Finite Group Databasebeta

← C2×#24918464 #36275658

Subgroups — C2×#24918464 #36275658

Order 21248.

2242 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128255C211yesmaximal, characteristic, complemented
2C2×#124×D83C211yesmaximal, characteristic
3#24918464C2116yesmaximal, direct product factor
4C2×#19128094C211yesmaximal, characteristic, complemented
5C2×#19128092C211yesmaximal, characteristic, complemented
6C2×#19128062C211yesmaximal, characteristic, complemented
7C2×#19128059C211yesmaximal, characteristic, complemented
8C2×#19127924C211yesmaximal, characteristic, complemented
9C2×#19127923C211yesmaximal, characteristic, complemented
10C2×#19127920C211yesmaximal, characteristic, complemented
11C2×#19127858C211yesmaximal, characteristic, complemented
12C2×#19127855C211yesmaximal, characteristic, complemented
13C2×#19127853C211yesmaximal, characteristic
14C2×#19127850C211yesmaximal, characteristic
15C2×#19127757C211yesmaximal, characteristic, complemented
16C2×#464×C83C211yesmaximal, characteristic, complemented
17C22×Q8×D83C2211yescharacteristic
18C22×D4×D83C2211yescharacteristic
19C22×Dic332C2211yescharacteristic, complemented
20C22×#13050580C2211yescharacteristic, complemented
21C22×#13050580C2211yescharacteristic, complemented
22C22×#13050579C2211yescharacteristic
23C22×#13050578C2211yescharacteristic
24C22×#13050577C2211yescharacteristic
25#19128255—24no—
26#19128255C2218yescomplemented
27C2×#14581791C2211yescharacteristic, complemented
28C2×#14581790C2211yescharacteristic, complemented
29C2×#14581782—21no—
30C2×#14581781C2211yescharacteristic
31C2×#14581780C2211yescharacteristic
32C2×#14581779C2211yescharacteristic
33C2×#14581778—21no—
34C2×#14581778—21no—
35#124×D83—24no—
36#124×D83C2218yes—
37C2×#14581772C2211yescharacteristic
38C2×#14581770—21no—
39C2×#14581768C2211yescharacteristic
40C2×C4×Dic166—21no—
41C2×C4×Dic166C2211yescharacteristic, complemented
42C2×#14581749—21no—
43C2×C22⋊C4×D83—21no—
44C2×C22⋊C4×D83—21no—
45C2×C42×D83C2211yescharacteristic
46#19128094C2218yescomplemented
47#19128092C2218yescomplemented
48#19128062C2218yescomplemented
49#19128059C2218yescomplemented
50#19127924C2218yescomplemented
51#19127923C2218yescomplemented
52#19127920C2218yescomplemented
53#19127858C2218yescomplemented
54#19127855C2218yescomplemented
55#19127853C2218yes—
56#19127850C2218yes—
57#19127757C2218yescomplemented
58C2×C4⋊(C83⋊C8)C2211yescharacteristic, complemented
59C2×#14581717C2211yescharacteristic, complemented
60C2×#14581716C2211yescharacteristic, complemented
61C2×#14581715C2211yescharacteristic, complemented
62C2×#14581714C2211yescharacteristic
63C2×#14581713C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×(C2×D83)⋊C8C2211yescharacteristic
66C2×(C2×D83)⋊C8C2211yescharacteristic
67C2×#14581702C2211yescharacteristic, complemented
68C2×#14581702C2211yescharacteristic, complemented
69C22×Q16×C83C2211yescharacteristic, complemented
70C22×SD16×C83C2211yescharacteristic
71C2×#124×C83C2211yescharacteristic
72C2×C4×Q8×C83C2211yescharacteristic, complemented
73#464×C83C2218yescomplemented
74C2×C4⋊C8×C83C2211yescharacteristic, complemented
75C2×#103×C83C2211yescharacteristic, complemented
76C2×#102×C83C2211yescharacteristic
77C24×D83—21no—
78C22×Dic166—21no—
79C22×Dic166—21no—
80C22×Dic166C2311yescharacteristic
81C22×Dic166C2311yescharacteristic
82C2×Q8×D83—22no—
83C2×Q8×D83—42no—
84C2×Q8×D83—42no—
85C2×Q8×D83C2314yes—
86C22×D332C2311yescharacteristic
87C22×C22⋊D83—21no—
88C2×D4×D83—22no—
89C2×D4×D83—42no—
90C2×D4×D83—42no—
91C2×D4×D83C2314yes—
92C22×C4×D83—21no—
93C22×C4×D83D411yescharacteristic
94C22×C4×D83D411yescharacteristic
95C22×C4×D83C2311yescharacteristic
96C2×Dic332—42no—
97C2×Dic332C2314yescomplemented
98C2×#13050580—42no—
99C2×#13050580—42no—
100C2×#13050580C2314yescomplemented
101C2×#13050580C2314yescomplemented
102C2×#13050579—42no—
103C2×#13050579C2314yes—
104C2×#13050578—42no—
105C2×#13050578C2314yes—
106C2×#13050577—42no—
107C2×#13050577C2314yes—
108C22×C83⋊C8C2311yescharacteristic
109C22×C83⋊C8C2311yescharacteristic
110#14581791—22no—
111#14581791C2314yescomplemented
112#14581790—22no—
113#14581790C2314yescomplemented
114#14581782—28no—
115#14581781—22no—
116#14581781C2314yes—
117#14581780—22no—
118#14581780C2314yes—
119#14581779—22no—
120#14581779C2314yes—
121#14581778—28no—
122#14581778—28no—
123#14581772—22no—
124#14581772C2314yes—
125#14581770—28no—
126#14581768—22no—
127#14581768C2314yes—
128C4×Dic166—28no—
129C4×Dic166—22no—
130C4×Dic166C2314yescomplemented
131#14581749—28no—
132C2×C4⋊Dic83—21no—
133C2×C4⋊Dic83C2311yescharacteristic
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4—21no—
137C2×Dic83⋊C4—21no—
138C2×Dic83⋊C4—21no—
139C2×C22⋊Dic83—21no—
140C2×C22⋊Dic83—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—21no—
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4—21no—
146C2×(C2×D83)⋊C4—21no—
147C22⋊C4×D83—28no—
148C22⋊C4×D83—28no—
149C2×C4×Dic83—21no—
150C2×C4×Dic83D411yescharacteristic
151C2×C4×Dic83D411yescharacteristic
152C2×C4×Dic83C2311yescharacteristic
153C42×D83D414yes—
154C42×D83C2314yes—
155C4⋊(C83⋊C8)C2314yescomplemented
156#14581717C2314yescomplemented
157#14581716C2314yescomplemented
158#14581715C2314yescomplemented
159#14581714C2314yes—
160#14581713C2314yes—
161#14581712C2314yes—
162(C2×D83)⋊C8C2314yes—
163(C2×D83)⋊C8C2314yes—
164#14581702C2314yescomplemented
165#14581702C2314yescomplemented
166C22×Q8×C83C2311yescharacteristic
167C22×Q8×C83C2311yescharacteristic
168C22×D4×C83C2311yescharacteristic
169C2×Q16×C83—42no—
170C2×Q16×C83C2314yescomplemented
171C2×SD16×C83—42no—
172C2×SD16×C83C2314yes—
173C22×C8×C83C2311yescharacteristic
174C22×C8×C83C2311yescharacteristic
175#124×C83—22no—
176#124×C83C2314yes—
177C4×Q8×C83—22no—
178C4×Q8×C83C2314yescomplemented
179C2×C4⋊C4×C83—21no—
180C2×C4⋊C4×C83C2311yescharacteristic
181C2×C22⋊C4×C83—21no—
182C2×C22⋊C4×C83—21no—
183C2×C42×C83—21no—
184C2×C42×C83C2311yescharacteristic
185C4⋊C8×C83C2314yescomplemented
186#103×C83C2314yescomplemented
187#102×C83C2314yes—
188C23×D83—21no—
189C23×D83—24no—
190C23×D83—44no—
191C23×D83—44no—
192C23×D83—44no—
193C23×D83C2×D411yescharacteristic
194C2×Dic166—22no—
195C2×Dic166—22no—
196C2×Dic166—22no—
197C2×Dic166—22no—
198C2×Dic166—21no—
199C2×Dic166—21no—
200C2×Dic166—24no—
201C2×Dic166—24no—
202C2×Dic166—44no—
203C2×Dic166—44no—
204C2×Dic166C2412yes—
205C2×Dic166C2412yes—
206Q8×D83—44no—
207Q8×D83—44no—
208Q8×D83—48no—
209C2×D332—22no—
210C2×D332—22no—
211C2×D332—21no—
212C2×D332C2412yes—
213C2×C22⋊D83—24no—
214C2×C22⋊D83—44no—
215D4×D83—44no—
216D4×D83—44no—
217D4×D83—48no—
218C22×Dic83—21no—
219C22×Dic83—21no—
220C22×Dic83—21no—
221C22×Dic83C2×D411yescharacteristic
222C22×Dic83C2×D411yescharacteristic
223C22×Dic83C2×D411yescharacteristic
224C2×C4×D83—24no—
225C2×C4×D83—22no—
226C2×C4×D83—22no—
227C2×C4×D83—24no—
228C2×C4×D83—42no—
229C2×C4×D83—44no—
230C2×C4×D83C2×D412yes—
231C2×C4×D83C2×D414yes—
232C2×C4×D83C2×D414yes—
233C2×C4×D83C2412yes—
234Dic332—44no—
235#13050580—44no—
236#13050580—44no—
237#13050579—44no—
238#13050578—44no—
239#13050577—44no—
240C2×C83⋊C8—22no—
241C2×C83⋊C8—22no—
242C2×C83⋊C8C2412yes—
243C2×C83⋊C8C2412yes—
244C4⋊Dic83—21no—
245C4⋊Dic83—24no—
246C4⋊Dic83C2412yes—
247Dic83⋊C4—24no—
248Dic83⋊C4—24no—
249Dic83⋊C4—24no—
250Dic83⋊C4—24no—
251Dic83⋊C4—24no—
252C22⋊Dic83—24no—
253C22⋊Dic83—24no—
254(C2×D83)⋊C4—24no—
255(C2×D83)⋊C4—24no—
256(C2×D83)⋊C4—24no—
257(C2×D83)⋊C4—24no—
258(C2×D83)⋊C4—24no—
259(C2×D83)⋊C4—24no—
260C4×Dic83—24no—
261C4×Dic83C2×D414yes—
262C4×Dic83C2×D414yes—
263C4×Dic83C2×D412yes—
264C4×Dic83C2412yes—
265C24×C83—21no—
266C2×Q8×C83—21no—
267C2×Q8×C83—21no—
268C2×Q8×C83—22no—
269C2×Q8×C83—22no—
270C2×Q8×C83—22no—
271C2×Q8×C83—22no—
272C2×Q8×C83C2412yes—
273C2×Q8×C83C2412yes—
274C2×D4×C83—21no—
275C2×D4×C83—22no—
276C2×D4×C83—22no—
277C2×D4×C83C2412yes—
278C22×C4×C83—21no—
279C22×C4×C83—21no—
280C22×C4×C83—21no—
281C22×C4×C83C2×D411yescharacteristic
282C22×C4×C83C2×D411yescharacteristic
283C22×C4×C83C2411yescharacteristic
284Q16×C83—44no—
285SD16×C83—44no—
286C2×C8×C83—22no—
287C2×C8×C83—22no—
288C2×C8×C83C2412yes—
289C2×C8×C83C2412yes—
290C4⋊C4×C83—24no—
291C4⋊C4×C83—21no—
292C4⋊C4×C83C2412yes—
293C22⋊C4×C83—24no—
294C22⋊C4×C83—24no—
295C42×C83—24no—
296C42×C83C2×D412yes—
297C42×C83C2412yes—
298C23×C83—22no—
299C23×C83—42no—
300C23×C83—42no—
301C23×C83—42no—
302C23×C83C22×D411yescharacteristic
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—22no—
306C22×D83—48no—
307C22×D83—48no—
308C22×D83—42no—
309C22×D83—42no—
310C22×D83—42no—
311C22×D83—48no—
312C22×D83—816no—
313C22×D83#13714yes—
314C22×D83C22×D412yes—
315Q8×C83—22no—
316Q8×C83—22no—
317Q8×C83—22no—
318Q8×C83—22no—
319Q8×C83—42no—
320Q8×C83—42no—
321D4×C83—22no—
322D4×C83—22no—
323D4×C83—42no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—42no—
330C2×C4×C83—42no—
331C2×C4×C83—42no—
332C2×C4×C83C22×D412yes—
333C2×C4×C83C22×D412yes—
334C2×C4×C83C22×D411yescharacteristic
335C2×C4×C83H(5,𝔽2)12yes—
336C2×C4×C83H(5,𝔽2)12yes—
337C2×C4×C83C2511yescharacteristic
338C22⋊D83—48no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—42no—
346C2×Dic83—42no—
347C2×Dic83—42no—
348C2×Dic83C22×D412yes—
349C2×Dic83C22×D412yes—
350C2×Dic83C22×D412yes—
351D332—22no—
352D332—22no—
353D332—42no—
354C4×D83—28no—
355C4×D83—24no—
356C4×D83—22no—
357C4×D83—22no—
358C4×D83—44no—
359C4×D83—48no—
360Dic166—22no—
361Dic166—22no—
362Dic166—22no—
363Dic166—22no—
364Dic166—48no—
365Dic166—48no—
366Dic166—42no—
367Dic166—42no—
368C8×C83—22no—
369C8×C83—22no—
370C83⋊C8—22no—
371C83⋊C8—22no—
372C22×C83—42no—
373C22×C83—42no—
374C22×C83—42no—
375C22×C83—84no—
376C22×C83#53512yes—
377C22×C83C2×#13712yes—
378C22×C83#57512yes—
379C22×C83C23×D411yescharacteristic
380C2×D83—22no—
381C2×D83—28no—
382C2×D83—22no—
383C2×D83—42no—
384C2×D83—42no—
385C2×D83—42no—
386C2×D83—816no—
387C2×D83—84no—
388C2×D83C2×#13714yes—
389C4×C83—22no—
390C4×C83—22no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83#53512yes—
395C4×C83C2×H(5,𝔽2)11yescharacteristic
396C4×C83C2×H(5,𝔽2)11yescharacteristic
397Dic83—22no—
398Dic83—22no—
399Dic83—22no—
400Dic83—42no—
401Dic83—42no—
402Dic83—42no—
403C2×#3215—831nomaximal, Sylow
404C2×C83—82no—
405C2×C83#321514yescomplemented
406C2×C83C2×#53511yescharacteristic
407C2×C83C22×#13711yescharacteristic
408C2×C83C2×#57511yescharacteristic
409D83—24no—
410D83—82no—
411C2×#533—831no—
412C22×#124—831no—
413#3215—8316no—
414C2×#497—831no—
415C2×#497—831no—
416C2×#489—831no—
417C2×#489—831no—
418C2×#464—831no—
419C2×#464—831no—
420C2×#464—831no—
421C2×#464D8311yescharacteristic, complemented
422C2×#451—831no—
423C2×#451—831no—
424C2×#450—831no—
425C2×#450—831no—
426C2×#432—831no—
427C83C2×#321511yescharacteristic, complemented, Sylow
428C23×Q8—831no—
429C23×D4—831no—
430C22×Q16—831no—
431C22×Q16—831no—
432C22×Q16—831no—
433C22×Q16C2×D8311yescharacteristic, complemented
434C22×SD16—831no—
435C22×SD16—831no—
436C22×SD16—831no—
437C22×SD16C2×D8311yescharacteristic
438#533—838no—
439#533—1664no—
440C2×C4⋊Q8—831no—
441C2×C4⋊Q8—831no—
442C2×#125—1661no—
443C2×#124—831no—
444C2×#124—831no—
445C2×#124—838no—
446C2×#124—831no—
447C2×#124—1661no—
448C2×#124—1661no—
449C2×#124—1664no—
450C2×#124C2×D8311yescharacteristic
451C2×C22⋊Q8—831no—
452C2×C22⋊Q8—831no—
453C2×C22⋊Q8—1661no—
454C2×C4×Q8—831no—
455C2×C4×Q8—1661no—
456C2×C4×Q8C2×D8311yescharacteristic, complemented
457C2×#117—1661no—
458C22×C22⋊C4—1661no—
459C22×C22⋊C4—1661no—
460C22×C42—831no—
461#497—838no—
462#497—838no—
463#489—838no—
464#489—838no—
465#464—838no—
466#464—838no—
467#464—838no—
468#464C2×D8318yescomplemented
469#451—838no—
470#451—838no—
471#450—838no—
472#450—838no—
473#432—838no—
474C2×C4⋊C8—831no—
475C2×C4⋊C8C2×D8311yescharacteristic, complemented
476C2×#103—831no—
477C2×#103—831no—
478C2×#103—831no—
479C2×#103C2×D8311yescharacteristic, complemented
480C2×#102—831no—
481C2×#102—831no—
482C2×#102—831no—
483C2×#102C2×D8311yescharacteristic
484C2×C22⋊C8—831no—
485C2×C22⋊C8—831no—
486C2×#97—831no—
487C2×#97—831no—
488C25—1661no—
489C22×Q8—3322no—
490C22×Q8—3322no—
491C22×Q8—834no—
492C22×Q8—831no—
493C22×Q8—831no—
494C22×Q8—1661no—
495C22×Q8—1661no—
496C22×Q8—1662no—
497C22×Q8C22×D8311yescharacteristic
498C22×Q8C22×D8311yescharacteristic
499C22×D4—3322no—
500C22×D4—3322no—
501C22×D4—834no—
502C22×D4—831no—
503C22×D4—1662no—
504C22×D4—1661no—
505C22×D4C22×D8311yescharacteristic
506C23×C4—831no—
507C23×C4—831no—
508C23×C4—831no—
509C23×C4—1661no—
510C2×Q16—42no—
511C2×Q16—3322no—
512C2×Q16—3322no—
513C2×Q16—3322no—
514C2×Q16—834no—
515C2×Q16—834no—
516C2×Q16—834no—
517C2×Q16C22×D8314yescomplemented
518C2×SD16—42no—
519C2×SD16—3322no—
520C2×SD16—3322no—
521C2×SD16—3322no—
522C2×SD16—834no—
523C2×SD16—834no—
524C2×SD16—834no—
525C2×SD16C22×D8314yes—
526C22×C8—831no—
527C22×C8—831no—
528C22×C8C22×D8311yescharacteristic
529C22×C8C22×D8311yescharacteristic
530C4⋊Q8—834no—
531C4⋊Q8—834no—
532C4⋊Q8—1662no—
533C4⋊Q8—1662no—
534#125—1668no—
535#124—22no—
536#124—834no—
537#124—834no—
538#124—834no—
539#124—1668no—
540#124—1668no—
541#124—1662no—
542#124—1662no—
543#124—1662no—
544#124C22×D8314yes—
545C22⋊Q8—834no—
546C22⋊Q8—834no—
547C22⋊Q8—1668no—
548C22⋊Q8—1662no—
549C22⋊Q8—1662no—
550C4×Q8—22no—
551C4×Q8—834no—
552C4×Q8—1668no—
553C4×Q8—1662no—
554C4×Q8C22×D8314yescomplemented
555#117—1668no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—831no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4—1661no—
560C2×C4⋊C4—1661no—
561C2×C4⋊C4—1661no—
562C2×C4⋊C4—1661no—
563C2×C4⋊C4—1661no—
564C2×C4⋊C4C22×D8311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—1668no—
568C2×C22⋊C4—1668no—
569C2×C22⋊C4—1661no—
570C2×C22⋊C4—1661no—
571C2×C22⋊C4—1661no—
572C2×C22⋊C4—1661no—
573C2×C22⋊C4—1661no—
574C2×C22⋊C4—1661no—
575C2×C22⋊C4—1661no—
576C2×C22⋊C4—1661no—
577C2×C42—21no—
578C2×C42—831no—
579C2×C42—831no—
580C2×C42—831no—
581C2×C42—834no—
582C2×C42—834no—
583C2×C42—1661no—
584C2×C42C22×D8311yescharacteristic
585C4⋊C8—834no—
586C4⋊C8C22×D8314yescomplemented
587#103—834no—
588#103—834no—
589#103—834no—
590#103C22×D8314yescomplemented
591#102—834no—
592#102—834no—
593#102—834no—
594#102C22×D8314yes—
595C22⋊C8—834no—
596C22⋊C8—834no—
597#97—834no—
598#97—834no—
599C24—21no—
600C24—3324no—
601C24—3324no—
602C24—3324no—
603C24—831no—
604C24—1664no—
605C24—1661no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—22no—
609C2×Q8—22no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—3324no—
613C2×Q8—3324no—
614C2×Q8—3324no—
615C2×Q8—3324no—
616C2×Q8—3328no—
617C2×Q8—832no—
618C2×Q8—832no—
619C2×Q8—1664no—
620C2×Q8—1664no—
621C2×Q8—1662no—
622C2×Q8—1662no—
623C2×Q8—1662no—
624C2×Q8—1662no—
625C2×Q8—1661no—
626C2×Q8—1661no—
627C2×Q8C23×D8312yes—
628C2×Q8C23×D8312yes—
629C2×D4—21no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—3324no—
633C2×D4—3324no—
634C2×D4—3328no—
635C2×D4—3324no—
636C2×D4—832no—
637C2×D4—1664no—
638C2×D4—1661no—
639C2×D4—1662no—
640C2×D4—1662no—
641C2×D4C23×D8312yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—3322no—
646C22×C4—3324no—
647C22×C4—834no—
648C22×C4—831no—
649C22×C4—831no—
650C22×C4—831no—
651C22×C4—834no—
652C22×C4—832no—
653C22×C4—832no—
654C22×C4—1664no—
655C22×C4—1664no—
656C22×C4—1661no—
657C22×C4—1661no—
658C22×C4—1661no—
659C22×C4—1662no—
660C22×C4—1662no—
661C22×C4D4×D8311yescharacteristic
662C22×C4D4×D8311yescharacteristic
663C22×C4C23×D8311yescharacteristic
664Q16—44no—
665Q16—3324no—
666Q16—3324no—
667Q16—3324no—
668SD16—44no—
669SD16—3324no—
670SD16—3324no—
671SD16—3324no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—832no—
675C2×C8—832no—
676C2×C8—1662no—
677C2×C8—1662no—
678C2×C8C23×D8312yes—
679C2×C8C23×D8312yes—
680C4⋊C4—24no—
681C4⋊C4—21no—
682C4⋊C4—832no—
683C4⋊C4—1664no—
684C4⋊C4—1664no—
685C4⋊C4—1664no—
686C4⋊C4—1664no—
687C4⋊C4—1664no—
688C4⋊C4—1661no—
689C4⋊C4—1664no—
690C4⋊C4C23×D8312yes—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—1664no—
694C22⋊C4—1664no—
695C22⋊C4—1664no—
696C22⋊C4—1664no—
697C22⋊C4—1664no—
698C22⋊C4—1664no—
699C22⋊C4—1664no—
700C22⋊C4—1664no—
701C42—24no—
702C42—834no—
703C42—834no—
704C42—832no—
705C42—832no—
706C42—1664no—
707C42D4×D8312yes—
708C42C23×D8312yes—
709C23—22no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—3328no—
714C23—3328no—
715C23—3328no—
716C23—3322no—
717C23—3322no—
718C23—3322no—
719C23—834no—
720C23—832no—
721C23—66416no—
722C23—1662no—
723C23—1662no—
724C23—1662no—
725C23C2×D4×D8311yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—22no—
729Q8—22no—
730Q8—42no—
731Q8—42no—
732Q8—3328no—
733Q8—3328no—
734Q8—3322no—
735Q8—3322no—
736Q8—1662no—
737Q8—1662no—
738Q8—1662no—
739Q8—1662no—
740D4—22no—
741D4—22no—
742D4—42no—
743D4—3328no—
744D4—3322no—
745D4—1662no—
746D4—1662no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—3324no—
756C2×C4—3328no—
757C2×C4—3322no—
758C2×C4—3322no—
759C2×C4—3322no—
760C2×C4—832no—
761C2×C4—832no—
762C2×C4—832no—
763C2×C4—1668no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4—1664no—
771C2×C4—1662no—
772C2×C4—1662no—
773C2×C4C2×D4×D8312yes—
774C2×C4C2×D4×D8312yes—
775C2×C4C2×D4×D8311yescharacteristic
776C2×C4#1458183712yes—
777C2×C4#1458183812yes—
778C2×C4C24×D8311yescharacteristic
779C8—22no—
780C8—22no—
781C8—1662no—
782C8—1662no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—84no—
787C22—3322no—
788C22—3322no—
789C22—3322no—
790C22—834no—
791C22—66416no—
792C22—6644no—
793C22—1662no—
794C22—1668no—
795C22—1662no—
796C22#1912826712yes—
797C22#137×D8312yes—
798C22#1912849812yes—
799C22C22×D4×D8311yescharacteristic
800C4—22no—
801C4—22no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—3322no—
806C4—3322no—
807C4—3322no—
808C4—1662no—
809C4—1662no—
810C4—1662no—
811C4#1912826712yes—
812C4C2×#1458183711yescharacteristic
813C4C2×#1458183811yescharacteristic
814C2—82no—
815C2—6642no—
816C2—1664no—
817C2#2491846414yesdirect product factor
818C2C2×#1912826711yescharacteristic
819C2C2×#137×D8311yescharacteristic
820C2C2×#1912849811yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#464×C83C2
socleC23×C83C22×D4
prime radicalC22×D4×D83C22
hypercenterC2×#464D83
hypocenterC83C2×#3215
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C2×#19128255C2semidirect
3. #24918464C2direct (N × H)
4. C2×#19128094C2semidirect
5. C2×#19128092C2semidirect
6. C2×#19128062C2semidirect
7. C2×#19128059C2semidirect
8. C2×#19127924C2semidirect
9. C2×#19127923C2semidirect
10. C2×#19127920C2semidirect
11. C2×#19127858C2semidirect
12. C2×#19127855C2semidirect
15. C2×#19127757C2semidirect
16. C2×#464×C83C2semidirect
19. C22×Dic332C22semidirect
20. C22×#13050580C22semidirect
21. C22×#13050580C22semidirect
26. #19128255C22semidirect
27. C2×#14581791C22semidirect
28. C2×#14581790C22semidirect
41. C2×C4×Dic166C22semidirect
46. #19128094C22semidirect
47. #19128092C22semidirect
48. #19128062C22semidirect
49. #19128059C22semidirect
50. #19127924C22semidirect
51. #19127923C22semidirect
52. #19127920C22semidirect
53. #19127858C22semidirect
54. #19127855C22semidirect
57. #19127757C22semidirect
58. C2×C4⋊(C83⋊C8)C22semidirect
59. C2×#14581717C22semidirect
60. C2×#14581716C22semidirect
61. C2×#14581715C22semidirect
67. C2×#14581702C22semidirect
68. C2×#14581702C22semidirect
69. C22×Q16×C83C22semidirect
72. C2×C4×Q8×C83C22semidirect
73. #464×C83C22semidirect
74. C2×C4⋊C8×C83C22semidirect
75. C2×#103×C83C22semidirect
97. C2×Dic332C23semidirect
100. C2×#13050580C23semidirect
101. C2×#13050580C23semidirect
111. #14581791C23semidirect
113. #14581790C23semidirect
130. C4×Dic166C23semidirect
155. C4⋊(C83⋊C8)C23semidirect
156. #14581717C23semidirect
157. #14581716C23semidirect
158. #14581715C23semidirect
164. #14581702C23semidirect
165. #14581702C23semidirect
170. C2×Q16×C83C23semidirect
178. C4×Q8×C83C23semidirect
185. C4⋊C8×C83C23semidirect
186. #103×C83C23semidirect
405. C2×C83#3215semidirect
421. C2×#464D83semidirect
427. C83C2×#3215semidirect
433. C22×Q16C2×D83semidirect
456. C2×C4×Q8C2×D83semidirect
468. #464C2×D83semidirect
475. C2×C4⋊C8C2×D83semidirect
479. C2×#103C2×D83semidirect
517. C2×Q16C22×D83semidirect
554. C4×Q8C22×D83semidirect
586. C4⋊C8C22×D83semidirect
590. #103C22×D83semidirect
817. C2#24918464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282552
C2×#124×D832
#249184642
C2×#191280942
C2×#191280922
C2×#191280622
C2×#191280592
C2×#191279242
C2×#191279232
C2×#191279202
C2×#191278582
C2×#191278552
C2×#191278532
C2×#191278502
C2×#191277572
C2×#464×C832
C2×#321583