Finite Group Databasebeta

← C2×#23775800 #35166739

Subgroups — C2×#23775800 #35166739

Order 20224.

1994 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×#19099261C211yesmaximal, characteristic, complemented
3#23775800C2116yesmaximal, direct product factor
4C2×#19098963C211yesmaximal, characteristic, complemented
5C2×#19098882C211yesmaximal, characteristic, complemented
6C2×#19098889C211yesmaximal, characteristic, complemented
7C2×#19098886C211yesmaximal, characteristic, complemented
8C2×#19098865C211yesmaximal, characteristic, complemented
9C2×#19098862C211yesmaximal, characteristic, complemented
10C2×#19098798C211yesmaximal, characteristic, complemented
11C2×#19098797C211yesmaximal, characteristic, complemented
12C2×#19098643C211yesmaximal, characteristic, complemented
13C2×(C22⋊D79)⋊C8C211yesmaximal, characteristic, complemented
14C2×#19098598C211yesmaximal, characteristic, complemented
15C22×#14579094C211yesmaximal, characteristic, complemented
16C2×#481×C79C211yesmaximal, characteristic, complemented
17C22×#11929609C2211yescharacteristic
18C23×C79⋊C8C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099265—24no—
21#19099265C2218yescomplemented
22#19099261—24no—
23#19099261C2218yescomplemented
24C2×#14579156—21no—
25C2×#14579154—21no—
26C2×#14579152C2211yescharacteristic
27C2×#14579152C2211yescharacteristic
28C2×#14579146—21no—
29C2×#14579145—21no—
30C2×#14579136C2211yescharacteristic
31C2×#14579135—21no—
32C2×#14579135C2211yescharacteristic
33C2×#14579133—21no—
34C2×#14579132C2211yescharacteristic
35C2×D4×Dic79—21no—
36C2×D4×Dic79C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×C4×C22⋊D79—21no—
39C2×C4×C22⋊D79C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×#14579119C2211yescharacteristic
42C22×C4⋊Dic79C2211yescharacteristic
43#19098963C2218yescomplemented
44#19098889C2218yescomplemented
45#19098886C2218yescomplemented
46#19098882C2218yescomplemented
47#19098865C2218yescomplemented
48#19098862C2218yescomplemented
49#19098798C2218yescomplemented
50#19098797C2218yescomplemented
51#19098643C2218yescomplemented
52(C22⋊D79)⋊C8C2218yescomplemented
53#19098598C2218yescomplemented
54C2×#14579094C2211yescharacteristic
55C2×#14579094C2211yescharacteristic
56C2×#14579094C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579094C2211yescharacteristic
59C2×#14579094C2218yescomplemented
60C2×#14579093C2211yescharacteristic
61C2×#14579093C2211yescharacteristic
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×C8×Dic79C2211yescharacteristic
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
77C22×D316—21no—
78C22×D316C2311yescharacteristic
79C22×C22⋊D79—21no—
80C22×C22⋊D79—21no—
81C22×C22⋊D79D411yescharacteristic
82C23×Dic79—21no—
83C23×Dic79—21no—
84C22×C4×D79—21no—
85C22×C4×D79C2311yescharacteristic
86C2×#11929609—24no—
87C2×#11929609C2314yes—
88C22×C79⋊C8—24no—
89C22×C79⋊C8C2314yes—
90C22×C79⋊C8C2311yescharacteristic
91C22×C79⋊C8C2311yescharacteristic
92C2×C8×D79—24no—
93C2×C8×D79C2314yes—
94#14579156—28no—
95#14579154—28no—
96#14579152—22no—
97#14579152—22no—
98#14579152C2314yes—
99#14579152C2314yes—
100#14579146—28no—
101#14579145—28no—
102#14579136—22no—
103#14579136C2314yes—
104#14579135—22no—
105#14579135—28no—
106#14579135C2314yes—
107#14579133—28no—
108#14579132—22no—
109#14579132C2314yes—
110D4×Dic79—28no—
111D4×Dic79—22no—
112D4×Dic79C2314yes—
113#14579123—22no—
114#14579123C2314yes—
115C4×C22⋊D79—28no—
116C4×C22⋊D79D414yes—
117C4×C22⋊D79C2314yes—
118#14579119—22no—
119#14579119—22no—
120#14579119C2314yes—
121#14579119C2314yes—
122C2×C4⋊Dic79—22no—
123C2×C4⋊Dic79—21no—
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⋊C4D411yescharacteristic
133C2×C22⋊Dic79—21no—
134C2×C22⋊Dic79—21no—
135C2×C22⋊Dic79D411yescharacteristic
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×(C2×D79)⋊C4—21no—
141C2×(C2×D79)⋊C4D411yescharacteristic
142C2×C4×Dic79—21no—
143C2×C4×Dic79—21no—
144C2×C4×Dic79C2311yescharacteristic
145#14579094C2314yes—
146#14579094C2314yes—
147#14579094C2314yes—
148#14579094C2314yes—
149#14579094C2314yes—
150#14579093C2314yes—
151#14579093C2314yes—
152Dic79⋊C8C2314yes—
153#14579083C2314yes—
154#14579083C2314yes—
155#14579082C2314yes—
156#14579081C2314yes—
157(C2×D79)⋊C8C2314yes—
158C8×Dic79C2314yes—
159C22×D4×C79—21no—
160C22×D4×C79C2311yescharacteristic
161C23×C4×C79—21no—
162C23×C4×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164C22×C8×C79C2311yescharacteristic
165#121×C79—22no—
166#121×C79C2314yes—
167C2×C4⋊C4×C79—22no—
168C2×C4⋊C4×C79—21no—
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C4⋊C4×C79C2311yescharacteristic
172C2×C4⋊C4×C79C2314yes—
173C2×C22⋊C4×C79—21no—
174#106×C79C2314yes—
175#106×C79C2314yes—
176#102×C79C2314yes—
177#102×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C23×D79—21no—
180C23×D79C2×D411yescharacteristic
181C2×D316—24no—
182C2×D316—21no—
183C2×D316—22no—
184C2×D316—22no—
185C2×D316—82no—
186C2×D316C2412yes—
187C2×C22⋊D79—24no—
188C2×C22⋊D79—24no—
189C2×C22⋊D79—24no—
190C2×C22⋊D79—44no—
191C2×C22⋊D79—82no—
192C2×C22⋊D79C2×D414yes—
193C22×Dic79—24no—
194C22×Dic79—21no—
195C22×Dic79—21no—
196C22×Dic79—21no—
197C22×Dic79—24no—
198C22×Dic79—82no—
199C22×Dic79—82no—
200C22×Dic79C2×D411yescharacteristic
201C22×Dic79C2×D411yescharacteristic
202C22×Dic79C2×D411yescharacteristic
203C2×C4×D79—24no—
204C2×C4×D79—22no—
205C2×C4×D79—22no—
206C2×C4×D79—82no—
207C2×C4×D79C2×D412yes—
208C2×C4×D79C2412yes—
209#11929609—28no—
210C2×C79⋊C8—28no—
211C2×C79⋊C8—22no—
212C2×C79⋊C8#4114yes—
213C2×C79⋊C8C2412yes—
214C2×C79⋊C8C2412yes—
215C8×D79—28no—
216C4⋊Dic79—24no—
217C4⋊Dic79—24no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79—24no—
221C4⋊Dic79—21no—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225Dic79⋊C4—24no—
226Dic79⋊C4—24no—
227Dic79⋊C4C2×D414yes—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230C22⋊Dic79C2×D414yes—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
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×C79C2×D411yescharacteristic
243C2×D4×C79—24no—
244C2×D4×C79—21no—
245C2×D4×C79—22no—
246C2×D4×C79—22no—
247C2×D4×C79—44no—
248C2×D4×C79C2412yes—
249C22×C4×C79—22no—
250C22×C4×C79—22no—
251C22×C4×C79—21no—
252C22×C4×C79—21no—
253C22×C4×C79—21no—
254C22×C4×C79—24no—
255C22×C4×C79—82no—
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D412yes—
258C22×C4×C79C2412yes—
259C22×C4×C79C2411yescharacteristic
260C2×C8×C79—22no—
261C2×C8×C79—22no—
262C2×C8×C79C2412yes—
263C2×C8×C79C2412yes—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79—24no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79C2412yes—
269C4⋊C4×C79C2412yes—
270C4⋊C4×C79C2412yes—
271C22⋊C4×C79—24no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—42no—
276C23×C79—42no—
277C23×C79—42no—
278C23×C79#13514yes—
279C23×C79C22×D412yes—
280C23×C79C22×D411yescharacteristic
281C22×D79—22no—
282C22×D79—22no—
283C22×D79—22no—
284C22×D79—22no—
285C22×D79—42no—
286C22×D79—42no—
287C22×D79—42no—
288C22×D79C22×D412yes—
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×C79—84no—
304C2×C4×C79C22×D412yes—
305C2×C4×C79C22×D411yescharacteristic
306C2×C4×C79C2×#4112yes—
307C2×C4×C792−1+412yes—
308C2×C4×C79C2511yescharacteristic
309C22⋊D79—28no—
310C22⋊D79—48no—
311C22⋊D79—84no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—22no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—42no—
321C2×Dic79—84no—
322C2×Dic79—84no—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325C2×Dic79C22×D412yes—
326D316—22no—
327D316—22no—
328D316—42no—
329D316—84no—
330C4×D79—24no—
331C4×D79—22no—
332C4×D79—22no—
333C4×D79—84no—
334C8×C79—22no—
335C8×C79—22no—
336C79⋊C8—22no—
337C79⋊C8C2×#4114yes—
338C22×C79—28no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—42no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79—84no—
345C22×C79#54712yes—
346C22×C79C2×#13514yes—
347C22×C79C2×#13512yes—
348C22×C79#57612yes—
349C22×C79C23×D411yescharacteristic
350C2×D79—22no—
351C2×D79—22no—
352C2×D79—22no—
353C2×D79—44no—
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—42no—
357C2×D79—84no—
358C4×C79—22no—
359C4×C79—42no—
360C4×C79—42no—
361C4×C79—42no—
362C4×C79#54712yes—
363C4×C79C22×#4111yescharacteristic
364C4×C79C2×2−1+411yescharacteristic
365Dic79—22no—
366Dic79—22no—
367Dic79—22no—
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371C2×#3339—791nomaximal, Sylow
372C2×C79—24no—
373C2×C79—82no—
374C2×C79#333914yescomplemented
375C2×C79C2×#54711yescharacteristic
376C2×C79C22×#13511yescharacteristic
377C2×C79C2×#57611yescharacteristic
378D79—42no—
379D79—82no—
380C2×#553—791no—
381C2×#553—791no—
382#3339—7916no—
383C2×#499—791no—
384C2×#481—791no—
385C2×#481D7911yescharacteristic, complemented
386C2×#482—791no—
387C2×#482—791no—
388C2×#478—791no—
389C2×#478—791no—
390C2×#466—791no—
391C2×#466—791no—
392C2×C4×D8—791no—
393C2×C8×D4—791no—
394C2×#427—791no—
395C22×#107—791no—
396C79C2×#333911yescharacteristic, complemented, Sylow
397C22×D8—791no—
398C23×C8—791no—
399C23×C8—791no—
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—791no—
413C2×#121—1581no—
414C2×#121—1581no—
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⋊C4C2×D7911yescharacteristic
425#499—798no—
426#482—798no—
427#482—798no—
428#481—798no—
429#481C2×D7918yescomplemented
430#478—798no—
431#478—798no—
432#466—798no—
433#466—798no—
434C4×D8—798no—
435C8×D4—798no—
436#427—798no—
437C2×#107—791no—
438C2×#107—791no—
439C2×#107—798no—
440C2×#107—791no—
441C2×#107—791no—
442C2×#107—791no—
443C2×#106—791no—
444C2×#106—791no—
445C2×#106C2×D7911yescharacteristic
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⋊C8C2×D7911yescharacteristic
456C2×C4×C8—791no—
457C22×D4—21no—
458C22×D4—791no—
459C22×D4—791no—
460C22×D4—1581no—
461C22×D4—1581no—
462C22×D4—1581no—
463C22×D4C22×D7911yescharacteristic
464C23×C4—21no—
465C23×C4—791no—
466C23×C4—1581no—
467C23×C4—1581no—
468C23×C4—1581no—
469C23×C4C22×D7911yescharacteristic
470C2×D8—794no—
471C2×D8—1584no—
472C22×C8—791no—
473C22×C8—791no—
474C22×C8—794no—
475C22×C8—794no—
476C22×C8—1584no—
477C22×C8—1584no—
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—794no—
490#121—794no—
491#121—794no—
492#121—1582no—
493#121—1588no—
494#121—1582no—
495#121—1588no—
496#121—1582no—
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—21no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—791no—
514C2×C4⋊C4—791no—
515C2×C4⋊C4—794no—
516C2×C4⋊C4—791no—
517C2×C4⋊C4—1581no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4—1581no—
521C2×C4⋊C4—1581no—
522C2×C4⋊C4—1582no—
523C2×C4⋊C4C22×D7911yescharacteristic
524C2×C4⋊C4C22×D7911yescharacteristic
525C2×C4⋊C4C22×D7914yes—
526C2×C4⋊C4C22×D7911yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—791no—
529C2×C22⋊C4—791no—
530C2×C22⋊C4—1581no—
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#106C22×D7914yes—
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⋊C8C22×D7914yes—
558C4×C8—794no—
559C24—21no—
560C24—791no—
561C24—1581no—
562C24D4×D7911yescharacteristic
563C2×D4—24no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—3164no—
569C2×D4—794no—
570C2×D4—792no—
571C2×D4—6322no—
572C2×D4—6322no—
573C2×D4—1584no—
574C2×D4—1584no—
575C2×D4—1584no—
576C2×D4—1584no—
577C2×D4—1582no—
578C2×D4—1582no—
579C2×D4—1581no—
580C2×D4C23×D7912yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—82no—
588C22×C4—791no—
589C22×C4—791no—
590C22×C4—791no—
591C22×C4—792no—
592C22×C4—792no—
593C22×C4—6322no—
594C22×C4—6322no—
595C22×C4—6322no—
596C22×C4—1584no—
597C22×C4—1581no—
598C22×C4—1581no—
599C22×C4—1581no—
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—1588no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—794no—
612C2×C8—792no—
613C2×C8—792no—
614C2×C8—1588no—
615C2×C8—1588no—
616C2×C8—1582no—
617C2×C8C23×D7912yes—
618C2×C8C23×D7912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—794no—
624C4⋊C4—792no—
625C4⋊C4—792no—
626C4⋊C4—792no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1584no—
630C4⋊C4—1584no—
631C4⋊C4—1581no—
632C4⋊C4—1581no—
633C4⋊C4—1584no—
634C4⋊C4—1581no—
635C4⋊C4C23×D7912yes—
636C4⋊C4C23×D7912yes—
637C4⋊C4C23×D7912yes—
638C22⋊C4—24no—
639C22⋊C4—794no—
640C22⋊C4—794no—
641C22⋊C4—1584no—
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—42no—
656C23—42no—
657C23—42no—
658C23—3162no—
659C23—3162no—
660C23—3162no—
661C23—792no—
662C23—1582no—
663C23—1582no—
664C23—1582no—
665C23—1582no—
666C23#1457918214yes—
667C23C2×D4×D7912yes—
668C23C2×D4×D7911yescharacteristic
669D4—22no—
670D4—22no—
671D4—48no—
672D4—42no—
673D4—3168no—
674D4—3162no—
675D4—6324no—
676D4—6324no—
677D4—1588no—
678D4—1582no—
679D4—1582no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—84no—
691C2×C4—3162no—
692C2×C4—3162no—
693C2×C4—3162no—
694C2×C4—792no—
695C2×C4—792no—
696C2×C4—792no—
697C2×C4—6324no—
698C2×C4—6324no—
699C2×C4—6324no—
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×C4#41×D7912yes—
712C2×C4#1457920812yes—
713C2×C4C24×D7911yescharacteristic
714C8—22no—
715C8—22no—
716C8—794no—
717C8—1582no—
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—84no—
725C22—3164no—
726C22—3162no—
727C22—3162no—
728C22—3162no—
729C22—6324no—
730C22—1582no—
731C22—1582no—
732C22—1582no—
733C22#1909921112yes—
734C22C2×#1457918214yes—
735C22C2×#1457918212yes—
736C22#1909936712yes—
737C22C22×D4×D7911yescharacteristic
738C4—22no—
739C4—42no—
740C4—42no—
741C4—42no—
742C4—3162no—
743C4—3162no—
744C4—3162no—
745C4—1582no—
746C4—1582no—
747C4—1582no—
748C4#1909921112yes—
749C4C2×#41×D7911yescharacteristic
750C4C2×#1457920811yescharacteristic
751C2—24no—
752C2—82no—
753C2—3162no—
754C2—6322no—
755C2#2377580014yesdirect product factor
756C2C2×#1909921111yescharacteristic
757C2C22×#1457918211yescharacteristic
758C2C2×#1909936711yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#481×C79C2
socleC23×C79C22×D4
hypercenterC2×#481D79
hypocenterC79C2×#3339
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×#19099265C2semidirect
2. C2×#19099261C2semidirect
3. #23775800C2direct (N × H)
4. C2×#19098963C2semidirect
5. C2×#19098882C2semidirect
6. C2×#19098889C2semidirect
7. C2×#19098886C2semidirect
8. C2×#19098865C2semidirect
9. C2×#19098862C2semidirect
10. C2×#19098798C2semidirect
11. C2×#19098797C2semidirect
12. C2×#19098643C2semidirect
13. C2×(C22⋊D79)⋊C8C2semidirect
14. C2×#19098598C2semidirect
15. C22×#14579094C2semidirect
16. C2×#481×C79C2semidirect
21. #19099265C22semidirect
23. #19099261C22semidirect
43. #19098963C22semidirect
44. #19098889C22semidirect
45. #19098886C22semidirect
46. #19098882C22semidirect
47. #19098865C22semidirect
48. #19098862C22semidirect
49. #19098798C22semidirect
50. #19098797C22semidirect
51. #19098643C22semidirect
52. (C22⋊D79)⋊C8C22semidirect
53. #19098598C22semidirect
59. C2×#14579094C22semidirect
71. #481×C79C22semidirect
374. C2×C79#3339semidirect
385. C2×#481D79semidirect
396. C79C2×#3339semidirect
429. #481C2×D79semidirect
755. C2#23775800direct (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×#190992612
#237758002
C2×#190989632
C2×#190988822
C2×#190988892
C2×#190988862
C2×#190988652
C2×#190988622
C2×#190987982
C2×#190987972
C2×#190986432
C2×(C22⋊D79)⋊C82
C2×#190985982
C22×#145790942
C2×#481×C792
C2×#333979