⋊C4C22×D414yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—41no—
638C22⋊C4—41no—
639C22⋊C4—41no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—82no—
649C22⋊C4—82no—
650C22⋊C4—82no—
651C22⋊C4—82no—
652C22⋊C4—82no—
653C22⋊C4—82no—
654C42—22no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—22no—
667C42—22no—
668C42—44no—
669C42—44no—
670C42—82no—
671C42—82no—
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—48no—
698Q8—44no—
699Q8—44no—
700Q8—44no—
701Q8—88no—
702Q8—84no—
703Q8—84no—
704D4—44no—
705D4—44no—
706D4—44no—
707D4—88no—
708D4—84no—
709D4—84no—
710D4—164no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—28no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—21no—
726C2×C4—21no—
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—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
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—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—88no—
770C2×C4—88no—
771C2×C4D4212yes—
772C2×C4D4212yes—
773C2×C4C2×#13712yes—
774C2×C4C2×#13712yes—
775C2×C4#57512yes—
776C2×C4#57612yes—
777C2×C4#57812yes—
778C2×C4C23×D411yescharacteristic
779C2×C4C2×H(5,𝔽2)11yescharacteristic
780C2×C4#58512yes—
781C2×C4#58512yes—
782C8—24no—
783C8—42no—
784C8—42no—
785C8—42no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—82no—
807C22#344911yescharacteristic
808C22C2×D4211yescharacteristic
809C22#350011yescharacteristic
810C22C22×#13711yescharacteristic
811C22C2×#57511yescharacteristic
812C22C2×#57611yescharacteristic
813C22C2×#57811yescharacteristic
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—44no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—44no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#326814yes—
832C4#327014yes—
833C4#350012yes—
834C4#356212yes—
835C2—42no—
836C2—81no—
837C2—162no—
838C2#3935711yescharacteristic
839C2#6096611yescharacteristic
840C2#6101411yescharacteristic
841C2C2×#326811yescharacteristic
842C2C2×#327011yescharacteristic
843C2#6253711yescharacteristic
844C2#6254511yescharacteristic
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×#3230C2semidirect
2. C2×#3210C2semidirect
4. #36129C2semidirect
5. #33252C2semidirect
6. #31169C2semidirect
7. #31041C2semidirect
8. #29876C2semidirect
9. #29807C2semidirect
10. #28655C2semidirect
11. #28616C2semidirect
12. #27252C2semidirect
13. #26948C2semidirect
14. #25903C2semidirect
15. #25857C2semidirect
16. #25674C2semidirect
17. #25600C2semidirect
18. #21647C2semidirect
19. #21265C2semidirect
170. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#32102
#361502
#361292
#332522
#311692
#310412
#298762
#298072
#286552
#286162
#272522
#269482
#259032
#258572
#256742
#256002
#216472
#212652