Finite Group Databasebeta

← #6815272

Subgroups — #6815272

Order 512.

2060 conjugacy classes of subgroups.

The subgroup lattice has 855 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3227C211yesmaximal, characteristic, complemented
2C2×#3229C211yesmaximal, characteristic, complemented
3#36129C211yesmaximal, characteristic, complemented
4#36122C211yesmaximal, characteristic
5#33239C211yesmaximal, characteristic, complemented
6#31240C214yesmaximal, complemented
7#31189C214yesmaximal, complemented
8#29845C211yesmaximal, characteristic, complemented
9#29843C211yesmaximal, characteristic, complemented
10#28654C211yesmaximal, characteristic, complemented
11#28653C211yesmaximal, characteristic, complemented
12#26788C214yesmaximal, complemented
13#26786C214yesmaximal, complemented
14#25811C211yesmaximal, characteristic, complemented
15#25811C211yesmaximal, characteristic, complemented
16#25598C211yesmaximal, characteristic, complemented
17#25597C211yesmaximal, characteristic, complemented
18C4×#498C211yesmaximal, characteristic, complemented
19#21264C211yesmaximal, characteristic, complemented
20C2×#548—21no—
21C2×#533C2211yescharacteristic
22C2×#532C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25#3229—28no—
26#3227—28no—
27C2×#498C2211yescharacteristic
28C2×#498C2211yescharacteristic
29C2×#498C2211yescharacteristic
30C2×#498C2211yescharacteristic
31C2×#492C2211yescharacteristic
32C2×#487C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#481C2214yes—
37C2×#483C2214yes—
38C2×#475C2214yes—
39C2×#476C2214yes—
40C2×#431C2211yescharacteristic
41C2×#431C2211yescharacteristic
42#2862C2211yescharacteristic
43#2858C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2856C2211yescharacteristic
48#2550—21no—
49#2545—21no—
50#2492C2212yes—
51#2491—21no—
52#2491C2212yes—
53#2452—21no—
54#2452C2212yes—
55#2451C2212yes—
56#2446—21no—
57#2442—21no—
58#2439—21no—
59#2436—21no—
60#2432—21no—
61#2429—21no—
62#2417C2212yes—
63#2416—21no—
64#2416C2212yes—
65#2409—21no—
66#2361—21no—
67#2361C2212yes—
68#2360C2212yes—
69#2352—21no—
70Q8×C22⋊C4—21no—
71C4×C4⋊Q8C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C42×D4C2211yescharacteristic
74#2066C2214yes—
75#2066C2214yes—
76#2065C2214yes—
77#2065C2214yes—
78#2058C2214yes—
79#2058C2214yes—
80#2035C2214yes—
81#2034C2214yes—
82#2000C2214yes—
83#2000C2214yes—
84#1990C2211yescharacteristic
85#1990C2211yescharacteristic
86#1990C2211yescharacteristic
87#1990C2211yescharacteristic
88#1968C2214yes—
89#1968C2214yes—
90#1957C2211yescharacteristic
91#1956C2211yescharacteristic
92#1954C2212yes—
93#1941C2214yes—
94#1939C2212yes—
95#1927C2214yes—
96#1926C2214yes—
97#1923C2212yes—
98#1923C2212yes—
99#1880C2214yes—
100#1877C2214yes—
101#1853C2214yes—
102#1853C2214yes—
103#1844C2211yescharacteristic
104C4×#106C2214yes—
105C4×C4⋊C8C2211yescharacteristic
106C4×C22⋊C8C2211yescharacteristic
107C4×C22⋊C8C2211yescharacteristic
108C42×C8C2211yescharacteristic
109C22×#41—21no—
110C23×Q8—21no—
111C23×Q8—21no—
112C22×SD16C2314yes—
113#548—48no—
114#533—24no—
115#533—42no—
116#532—24no—
117#532—42no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—21no—
121C2×C4⋊Q8—21no—
122C2×C4⋊Q8—21no—
123C2×C4⋊Q8—21no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8—42no—
126C2×C4⋊Q8C2311yescharacteristic
127C2×C4⋊Q8C2311yescharacteristic
128C2×C4⋊Q8C2311yescharacteristic
129C2×C4⋊Q8C2312yes—
130C2×C4⋊Q8C2312yes—
131C2×C4⋊Q8C2311yescharacteristic
132C2×C4⋊Q8C2311yescharacteristic
133C2×#127C2311yescharacteristic
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—22no—
143C2×C22⋊Q8C2312yes—
144C2×C22⋊Q8C2312yes—
145C2×#121—22no—
146C2×#121—21no—
147C2×#121—21no—
148C2×#121—21no—
149C2×#121C2312yes—
150C2×#121C2312yes—
151C2×C4×Q8—21no—
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8C2312yes—
155C2×C4×D4—22no—
156C2×C4×D4—21no—
157C2×C4×D4D411yescharacteristic
158C2×C4×D4D411yescharacteristic
159C2×C4×D4C2312yes—
160C2×C4×D4C2311yescharacteristic
161C2×#117—21no—
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#498—24no—
169#498—24no—
170#498—42no—
171#498D418yescomplemented
172#492—42no—
173#487—24no—
174#487—24no—
175#486—24no—
176#486—24no—
177#483—216no—
178#481—216no—
179#476—216no—
180#475—216no—
181#431—24no—
182#431—24no—
183C2×#106C2314yes—
184C2×#106C2314yes—
185C2×#106C2314yes—
186C2×#106C2314yes—
187C2×#106C2314yes—
188C2×C4⋊C8C2312yes—
189C2×C4⋊C8C2312yes—
190C2×C4⋊C8C2312yes—
191C2×#103C2314yes—
192C2×#103C2314yes—
193C2×#103C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×C22⋊C8C2312yes—
198C2×C22⋊C8C2312yes—
199C2×C22⋊C8C2312yes—
200C2×C22⋊C8C2312yes—
201C2×C4×C8C2311yescharacteristic
202C2×C4×C8C2311yescharacteristic
203C2×C4×C8C2311yescharacteristic
204C2×C4×C8C2312yes—
205C2×C4×C8C2312yes—
206C2×C4×C8C2311yescharacteristic
207#400—22no—
208#398—22no—
209#398—22no—
210#396—22no—
211#396—22no—
212#396—22no—
213#395—22no—
214#394—22no—
215#394—22no—
216#393—22no—
217#393—22no—
218#393—22no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#391—21no—
225#391—22no—
226#391—22no—
227#391C2312yes—
228#391C2312yes—
229#391C2312yes—
230#390—21no—
231#390—21no—
232#390—21no—
233#390—21no—
234#390C2312yes—
235#390C2312yes—
236#390C2312yes—
237#389—21no—
238#389—21no—
239#389—21no—
240#389—21no—
241#389—21no—
242#389—21no—
243#389—22no—
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#389C2312yes—
248#388—22no—
249#388—22no—
250#388—22no—
251#387—22no—
252#387—22no—
253#386—22no—
254#386—22no—
255#386—22no—
256#385—22no—
257#385—22no—
258#385—22no—
259#384C2311yescharacteristic
260#384C2311yescharacteristic
261#382—21no—
262#382—21no—
263#380—21no—
264#380—21no—
265#380—21no—
266#380—21no—
267#380—22no—
268#380C2312yes—
269#380C2312yes—
270C4×C4⋊C4—21no—
271C4×C4⋊C4—21no—
272C4×C4⋊C4D411yescharacteristic
273C4×C4⋊C4D411yescharacteristic
274C4×C4⋊C4C2312yes—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2311yescharacteristic
277C4×C22⋊C4—22no—
278C4×C22⋊C4D411yescharacteristic
279C4×C22⋊C4D411yescharacteristic
280C4×C22⋊C4D411yescharacteristic
281C4×C22⋊C4D411yescharacteristic
282C4×C22⋊C4C2311yescharacteristic
283C4×C22⋊C4C2311yescharacteristic
284C43C2311yescharacteristic
285#340C2314yes—
286#340C2314yes—
287#340C2314yes—
288#340C2314yes—
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—22no—
301C22×Q8—44no—
302C22×Q8—44no—
303C22×Q8—44no—
304C22×Q8—44no—
305C22×Q8—82no—
306C22×Q8—82no—
307C22×Q8C2412yes—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—21no—
311C22×D4—21no—
312C22×D4C2×D411yescharacteristic
313C22×D4C2412yes—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4C2×D411yescharacteristic
318C23×C4C2×D411yescharacteristic
319C23×C4C2×D411yescharacteristic
320C23×C4C2×D411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C2×SD16—28no—
324C2×SD16—44no—
325C2×SD16—44no—
326C22×C8C2412yes—
327C22×C8C2412yes—
328C22×C8C2412yes—
329C22×C8C2412yes—
330C4⋊Q8—24no—
331C4⋊Q8—24no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—42no—
341C4⋊Q8—42no—
342C4⋊Q8—44no—
343C4⋊Q8—44no—
344C4⋊Q8—44no—
345C4⋊Q8—44no—
346C4⋊Q8C2×D414yes—
347C4⋊Q8C2×D414yes—
348#127—22no—
349#127—22no—
350#125—44no—
351#124—44no—
352#124—48no—
353#124—44no—
354#124—82no—
355C22⋊Q8—24no—
356C22⋊Q8—44no—
357C22⋊Q8—42no—
358C22⋊Q8—44no—
359C22⋊Q8—44no—
360C22⋊Q8—48no—
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—42no—
371C4×Q8—44no—
372C4×Q8—44no—
373C4×Q8—82no—
374C4×D4—24no—
375C4×D4—42no—
376C4×D4—44no—
377C4×D4—42no—
378C4×D4—42no—
379C4×D4—48no—
380C4×D4SD1618yescomplemented
381#117—44no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—44no—
408C2×C4⋊C4—44no—
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×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
432C2×C22⋊C4C2×D411yescharacteristic
433C2×C22⋊C4C2×D411yescharacteristic
434C2×C22⋊C4C2×D411yescharacteristic
435C2×C22⋊C4C2×D411yescharacteristic
436C2×C22⋊C4C2×D411yescharacteristic
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C2×D411yescharacteristic
445C2×C42C2×D411yescharacteristic
446C2×C42C2×D411yescharacteristic
447C2×C42C2×D411yescharacteristic
448C2×C42C2×D411yescharacteristic
449C2×C42C2×D411yescharacteristic
450C2×C42C2×D411yescharacteristic
451C2×C42C2×D411yescharacteristic
452C2×C42C2411yescharacteristic
453C2×C42C2411yescharacteristic
454C2×C42C2411yescharacteristic
455C2×C42C2411yescharacteristic
456C2×C42C2411yescharacteristic
457#106—28no—
458#106—28no—
459#106—44no—
460#106—44no—
461#106C2×D4116yes—
462C4⋊C8—24no—
463C4⋊C8—24no—
464C4⋊C8—42no—
465#103—28no—
466#103—28no—
467#103—44no—
468#102—28no—
469#102—28no—
470#102—44no—
471C22⋊C8—24no—
472C22⋊C8—24no—
473C22⋊C8—24no—
474C22⋊C8—24no—
475C4×C8—24no—
476C4×C8—22no—
477C4×C8—22no—
478C4×C8—22no—
479C4×C8—42no—
480C4×C8C2×D414yes—
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#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—24no—
507C2×Q8—22no—
508C2×Q8—22no—
509C2×Q8—24no—
510C2×Q8—24no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—42no—
515C2×Q8—42no—
516C2×Q8—42no—
517C2×Q8—44no—
518C2×Q8—42no—
519C2×Q8—42no—
520C2×Q8—42no—
521C2×Q8—42no—
522C2×Q8—42no—
523C2×Q8—42no—
524C2×Q8—42no—
525C2×Q8—82no—
526C2×Q8—82no—
527C2×Q8—816no—
528C2×Q8—816no—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—42no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—82no—
547C2×D4C2×SD1614yes—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4C2×SD1614yes—
583C22×C4C2×SD1614yes—
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C22×D411yescharacteristic
592C22×C4C22×D411yescharacteristic
593C22×C4C22×D411yescharacteristic
594C22×C4C22×D411yescharacteristic
595C22×C4C22×D411yescharacteristic
596C22×C4C2511yescharacteristic
597SD16—88no—
598C2×C8—22no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—22no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8C22×D414yes—
609C2×C82−1+414yes—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—42no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—82no—
640C4⋊C4—82no—
641C4⋊C4C2×SD1614yes—
642C4⋊C4C22×D414yes—
643C4⋊C4C22×D414yes—
644C22⋊C4—41no—
645C22⋊C4—41no—
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⋊C4C2×SD1614yes—
662C22⋊C4C2×SD1614yes—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—22no—
668C42—22no—
669C42—22no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—21no—
674C42—22no—
675C42—22no—
676C42—44no—
677C42—44no—
678C42—82no—
679C42C2×SD1614yes—
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—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23C22×SD1612yes—
702C23C22×SD1612yes—
703C23C23×D411yescharacteristic
704Q8—48no—
705Q8—48no—
706Q8—44no—
707Q8—44no—
708Q8—88no—
709Q8—88no—
710Q8—84no—
711Q8—84no—
712D4—44no—
713D4—44no—
714D4—44no—
715D4—88no—
716D4—88no—
717D4—84no—
718D4—84no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—24no—
737C2×C4—24no—
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—21no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
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×C4—88no—
777C2×C4D4212yes—
778C2×C4D4212yes—
779C2×C4C22×SD1612yes—
780C2×C4C22×SD1612yes—
781C2×C4C22×SD1612yes—
782C2×C4C22×SD1612yes—
783C2×C4C22×SD1612yes—
784C2×C4#57512yes—
785C2×C4#57712yes—
786C2×C4#57712yes—
787C2×C4C23×D411yescharacteristic
788C2×C4C2×H(5,𝔽2)11yescharacteristic
789C2×C4C2×2−1+412yes—
790C2×C4#58512yes—
791C8—24no—
792C8—24no—
793C8—42no—
794C8—42no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22#344911yescharacteristic
817C22C2×D4211yescharacteristic
818C22#349911yescharacteristic
819C22C23×SD1611yescharacteristic
820C22C2×#57511yescharacteristic
821C22C2×#57711yescharacteristic
822C22C2×#57711yescharacteristic
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—44no—
832C4—44no—
833C4—41no—
834C4—41no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4#327514yes—
841C4D4×SD1614yes—
842C4#349712yes—
843C4#356112yes—
844C2—42no—
845C2—42no—
846C2—162no—
847C2#3935611yescharacteristic
848C2#6094111yescharacteristic
849C2#6101511yescharacteristic
850C2C2×#327511yescharacteristic
851C2C2×D4×SD1611yescharacteristic
852C2#6246911yescharacteristic
853C2#6248311yescharacteristic
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×#3227C2semidirect
2. C2×#3229C2semidirect
3. #36129C2semidirect
5. #33239C2semidirect
6. #31240C2semidirect
7. #31189C2semidirect
8. #29845C2semidirect
9. #29843C2semidirect
10. #28654C2semidirect
11. #28653C2semidirect
12. #26788C2semidirect
13. #26786C2semidirect
14. #25811C2semidirect
15. #25811C2semidirect
16. #25598C2semidirect
17. #25597C2semidirect
18. C4×#498C2semidirect
19. #21264C2semidirect
171. #498D4semidirect
380. C4×D4SD16semidirect

Maximal subgroups

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

subgroupindex
C2×#32272
C2×#32292
#361292
#361222
#332392
#312402
#311892
#298452
#298432
#286542
#286532
#267882
#267862
#258112
#255982
#255972
C4×#4982
#212642