Finite Group Databasebeta

← C2×#23776484 #35169295

Subgroups — C2×#23776484 #35169295

Order 20224.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099298C211yesmaximal, characteristic, complemented
2#23776484C2116yesmaximal, direct product factor
3C2×#19098953C211yesmaximal, characteristic, complemented
4C2×#19098950C211yesmaximal, characteristic, complemented
5C2×#19098945C211yesmaximal, characteristic, complemented
6C2×#19098785C211yesmaximal, characteristic, complemented
7C2×#19098782C211yesmaximal, characteristic, complemented
8C2×#19098778C211yesmaximal, characteristic, complemented
9C2×#19098775C211yesmaximal, characteristic, complemented
10C2×#19098758C211yesmaximal, characteristic, complemented
11C2×#19098755C211yesmaximal, characteristic, complemented
12C2×#19098694C211yesmaximal, characteristic, complemented
13C2×#19098663C211yesmaximal, characteristic, complemented
14C2×#19098661C211yesmaximal, characteristic, complemented
15C2×C4×#11929609C211yesmaximal, characteristic, complemented
16C2×#559×C79C211yesmaximal, characteristic, complemented
17C22×#11929614C2211yescharacteristic
18C22×#11929612C2211yescharacteristic
19C22×#11929612C2211yescharacteristic
20C22×#11929611C2211yescharacteristic
21C22×#11929611C2211yescharacteristic
22C22×#11929609C2211yescharacteristic
23C22×#11929609C2211yescharacteristic
24C22×#11929609C2211yescharacteristic
25C22×#11929609C2211yescharacteristic
26#19099298—24no—
27#19099298C2218yescomplemented
28C2×#14579158C2211yescharacteristic
29C2×#14579150—21no—
30C2×#14579149C2211yescharacteristic
31C2×#14579149C2211yescharacteristic
32C2×#14579146—21no—
33C2×#14579146—21no—
34C2×C4×Dic158C2211yescharacteristic
35C2×C4×D316C2211yescharacteristic
36C2×C4×D316C2211yescharacteristic
37C2×#14579123—21no—
38#19098953C2218yescomplemented
39#19098950C2218yescomplemented
40#19098945C2218yescomplemented
41#19098785C2218yescomplemented
42#19098782C2218yescomplemented
43#19098778C2218yescomplemented
44#19098775C2218yescomplemented
45#19098758C2218yescomplemented
46#19098755C2218yescomplemented
47#19098694C2218yescomplemented
48#19098663C2218yescomplemented
49#19098661C2218yescomplemented
50C4×#11929609C2218yescomplemented
51C2×#14579094C2211yescharacteristic
52C2×C4⋊(C79⋊C8)C2211yescharacteristic
53C2×C4⋊(C79⋊C8)C2211yescharacteristic
54C2×C4⋊(C79⋊C8)C2211yescharacteristic
55C2×#14579085C2211yescharacteristic
56C2×#14579084C2211yescharacteristic
57C2×#14579082C2211yescharacteristic
58C2×#14579082C2211yescharacteristic
59C2×#14579081C2211yescharacteristic
60C2×#14579081C2211yescharacteristic
61C2×#14579072C2211yescharacteristic
62C2×#14579072C2211yescharacteristic
63C2×C4×C79⋊C8C2211yescharacteristic
64#559×C79—24no—
65#559×C79C2218yescomplemented
66C2×#127×C79C2211yescharacteristic
67C2×#124×C79—21no—
68C2×#124×C79C2211yescharacteristic
69C2×#124×C79C2211yescharacteristic
70C2×#123×C79—21no—
71C2×#123×C79—21no—
72C2×C4×Q8×C79C2211yescharacteristic
73C2×C4×Q8×C79C2211yescharacteristic
74C2×C4×D4×C79—21no—
75C2×C4×D4×C79C2211yescharacteristic
76C2×C4×D4×C79C2211yescharacteristic
77C22×Dic158C2311yescharacteristic
78C22×D316—21no—
79C22×D316—21no—
80C22×D316C2311yescharacteristic
81C22×D316C2311yescharacteristic
82C22×C4×D79—21no—
83C22×C4×D79—21no—
84C2×#11929614—42no—
85C2×#11929614C2314yes—
86C2×#11929612—24no—
87C2×#11929612—42no—
88C2×#11929612C2314yes—
89C2×#11929612C2314yes—
90C2×#11929611—24no—
91C2×#11929611—42no—
92C2×#11929611C2314yes—
93C2×#11929611C2314yes—
94C2×#11929609—24no—
95C2×#11929609—42no—
96C2×#11929609—42no—
97C2×#11929609—42no—
98C2×#11929609C2314yes—
99C2×#11929609C2314yes—
100C2×#11929609C2314yes—
101C2×#11929609C2314yes—
102C22×C79⋊C8C2311yescharacteristic
103C22×C79⋊C8C2311yescharacteristic
104C22×C79⋊C8C2311yescharacteristic
105C22×C79⋊C8C2311yescharacteristic
106#14579158—22no—
107#14579158C2314yes—
108#14579150—28no—
109#14579149—22no—
110#14579149—22no—
111#14579149C2314yes—
112#14579149C2314yes—
113#14579146—28no—
114#14579146—28no—
115C4×Dic158—22no—
116C4×Dic158C2314yes—
117C4×D316—22no—
118C4×D316—22no—
119C4×D316C2314yes—
120C4×D316C2314yes—
121#14579123—28no—
122C2×C4⋊Dic79C2311yescharacteristic
123C2×Dic79⋊C4—21no—
124C2×(C2×D79)⋊C4—21no—
125C2×(C2×D79)⋊C4—21no—
126C2×(C2×D79)⋊C4—21no—
127C2×(C2×D79)⋊C4—21no—
128C2×(C2×D79)⋊C4—21no—
129C2×(C2×D79)⋊C4—21no—
130C2×C4×Dic79—21no—
131#14579094C2314yes—
132C4⋊(C79⋊C8)C2314yes—
133C4⋊(C79⋊C8)C2314yes—
134C4⋊(C79⋊C8)C2314yes—
135#14579085C2314yes—
136#14579084C2314yes—
137#14579082C2314yes—
138#14579082C2314yes—
139#14579081C2314yes—
140#14579081C2314yes—
141#14579072C2314yes—
142#14579072C2314yes—
143C4×C79⋊C8C2314yes—
144C22×Q8×C79D411yescharacteristic
145C22×Q8×C79C2311yescharacteristic
146C22×D4×C79—21no—
147C22×D4×C79—21no—
148C22×D4×C79C2311yescharacteristic
149C22×D4×C79C2311yescharacteristic
150C23×C4×C79—21no—
151C23×C4×C79—21no—
152#127×C79—22no—
153#127×C79C2314yes—
154#124×C79—28no—
155#124×C79—22no—
156#124×C79—22no—
157#124×C79C2314yes—
158#124×C79C2314yes—
159#123×C79—28no—
160#123×C79—28no—
161C4×Q8×C79—22no—
162C4×Q8×C79D414yes—
163C4×Q8×C79C2314yes—
164C4×Q8×C79C2314yes—
165C4×D4×C79—28no—
166C4×D4×C79—22no—
167C4×D4×C79—22no—
168C4×D4×C79C2314yes—
169C4×D4×C79C2314yes—
170C2×C4⋊C4×C79—21no—
171C2×C4⋊C4×C79D411yescharacteristic
172C2×C4⋊C4×C79D411yescharacteristic
173C2×C4⋊C4×C79D411yescharacteristic
174C2×C4⋊C4×C79C2311yescharacteristic
175C2×C22⋊C4×C79—21no—
176C2×C22⋊C4×C79—21no—
177C2×C22⋊C4×C79—21no—
178C2×C22⋊C4×C79—21no—
179C2×C22⋊C4×C79—21no—
180C2×C22⋊C4×C79—21no—
181C2×C42×C79—21no—
182C2×C42×C79C2311yescharacteristic
183C2×C42×C79C2311yescharacteristic
184C2×C42×C79C2311yescharacteristic
185C23×D79—21no—
186C23×D79—21no—
187C2×Dic158—21no—
188C2×Dic158—22no—
189C2×Dic158—22no—
190C2×Dic158C2412yes—
191C2×D316—24no—
192C2×D316—21no—
193C2×D316—21no—
194C2×D316—24no—
195C2×D316—22no—
196C2×D316—22no—
197C2×D316—22no—
198C2×D316—22no—
199C2×D316—44no—
200C2×D316—82no—
201C2×D316C2412yes—
202C2×D316C2412yes—
203C22×Dic79—21no—
204C22×Dic79—21no—
205C2×C4×D79—24no—
206C2×C4×D79—24no—
207C2×C4×D79—82no—
208C2×C4×D79—82no—
209#11929614—44no—
210#11929612—28no—
211#11929612—44no—
212#11929611—28no—
213#11929611—44no—
214#11929609—28no—
215#11929609—44no—
216#11929609—44no—
217#11929609—44no—
218C2×C79⋊C8—22no—
219C2×C79⋊C8—22no—
220C2×C79⋊C8—22no—
221C2×C79⋊C8#4114yes—
222C2×C79⋊C8C2412yes—
223C2×C79⋊C8C2412yes—
224C2×C79⋊C8C2412yes—
225C2×C79⋊C8C2412yes—
226C4⋊Dic79—21no—
227C4⋊Dic79C2412yes—
228Dic79⋊C4—24no—
229(C2×D79)⋊C4—24no—
230(C2×D79)⋊C4—24no—
231(C2×D79)⋊C4—24no—
232(C2×D79)⋊C4—24no—
233(C2×D79)⋊C4—24no—
234(C2×D79)⋊C4—24no—
235C4×Dic79—24no—
236C24×C79—21no—
237C24×C79—21no—
238C2×Q8×C79—21no—
239C2×Q8×C79—22no—
240C2×Q8×C79—22no—
241C2×Q8×C79—42no—
242C2×Q8×C79C2×D414yes—
243C2×Q8×C79C2412yes—
244C2×D4×C79—21no—
245C2×D4×C79—21no—
246C2×D4×C79—24no—
247C2×D4×C79—24no—
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—21no—
257C22×C4×C79—21no—
258C22×C4×C79—24no—
259C22×C4×C79—24no—
260C22×C4×C79—82no—
261C22×C4×C79—82no—
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79C2×D411yescharacteristic
265C22×C4×C79C2×D411yescharacteristic
266C22×C4×C79C2×D411yescharacteristic
267C22×C4×C79C2×D411yescharacteristic
268C22×C4×C79C2411yescharacteristic
269C4⋊C4×C79—24no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79C2×D414yes—
272C4⋊C4×C79C2×D414yes—
273C4⋊C4×C79C2×D414yes—
274C4⋊C4×C79C2412yes—
275C22⋊C4×C79—24no—
276C22⋊C4×C79—24no—
277C22⋊C4×C79—24no—
278C22⋊C4×C79—24no—
279C22⋊C4×C79—24no—
280C22⋊C4×C79—24no—
281C42×C79—24no—
282C42×C79C2×D412yes—
283C42×C79C2×D412yes—
284C42×C79C2×D412yes—
285C42×C79C2412yes—
286C42×C79C2412yes—
287C42×C79C2412yes—
288C23×C79—22no—
289C23×C79—22no—
290C23×C79—42no—
291C23×C79—42no—
292C23×C79—42no—
293C23×C79—42no—
294C23×C79—42no—
295C23×C79—42no—
296C23×C79C22×D411yescharacteristic
297C22×D79—22no—
298C22×D79—22no—
299C22×D79—42no—
300C22×D79—42no—
301C22×D79—42no—
302C22×D79—42no—
303C22×D79—42no—
304C22×D79—42no—
305Q8×C79—22no—
306Q8×C79—22no—
307Q8×C79—44no—
308Q8×C79—42no—
309D4×C79—22no—
310D4×C79—22no—
311D4×C79—22no—
312D4×C79—22no—
313D4×C79—48no—
314D4×C79—42no—
315D4×C79—42no—
316D4×C79—84no—
317C2×C4×C79—22no—
318C2×C4×C79—22no—
319C2×C4×C79—22no—
320C2×C4×C79—22no—
321C2×C4×C79—22no—
322C2×C4×C79—22no—
323C2×C4×C79—22no—
324C2×C4×C79—22no—
325C2×C4×C79—42no—
326C2×C4×C79—42no—
327C2×C4×C79—84no—
328C2×C4×C79—84no—
329C2×C4×C79C22×D412yes—
330C2×C4×C79C22×D412yes—
331C2×C4×C79C22×D412yes—
332C2×C4×C79C22×D412yes—
333C2×C4×C79C22×D412yes—
334C2×C4×C79C22×D412yes—
335C2×C4×C79C22×D411yescharacteristic
336C2×C4×C79C2×#4112yes—
337C2×C4×C79H(5,𝔽2)12yes—
338C2×C4×C79C2511yescharacteristic
339C2×Dic79—22no—
340C2×Dic79—22no—
341C2×Dic79—42no—
342C2×Dic79—42no—
343D316—22no—
344D316—22no—
345D316—22no—
346D316—22no—
347D316—48no—
348D316—42no—
349D316—42no—
350D316—84no—
351C4×D79—84no—
352C4×D79—84no—
353Dic158—22no—
354Dic158—22no—
355Dic158—42no—
356C79⋊C8—22no—
357C79⋊C8—22no—
358C79⋊C8—22no—
359C79⋊C8C2×#4114yes—
360C22×C79—42no—
361C22×C79—42no—
362C22×C79—42no—
363C22×C79—42no—
364C22×C79—42no—
365C22×C79—42no—
366C22×C79—84no—
367C22×C79—84no—
368C22×C79#55012yes—
369C22×C79#57512yes—
370C22×C79#57612yes—
371C22×C79C23×D411yescharacteristic
372C2×D79—42no—
373C2×D79—42no—
374C2×D79—42no—
375C2×D79—42no—
376C2×D79—42no—
377C2×D79—42no—
378C2×D79—84no—
379C2×D79—84no—
380C4×C79—22no—
381C4×C79—22no—
382C4×C79—22no—
383C4×C79—22no—
384C4×C79—22no—
385C4×C79—22no—
386C4×C79—42no—
387C4×C79—42no—
388C4×C79#55012yes—
389C4×C79C22×#4111yescharacteristic
390C4×C79C2×H(5,𝔽2)11yescharacteristic
391Dic79—42no—
392Dic79—42no—
393C2×#3403—791nomaximal, Sylow
394C2×C79—82no—
395C2×C79—82no—
396C2×C79#340314yescomplemented
397C2×C79C2×#55011yescharacteristic
398C2×C79C2×#57511yescharacteristic
399C2×C79C2×#57611yescharacteristic
400D79—82no—
401D79—82no—
402C2×#559—791no—
403C2×#559D7911yescharacteristic, complemented
404#3403—7916no—
405C2×#496—791no—
406C2×#496—791no—
407C2×#495—791no—
408C2×#464—791no—
409C2×#464—791no—
410C2×#463—791no—
411C2×#463—791no—
412C2×#459—791no—
413C2×#459—791no—
414C2×#446—791no—
415C2×#440—791no—
416C2×#440—791no—
417C2×C4×D8—791no—
418C79C2×#340311yescharacteristic, complemented, Sylow
419C22×Q16—791no—
420C22×SD16—791no—
421C22×SD16—791no—
422C22×SD16—791no—
423C22×SD16—791no—
424C22×D8—791no—
425C22×D8—791no—
426C22×D8—791no—
427C22×D8—791no—
428#559—24no—
429#559—798no—
430#559—1584no—
431#559C2×D7918yescomplemented
432C2×#127—791no—
433C2×#127C2×D7911yescharacteristic
434C2×#124—21no—
435C2×#124—791no—
436C2×#124—791no—
437C2×#124—1581no—
438C2×#124C2×D7911yescharacteristic
439C2×#124C2×D7911yescharacteristic
440C2×#123—21no—
441C2×#123—21no—
442C2×#123—1581no—
443C2×#123—1581no—
444C2×C4×Q8—791no—
445C2×C4×Q8C2×D7911yescharacteristic
446C2×C4×Q8C2×D7911yescharacteristic
447C2×C4×D4—21no—
448C2×C4×D4—791no—
449C2×C4×D4—791no—
450C2×C4×D4—1581no—
451C2×C4×D4C2×D7911yescharacteristic
452C2×C4×D4C2×D7911yescharacteristic
453#496—798no—
454#496—798no—
455#495—798no—
456#464—798no—
457#464—798no—
458#463—798no—
459#463—798no—
460#459—798no—
461#459—798no—
462#446—798no—
463#440—798no—
464#440—798no—
465C4×D8—798no—
466C2×#107—791no—
467C2×C4⋊C8—791no—
468C2×C4⋊C8—791no—
469C2×C4⋊C8—791no—
470C2×#103—791no—
471C2×#103—791no—
472C2×#102—791no—
473C2×#102—791no—
474C2×#102—791no—
475C2×#102—791no—
476C2×#97—791no—
477C2×#97—791no—
478C2×C4×C8—791no—
479C22×Q8—791no—
480C22×Q8C22⋊D7911yescharacteristic
481C22×Q8C22×D7911yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—791no—
485C22×D4—791no—
486C22×D4—1581no—
487C22×D4—1581no—
488C22×D4C22×D7911yescharacteristic
489C22×D4C22×D7911yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—1581no—
493C23×C4—1581no—
494C2×Q16—3162no—
495C2×Q16—794no—
496C2×SD16—3162no—
497C2×SD16—3162no—
498C2×SD16—794no—
499C2×SD16—794no—
500C2×SD16—794no—
501C2×SD16—794no—
502C2×SD16—1584no—
503C2×SD16—1584no—
504C2×D8—3162no—
505C2×D8—3162no—
506C2×D8—3162no—
507C2×D8—794no—
508C2×D8—794no—
509C2×D8—794no—
510C2×D8—794no—
511C2×D8—1584no—
512C22×C8—791no—
513C22×C8—791no—
514C22×C8—791no—
515C22×C8—791no—
516#127—22no—
517#127—794no—
518#127—1582no—
519#127C22×D7914yes—
520#124—28no—
521#124—22no—
522#124—22no—
523#124—794no—
524#124—794no—
525#124—1588no—
526#124—1582no—
527#124—1582no—
528#124C22×D7914yes—
529#124C22×D7914yes—
530#123—28no—
531#123—28no—
532#123—1588no—
533#123—1588no—
534C4×Q8—22no—
535C4×Q8—794no—
536C4×Q8—1582no—
537C4×Q8C22⋊D7914yes—
538C4×Q8C22×D7914yes—
539C4×Q8C22×D7914yes—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—794no—
544C4×D4—794no—
545C4×D4—1588no—
546C4×D4—1582no—
547C4×D4—1582no—
548C4×D4C22×D7914yes—
549C4×D4C22×D7914yes—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—791no—
552C2×C4⋊C4—1581no—
553C2×C4⋊C4C22⋊D7911yescharacteristic
554C2×C4⋊C4C22⋊D7911yescharacteristic
555C2×C4⋊C4C22⋊D7911yescharacteristic
556C2×C4⋊C4C22×D7911yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1581no—
564C2×C22⋊C4—1581no—
565C2×C22⋊C4—1581no—
566C2×C22⋊C4—1581no—
567C2×C22⋊C4—1581no—
568C2×C22⋊C4—1581no—
569C2×C42—21no—
570C2×C42—1581no—
571C2×C42C22×D7911yescharacteristic
572C2×C42C22×D7911yescharacteristic
573C2×C42C22×D7911yescharacteristic
574#107—794no—
575C4⋊C8—794no—
576C4⋊C8—794no—
577C4⋊C8—794no—
578#103—794no—
579#103—794no—
580#102—794no—
581#102—794no—
582#102—794no—
583#102—794no—
584#97—794no—
585#97—794no—
586C4×C8—794no—
587C24—21no—
588C24—21no—
589C24—1581no—
590C24—1581no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—42no—
595C2×Q8—792no—
596C2×Q8—1582no—
597C2×Q8—1582no—
598C2×Q8—1581no—
599C2×Q8C2×C22⋊D7914yes—
600C2×Q8C23×D7912yes—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—44no—
610C2×D4—82no—
611C2×D4—3164no—
612C2×D4—792no—
613C2×D4—792no—
614C2×D4—6322no—
615C2×D4—1582no—
616C2×D4—1582no—
617C2×D4—1582no—
618C2×D4—1582no—
619C2×D4—1584no—
620C2×D4—1581no—
621C2×D4—1581no—
622C2×D4—1584no—
623C2×D4C23×D7912yes—
624C2×D4C23×D7912yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—82no—
630C22×C4—82no—
631C22×C4—6322no—
632C22×C4—6322no—
633C22×C4—1581no—
634C22×C4—1581no—
635C22×C4—1584no—
636C22×C4—1584no—
637C22×C4C2×C22⋊D7911yescharacteristic
638C22×C4C2×C22⋊D7911yescharacteristic
639C22×C4C2×C22⋊D7911yescharacteristic
640C22×C4C2×C22⋊D7911yescharacteristic
641C22×C4C2×C22⋊D7911yescharacteristic
642C22×C4C2×C22⋊D7911yescharacteristic
643C22×C4C23×D7911yescharacteristic
644Q16—3164no—
645SD16—3164no—
646SD16—3164no—
647SD16—1588no—
648SD16—1588no—
649D8—3164no—
650D8—3164no—
651D8—3164no—
652D8—1588no—
653C2×C8—794no—
654C2×C8—792no—
655C2×C8—792no—
656C2×C8—792no—
657C2×C8—792no—
658C2×C8—1582no—
659C2×C8—1582no—
660C2×C8—1582no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—792no—
664C4⋊C4—1584no—
665C4⋊C4—1581no—
666C4⋊C4C2×C22⋊D7914yes—
667C4⋊C4C2×C22⋊D7914yes—
668C4⋊C4C2×C22⋊D7914yes—
669C4⋊C4C23×D7912yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—1584no—
677C22⋊C4—1584no—
678C22⋊C4—1584no—
679C22⋊C4—1584no—
680C22⋊C4—1584no—
681C22⋊C4—1584no—
682C42—24no—
683C42—1584no—
684C42C2×C22⋊D7912yes—
685C42C2×C22⋊D7912yes—
686C42C2×C22⋊D7912yes—
687C42C23×D7912yes—
688C42C23×D7912yes—
689C42C23×D7912yes—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—3162no—
699C23—3162no—
700C23—3162no—
701C23—3162no—
702C23—3162no—
703C23—3162no—
704C23—1582no—
705C23—1582no—
706C23C22×C22⋊D7911yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—44no—
710Q8—42no—
711Q8—3162no—
712Q8—1582no—
713Q8—1582no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—48no—
719D4—42no—
720D4—42no—
721D4—84no—
722D4—3168no—
723D4—3162no—
724D4—3162no—
725D4—6324no—
726D4—1582no—
727D4—1582no—
728D4—1582no—
729D4—1582no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—84no—
741C2×C4—84no—
742C2×C4—3162no—
743C2×C4—3162no—
744C2×C4—6324no—
745C2×C4—6324no—
746C2×C4—1582no—
747C2×C4—1582no—
748C2×C4C22×C22⋊D7912yes—
749C2×C4C22×C22⋊D7912yes—
750C2×C4C22×C22⋊D7912yes—
751C2×C4C22×C22⋊D7912yes—
752C2×C4C22×C22⋊D7912yes—
753C2×C4C22×C22⋊D7912yes—
754C2×C4C22×C22⋊D7911yescharacteristic
755C2×C4#41×D7912yes—
756C2×C4#1457920712yes—
757C2×C4C24×D7911yescharacteristic
758C8—794no—
759C8—1582no—
760C8—1582no—
761C8—1582no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—3162no—
771C22—3162no—
772C22—3162no—
773C22—3162no—
774C22—3162no—
775C22—3162no—
776C22—6324no—
777C22—6324no—
778C22#1909923212yes—
779C22#1909936112yes—
780C22#1909936612yes—
781C22C23×C22⋊D7911yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—3162no—
791C4—3162no—
792C4#1909923212yes—
793C4C2×#41×D7911yescharacteristic
794C4C2×#1457920711yescharacteristic
795C2—82no—
796C2—82no—
797C2—6322no—
798C2—6322no—
799C2#2377648414yesdirect product factor
800C2C2×#1909923211yescharacteristic
801C2C2×#1909936111yescharacteristic
802C2C2×#1909936611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#559×C79C2
socleC23×C79C22×D4
hypercenterC2×#559D79
hypocenterC79C2×#3403
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×#19099298C2semidirect
2. #23776484C2direct (N × H)
3. C2×#19098953C2semidirect
4. C2×#19098950C2semidirect
5. C2×#19098945C2semidirect
6. C2×#19098785C2semidirect
7. C2×#19098782C2semidirect
8. C2×#19098778C2semidirect
9. C2×#19098775C2semidirect
10. C2×#19098758C2semidirect
11. C2×#19098755C2semidirect
12. C2×#19098694C2semidirect
13. C2×#19098663C2semidirect
14. C2×#19098661C2semidirect
15. C2×C4×#11929609C2semidirect
16. C2×#559×C79C2semidirect
27. #19099298C22semidirect
38. #19098953C22semidirect
39. #19098950C22semidirect
40. #19098945C22semidirect
41. #19098785C22semidirect
42. #19098782C22semidirect
43. #19098778C22semidirect
44. #19098775C22semidirect
45. #19098758C22semidirect
46. #19098755C22semidirect
47. #19098694C22semidirect
48. #19098663C22semidirect
49. #19098661C22semidirect
50. C4×#11929609C22semidirect
65. #559×C79C22semidirect
396. C2×C79#3403semidirect
403. C2×#559D79semidirect
418. C79C2×#3403semidirect
431. #559C2×D79semidirect
799. C2#23776484direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190992982
#237764842
C2×#190989532
C2×#190989502
C2×#190989452
C2×#190987852
C2×#190987822
C2×#190987782
C2×#190987752
C2×#190987582
C2×#190987552
C2×#190986942
C2×#190986632
C2×#190986612
C2×C4×#119296092
C2×#559×C792
C2×#340379