Finite Group Databasebeta

← C2×#23775902 #35166866

Subgroups — C2×#23775902 #35166866

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×#19099278C211yesmaximal, characteristic, complemented
2C2×#19099259C211yesmaximal, characteristic, complemented
3#23775902C2116yesmaximal, direct product factor
4C2×#19098972C211yesmaximal, characteristic, complemented
5C2×#19098888C211yesmaximal, characteristic, complemented
6C2×#19098888C211yesmaximal, characteristic, complemented
7C2×#19098888C211yesmaximal, characteristic, complemented
8C2×#19098877C211yesmaximal, characteristic, complemented
9C2×#19098864C211yesmaximal, characteristic, complemented
10C2×#19098844C211yesmaximal, characteristic, complemented
11C2×#19098816C211yesmaximal, characteristic, complemented
12C2×#19098799C211yesmaximal, characteristic, complemented
13C2×#19098676C211yesmaximal, characteristic, complemented
14C2×#19098605C211yesmaximal, characteristic, complemented
15C2×#19098601C211yesmaximal, characteristic, complemented
16C2×#435×C79C211yesmaximal, characteristic, complemented
17C22×D632C2211yescharacteristic
18#19099278—24no—
19#19099278C2218yescomplemented
20#19099259—24no—
21#19099259C2218yescomplemented
22C2×#14579161C2211yescharacteristic
23C2×#14579156—21no—
24C2×#14579153C2211yescharacteristic
25C2×#14579147—21no—
26C2×#14579147—21no—
27C2×#14579143—21no—
28C2×#14579135C2211yescharacteristic
29C2×#14579135C2211yescharacteristic
30C2×#14579135C2211yescharacteristic
31C2×#14579135C2211yescharacteristic
32C2×#14579133—21no—
33C2×#14579132—21no—
34C2×C4×D316C2211yescharacteristic
35C2×C4×D316C2211yescharacteristic
36C2×(C22⋊D79)⋊C4—21no—
37C2×#14579120C2211yescharacteristic
38C2×#14579120C2211yescharacteristic
39C2×#14579120C2211yescharacteristic
40C2×#14579119—21no—
41C22×C4⋊Dic79C2211yescharacteristic
42#19098972C2218yescomplemented
43#19098888C2218yescomplemented
44#19098888C2218yescomplemented
45#19098888C2218yescomplemented
46#19098877C2218yescomplemented
47#19098864C2218yescomplemented
48#19098844C2218yescomplemented
49#19098816C2218yescomplemented
50#19098799C2218yescomplemented
51#19098676C2218yescomplemented
52#19098605C2218yescomplemented
53#19098601C2218yescomplemented
54C2×#14579095C2211yescharacteristic
55C2×#14579095C2211yescharacteristic
56C2×#14579095C2211yescharacteristic
57C2×#14579095C2211yescharacteristic
58C2×#14579095C2211yescharacteristic
59C2×#14579093C2211yescharacteristic
60C2×#14579093C2211yescharacteristic
61C2×#14579093C2211yescharacteristic
62C2×#14579093C2211yescharacteristic
63C2×#14579083C2211yescharacteristic
64C2×#14579083C2211yescharacteristic
65C2×#14579083C2211yescharacteristic
66C2×#14579083C2211yescharacteristic
67C2×#14579083C2211yescharacteristic
68C2×#14579083C2211yescharacteristic
69C22×M16×C79C2211yescharacteristic
70C23×C8×C79C2211yescharacteristic
71C2×C4×D4×C79C2211yescharacteristic
72#435×C79C2218yescomplemented
73C2×C4⋊C8×C79C2211yescharacteristic
74C2×C22⋊C8×C79C2211yescharacteristic
75C2×C22⋊C8×C79C2211yescharacteristic
76C2×#97×C79C2211yescharacteristic
77C22×Dic158—21no—
78C22×D316C2311yescharacteristic
79C22×D316C2311yescharacteristic
80C22×C22⋊D79—21no—
81C22×C22⋊D79—21no—
82C22×C22⋊D79—21no—
83C22×C22⋊D79—21no—
84C23×Dic79—21no—
85C22×C4×D79—21no—
86C22×C4×D79—21no—
87C2×D632—24no—
88C2×D632C2314yes—
89#14579161—22no—
90#14579161C2314yes—
91#14579156—28no—
92#14579153—22no—
93#14579153C2314yes—
94#14579147—28no—
95#14579147—28no—
96#14579143—28no—
97#14579135—22no—
98#14579135—22no—
99#14579135—22no—
100#14579135—22no—
101#14579135C2314yes—
102#14579135C2314yes—
103#14579135C2314yes—
104#14579135C2314yes—
105#14579133—28no—
106#14579132—28no—
107C4×D316—22no—
108C4×D316—22no—
109C4×D316C2314yes—
110C4×D316C2314yes—
111(C22⋊D79)⋊C4—28no—
112#14579120—22no—
113#14579120—22no—
114#14579120—22no—
115#14579120C2314yes—
116#14579120C2314yes—
117#14579120C2314yes—
118#14579119—28no—
119C2×C4⋊Dic79—22no—
120C2×C4⋊Dic79—21no—
121C2×C4⋊Dic79—21no—
122C2×C4⋊Dic79C2314yes—
123C2×C4⋊Dic79C2311yescharacteristic
124C2×C4⋊Dic79C2311yescharacteristic
125C2×C4⋊Dic79C2311yescharacteristic
126C2×C4⋊Dic79C2311yescharacteristic
127C2×C4⋊Dic79C2311yescharacteristic
128C2×C4⋊Dic79C2311yescharacteristic
129C2×Dic79⋊C4—21no—
130C2×Dic79⋊C4—21no—
131C2×C22⋊Dic79—21no—
132C2×C22⋊Dic79—21no—
133C2×C22⋊Dic79—21no—
134C2×(C2×D79)⋊C4—21no—
135C2×(C2×D79)⋊C4—21no—
136C2×(C2×D79)⋊C4—21no—
137C2×(C2×D79)⋊C4—21no—
138C2×(C2×D79)⋊C4—21no—
139C2×(C2×D79)⋊C4—21no—
140C2×C4×Dic79—21no—
141C2×C4×Dic79—21no—
142C2×C4×Dic79—21no—
143#14579095C2314yes—
144#14579095C2314yes—
145#14579095C2314yes—
146#14579095C2314yes—
147#14579095C2314yes—
148#14579093C2314yes—
149#14579093C2314yes—
150#14579093C2314yes—
151#14579093C2314yes—
152#14579083C2314yes—
153#14579083C2314yes—
154#14579083C2314yes—
155#14579083C2314yes—
156#14579083C2314yes—
157#14579083C2314yes—
158C22×D4×C79D411yescharacteristic
159C23×C4×C79C2311yescharacteristic
160C23×C4×C79C2311yescharacteristic
161C2×M16×C79—24no—
162C2×M16×C79C2314yes—
163C22×C8×C79—24no—
164C22×C8×C79C2311yescharacteristic
165C22×C8×C79C2311yescharacteristic
166C22×C8×C79C2314yes—
167C22×C8×C79C2311yescharacteristic
168C22×C8×C79C2311yescharacteristic
169C4×D4×C79D414yes—
170C4×D4×C79C2314yes—
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C22⋊C4×C79D411yescharacteristic
173C2×C22⋊C4×C79D411yescharacteristic
174C2×C42×C79C2311yescharacteristic
175C4⋊C8×C79C2314yes—
176C22⋊C8×C79C2314yes—
177C22⋊C8×C79C2314yes—
178#97×C79C2314yes—
179C23×D79—21no—
180C23×D79—21no—
181C2×Dic158—24no—
182C2×Dic158—82no—
183C2×D316—21no—
184C2×D316—21no—
185C2×D316—22no—
186C2×D316—22no—
187C2×D316—22no—
188C2×D316—22no—
189C2×D316C2412yes—
190C2×D316C2412yes—
191C2×C22⋊D79—24no—
192C2×C22⋊D79—24no—
193C2×C22⋊D79—24no—
194C2×C22⋊D79—24no—
195C2×C22⋊D79—44no—
196C2×C22⋊D79—82no—
197C2×C22⋊D79—82no—
198C2×C22⋊D79—82no—
199C22×Dic79—21no—
200C22×Dic79—21no—
201C22×Dic79—21no—
202C22×Dic79—21no—
203C22×Dic79—21no—
204C22×Dic79—21no—
205C22×Dic79—24no—
206C22×Dic79—82no—
207C2×C4×D79—24no—
208C2×C4×D79—24no—
209C2×C4×D79—44no—
210C2×C4×D79—82no—
211D632—28no—
212C4⋊Dic79—21no—
213C4⋊Dic79—21no—
214C4⋊Dic79—24no—
215C4⋊Dic79—24no—
216C4⋊Dic79—21no—
217C4⋊Dic79—21no—
218C4⋊Dic79—21no—
219C4⋊Dic79—21no—
220C4⋊Dic79C2412yes—
221C4⋊Dic79C2412yes—
222C4⋊Dic79C2412yes—
223C4⋊Dic79C2412yes—
224C4⋊Dic79C2412yes—
225C4⋊Dic79C2412yes—
226Dic79⋊C4—24no—
227Dic79⋊C4—24no—
228C22⋊Dic79—24no—
229C22⋊Dic79—24no—
230C22⋊Dic79—24no—
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)⋊C4—24no—
237C4×Dic79—24no—
238C4×Dic79—24no—
239C4×Dic79—24no—
240C24×C79C2×D411yescharacteristic
241C24×C79C2×D411yescharacteristic
242C2×D4×C79—42no—
243C2×D4×C79C2×D414yes—
244C22×C4×C79—22no—
245C22×C4×C79—22no—
246C22×C4×C79—22no—
247C22×C4×C79—22no—
248C22×C4×C79C2×D411yescharacteristic
249C22×C4×C79C2×D411yescharacteristic
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D412yes—
253C22×C4×C79C2×D412yes—
254C22×C4×C79C2412yes—
255C22×C4×C79C2412yes—
256C22×C4×C79C2411yescharacteristic
257M16×C79—28no—
258C2×C8×C79—28no—
259C2×C8×C79—22no—
260C2×C8×C79—22no—
261C2×C8×C79—22no—
262C2×C8×C79#4114yes—
263C2×C8×C79C2412yes—
264C2×C8×C79C2412yes—
265C2×C8×C79C2412yes—
266C2×C8×C79C2412yes—
267C4⋊C4×C79C2×D414yes—
268C22⋊C4×C79C2×D414yes—
269C22⋊C4×C79C2×D414yes—
270C42×C79C2×D412yes—
271C42×C79C2412yes—
272C23×C79—22no—
273C23×C79—22no—
274C23×C79—22no—
275C23×C79—22no—
276C23×C79—22no—
277C23×C79—22no—
278C23×C79C22×D412yes—
279C23×C79C22×D412yes—
280C23×C79C22×D411yescharacteristic
281C22×D79—22no—
282C22×D79—22no—
283C22×D79—42no—
284C22×D79—42no—
285C22×D79—42no—
286C22×D79—42no—
287C22×D79—42no—
288C22×D79—42no—
289D4×C79—44no—
290C2×C4×C79—22no—
291C2×C4×C79—22no—
292C2×C4×C79—22no—
293C2×C4×C79—22no—
294C2×C4×C79—24no—
295C2×C4×C79—24no—
296C2×C4×C79—22no—
297C2×C4×C79—22no—
298C2×C4×C79—22no—
299C2×C4×C79—22no—
300C2×C4×C79C22×D412yes—
301C2×C4×C79C22×D412yes—
302C2×C4×C79C22×D412yes—
303C2×C4×C79C22×D412yes—
304C2×C4×C79C22×D411yescharacteristic
305C2×C4×C79C2×#4112yes—
306C2×C4×C792−1+412yes—
307C2×C4×C79C2511yescharacteristic
308C22⋊D79—48no—
309C22⋊D79—84no—
310C22⋊D79—84no—
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—42no—
322C2×Dic79—42no—
323C2×Dic79—42no—
324C2×Dic79—84no—
325D316—22no—
326D316—22no—
327D316—22no—
328D316—22no—
329D316—42no—
330D316—42no—
331C4×D79—48no—
332C4×D79—84no—
333Dic158—84no—
334C8×C79—22no—
335C8×C79—22no—
336C8×C79—22no—
337C8×C79C2×#4114yes—
338C22×C79—22no—
339C22×C79—22no—
340C22×C79—22no—
341C22×C79—22no—
342C22×C79—22no—
343C22×C79—22no—
344C22×C79—44no—
345C22×C79—44no—
346C22×C79#54712yes—
347C22×C79#57512yes—
348C22×C79#57612yes—
349C22×C79C23×D411yescharacteristic
350C2×D79—42no—
351C2×D79—42no—
352C2×D79—42no—
353C2×D79—42no—
354C2×D79—42no—
355C2×D79—42no—
356C2×D79—84no—
357C2×D79—84no—
358C4×C79—22no—
359C4×C79—22no—
360C4×C79—22no—
361C4×C79—22no—
362C4×C79#54712yes—
363C4×C79C22×#4111yescharacteristic
364C4×C79C2×2−1+411yescharacteristic
365Dic79—42no—
366Dic79—42no—
367Dic79—42no—
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371C2×#3347—791nomaximal, Sylow
372C2×C79—42no—
373C2×C79—42no—
374C2×C79#334714yescomplemented
375C2×C79C2×#54711yescharacteristic
376C2×C79C2×#57511yescharacteristic
377C2×C79C2×#57611yescharacteristic
378D79—82no—
379D79—82no—
380C2×#555—791no—
381C2×#553—791no—
382#3347—7916no—
383C2×#501—791no—
384C2×#482—791no—
385C2×#482—791no—
386C2×#482—791no—
387C2×#480—791no—
388C2×#478—791no—
389C2×#474—791no—
390C2×#469—791no—
391C2×#466—791no—
392C2×#442—791no—
393C2×#435D7911yescharacteristic, complemented
394C2×#428—791no—
395C2×#427—791no—
396C79C2×#334711yescharacteristic, complemented, Sylow
397C22×D8—791no—
398C22×M16C2×D7911yescharacteristic
399C23×C8C2×D7911yescharacteristic
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—791no—
414C2×#121—1581no—
415C2×#121—1581no—
416C2×C4×D4—791no—
417C2×C4×D4—791no—
418C2×C4×D4—1581no—
419C2×C4×D4C2×D7911yescharacteristic
420C2×#117—791no—
421C2×#117—791no—
422C2×#117—791no—
423C2×#117—1581no—
424C22×C4⋊C4—791no—
425#501—798no—
426#482—798no—
427#482—798no—
428#482—798no—
429#480—798no—
430#478—798no—
431#474—798no—
432#469—798no—
433#466—798no—
434#442—798no—
435#435C2×D7918yescomplemented
436#428—798no—
437#427—798no—
438C2×#107—791no—
439C2×#107—791no—
440C2×#107—791no—
441C2×#107—791no—
442C2×#107—791no—
443C2×#106—791no—
444C2×#106—791no—
445C2×#106—791no—
446C2×#106—791no—
447C2×C4⋊C8C2×D7911yescharacteristic
448C2×#102—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×#102—791no—
453C2×#102—791no—
454C2×C22⋊C8C2×D7911yescharacteristic
455C2×C22⋊C8C2×D7911yescharacteristic
456C2×#97C2×D7911yescharacteristic
457C22×Q8—1581no—
458C22×D4—791no—
459C22×D4—791no—
460C22×D4—1581no—
461C22×D4—1581no—
462C22×D4—1581no—
463C22×D4—1581no—
464C22×D4D31611yescharacteristic
465C23×C4—1581no—
466C23×C4—1581no—
467C23×C4—1581no—
468C23×C4C22×D7911yescharacteristic
469C23×C4C22×D7911yescharacteristic
470C2×D8—794no—
471C2×D8—1584no—
472C2×M16—24no—
473C2×M16C22×D7914yes—
474C22×C8—24no—
475C22×C8C22×D7911yescharacteristic
476C22×C8C22×D7914yes—
477C22×C8C22×D7911yescharacteristic
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—794no—
489#121—794no—
490#121—794no—
491#121—794no—
492#121—1588no—
493#121—1588no—
494#121—1582no—
495#121—1582no—
496#121—1582no—
497#121—1582no—
498C4×D4—794no—
499C4×D4—794no—
500C4×D4—1588no—
501C4×D4—1582no—
502C4×D4—1582no—
503C4×D4D31614yes—
504C4×D4C22×D7914yes—
505#117—794no—
506#117—794no—
507#117—794no—
508#117—1582no—
509#117—1582no—
510#117—1582no—
511#117—1588no—
512C2×C4⋊C4—791no—
513C2×C4⋊C4—791no—
514C2×C4⋊C4—794no—
515C2×C4⋊C4—791no—
516C2×C4⋊C4—791no—
517C2×C4⋊C4—791no—
518C2×C4⋊C4—791no—
519C2×C4⋊C4—1581no—
520C2×C4⋊C4—1582no—
521C2×C4⋊C4—1581no—
522C2×C4⋊C4—1581no—
523C2×C4⋊C4—1581no—
524C2×C4⋊C4D31611yescharacteristic
525C2×C22⋊C4—1581no—
526C2×C22⋊C4—1581no—
527C2×C22⋊C4—1581no—
528C2×C22⋊C4—1581no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C22⋊C4—1581no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4D31611yescharacteristic
535C2×C22⋊C4D31611yescharacteristic
536C2×C42—1581no—
537C2×C42—1581no—
538C2×C42—1581no—
539C2×C42C22×D7911yescharacteristic
540#107—794no—
541#107—794no—
542#107—794no—
543#107—794no—
544#107—794no—
545#106—794no—
546#106—794no—
547#106—794no—
548#106—794no—
549C4⋊C8C22×D7914yes—
550#102—794no—
551#102—794no—
552#102—794no—
553#102—794no—
554#102—794no—
555#102—794no—
556C22⋊C8C22×D7914yes—
557C22⋊C8C22×D7914yes—
558#97C22×D7914yes—
559C24—1581no—
560C24—1581no—
561C24C2×D31611yescharacteristic
562C24C2×D31611yescharacteristic
563C2×Q8—6322no—
564C2×Q8—1584no—
565C2×D4—42no—
566C2×D4—3164no—
567C2×D4—792no—
568C2×D4—792no—
569C2×D4—6322no—
570C2×D4—6322no—
571C2×D4—6322no—
572C2×D4—1584no—
573C2×D4—1584no—
574C2×D4—1584no—
575C2×D4—1584no—
576C2×D4—1582no—
577C2×D4—1582no—
578C2×D4—1582no—
579C2×D4—1582no—
580C2×D4—1581no—
581C2×D4—1581no—
582C2×D4C2×D31614yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—3164no—
588C22×C4—6322no—
589C22×C4—6322no—
590C22×C4—1581no—
591C22×C4—1581no—
592C22×C4—1581no—
593C22×C4—1581no—
594C22×C4—1581no—
595C22×C4—1581no—
596C22×C4—1584no—
597C22×C4—1584no—
598C22×C4—1584no—
599C22×C4C2×D31612yes—
600C22×C4C2×D31612yes—
601C22×C4C2×D31611yescharacteristic
602C22×C4C2×D31611yescharacteristic
603C22×C4C2×D31611yescharacteristic
604C22×C4C2×D31611yescharacteristic
605C22×C4C23×D7912yes—
606C22×C4C23×D7912yes—
607C22×C4C23×D7911yescharacteristic
608D8—1588no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#1192962314yes—
615C2×C8C23×D7912yes—
616C2×C8C23×D7912yes—
617C2×C8C23×D7912yes—
618C2×C8C23×D7912yes—
619C4⋊C4—792no—
620C4⋊C4—792no—
621C4⋊C4—792no—
622C4⋊C4—792no—
623C4⋊C4—792no—
624C4⋊C4—792no—
625C4⋊C4—1584no—
626C4⋊C4—1584no—
627C4⋊C4—1581no—
628C4⋊C4—1581no—
629C4⋊C4—1584no—
630C4⋊C4—1581no—
631C4⋊C4—1581no—
632C4⋊C4—1581no—
633C4⋊C4—1581no—
634C4⋊C4—1584no—
635C4⋊C4C2×D31614yes—
636C22⋊C4—1584no—
637C22⋊C4—1584no—
638C22⋊C4—1584no—
639C22⋊C4—1584no—
640C22⋊C4—1584no—
641C22⋊C4—1584no—
642C22⋊C4—1584no—
643C22⋊C4—1584no—
644C22⋊C4—1584no—
645C22⋊C4C2×D31614yes—
646C22⋊C4C2×D31614yes—
647C42—1584no—
648C42—1584no—
649C42—1584no—
650C42C2×D31612yes—
651C42C23×D7912yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—3162no—
659C23—3162no—
660C23—3162no—
661C23—3162no—
662C23—3162no—
663C23—3162no—
664C23—1582no—
665C23—1582no—
666C23C22×D31612yes—
667C23C22×D31612yes—
668C23C22×D31611yescharacteristic
669Q8—6324no—
670D4—44no—
671D4—3168no—
672D4—3162no—
673D4—3162no—
674D4—6324no—
675D4—6324no—
676D4—6324no—
677D4—1582no—
678D4—1582no—
679D4—1582no—
680D4—1582no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—3168no—
692C2×C4—3162no—
693C2×C4—3162no—
694C2×C4—3162no—
695C2×C4—3162no—
696C2×C4—3162no—
697C2×C4—3162no—
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×C4C22×D31612yes—
707C2×C4C22×D31612yes—
708C2×C4C22×D31612yes—
709C2×C4C22×D31612yes—
710C2×C4C22×D31611yescharacteristic
711C2×C4C2×#1192962312yes—
712C2×C4#1457920812yes—
713C2×C4C24×D7911yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#1192962314yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—3162no—
727C22—3162no—
728C22—3162no—
729C22—3162no—
730C22—3162no—
731C22—3162no—
732C22—6324no—
733C22—6324no—
734C22#1909921712yes—
735C22#1909936312yes—
736C22#1909936812yes—
737C22C23×D31611yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—3162no—
743C4—3162no—
744C4—3162no—
745C4—3162no—
746C4—3162no—
747C4—3162no—
748C4#1909921712yes—
749C4C22×#1192962311yescharacteristic
750C4C2×#1457920811yescharacteristic
751C2—42no—
752C2—42no—
753C2—6322no—
754C2—6322no—
755C2#2377590214yesdirect product factor
756C2C2×#1909921711yescharacteristic
757C2C2×#1909936311yescharacteristic
758C2C2×#1909936811yescharacteristic
subgroupG/H
centerC23C22×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#435×C79C2
socleC23×C79C22×D4
hypercenterC2×#435D79
hypocenterC79C2×#3347
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#19099278C2semidirect
2. C2×#19099259C2semidirect
3. #23775902C2direct (N × H)
4. C2×#19098972C2semidirect
5. C2×#19098888C2semidirect
6. C2×#19098888C2semidirect
7. C2×#19098888C2semidirect
8. C2×#19098877C2semidirect
9. C2×#19098864C2semidirect
10. C2×#19098844C2semidirect
11. C2×#19098816C2semidirect
12. C2×#19098799C2semidirect
13. C2×#19098676C2semidirect
14. C2×#19098605C2semidirect
15. C2×#19098601C2semidirect
16. C2×#435×C79C2semidirect
19. #19099278C22semidirect
21. #19099259C22semidirect
42. #19098972C22semidirect
43. #19098888C22semidirect
44. #19098888C22semidirect
45. #19098888C22semidirect
46. #19098877C22semidirect
47. #19098864C22semidirect
48. #19098844C22semidirect
49. #19098816C22semidirect
50. #19098799C22semidirect
51. #19098676C22semidirect
52. #19098605C22semidirect
53. #19098601C22semidirect
72. #435×C79C22semidirect
374. C2×C79#3347semidirect
393. C2×#435D79semidirect
396. C79C2×#3347semidirect
435. #435C2×D79semidirect
755. C2#23775902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992782
C2×#190992592
#237759022
C2×#190989722
C2×#190988882
C2×#190988772
C2×#190988642
C2×#190988442
C2×#190988162
C2×#190987992
C2×#190986762
C2×#190986052
C2×#190986012
C2×#435×C792
C2×#334779