Finite Group Databasebeta

← #6686426

Subgroups — #6686426

Order 512.

2025 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3230C211yesmaximal, characteristic, complemented
2C2×#3182C211yesmaximal, characteristic, complemented
3#36134C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33212C211yesmaximal, characteristic, complemented
6#30692C214yesmaximal, complemented
7#30579C214yesmaximal, complemented
8#30276C211yesmaximal, characteristic, complemented
9#29843C211yesmaximal, characteristic, complemented
10#28689C211yesmaximal, characteristic, complemented
11#28614C211yesmaximal, characteristic, complemented
12#26571C214yesmaximal, complemented
13#26397C214yesmaximal, complemented
14#25813C211yesmaximal, characteristic, complemented
15#25674C211yesmaximal, characteristic, complemented
16#25673C211yesmaximal, characteristic, complemented
17#25598C211yesmaximal, characteristic, complemented
18#22218C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#532C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3230—28no—
26#3182—28no—
27C2×#500C2211yescharacteristic
28C2×#500C2211yescharacteristic
29C2×#500C2211yescharacteristic
30C2×#500C2211yescharacteristic
31C2×#492C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#484C2214yes—
37C2×#477C2214yes—
38C2×#468C2214yes—
39C2×#440C2214yes—
40C2×#431C2211yescharacteristic
41C2×C4×M16C2211yescharacteristic
42#2868C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2552—21no—
49#2545—21no—
50#2542—21no—
51#2538C2212yes—
52#2491—21no—
53#2491C2212yes—
54#2452—21no—
55#2452C2212yes—
56#2441—21no—
57#2441—21no—
58#2436—21no—
59#2432—21no—
60#2429—21no—
61#2429—21no—
62#2423C2212yes—
63#2423C2212yes—
64#2416—21no—
65#2416C2212yes—
66#2365—21no—
67#2361—21no—
68#2361C2212yes—
69#2354—21no—
70Q8×C4⋊C4C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2093C2214yes—
75#2093C2214yes—
76#2083C2214yes—
77#2065C2214yes—
78#2057C2214yes—
79#2055C2214yes—
80#2036C2214yes—
81#2034C2214yes—
82#2033C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1957C2211yescharacteristic
89#1956C2211yescharacteristic
90#1947C2214yes—
91#1944C2214yes—
92#1927C2214yes—
93#1924C2212yes—
94#1917C2212yes—
95#1880C2214yes—
96#1880C2214yes—
97#1870C2212yes—
98#1865C2214yes—
99#1863C2214yes—
100#1862C2214yes—
101#1852C2214yes—
102#1851C2212yes—
103#1844C2211yescharacteristic
104#1809C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108#1744C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C22×SD16C2314yes—
112C22×M16C2312yes—
113#548—48no—
114#533—24no—
115#533—24no—
116#533—42no—
117#533—42no—
118#532—24no—
119#532—42no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—21no—
125C2×C4⋊Q8—42no—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2311yescharacteristic
130C2×C4⋊Q8C2312yes—
131C2×C4⋊Q8C2311yescharacteristic
132C2×#127C2311yescharacteristic
133C2×#125—21no—
134C2×#125—21no—
135C2×#124—22no—
136C2×#124—21no—
137C2×#124—21no—
138C2×#124—21no—
139C2×C22⋊Q8—21no—
140C2×C22⋊Q8—21no—
141C2×C22⋊Q8—21no—
142C2×C22⋊Q8—21no—
143C2×C22⋊Q8—21no—
144C2×C22⋊Q8—22no—
145C2×C22⋊Q8C2312yes—
146C2×C22⋊Q8C2312yes—
147C2×#121—22no—
148C2×#121—21no—
149C2×#121—21no—
150C2×#121—21no—
151C2×#121C2312yes—
152C2×#121C2312yes—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8C2312yes—
157C2×C4×Q8C2312yes—
158C2×C4×Q8C2312yes—
159C2×C4×D4—22no—
160C2×C4×D4—21no—
161C2×C4×D4D411yescharacteristic
162C2×C4×D4D411yescharacteristic
163C2×C4×D4C2312yes—
164C2×C4×D4C2311yescharacteristic
165C2×#117—21no—
166C2×#117—21no—
167C22×C4⋊C4—21no—
168C22×C4⋊C4C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#500—24no—
172#500—24no—
173#500—24no—
174#500—42no—
175#492—24no—
176#487—24no—
177#487D418yescomplemented
178#486—24no—
179#486—42no—
180#484—216no—
181#477—216no—
182#468—216no—
183#440—216no—
184#431—24no—
185C2×#107C2314yes—
186C2×#107C2314yes—
187C2×#107C2314yes—
188C2×#107C2314yes—
189C2×#106C2314yes—
190C2×C4⋊C8C2312yes—
191C2×C4⋊C8C2312yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#103C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C4×M16—24no—
202C2×#97C2312yes—
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2311yescharacteristic
205C2×C4×C8C2311yescharacteristic
206C2×C4×C8C2311yescharacteristic
207#399—22no—
208#399—22no—
209#398—22no—
210#398—22no—
211#396—22no—
212#396—22no—
213#396—22no—
214#396—22no—
215#394—22no—
216#394—22no—
217#393—22no—
218#393—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391C2312yes—
224#390—22no—
225#390—21no—
226#390—21no—
227#390—21no—
228#390—21no—
229#390C2312yes—
230#390C2312yes—
231#390C2312yes—
232#389—22no—
233#389—21no—
234#389—21no—
235#389—21no—
236#389—21no—
237#389—21no—
238#389—21no—
239#389—22no—
240#389—22no—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#388—22no—
246#388—22no—
247#388—22no—
248#388—22no—
249#387—22no—
250#387—22no—
251#386—22no—
252#386—22no—
253#385—22no—
254#385—22no—
255#384—22no—
256#384—21no—
257#384—21no—
258#384C2311yescharacteristic
259#384C2311yescharacteristic
260#384C2312yes—
261#384C2312yes—
262#380—21no—
263#380—21no—
264#380—21no—
265#380C2312yes—
266#380C2312yes—
267#380C2312yes—
268C4×C4⋊C4—22no—
269C4×C4⋊C4—21no—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4D411yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2311yescharacteristic
276C4×C22⋊C4D411yescharacteristic
277C4×C22⋊C4D411yescharacteristic
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4C2311yescharacteristic
281C4×C22⋊C4C2311yescharacteristic
282C43C2311yescharacteristic
283#340C2314yes—
284#340C2314yes—
285#340C2314yes—
286#340C2314yes—
287#336C2312yes—
288#336C2312yes—
289#336C2312yes—
290#336C2312yes—
291#336C2312yes—
292C2×#41—44no—
293C2×#41—44no—
294C2×#41—82no—
295C22×Q8—21no—
296C22×Q8—21no—
297C22×Q8—21no—
298C22×Q8—21no—
299C22×Q8—22no—
300C22×Q8—44no—
301C22×Q8—44no—
302C22×Q8—82no—
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×SD16—28no—
319C2×SD16—28no—
320C2×SD16—44no—
321C2×M16—24no—
322C2×M16—24no—
323C2×M16—42no—
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⋊Q8—44no—
341C4⋊Q8—82no—
342C4⋊Q8C2×D414yes—
343C4⋊Q8C2×D414yes—
344#127—22no—
345#127—22no—
346#125—44no—
347#125—44no—
348#124—44no—
349#124—48no—
350#124—44no—
351#124—82no—
352C22⋊Q8—24no—
353C22⋊Q8—24no—
354C22⋊Q8—42no—
355C22⋊Q8—42no—
356C22⋊Q8—44no—
357C22⋊Q8—44no—
358C22⋊Q8—48no—
359C22⋊Q8—44no—
360C22⋊Q8—82no—
361C22⋊Q8—82no—
362#121—24no—
363#121—44no—
364#121—42no—
365#121—44no—
366#121—44no—
367#121—48no—
368#121—44no—
369C4×Q8—24no—
370C4×Q8—24no—
371C4×Q8—44no—
372C4×Q8—42no—
373C4×Q8—42no—
374C4×Q8—44no—
375C4×Q8—44no—
376C4×Q8—44no—
377C4×D4—24no—
378C4×D4—24no—
379C4×D4—24no—
380C4×D4—42no—
381C4×D4—44no—
382C4×D4—42no—
383C4×D4—48no—
384#117—44no—
385#117—44no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—44no—
414C2×C4⋊C4C2×D411yescharacteristic
415C2×C4⋊C4C2×D411yescharacteristic
416C2×C4⋊C4C2×D411yescharacteristic
417C2×C4⋊C4C2412yes—
418C2×C4⋊C4C2412yes—
419C2×C4⋊C4C2412yes—
420C2×C4⋊C4C2412yes—
421C2×C4⋊C4C2412yes—
422C2×C4⋊C4C2412yes—
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⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4C2×D411yescharacteristic
438C2×C22⋊C4C2×D411yescharacteristic
439C2×C22⋊C4C2×D411yescharacteristic
440C2×C22⋊C4C2×D411yescharacteristic
441C2×C22⋊C4C2×D411yescharacteristic
442C2×C22⋊C4C2×D411yescharacteristic
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42C2×D411yescharacteristic
452C2×C42C2×D411yescharacteristic
453C2×C42C2×D411yescharacteristic
454C2×C42C2×D411yescharacteristic
455C2×C42C2×D411yescharacteristic
456C2×C42C2×D411yescharacteristic
457C2×C42C2×D411yescharacteristic
458C2×C42C2×D411yescharacteristic
459C2×C42C2411yescharacteristic
460C2×C42C2411yescharacteristic
461C2×C42C2411yescharacteristic
462C2×C42C2411yescharacteristic
463C2×C42C2411yescharacteristic
464#107—28no—
465#107—28no—
466#107—28no—
467#107—44no—
468#106—44no—
469C4⋊C8—24no—
470C4⋊C8—24no—
471#103—28no—
472#103—44no—
473#103C2×D4116yes—
474#102—28no—
475#102—44no—
476#102—44no—
477C22⋊C8—24no—
478C22⋊C8—24no—
479C22⋊C8—42no—
480#97—24no—
481C4×C8—22no—
482C4×C8—22no—
483C4×C8—22no—
484C4×C8C2×D414yes—
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#95—22no—
495#95C2×D411yescharacteristic
496#95C2×D411yescharacteristic
497#95C2×D411yescharacteristic
498#95C2×D411yescharacteristic
499#95C2×D411yescharacteristic
500#95C2×D411yescharacteristic
501C24—22no—
502C24C22×D411yescharacteristic
503C24C22×D411yescharacteristic
504#41—816no—
505C2×Q8—24no—
506C2×Q8—22no—
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—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—82no—
523C2×Q8—816no—
524C2×Q8C22×D414yes—
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—41no—
532C2×D4—44no—
533C2×D4—44no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—42no—
538C2×D4—42no—
539C2×D4—42no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—82no—
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—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4#13714yes—
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×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C2511yescharacteristic
590SD16—416no—
591M16—48no—
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×C8—22no—
601C2×C8—22no—
602C2×C8C22×D414yes—
603C2×C82−1+414yes—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—41no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—44no—
631C4⋊C4—42no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—42no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4—82no—
640C4⋊C4—82no—
641C4⋊C4C22×D414yes—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—41no—
647C22⋊C4—41no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—82no—
659C22⋊C4—82no—
660C22⋊C4—82no—
661C22⋊C4—82no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—22no—
674C42—22no—
675C42—44no—
676C42—44no—
677C42—44no—
678C42—44no—
679C42AGL(1,ℤ/8)14yes—
680C42C22×D412yes—
681C42H(5,𝔽2)12yes—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23C2×#13712yes—
703C23C23×D411yescharacteristic
704Q8—28no—
705Q8—48no—
706Q8—44no—
707Q8—88no—
708Q8—84no—
709Q8—84no—
710Q8—84no—
711D4—44no—
712D4—44no—
713D4—44no—
714D4—88no—
715D4—88no—
716D4—84no—
717D4—84no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—28no—
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—24no—
734C2×C4—24no—
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—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
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—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—88no—
775C2×C4—88no—
776C2×C4D4212yes—
777C2×C4D4212yes—
778C2×C4C2×AGL(1,ℤ/8)12yes—
779C2×C4C2×AGL(1,ℤ/8)12yes—
780C2×C4C2×AGL(1,ℤ/8)12yes—
781C2×C4C2×#13712yes—
782C2×C4C2×#13712yes—
783C2×C4#57612yes—
784C2×C4#57812yes—
785C2×C4C23×D411yescharacteristic
786C2×C4C2×H(5,𝔽2)11yescharacteristic
787C2×C4C2×2−1+412yes—
788C2×C4#58512yes—
789C8—24no—
790C8—24no—
791C8—42no—
792C8—42no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22#344911yescharacteristic
815C22C2×D4211yescharacteristic
816C22#349911yescharacteristic
817C22C22×AGL(1,ℤ/8)11yescharacteristic
818C22C22×#13711yescharacteristic
819C22C2×#57611yescharacteristic
820C22C2×#57811yescharacteristic
821C4—22no—
822C4—22no—
823C4—22no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—44no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—44no—
833C4—82no—
834C4—82no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4#327014yes—
839C4#327414yes—
840C4#348912yes—
841C4#355412yes—
842C2—42no—
843C2—81no—
844C2—162no—
845C2#3768011yescharacteristic
846C2#6096911yescharacteristic
847C2#6101411yescharacteristic
848C2C2×#327011yescharacteristic
849C2C2×#327411yescharacteristic
850C2#6247911yescharacteristic
851C2#6248011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
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×#3182C2semidirect
3. #36134C2semidirect
5. #33212C2semidirect
6. #30692C2semidirect
7. #30579C2semidirect
8. #30276C2semidirect
9. #29843C2semidirect
10. #28689C2semidirect
11. #28614C2semidirect
12. #26571C2semidirect
13. #26397C2semidirect
14. #25813C2semidirect
15. #25674C2semidirect
16. #25673C2semidirect
17. #25598C2semidirect
18. #22218C2semidirect
19. #21102C2semidirect
177. #487D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32302
C2×#31822
#361342
#361222
#332122
#306922
#305792
#302762
#298432
#286892
#286142
#265712
#263972
#258132
#256742
#256732
#255982
#222182
#211022