Finite Group Databasebeta

← C2×#24918339 #36275084

Subgroups — C2×#24918339 #36275084

Order 21248.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128272C211yesmaximal, characteristic, complemented
2#24918339C2116yesmaximal, direct product factor
3C2×#19128036C211yesmaximal, characteristic, complemented
4C2×#19128039C211yesmaximal, characteristic, complemented
5C2×#19128022C211yesmaximal, characteristic, complemented
6C2×#19128031C211yesmaximal, characteristic, complemented
7C2×#19127957C211yesmaximal, characteristic, complemented
8C2×#19127945C211yesmaximal, characteristic, complemented
9C2×#19127940C211yesmaximal, characteristic, complemented
10C2×#19127928C211yesmaximal, characteristic, complemented
11C2×#19127863C211yesmaximal, characteristic, complemented
12C2×#19127863C211yesmaximal, characteristic, complemented
13C2×#19127856C211yesmaximal, characteristic, complemented
14C2×#19127839C211yesmaximal, characteristic, complemented
15C2×#19127668C211yesmaximal, characteristic, complemented
16C2×#537×C83C211yesmaximal, characteristic
17C23×Dic166C2211yescharacteristic
18C22×#13050580C2211yescharacteristic
19C22×#13050580C2211yescharacteristic
20C22×#13050578C2211yescharacteristic
21C22×#13050578C2211yescharacteristic
22C22×#13050574C2211yescharacteristic
23C23×C83⋊C8C2211yescharacteristic
24#19128272—24no—
25#19128272C2218yescomplemented
26C2×#14581790—21no—
27C2×#14581779—21no—
28C2×#14581773—21no—
29C2×#14581773—21no—
30C2×#14581771C2211yescharacteristic
31C2×#14581771C2211yescharacteristic
32C2×#14581771C2211yescharacteristic
33C2×#14581771C2211yescharacteristic
34C2×#14581751C2211yescharacteristic
35#19128039C2218yescomplemented
36#19128036C2218yescomplemented
37#19128031C2218yescomplemented
38#19128022C2218yescomplemented
39#19127957C2218yescomplemented
40#19127945C2218yescomplemented
41#19127940C2218yescomplemented
42#19127928C2218yescomplemented
43#19127863C2218yescomplemented
44#19127863C2218yescomplemented
45#19127856C2218yescomplemented
46#19127839C2218yescomplemented
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581716C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581715C2211yescharacteristic
56C2×#14581715C2211yescharacteristic
57C2×#14581713C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59#19127668C2218yescomplemented
60C2×C22⋊(C83⋊C8)C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×C22⋊(C83⋊C8)C2211yescharacteristic
64C22×#41×C83C2211yescharacteristic
65C22×#41×C83C2211yescharacteristic
66#537×C83—24no—
67#537×C83C2218yes—
68C2×C22⋊Q8×C83—21no—
69C2×C22⋊Q8×C83C2211yescharacteristic
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×#121×C83—21no—
72C2×#121×C83—21no—
73C2×#121×C83—21no—
74C2×#121×C83C2211yescharacteristic
75C2×#121×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—22no—
79C22×Dic166—42no—
80C22×Dic166—42no—
81C22×Dic166C2311yescharacteristic
82C22×Dic166C2311yescharacteristic
83C22×Dic166C2314yes—
84C23×Dic83—21no—
85C2×#13050580—42no—
86C2×#13050580—42no—
87C2×#13050580C2314yes—
88C2×#13050580C2314yes—
89C2×#13050578—42no—
90C2×#13050578—42no—
91C2×#13050578C2314yes—
92C2×#13050578C2314yes—
93C2×#13050574—42no—
94C2×#13050574C2314yes—
95C22×C83⋊C8—42no—
96C22×C83⋊C8C2311yescharacteristic
97C22×C83⋊C8C2311yescharacteristic
98C22×C83⋊C8C2311yescharacteristic
99C22×C83⋊C8C2311yescharacteristic
100C22×C83⋊C8C2314yes—
101#14581790—28no—
102#14581779—28no—
103#14581773—28no—
104#14581773—28no—
105#14581771—22no—
106#14581771—22no—
107#14581771—22no—
108#14581771—22no—
109#14581771C2314yes—
110#14581771C2314yes—
111#14581771C2314yes—
112#14581771C2314yes—
113#14581751—22no—
114#14581751C2314yes—
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×Dic83⋊C4—21no—
118C2×Dic83⋊C4—21no—
119C2×Dic83⋊C4—21no—
120C2×Dic83⋊C4—21no—
121C2×C22⋊Dic83—21no—
122C2×C22⋊Dic83—21no—
123C2×C22⋊Dic83—21no—
124C2×C22⋊Dic83—21no—
125C2×C22⋊Dic83—21no—
126C2×C4×Dic83—21no—
127#14581725C2314yes—
128#14581725C2314yes—
129#14581723C2314yes—
130#14581723C2314yes—
131#14581716C2314yes—
132#14581716C2314yes—
133#14581715C2314yes—
134#14581715C2314yes—
135#14581715C2314yes—
136#14581715C2314yes—
137#14581713C2314yes—
138#14581713C2314yes—
139C22⋊(C83⋊C8)C2314yes—
140C22⋊(C83⋊C8)C2314yes—
141C22⋊(C83⋊C8)C2314yes—
142C22⋊(C83⋊C8)C2314yes—
143C2×#41×C83—22no—
144C2×#41×C83—42no—
145C2×#41×C83—42no—
146C2×#41×C83—42no—
147C2×#41×C83—42no—
148C2×#41×C83D414yes—
149C2×#41×C83C2314yes—
150C2×#41×C83C2314yes—
151C22×Q8×C83D411yescharacteristic
152C22×Q8×C83C2311yescharacteristic
153C22×D4×C83—21no—
154C22×D4×C83—21no—
155C22×D4×C83—21no—
156C22×D4×C83D411yescharacteristic
157C22×D4×C83D411yescharacteristic
158C22×D4×C83D411yescharacteristic
159C22×D4×C83C2311yescharacteristic
160C23×C4×C83—21no—
161C23×C4×C83—21no—
162C23×C4×C83C2311yescharacteristic
163C23×C4×C83C2311yescharacteristic
164C23×C4×C83C2311yescharacteristic
165C22⋊Q8×C83—28no—
166C22⋊Q8×C83—22no—
167C22⋊Q8×C83—22no—
168C22⋊Q8×C83C2314yes—
169C22⋊Q8×C83C2314yes—
170#121×C83—28no—
171#121×C83—28no—
172#121×C83—28no—
173#121×C83—22no—
174#121×C83—22no—
175#121×C83C2314yes—
176#121×C83C2314yes—
177C2×C4⋊C4×C83—21no—
178C2×C4⋊C4×C83—22no—
179C2×C4⋊C4×C83—21no—
180C2×C4⋊C4×C83—21no—
181C2×C4⋊C4×C83C2311yescharacteristic
182C2×C4⋊C4×C83C2311yescharacteristic
183C2×C4⋊C4×C83C2314yes—
184C2×C22⋊C4×C83—21no—
185C2×C22⋊C4×C83—21no—
186C2×C22⋊C4×C83—21no—
187C2×C22⋊C4×C83—21no—
188C2×Dic166—22no—
189C2×Dic166—22no—
190C2×Dic166—22no—
191C2×Dic166—22no—
192C2×Dic166—21no—
193C2×Dic166—21no—
194C2×Dic166—24no—
195C2×Dic166—44no—
196C2×Dic166—44no—
197C2×Dic166—44no—
198C2×Dic166—48no—
199C2×Dic166C2412yes—
200C2×Dic166C2412yes—
201C22×Dic83—24no—
202C22×Dic83—21no—
203C22×Dic83—21no—
204C22×Dic83—21no—
205C22×Dic83—21no—
206C22×Dic83—44no—
207#13050580—44no—
208#13050580—44no—
209#13050578—44no—
210#13050578—44no—
211#13050574—44no—
212C2×C83⋊C8—22no—
213C2×C83⋊C8—22no—
214C2×C83⋊C8—22no—
215C2×C83⋊C8—22no—
216C2×C83⋊C8—44no—
217C2×C83⋊C8C2412yes—
218C2×C83⋊C8C2412yes—
219C2×C83⋊C8C2412yes—
220C2×C83⋊C8C2412yes—
221C4⋊Dic83—21no—
222C4⋊Dic83—21no—
223C4⋊Dic83C2412yes—
224C4⋊Dic83C2412yes—
225Dic83⋊C4—24no—
226Dic83⋊C4—24no—
227Dic83⋊C4—24no—
228Dic83⋊C4—24no—
229C22⋊Dic83—24no—
230C22⋊Dic83—24no—
231C22⋊Dic83—24no—
232C22⋊Dic83—24no—
233C22⋊Dic83—24no—
234C4×Dic83—24no—
235C24×C83—21no—
236C24×C83C2×D411yescharacteristic
237C24×C83C2×D411yescharacteristic
238C24×C83C2×D411yescharacteristic
239#41×C83—48no—
240#41×C83—44no—
241#41×C83—44no—
242#41×C83—44no—
243#41×C83—44no—
244#41×C83—48no—
245C2×Q8×C83—21no—
246C2×Q8×C83—22no—
247C2×Q8×C83—22no—
248C2×Q8×C83—42no—
249C2×Q8×C83C2×D414yes—
250C2×Q8×C83C2412yes—
251C2×D4×C83—24no—
252C2×D4×C83—24no—
253C2×D4×C83—24no—
254C2×D4×C83—21no—
255C2×D4×C83—22no—
256C2×D4×C83—22no—
257C2×D4×C83—42no—
258C2×D4×C83—42no—
259C2×D4×C83—42no—
260C2×D4×C83—44no—
261C2×D4×C83—82no—
262C2×D4×C83—82no—
263C2×D4×C83C2×D414yes—
264C2×D4×C83C2×D414yes—
265C2×D4×C83C2×D414yes—
266C2×D4×C83C2412yes—
267C22×C4×C83—22no—
268C22×C4×C83—22no—
269C22×C4×C83—22no—
270C22×C4×C83—22no—
271C22×C4×C83—22no—
272C22×C4×C83—22no—
273C22×C4×C83—21no—
274C22×C4×C83—21no—
275C22×C4×C83—21no—
276C22×C4×C83—24no—
277C22×C4×C83—24no—
278C22×C4×C83—44no—
279C22×C4×C83—82no—
280C22×C4×C83C2×D412yes—
281C22×C4×C83C2×D412yes—
282C22×C4×C83C2×D411yescharacteristic
283C22×C4×C83C2×D412yes—
284C22×C4×C83C2×D411yescharacteristic
285C22×C4×C83C2×D411yescharacteristic
286C22×C4×C83C2412yes—
287C22×C4×C83C2412yes—
288C22×C4×C83C2412yes—
289C22×C4×C83C2411yescharacteristic
290C4⋊C4×C83—24no—
291C4⋊C4×C83—21no—
292C4⋊C4×C83—21no—
293C4⋊C4×C83—24no—
294C4⋊C4×C83—24no—
295C4⋊C4×C83C2412yes—
296C4⋊C4×C83C2412yes—
297C22⋊C4×C83—24no—
298C22⋊C4×C83—24no—
299C22⋊C4×C83—24no—
300C22⋊C4×C83—24no—
301C23×C83—22no—
302C23×C83—22no—
303C23×C83—22no—
304C23×C83—22no—
305C23×C83—22no—
306C23×C83—22no—
307C23×C83—22no—
308C23×C83—22no—
309C23×C83—22no—
310C23×C83—22no—
311C23×C83—42no—
312C23×C83—42no—
313C23×C83—42no—
314C23×C83C22×D412yes—
315C23×C83C22×D412yes—
316C23×C83C22×D412yes—
317C23×C83C22×D411yescharacteristic
318Q8×C83—22no—
319Q8×C83—22no—
320Q8×C83—44no—
321Q8×C83—42no—
322D4×C83—22no—
323D4×C83—22no—
324D4×C83—44no—
325D4×C83—44no—
326D4×C83—44no—
327D4×C83—48no—
328D4×C83—42no—
329D4×C83—84no—
330D4×C83—84no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—24no—
335C2×C4×C83—24no—
336C2×C4×C83—24no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—48no—
347C2×C4×C83—42no—
348C2×C4×C83—42no—
349C2×C4×C83—42no—
350C2×C4×C83—84no—
351C2×C4×C83C22×D412yes—
352C2×C4×C83C22×D412yes—
353C2×C4×C83C22×D412yes—
354C2×C4×C83C22×D411yescharacteristic
355C2×C4×C83H(5,𝔽2)12yes—
356C2×C4×C83H(5,𝔽2)12yes—
357C2×C4×C83C2511yescharacteristic
358C2×Dic83—22no—
359C2×Dic83—22no—
360C2×Dic83—22no—
361C2×Dic83—22no—
362C2×Dic83—48no—
363C2×Dic83—42no—
364C2×Dic83—42no—
365C2×Dic83—42no—
366C2×Dic83—42no—
367Dic166—22no—
368Dic166—22no—
369Dic166—22no—
370Dic166—22no—
371Dic166—48no—
372Dic166—42no—
373Dic166—42no—
374C83⋊C8—22no—
375C83⋊C8—22no—
376C83⋊C8—22no—
377C83⋊C8—22no—
378C22×C83—22no—
379C22×C83—22no—
380C22×C83—22no—
381C22×C83—22no—
382C22×C83—22no—
383C22×C83—22no—
384C22×C83—22no—
385C22×C83—22no—
386C22×C83—22no—
387C22×C83—44no—
388C22×C83—44no—
389C22×C83—44no—
390C22×C83—42no—
391C22×C83—42no—
392C22×C83—42no—
393C22×C83—84no—
394C22×C83#53412yes—
395C22×C83#57712yes—
396C22×C83#57812yes—
397C22×C83C23×D411yescharacteristic
398C4×C83—22no—
399C4×C83—22no—
400C4×C83—22no—
401C4×C83—42no—
402C4×C83—42no—
403C4×C83—42no—
404C4×C83#53412yes—
405C4×C83C2×H(5,𝔽2)11yescharacteristic
406C4×C83C2×H(5,𝔽2)11yescharacteristic
407Dic83—42no—
408Dic83—42no—
409Dic83—42no—
410Dic83—42no—
411C2×#3201—831nomaximal, Sylow
412C2×C83—42no—
413C2×C83—42no—
414C2×C83—42no—
415C2×C83—82no—
416C2×C83#320114yescomplemented
417C2×C83C2×#53411yescharacteristic
418C2×C83C2×#57711yescharacteristic
419C2×C83C2×#57811yescharacteristic
420C2×#537D8311yescharacteristic
421C2×#536—831no—
422#3201—8316no—
423C2×#484—831no—
424C2×#485—831no—
425C2×#482—831no—
426C2×#483—831no—
427C2×#470—831no—
428C2×#468—831no—
429C2×#467—831no—
430C2×#465—831no—
431C2×#452—831no—
432C2×#452—831no—
433C2×#451—831no—
434C2×#448—831no—
435C2×#408—831no—
436C83C2×#320111yescharacteristic, complemented, Sylow
437C22×#41C2×D8311yescharacteristic
438C22×#41C2×D8311yescharacteristic
439C23×Q8—831no—
440C22×Q16—831no—
441C22×Q16—831no—
442C22×SD16—831no—
443C22×SD16—831no—
444C22×M16—831no—
445C23×C8—831no—
446#537—24no—
447#537C2×D8318yes—
448#536—838no—
449#536—1664no—
450C2×C4⋊Q8—1661no—
451C2×#124—1661no—
452C2×#123—1661no—
453C2×#123—1661no—
454C2×C22⋊Q8—21no—
455C2×C22⋊Q8—831no—
456C2×C22⋊Q8—831no—
457C2×C22⋊Q8—831no—
458C2×C22⋊Q8—831no—
459C2×C22⋊Q8C2×D8311yescharacteristic
460C2×C22⋊Q8C2×D8311yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C2×D8311yescharacteristic
465C2×#121C2×D8311yescharacteristic
466C2×#117—831no—
467C22×C4⋊C4C2×D8311yescharacteristic
468#485—838no—
469#484—838no—
470#483—838no—
471#482—838no—
472#470—838no—
473#468—838no—
474#467—838no—
475#465—838no—
476#452—838no—
477#452—838no—
478#451—838no—
479#448—838no—
480C2×#107—831no—
481C2×#107—831no—
482C2×#106—831no—
483C2×#106—831no—
484C2×#103—831no—
485C2×#103—831no—
486C2×#103—831no—
487C2×#103—831no—
488C2×#103—831no—
489C2×#103—831no—
490C2×#102—831no—
491C2×#102—831no—
492#408—838no—
493C2×C22⋊C8—831no—
494C2×C22⋊C8—831no—
495C2×C22⋊C8—831no—
496C2×C22⋊C8—831no—
497C2×#41—22no—
498C2×#41—42no—
499C2×#41—42no—
500C2×#41—42no—
501C2×#41—42no—
502C2×#41C22⋊D8314yes—
503C2×#41C22×D8314yes—
504C2×#41C22×D8314yes—
505C22×Q8—3322no—
506C22×Q8—3322no—
507C22×Q8—834no—
508C22×Q8—831no—
509C22×Q8—831no—
510C22×Q8—1661no—
511C22×Q8—1662no—
512C22×Q8C22⋊D8311yescharacteristic
513C22×Q8C22×D8311yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4C22⋊D8311yescharacteristic
518C22×D4C22⋊D8311yescharacteristic
519C22×D4C22⋊D8311yescharacteristic
520C22×D4C22×D8311yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—1661no—
524C23×C4C22×D8311yescharacteristic
525C23×C4C22×D8311yescharacteristic
526C23×C4C22×D8311yescharacteristic
527C2×Q16—3322no—
528C2×Q16—3322no—
529C2×Q16—834no—
530C2×Q16—834no—
531C2×SD16—3322no—
532C2×SD16—3322no—
533C2×SD16—834no—
534C2×SD16—834no—
535C2×M16—3322no—
536C2×M16—834no—
537C22×C8—3322no—
538C22×C8—834no—
539C22×C8—831no—
540C22×C8—831no—
541C22×C8—831no—
542C22×C8—831no—
543C4⋊Q8—1668no—
544#124—1668no—
545#123—1668no—
546#123—1668no—
547C22⋊Q8—28no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—834no—
551C22⋊Q8—834no—
552C22⋊Q8—834no—
553C22⋊Q8—834no—
554C22⋊Q8—1662no—
555C22⋊Q8—1662no—
556C22⋊Q8—1662no—
557C22⋊Q8—1662no—
558C22⋊Q8C22×D8314yes—
559C22⋊Q8C22×D8314yes—
560#121—28no—
561#121—28no—
562#121—28no—
563#121—22no—
564#121—22no—
565#121C22×D8314yes—
566#121C22×D8314yes—
567#117—834no—
568#117—1662no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—831no—
574C2×C4⋊C4—831no—
575C2×C4⋊C4—1661no—
576C2×C4⋊C4—1661no—
577C2×C4⋊C4—1661no—
578C2×C4⋊C4—1661no—
579C2×C4⋊C4C22×D8311yescharacteristic
580C2×C4⋊C4C22×D8311yescharacteristic
581C2×C4⋊C4C22×D8314yes—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—1661no—
587C2×C22⋊C4—1661no—
588C2×C22⋊C4—1661no—
589C2×C22⋊C4—1661no—
590C2×C22⋊C4—1661no—
591C2×C42—1661no—
592#107—834no—
593#107—834no—
594#106—834no—
595#106—834no—
596#103—834no—
597#103—834no—
598#103—834no—
599#103—834no—
600#103—834no—
601#103—834no—
602#102—834no—
603#102—834no—
604C22⋊C8—834no—
605C22⋊C8—834no—
606C22⋊C8—834no—
607C22⋊C8—834no—
608C24—21no—
609C24C2×C22⋊D8311yescharacteristic
610C24C2×C22⋊D8311yescharacteristic
611C24C2×C22⋊D8311yescharacteristic
612#41—48no—
613#41—44no—
614#41—44no—
615#41—44no—
616#41—44no—
617#41—48no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—42no—
622C2×Q8—3324no—
623C2×Q8—3328no—
624C2×Q8—3324no—
625C2×Q8—3324no—
626C2×Q8—832no—
627C2×Q8—832no—
628C2×Q8—1662no—
629C2×Q8—1662no—
630C2×Q8—1662no—
631C2×Q8—1662no—
632C2×Q8—1661no—
633C2×Q8—1661no—
634C2×Q8—1664no—
635C2×Q8C2×C22⋊D8314yes—
636C2×Q8C23×D8312yes—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—22no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—44no—
647C2×D4—82no—
648C2×D4—82no—
649C2×D4C2×C22⋊D8314yes—
650C2×D4C2×C22⋊D8314yes—
651C2×D4C2×C22⋊D8314yes—
652C2×D4C23×D8312yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—44no—
665C22×C4—82no—
666C22×C4—3324no—
667C22×C4—1664no—
668C22×C4—1661no—
669C22×C4—1661no—
670C22×C4—1661no—
671C22×C4—1661no—
672C22×C4C2×C22⋊D8312yes—
673C22×C4C2×C22⋊D8312yes—
674C22×C4C2×C22⋊D8312yes—
675C22×C4C2×C22⋊D8311yescharacteristic
676C22×C4C2×C22⋊D8311yescharacteristic
677C22×C4C2×C22⋊D8311yescharacteristic
678C22×C4C23×D8312yes—
679C22×C4C23×D8312yes—
680C22×C4C23×D8312yes—
681C22×C4C23×D8311yescharacteristic
682Q16—3324no—
683Q16—3324no—
684SD16—3324no—
685SD16—3324no—
686M16—3324no—
687C2×C8—3324no—
688C2×C8—832no—
689C2×C8—832no—
690C2×C8—832no—
691C2×C8—832no—
692C2×C8—1662no—
693C2×C8—1662no—
694C2×C8—1662no—
695C2×C8—1662no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—24no—
700C4⋊C4—24no—
701C4⋊C4—832no—
702C4⋊C4—832no—
703C4⋊C4—1661no—
704C4⋊C4—1661no—
705C4⋊C4—1664no—
706C4⋊C4—1664no—
707C4⋊C4—1664no—
708C4⋊C4—1664no—
709C4⋊C4C23×D8312yes—
710C4⋊C4C23×D8312yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—1664no—
716C22⋊C4—1664no—
717C22⋊C4—1664no—
718C22⋊C4—1664no—
719C22⋊C4—1664no—
720C42—1664no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23C22×C22⋊D8312yes—
735C23C22×C22⋊D8312yes—
736C23C22×C22⋊D8312yes—
737C23C22×C22⋊D8311yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—44no—
741Q8—42no—
742Q8—3328no—
743Q8—3322no—
744Q8—3322no—
745Q8—1662no—
746Q8—1662no—
747Q8—1662no—
748Q8—1662no—
749D4—22no—
750D4—22no—
751D4—44no—
752D4—44no—
753D4—44no—
754D4—48no—
755D4—42no—
756D4—84no—
757D4—84no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—84no—
778C2×C4—3328no—
779C2×C4—3322no—
780C2×C4—3322no—
781C2×C4—3322no—
782C2×C4—3322no—
783C2×C4—1662no—
784C2×C4—1662no—
785C2×C4—1662no—
786C2×C4—1662no—
787C2×C4C22×C22⋊D8312yes—
788C2×C4C22×C22⋊D8312yes—
789C2×C4C22×C22⋊D8312yes—
790C2×C4C22×C22⋊D8311yescharacteristic
791C2×C4#1458183712yes—
792C2×C4#1458183712yes—
793C2×C4C24×D8311yescharacteristic
794C8—1662no—
795C8—1662no—
796C8—1662no—
797C8—1662no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—84no—
814C22#1912826012yes—
815C22#1912851212yes—
816C22#1912851612yes—
817C22C23×C22⋊D8311yescharacteristic
818C4—22no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—3322no—
825C4—3322no—
826C4—3322no—
827C4—3322no—
828C4#1912826012yes—
829C4C2×#1458183711yescharacteristic
830C4C2×#1458183711yescharacteristic
831C2—42no—
832C2—42no—
833C2—42no—
834C2—82no—
835C2#2491833914yesdirect product factor
836C2C2×#1912826011yescharacteristic
837C2C2×#1912851211yescharacteristic
838C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
Fitting, prime radicalC2×#537×C83C2
socleC23×C83C22×D4
hypercenterC2×#537D83
hypocenterC83C2×#3201
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#19128272C2semidirect
2. #24918339C2direct (N × H)
3. C2×#19128036C2semidirect
4. C2×#19128039C2semidirect
5. C2×#19128022C2semidirect
6. C2×#19128031C2semidirect
7. C2×#19127957C2semidirect
8. C2×#19127945C2semidirect
9. C2×#19127940C2semidirect
10. C2×#19127928C2semidirect
11. C2×#19127863C2semidirect
12. C2×#19127863C2semidirect
13. C2×#19127856C2semidirect
14. C2×#19127839C2semidirect
15. C2×#19127668C2semidirect
25. #19128272C22semidirect
35. #19128039C22semidirect
36. #19128036C22semidirect
37. #19128031C22semidirect
38. #19128022C22semidirect
39. #19127957C22semidirect
40. #19127945C22semidirect
41. #19127940C22semidirect
42. #19127928C22semidirect
43. #19127863C22semidirect
44. #19127863C22semidirect
45. #19127856C22semidirect
46. #19127839C22semidirect
59. #19127668C22semidirect
416. C2×C83#3201semidirect
436. C83C2×#3201semidirect
835. C2#24918339direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282722
#249183392
C2×#191280362
C2×#191280392
C2×#191280222
C2×#191280312
C2×#191279572
C2×#191279452
C2×#191279402
C2×#191279282
C2×#191278632
C2×#191278562
C2×#191278392
C2×#191276682
C2×#537×C832
C2×#320183