Finite Group Databasebeta

← C2×#24919680 #36281218

Subgroups — C2×#24919680 #36281218

Order 21248.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128386C211yesmaximal, characteristic, complemented
2C2×#19128339C211yesmaximal, characteristic
3#24919680C2116yesmaximal, direct product factor
4C2×#19128057C211yesmaximal, characteristic, complemented
5C2×#19128019C211yesmaximal, characteristic, complemented
6C2×#19128041C211yesmaximal, characteristic, complemented
7C2×#19127999C211yesmaximal, characteristic, complemented
8C2×#19127958C211yesmaximal, characteristic, complemented
9C2×#19127947C211yesmaximal, characteristic, complemented
10C2×#19127926C211yesmaximal, characteristic, complemented
11C2×#19127863C211yesmaximal, characteristic, complemented
12C2×#19127853C211yesmaximal, characteristic, complemented
13C2×#19127792C211yesmaximal, characteristic, complemented
14C2×#19127777C211yesmaximal, characteristic, complemented
15C2×#19127704C211yesmaximal, characteristic, complemented
16C2×#417×C83C211yesmaximal, characteristic, complemented
17C22×D4×D83C2211yescharacteristic
18C22×#13050580C2211yescharacteristic, complemented
19C22×#13050579C2211yescharacteristic
20C22×#13050578C2211yescharacteristic
21C22×#13050573C2211yescharacteristic
22#19128386—24no—
23#19128386C2218yescomplemented
24#19128339—24no—
25#19128339C2218yes—
26C2×#14581787—21no—
27C2×#14581783C2211yescharacteristic, complemented
28C2×#14581782—21no—
29C2×#14581781C2211yescharacteristic
30C2×#14581775—21no—
31C2×#14581775—21no—
32C2×#14581772C2211yescharacteristic
33C2×#14581771C2211yescharacteristic, complemented
34C2×#14581768C2211yescharacteristic
35C2×#14581766C2211yescharacteristic
36C2×#14581764—21no—
37C2×#14581760—21no—
38C2×#14581757C2211yescharacteristic, complemented
39C2×D4×Dic83C2211yescharacteristic
40C2×C4×C22⋊D83C2211yescharacteristic
41C2×#14581751—21no—
42C2×#14581750C2211yescharacteristic
43C22×(C2×D83)⋊C4—21no—
44#19128057C2218yescomplemented
45#19128041C2218yescomplemented
46#19128019C2218yescomplemented
47#19127999C2218yescomplemented
48#19127958C2218yescomplemented
49#19127947C2218yescomplemented
50#19127926C2218yescomplemented
51#19127863C2218yescomplemented
52#19127853C2218yescomplemented
53#19127792C2218yescomplemented
54#19127777C2218yescomplemented
55C2×#14581726C2211yescharacteristic, complemented
56C2×#14581723C2211yescharacteristic, complemented
57C2×#14581723C2211yescharacteristic, complemented
58C2×Dic83⋊C8C2211yescharacteristic, complemented
59#19127704C2218yescomplemented
60C2×#14581717C2211yescharacteristic, complemented
61C2×#14581716C2211yescharacteristic, complemented
62C2×#14581714C2211yescharacteristic
63C2×#14581713C2211yescharacteristic
64C2×#14581712C2211yescharacteristic
65C2×#14581712C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic, complemented
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic, complemented
69C22×#41×C83C2211yescharacteristic
70C22×M16×C83C2211yescharacteristic, complemented
71C22×C4⋊C4×C83C2211yescharacteristic, complemented
72#417×C83C2218yescomplemented
73C2×#103×C83C2211yescharacteristic, complemented
74C2×#103×C83C2211yescharacteristic, complemented
75C2×#102×C83C2211yescharacteristic
76C2×#102×C83C2211yescharacteristic
77C24×D83—21no—
78C22×Dic166C2311yescharacteristic
79C22×D332C2311yescharacteristic
80C22×C22⋊D83—21no—
81C22×C22⋊D83—21no—
82C22×C22⋊D83D411yescharacteristic
83C2×D4×D83—22no—
84C2×D4×D83—24no—
85C2×D4×D83—42no—
86C2×D4×D83C2314yes—
87C23×Dic83—21no—
88C22×C4×D83C2311yescharacteristic
89C2×#13050580—42no—
90C2×#13050580C2314yescomplemented
91C2×#13050579—42no—
92C2×#13050579C2314yes—
93C2×#13050578—24no—
94C2×#13050578C2314yes—
95C2×#13050573—42no—
96C2×#13050573C2314yes—
97C22×C83⋊C8C2311yescharacteristic
98C22×C83⋊C8C2311yescharacteristic
99#14581787—28no—
100#14581783—22no—
101#14581783C2314yescomplemented
102#14581782—28no—
103#14581781—22no—
104#14581781C2314yes—
105#14581775—28no—
106#14581775—28no—
107#14581772—22no—
108#14581772C2314yes—
109#14581771—22no—
110#14581771C2314yescomplemented
111#14581768—22no—
112#14581768C2314yes—
113#14581766—22no—
114#14581766C2314yes—
115#14581764—28no—
116#14581760—28no—
117#14581757—22no—
118#14581757C2314yescomplemented
119D4×Dic83—22no—
120D4×Dic83C2314yes—
121C4×C22⋊D83D414yes—
122C4×C22⋊D83C2314yes—
123#14581751—28no—
124#14581750—22no—
125#14581750C2314yes—
126C2×C4⋊Dic83—21no—
127C2×C4⋊Dic83—21no—
128C2×C4⋊Dic83C2311yescharacteristic
129C2×C4⋊Dic83C2311yescharacteristic
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4D411yescharacteristic
135C2×C22⋊Dic83—21no—
136C2×C22⋊Dic83—21no—
137C2×C22⋊Dic83D411yescharacteristic
138C2×(C2×D83)⋊C4—21no—
139C2×(C2×D83)⋊C4—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4—28no—
144C2×(C2×D83)⋊C4—21no—
145C2×(C2×D83)⋊C4D411yescharacteristic
146C2×C4×Dic83—21no—
147C2×C4×Dic83—21no—
148C2×C4×Dic83C2311yescharacteristic
149#14581726C2314yescomplemented
150#14581723C2314yescomplemented
151#14581723C2314yescomplemented
152Dic83⋊C8C2314yescomplemented
153#14581717C2314yescomplemented
154#14581716C2314yescomplemented
155#14581714C2314yes—
156#14581713C2314yes—
157#14581712C2314yes—
158#14581712C2314yes—
159C22⋊(C83⋊C8)C2314yescomplemented
160(C2×D83)⋊C8C2314yes—
161C8×Dic83C2314yescomplemented
162C2×#41×C83—22no—
163C2×#41×C83—24no—
164C2×#41×C83—42no—
165C2×#41×C83C2314yes—
166C22×Q8×C83C2311yescharacteristic
167C22×D4×C83—21no—
168C22×D4×C83C2311yescharacteristic
169C23×C4×C83—21no—
170C23×C4×C83—21no—
171C23×C4×C83C2311yescharacteristic
172C2×M16×C83—42no—
173C2×M16×C83C2314yescomplemented
174C22×C8×C83C2311yescharacteristic
175C22×C8×C83C2311yescharacteristic
176C2×C4⋊C4×C83—22no—
177C2×C4⋊C4×C83—21no—
178C2×C4⋊C4×C83C2311yescharacteristic
179C2×C4⋊C4×C83C2311yescharacteristic
180C2×C4⋊C4×C83C2314yescomplemented
181#103×C83C2314yescomplemented
182#103×C83C2314yescomplemented
183#102×C83C2314yes—
184#102×C83C2314yes—
185C23×D83—21no—
186C23×D83—24no—
187C23×D83—44no—
188C23×D83—44no—
189C23×D83—82no—
190C23×D83C2×D411yescharacteristic
191C2×Dic166—22no—
192C2×Dic166—22no—
193C2×Dic166—21no—
194C2×Dic166C2412yes—
195C2×D332—22no—
196C2×D332—22no—
197C2×D332—21no—
198C2×D332C2412yes—
199C2×C22⋊D83—24no—
200C2×C22⋊D83—24no—
201C2×C22⋊D83—42no—
202C2×C22⋊D83—44no—
203C2×C22⋊D83—82no—
204C2×C22⋊D83C2×D414yes—
205D4×D83—28no—
206D4×D83—44no—
207D4×D83—48no—
208C22×Dic83—21no—
209C22×Dic83—21no—
210C22×Dic83—21no—
211C22×Dic83—24no—
212C22×Dic83—82no—
213C22×Dic83C2×D411yescharacteristic
214C22×Dic83C2×D411yescharacteristic
215C22×Dic83C2×D411yescharacteristic
216C2×C4×D83—22no—
217C2×C4×D83—22no—
218C2×C4×D83C2×D412yes—
219C2×C4×D83C2412yes—
220#13050580—44no—
221#13050579—44no—
222#13050578—28no—
223#13050573—44no—
224C2×C83⋊C8—22no—
225C2×C83⋊C8—22no—
226C2×C83⋊C8C2412yes—
227C2×C83⋊C8C2412yes—
228C4⋊Dic83—21no—
229C4⋊Dic83—21no—
230C4⋊Dic83—24no—
231C4⋊Dic83—24no—
232C4⋊Dic83C2412yes—
233C4⋊Dic83C2412yes—
234Dic83⋊C4—24no—
235Dic83⋊C4—24no—
236Dic83⋊C4—24no—
237Dic83⋊C4—24no—
238Dic83⋊C4C2×D414yes—
239C22⋊Dic83—24no—
240C22⋊Dic83—24no—
241C22⋊Dic83C2×D414yes—
242(C2×D83)⋊C4—24no—
243(C2×D83)⋊C4—24no—
244(C2×D83)⋊C4—24no—
245(C2×D83)⋊C4—24no—
246(C2×D83)⋊C4—24no—
247(C2×D83)⋊C4—24no—
248(C2×D83)⋊C4C2×D414yes—
249C4×Dic83—24no—
250C4×Dic83—24no—
251C4×Dic83C2×D412yes—
252C4×Dic83C2412yes—
253C24×C83—21no—
254C24×C83C2×D411yescharacteristic
255#41×C83—28no—
256#41×C83—44no—
257#41×C83—48no—
258C2×Q8×C83—21no—
259C2×Q8×C83—22no—
260C2×Q8×C83—22no—
261C2×Q8×C83C2412yes—
262C2×D4×C83—24no—
263C2×D4×C83—21no—
264C2×D4×C83—22no—
265C2×D4×C83—44no—
266C2×D4×C83#4114yes—
267C2×D4×C83C2412yes—
268C22×C4×C83—22no—
269C22×C4×C83—22no—
270C22×C4×C83—24no—
271C22×C4×C83—21no—
272C22×C4×C83—21no—
273C22×C4×C83—21no—
274C22×C4×C83—24no—
275C22×C4×C83—44no—
276C22×C4×C83—44no—
277C22×C4×C83C2×D412yes—
278C22×C4×C83C2×D411yescharacteristic
279C22×C4×C83C2412yes—
280C22×C4×C83C2411yescharacteristic
281M16×C83—44no—
282C2×C8×C83—22no—
283C2×C8×C83—22no—
284C2×C8×C83C2412yes—
285C2×C8×C83C2412yes—
286C4⋊C4×C83—21no—
287C4⋊C4×C83—24no—
288C4⋊C4×C83—21no—
289C4⋊C4×C83C2412yes—
290C4⋊C4×C83C2412yes—
291C23×C83—22no—
292C23×C83—24no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—42no—
297C23×C83—42no—
298C23×C83C22×D412yes—
299C23×C83C22×D411yescharacteristic
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—48no—
305C22×D83—48no—
306C22×D83—42no—
307C22×D83—42no—
308C22×D83—42no—
309C22×D83—84no—
310C22×D83—816no—
311C22×D83C22×D412yes—
312Q8×C83—22no—
313Q8×C83—22no—
314Q8×C83—42no—
315D4×C83—24no—
316D4×C83—22no—
317D4×C83—48no—
318D4×C83C2×#4114yes—
319C2×C4×C83—22no—
320C2×C4×C83—24no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—48no—
327C2×C4×C83—48no—
328C2×C4×C83—42no—
329C2×C4×C83—42no—
330C2×C4×C83—42no—
331C2×C4×C83C22×D412yes—
332C2×C4×C83C22×D411yescharacteristic
333C2×C4×C83C2×#4112yes—
334C2×C4×C83H(5,𝔽2)12yes—
335C2×C4×C83C2511yescharacteristic
336C22⋊D83—44no—
337C22⋊D83—48no—
338C22⋊D83—84no—
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×Dic83—84no—
349C2×Dic83C22×D412yes—
350C2×Dic83C22×D412yes—
351C2×Dic83C22×D412yes—
352D332—22no—
353D332—22no—
354D332—42no—
355C4×D83—24no—
356C4×D83—22no—
357C4×D83—22no—
358Dic166—22no—
359Dic166—22no—
360Dic166—42no—
361C8×C83—22no—
362C8×C83—22no—
363C83⋊C8—22no—
364C83⋊C8—22no—
365C22×C83—24no—
366C22×C83—22no—
367C22×C83—22no—
368C22×C83—22no—
369C22×C83—48no—
370C22×C83—44no—
371C22×C83—42no—
372C22×C83—42no—
373C22×C83#54612yes—
374C22×C83#57512yes—
375C22×C83#57712yes—
376C22×C83C23×D411yescharacteristic
377C2×D83—22no—
378C2×D83—22no—
379C2×D83—22no—
380C2×D83—44no—
381C2×D83—42no—
382C2×D83—42no—
383C2×D83—42no—
384C2×D83—816no—
385C2×D83—84no—
386C4×C83—22no—
387C4×C83—42no—
388C4×C83—42no—
389C4×C83—42no—
390C4×C83#54612yes—
391C4×C83C22×#4111yescharacteristic
392C4×C83C2×H(5,𝔽2)11yescharacteristic
393Dic83—22no—
394Dic83—22no—
395Dic83—22no—
396Dic83—42no—
397Dic83—42no—
398Dic83—42no—
399C2×#3323—831nomaximal, Sylow
400C2×C83—44no—
401C2×C83—42no—
402C2×C83#332314yescomplemented
403C2×C83C2×#54611yescharacteristic
404C2×C83C2×#57511yescharacteristic
405C2×C83C2×#57711yescharacteristic
406D83—42no—
407D83—82no—
408C2×#552—831no—
409C2×#546—831no—
410#3323—8316no—
411C2×#488—831no—
412C2×#481—831no—
413C2×#485—831no—
414C2×#478—831no—
415C2×#470—831no—
416C2×#468—831no—
417C2×#464—831no—
418C2×#452—831no—
419C2×#450—831no—
420C2×C4×SD16—831no—
421C2×#436—831no—
422C2×#417D8311yescharacteristic, complemented
423C2×#418—831no—
424C83C2×#332311yescharacteristic, complemented, Sylow
425C22×#41C2×D8311yescharacteristic
426C23×D4—831no—
427C22×Q16—831no—
428C22×SD16—831no—
429C22×SD16—831no—
430C22×M16—831no—
431C22×M16C2×D8311yescharacteristic, complemented
432#552—838no—
433#552—1664no—
434#546—838no—
435#546—1664no—
436C2×#126—1661no—
437C2×#125—831no—
438C2×#125—1661no—
439C2×#124—831no—
440C2×#123—1661no—
441C2×#123—1661no—
442C2×C22⋊Q8—831no—
443C2×C22⋊Q8—831no—
444C2×C22⋊Q8—831no—
445C2×#121—831no—
446C2×#121—1661no—
447C2×#120—1661no—
448C2×C4×Q8—831no—
449C2×C4×D4—831no—
450C2×C4×D4—831no—
451C2×#117—831no—
452C2×#117—1661no—
453C22×C4⋊C4C2×D8311yescharacteristic, complemented
454C22×C22⋊C4—1661no—
455#488—838no—
456#485—838no—
457#481—838no—
458#478—838no—
459#470—838no—
460#468—838no—
461#464—838no—
462#452—838no—
463#450—838no—
464C4×SD16—838no—
465#436—838no—
466C2×#107—831no—
467C2×#106—831no—
468C2×#106—831no—
469C2×C4⋊C8—831no—
470#418—838no—
471#417C2×D8318yescomplemented
472C2×#103—831no—
473C2×#103—831no—
474C2×#103C2×D8311yescharacteristic, complemented
475C2×#103C2×D8311yescharacteristic, complemented
476C2×#102—831no—
477C2×#102—831no—
478C2×#102—831no—
479C2×#102—831no—
480C2×#102C2×D8311yescharacteristic
481C2×#102C2×D8311yescharacteristic
482C2×C22⋊C8—831no—
483C2×C22⋊C8—831no—
484C2×C4×C8—831no—
485C25—1661no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C22×D8314yes—
490C22×Q8—831no—
491C22×Q8C22×D8311yescharacteristic
492C22×D4—21no—
493C22×D4—3322no—
494C22×D4—831no—
495C22×D4—834no—
496C22×D4—831no—
497C22×D4—1662no—
498C22×D4—1661no—
499C22×D4—1664no—
500C22×D4—1661no—
501C22×D4C22×D8311yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—831no—
505C23×C4—1661no—
506C23×C4C22×D8311yescharacteristic
507C2×Q16—3322no—
508C2×Q16—834no—
509C2×SD16—3322no—
510C2×SD16—834no—
511C2×SD16—834no—
512C2×SD16—1664no—
513C2×M16—42no—
514C2×M16—3322no—
515C2×M16—834no—
516C2×M16C22×D8314yescomplemented
517C22×C8—831no—
518C22×C8—831no—
519C22×C8C22×D8311yescharacteristic
520C22×C8C22×D8311yescharacteristic
521#126—1668no—
522#125—834no—
523#125—1662no—
524#125—1668no—
525#124—834no—
526#124—1662no—
527#123—1668no—
528#123—1668no—
529C22⋊Q8—834no—
530C22⋊Q8—834no—
531C22⋊Q8—834no—
532C22⋊Q8—1662no—
533C22⋊Q8—1662no—
534C22⋊Q8—1662no—
535#121—834no—
536#121—1668no—
537#121—1662no—
538#120—1668no—
539C4×Q8—834no—
540C4×Q8—1662no—
541C4×D4—834no—
542C4×D4—834no—
543C4×D4—834no—
544C4×D4—1662no—
545#117—834no—
546#117—1668no—
547#117—1662no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—831no—
551C2×C4⋊C4—831no—
552C2×C4⋊C4—831no—
553C2×C4⋊C4—1661no—
554C2×C4⋊C4—1661no—
555C2×C4⋊C4—1661no—
556C2×C4⋊C4—1661no—
557C2×C4⋊C4—1661no—
558C2×C4⋊C4—1661no—
559C2×C4⋊C4C22×D8311yescharacteristic
560C2×C4⋊C4C22×D8311yescharacteristic
561C2×C4⋊C4C22×D8314yescomplemented
562C2×C22⋊C4—831no—
563C2×C22⋊C4—831no—
564C2×C22⋊C4—1668no—
565C2×C22⋊C4—1661no—
566C2×C22⋊C4—1661no—
567C2×C22⋊C4—1661no—
568C2×C22⋊C4—1661no—
569C2×C22⋊C4—1661no—
570C2×C22⋊C4—1661no—
571C2×C22⋊C4—1661no—
572C2×C22⋊C4—1661no—
573C2×C42—831no—
574C2×C42—1661no—
575C2×C42—1661no—
576#107—834no—
577#106—834no—
578#106—834no—
579C4⋊C8—834no—
580#103—834no—
581#103—834no—
582#103C22×D8314yescomplemented
583#103C22×D8314yescomplemented
584#102—834no—
585#102—834no—
586#102—834no—
587#102—834no—
588#102C22×D8314yes—
589#102C22×D8314yes—
590C22⋊C8—834no—
591C22⋊C8—834no—
592C4×C8—834no—
593C24—21no—
594C24—3324no—
595C24—3324no—
596C24—831no—
597C24—6642no—
598C24—1664no—
599C24—1661no—
600C24D4×D8311yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—832no—
608C2×Q8—1662no—
609C2×Q8—1662no—
610C2×Q8—1661no—
611C2×Q8C23×D8312yes—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4—3328no—
617C2×D4—3324no—
618C2×D4—3324no—
619C2×D4—3322no—
620C2×D4—834no—
621C2×D4—832no—
622C2×D4—6642no—
623C2×D4—1664no—
624C2×D4—1668no—
625C2×D4—1664no—
626C2×D4—1661no—
627C2×D4—1662no—
628C2×D4—1662no—
629C2×D4#1305059014yes—
630C2×D4C23×D8312yes—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—24no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—831no—
641C22×C4—831no—
642C22×C4—831no—
643C22×C4—832no—
644C22×C4—832no—
645C22×C4—6642no—
646C22×C4—1661no—
647C22×C4—1661no—
648C22×C4—1661no—
649C22×C4—1664no—
650C22×C4—1662no—
651C22×C4—1662no—
652C22×C4D4×D8312yes—
653C22×C4D4×D8311yescharacteristic
654C22×C4C23×D8312yes—
655C22×C4C23×D8311yescharacteristic
656Q16—3324no—
657SD16—3324no—
658SD16—1668no—
659M16—44no—
660M16—3324no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—832no—
664C2×C8—832no—
665C2×C8—1662no—
666C2×C8—1662no—
667C2×C8C23×D8312yes—
668C2×C8C23×D8312yes—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—24no—
672C4⋊C4—834no—
673C4⋊C4—832no—
674C4⋊C4—832no—
675C4⋊C4—1664no—
676C4⋊C4—1664no—
677C4⋊C4—1664no—
678C4⋊C4—1664no—
679C4⋊C4—1664no—
680C4⋊C4—1661no—
681C4⋊C4—1661no—
682C4⋊C4—1664no—
683C4⋊C4C23×D8312yes—
684C4⋊C4C23×D8312yes—
685C22⋊C4—834no—
686C22⋊C4—834no—
687C22⋊C4—1664no—
688C22⋊C4—1664no—
689C22⋊C4—1664no—
690C22⋊C4—1664no—
691C22⋊C4—1664no—
692C22⋊C4—1664no—
693C22⋊C4—1664no—
694C22⋊C4—1664no—
695C42—832no—
696C42—832no—
697C42—1664no—
698C42—1664no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—3328no—
707C23—3328no—
708C23—3322no—
709C23—3322no—
710C23—3322no—
711C23—832no—
712C23—66416no—
713C23—6644no—
714C23—1662no—
715C23—1662no—
716C23—1662no—
717C23—1662no—
718C23C2×D4×D8312yes—
719C23C2×D4×D8311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—3322no—
724Q8—1662no—
725Q8—1662no—
726D4—24no—
727D4—22no—
728D4—48no—
729D4—3328no—
730D4—3324no—
731D4—3322no—
732D4—6644no—
733D4—1662no—
734D4—1662no—
735D4C2×#1305059014yes—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—48no—
744C2×C4—48no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—3322no—
749C2×C4—3322no—
750C2×C4—3322no—
751C2×C4—832no—
752C2×C4—832no—
753C2×C4—832no—
754C2×C4—6644no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1664no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4C2×D4×D8312yes—
765C2×C4C2×D4×D8311yescharacteristic
766C2×C4C2×#1305059012yes—
767C2×C4#1458183712yes—
768C2×C4C24×D8311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1662no—
772C8—1662no—
773C22—22no—
774C22—24no—
775C22—22no—
776C22—22no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—48no—
781C22—3324no—
782C22—3322no—
783C22—3322no—
784C22—3322no—
785C22—66416no—
786C22—6644no—
787C22—1662no—
788C22—1662no—
789C22—1662no—
790C22#1912834112yes—
791C22#1912849712yes—
792C22#1912851012yes—
793C22C22×D4×D8311yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—3322no—
799C4—3322no—
800C4—3322no—
801C4—1662no—
802C4—1662no—
803C4—1662no—
804C4#1912834112yes—
805C4C22×#1305059011yescharacteristic
806C4C2×#1458183711yescharacteristic
807C2—42no—
808C2—44no—
809C2—3322no—
810C2—6642no—
811C2#2491968014yesdirect product factor
812C2C2×#1912834111yescharacteristic
813C2C2×#1912849711yescharacteristic
814C2C2×#1912851011yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#417×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128339C2
hypercenterC2×#417D83
hypocenterC83C2×#3323
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#19128386C2semidirect
3. #24919680C2direct (N × H)
4. C2×#19128057C2semidirect
5. C2×#19128019C2semidirect
6. C2×#19128041C2semidirect
7. C2×#19127999C2semidirect
8. C2×#19127958C2semidirect
9. C2×#19127947C2semidirect
10. C2×#19127926C2semidirect
11. C2×#19127863C2semidirect
12. C2×#19127853C2semidirect
13. C2×#19127792C2semidirect
14. C2×#19127777C2semidirect
15. C2×#19127704C2semidirect
16. C2×#417×C83C2semidirect
18. C22×#13050580C22semidirect
23. #19128386C22semidirect
27. C2×#14581783C22semidirect
33. C2×#14581771C22semidirect
38. C2×#14581757C22semidirect
44. #19128057C22semidirect
45. #19128041C22semidirect
46. #19128019C22semidirect
47. #19127999C22semidirect
48. #19127958C22semidirect
49. #19127947C22semidirect
50. #19127926C22semidirect
51. #19127863C22semidirect
52. #19127853C22semidirect
53. #19127792C22semidirect
54. #19127777C22semidirect
55. C2×#14581726C22semidirect
56. C2×#14581723C22semidirect
57. C2×#14581723C22semidirect
58. C2×Dic83⋊C8C22semidirect
59. #19127704C22semidirect
60. C2×#14581717C22semidirect
61. C2×#14581716C22semidirect
66. C2×C22⋊(C83⋊C8)C22semidirect
68. C2×C8×Dic83C22semidirect
70. C22×M16×C83C22semidirect
71. C22×C4⋊C4×C83C22semidirect
72. #417×C83C22semidirect
73. C2×#103×C83C22semidirect
74. C2×#103×C83C22semidirect
90. C2×#13050580C23semidirect
101. #14581783C23semidirect
110. #14581771C23semidirect
118. #14581757C23semidirect
149. #14581726C23semidirect
150. #14581723C23semidirect
151. #14581723C23semidirect
152. Dic83⋊C8C23semidirect
153. #14581717C23semidirect
154. #14581716C23semidirect
159. C22⋊(C83⋊C8)C23semidirect
161. C8×Dic83C23semidirect
173. C2×M16×C83C23semidirect
180. C2×C4⋊C4×C83C23semidirect
181. #103×C83C23semidirect
182. #103×C83C23semidirect
402. C2×C83#3323semidirect
422. C2×#417D83semidirect
424. C83C2×#3323semidirect
431. C22×M16C2×D83semidirect
453. C22×C4⋊C4C2×D83semidirect
471. #417C2×D83semidirect
474. C2×#103C2×D83semidirect
475. C2×#103C2×D83semidirect
516. C2×M16C22×D83semidirect
561. C2×C4⋊C4C22×D83semidirect
582. #103C22×D83semidirect
583. #103C22×D83semidirect
811. C2#24919680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283862
C2×#191283392
#249196802
C2×#191280572
C2×#191280192
C2×#191280412
C2×#191279992
C2×#191279582
C2×#191279472
C2×#191279262
C2×#191278632
C2×#191278532
C2×#191277922
C2×#191277772
C2×#191277042
C2×#417×C832
C2×#332383