Finite Group Databasebeta

← C2×#24917825 #36273649

Subgroups — C2×#24917825 #36273649

Order 21248.

2070 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128328C211yesmaximal, characteristic, complemented
2C2×#19128271C211yesmaximal, characteristic
3#24917825C2116yesmaximal, direct product factor
4C2×#19128070C211yesmaximal, characteristic, complemented
5C2×#19128068C211yesmaximal, characteristic, complemented
6C2×#19128059C211yesmaximal, characteristic, complemented
7C2×#19128055C211yesmaximal, characteristic, complemented
8C2×#19128054C211yesmaximal, characteristic, complemented
9C2×#19128053C211yesmaximal, characteristic, complemented
10C2×#19128050C211yesmaximal, characteristic, complemented
11C2×#19127699C211yesmaximal, characteristic
12C2×#19127708C211yesmaximal, characteristic, complemented
13C2×#19127694C211yesmaximal, characteristic
14C2×#103×D83C211yesmaximal, characteristic, complemented
15C2×#19127658C211yesmaximal, characteristic, complemented
16C2×#489×C83C211yesmaximal, characteristic, complemented
17C22×#13050589C2211yescharacteristic
18C22×Q8×D83C2211yescharacteristic
19C22×#13050573C2211yescharacteristic
20C22×C8×D83C2211yescharacteristic
21#19128328—24no—
22#19128328C2218yescomplemented
23#19128271—24no—
24#19128271C2218yes—
25C2×#14581792C2211yescharacteristic
26C2×#14581791C2211yescharacteristic
27C2×#14581790—21no—
28C2×#14581790C2211yescharacteristic
29C2×#14581784C2211yescharacteristic
30C2×#14581783C2211yescharacteristic
31C2×#14581782—21no—
32C2×#14581779C2211yescharacteristic
33C2×#14581774—21no—
34C2×#14581774—21no—
35C2×#14581770—21no—
36C2×#14581769—21no—
37C2×#14581769—21no—
38C2×#14581768—21no—
39C2×#14581750C2211yescharacteristic
40C2×#14581749C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128070C2218yescomplemented
43#19128068C2218yescomplemented
44#19128059C2218yescomplemented
45#19128055C2218yescomplemented
46#19128054C2218yescomplemented
47#19128053C2218yescomplemented
48#19128050C2218yescomplemented
49#19127708C2218yescomplemented
50#19127699C2218yes—
51#19127694C2218yes—
52C2×#14581717C2211yescharacteristic
53C2×#14581717C2211yescharacteristic
54C2×#14581717C2211yescharacteristic
55C2×#14581717C2211yescharacteristic
56C2×#14581716C2211yescharacteristic
57C2×#14581716C2211yescharacteristic
58C2×#14581715C2211yescharacteristic
59C2×#14581715C2211yescharacteristic
60C2×#14581715C2211yescharacteristic
61C2×#14581715C2211yescharacteristic
62#103×D83C2218yescomplemented
63C2×#14581713C2211yescharacteristic
64C2×#14581713C2211yescharacteristic
65#19127658C2218yescomplemented
66C2×#14581702C2211yescharacteristic
67C2×C4×C83⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C2×C4⋊Q8×C83C2211yescharacteristic
70C2×#124×C83C2211yescharacteristic
71#489×C83C2218yescomplemented
72C2×#103×C83C2211yescharacteristic
73C2×#103×C83C2211yescharacteristic
74C2×#102×C83C2211yescharacteristic
75C2×#102×C83C2211yescharacteristic
76C2×#97×C83C2211yescharacteristic
77C2×#13050589—22no—
78C2×#13050589—24no—
79C2×#13050589—24no—
80C2×#13050589C2314yes—
81C22×Dic166—21no—
82C22×Dic166—21no—
83C22×Dic166C2311yescharacteristic
84C22×Dic166C2311yescharacteristic
85C2×Q8×D83—22no—
86C2×Q8×D83—24no—
87C2×Q8×D83—24no—
88C2×Q8×D83C2314yes—
89C22×C22⋊D83—21no—
90C23×Dic83—21no—
91C22×C4×D83—21no—
92C22×C4×D83—21no—
93C22×C4×D83C2311yescharacteristic
94C2×#13050573—24no—
95C2×#13050573C2314yes—
96C22×C83⋊C8C2311yescharacteristic
97C22×C83⋊C8C2311yescharacteristic
98C2×C8×D83—24no—
99C2×C8×D83C2314yes—
100#14581792—22no—
101#14581792C2314yes—
102#14581791—22no—
103#14581791C2314yes—
104#14581790—28no—
105#14581790—22no—
106#14581790C2314yes—
107#14581784—22no—
108#14581784C2314yes—
109#14581783—22no—
110#14581783C2314yes—
111#14581782—28no—
112#14581779—22no—
113#14581779C2314yes—
114#14581774—28no—
115#14581774—28no—
116#14581770—28no—
117#14581769—28no—
118#14581769—28no—
119#14581768—28no—
120#14581750—22no—
121#14581750C2314yes—
122#14581749D414yes—
123#14581749C2314yes—
124C2×C4⋊Dic83—21no—
125C2×C4⋊Dic83—21no—
126C2×C4⋊Dic83—21no—
127C2×C4⋊Dic83C2311yescharacteristic
128C2×C4⋊Dic83C2311yescharacteristic
129C2×Dic83⋊C4—21no—
130C2×Dic83⋊C4—21no—
131C2×Dic83⋊C4—21no—
132C2×Dic83⋊C4—21no—
133C2×Dic83⋊C4—21no—
134C2×Dic83⋊C4—21no—
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4D411yescharacteristic
137C2×Dic83⋊C4D411yescharacteristic
138C4⋊C4×D83—22no—
139C4⋊C4×D83C2314yes—
140C2×C22⋊Dic83—21no—
141C2×C22⋊Dic83—21no—
142C2×(C2×D83)⋊C4—21no—
143C2×(C2×D83)⋊C4D411yescharacteristic
144C2×(C2×D83)⋊C4D411yescharacteristic
145C2×C4×Dic83—21no—
146C2×C4×Dic83C2311yescharacteristic
147#14581717C2314yes—
148#14581717C2314yes—
149#14581717C2314yes—
150#14581717C2314yes—
151#14581716C2314yes—
152#14581716C2314yes—
153#14581715C2314yes—
154#14581715C2314yes—
155#14581715C2314yes—
156#14581715C2314yes—
157#14581713C2314yes—
158#14581713C2314yes—
159#14581702C2314yes—
160C4×C83⋊C8C2314yes—
161C8×Dic83C2314yes—
162C22×Q8×C83—21no—
163C22×Q8×C83C2311yescharacteristic
164C22×D4×C83C2311yescharacteristic
165C22×C8×C83C2311yescharacteristic
166C22×C8×C83C2311yescharacteristic
167C4⋊Q8×C83—22no—
168C4⋊Q8×C83C2314yes—
169#124×C83—22no—
170#124×C83C2314yes—
171C2×C4⋊C4×C83—21no—
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C42×C83C2311yescharacteristic
177#103×C83C2314yes—
178#103×C83C2314yes—
179#102×C83C2314yes—
180#102×C83C2314yes—
181#97×C83C2314yes—
182C23×D83C2×D411yescharacteristic
183#13050589—28no—
184#13050589—28no—
185#13050589—48no—
186C2×Dic166—22no—
187C2×Dic166—22no—
188C2×Dic166—22no—
189C2×Dic166—22no—
190C2×Dic166—21no—
191C2×Dic166—21no—
192C2×Dic166—24no—
193C2×Dic166—24no—
194C2×Dic166—44no—
195C2×Dic166—82no—
196C2×Dic166C2412yes—
197C2×Dic166C2412yes—
198Q8×D83—28no—
199Q8×D83—28no—
200Q8×D83—48no—
201C2×C22⋊D83—24no—
202C2×C22⋊D83—44no—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C22×Dic83—21no—
206C22×Dic83—21no—
207C22×Dic83—24no—
208C22×Dic83—44no—
209C22×Dic83C2×D411yescharacteristic
210C22×Dic83C2×D411yescharacteristic
211C22×Dic83C2×D411yescharacteristic
212C2×C4×D83—24no—
213C2×C4×D83—24no—
214C2×C4×D83—44no—
215C2×C4×D83—82no—
216C2×C4×D83C2×D412yes—
217C2×C4×D83#4114yes—
218C2×C4×D83#4114yes—
219C2×C4×D83C2412yes—
220#13050573—28no—
221C2×C83⋊C8—22no—
222C2×C83⋊C8—22no—
223C2×C83⋊C8C2412yes—
224C2×C83⋊C8C2412yes—
225C8×D83—28no—
226C4⋊Dic83—24no—
227C4⋊Dic83—24no—
228C4⋊Dic83—21no—
229C4⋊Dic83—21no—
230C4⋊Dic83—24no—
231C4⋊Dic83C2412yes—
232C4⋊Dic83C2412yes—
233Dic83⋊C4—24no—
234Dic83⋊C4—24no—
235Dic83⋊C4—24no—
236Dic83⋊C4—24no—
237Dic83⋊C4—24no—
238Dic83⋊C4—24no—
239Dic83⋊C4—24no—
240Dic83⋊C4C2×D414yes—
241Dic83⋊C4C2×D414yes—
242C22⋊Dic83—24no—
243C22⋊Dic83—24no—
244(C2×D83)⋊C4—24no—
245(C2×D83)⋊C4C2×D414yes—
246(C2×D83)⋊C4C2×D414yes—
247C4×Dic83—24no—
248C4×Dic83C2×D412yes—
249C4×Dic83C2412yes—
250C24×C83—21no—
251C2×Q8×C83—21no—
252C2×Q8×C83—24no—
253C2×Q8×C83—22no—
254C2×Q8×C83—22no—
255C2×Q8×C83—82no—
256C2×Q8×C83C2412yes—
257C2×D4×C83—21no—
258C2×D4×C83—22no—
259C2×D4×C83—22no—
260C2×D4×C83C2412yes—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83C2×D411yescharacteristic
265C22×C4×C83C2×D411yescharacteristic
266C22×C4×C83C2411yescharacteristic
267C2×C8×C83—22no—
268C2×C8×C83—22no—
269C2×C8×C83C2412yes—
270C2×C8×C83C2412yes—
271C4⋊C4×C83—24no—
272C4⋊C4×C83—21no—
273C4⋊C4×C83—21no—
274C4⋊C4×C83C2412yes—
275C4⋊C4×C83C2412yes—
276C22⋊C4×C83—24no—
277C22⋊C4×C83—24no—
278C42×C83C2×D412yes—
279C42×C83C2412yes—
280C23×C83—22no—
281C23×C83—42no—
282C23×C83—42no—
283C23×C83—42no—
284C23×C83C22×D411yescharacteristic
285C22×D83—22no—
286C22×D83—22no—
287C22×D83#12414yes—
288C22×D83C22×D412yes—
289Q8×C83—22no—
290Q8×C83—22no—
291Q8×C83—42no—
292Q8×C83—84no—
293D4×C83—22no—
294D4×C83—22no—
295D4×C83—42no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—22no—
299C2×C4×C83—22no—
300C2×C4×C83—22no—
301C2×C4×C83—42no—
302C2×C4×C83—42no—
303C2×C4×C83—42no—
304C2×C4×C83C22×D412yes—
305C2×C4×C83C22×D412yes—
306C2×C4×C83C22×D411yescharacteristic
307C2×C4×C83C2×#4112yes—
308C2×C4×C83C2×#4112yes—
309C2×C4×C83C2511yescharacteristic
310C22⋊D83—48no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—42no—
318C2×Dic83—42no—
319C2×Dic83—42no—
320C2×Dic83—42no—
321C2×Dic83—48no—
322C2×Dic83#12414yes—
323C2×Dic83C22×D412yes—
324C2×Dic83C22×D412yes—
325C2×Dic83C22×D412yes—
326C4×D83—48no—
327C4×D83—84no—
328C4×D83#12418yes—
329C4×D83C2×#4114yes—
330C4×D83C2×#4114yes—
331Dic166—22no—
332Dic166—22no—
333Dic166—22no—
334Dic166—22no—
335Dic166—42no—
336Dic166—42no—
337Dic166—48no—
338Dic166—84no—
339C8×C83—22no—
340C8×C83—22no—
341C83⋊C8—22no—
342C83⋊C8—22no—
343C22×C83—42no—
344C22×C83—42no—
345C22×C83—42no—
346C22×C83—84no—
347C22×C83C2×#12412yes—
348C22×C83#57712yes—
349C22×C83#57812yes—
350C22×C83C23×D411yescharacteristic
351C2×D83—28no—
352C2×D83—22no—
353C2×D83—22no—
354C2×D83C2×#12414yes—
355C4×C83—22no—
356C4×C83—22no—
357C4×C83—42no—
358C4×C83—42no—
359C4×C83—42no—
360C4×C83C2×#12412yes—
361C4×C83C22×#4111yescharacteristic
362C4×C83C22×#4111yescharacteristic
363Dic83—22no—
364Dic83—22no—
365Dic83—42no—
366Dic83—42no—
367Dic83—42no—
368Dic83—42no—
369Dic83C2×#12414yes—
370C2×#3137—831nomaximal, Sylow
371C2×C83—82no—
372C2×C83#313714yescomplemented
373C2×C83C22×#12411yescharacteristic
374C2×C83C2×#57711yescharacteristic
375C2×C83C2×#57811yescharacteristic
376D83—24no—
377C2×#544—831no—
378C2×#536—831no—
379#3137—8316no—
380C2×#491—831no—
381C2×#491—831no—
382C2×#489—831no—
383C2×#489D8311yescharacteristic, complemented
384C2×#488—831no—
385C2×#488—831no—
386C2×#487—831no—
387C2×#487—831no—
388C2×#417—831no—
389C2×#419—831no—
390C2×#416—831no—
391C22×#103—831no—
392C2×#405—831no—
393C83C2×#313711yescharacteristic, complemented, Sylow
394C22×#41—831no—
395C23×Q8—831no—
396C22×M16—831no—
397C23×C8—831no—
398#544—838no—
399#544—1664no—
400#536—838no—
401#536—1664no—
402C2×C4⋊Q8—831no—
403C2×C4⋊Q8—831no—
404C2×C4⋊Q8—831no—
405C2×C4⋊Q8—1661no—
406C2×C4⋊Q8C2×D8311yescharacteristic
407C2×#125—831no—
408C2×#125—831no—
409C2×#125—1661no—
410C2×#124—831no—
411C2×#124C2×D8311yescharacteristic
412C2×#123—1661no—
413C2×#123—1661no—
414C2×C22⋊Q8—1661no—
415C2×C22⋊Q8—1661no—
416C2×C22⋊Q8—1661no—
417C2×C22⋊Q8—1661no—
418C2×#117—831no—
419C2×#117—831no—
420C22×C4⋊C4—831no—
421#491—838no—
422#491—838no—
423#489—838no—
424#489C2×D8318yescomplemented
425#488—838no—
426#488—838no—
427#487—838no—
428#487—838no—
429#419—838no—
430#417—838no—
431#416—838no—
432C2×#103—831no—
433C2×#103—831no—
434C2×#103—831no—
435C2×#103—831no—
436C2×#103—831no—
437C2×#103—831no—
438C2×#103—831no—
439C2×#103—831no—
440C2×#103—831no—
441C2×#103—831no—
442C2×#103—838no—
443C2×#103C2×D8311yescharacteristic
444C2×#103C2×D8311yescharacteristic
445C2×#102—831no—
446C2×#102—831no—
447C2×#102C2×D8311yescharacteristic
448C2×#102C2×D8311yescharacteristic
449#405—838no—
450C2×#97—831no—
451C2×#97C2×D8311yescharacteristic
452C2×C4×C8—831no—
453C2×C4×C8—831no—
454C2×#41—834no—
455C2×#41—1664no—
456C2×#41—1664no—
457C2×#41—1662no—
458C22×Q8—21no—
459C22×Q8—834no—
460C22×Q8—831no—
461C22×Q8—831no—
462C22×Q8—1661no—
463C22×Q8—1661no—
464C22×Q8—1664no—
465C22×Q8—1664no—
466C22×Q8—1662no—
467C22×Q8C22×D8311yescharacteristic
468C22×D4—1661no—
469C22×D4C22×D8311yescharacteristic
470C23×C4—831no—
471C23×C4—1661no—
472C23×C4—1661no—
473C23×C4—1661no—
474C2×M16—834no—
475C2×M16—1664no—
476C22×C8—831no—
477C22×C8—831no—
478C22×C8—834no—
479C22×C8—1664no—
480C22×C8C22×D8311yescharacteristic
481C22×C8C22×D8311yescharacteristic
482C4⋊Q8—22no—
483C4⋊Q8—834no—
484C4⋊Q8—834no—
485C4⋊Q8—834no—
486C4⋊Q8—1662no—
487C4⋊Q8—1662no—
488C4⋊Q8—1668no—
489C4⋊Q8—1662no—
490C4⋊Q8C22×D8314yes—
491#125—834no—
492#125—834no—
493#125—1662no—
494#125—1668no—
495#125—1662no—
496#124—22no—
497#124—834no—
498#124—1662no—
499#124C22×D8314yes—
500#123—1668no—
501#123—1668no—
502C22⋊Q8—1668no—
503C22⋊Q8—1668no—
504C22⋊Q8—1668no—
505C22⋊Q8—1668no—
506#117—834no—
507#117—834no—
508#117—834no—
509#117—1662no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—831no—
512C2×C4⋊C4—831no—
513C2×C4⋊C4—831no—
514C2×C4⋊C4—831no—
515C2×C4⋊C4—834no—
516C2×C4⋊C4—1662no—
517C2×C4⋊C4—1661no—
518C2×C4⋊C4—1661no—
519C2×C4⋊C4—1661no—
520C2×C4⋊C4—1661no—
521C2×C4⋊C4—1661no—
522C2×C4⋊C4—1661no—
523C2×C4⋊C4—1661no—
524C2×C4⋊C4—1661no—
525C2×C4⋊C4—1661no—
526C2×C4⋊C4—1661no—
527C2×C4⋊C4C22×D8311yescharacteristic
528C2×C4⋊C4C22×D8311yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—831no—
532C2×C22⋊C4—831no—
533C2×C22⋊C4—1661no—
534C2×C22⋊C4—1661no—
535C2×C22⋊C4—1661no—
536C2×C42—831no—
537C2×C42—1661no—
538C2×C42C22×D8311yescharacteristic
539#103—834no—
540#103—834no—
541#103—834no—
542#103—834no—
543#103—834no—
544#103—834no—
545#103—834no—
546#103—834no—
547#103—834no—
548#103—834no—
549#103C22×D8314yes—
550#103C22×D8314yes—
551#102—834no—
552#102—834no—
553#102C22×D8314yes—
554#102C22×D8314yes—
555#97—834no—
556#97C22×D8314yes—
557C4×C8—834no—
558C4×C8—834no—
559C24—21no—
560C24—831no—
561#41—3328no—
562#41—1668no—
563#41—1668no—
564C2×Q8—21no—
565C2×Q8—24no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—82no—
569C2×Q8—3324no—
570C2×Q8—3328no—
571C2×Q8—832no—
572C2×Q8—832no—
573C2×Q8—6642no—
574C2×Q8—1664no—
575C2×Q8—1664no—
576C2×Q8—1668no—
577C2×Q8—1668no—
578C2×Q8—1662no—
579C2×Q8—1662no—
580C2×Q8—1662no—
581C2×Q8—1662no—
582C2×Q8—1661no—
583C2×Q8—1661no—
584C2×Q8C23×D8312yes—
585C2×D4—21no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—3324no—
589C2×D4—1664no—
590C2×D4C23×D8312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—3324no—
595C22×C4—3324no—
596C22×C4—831no—
597C22×C4—832no—
598C22×C4—834no—
599C22×C4—834no—
600C22×C4—832no—
601C22×C4—831no—
602C22×C4—831no—
603C22×C4—6642no—
604C22×C4—1664no—
605C22×C4—1664no—
606C22×C4—1664no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1661no—
610C22×C4—1661no—
611C22×C4D4×D8311yescharacteristic
612C22×C4D4×D8311yescharacteristic
613C22×C4C23×D8311yescharacteristic
614M16—1668no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—832no—
618C2×C8—832no—
619C2×C8—1668no—
620C2×C8—1662no—
621C2×C8—1662no—
622C2×C8C23×D8312yes—
623C2×C8C23×D8312yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—834no—
628C4⋊C4—834no—
629C4⋊C4—832no—
630C4⋊C4—832no—
631C4⋊C4—1664no—
632C4⋊C4—1664no—
633C4⋊C4—1664no—
634C4⋊C4—1664no—
635C4⋊C4—1664no—
636C4⋊C4—1664no—
637C4⋊C4—1661no—
638C4⋊C4—1661no—
639C4⋊C4—1664no—
640C4⋊C4—1664no—
641C4⋊C4—1664no—
642C4⋊C4—1664no—
643C4⋊C4C23×D8312yes—
644C4⋊C4C23×D8312yes—
645C22⋊C4—24no—
646C22⋊C4—24no—
647C22⋊C4—834no—
648C22⋊C4—834no—
649C22⋊C4—1664no—
650C22⋊C4—1664no—
651C22⋊C4—1664no—
652C42—832no—
653C42—832no—
654C42—1664no—
655C42D4×D8312yes—
656C42C23×D8312yes—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—834no—
662C23—832no—
663C23—1662no—
664C23—1662no—
665C23C2×D4×D8311yescharacteristic
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—84no—
670Q8—3328no—
671Q8—3322no—
672Q8—3322no—
673Q8—6644no—
674Q8—1662no—
675Q8—1662no—
676Q8—1662no—
677Q8—1662no—
678D4—22no—
679D4—22no—
680D4—42no—
681D4—3328no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—3328no—
691C2×C4—3322no—
692C2×C4—3322no—
693C2×C4—3322no—
694C2×C4—3322no—
695C2×C4—3328no—
696C2×C4—834no—
697C2×C4—832no—
698C2×C4—838no—
699C2×C4—834no—
700C2×C4—834no—
701C2×C4—832no—
702C2×C4—832no—
703C2×C4—6644no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1662no—
709C2×C4—1662no—
710C2×C4C2×D4×D8312yes—
711C2×C4C2×D4×D8312yes—
712C2×C4C2×D4×D8311yescharacteristic
713C2×C4#41×D8312yes—
714C2×C4#41×D8312yes—
715C2×C4C24×D8311yescharacteristic
716C8—22no—
717C8—22no—
718C8—1662no—
719C8—1662no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—84no—
724C22—834no—
725C22—1668no—
726C22—1662no—
727C22—1662no—
728C22#124×D8312yes—
729C22#1912851112yes—
730C22#1912851712yes—
731C22C22×D4×D8311yescharacteristic
732C4—22no—
733C4—22no—
734C4—42no—
735C4—42no—
736C4—42no—
737C4—3322no—
738C4—3322no—
739C4—3322no—
740C4—3322no—
741C4—834no—
742C4—1662no—
743C4—1662no—
744C4#124×D8312yes—
745C4C2×#41×D8311yescharacteristic
746C4C2×#41×D8311yescharacteristic
747C2—82no—
748C2—1664no—
749C2#2491782514yesdirect product factor
750C2C2×#124×D8311yescharacteristic
751C2C2×#1912851111yescharacteristic
752C2C2×#1912851711yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#489×C83C2
socleC23×C83C22×D4
prime radicalC22×#13050589C22
hypercenterC2×#489D83
hypocenterC83C2×#3137
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×#19128328C2semidirect
3. #24917825C2direct (N × H)
4. C2×#19128070C2semidirect
5. C2×#19128068C2semidirect
6. C2×#19128059C2semidirect
7. C2×#19128055C2semidirect
8. C2×#19128054C2semidirect
9. C2×#19128053C2semidirect
10. C2×#19128050C2semidirect
12. C2×#19127708C2semidirect
14. C2×#103×D83C2semidirect
15. C2×#19127658C2semidirect
16. C2×#489×C83C2semidirect
22. #19128328C22semidirect
42. #19128070C22semidirect
43. #19128068C22semidirect
44. #19128059C22semidirect
45. #19128055C22semidirect
46. #19128054C22semidirect
47. #19128053C22semidirect
48. #19128050C22semidirect
49. #19127708C22semidirect
62. #103×D83C22semidirect
65. #19127658C22semidirect
71. #489×C83C22semidirect
372. C2×C83#3137semidirect
383. C2×#489D83semidirect
393. C83C2×#3137semidirect
424. #489C2×D83semidirect
749. C2#24917825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283282
C2×#191282712
#249178252
C2×#191280702
C2×#191280682
C2×#191280592
C2×#191280552
C2×#191280542
C2×#191280532
C2×#191280502
C2×#191276992
C2×#191277082
C2×#191276942
C2×#103×D832
C2×#191276582
C2×#489×C832
C2×#313783