Finite Group Databasebeta

← C2×#24920074 #36283138

Subgroups — C2×#24920074 #36283138

Order 21248.

1866 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128419C211yesmaximal, characteristic
2C2×#19128406C211yesmaximal, characteristic
3#24920074C2116yesmaximal, direct product factor
4C2×#19128098C211yesmaximal, characteristic, complemented
5C2×#19128044C211yesmaximal, characteristic, complemented
6C2×#19128042C211yesmaximal, characteristic, complemented
7C2×#19128033C211yesmaximal, characteristic, complemented
8C2×#19128031C211yesmaximal, characteristic, complemented
9C2×#19127995C211yesmaximal, characteristic, complemented
10C2×#19127985C211yesmaximal, characteristic, complemented
11C2×#19127960C211yesmaximal, characteristic, complemented
12C2×#19127959C211yesmaximal, characteristic, complemented
13C2×#19127795C211yesmaximal, characteristic, complemented
14C2×#19127777C211yesmaximal, characteristic
15C2×#19127742C211yesmaximal, characteristic, complemented
16C2×#428×C83C211yesmaximal, characteristic, complemented
17C22×Dic332C2211yescharacteristic
18C22×#13050573C2211yescharacteristic
19#19128419—24no—
20#19128419C2218yes—
21#19128406—24no—
22#19128406C2218yes—
23C2×#14581791C2211yescharacteristic
24C2×#14581791C2211yescharacteristic
25C2×#14581786—21no—
26C2×#14581785—21no—
27C2×#14581782—21no—
28C2×#14581778—21no—
29C2×#14581772C2211yescharacteristic
30C2×#14581772C2211yescharacteristic
31C2×#14581771—21no—
32C2×#14581771C2211yescharacteristic
33C2×#14581771C2211yescharacteristic
34C2×#14581770—21no—
35C2×C4×Dic166—21no—
36C2×#14581757C2211yescharacteristic
37C2×#14581757C2211yescharacteristic
38C2×C4×C22⋊D83—21no—
39C2×C4×C22⋊D83C2211yescharacteristic
40C2×#14581750C2211yescharacteristic
41C2×C4⋊C4×D83C2211yescharacteristic
42#19128098C2218yescomplemented
43#19128044C2218yescomplemented
44#19128042C2218yescomplemented
45#19128033C2218yescomplemented
46#19128031C2218yescomplemented
47#19127995C2218yescomplemented
48#19127985C2218yescomplemented
49#19127960C2218yescomplemented
50#19127959C2218yescomplemented
51#19127795C2218yescomplemented
52#19127777C2218yes—
53#19127742C2218yescomplemented
54C2×#14581725C2211yescharacteristic
55C2×#14581724C2211yescharacteristic
56C2×#14581723C2211yescharacteristic
57C2×#14581723C2211yescharacteristic
58C2×#14581723C2211yescharacteristic
59C2×Dic83⋊C8C2211yescharacteristic
60C2×#14581717C2211yescharacteristic
61C2×#14581717C2211yescharacteristic
62C2×#14581715C2211yescharacteristic
63C2×#14581715C2211yescharacteristic
64C2×#14581715C2211yescharacteristic
65C2×#14581715C2211yescharacteristic
66C2×C22⋊(C83⋊C8)C2211yescharacteristic
67C2×(C2×D83)⋊C8C2211yescharacteristic
68C2×C8×Dic83C2211yescharacteristic
69C22×M16×C83C2211yescharacteristic
70C2×#117×C83C2211yescharacteristic
71C22×C4⋊C4×C83C2211yescharacteristic
72#428×C83C2218yescomplemented
73C2×#107×C83C2211yescharacteristic
74C2×#107×C83C2211yescharacteristic
75C2×#106×C83C2211yescharacteristic
76C2×#106×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166—21no—
79C22×Dic166C2311yescharacteristic
80C22×Dic166C2311yescharacteristic
81C22×C22⋊D83D411yescharacteristic
82C22×C4×D83—21no—
83C22×C4×D83C2311yescharacteristic
84C2×Dic332—24no—
85C2×Dic332C2314yes—
86C2×#13050573—24no—
87C2×#13050573C2314yes—
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90#14581791—22no—
91#14581791—22no—
92#14581791C2314yes—
93#14581791C2314yes—
94#14581786—28no—
95#14581785—28no—
96#14581782—28no—
97#14581778—28no—
98#14581772—22no—
99#14581772—22no—
100#14581772C2314yes—
101#14581772C2314yes—
102#14581771—28no—
103#14581771—22no—
104#14581771—22no—
105#14581771C2314yes—
106#14581771C2314yes—
107#14581770—28no—
108C4×Dic166—28no—
109#14581757—22no—
110#14581757—22no—
111#14581757C2314yes—
112#14581757C2314yes—
113C4×C22⋊D83—28no—
114C4×C22⋊D83D414yes—
115C4×C22⋊D83C2314yes—
116#14581750—22no—
117#14581750C2314yes—
118C2×C4⋊Dic83—21no—
119C2×C4⋊Dic83—21no—
120C2×C4⋊Dic83C2311yescharacteristic
121C2×C4⋊Dic83C2311yescharacteristic
122C2×Dic83⋊C4—21no—
123C2×Dic83⋊C4—21no—
124C2×Dic83⋊C4—21no—
125C2×Dic83⋊C4—21no—
126C2×Dic83⋊C4—21no—
127C2×Dic83⋊C4—21no—
128C2×Dic83⋊C4—21no—
129C2×Dic83⋊C4D411yescharacteristic
130C4⋊C4×D83—22no—
131C4⋊C4×D83C2314yes—
132C2×C22⋊Dic83—21no—
133C2×C22⋊Dic83—21no—
134C2×C22⋊Dic83D411yescharacteristic
135C2×(C2×D83)⋊C4—21no—
136C2×(C2×D83)⋊C4—21no—
137C2×(C2×D83)⋊C4—21no—
138C2×(C2×D83)⋊C4D411yescharacteristic
139C2×C4×Dic83—21no—
140C2×C4×Dic83—21no—
141C2×C4×Dic83—21no—
142C2×C4×Dic83C2311yescharacteristic
143#14581725C2314yes—
144#14581724C2314yes—
145#14581723C2314yes—
146#14581723C2314yes—
147#14581723C2314yes—
148Dic83⋊C8C2314yes—
149#14581717C2314yes—
150#14581717C2314yes—
151#14581715C2314yes—
152#14581715C2314yes—
153#14581715C2314yes—
154#14581715C2314yes—
155C22⋊(C83⋊C8)C2314yes—
156(C2×D83)⋊C8C2314yes—
157C8×Dic83C2314yes—
158C23×C4×C83—21no—
159C23×C4×C83C2311yescharacteristic
160C2×M16×C83—24no—
161C2×M16×C83C2314yes—
162C22×C8×C83C2311yescharacteristic
163C22×C8×C83C2311yescharacteristic
164#117×C83—22no—
165#117×C83C2314yes—
166C2×C4⋊C4×C83—22no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83C2311yescharacteristic
169C2×C4⋊C4×C83C2314yes—
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C22⋊C4×C83—21no—
174C2×C42×C83—21no—
175#107×C83C2314yes—
176#107×C83C2314yes—
177#106×C83C2314yes—
178#106×C83C2314yes—
179C23×D83C2×D411yescharacteristic
180C2×Dic166—22no—
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—22no—
184C2×Dic166—21no—
185C2×Dic166—21no—
186C2×Dic166—24no—
187C2×Dic166—24no—
188C2×Dic166—44no—
189C2×Dic166—82no—
190C2×Dic166C2412yes—
191C2×Dic166C2412yes—
192C2×C22⋊D83—24no—
193C2×C22⋊D83C2×D414yes—
194C22×Dic83—21no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C22×Dic83C2×D411yescharacteristic
199C22×Dic83C2×D411yescharacteristic
200C22×Dic83C2×D411yescharacteristic
201C2×C4×D83—22no—
202C2×C4×D83—22no—
203C2×C4×D83—24no—
204C2×C4×D83—82no—
205C2×C4×D83C2×D412yes—
206C2×C4×D83C2412yes—
207Dic332—28no—
208#13050573—28no—
209C2×C83⋊C8—22no—
210C2×C83⋊C8—22no—
211C2×C83⋊C8C2412yes—
212C2×C83⋊C8C2412yes—
213C4⋊Dic83—21no—
214C4⋊Dic83—21no—
215C4⋊Dic83—24no—
216C4⋊Dic83—24no—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221Dic83⋊C4—24no—
222Dic83⋊C4—24no—
223Dic83⋊C4—24no—
224Dic83⋊C4—24no—
225Dic83⋊C4—24no—
226Dic83⋊C4C2×D414yes—
227C22⋊Dic83—24no—
228C22⋊Dic83—24no—
229C22⋊Dic83C2×D414yes—
230(C2×D83)⋊C4—24no—
231(C2×D83)⋊C4—24no—
232(C2×D83)⋊C4—24no—
233(C2×D83)⋊C4C2×D414yes—
234C4×Dic83—24no—
235C4×Dic83—24no—
236C4×Dic83—24no—
237C4×Dic83C2×D412yes—
238C4×Dic83C2412yes—
239C24×C83C2×D411yescharacteristic
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—24no—
247C22×C4×C83—82no—
248C22×C4×C83C2×D412yes—
249C22×C4×C83C2×D411yescharacteristic
250C22×C4×C83C2412yes—
251C22×C4×C83C2411yescharacteristic
252M16×C83—28no—
253C2×C8×C83—22no—
254C2×C8×C83#4114yes—
255C2×C8×C83C2412yes—
256C2×C8×C83C2412yes—
257C4⋊C4×C83—24no—
258C4⋊C4×C83—21no—
259C4⋊C4×C83—21no—
260C4⋊C4×C83—21no—
261C4⋊C4×C83—21no—
262C4⋊C4×C83C2412yes—
263C4⋊C4×C83C2412yes—
264C4⋊C4×C83C2412yes—
265C4⋊C4×C83C2412yes—
266C22⋊C4×C83—24no—
267C42×C83—24no—
268C23×C83—22no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83C22×D412yes—
272C23×C83C22×D411yescharacteristic
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83C22×D412yes—
277C2×C4×C83—22no—
278C2×C4×C83—24no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83—42no—
286C2×C4×C83—42no—
287C2×C4×C83—42no—
288C2×C4×C83—42no—
289C2×C4×C83—84no—
290C2×C4×C83C22×D412yes—
291C2×C4×C83C22×D411yescharacteristic
292C2×C4×C83C2×#4112yes—
293C2×C4×C832−1+412yes—
294C2×C4×C83C2511yescharacteristic
295C22⋊D83—28no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—42no—
303C2×Dic83—42no—
304C2×Dic83—42no—
305C2×Dic83—42no—
306C2×Dic83#13714yes—
307C2×Dic83C22×D412yes—
308C2×Dic83C22×D412yes—
309C2×Dic83C22×D412yes—
310C4×D83—24no—
311C4×D83—22no—
312C4×D83—22no—
313C4×D83—84no—
314Dic166—22no—
315Dic166—22no—
316Dic166—22no—
317Dic166—22no—
318Dic166—42no—
319Dic166—42no—
320Dic166—48no—
321Dic166—84no—
322C8×C83—22no—
323C8×C83C2×#4114yes—
324C83⋊C8—22no—
325C83⋊C8—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83—22no—
329C22×C83—44no—
330C22×C83#54712yes—
331C22×C83C2×#13712yes—
332C22×C83#57712yes—
333C22×C83C23×D411yescharacteristic
334C2×D83—22no—
335C2×D83—22no—
336C2×D83—22no—
337C2×D83—44no—
338C4×C83—22no—
339C4×C83—42no—
340C4×C83—42no—
341C4×C83—42no—
342C4×C83—42no—
343C4×C83#54712yes—
344C4×C83C22×#4111yescharacteristic
345C4×C83C2×2−1+411yescharacteristic
346Dic83—22no—
347Dic83—22no—
348Dic83—42no—
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352Dic83C2×#13714yes—
353C2×#3356—831nomaximal, Sylow
354C2×C83—42no—
355C2×C83#335614yescomplemented
356C2×C83C2×#54711yescharacteristic
357C2×C83C22×#13711yescharacteristic
358C2×C83C2×#57711yescharacteristic
359D83—42no—
360C2×#556—831no—
361C2×#554—831no—
362#3356—8316no—
363C2×#498—831no—
364C2×#485—831no—
365C2×#485—831no—
366C2×#483—831no—
367C2×#483—831no—
368C2×#477—831no—
369C2×#475—831no—
370C2×#470—831no—
371C2×#470—831no—
372C2×C4×Q16—831no—
373C2×#436—831no—
374C2×#428—831no—
375C2×#428D8311yescharacteristic, complemented
376C83C2×#335611yescharacteristic, complemented, Sylow
377C22×Q16—831no—
378C22×M16—831no—
379C22×M16C2×D8311yescharacteristic
380#556—838no—
381#556—1664no—
382#554—838no—
383#554—1664no—
384C2×C4⋊Q8—831no—
385C2×C4⋊Q8—831no—
386C2×#126—1661no—
387C2×#126—1661no—
388C2×#125—1661no—
389C2×#124—1661no—
390C2×C22⋊Q8—831no—
391C2×C22⋊Q8—831no—
392C2×C22⋊Q8—831no—
393C2×C22⋊Q8—831no—
394C2×C22⋊Q8—1661no—
395C2×C22⋊Q8—1661no—
396C2×C4×Q8—831no—
397C2×C4×Q8—831no—
398C2×C4×Q8—1661no—
399C2×C4×D4—831no—
400C2×C4×D4—1661no—
401C2×#117—831no—
402C2×#117C2×D8311yescharacteristic
403C22×C4⋊C4—831no—
404C22×C4⋊C4C2×D8311yescharacteristic
405#498—838no—
406#485—838no—
407#485—838no—
408#483—838no—
409#483—838no—
410#477—838no—
411#475—838no—
412#470—838no—
413#470—838no—
414C4×Q16—838no—
415#436—838no—
416#428—838no—
417#428C2×D8318yescomplemented
418C2×#107—831no—
419C2×#107C2×D8311yescharacteristic
420C2×#107C2×D8311yescharacteristic
421C2×#106—831no—
422C2×#106—831no—
423C2×#106—831no—
424C2×#106—831no—
425C2×#106C2×D8311yescharacteristic
426C2×#106C2×D8311yescharacteristic
427C2×C4⋊C8—831no—
428C2×#103—831no—
429C2×#103—831no—
430C2×#103—831no—
431C2×#103—831no—
432C2×#103—831no—
433C2×#103—831no—
434C2×C22⋊C8—831no—
435C2×C22⋊C8—831no—
436C2×C4×C8—831no—
437C22×Q8—831no—
438C22×Q8—831no—
439C22×Q8—1661no—
440C22×Q8—1661no—
441C22×D4—831no—
442C23×C4—21no—
443C23×C4—831no—
444C23×C4—1661no—
445C23×C4C22×D8311yescharacteristic
446C2×Q16—834no—
447C2×Q16—1664no—
448C2×M16—24no—
449C2×M16—834no—
450C2×M16—1664no—
451C2×M16C22×D8314yes—
452C22×C8—831no—
453C22×C8—831no—
454C22×C8C22×D8311yescharacteristic
455C22×C8C22×D8311yescharacteristic
456C4⋊Q8—834no—
457C4⋊Q8—834no—
458C4⋊Q8—1662no—
459C4⋊Q8—1662no—
460#126—1668no—
461#126—1668no—
462#125—1668no—
463#124—1668no—
464C22⋊Q8—834no—
465C22⋊Q8—834no—
466C22⋊Q8—834no—
467C22⋊Q8—834no—
468C22⋊Q8—1668no—
469C22⋊Q8—1668no—
470C22⋊Q8—1662no—
471C22⋊Q8—1662no—
472C22⋊Q8—1662no—
473C22⋊Q8—1662no—
474C4×Q8—834no—
475C4×Q8—834no—
476C4×Q8—1668no—
477C4×Q8—1662no—
478C4×Q8—1662no—
479C4×D4—834no—
480C4×D4—834no—
481C4×D4—1668no—
482#117—22no—
483#117—834no—
484#117—1662no—
485#117C22×D8314yes—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4—834no—
492C2×C4⋊C4—1662no—
493C2×C4⋊C4—1661no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1661no—
497C2×C4⋊C4—1661no—
498C2×C4⋊C4—1661no—
499C2×C4⋊C4—1661no—
500C2×C4⋊C4—1661no—
501C2×C4⋊C4—1661no—
502C2×C4⋊C4C22×D8311yescharacteristic
503C2×C4⋊C4C22×D8311yescharacteristic
504C2×C4⋊C4C22×D8314yes—
505C2×C4⋊C4C22×D8311yescharacteristic
506C2×C4⋊C4C22×D8311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—831no—
509C2×C22⋊C4—831no—
510C2×C22⋊C4—1661no—
511C2×C22⋊C4—1661no—
512C2×C22⋊C4—1661no—
513C2×C22⋊C4—1661no—
514C2×C22⋊C4—1661no—
515C2×C42—21no—
516C2×C42—831no—
517C2×C42—1661no—
518C2×C42—1661no—
519C2×C42—1661no—
520#107—834no—
521#107C22×D8314yes—
522#107C22×D8314yes—
523#106—834no—
524#106—834no—
525#106—834no—
526#106—834no—
527#106C22×D8314yes—
528#106C22×D8314yes—
529C4⋊C8—834no—
530#103—834no—
531#103—834no—
532#103—834no—
533#103—834no—
534#103—834no—
535#103—834no—
536C22⋊C8—834no—
537C22⋊C8—834no—
538C4×C8—834no—
539C24—831no—
540C24D4×D8311yescharacteristic
541C2×Q8—3324no—
542C2×Q8—832no—
543C2×Q8—832no—
544C2×Q8—6642no—
545C2×Q8—1664no—
546C2×Q8—1664no—
547C2×Q8—1662no—
548C2×Q8—1662no—
549C2×Q8—1662no—
550C2×Q8—1662no—
551C2×Q8—1661no—
552C2×Q8—1661no—
553C2×D4—834no—
554C2×D4—1664no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—82no—
563C22×C4—831no—
564C22×C4—831no—
565C22×C4—831no—
566C22×C4—832no—
567C22×C4—832no—
568C22×C4—6642no—
569C22×C4—1664no—
570C22×C4—1661no—
571C22×C4—1661no—
572C22×C4—1661no—
573C22×C4—1661no—
574C22×C4—1662no—
575C22×C4—1662no—
576C22×C4D4×D8312yes—
577C22×C4D4×D8311yescharacteristic
578C22×C4C23×D8312yes—
579C22×C4C23×D8311yescharacteristic
580Q16—1668no—
581M16—28no—
582M16—1668no—
583C2×C8—22no—
584C2×C8—832no—
585C2×C8—832no—
586C2×C8—1662no—
587C2×C8—1662no—
588C2×C8#1305059014yes—
589C2×C8C23×D8312yes—
590C2×C8C23×D8312yes—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—834no—
597C4⋊C4—832no—
598C4⋊C4—832no—
599C4⋊C4—1664no—
600C4⋊C4—1664no—
601C4⋊C4—1664no—
602C4⋊C4—1664no—
603C4⋊C4—1664no—
604C4⋊C4—1664no—
605C4⋊C4—1664no—
606C4⋊C4—1661no—
607C4⋊C4—1661no—
608C4⋊C4—1664no—
609C4⋊C4—1664no—
610C4⋊C4C23×D8312yes—
611C4⋊C4C23×D8312yes—
612C4⋊C4C23×D8312yes—
613C4⋊C4C23×D8312yes—
614C22⋊C4—24no—
615C22⋊C4—834no—
616C22⋊C4—834no—
617C22⋊C4—1664no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C22⋊C4—1664no—
621C22⋊C4—1664no—
622C42—24no—
623C42—832no—
624C42—832no—
625C42—1664no—
626C42—1664no—
627C42—1664no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—832no—
632C23—1662no—
633C23—1662no—
634C23—1662no—
635C23C2×D4×D8312yes—
636C23C2×D4×D8311yescharacteristic
637Q8—3328no—
638Q8—3322no—
639Q8—3322no—
640Q8—6644no—
641Q8—1662no—
642Q8—1662no—
643Q8—1662no—
644Q8—1662no—
645D4—1668no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—84no—
659C2×C4—3322no—
660C2×C4—3322no—
661C2×C4—3322no—
662C2×C4—3322no—
663C2×C4—834no—
664C2×C4—832no—
665C2×C4—832no—
666C2×C4—832no—
667C2×C4—6644no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1664no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4C2×D4×D8312yes—
678C2×C4C2×D4×D8311yescharacteristic
679C2×C4C2×#1305059012yes—
680C2×C4#1458184012yes—
681C2×C4C24×D8311yescharacteristic
682C8—22no—
683C8—1662no—
684C8—1662no—
685C8C2×#1305059014yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—44no—
690C22—3324no—
691C22—1662no—
692C22—1662no—
693C22—1662no—
694C22#1912835212yes—
695C22#137×D8312yes—
696C22#1912851112yes—
697C22C22×D4×D8311yescharacteristic
698C4—22no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3322no—
704C4—3322no—
705C4—3322no—
706C4—3322no—
707C4—834no—
708C4—1662no—
709C4—1662no—
710C4#1912835212yes—
711C4C22×#1305059011yescharacteristic
712C4C2×#1458184011yescharacteristic
713C2—42no—
714C2—3322no—
715C2#2492007414yesdirect product factor
716C2C2×#1912835211yescharacteristic
717C2C2×#137×D8311yescharacteristic
718C2C2×#1912851111yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#428×C83C2
socleC23×C83C22×D4
prime radicalC22×C22⋊D83D4
hypercenterC2×#428D83
hypocenterC83C2×#3356
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #24920074C2direct (N × H)
4. C2×#19128098C2semidirect
5. C2×#19128044C2semidirect
6. C2×#19128042C2semidirect
7. C2×#19128033C2semidirect
8. C2×#19128031C2semidirect
9. C2×#19127995C2semidirect
10. C2×#19127985C2semidirect
11. C2×#19127960C2semidirect
12. C2×#19127959C2semidirect
13. C2×#19127795C2semidirect
15. C2×#19127742C2semidirect
16. C2×#428×C83C2semidirect
42. #19128098C22semidirect
43. #19128044C22semidirect
44. #19128042C22semidirect
45. #19128033C22semidirect
46. #19128031C22semidirect
47. #19127995C22semidirect
48. #19127985C22semidirect
49. #19127960C22semidirect
50. #19127959C22semidirect
51. #19127795C22semidirect
53. #19127742C22semidirect
72. #428×C83C22semidirect
355. C2×C83#3356semidirect
375. C2×#428D83semidirect
376. C83C2×#3356semidirect
417. #428C2×D83semidirect
715. C2#24920074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284192
C2×#191284062
#249200742
C2×#191280982
C2×#191280442
C2×#191280422
C2×#191280332
C2×#191280312
C2×#191279952
C2×#191279852
C2×#191279602
C2×#191279592
C2×#191277952
C2×#191277772
C2×#191277422
C2×#428×C832
C2×#335683