Finite Group Databasebeta

← C2×#23775990 #35166980

Subgroups — C2×#23775990 #35166980

Order 20224.

2146 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099277C211yesmaximal, characteristic, complemented
2C2×#19099213C211yesmaximal, characteristic, complemented
3#23775990C2116yesmaximal, direct product factor
4C2×#19098960C211yesmaximal, characteristic, complemented
5C2×#19098880C211yesmaximal, characteristic, complemented
6C2×#19098879C211yesmaximal, characteristic, complemented
7C2×#19098885C211yesmaximal, characteristic, complemented
8C2×#19098884C211yesmaximal, characteristic, complemented
9C2×#19098851C211yesmaximal, characteristic, complemented
10C2×#19098841C211yesmaximal, 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×#11929623—21no—
18C22×#11929607C2211yescharacteristic
19#19099277—24no—
20#19099277C2218yescomplemented
21#19099213—24no—
22#19099213C2218yescomplemented
23C2×#14579160C2211yescharacteristic
24C2×#14579160C2211yescharacteristic
25C2×#14579148—21no—
26C2×#14579147—21no—
27C2×#14579143—21no—
28C2×#14579142—21no—
29C2×#14579138—21no—
30C2×#14579133—21no—
31C2×#14579132C2211yescharacteristic
32C2×#14579132C2211yescharacteristic
33C2×D4×Dic79C2211yescharacteristic
34C2×D4×Dic79C2211yescharacteristic
35C2×C4×C22⋊D79C2211yescharacteristic
36C2×#14579120C2211yescharacteristic
37C2×#14579119C2211yescharacteristic
38C2×#14579117—21no—
39C22×C4⋊Dic79C2211yescharacteristic
40C2×C4⋊C4×D79C2211yescharacteristic
41#19098960C2218yescomplemented
42#19098885C2218yescomplemented
43#19098884C2218yescomplemented
44#19098880C2218yescomplemented
45#19098879C2218yescomplemented
46#19098851C2218yescomplemented
47#19098841C2218yescomplemented
48#19098813C2218yescomplemented
49D8×Dic79C2218yescomplemented
50#19098639C2218yescomplemented
51#19098605C2218yescomplemented
52#19098602C2218yescomplemented
53C2×#14579095C2211yescharacteristic
54C2×#14579095C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579093C2211yescharacteristic
57C2×#14579093C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
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
77C2×#11929623—28no—
78C2×#11929623—48no—
79C22×Dic158—21no—
80C22×Dic158—21no—
81C22×C22⋊D79—21no—
82C22×C22⋊D79—21no—
83C22×C22⋊D79D411yescharacteristic
84C23×Dic79—21no—
85C23×Dic79—21no—
86C23×Dic79—21no—
87C22×C4×D79—21no—
88C22×C4×D79C2311yescharacteristic
89C2×#11929607—24no—
90C2×#11929607C2314yes—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93#14579160—22no—
94#14579160—22no—
95#14579160C2314yes—
96#14579160C2314yes—
97#14579148—28no—
98#14579147—28no—
99#14579143—28no—
100#14579142—28no—
101#14579138—28no—
102#14579133—28no—
103#14579132—22no—
104#14579132—22no—
105#14579132C2314yes—
106#14579132C2314yes—
107D4×Dic79—22no—
108D4×Dic79—22no—
109D4×Dic79C2314yes—
110D4×Dic79C2314yes—
111C4×C22⋊D79D414yes—
112C4×C22⋊D79C2314yes—
113#14579120—22no—
114#14579120C2314yes—
115#14579119—22no—
116#14579119C2314yes—
117#14579117—28no—
118C2×C4⋊Dic79—22no—
119C2×C4⋊Dic79—21no—
120C2×C4⋊Dic79C2314yes—
121C2×C4⋊Dic79C2311yescharacteristic
122C2×C4⋊Dic79C2311yescharacteristic
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
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⋊Dic79—21no—
135C2×C22⋊Dic79—21no—
136C2×C22⋊Dic79D411yescharacteristic
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4D411yescharacteristic
139C2×C4×Dic79—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79C2311yescharacteristic
142#14579095C2314yes—
143#14579095C2314yes—
144#14579094C2314yes—
145#14579093C2314yes—
146#14579093C2314yes—
147#14579092C2314yes—
148#14579092C2314yes—
149#14579092C2314yes—
150Dic79⋊C8C2314yes—
151#14579082C2314yes—
152#14579082C2314yes—
153#14579082C2314yes—
154#14579082C2314yes—
155C22⋊(C79⋊C8)C2314yes—
156(C2×D79)⋊C8C2314yes—
157C8×Dic79C2314yes—
158C22×D4×C79—21no—
159C22×D4×C79—21no—
160C22×D4×C79C2311yescharacteristic
161C22×D4×C79C2311yescharacteristic
162C23×C4×C79C2311yescharacteristic
163C2×D8×C79—24no—
164C2×D8×C79C2314yes—
165C2×M16×C79—24no—
166C2×M16×C79C2314yes—
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169#121×C79—22no—
170#121×C79—22no—
171#121×C79C2314yes—
172#121×C79C2314yes—
173C2×C4⋊C4×C79C2311yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177#106×C79C2314yes—
178#102×C79C2314yes—
179#102×C79C2314yes—
180C23×D79C2×D411yescharacteristic
181#11929623—432no—
182C2×Dic158—24no—
183C2×Dic158—24no—
184C2×Dic158—44no—
185C2×Dic158—82no—
186C2×C22⋊D79—24no—
187C2×C22⋊D79—24no—
188C2×C22⋊D79—24no—
189C2×C22⋊D79—44no—
190C2×C22⋊D79—82no—
191C2×C22⋊D79C2×D414yes—
192C22×Dic79—24no—
193C22×Dic79—24no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—24no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—44no—
200C22×Dic79—44no—
201C22×Dic79—44no—
202C22×Dic79C2×D411yescharacteristic
203C22×Dic79C2×D411yescharacteristic
204C22×Dic79C2×D411yescharacteristic
205C2×C4×D79—24no—
206C2×C4×D79—22no—
207C2×C4×D79—22no—
208C2×C4×D79—44no—
209C2×C4×D79C2×D412yes—
210C2×C4×D79C2412yes—
211#11929607—28no—
212C2×C79⋊C8—22no—
213C2×C79⋊C8—22no—
214C2×C79⋊C8C2412yes—
215C2×C79⋊C8C2412yes—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79—24no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4C2×D414yes—
229C22⋊Dic79—24no—
230C22⋊Dic79—24no—
231C22⋊Dic79—24no—
232C22⋊Dic79—24no—
233C22⋊Dic79—24no—
234C22⋊Dic79C2×D414yes—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4C2×D414yes—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79C2×D412yes—
240C4×Dic79C2412yes—
241C24×C79—21no—
242C24×C79—21no—
243C24×C79C2×D411yescharacteristic
244C2×D4×C79—24no—
245C2×D4×C79—24no—
246C2×D4×C79—21no—
247C2×D4×C79—21no—
248C2×D4×C79—22no—
249C2×D4×C79—22no—
250C2×D4×C79—22no—
251C2×D4×C79—22no—
252C2×D4×C79—44no—
253C2×D4×C79—82no—
254C2×D4×C79C2412yes—
255C2×D4×C79C2412yes—
256C22×C4×C79—22no—
257C22×C4×C79—22no—
258C22×C4×C79—21no—
259C22×C4×C79—21no—
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D412yes—
262C22×C4×C79C2412yes—
263C22×C4×C79C2411yescharacteristic
264D8×C79—28no—
265M16×C79—28no—
266C2×C8×C79—22no—
267C2×C8×C79#4114yescomplemented
268C2×C8×C79C2412yes—
269C2×C8×C79C2412yes—
270C4⋊C4×C79—21no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79C2412yes—
273C4⋊C4×C79C2412yes—
274C22⋊C4×C79—24no—
275C22⋊C4×C79—24no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—22no—
280C23×C79—22no—
281C23×C79—42no—
282C23×C79—42no—
283C23×C79—42no—
284C23×C79—42no—
285C23×C79—42no—
286C23×C79—42no—
287C23×C79C22×D412yes—
288C23×C79C22×D411yescharacteristic
289C22×D79—22no—
290C22×D79—22no—
291C22×D79—22no—
292C22×D79C22×D412yes—
293D4×C79—22no—
294D4×C79—22no—
295D4×C79—22no—
296D4×C79—22no—
297D4×C79—48no—
298D4×C79—42no—
299D4×C79—42no—
300D4×C79—84no—
301C2×C4×C79—22no—
302C2×C4×C79—24no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—42no—
308C2×C4×C79—42no—
309C2×C4×C79C22×D412yes—
310C2×C4×C79C22×D411yescharacteristic
311C2×C4×C79C2×#4112yes—
312C2×C4×C792−1+412yes—
313C2×C4×C79C2511yescharacteristic
314C22⋊D79—28no—
315C22⋊D79—48no—
316C22⋊D79—84no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—22no—
323C2×Dic79—48no—
324C2×Dic79—42no—
325C2×Dic79—42no—
326C2×Dic79—42no—
327C2×Dic79—42no—
328C2×Dic79—48no—
329C2×Dic79—48no—
330C2×Dic79AGL(1,ℤ/8)14yes—
331C2×Dic79C22×D412yes—
332C2×Dic79C22×D412yes—
333C2×Dic79C22×D412yes—
334C4×D79—24no—
335C4×D79—22no—
336C4×D79—22no—
337C4×D79—48no—
338Dic158—48no—
339Dic158—84no—
340C8×C79—22no—
341C8×C79C2×#4114yescomplemented
342C79⋊C8—22no—
343C79⋊C8—22no—
344C22×C79—22no—
345C22×C79—22no—
346C22×C79—22no—
347C22×C79—44no—
348C22×C79—42no—
349C22×C79—42no—
350C22×C79—42no—
351C22×C79—42no—
352C22×C79—42no—
353C22×C79—42no—
354C22×C79—84no—
355C22×C79—84no—
356C22×C79#54712yes—
357C22×C79C2×AGL(1,ℤ/8)12yes—
358C22×C79#57712yes—
359C22×C79C23×D411yescharacteristic
360C2×D79—22no—
361C2×D79—22no—
362C2×D79—22no—
363C2×D79—44no—
364C4×C79—22no—
365C4×C79—42no—
366C4×C79—42no—
367C4×C79#54712yes—
368C4×C79C22×#4111yescharacteristic
369C4×C79C2×2−1+411yescharacteristic
370Dic79—22no—
371Dic79—22no—
372Dic79—42no—
373Dic79—42no—
374Dic79—42no—
375Dic79—42no—
376Dic79C2×AGL(1,ℤ/8)14yes—
377C2×#3354—791nomaximal, Sylow
378C2×C79—42no—
379C2×C79—82no—
380C2×C79—82no—
381C2×C79#335414yescomplemented
382C2×C79C2×#54711yescharacteristic
383C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
384C2×C79C2×#57711yescharacteristic
385D79—42no—
386C2×#555—791no—
387C2×#547—791no—
388#3354—7916no—
389C2×#498—791no—
390C2×#481—791no—
391C2×#481—791no—
392C2×#482—791no—
393C2×#482—791no—
394C2×#476—791no—
395C2×#474—791no—
396C2×#469—791no—
397C2×#469D7911yescharacteristic, complemented
398C2×C4×D8—791no—
399C2×#436—791no—
400C2×#428—791no—
401C2×#428—791no—
402C79C2×#335411yescharacteristic, complemented, Sylow
403C22×#41—1581no—
404C22×D8C2×D7911yescharacteristic
405C22×M16—791no—
406C22×M16C2×D7911yescharacteristic
407#555—798no—
408#555—1584no—
409#547—798no—
410#547—1584no—
411C2×C4⋊Q8—791no—
412C2×C4⋊Q8—791no—
413C2×#124—1581no—
414C2×#124—1581no—
415C2×#123—1581no—
416C2×#123—1581no—
417C2×C22⋊Q8—1581no—
418C2×#121—791no—
419C2×#121—791no—
420C2×#121—1581no—
421C2×#121C2×D7911yescharacteristic
422C2×#121C2×D7911yescharacteristic
423C2×C4×D4—791no—
424C2×C4×D4—791no—
425C2×C4×D4—791no—
426C2×#117—791no—
427C2×#117—791no—
428C2×#117—1581no—
429C22×C4⋊C4—791no—
430C22×C4⋊C4—791no—
431#498—798no—
432#482—798no—
433#482—798no—
434#481—798no—
435#481—798no—
436#476—798no—
437#474—798no—
438#469—798no—
439#469C2×D7918yescomplemented
440C4×D8—798no—
441#436—798no—
442#428—798no—
443#428—798no—
444C2×#107—791no—
445C2×#107—791no—
446C2×#107—791no—
447C2×#106—791no—
448C2×#106—791no—
449C2×#106—791no—
450C2×#106—791no—
451C2×#106—791no—
452C2×#106C2×D7911yescharacteristic
453C2×C4⋊C8—791no—
454C2×#102—791no—
455C2×#102—791no—
456C2×#102—791no—
457C2×#102—791no—
458C2×#102C2×D7911yescharacteristic
459C2×#102C2×D7911yescharacteristic
460C2×C22⋊C8—791no—
461C2×C22⋊C8—791no—
462C2×C4×C8—791no—
463C2×#41—3168no—
464C2×#41—1588no—
465C22×Q8—1581no—
466C22×Q8—1581no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—791no—
470C22×D4—1581no—
471C22×D4—1581no—
472C22×D4C22×D7911yescharacteristic
473C22×D4C22×D7911yescharacteristic
474C23×C4—791no—
475C23×C4—1581no—
476C23×C4—1581no—
477C23×C4—1581no—
478C23×C4—1581no—
479C23×C4C22×D7911yescharacteristic
480C2×D8—24no—
481C2×D8C22×D7914yes—
482C2×M16—24no—
483C2×M16—794no—
484C2×M16—1584no—
485C2×M16C22×D7914yes—
486C22×C8—791no—
487C22×C8—791no—
488C22×C8C22×D7911yescharacteristic
489C22×C8C22×D7911yescharacteristic
490C4⋊Q8—794no—
491C4⋊Q8—794no—
492C4⋊Q8—1582no—
493C4⋊Q8—1582no—
494#124—1588no—
495#124—1588no—
496#123—1588no—
497#123—1588no—
498C22⋊Q8—1588no—
499#121—22no—
500#121—22no—
501#121—794no—
502#121—794no—
503#121—1582no—
504#121—1582no—
505#121—1588no—
506#121C22×D7914yes—
507#121C22×D7914yes—
508C4×D4—794no—
509C4×D4—794no—
510C4×D4—794no—
511C4×D4—794no—
512C4×D4—1582no—
513C4×D4—1582no—
514#117—794no—
515#117—794no—
516#117—1588no—
517#117—1582no—
518#117—1582no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—794no—
523C2×C4⋊C4—791no—
524C2×C4⋊C4—791no—
525C2×C4⋊C4—794no—
526C2×C4⋊C4—1582no—
527C2×C4⋊C4—1581no—
528C2×C4⋊C4—1581no—
529C2×C4⋊C4—1581no—
530C2×C4⋊C4—1581no—
531C2×C4⋊C4—1582no—
532C2×C4⋊C4C22×D7911yescharacteristic
533C2×C4⋊C4C22×D7911yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—791no—
537C2×C22⋊C4—791no—
538C2×C22⋊C4—1581no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C22⋊C4—1581no—
542C2×C22⋊C4—1581no—
543C2×C22⋊C4—1581no—
544C2×C42—791no—
545C2×C42—1581no—
546C2×C42—1581no—
547#107—794no—
548#107—794no—
549#107—794no—
550#106—794no—
551#106—794no—
552#106—794no—
553#106—794no—
554#106—794no—
555#106C22×D7914yes—
556C4⋊C8—794no—
557#102—794no—
558#102—794no—
559#102—794no—
560#102—794no—
561#102C22×D7914yes—
562#102C22×D7914yes—
563C22⋊C8—794no—
564C22⋊C8—794no—
565C4×C8—794no—
566C24—21no—
567C24—21no—
568C24—791no—
569C24D4×D7911yescharacteristic
570#41—31632no—
571C2×Q8—3164no—
572C2×Q8—6322no—
573C2×Q8—1584no—
574C2×Q8—1584no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—44no—
584C2×D4—82no—
585C2×D4—3164no—
586C2×D4—794no—
587C2×D4—6322no—
588C2×D4—1584no—
589C2×D4—1584no—
590C2×D4—1584no—
591C2×D4C23×D7912yes—
592C2×D4C23×D7912yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—3164no—
598C22×C4—3164no—
599C22×C4—3164no—
600C22×C4—3164no—
601C22×C4—791no—
602C22×C4—791no—
603C22×C4—791no—
604C22×C4—792no—
605C22×C4—792no—
606C22×C4—1584no—
607C22×C4—1584no—
608C22×C4—1584no—
609C22×C4—1584no—
610C22×C4—1581no—
611C22×C4—1581no—
612C22×C4—1581no—
613C22×C4—1581no—
614C22×C4—1582no—
615C22×C4—1582no—
616C22×C4D4×D7912yes—
617C22×C4D4×D7911yescharacteristic
618C22×C4C23×D7912yes—
619C22×C4C23×D7911yescharacteristic
620D8—28no—
621M16—28no—
622M16—1588no—
623C2×C8—22no—
624C2×C8—792no—
625C2×C8—792no—
626C2×C8—1582no—
627C2×C8—1582no—
628C2×C8#1192962314yescomplemented
629C2×C8C23×D7912yes—
630C2×C8C23×D7912yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—794no—
634C4⋊C4—792no—
635C4⋊C4—792no—
636C4⋊C4—792no—
637C4⋊C4—792no—
638C4⋊C4—1584no—
639C4⋊C4—1584no—
640C4⋊C4—1584no—
641C4⋊C4—1581no—
642C4⋊C4—1581no—
643C4⋊C4—1584no—
644C4⋊C4—1581no—
645C4⋊C4—1581no—
646C4⋊C4C23×D7912yes—
647C4⋊C4C23×D7912yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—794no—
651C22⋊C4—794no—
652C22⋊C4—1584no—
653C22⋊C4—1584no—
654C22⋊C4—1584no—
655C22⋊C4—1584no—
656C22⋊C4—1584no—
657C22⋊C4—1584no—
658C42—792no—
659C42—792no—
660C42—1584no—
661C42—1584no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—792no—
674C23—1582no—
675C23—1582no—
676C23—1582no—
677C23C2×D4×D7912yes—
678C23C2×D4×D7911yescharacteristic
679Q8—3168no—
680Q8—6324no—
681D4—22no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—48no—
686D4—42no—
687D4—42no—
688D4—84no—
689D4—3168no—
690D4—6324no—
691D4—1588no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—3168no—
701C2×C4—3168no—
702C2×C4—3162no—
703C2×C4—3162no—
704C2×C4—3162no—
705C2×C4—3162no—
706C2×C4—3168no—
707C2×C4—3168no—
708C2×C4—794no—
709C2×C4—792no—
710C2×C4—792no—
711C2×C4—792no—
712C2×C4—1582no—
713C2×C4—1582no—
714C2×C4—1582no—
715C2×C4—1582no—
716C2×C4—1582no—
717C2×C4—1582no—
718C2×C4—1582no—
719C2×C4—1584no—
720C2×C4—1582no—
721C2×C4C2×D4×D7912yes—
722C2×C4C2×D4×D7911yescharacteristic
723C2×C4C2×#1192962312yes—
724C2×C4#1457920812yes—
725C2×C4C24×D7911yescharacteristic
726C8—22no—
727C8—1582no—
728C8—1582no—
729C8C2×#1192962314yescomplemented
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—84no—
742C22—3164no—
743C22—1582no—
744C22—1582no—
745C22—1582no—
746C22#1909921312yes—
747C22AGL(1,ℤ/8)×D7912yes—
748C22#1909937312yes—
749C22C22×D4×D7911yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—3162no—
754C4—3162no—
755C4—3162no—
756C4—3162no—
757C4—794no—
758C4—1582no—
759C4—1582no—
760C4#1909921312yes—
761C4C22×#1192962311yescharacteristic
762C4C2×#1457920811yescharacteristic
763C2—42no—
764C2—82no—
765C2—82no—
766C2—3162no—
767C2#2377599014yesdirect product factor
768C2C2×#1909921311yescharacteristic
769C2C2×AGL(1,ℤ/8)×D7911yescharacteristic
770C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#469×C79C2
socleC23×C79C22×D4
hypercenterC2×#469D79
hypocenterC79C2×#3354
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×#19099277C2semidirect
2. C2×#19099213C2semidirect
3. #23775990C2direct (N × H)
4. C2×#19098960C2semidirect
5. C2×#19098880C2semidirect
6. C2×#19098879C2semidirect
7. C2×#19098885C2semidirect
8. C2×#19098884C2semidirect
9. C2×#19098851C2semidirect
10. C2×#19098841C2semidirect
11. C2×#19098813C2semidirect
12. C2×D8×Dic79C2semidirect
13. C2×#19098639C2semidirect
14. C2×#19098605C2semidirect
15. C2×#19098602C2semidirect
16. C2×#469×C79C2semidirect
20. #19099277C22semidirect
22. #19099213C22semidirect
41. #19098960C22semidirect
42. #19098885C22semidirect
43. #19098884C22semidirect
44. #19098880C22semidirect
45. #19098879C22semidirect
46. #19098851C22semidirect
47. #19098841C22semidirect
48. #19098813C22semidirect
49. D8×Dic79C22semidirect
50. #19098639C22semidirect
51. #19098605C22semidirect
52. #19098602C22semidirect
73. #469×C79C22semidirect
267. C2×C8×C79#41semidirect
341. C8×C79C2×#41semidirect
381. C2×C79#3354semidirect
397. C2×#469D79semidirect
402. C79C2×#3354semidirect
439. #469C2×D79semidirect
628. C2×C8#11929623semidirect
729. C8C2×#11929623semidirect
767. C2#23775990direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992772
C2×#190992132
#237759902
C2×#190989602
C2×#190988802
C2×#190988792
C2×#190988852
C2×#190988842
C2×#190988512
C2×#190988412
C2×#190988132
C2×D8×Dic792
C2×#190986392
C2×#190986052
C2×#190986022
C2×#469×C792
C2×#335479