Finite Group Databasebeta

← C2×#23775979 #35166968

Subgroups — C2×#23775979 #35166968

Order 20224.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099284C211yesmaximal, characteristic, complemented
2C2×#19099213C211yesmaximal, characteristic
3#23775979C2116yesmaximal, direct product factor
4C2×#19098967C211yesmaximal, characteristic, complemented
5C2×#19098897C211yesmaximal, characteristic, complemented
6C2×#19098896C211yesmaximal, characteristic, complemented
7C2×#19098886C211yesmaximal, characteristic, complemented
8C2×#19098884C211yesmaximal, characteristic, complemented
9C2×#19098846C211yesmaximal, characteristic, complemented
10C2×#19098841C211yesmaximal, characteristic, complemented
11C2×#19098806C211yesmaximal, characteristic, complemented
12C2×SD16×Dic79C211yesmaximal, characteristic, complemented
13C2×#19098639C211yesmaximal, characteristic, complemented
14C2×#19098605C211yesmaximal, characteristic, complemented
15C2×#19098604C211yesmaximal, characteristic, complemented
16C2×#468×C79C211yesmaximal, characteristic, complemented
17C22×#11929623—21no—
18C22×#11929607C2211yescharacteristic
19#19099284—24no—
20#19099284C2218yescomplemented
21#19099213—24no—
22#19099213C2218yes—
23C2×#14579160C2211yescharacteristic
24C2×#14579160C2211yescharacteristic
25C2×#14579156—21no—
26C2×#14579154—21no—
27C2×#14579147—21no—
28C2×#14579143—21no—
29C2×#14579142—21no—
30C2×#14579138—21no—
31C2×#14579137C2211yescharacteristic
32C2×#14579132C2211yescharacteristic
33C2×Q8×Dic79C2211yescharacteristic
34C2×#14579126—21no—
35C2×D4×Dic79C2211yescharacteristic
36C2×C4×C22⋊D79C2211yescharacteristic
37C2×#14579120C2211yescharacteristic
38C2×#14579119C2211yescharacteristic
39C22×C4⋊Dic79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41#19098967C2218yescomplemented
42#19098897C2218yescomplemented
43#19098896C2218yescomplemented
44#19098886C2218yescomplemented
45#19098884C2218yescomplemented
46#19098846C2218yescomplemented
47#19098841C2218yescomplemented
48#19098806C2218yescomplemented
49SD16×Dic79C2218yescomplemented
50#19098639C2218yescomplemented
51#19098605C2218yescomplemented
52#19098604C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579093C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×Dic79⋊C8C2211yescharacteristic
62C2×#14579085C2211yescharacteristic
63C2×#14579085C2211yescharacteristic
64C2×#14579082C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
69C22×SD16×C79C2211yescharacteristic
70C22×M16×C79C2211yescharacteristic
71C2×C22⋊Q8×C79C2211yescharacteristic
72C2×#121×C79C2211yescharacteristic
73#468×C79C2218yescomplemented
74C2×#107×C79C2211yescharacteristic
75C2×#103×C79C2211yescharacteristic
76C2×#102×C79C2211yescharacteristic
77C2×#11929623—28no—
78C2×#11929623—48no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×C22⋊D79—21no—
82C22×C22⋊D79D411yescharacteristic
83C23×Dic79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C22×C4×D79C2311yescharacteristic
87C2×#11929607—24no—
88C2×#11929607C2314yes—
89C22×C79⋊C8C2311yescharacteristic
90C22×C79⋊C8C2311yescharacteristic
91#14579160—22no—
92#14579160—22no—
93#14579160C2314yes—
94#14579160C2314yes—
95#14579156—28no—
96#14579154—28no—
97#14579147—28no—
98#14579143—28no—
99#14579142—28no—
100#14579138—28no—
101#14579137—22no—
102#14579137C2314yes—
103#14579132—22no—
104#14579132C2314yes—
105Q8×Dic79—22no—
106Q8×Dic79C2314yes—
107#14579126—28no—
108D4×Dic79—22no—
109D4×Dic79C2314yes—
110C4×C22⋊D79D414yes—
111C4×C22⋊D79C2314yes—
112#14579120—22no—
113#14579120C2314yes—
114#14579119—22no—
115#14579119C2314yes—
116C2×C4⋊Dic79—22no—
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⋊C4—21no—
128C2×Dic79⋊C4D411yescharacteristic
129C4⋊C4×D79—22no—
130C4⋊C4×D79C2314yes—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79D411yescharacteristic
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4D411yescharacteristic
138C2×C4×Dic79—21no—
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142#14579095C2314yes—
143#14579095C2314yes—
144#14579094C2314yes—
145#14579094C2314yes—
146#14579094C2314yes—
147#14579093C2314yes—
148#14579093C2314yes—
149#14579092C2314yes—
150Dic79⋊C8C2314yes—
151#14579085C2314yes—
152#14579085C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156(C2×D79)⋊C8C2314yes—
157C8×Dic79C2314yes—
158C22×Q8×C79C2311yescharacteristic
159C22×D4×C79—21no—
160C22×D4×C79C2311yescharacteristic
161C23×C4×C79C2311yescharacteristic
162C2×SD16×C79—24no—
163C2×SD16×C79C2314yes—
164C2×M16×C79—24no—
165C2×M16×C79C2314yes—
166C22×C8×C79C2311yescharacteristic
167C22×C8×C79C2311yescharacteristic
168C22⋊Q8×C79—22no—
169C22⋊Q8×C79C2314yes—
170#121×C79—22no—
171#121×C79C2314yes—
172C2×C4⋊C4×C79—21no—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177#107×C79C2314yes—
178#103×C79C2314yes—
179#102×C79C2314yes—
180C23×D79C2×D411yescharacteristic
181#11929623—432no—
182C2×Dic158—24no—
183C2×Dic158—24no—
184C2×Dic158—44no—
185C2×Dic158—44no—
186C2×C22⋊D79—24no—
187C2×C22⋊D79—24no—
188C2×C22⋊D79—44no—
189C2×C22⋊D79C2×D414yes—
190C22×Dic79—24no—
191C22×Dic79—21no—
192C22×Dic79—21no—
193C22×Dic79—24no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—44no—
197C22×Dic79—44no—
198C22×Dic79C2×D411yescharacteristic
199C22×Dic79C2×D411yescharacteristic
200C22×Dic79C2×D411yescharacteristic
201C2×C4×D79—24no—
202C2×C4×D79—22no—
203C2×C4×D79—22no—
204C2×C4×D79—44no—
205C2×C4×D79C2×D412yes—
206C2×C4×D79C2412yes—
207#11929607—28no—
208C2×C79⋊C8—22no—
209C2×C79⋊C8—22no—
210C2×C79⋊C8C2412yes—
211C2×C79⋊C8C2412yes—
212C4⋊Dic79—24no—
213C4⋊Dic79—21no—
214C4⋊Dic79—21no—
215C4⋊Dic79—24no—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79C2412yes—
219C4⋊Dic79C2412yes—
220C4⋊Dic79C2412yes—
221C4⋊Dic79C2412yes—
222Dic79⋊C4—24no—
223Dic79⋊C4—24no—
224Dic79⋊C4—24no—
225Dic79⋊C4—24no—
226Dic79⋊C4C2×D414yes—
227C22⋊Dic79—24no—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230C22⋊Dic79C2×D414yes—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4C2×D414yes—
234C4×Dic79—24no—
235C4×Dic79—24no—
236C4×Dic79—24no—
237C4×Dic79C2×D412yes—
238C4×Dic79C2412yes—
239C24×C79—21no—
240C24×C79C2×D411yescharacteristic
241C2×Q8×C79—21no—
242C2×Q8×C79—22no—
243C2×Q8×C79—22no—
244C2×Q8×C79C2412yes—
245C2×D4×C79—24no—
246C2×D4×C79—21no—
247C2×D4×C79—22no—
248C2×D4×C79—22no—
249C2×D4×C79—44no—
250C2×D4×C79C2412yes—
251C22×C4×C79—22no—
252C22×C4×C79—22no—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79—21no—
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2411yescharacteristic
260SD16×C79—28no—
261M16×C79—28no—
262C2×C8×C79—22no—
263C2×C8×C79#4114yescomplemented
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C4⋊C4×C79—24no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79—21no—
269C4⋊C4×C79C2412yes—
270C4⋊C4×C79C2412yes—
271C22⋊C4×C79—24no—
272C22⋊C4×C79—24no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—42no—
278C23×C79—42no—
279C23×C79—42no—
280C23×C79C22×D412yes—
281C23×C79C22×D411yescharacteristic
282C22×D79—22no—
283C22×D79—22no—
284C22×D79—22no—
285C22×D79C22×D412yes—
286Q8×C79—22no—
287Q8×C79—22no—
288Q8×C79—42no—
289D4×C79—22no—
290D4×C79—22no—
291D4×C79—48no—
292D4×C79—42no—
293C2×C4×C79—22no—
294C2×C4×C79—24no—
295C2×C4×C79—22no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79—42no—
301C2×C4×C79—42no—
302C2×C4×C79—42no—
303C2×C4×C79C22×D412yes—
304C2×C4×C79C22×D411yescharacteristic
305C2×C4×C79C2×#4112yes—
306C2×C4×C792−1+412yes—
307C2×C4×C79C2511yescharacteristic
308C22⋊D79—28no—
309C22⋊D79—48no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—48no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—42no—
321C2×Dic79—48no—
322C2×Dic79AGL(1,ℤ/8)14yes—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325C2×Dic79C22×D412yes—
326C4×D79—24no—
327C4×D79—22no—
328C4×D79—22no—
329C4×D79—48no—
330Dic158—48no—
331Dic158—48no—
332C8×C79—22no—
333C8×C79C2×#4114yescomplemented
334C79⋊C8—22no—
335C79⋊C8—22no—
336C22×C79—22no—
337C22×C79—22no—
338C22×C79—22no—
339C22×C79—44no—
340C22×C79—42no—
341C22×C79—42no—
342C22×C79—42no—
343C22×C79—84no—
344C22×C79#54712yes—
345C22×C79C2×AGL(1,ℤ/8)12yes—
346C22×C79#57812yes—
347C22×C79C23×D411yescharacteristic
348C2×D79—22no—
349C2×D79—22no—
350C2×D79—22no—
351C2×D79—44no—
352C4×C79—22no—
353C4×C79—42no—
354C4×C79—42no—
355C4×C79—42no—
356C4×C79#54712yes—
357C4×C79C22×#4111yescharacteristic
358C4×C79C2×2−1+411yescharacteristic
359Dic79—22no—
360Dic79—22no—
361Dic79—42no—
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365Dic79C2×AGL(1,ℤ/8)14yes—
366C2×#3353—791nomaximal, Sylow
367C2×C79—42no—
368C2×C79—82no—
369C2×C79#335314yescomplemented
370C2×C79C2×#54711yescharacteristic
371C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
372C2×C79C2×#57811yescharacteristic
373D79—42no—
374C2×#556—791no—
375C2×#547—791no—
376#3353—7916no—
377C2×#500—791no—
378C2×#484—791no—
379C2×#484—791no—
380C2×#482—791no—
381C2×#482—791no—
382C2×#475—791no—
383C2×#474—791no—
384C2×#468—791no—
385C2×#468D7911yescharacteristic, complemented
386C2×C4×SD16—791no—
387C2×#436—791no—
388C2×#428—791no—
389C2×#428—791no—
390C79C2×#335311yescharacteristic, complemented, Sylow
391C22×#41—1581no—
392C22×SD16C2×D7911yescharacteristic
393C22×M16—791no—
394C22×M16C2×D7911yescharacteristic
395#556—798no—
396#556—1584no—
397#547—798no—
398#547—1584no—
399C2×C4⋊Q8—791no—
400C2×C4⋊Q8—791no—
401C2×#126—1581no—
402C2×#126—1581no—
403C2×#124—1581no—
404C2×#123—1581no—
405C2×#123—1581no—
406C2×C22⋊Q8—791no—
407C2×C22⋊Q8—1581no—
408C2×C22⋊Q8C2×D7911yescharacteristic
409C2×#121—791no—
410C2×#121C2×D7911yescharacteristic
411C2×C4×Q8—791no—
412C2×C4×Q8—1581no—
413C2×C4×D4—791no—
414C2×C4×D4—791no—
415C2×#117—791no—
416C2×#117—791no—
417C22×C4⋊C4—791no—
418C22×C4⋊C4—791no—
419#500—798no—
420#484—798no—
421#484—798no—
422#482—798no—
423#482—798no—
424#475—798no—
425#474—798no—
426#468—798no—
427#468C2×D7918yescomplemented
428C4×SD16—798no—
429#436—798no—
430#428—798no—
431#428—798no—
432C2×#107—791no—
433C2×#107—791no—
434C2×#107—791no—
435C2×#107—791no—
436C2×#107—791no—
437C2×#107C2×D7911yescharacteristic
438C2×#106—791no—
439C2×#106—791no—
440C2×#106—791no—
441C2×C4⋊C8—791no—
442C2×#103—791no—
443C2×#103—791no—
444C2×#103C2×D7911yescharacteristic
445C2×#102—791no—
446C2×#102—791no—
447C2×#102C2×D7911yescharacteristic
448C2×C22⋊C8—791no—
449C2×C22⋊C8—791no—
450C2×C4×C8—791no—
451C2×#41—3168no—
452C2×#41—1588no—
453C22×Q8—1581no—
454C22×Q8—1581no—
455C22×Q8C22×D7911yescharacteristic
456C22×D4—21no—
457C22×D4—791no—
458C22×D4—1581no—
459C22×D4C22×D7911yescharacteristic
460C23×C4—791no—
461C23×C4—1581no—
462C23×C4—1581no—
463C23×C4—1581no—
464C23×C4C22×D7911yescharacteristic
465C2×SD16—24no—
466C2×SD16C22×D7914yes—
467C2×M16—24no—
468C2×M16—794no—
469C2×M16—1584no—
470C2×M16C22×D7914yes—
471C22×C8—791no—
472C22×C8—791no—
473C22×C8C22×D7911yescharacteristic
474C22×C8C22×D7911yescharacteristic
475C4⋊Q8—794no—
476C4⋊Q8—794no—
477C4⋊Q8—1582no—
478C4⋊Q8—1582no—
479#126—1588no—
480#126—1588no—
481#124—1588no—
482#123—1588no—
483#123—1588no—
484C22⋊Q8—22no—
485C22⋊Q8—794no—
486C22⋊Q8—1588no—
487C22⋊Q8—1582no—
488C22⋊Q8C22×D7914yes—
489#121—22no—
490#121—794no—
491#121—1582no—
492#121C22×D7914yes—
493C4×Q8—794no—
494C4×Q8—1582no—
495C4×Q8—1588no—
496C4×D4—794no—
497C4×D4—794no—
498C4×D4—794no—
499C4×D4—1582no—
500#117—794no—
501#117—794no—
502#117—1582no—
503#117—1582no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—791no—
506C2×C4⋊C4—791no—
507C2×C4⋊C4—791no—
508C2×C4⋊C4—794no—
509C2×C4⋊C4—791no—
510C2×C4⋊C4—791no—
511C2×C4⋊C4—794no—
512C2×C4⋊C4—1582no—
513C2×C4⋊C4—1581no—
514C2×C4⋊C4—1581no—
515C2×C4⋊C4—1581no—
516C2×C4⋊C4—1581no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1582no—
520C2×C4⋊C4C22×D7911yescharacteristic
521C2×C4⋊C4C22×D7911yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—791no—
525C2×C22⋊C4—791no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C42—791no—
532C2×C42—1581no—
533C2×C42—1581no—
534C2×C42—1581no—
535#107—794no—
536#107—794no—
537#107—794no—
538#107—794no—
539#107—794no—
540#107C22×D7914yes—
541#106—794no—
542#106—794no—
543#106—794no—
544C4⋊C8—794no—
545#103—794no—
546#103—794no—
547#103C22×D7914yes—
548#102—794no—
549#102—794no—
550#102C22×D7914yes—
551C22⋊C8—794no—
552C22⋊C8—794no—
553C4×C8—794no—
554C24—21no—
555C24—791no—
556C24D4×D7911yescharacteristic
557#41—31632no—
558C2×Q8—21no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—3164no—
562C2×Q8—3164no—
563C2×Q8—1584no—
564C2×Q8—1584no—
565C2×Q8C23×D7912yes—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—44no—
571C2×D4—3164no—
572C2×D4—794no—
573C2×D4—1584no—
574C2×D4—1584no—
575C2×D4C23×D7912yes—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—3164no—
582C22×C4—3164no—
583C22×C4—3164no—
584C22×C4—791no—
585C22×C4—791no—
586C22×C4—791no—
587C22×C4—792no—
588C22×C4—792no—
589C22×C4—1584no—
590C22×C4—1584no—
591C22×C4—1584no—
592C22×C4—1581no—
593C22×C4—1581no—
594C22×C4—1581no—
595C22×C4—1581no—
596C22×C4—1582no—
597C22×C4—1582no—
598C22×C4D4×D7912yes—
599C22×C4D4×D7911yescharacteristic
600C22×C4C23×D7912yes—
601C22×C4C23×D7911yescharacteristic
602SD16—28no—
603M16—28no—
604M16—1588no—
605C2×C8—22no—
606C2×C8—792no—
607C2×C8—792no—
608C2×C8—1582no—
609C2×C8—1582no—
610C2×C8#1192962314yescomplemented
611C2×C8C23×D7912yes—
612C2×C8C23×D7912yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—794no—
617C4⋊C4—792no—
618C4⋊C4—792no—
619C4⋊C4—792no—
620C4⋊C4—792no—
621C4⋊C4—1584no—
622C4⋊C4—1584no—
623C4⋊C4—1584no—
624C4⋊C4—1584no—
625C4⋊C4—1584no—
626C4⋊C4—1581no—
627C4⋊C4—1581no—
628C4⋊C4—1584no—
629C4⋊C4—1581no—
630C4⋊C4—1581no—
631C4⋊C4C23×D7912yes—
632C4⋊C4C23×D7912yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—794no—
636C22⋊C4—794no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C22⋊C4—1584no—
640C22⋊C4—1584no—
641C22⋊C4—1584no—
642C42—792no—
643C42—792no—
644C42—1584no—
645C42—1584no—
646C42—1584no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—792no—
655C23—1582no—
656C23—1582no—
657C23—1582no—
658C23C2×D4×D7912yes—
659C23C2×D4×D7911yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—3168no—
664Q8—3168no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—42no—
669D4—3168no—
670D4—1588no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—3168no—
682C2×C4—3168no—
683C2×C4—3162no—
684C2×C4—3162no—
685C2×C4—3162no—
686C2×C4—3162no—
687C2×C4—3168no—
688C2×C4—794no—
689C2×C4—792no—
690C2×C4—792no—
691C2×C4—792no—
692C2×C4—1582no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4—1582no—
697C2×C4—1582no—
698C2×C4—1582no—
699C2×C4—1584no—
700C2×C4—1582no—
701C2×C4C2×D4×D7912yes—
702C2×C4C2×D4×D7911yescharacteristic
703C2×C4C2×#1192962312yes—
704C2×C4#1457920812yes—
705C2×C4C24×D7911yescharacteristic
706C8—22no—
707C8—1582no—
708C8—1582no—
709C8C2×#1192962314yescomplemented
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—3164no—
719C22—1582no—
720C22—1582no—
721C22—1582no—
722C22#1909921312yes—
723C22AGL(1,ℤ/8)×D7912yes—
724C22#1909937912yes—
725C22C22×D4×D7911yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—3162no—
731C4—3162no—
732C4—3162no—
733C4—3162no—
734C4—794no—
735C4—1582no—
736C4—1582no—
737C4#1909921312yes—
738C4C22×#1192962311yescharacteristic
739C4C2×#1457920811yescharacteristic
740C2—42no—
741C2—82no—
742C2—3162no—
743C2#2377597914yesdirect product factor
744C2C2×#1909921311yescharacteristic
745C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
746C2C2×#1909937911yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#468×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099213C2
hypercenterC2×#468D79
hypocenterC79C2×#3353
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#19099284C2semidirect
3. #23775979C2direct (N × H)
4. C2×#19098967C2semidirect
5. C2×#19098897C2semidirect
6. C2×#19098896C2semidirect
7. C2×#19098886C2semidirect
8. C2×#19098884C2semidirect
9. C2×#19098846C2semidirect
10. C2×#19098841C2semidirect
11. C2×#19098806C2semidirect
12. C2×SD16×Dic79C2semidirect
13. C2×#19098639C2semidirect
14. C2×#19098605C2semidirect
15. C2×#19098604C2semidirect
16. C2×#468×C79C2semidirect
20. #19099284C22semidirect
41. #19098967C22semidirect
42. #19098897C22semidirect
43. #19098896C22semidirect
44. #19098886C22semidirect
45. #19098884C22semidirect
46. #19098846C22semidirect
47. #19098841C22semidirect
48. #19098806C22semidirect
49. SD16×Dic79C22semidirect
50. #19098639C22semidirect
51. #19098605C22semidirect
52. #19098604C22semidirect
73. #468×C79C22semidirect
263. C2×C8×C79#41semidirect
333. C8×C79C2×#41semidirect
369. C2×C79#3353semidirect
385. C2×#468D79semidirect
390. C79C2×#3353semidirect
427. #468C2×D79semidirect
610. C2×C8#11929623semidirect
709. C8C2×#11929623semidirect
743. C2#23775979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992842
C2×#190992132
#237759792
C2×#190989672
C2×#190988972
C2×#190988962
C2×#190988862
C2×#190988842
C2×#190988462
C2×#190988412
C2×#190988062
C2×SD16×Dic792
C2×#190986392
C2×#190986052
C2×#190986042
C2×#468×C792
C2×#335379