Finite Group Databasebeta

← #6451401

Subgroups — #6451401

Order 512.

1810 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34934C211yesmaximal, characteristic
2C4×#557C211yesmaximal, characteristic, complemented
3#27490C212yesmaximal, complemented
4#27194C212yesmaximal, complemented
5#27066C212yesmaximal, complemented
6#26588C212yesmaximal, complemented
7#26528C211yesmaximal, characteristic, complemented
8#26318C211yesmaximal, characteristic, complemented
9#26088C211yesmaximal, characteristic, complemented
10#25630C211yesmaximal, characteristic, complemented
11#25366C211yesmaximal, characteristic
12#25058C211yesmaximal, characteristic, complemented
13#24628C211yesmaximal, characteristic
14#24187C211yesmaximal, characteristic, complemented
15#23799C212yesmaximal, complemented
16#23677C212yesmaximal, complemented
17C4×#492C211yesmaximal, characteristic, complemented
18C4×#460C211yesmaximal, characteristic, complemented
19C4×#460C212yesmaximal, complemented
20C4×#461C211yesmaximal, characteristic, complemented
21#21339C211yesmaximal, characteristic, complemented
22#21115C212yesmaximal, complemented
23C42×SD16C211yesmaximal, characteristic, complemented
24C2×#557C2211yescharacteristic
25C2×#529—21no—
26C2×#492C2211yescharacteristic
27C2×#460C2212yes—
28C2×#460C2211yescharacteristic
29C2×#461C2211yescharacteristic
30C2×C4×SD16C2211yescharacteristic
31C2×C4×SD16C2211yescharacteristic
32C2×C4×SD16C2211yescharacteristic
33C2×C4×SD16C2212yes—
34C2×C4×SD16C2212yes—
35C2×C4×SD16C2212yes—
36C2×C4×SD16C2212yes—
37#2554—22no—
38#2552C2211yescharacteristic
39#2548C2211yescharacteristic
40#2541C2211yescharacteristic
41#2538C2211yescharacteristic
42#2512C2212yes—
43#2490—21no—
44#2445C2212yes—
45#2426—21no—
46#2392—22no—
47#2370—21no—
48#2370—22no—
49#2365C2211yescharacteristic
50#2365C2212yes—
51#2355C2211yescharacteristic
52#2355C2212yes—
53#2351—21no—
54Q8×C4⋊C4C2211yescharacteristic
55C4×C4⋊Q8C2212yes—
56C4×C4⋊Q8C2211yescharacteristic
57C4×#127C2211yescharacteristic
58C4×#127C2212yes—
59C4×#125—22no—
60C4×#125—21no—
61C4×#121—21no—
62#2293C2212yes—
63C42×Q8—21no—
64C42×Q8C2211yescharacteristic
65C42×Q8C2212yes—
66C42×Q8C2211yescharacteristic
67C42×D4C2211yescharacteristic
68#2096C2212yes—
69#2096C2212yes—
70#2094C2212yes—
71#2094C2212yes—
72#2084C2212yes—
73#2071C2212yes—
74#2066C2212yes—
75#2066C2212yes—
76#2055C2212yes—
77#2055C2212yes—
78#2043C2212yes—
79#2014C2212yes—
80#2014C2212yes—
81#2013C2212yes—
82#2013C2212yes—
83#2013C2212yes—
84#1984C2211yescharacteristic
85#1984C2211yescharacteristic
86#1982C2211yescharacteristic
87#1982C2212yes—
88#1981C2211yescharacteristic
89#1968C2212yes—
90#1968C2212yes—
91#1957C2211yescharacteristic
92#1956C2211yescharacteristic
93#1948C2212yes—
94#1948C2211yescharacteristic
95#1948C2211yescharacteristic
96#1939C2211yescharacteristic
97#1939C2211yescharacteristic
98#1927C2212yes—
99#1926C2212yes—
100#1926C2212yes—
101#1926C2212yes—
102#1926C2212yes—
103#1926C2212yes—
104#1919C2212yes—
105#1919C2212yes—
106#1916C2212yes—
107#1916C2212yes—
108#1880C2212yes—
109#1880C2212yes—
110#1880C2212yes—
111#1880C2212yes—
112#1880C2212yes—
113#1877C2212yes—
114#1865C2212yes—
115#1865C2212yes—
116#1844C2211yescharacteristic
117#1803C2211yescharacteristic
118#1803C2212yes—
119#1802C2211yescharacteristic
120C4×#106C2211yescharacteristic
121C4×#106C2211yescharacteristic
122C4×#106C2211yescharacteristic
123C4×C4⋊C8C2212yes—
124C4×C4⋊C8C2211yescharacteristic
125C4×#103C2211yescharacteristic
126C4×#103C2211yescharacteristic
127C4×#103C2211yescharacteristic
128C4×#103C2212yes—
129C4×#102C2211yescharacteristic
130C4×#102C2211yescharacteristic
131C4×#102C2211yescharacteristic
132C4×#102C2212yes—
133#1744C2212yes—
134C42×C8C2211yescharacteristic
135C22×SD16C2311yescharacteristic
136C22×SD16C2312yes—
137C22×SD16C2312yes—
138C22×SD16C2312yes—
139C22×SD16C2312yes—
140#557—24no—
141#557—24no—
142C2×C4⋊Q8C2312yes—
143C2×C4⋊Q8C2311yescharacteristic
144C2×#127C2311yescharacteristic
145C2×#127C2312yes—
146#529—48no—
147C2×#126—22no—
148C2×#125—21no—
149C2×#125—22no—
150C2×#125—21no—
151C2×#124—21no—
152C2×#123—22no—
153C2×C22⋊Q8—21no—
154C2×#121—21no—
155C2×#121—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8D411yescharacteristic
159C2×C4×Q8D411yescharacteristic
160C2×C4×Q8C2311yescharacteristic
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2312yes—
163C2×C4×Q8C2312yes—
164C2×C4×Q8C2311yescharacteristic
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2311yescharacteristic
167C2×C4×D4—22no—
168C2×C4×D4—21no—
169C2×C4×D4—21no—
170C2×C4×D4—22no—
171C2×C4×D4C2311yescharacteristic
172C2×C4×D4C2312yes—
173C2×C4×D4C2311yescharacteristic
174C2×C4×D4C2311yescharacteristic
175C2×#117—22no—
176C22×C42—21no—
177#492—24no—
178#461—24no—
179#460—24no—
180#460—28no—
181C4×SD16—24no—
182C4×SD16—24no—
183C4×SD16—24no—
184C4×SD16—28no—
185C4×SD16—44no—
186C4×SD16—44no—
187C4×SD16—44no—
188C2×#106C2311yescharacteristic
189C2×#106C2312yes—
190C2×#106C2311yescharacteristic
191C2×#106C2311yescharacteristic
192C2×#106C2312yes—
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2311yescharacteristic
197C2×C4⋊C8C2311yescharacteristic
198C2×C4⋊C8C2312yes—
199C2×#103C2311yescharacteristic
200C2×#103C2312yes—
201C2×#103C2311yescharacteristic
202C2×#103C2311yescharacteristic
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#102C2311yescharacteristic
209C2×#102C2312yes—
210C2×#102C2311yescharacteristic
211C2×#102C2312yes—
212C2×#102C2312yes—
213C2×#102C2312yes—
214C2×#102C2312yes—
215C2×#102C2312yes—
216C2×#102C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219C2×C4×C8C2312yes—
220C2×C4×C8C2311yescharacteristic
221C2×C4×C8C2311yescharacteristic
222C2×C4×C8C2311yescharacteristic
223C2×C4×C8C2311yescharacteristic
224#398—22no—
225#397—22no—
226#396—22no—
227#396—22no—
228#394—22no—
229#394—22no—
230#394—22no—
231#392—22no—
232#391C2312yes—
233#391C2312yes—
234#391C2312yes—
235#390—21no—
236#390—21no—
237#390—22no—
238#390—22no—
239#390—21no—
240#390C2312yes—
241#390C2312yes—
242#390C2312yes—
243#390C2312yes—
244#390C2312yes—
245#389—21no—
246#389—22no—
247#389—21no—
248#389—22no—
249#389—21no—
250#389—21no—
251#389—22no—
252#389—21no—
253#389—22no—
254#389C2312yes—
255#389C2312yes—
256#388—22no—
257#388—22no—
258#388—22no—
259#387—22no—
260#387—22no—
261#387—22no—
262#387—22no—
263#387—22no—
264#387—22no—
265#386—22no—
266#384C2312yes—
267#384C2311yescharacteristic
268#384C2311yescharacteristic
269#384C2312yes—
270#382—21no—
271#382—22no—
272#380—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—22no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—22no—
277C4×C4⋊C4—22no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—22no—
281C4×C4⋊C4—22no—
282C4×C4⋊C4—21no—
283C4×C4⋊C4—21no—
284C4×C4⋊C4—22no—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—22no—
287C4×C4⋊C4D412yes—
288C4×C4⋊C4D411yescharacteristic
289C4×C4⋊C4D411yescharacteristic
290C4×C4⋊C4D412yes—
291C4×C4⋊C4C2312yes—
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2312yes—
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C4⋊C4C2311yescharacteristic
297C4×C4⋊C4C2311yescharacteristic
298C4×C4⋊C4C2311yescharacteristic
299C4×C4⋊C4C2312yes—
300C4×C4⋊C4C2311yescharacteristic
301C4×C22⋊C4—21no—
302C4×C22⋊C4—22no—
303C4×C22⋊C4—21no—
304C4×C22⋊C4—21no—
305C43—22no—
306C43—21no—
307C43C2311yescharacteristic
308C43C2312yes—
309#340C2311yescharacteristic
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2312yes—
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2311yescharacteristic
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2312yes—
323#336C2312yes—
324#336C2312yes—
325#336C2312yes—
326C22×Q8C2×D411yescharacteristic
327C22×Q8C2411yescharacteristic
328C22×Q8C2412yes—
329C22×D4—21no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—21no—
333C22×D4C2412yes—
334C22×D4C2411yescharacteristic
335C23×C4—21no—
336C23×C4—22no—
337C23×C4—21no—
338C23×C4—21no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16—24no—
342C2×SD16—24no—
343C2×SD16—24no—
344C2×SD16—24no—
345C2×SD16—24no—
346C2×SD16—22no—
347C2×SD16—24no—
348C2×SD16—24no—
349C2×SD16—42no—
350C2×SD16—42no—
351C2×SD16—42no—
352C2×SD16—42no—
353C2×SD16—42no—
354C22×C8C2412yes—
355C22×C8C2412yes—
356C22×C8C2411yescharacteristic
357C22×C8C2411yescharacteristic
358C22×C8C2411yescharacteristic
359C22×C8C2411yescharacteristic
360C4⋊Q8—24no—
361C4⋊Q8—24no—
362C4⋊Q8—22no—
363C4⋊Q8#4114yes—
364#127—24no—
365#127—22no—
366#127—22no—
367#127—42no—
368#126—48no—
369#125—216no—
370#125—28no—
371#125—44no—
372#124—44no—
373#123—48no—
374C22⋊Q8—44no—
375#121—44no—
376#121—44no—
377C4×Q8—28no—
378C4×Q8—24no—
379C4×Q8—24no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8—24no—
385C4×Q8—22no—
386C4×Q8—24no—
387C4×Q8—22no—
388C4×Q8—24no—
389C4×Q8—42no—
390C4×Q8—41no—
391C4×Q8—42no—
392C4×Q8—44no—
393C4×Q8SD1618yescomplemented
394C4×Q8#4114yes—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—24no—
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—24no—
402C4×D4—41no—
403C4×D4—44no—
404C4×D4—48no—
405C4×D4—82no—
406C4×D4—84no—
407#117—48no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4C2×D411yescharacteristic
429C2×C4⋊C4C2×D411yescharacteristic
430C2×C4⋊C4C2×D412yes—
431C2×C4⋊C4C2×D412yes—
432C2×C4⋊C4C2×D411yescharacteristic
433C2×C4⋊C4C2×D412yes—
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2412yes—
438C2×C4⋊C4C2411yescharacteristic
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2411yescharacteristic
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C42—22no—
457C2×C42—21no—
458C2×C42—22no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—22no—
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—22no—
470C2×C42—44no—
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D412yes—
474C2×C42C2×D412yes—
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D412yes—
477C2×C42C2×D412yes—
478C2×C42C2×D411yescharacteristic
479C2×C42C2411yescharacteristic
480C2×C42C2412yes—
481C2×C42C2412yes—
482C2×C42C2411yescharacteristic
483C2×C42C2411yescharacteristic
484#106—22no—
485#106—24no—
486#106—22no—
487#106—22no—
488#106—42no—
489#106—42no—
490#106—42no—
491C4⋊C8—24no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494C4⋊C8—42no—
495#103—22no—
496#103—24no—
497#103—22no—
498#103—24no—
499#103—22no—
500#103—42no—
501#103—42no—
502#103—42no—
503#103—42no—
504#102—24no—
505#102—22no—
506#102—22no—
507#102—24no—
508#102—24no—
509#102—42no—
510#102—42no—
511#102—42no—
512#102#4114yes—
513C4×C8—22no—
514C4×C8—22no—
515C4×C8—22no—
516C4×C8—22no—
517C4×C8—24no—
518C4×C8—41no—
519C4×C8#4114yes—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—22no—
524#95—22no—
525#95—21no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—22no—
531#95—22no—
532#95—21no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95C2×D412yes—
537#95C2×D412yes—
538#95C2×D412yes—
539C24—21no—
540C24—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—21no—
553C2×Q8C2×SD1614yes—
554C2×Q8C2×#4114yes—
555C2×Q8C2×#4112yes—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—81no—
576C2×D4—82no—
577C2×D4—82no—
578C2×D4—81no—
579C2×D4C2×#4112yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—44no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—44no—
601C22×C4—81no—
602C22×C4C22×D411yescharacteristic
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D411yescharacteristic
606C22×C4C22×D411yescharacteristic
607C22×C4C22×D411yescharacteristic
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C2511yescharacteristic
613SD16—28no—
614SD16—48no—
615SD16—48no—
616SD16—48no—
617SD16—48no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—21no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8C2×#4112yes—
634C2×C8C2×#4112yes—
635C2×C8C2×#4112yes—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—42no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—42no—
668C4⋊C4—44no—
669C4⋊C4—42no—
670C4⋊C4—81no—
671C4⋊C4—82no—
672C4⋊C4—81no—
673C4⋊C4—82no—
674C4⋊C4C2×SD1614yes—
675C4⋊C4C2×SD1618yes—
676C4⋊C4C2×#4112yes—
677C4⋊C4C2×#4112yes—
678C22⋊C4—42no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—82no—
689C22⋊C4—82no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C42—28no—
693C42—24no—
694C42—22no—
695C42—22no—
696C42—24no—
697C42—21no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—21no—
702C42—22no—
703C42—41no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—44no—
708C42—44no—
709C42—42no—
710C42—44no—
711C42—42no—
712C42—42no—
713C42—42no—
714C42—42no—
715C42—42no—
716C42—81no—
717C42—82no—
718C42C2×SD1614yes—
719C42C2×SD1618yes—
720C42C2×#4112yes—
721C42C2×#4112yes—
722C42C2×#4112yes—
723C42H(5,𝔽2)12yes—
724C23—22no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23C23×D411yescharacteristic
739Q8—28no—
740Q8—22no—
741Q8—22no—
742Q8—24no—
743Q8—24no—
744Q8—42no—
745Q8—42no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—42no—
751D4—41no—
752D4—42no—
753D4—41no—
754D4—42no—
755D4—42no—
756D4—88no—
757D4—84no—
758D4—88no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—84no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—88no—
813C2×C4#52512yes—
814C2×C4#52512yes—
815C2×C4#55012yes—
816C2×C4#55012yes—
817C2×C4C22×SD1612yes—
818C2×C4C22×SD1614yes—
819C2×C4C22×SD1614yes—
820C2×C4C22×SD1612yes—
821C2×C4C22×SD1612yes—
822C2×C4#57512yes—
823C2×C4#57712yes—
824C2×C4C22×#4111yescharacteristic
825C2×C4C22×#4111yescharacteristic
826C2×C4C22×#4111yescharacteristic
827C2×C4C22×#4111yescharacteristic
828C2×C4C2×H(5,𝔽2)11yescharacteristic
829C2×C4#58511yescharacteristic
830C8—22no—
831C8—22no—
832C8—22no—
833C8—41no—
834C8—42no—
835C8—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22C2×#52511yescharacteristic
851C22C2×#55011yescharacteristic
852C22D4×#4111yescharacteristic
853C22C23×SD1611yescharacteristic
854C22C2×#57511yescharacteristic
855C22C2×#57711yescharacteristic
856C22#358411yescharacteristic
857C4—24no—
858C4—22no—
859C4—22no—
860C4—22no—
861C4—24no—
862C4—41no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—44no—
869C4—81no—
870C4—81no—
871C4—82no—
872C4—82no—
873C4—81no—
874C4—81no—
875C4#310314yes—
876C4#339214yes—
877C4#344411yescharacteristic
878C4#346011yescharacteristic
879C4#347511yescharacteristic
880C4#348111yescharacteristic
881C2—82no—
882C2—162no—
883C2#3472711yescharacteristic
884C2C2×#310311yescharacteristic
885C2#6057211yescharacteristic
886C2C2×#339211yescharacteristic
887C2#6140111yescharacteristic
888C2SD16×#4111yescharacteristic
889C2#6144811yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutator, Frattini, cosocleC22×C4C25
socleC23C23×D4
prime radical#2541C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C42×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C4×#557C2semidirect
3. #27490C2semidirect
4. #27194C2semidirect
5. #27066C2semidirect
6. #26588C2semidirect
7. #26528C2semidirect
8. #26318C2semidirect
9. #26088C2semidirect
10. #25630C2semidirect
12. #25058C2semidirect
14. #24187C2semidirect
15. #23799C2semidirect
16. #23677C2semidirect
17. C4×#492C2semidirect
18. C4×#460C2semidirect
19. C4×#460C2semidirect
20. C4×#461C2semidirect
21. #21339C2semidirect
22. #21115C2semidirect
23. C42×SD16C2semidirect
393. C4×Q8SD16semidirect

Maximal subgroups

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

subgroupindex
#349342
C4×#5572
#274902
#271942
#270662
#265882
#265282
#263182
#260882
#256302
#253662
#250582
#246282
#241872
#237992
#236772
C4×#4922
C4×#4602
C4×#4612
#213392
#211152
C42×SD162