Finite Group Databasebeta

← C2×#23776001 #35166992

Subgroups — C2×#23776001 #35166992

Order 20224.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099265C211yesmaximal, characteristic, complemented
2C2×#19099260C211yesmaximal, characteristic, complemented
3#23776001C2116yesmaximal, direct product factor
4C2×#19098963C211yesmaximal, characteristic, complemented
5C2×#19098886C211yesmaximal, characteristic, complemented
6C2×#19098884C211yesmaximal, characteristic, complemented
7C2×#19098875C211yesmaximal, characteristic, complemented
8C2×#19098874C211yesmaximal, characteristic, complemented
9C2×#19098865C211yesmaximal, characteristic, complemented
10C2×#19098861C211yesmaximal, characteristic, complemented
11C2×#19098813C211yesmaximal, characteristic, complemented
12C2×D8×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098639C211yesmaximal, characteristic, complemented
14C2×#19098605C211yesmaximal, characteristic, complemented
15C2×#19098602C211yesmaximal, characteristic, complemented
16C2×#469×C79C211yesmaximal, characteristic, complemented
17C22×#11929607C2211yescharacteristic
18#19099265—24no—
19#19099265C2218yescomplemented
20#19099260—24no—
21#19099260C2218yescomplemented
22C2×#14579154—21no—
23C2×#14579154—21no—
24C2×#14579152C2211yescharacteristic
25C2×#14579152C2211yescharacteristic
26C2×#14579145—21no—
27C2×#14579142—21no—
28C2×#14579133—21no—
29C2×#14579132—21no—
30C2×#14579132C2211yescharacteristic
31C2×#14579132C2211yescharacteristic
32C2×D4×Dic79—21no—
33C2×D4×Dic79C2211yescharacteristic
34C2×D4×Dic79C2211yescharacteristic
35C2×C4×C22⋊D79C2211yescharacteristic
36C2×(C22⋊D79)⋊C4—21no—
37C2×#14579120C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C22×C4⋊Dic79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41#19098963C2218yescomplemented
42#19098886C2218yescomplemented
43#19098884C2218yescomplemented
44#19098875C2218yescomplemented
45#19098874C2218yescomplemented
46#19098865C2218yescomplemented
47#19098861C2218yescomplemented
48#19098813C2218yescomplemented
49D8×Dic79C2218yescomplemented
50#19098639C2218yescomplemented
51#19098605C2218yescomplemented
52#19098602C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579082C2211yescharacteristic
63C2×#14579082C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×D8×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×#121×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#469×C79C2218yescomplemented
74C2×#106×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C22×C22⋊D79—21no—
78C22×C22⋊D79—21no—
79C22×C22⋊D79D411yescharacteristic
80C23×Dic79—21no—
81C23×Dic79—21no—
82C23×Dic79—21no—
83C22×C4×D79—21no—
84C22×C4×D79C2311yescharacteristic
85C2×#11929607—24no—
86C2×#11929607C2314yes—
87C22×C79⋊C8C2311yescharacteristic
88C22×C79⋊C8C2311yescharacteristic
89#14579154—28no—
90#14579154—28no—
91#14579152—22no—
92#14579152—22no—
93#14579152C2314yes—
94#14579152C2314yes—
95#14579145—28no—
96#14579142—28no—
97#14579133—28no—
98#14579132—28no—
99#14579132—22no—
100#14579132—22no—
101#14579132C2314yes—
102#14579132C2314yes—
103D4×Dic79—28no—
104D4×Dic79—22no—
105D4×Dic79—22no—
106D4×Dic79C2314yes—
107D4×Dic79C2314yes—
108C4×C22⋊D79D414yes—
109C4×C22⋊D79C2314yes—
110(C22⋊D79)⋊C4—28no—
111#14579120—22no—
112#14579120C2314yes—
113#14579119—22no—
114#14579119C2314yes—
115C2×C4⋊Dic79—22no—
116C2×C4⋊Dic79—21no—
117C2×C4⋊Dic79—21no—
118C2×C4⋊Dic79—21no—
119C2×C4⋊Dic79C2314yes—
120C2×C4⋊Dic79C2311yescharacteristic
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×Dic79⋊C4—21no—
125C2×Dic79⋊C4—21no—
126C2×Dic79⋊C4—21no—
127C2×Dic79⋊C4D411yescharacteristic
128C4⋊C4×D79—22no—
129C4⋊C4×D79C2314yes—
130C2×C22⋊Dic79—21no—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79D411yescharacteristic
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4D411yescharacteristic
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79C2311yescharacteristic
141#14579095C2314yes—
142#14579095C2314yes—
143#14579094C2314yes—
144#14579094C2314yes—
145#14579094C2314yes—
146#14579093C2314yes—
147#14579093C2314yes—
148#14579092C2314yes—
149Dic79⋊C8C2314yes—
150#14579082C2314yes—
151#14579082C2314yes—
152#14579082C2314yes—
153#14579082C2314yes—
154C22⋊(C79⋊C8)C2314yes—
155(C2×D79)⋊C8C2314yes—
156C8×Dic79C2314yes—
157C22×D4×C79—21no—
158C22×D4×C79—21no—
159C22×D4×C79C2311yescharacteristic
160C22×D4×C79C2311yescharacteristic
161C23×C4×C79C2311yescharacteristic
162C2×D8×C79—24no—
163C2×D8×C79C2314yes—
164C2×M16×C79—24no—
165C2×M16×C79C2314yes—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168#121×C79—22no—
169#121×C79—22no—
170#121×C79C2314yes—
171#121×C79C2314yes—
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C22⋊C4×C79—21no—
175C2×C22⋊C4×C79—21no—
176#106×C79C2314yes—
177#102×C79C2314yes—
178#102×C79C2314yes—
179C23×D79C2×D411yescharacteristic
180C2×C22⋊D79—24no—
181C2×C22⋊D79—24no—
182C2×C22⋊D79—42no—
183C2×C22⋊D79—44no—
184C2×C22⋊D79—82no—
185C2×C22⋊D79C2×D414yes—
186C22×Dic79—24no—
187C22×Dic79—24no—
188C22×Dic79—21no—
189C22×Dic79—21no—
190C22×Dic79—21no—
191C22×Dic79—21no—
192C22×Dic79—24no—
193C22×Dic79—82no—
194C22×Dic79—82no—
195C22×Dic79—82no—
196C22×Dic79C2×D411yescharacteristic
197C22×Dic79C2×D411yescharacteristic
198C22×Dic79C2×D411yescharacteristic
199C2×C4×D79—24no—
200C2×C4×D79—22no—
201C2×C4×D79—22no—
202C2×C4×D79—82no—
203C2×C4×D79C2×D412yes—
204C2×C4×D79C2412yes—
205#11929607—28no—
206C2×C79⋊C8—22no—
207C2×C79⋊C8—22no—
208C2×C79⋊C8C2412yes—
209C2×C79⋊C8C2412yes—
210C4⋊Dic79—24no—
211C4⋊Dic79—24no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79—24no—
216C4⋊Dic79—21no—
217C4⋊Dic79C2412yes—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220C4⋊Dic79C2412yes—
221Dic79⋊C4—24no—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4C2×D414yes—
225C22⋊Dic79—24no—
226C22⋊Dic79—24no—
227C22⋊Dic79—24no—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230C22⋊Dic79C2×D414yes—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4C2×D414yes—
233C4×Dic79—24no—
234C4×Dic79—24no—
235C4×Dic79C2×D412yes—
236C4×Dic79C2412yes—
237C24×C79—21no—
238C24×C79—21no—
239C24×C79C2×D411yescharacteristic
240C2×D4×C79—24no—
241C2×D4×C79—24no—
242C2×D4×C79—21no—
243C2×D4×C79—21no—
244C2×D4×C79—22no—
245C2×D4×C79—22no—
246C2×D4×C79—22no—
247C2×D4×C79—22no—
248C2×D4×C79—44no—
249C2×D4×C79—82no—
250C2×D4×C79C2412yes—
251C2×D4×C79C2412yes—
252C22×C4×C79—22no—
253C22×C4×C79—22no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2411yescharacteristic
260D8×C79—28no—
261M16×C79—28no—
262C2×C8×C79—22no—
263C2×C8×C79#4114yes—
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C4⋊C4×C79—21no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79C2412yes—
269C4⋊C4×C79C2412yes—
270C22⋊C4×C79—24no—
271C22⋊C4×C79—24no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—42no—
278C23×C79—42no—
279C23×C79—42no—
280C23×C79—42no—
281C23×C79—42no—
282C23×C79—42no—
283C23×C79C22×D412yes—
284C23×C79C22×D411yescharacteristic
285C22×D79—22no—
286C22×D79—22no—
287C22×D79—22no—
288C22×D79C22×D412yes—
289D4×C79—22no—
290D4×C79—22no—
291D4×C79—22no—
292D4×C79—22no—
293D4×C79—48no—
294D4×C79—42no—
295D4×C79—42no—
296D4×C79—84no—
297C2×C4×C79—22no—
298C2×C4×C79—24no—
299C2×C4×C79—22no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—42no—
304C2×C4×C79—42no—
305C2×C4×C79C22×D412yes—
306C2×C4×C79C22×D411yescharacteristic
307C2×C4×C79C2×#4112yes—
308C2×C4×C792−1+412yes—
309C2×C4×C79C2511yescharacteristic
310C22⋊D79—44no—
311C22⋊D79—48no—
312C22⋊D79—84no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—42no—
321C2×Dic79—42no—
322C2×Dic79—42no—
323C2×Dic79—42no—
324C2×Dic79—84no—
325C2×Dic79—84no—
326C2×Dic79—84no—
327C2×Dic79C22×D412yes—
328C2×Dic79C22×D412yes—
329C2×Dic79C22×D412yes—
330C4×D79—24no—
331C4×D79—22no—
332C4×D79—22no—
333C4×D79—84no—
334C8×C79—22no—
335C8×C79C2×#4114yes—
336C79⋊C8—22no—
337C79⋊C8—22no—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—44no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—42no—
346C22×C79—42no—
347C22×C79—42no—
348C22×C79—84no—
349C22×C79—84no—
350C22×C79#54712yes—
351C22×C79#57512yes—
352C22×C79#57612yes—
353C22×C79C23×D411yescharacteristic
354C2×D79—22no—
355C2×D79—22no—
356C2×D79—22no—
357C2×D79—44no—
358C4×C79—22no—
359C4×C79—42no—
360C4×C79—42no—
361C4×C79#54712yes—
362C4×C79C22×#4111yescharacteristic
363C4×C79C2×2−1+411yescharacteristic
364Dic79—22no—
365Dic79—22no—
366Dic79—22no—
367Dic79—42no—
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371C2×#3355—791nomaximal, Sylow
372C2×C79—42no—
373C2×C79—82no—
374C2×C79—82no—
375C2×C79#335514yescomplemented
376C2×C79C2×#54711yescharacteristic
377C2×C79C2×#57511yescharacteristic
378C2×C79C2×#57611yescharacteristic
379D79—42no—
380C2×#553—791no—
381C2×#553—791no—
382#3355—7916no—
383C2×#499—791no—
384C2×#482—791no—
385C2×#482—791no—
386C2×#480—791no—
387C2×#480—791no—
388C2×#478—791no—
389C2×#478—791no—
390C2×#469—791no—
391C2×#469D7911yescharacteristic, complemented
392C2×C4×D8—791no—
393C2×#436—791no—
394C2×#428—791no—
395C2×#428—791no—
396C79C2×#335511yescharacteristic, complemented, Sylow
397C22×D8C2×D7911yescharacteristic
398C22×M16—791no—
399C22×M16C2×D7911yescharacteristic
400#553—798no—
401#553—798no—
402#553—1584no—
403#553—1584no—
404C2×#126—1581no—
405C2×#126—1581no—
406C2×#125—791no—
407C2×#125—791no—
408C2×#123—1581no—
409C2×#123—1581no—
410C2×#121—791no—
411C2×#121—791no—
412C2×#121—1581no—
413C2×#121—1581no—
414C2×#121C2×D7911yescharacteristic
415C2×#121C2×D7911yescharacteristic
416C2×C4×D4—791no—
417C2×C4×D4—791no—
418C2×C4×D4—791no—
419C2×C4×D4—1581no—
420C2×C4×D4—1581no—
421C2×#117—791no—
422C2×#117—791no—
423C22×C4⋊C4—791no—
424C22×C4⋊C4—791no—
425#499—798no—
426#482—798no—
427#482—798no—
428#480—798no—
429#480—798no—
430#478—798no—
431#478—798no—
432#469—798no—
433#469C2×D7918yescomplemented
434C4×D8—798no—
435#436—798no—
436#428—798no—
437#428—798no—
438C2×#107—791no—
439C2×#107—791no—
440C2×#107—791no—
441C2×#107—791no—
442C2×#107—791no—
443C2×#106—791no—
444C2×#106—791no—
445C2×#106—791no—
446C2×#106C2×D7911yescharacteristic
447C2×C4⋊C8—791no—
448C2×#102—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×#102C2×D7911yescharacteristic
453C2×#102C2×D7911yescharacteristic
454C2×C22⋊C8—791no—
455C2×C22⋊C8—791no—
456C2×C4×C8—791no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—791no—
460C22×D4—1581no—
461C22×D4—1581no—
462C22×D4C22×D7911yescharacteristic
463C22×D4C22×D7911yescharacteristic
464C23×C4—791no—
465C23×C4—1581no—
466C23×C4—1581no—
467C23×C4—1581no—
468C23×C4—1581no—
469C23×C4C22×D7911yescharacteristic
470C2×D8—24no—
471C2×D8C22×D7914yes—
472C2×M16—24no—
473C2×M16—794no—
474C2×M16—1584no—
475C2×M16C22×D7914yes—
476C22×C8—791no—
477C22×C8—791no—
478C22×C8C22×D7911yescharacteristic
479C22×C8C22×D7911yescharacteristic
480#126—1588no—
481#126—1588no—
482#125—794no—
483#125—794no—
484#125—1582no—
485#125—1582no—
486#123—1588no—
487#123—1588no—
488#121—22no—
489#121—22no—
490#121—794no—
491#121—794no—
492#121—1582no—
493#121—1582no—
494#121—1588no—
495#121—1588no—
496#121C22×D7914yes—
497#121C22×D7914yes—
498C4×D4—794no—
499C4×D4—794no—
500C4×D4—794no—
501C4×D4—794no—
502C4×D4—1582no—
503C4×D4—1582no—
504C4×D4—1588no—
505C4×D4—1588no—
506#117—794no—
507#117—794no—
508#117—1582no—
509#117—1582no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—791no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—791no—
514C2×C4⋊C4—794no—
515C2×C4⋊C4—791no—
516C2×C4⋊C4—794no—
517C2×C4⋊C4—1582no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4—1581no—
521C2×C4⋊C4—1581no—
522C2×C4⋊C4—1581no—
523C2×C4⋊C4—1581no—
524C2×C4⋊C4—1582no—
525C2×C4⋊C4C22×D7911yescharacteristic
526C2×C4⋊C4C22×D7911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—791no—
530C2×C22⋊C4—791no—
531C2×C22⋊C4—1581no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4—1581no—
536C2×C22⋊C4—1581no—
537C2×C42—791no—
538C2×C42—1581no—
539C2×C42—1581no—
540#107—794no—
541#107—794no—
542#107—794no—
543#107—794no—
544#107—794no—
545#106—794no—
546#106—794no—
547#106—794no—
548#106C22×D7914yes—
549C4⋊C8—794no—
550#102—794no—
551#102—794no—
552#102—794no—
553#102—794no—
554#102C22×D7914yes—
555#102C22×D7914yes—
556C22⋊C8—794no—
557C22⋊C8—794no—
558C4×C8—794no—
559C24—21no—
560C24—21no—
561C24—791no—
562C24D4×D7911yescharacteristic
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—3164no—
574C2×D4—3162no—
575C2×D4—794no—
576C2×D4—6322no—
577C2×D4—1584no—
578C2×D4—1584no—
579C2×D4C23×D7912yes—
580C2×D4C23×D7912yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—791no—
586C22×C4—791no—
587C22×C4—791no—
588C22×C4—792no—
589C22×C4—792no—
590C22×C4—6322no—
591C22×C4—6322no—
592C22×C4—6322no—
593C22×C4—6322no—
594C22×C4—1584no—
595C22×C4—1581no—
596C22×C4—1581no—
597C22×C4—1581no—
598C22×C4—1581no—
599C22×C4—1584no—
600C22×C4—1584no—
601C22×C4—1584no—
602C22×C4—1582no—
603C22×C4—1582no—
604C22×C4D4×D7912yes—
605C22×C4D4×D7911yescharacteristic
606C22×C4C23×D7912yes—
607C22×C4C23×D7911yescharacteristic
608D8—28no—
609M16—28no—
610M16—1588no—
611C2×C8—22no—
612C2×C8—792no—
613C2×C8—792no—
614C2×C8—1582no—
615C2×C8—1582no—
616C2×C8#1192962314yes—
617C2×C8C23×D7912yes—
618C2×C8C23×D7912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—794no—
622C4⋊C4—792no—
623C4⋊C4—792no—
624C4⋊C4—792no—
625C4⋊C4—792no—
626C4⋊C4—1584no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1581no—
632C4⋊C4—1581no—
633C4⋊C4—1581no—
634C4⋊C4—1584no—
635C4⋊C4—1581no—
636C4⋊C4C23×D7912yes—
637C4⋊C4C23×D7912yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—794no—
641C22⋊C4—794no—
642C22⋊C4—1584no—
643C22⋊C4—1584no—
644C22⋊C4—1584no—
645C22⋊C4—1584no—
646C22⋊C4—1584no—
647C22⋊C4—1584no—
648C42—792no—
649C42—792no—
650C42—1584no—
651C42—1584no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—792no—
664C23—1582no—
665C23—1582no—
666C23—1582no—
667C23C2×D4×D7912yes—
668C23C2×D4×D7911yescharacteristic
669D4—22no—
670D4—22no—
671D4—22no—
672D4—22no—
673D4—48no—
674D4—42no—
675D4—42no—
676D4—84no—
677D4—3168no—
678D4—3164no—
679D4—6324no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—3162no—
689C2×C4—3162no—
690C2×C4—3162no—
691C2×C4—3162no—
692C2×C4—792no—
693C2×C4—792no—
694C2×C4—792no—
695C2×C4—6324no—
696C2×C4—6324no—
697C2×C4—6324no—
698C2×C4—6324no—
699C2×C4—1582no—
700C2×C4—1582no—
701C2×C4—1582no—
702C2×C4—1582no—
703C2×C4—1582no—
704C2×C4—1582no—
705C2×C4—1582no—
706C2×C4—1582no—
707C2×C4—1584no—
708C2×C4—1582no—
709C2×C4C2×D4×D7912yes—
710C2×C4C2×D4×D7911yescharacteristic
711C2×C4C2×#1192962312yes—
712C2×C4#1457920812yes—
713C2×C4C24×D7911yescharacteristic
714C8—22no—
715C8—1582no—
716C8—1582no—
717C8C2×#1192962314yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—84no—
729C22—84no—
730C22—3164no—
731C22—1582no—
732C22—1582no—
733C22—1582no—
734C22#1909921312yes—
735C22#1909935912yes—
736C22#1909936712yes—
737C22C22×D4×D7911yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—3162no—
742C4—3162no—
743C4—3162no—
744C4—3162no—
745C4—1582no—
746C4—1582no—
747C4—1582no—
748C4#1909921312yes—
749C4C22×#1192962311yescharacteristic
750C4C2×#1457920811yescharacteristic
751C2—42no—
752C2—82no—
753C2—82no—
754C2—3162no—
755C2#2377600114yesdirect product factor
756C2C2×#1909921311yescharacteristic
757C2C2×#1909935911yescharacteristic
758C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#469×C79C2
socleC23×C79C22×D4
hypercenterC2×#469D79
hypocenterC79C2×#3355
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C2×#19099265C2semidirect
2. C2×#19099260C2semidirect
3. #23776001C2direct (N × H)
4. C2×#19098963C2semidirect
5. C2×#19098886C2semidirect
6. C2×#19098884C2semidirect
7. C2×#19098875C2semidirect
8. C2×#19098874C2semidirect
9. C2×#19098865C2semidirect
10. C2×#19098861C2semidirect
11. C2×#19098813C2semidirect
12. C2×D8×Dic79C2semidirect
13. C2×#19098639C2semidirect
14. C2×#19098605C2semidirect
15. C2×#19098602C2semidirect
16. C2×#469×C79C2semidirect
19. #19099265C22semidirect
21. #19099260C22semidirect
41. #19098963C22semidirect
42. #19098886C22semidirect
43. #19098884C22semidirect
44. #19098875C22semidirect
45. #19098874C22semidirect
46. #19098865C22semidirect
47. #19098861C22semidirect
48. #19098813C22semidirect
49. D8×Dic79C22semidirect
50. #19098639C22semidirect
51. #19098605C22semidirect
52. #19098602C22semidirect
73. #469×C79C22semidirect
375. C2×C79#3355semidirect
391. C2×#469D79semidirect
396. C79C2×#3355semidirect
433. #469C2×D79semidirect
755. C2#23776001direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992652
C2×#190992602
#237760012
C2×#190989632
C2×#190988862
C2×#190988842
C2×#190988752
C2×#190988742
C2×#190988652
C2×#190988612
C2×#190988132
C2×D8×Dic792
C2×#190986392
C2×#190986052
C2×#190986022
C2×#469×C792
C2×#335579