Finite Group Databasebeta

← C2×#23775868 #35166830

Subgroups — C2×#23775868 #35166830

Order 20224.

2158 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×#19099261C211yesmaximal, characteristic, complemented
2C2×#19099213C211yesmaximal, characteristic, complemented
3#23775868C2116yesmaximal, direct product factor
4C2×#19098970C211yesmaximal, characteristic, complemented
5C2×#19098883C211yesmaximal, characteristic, complemented
6C2×#19098885C211yesmaximal, characteristic, complemented
7C2×#19098877C211yesmaximal, characteristic, complemented
8C2×#19098861C211yesmaximal, characteristic, complemented
9C2×#19098852C211yesmaximal, characteristic, complemented
10C2×#19098815C211yesmaximal, characteristic, complemented
11C2×#19098797C211yesmaximal, characteristic, complemented
12C2×#19098672C211yesmaximal, characteristic, complemented
13C2×#19098631C211yesmaximal, characteristic, complemented
14C2×#19098602C211yesmaximal, characteristic, complemented
15C22×#14579092C211yesmaximal, characteristic, complemented
16C2×#481×C79C211yesmaximal, characteristic, complemented
17C22×#11929623—21no—
18C22×#11929609C2211yescharacteristic
19C22×#11929607C2211yescharacteristic
20C23×C79⋊C8C2211yescharacteristic
21#19099261—24no—
22#19099261C2218yescomplemented
23#19099213—24no—
24#19099213C2218yescomplemented
25C2×#14579160C2211yescharacteristic
26C2×#14579156—21no—
27C2×#14579152C2211yescharacteristic
28C2×#14579146—21no—
29C2×#14579143—21no—
30C2×#14579142—21no—
31C2×#14579138—21no—
32C2×#14579136C2211yescharacteristic
33C2×#14579135—21no—
34C2×#14579135C2211yescharacteristic
35C2×#14579132C2211yescharacteristic
36C2×D4×Dic79C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×C4×C22⋊D79—21no—
39C2×C4×C22⋊D79C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C22×C4⋊Dic79C2211yescharacteristic
42C2×C4⋊C4×D79C2211yescharacteristic
43#19098970C2218yescomplemented
44#19098885C2218yescomplemented
45#19098883C2218yescomplemented
46#19098877C2218yescomplemented
47#19098861C2218yescomplemented
48#19098852C2218yescomplemented
49#19098815C2218yescomplemented
50#19098797C2218yescomplemented
51#19098672C2218yescomplemented
52#19098631C2218yescomplemented
53#19098602C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579095C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579092C2211yescharacteristic
58C2×#14579092C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×#14579092C2218yescomplemented
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C2×#121×C79C2211yescharacteristic
70C22×C4⋊C4×C79C2211yescharacteristic
71#481×C79C2218yescomplemented
72C2×#106×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C2×#11929623—28no—
78C2×#11929623—48no—
79C22×Dic158—21no—
80C22×D316—21no—
81C22×D316C2311yescharacteristic
82C22×C22⋊D79—21no—
83C22×C22⋊D79—21no—
84C22×C22⋊D79D411yescharacteristic
85C23×Dic79—21no—
86C23×Dic79—21no—
87C22×C4×D79—21no—
88C22×C4×D79—21no—
89C22×C4×D79C2311yescharacteristic
90C2×#11929609—24no—
91C2×#11929609C2314yes—
92C2×#11929607—24no—
93C2×#11929607C2314yes—
94C22×C79⋊C8—24no—
95C22×C79⋊C8C2314yes—
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98#14579160—22no—
99#14579160C2314yes—
100#14579156—28no—
101#14579152—22no—
102#14579152C2314yes—
103#14579146—28no—
104#14579143—28no—
105#14579142—28no—
106#14579138—28no—
107#14579136—22no—
108#14579136C2314yes—
109#14579135—22no—
110#14579135—28no—
111#14579135C2314yes—
112#14579132—22no—
113#14579132C2314yes—
114D4×Dic79—22no—
115D4×Dic79C2314yes—
116#14579123—22no—
117#14579123C2314yes—
118C4×C22⋊D79—28no—
119C4×C22⋊D79D414yes—
120C4×C22⋊D79C2314yes—
121#14579119—22no—
122#14579119C2314yes—
123C2×C4⋊Dic79—22no—
124C2×C4⋊Dic79—21no—
125C2×C4⋊Dic79—21no—
126C2×C4⋊Dic79C2314yes—
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×C4⋊Dic79C2311yescharacteristic
130C2×Dic79⋊C4—21no—
131C2×Dic79⋊C4—21no—
132C2×Dic79⋊C4—21no—
133C2×Dic79⋊C4D411yescharacteristic
134C4⋊C4×D79—22no—
135C4⋊C4×D79C2314yes—
136C2×C22⋊Dic79—21no—
137C2×C22⋊Dic79—21no—
138C2×C22⋊Dic79D411yescharacteristic
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4—21no—
142C2×(C2×D79)⋊C4—21no—
143C2×(C2×D79)⋊C4D411yescharacteristic
144C2×C4×Dic79—21no—
145C2×C4×Dic79C2311yescharacteristic
146#14579095C2314yes—
147#14579095C2314yes—
148#14579094C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151#14579092C2314yes—
152#14579092C2314yes—
153Dic79⋊C8C2314yes—
154#14579083C2314yes—
155#14579083C2314yes—
156#14579082C2314yes—
157#14579081C2314yes—
158(C2×D79)⋊C8C2314yes—
159#14579071C2314yes—
160C22×D4×C79—21no—
161C22×D4×C79C2311yescharacteristic
162C23×C4×C79—21no—
163C23×C4×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166#121×C79—22no—
167#121×C79C2314yes—
168C2×C4⋊C4×C79—22no—
169C2×C4⋊C4×C79—21no—
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2311yescharacteristic
173C2×C4⋊C4×C79C2314yes—
174C2×C22⋊C4×C79—21no—
175#106×C79C2314yes—
176#106×C79C2314yes—
177#102×C79C2314yes—
178#102×C79C2314yes—
179C22⋊C8×C79C2314yes—
180C23×D79—21no—
181C23×D79C2×D411yescharacteristic
182#11929623—432no—
183C2×Dic158—24no—
184C2×Dic158—44no—
185C2×D316—24no—
186C2×D316—21no—
187C2×D316—22no—
188C2×D316—22no—
189C2×D316—82no—
190C2×D316C2412yes—
191C2×C22⋊D79—24no—
192C2×C22⋊D79—24no—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—44no—
195C2×C22⋊D79—44no—
196C2×C22⋊D79C2×D414yes—
197C22×Dic79—24no—
198C22×Dic79—21no—
199C22×Dic79—24no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79—44no—
203C22×Dic79—44no—
204C22×Dic79C2×D411yescharacteristic
205C22×Dic79C2×D411yescharacteristic
206C22×Dic79C2×D411yescharacteristic
207C2×C4×D79—24no—
208C2×C4×D79—24no—
209C2×C4×D79—22no—
210C2×C4×D79—22no—
211C2×C4×D79—44no—
212C2×C4×D79—82no—
213C2×C4×D79C2×D412yes—
214C2×C4×D79C2412yes—
215#11929609—28no—
216#11929607—28no—
217C2×C79⋊C8—28no—
218C2×C79⋊C8—22no—
219C2×C79⋊C8#4114yescomplemented
220C2×C79⋊C8C2412yes—
221C2×C79⋊C8C2412yes—
222C4⋊Dic79—24no—
223C4⋊Dic79—21no—
224C4⋊Dic79—21no—
225C4⋊Dic79—24no—
226C4⋊Dic79—21no—
227C4⋊Dic79C2412yes—
228C4⋊Dic79C2412yes—
229C4⋊Dic79C2412yes—
230Dic79⋊C4—24no—
231Dic79⋊C4—24no—
232Dic79⋊C4—24no—
233Dic79⋊C4C2×D414yes—
234C22⋊Dic79—24no—
235C22⋊Dic79—24no—
236C22⋊Dic79C2×D414yes—
237(C2×D79)⋊C4—24no—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4—24no—
241(C2×D79)⋊C4C2×D414yes—
242C4×Dic79—24no—
243C4×Dic79C2×D412yes—
244C4×Dic79C2412yes—
245C24×C79—21no—
246C24×C79C2×D411yescharacteristic
247C2×D4×C79—24no—
248C2×D4×C79—21no—
249C2×D4×C79—22no—
250C2×D4×C79—22no—
251C2×D4×C79—44no—
252C2×D4×C79C2412yes—
253C22×C4×C79—22no—
254C22×C4×C79—22no—
255C22×C4×C79—21no—
256C22×C4×C79—21no—
257C22×C4×C79—21no—
258C22×C4×C79—24no—
259C22×C4×C79—82no—
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D412yes—
262C22×C4×C79C2412yes—
263C22×C4×C79C2411yescharacteristic
264C2×C8×C79—22no—
265C2×C8×C79—22no—
266C2×C8×C79C2412yes—
267C2×C8×C79C2412yes—
268C4⋊C4×C79—21no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79—24no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79C2412yes—
273C4⋊C4×C79C2412yes—
274C4⋊C4×C79C2412yes—
275C22⋊C4×C79—24no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79—22no—
279C23×C79—42no—
280C23×C79—42no—
281C23×C79—42no—
282C23×C79AGL(1,ℤ/8)14yes—
283C23×C79C22×D412yes—
284C23×C79C22×D411yescharacteristic
285C22×D79—22no—
286C22×D79—22no—
287C22×D79—22no—
288C22×D79—22no—
289C22×D79—42no—
290C22×D79—42no—
291C22×D79—42no—
292C22×D79C22×D412yes—
293D4×C79—22no—
294D4×C79—22no—
295D4×C79—48no—
296D4×C79—42no—
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—22no—
304C2×C4×C79—42no—
305C2×C4×C79—42no—
306C2×C4×C79—42no—
307C2×C4×C79—84no—
308C2×C4×C79C22×D412yes—
309C2×C4×C79C22×D411yescharacteristic
310C2×C4×C79C2×#4112yes—
311C2×C4×C792−1+412yes—
312C2×C4×C79C2511yescharacteristic
313C22⋊D79—28no—
314C22⋊D79—48no—
315C22⋊D79—48no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—22no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—22no—
322C2×Dic79—48no—
323C2×Dic79—42no—
324C2×Dic79—42no—
325C2×Dic79—48no—
326C2×Dic79—42no—
327C2×Dic79C22×D412yes—
328C2×Dic79C22×D412yes—
329C2×Dic79C22×D412yes—
330D316—22no—
331D316—22no—
332D316—42no—
333D316—84no—
334C4×D79—24no—
335C4×D79—22no—
336C4×D79—22no—
337C4×D79—48no—
338C4×D79—84no—
339Dic158—48no—
340C8×C79—22no—
341C8×C79—22no—
342C79⋊C8—22no—
343C79⋊C8C2×#4114yescomplemented
344C22×C79—28no—
345C22×C79—22no—
346C22×C79—22no—
347C22×C79—42no—
348C22×C79—42no—
349C22×C79—42no—
350C22×C79—84no—
351C22×C79#54712yes—
352C22×C79C2×AGL(1,ℤ/8)14yes—
353C22×C79C2×AGL(1,ℤ/8)12yes—
354C22×C79#57712yes—
355C22×C79C23×D411yescharacteristic
356C2×D79—22no—
357C2×D79—22no—
358C2×D79—22no—
359C2×D79—44no—
360C2×D79—42no—
361C2×D79—42no—
362C2×D79—42no—
363C2×D79—84no—
364C4×C79—22no—
365C4×C79—42no—
366C4×C79—42no—
367C4×C79—42no—
368C4×C79#54712yes—
369C4×C79C22×#4111yescharacteristic
370C4×C79C2×2−1+411yescharacteristic
371Dic79—22no—
372Dic79—22no—
373Dic79—22no—
374Dic79—42no—
375Dic79—42no—
376Dic79—42no—
377C2×#3345—791nomaximal, Sylow
378C2×C79—24no—
379C2×C79—82no—
380C2×C79#334514yescomplemented
381C2×C79C2×#54711yescharacteristic
382C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
383C2×C79C2×#57711yescharacteristic
384D79—42no—
385D79—82no—
386C2×#553—791no—
387C2×#547—791no—
388#3345—7916no—
389C2×#501—791no—
390C2×#481—791no—
391C2×#481D7911yescharacteristic, complemented
392C2×#482—791no—
393C2×#480—791no—
394C2×#478—791no—
395C2×#476—791no—
396C2×#469—791no—
397C2×#466—791no—
398C2×#442—791no—
399C2×#435—791no—
400C2×#428—791no—
401C22×#106—791no—
402C79C2×#334511yescharacteristic, complemented, Sylow
403C22×#41—1581no—
404C22×D8—791no—
405C22×M16—791no—
406C23×C8—791no—
407#553—798no—
408#553—1584no—
409#547—798no—
410#547—1584no—
411C2×C4⋊Q8—791no—
412C2×#126—1581no—
413C2×#125—791no—
414C2×#123—1581no—
415C2×#123—1581no—
416C2×#123—1581no—
417C2×C22⋊Q8—1581no—
418C2×#121—791no—
419C2×#121—791no—
420C2×#121—791no—
421C2×#121—1581no—
422C2×#121C2×D7911yescharacteristic
423C2×C4×D4—791no—
424C2×C4×D4—791no—
425C2×C4×D4—791no—
426C2×C4×D4—1581no—
427C2×#117—791no—
428C22×C4⋊C4—791no—
429C22×C4⋊C4—791no—
430C22×C4⋊C4C2×D7911yescharacteristic
431#501—798no—
432#482—798no—
433#481—798no—
434#481C2×D7918yescomplemented
435#480—798no—
436#478—798no—
437#476—798no—
438#469—798no—
439#466—798no—
440#442—798no—
441#435—798no—
442#428—798no—
443C2×#107—791no—
444C2×#107—791no—
445C2×#107—791no—
446C2×#106—791no—
447C2×#106—791no—
448C2×#106—798no—
449C2×#106—791no—
450C2×#106—791no—
451C2×#106C2×D7911yescharacteristic
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⋊C8C2×D7911yescharacteristic
462C2×#97—791no—
463C2×#41—3168no—
464C2×#41—1588no—
465C22×Q8—1581no—
466C22×D4—21no—
467C22×D4—791no—
468C22×D4—791no—
469C22×D4—1581no—
470C22×D4—1581no—
471C22×D4—1581no—
472C22×D4C22×D7911yescharacteristic
473C23×C4—21no—
474C23×C4—791no—
475C23×C4—1581no—
476C23×C4—1581no—
477C23×C4—1581no—
478C23×C4—1581no—
479C23×C4C22×D7911yescharacteristic
480C2×D8—794no—
481C2×D8—1584no—
482C2×M16—794no—
483C2×M16—1584no—
484C22×C8—791no—
485C22×C8—791no—
486C22×C8—794no—
487C22×C8—1584no—
488C22×C8C22×D7911yescharacteristic
489C22×C8C22×D7911yescharacteristic
490C4⋊Q8—794no—
491C4⋊Q8—1582no—
492#126—1588no—
493#125—794no—
494#125—1582no—
495#123—1588no—
496#123—1588no—
497#123—1588no—
498C22⋊Q8—1588no—
499#121—22no—
500#121—794no—
501#121—794no—
502#121—794no—
503#121—1582no—
504#121—1588no—
505#121—1582no—
506#121—1582no—
507#121C22×D7914yes—
508C4×D4—794no—
509C4×D4—794no—
510C4×D4—794no—
511C4×D4—794no—
512C4×D4—1582no—
513C4×D4—1582no—
514C4×D4—1588no—
515#117—794no—
516#117—1582no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—791no—
520C2×C4⋊C4—791no—
521C2×C4⋊C4—791no—
522C2×C4⋊C4—794no—
523C2×C4⋊C4—791no—
524C2×C4⋊C4—794no—
525C2×C4⋊C4—1582no—
526C2×C4⋊C4—1581no—
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×C4⋊C4C22×D7911yescharacteristic
535C2×C4⋊C4C22×D7914yes—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—791no—
538C2×C22⋊C4—791no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4—1581no—
541C2×C22⋊C4—1581no—
542C2×C22⋊C4—1581no—
543C2×C22⋊C4—1581no—
544C2×C22⋊C4—1581no—
545C2×C42—791no—
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#106C22×D7914yes—
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⋊C8C22×D7914yes—
565#97—794no—
566C24—21no—
567C24—791no—
568C24—1581no—
569C24D4×D7911yescharacteristic
570#41—31632no—
571C2×Q8—3164no—
572C2×Q8—1584no—
573C2×D4—24no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—21no—
577C2×D4—44no—
578C2×D4—3164no—
579C2×D4—3164no—
580C2×D4—794no—
581C2×D4—792no—
582C2×D4—6322no—
583C2×D4—1584no—
584C2×D4—1584no—
585C2×D4—1584no—
586C2×D4—1584no—
587C2×D4—1582no—
588C2×D4—1582no—
589C2×D4—1581no—
590C2×D4C23×D7912yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—82no—
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—6322no—
607C22×C4—1584no—
608C22×C4—1584no—
609C22×C4—1584no—
610C22×C4—1584no—
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—1588no—
621M16—1588no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—794no—
625C2×C8—792no—
626C2×C8—792no—
627C2×C8—1588no—
628C2×C8—1582no—
629C2×C8C23×D7912yes—
630C2×C8C23×D7912yes—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—794no—
636C4⋊C4—792no—
637C4⋊C4—792no—
638C4⋊C4—792no—
639C4⋊C4—1584no—
640C4⋊C4—1584no—
641C4⋊C4—1584no—
642C4⋊C4—1584no—
643C4⋊C4—1581no—
644C4⋊C4—1581no—
645C4⋊C4—1584no—
646C4⋊C4—1581no—
647C4⋊C4C23×D7912yes—
648C4⋊C4C23×D7912yes—
649C4⋊C4C23×D7912yes—
650C22⋊C4—24no—
651C22⋊C4—794no—
652C22⋊C4—794no—
653C22⋊C4—1584no—
654C22⋊C4—1584no—
655C22⋊C4—1584no—
656C22⋊C4—1584no—
657C22⋊C4—1584no—
658C22⋊C4—1584no—
659C42—792no—
660C42—792no—
661C42—1584no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—3162no—
669C23—3162no—
670C23—3162no—
671C23—792no—
672C23—1582no—
673C23—1582no—
674C23—1582no—
675C23—1582no—
676C23#1457918814yes—
677C23C2×D4×D7912yes—
678C23C2×D4×D7911yescharacteristic
679Q8—3168no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—42no—
684D4—3168no—
685D4—3168no—
686D4—3162no—
687D4—6324no—
688D4—1588no—
689D4—1582no—
690D4—1582no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—84no—
702C2×C4—3168no—
703C2×C4—3162no—
704C2×C4—3162no—
705C2×C4—3168no—
706C2×C4—3162no—
707C2×C4—3168no—
708C2×C4—792no—
709C2×C4—792no—
710C2×C4—792no—
711C2×C4—6324no—
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×C4#41×D7912yes—
724C2×C4#1457920812yes—
725C2×C4C24×D7911yescharacteristic
726C8—22no—
727C8—22no—
728C8—794no—
729C8—1582no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—3164no—
738C22—3162no—
739C22—3162no—
740C22—3162no—
741C22—6324no—
742C22—1582no—
743C22—1582no—
744C22—1582no—
745C22#1909921112yes—
746C22C2×#1457918814yes—
747C22C2×#1457918812yes—
748C22#1909937312yes—
749C22C22×D4×D7911yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—3162no—
755C4—3162no—
756C4—3162no—
757C4—1582no—
758C4—1582no—
759C4—1582no—
760C4#1909921112yes—
761C4C2×#41×D7911yescharacteristic
762C4C2×#1457920811yescharacteristic
763C2—24no—
764C2—82no—
765C2—3162no—
766C2—6322no—
767C2#2377586814yesdirect product factor
768C2C2×#1909921111yescharacteristic
769C2C22×#1457918811yescharacteristic
770C2C2×#1909937311yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#481×C79C2
socleC23×C79C22×D4
hypercenterC2×#481D79
hypocenterC79C2×#3345
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#481

Complements

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

NH ≅ G/Ntype
1. C2×#19099261C2semidirect
2. C2×#19099213C2semidirect
3. #23775868C2direct (N × H)
4. C2×#19098970C2semidirect
5. C2×#19098883C2semidirect
6. C2×#19098885C2semidirect
7. C2×#19098877C2semidirect
8. C2×#19098861C2semidirect
9. C2×#19098852C2semidirect
10. C2×#19098815C2semidirect
11. C2×#19098797C2semidirect
12. C2×#19098672C2semidirect
13. C2×#19098631C2semidirect
14. C2×#19098602C2semidirect
15. C22×#14579092C2semidirect
16. C2×#481×C79C2semidirect
22. #19099261C22semidirect
24. #19099213C22semidirect
43. #19098970C22semidirect
44. #19098885C22semidirect
45. #19098883C22semidirect
46. #19098877C22semidirect
47. #19098861C22semidirect
48. #19098852C22semidirect
49. #19098815C22semidirect
50. #19098797C22semidirect
51. #19098672C22semidirect
52. #19098631C22semidirect
53. #19098602C22semidirect
61. C2×#14579092C22semidirect
71. #481×C79C22semidirect
219. C2×C79⋊C8#41semidirect
343. C79⋊C8C2×#41semidirect
380. C2×C79#3345semidirect
391. C2×#481D79semidirect
402. C79C2×#3345semidirect
434. #481C2×D79semidirect
767. C2#23775868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992612
C2×#190992132
#237758682
C2×#190989702
C2×#190988832
C2×#190988852
C2×#190988772
C2×#190988612
C2×#190988522
C2×#190988152
C2×#190987972
C2×#190986722
C2×#190986312
C2×#190986022
C22×#145790922
C2×#481×C792
C2×#334579