Finite Group Databasebeta

← C2×#23775893 #35166857

Subgroups — C2×#23775893 #35166857

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×#19099276C211yesmaximal, characteristic, complemented
2C2×#19099265C211yesmaximal, characteristic, complemented
3#23775893C2116yesmaximal, direct product factor
4C2×#19098970C211yesmaximal, characteristic, complemented
5C2×#19098889C211yesmaximal, characteristic, complemented
6C2×#19098885C211yesmaximal, characteristic, complemented
7C2×#19098877C211yesmaximal, characteristic, complemented
8C2×#19098866C211yesmaximal, characteristic, complemented
9C2×#19098841C211yesmaximal, characteristic, complemented
10C2×#19098814C211yesmaximal, characteristic, complemented
11C2×#19098798C211yesmaximal, characteristic, complemented
12C2×#19098672C211yesmaximal, characteristic, complemented
13C2×#19098637C211yesmaximal, characteristic, complemented
14C2×#19098606C211yesmaximal, characteristic, complemented
15C2×#19098600C211yesmaximal, characteristic, complemented
16C2×#482×C79C211yesmaximal, characteristic, complemented
17C22×#11929609C2211yescharacteristic
18C22×#11929608C2211yescharacteristic
19C22×C8×D79C2211yescharacteristic
20#19099276—24no—
21#19099276C2218yescomplemented
22#19099265—24no—
23#19099265C2218yescomplemented
24C2×#14579160C2211yescharacteristic
25C2×#14579154—21no—
26C2×#14579152C2211yescharacteristic
27C2×#14579149—21no—
28C2×#14579147—21no—
29C2×#14579145—21no—
30C2×#14579136C2211yescharacteristic
31C2×#14579135C2211yescharacteristic
32C2×#14579134—21no—
33C2×#14579133—21no—
34C2×#14579132C2211yescharacteristic
35C2×D4×Dic79—21no—
36C2×D4×Dic79C2211yescharacteristic
37C2×#14579123C2211yescharacteristic
38C2×C4×C22⋊D79C2211yescharacteristic
39C2×#14579119C2211yescharacteristic
40C2×#14579119C2211yescharacteristic
41C2×#14579118—21no—
42C22×C4⋊Dic79C2211yescharacteristic
43#19098970C2218yescomplemented
44#19098889C2218yescomplemented
45#19098885C2218yescomplemented
46#19098877C2218yescomplemented
47#19098866C2218yescomplemented
48#19098841C2218yescomplemented
49#19098814C2218yescomplemented
50#19098798C2218yescomplemented
51#19098672C2218yescomplemented
52#19098637C2218yescomplemented
53#19098606C2218yescomplemented
54#19098600C2218yescomplemented
55C2×#14579095C2211yescharacteristic
56C2×#14579095C2211yescharacteristic
57C2×#14579094C2211yescharacteristic
58C2×#14579094C2211yescharacteristic
59C2×#14579092C2211yescharacteristic
60C2×#14579092C2211yescharacteristic
61C2×#14579092C2211yescharacteristic
62C2×Dic79⋊C8C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579082C2211yescharacteristic
66C2×#14579081C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×#14579071C2211yescharacteristic
69C2×#121×C79C2211yescharacteristic
70C2×#117×C79C2211yescharacteristic
71#482×C79C2218yescomplemented
72C2×#107×C79C2211yescharacteristic
73C2×#106×C79C2211yescharacteristic
74C2×#102×C79C2211yescharacteristic
75C2×#102×C79C2211yescharacteristic
76C2×C22⋊C8×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×D316—21no—
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C22⋊D79—21no—
82C22×C22⋊D79D411yescharacteristic
83C23×Dic79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C22×C4×D79C2311yescharacteristic
87C2×#11929609—24no—
88C2×#11929609C2314yes—
89C2×#11929608—24no—
90C2×#11929608C2314yes—
91C22×C79⋊C8C2311yescharacteristic
92C22×C79⋊C8C2311yescharacteristic
93C2×C8×D79—24no—
94C2×C8×D79C2314yes—
95#14579160—22no—
96#14579160C2314yes—
97#14579154—28no—
98#14579152—22no—
99#14579152C2314yes—
100#14579149—28no—
101#14579147—28no—
102#14579145—28no—
103#14579136—22no—
104#14579136C2314yes—
105#14579135—22no—
106#14579135C2314yes—
107#14579134—28no—
108#14579133—28no—
109#14579132—22no—
110#14579132C2314yes—
111D4×Dic79—28no—
112D4×Dic79—22no—
113D4×Dic79C2314yes—
114#14579123—22no—
115#14579123C2314yes—
116C4×C22⋊D79D414yes—
117C4×C22⋊D79C2314yes—
118#14579119—22no—
119#14579119—22no—
120#14579119C2314yes—
121#14579119C2314yes—
122#14579118—28no—
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⋊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#14579095C2314yes—
146#14579095C2314yes—
147#14579094C2314yes—
148#14579094C2314yes—
149#14579092C2314yes—
150#14579092C2314yes—
151#14579092C2314yes—
152Dic79⋊C8C2314yes—
153#14579083C2314yes—
154#14579083C2314yes—
155#14579082C2314yes—
156#14579081C2314yes—
157(C2×D79)⋊C8C2314yes—
158#14579071C2314yes—
159C22×D4×C79—21no—
160C22×D4×C79C2311yescharacteristic
161C23×C4×C79C2311yescharacteristic
162C22×C8×C79C2311yescharacteristic
163C22×C8×C79C2311yescharacteristic
164#121×C79—22no—
165#121×C79C2314yes—
166#117×C79—22no—
167#117×C79C2314yes—
168C2×C4⋊C4×C79C2311yescharacteristic
169C2×C4⋊C4×C79C2311yescharacteristic
170C2×C4⋊C4×C79C2311yescharacteristic
171C2×C22⋊C4×C79—21no—
172C2×C22⋊C4×C79—21no—
173C2×C42×C79—21no—
174#107×C79C2314yes—
175#106×C79C2314yes—
176#102×C79C2314yes—
177#102×C79C2314yes—
178C22⋊C8×C79C2314yes—
179C23×D79—21no—
180C23×D79C2×D411yescharacteristic
181C2×Dic158—24no—
182C2×Dic158—82no—
183C2×D316—24no—
184C2×D316—21no—
185C2×D316—22no—
186C2×D316—22no—
187C2×D316—82no—
188C2×D316C2412yes—
189C2×C22⋊D79—24no—
190C2×C22⋊D79—24no—
191C2×C22⋊D79—42no—
192C2×C22⋊D79—82no—
193C2×C22⋊D79—82no—
194C2×C22⋊D79C2×D414yes—
195C22×Dic79—24no—
196C22×Dic79—21no—
197C22×Dic79—21no—
198C22×Dic79—21no—
199C22×Dic79—24no—
200C22×Dic79—82no—
201C22×Dic79—82no—
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#11929609—28no—
212#11929608—28no—
213C2×C79⋊C8—22no—
214C2×C79⋊C8#4114yes—
215C2×C79⋊C8C2412yes—
216C2×C79⋊C8C2412yes—
217C8×D79—28no—
218C4⋊Dic79—24no—
219C4⋊Dic79—21no—
220C4⋊Dic79—21no—
221C4⋊Dic79—24no—
222C4⋊Dic79—21no—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228Dic79⋊C4C2×D414yes—
229C22⋊Dic79—24no—
230C22⋊Dic79—24no—
231C22⋊Dic79C2×D414yes—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235(C2×D79)⋊C4—24no—
236(C2×D79)⋊C4—24no—
237(C2×D79)⋊C4C2×D414yes—
238C4×Dic79—24no—
239C4×Dic79—24no—
240C4×Dic79C2×D412yes—
241C4×Dic79C2412yes—
242C24×C79—21no—
243C24×C79C2×D411yescharacteristic
244C2×D4×C79—24no—
245C2×D4×C79—21no—
246C2×D4×C79—22no—
247C2×D4×C79—22no—
248C2×D4×C79—44no—
249C2×D4×C79C2412yes—
250C22×C4×C79—22no—
251C22×C4×C79—22no—
252C22×C4×C79—21no—
253C22×C4×C79—21no—
254C22×C4×C79—21no—
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D412yes—
257C22×C4×C79C2412yes—
258C22×C4×C79C2411yescharacteristic
259C2×C8×C79—22no—
260C2×C8×C79—22no—
261C2×C8×C79C2412yes—
262C2×C8×C79C2412yes—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79C2412yes—
267C4⋊C4×C79C2412yes—
268C4⋊C4×C79C2412yes—
269C22⋊C4×C79—24no—
270C22⋊C4×C79—24no—
271C42×C79—24no—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—42no—
277C23×C79—42no—
278C23×C79—42no—
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×C79C22×D412yes—
304C2×C4×C79C22×D411yescharacteristic
305C2×C4×C79C2×#4112yes—
306C2×C4×C792−1+412yes—
307C2×C4×C79C2511yescharacteristic
308C22⋊D79—44no—
309C22⋊D79—84no—
310C22⋊D79—84no—
311C2×Dic79—22no—
312C2×Dic79—22no—
313C2×Dic79—22no—
314C2×Dic79—22no—
315C2×Dic79—22no—
316C2×Dic79—22no—
317C2×Dic79—42no—
318C2×Dic79—42no—
319C2×Dic79—42no—
320C2×Dic79—84no—
321C2×Dic79—84no—
322C2×Dic79C22×D412yes—
323C2×Dic79C22×D412yes—
324C2×Dic79C22×D412yes—
325D316—22no—
326D316—22no—
327D316—42no—
328D316—84no—
329C4×D79—24no—
330C4×D79—22no—
331C4×D79—22no—
332C4×D79—48no—
333Dic158—84no—
334C8×C79—22no—
335C8×C79—22no—
336C79⋊C8—22no—
337C79⋊C8C2×#4114yes—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—44no—
342C22×C79—42no—
343C22×C79—42no—
344C22×C79—42no—
345C22×C79—84no—
346C22×C79#54712yes—
347C22×C79#57512yes—
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×#3347—791nomaximal, Sylow
372C2×C79—42no—
373C2×C79—82no—
374C2×C79#334714yescomplemented
375C2×C79C2×#54711yescharacteristic
376C2×C79C2×#57511yescharacteristic
377C2×C79C2×#57611yescharacteristic
378D79—42no—
379D79—82no—
380C2×#555—791no—
381C2×#553—791no—
382#3347—7916no—
383C2×#501—791no—
384C2×#482—791no—
385C2×#482—791no—
386C2×#482D7911yescharacteristic, complemented
387C2×#480—791no—
388C2×#478—791no—
389C2×#474—791no—
390C2×#469—791no—
391C2×#466—791no—
392C2×#442—791no—
393C2×#435—791no—
394C2×#428—791no—
395C2×#427—791no—
396C79C2×#334711yescharacteristic, complemented, Sylow
397C22×D8—791no—
398C22×M16—791no—
399C23×C8—791no—
400#555—798no—
401#555—1584no—
402#553—798no—
403#553—1584no—
404C2×C4⋊Q8—791no—
405C2×#126—1581no—
406C2×#125—791no—
407C2×#124—1581no—
408C2×#124—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×#117—791no—
421C2×#117—791no—
422C2×#117—1581no—
423C2×#117C2×D7911yescharacteristic
424C22×C4⋊C4—791no—
425#501—798no—
426#482—798no—
427#482—798no—
428#482C2×D7918yescomplemented
429#480—798no—
430#478—798no—
431#474—798no—
432#469—798no—
433#466—798no—
434#442—798no—
435#435—798no—
436#428—798no—
437#427—798no—
438C2×#107—791no—
439C2×#107—791no—
440C2×#107—791no—
441C2×#107—791no—
442C2×#107C2×D7911yescharacteristic
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⋊C8C2×D7911yescharacteristic
456C2×#97—791no—
457C22×Q8—1581no—
458C22×D4—21no—
459C22×D4—791no—
460C22×D4—791no—
461C22×D4—1581no—
462C22×D4—1581no—
463C22×D4—1581no—
464C22×D4C22×D7911yescharacteristic
465C23×C4—791no—
466C23×C4—1581no—
467C23×C4—1581no—
468C23×C4—1581no—
469C23×C4C22×D7911yescharacteristic
470C2×D8—794no—
471C2×D8—1584no—
472C2×M16—794no—
473C2×M16—1584no—
474C22×C8—791no—
475C22×C8—791no—
476C22×C8—794no—
477C22×C8—1584no—
478C22×C8C22×D7911yescharacteristic
479C22×C8C22×D7911yescharacteristic
480C4⋊Q8—794no—
481C4⋊Q8—1582no—
482#126—1588no—
483#125—794no—
484#125—1582no—
485#124—1588no—
486#124—1588no—
487#123—1588no—
488#121—22no—
489#121—794no—
490#121—794no—
491#121—794no—
492#121—1588no—
493#121—1582no—
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—
505#117—22no—
506#117—794no—
507#117—794no—
508#117—1588no—
509#117—1582no—
510#117—1582no—
511#117C22×D7914yes—
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—1582no—
522C2×C4⋊C4C22×D7911yescharacteristic
523C2×C4⋊C4C22×D7911yescharacteristic
524C2×C4⋊C4C22×D7911yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—791no—
528C2×C22⋊C4—791no—
529C2×C22⋊C4—1581no—
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×C42—21no—
537C2×C42—791no—
538C2×C42—1581no—
539C2×C42—1581no—
540#107—794no—
541#107—794no—
542#107—794no—
543#107—794no—
544#107C22×D7914yes—
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⋊C8C22×D7914yes—
558#97—794no—
559C24—21no—
560C24—791no—
561C24—1581no—
562C24D4×D7911yescharacteristic
563C2×Q8—6322no—
564C2×Q8—1584no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—3162no—
571C2×D4—794no—
572C2×D4—792no—
573C2×D4—6322no—
574C2×D4—6322no—
575C2×D4—6322no—
576C2×D4—1584no—
577C2×D4—1584no—
578C2×D4—1584no—
579C2×D4—1582no—
580C2×D4—1582no—
581C2×D4—1581no—
582C2×D4C23×D7912yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—3164no—
589C22×C4—791no—
590C22×C4—791no—
591C22×C4—791no—
592C22×C4—792no—
593C22×C4—792no—
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—
609M16—1588no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—794no—
613C2×C8—792no—
614C2×C8—792no—
615C2×C8—1588no—
616C2×C8—1582no—
617C2×C8C23×D7912yes—
618C2×C8C23×D7912yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—794no—
623C4⋊C4—792no—
624C4⋊C4—792no—
625C4⋊C4—792no—
626C4⋊C4—1584no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1581no—
630C4⋊C4—1581no—
631C4⋊C4—1584no—
632C4⋊C4—1581no—
633C4⋊C4C23×D7912yes—
634C4⋊C4C23×D7912yes—
635C4⋊C4C23×D7912yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—794no—
639C22⋊C4—794no—
640C22⋊C4—1584no—
641C22⋊C4—1584no—
642C22⋊C4—1584no—
643C22⋊C4—1584no—
644C22⋊C4—1584no—
645C22⋊C4—1584no—
646C22⋊C4—1584no—
647C42—24no—
648C42—792no—
649C42—792no—
650C42—1584no—
651C42—1584no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—3162no—
660C23—3162no—
661C23—3162no—
662C23—792no—
663C23—1582no—
664C23—1582no—
665C23—1582no—
666C23—1582no—
667C23C2×D4×D7912yes—
668C23C2×D4×D7911yescharacteristic
669Q8—6324no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—42no—
674D4—3164no—
675D4—3162no—
676D4—6324no—
677D4—6324no—
678D4—6324no—
679D4—1582no—
680D4—1582no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—3168no—
692C2×C4—3162no—
693C2×C4—3162no—
694C2×C4—3162no—
695C2×C4—792no—
696C2×C4—792no—
697C2×C4—792no—
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—22no—
719C22—22no—
720C22—22no—
721C22—44no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—3164no—
727C22—3162no—
728C22—3162no—
729C22—3162no—
730C22—6324no—
731C22—1582no—
732C22—1582no—
733C22—1582no—
734C22#1909921112yes—
735C22#1909935912yes—
736C22#1909936512yes—
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—42no—
752C2—82no—
753C2—3162no—
754C2—6322no—
755C2#2377589314yesdirect product factor
756C2C2×#1909921111yescharacteristic
757C2C2×#1909935911yescharacteristic
758C2C2×#1909936511yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#482×C79C2
socleC23×C79C22×D4
hypercenterC2×#482D79
hypocenterC79C2×#3347
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#19099276C2semidirect
2. C2×#19099265C2semidirect
3. #23775893C2direct (N × H)
4. C2×#19098970C2semidirect
5. C2×#19098889C2semidirect
6. C2×#19098885C2semidirect
7. C2×#19098877C2semidirect
8. C2×#19098866C2semidirect
9. C2×#19098841C2semidirect
10. C2×#19098814C2semidirect
11. C2×#19098798C2semidirect
12. C2×#19098672C2semidirect
13. C2×#19098637C2semidirect
14. C2×#19098606C2semidirect
15. C2×#19098600C2semidirect
16. C2×#482×C79C2semidirect
21. #19099276C22semidirect
23. #19099265C22semidirect
43. #19098970C22semidirect
44. #19098889C22semidirect
45. #19098885C22semidirect
46. #19098877C22semidirect
47. #19098866C22semidirect
48. #19098841C22semidirect
49. #19098814C22semidirect
50. #19098798C22semidirect
51. #19098672C22semidirect
52. #19098637C22semidirect
53. #19098606C22semidirect
54. #19098600C22semidirect
71. #482×C79C22semidirect
374. C2×C79#3347semidirect
386. C2×#482D79semidirect
396. C79C2×#3347semidirect
428. #482C2×D79semidirect
755. C2#23775893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992762
C2×#190992652
#237758932
C2×#190989702
C2×#190988892
C2×#190988852
C2×#190988772
C2×#190988662
C2×#190988412
C2×#190988142
C2×#190987982
C2×#190986722
C2×#190986372
C2×#190986062
C2×#190986002
C2×#482×C792
C2×#334779