Finite Group Databasebeta

← C2×#23774239 #35158897

Subgroups — C2×#23774239 #35158897

Order 20224.

2362 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099073C211yesmaximal, characteristic, complemented
2C2×#19099070C211yesmaximal, characteristic, complemented
3#23774239C2116yesmaximal, direct product factor
4C2×#19098905C211yesmaximal, characteristic, complemented
5C2×#19098902C211yesmaximal, characteristic, complemented
6C2×#19098885C211yesmaximal, characteristic, complemented
7C2×#19098884C211yesmaximal, characteristic, complemented
8C2×#19098820C211yesmaximal, characteristic, complemented
9C2×#19098813C211yesmaximal, characteristic, complemented
10C2×#19098808C211yesmaximal, characteristic, complemented
11C2×#19098806C211yesmaximal, characteristic, complemented
12C2×#19098725C211yesmaximal, characteristic, complemented
13C2×#19098722C211yesmaximal, characteristic, complemented
14C2×#19098705C211yesmaximal, characteristic, complemented
15C2×#19098525C211yesmaximal, characteristic, complemented
16C2×#449×C79C211yesmaximal, characteristic, complemented
17C22×#11929623C2211yescharacteristic
18C23×C4×D79C2211yescharacteristic
19C22×#11929614C2211yescharacteristic, complemented
20C22×#11929612C2211yescharacteristic, complemented
21C22×#11929607C2211yescharacteristic
22C22×#11929607C2211yescharacteristic
23#19099073—24no—
24#19099073C2218yescomplemented
25#19099070—24no—
26#19099070C2218yescomplemented
27C2×#14579143—21no—
28C2×#14579142—21no—
29C2×#14579141C2211yescharacteristic
30C2×#14579140C2211yescharacteristic
31C2×#14579137C2211yescharacteristic
32C2×#14579137C2211yescharacteristic
33C2×#14579132C2211yescharacteristic
34C2×#14579132C2211yescharacteristic
35C2×#14579132C2211yescharacteristic
36C2×#14579129—21no—
37C2×#14579129—21no—
38C2×D4×Dic79—21no—
39C2×C4×C22⋊D79—21no—
40C2×C4×C22⋊D79—21no—
41C2×(C22⋊D79)⋊C4—21no—
42C2×#14579120C2211yescharacteristic
43C2×#14579119C2211yescharacteristic
44#19098905C2218yescomplemented
45#19098902C2218yescomplemented
46#19098885C2218yescomplemented
47#19098884C2218yescomplemented
48#19098820C2218yescomplemented
49#19098813C2218yescomplemented
50#19098808C2218yescomplemented
51#19098806C2218yescomplemented
52#19098725C2218yescomplemented
53#19098722C2218yescomplemented
54#19098705C2218yescomplemented
55C2×#14579095C2211yescharacteristic, complemented
56C2×#14579094C2211yescharacteristic, complemented
57C2×#14579093C2211yescharacteristic, complemented
58C2×#14579092C2211yescharacteristic, complemented
59C2×#14579086C2211yescharacteristic, complemented
60C2×#14579086C2211yescharacteristic, complemented
61C2×#14579085C2211yescharacteristic, complemented
62C2×#14579082C2211yescharacteristic, complemented
63C2×#14579082C2211yescharacteristic, complemented
64C2×#14579082C2211yescharacteristic, complemented
65#19098525C2218yescomplemented
66C2×C22⋊(C79⋊C8)C2211yescharacteristic
67C2×(C2×D79)⋊C8C2211yescharacteristic
68C2×(C2×D79)⋊C8C2211yescharacteristic
69C22×#41×C79C2211yescharacteristic
70C22×SD16×C79C2211yescharacteristic, complemented
71C22×D8×C79C2211yescharacteristic, complemented
72C2×#121×C79C2211yescharacteristic
73#449×C79C2218yescomplemented
74C2×#103×C79C2211yescharacteristic, complemented
75C2×#102×C79C2211yescharacteristic, complemented
76C2×C22⋊C8×C79C2211yescharacteristic
77C24×D79D411yescharacteristic
78C2×#11929623—22no—
79C2×#11929623—42no—
80C2×#11929623—42no—
81C2×#11929623C2314yes—
82C22×Dic158C2311yescharacteristic
83C22×C22⋊D79—21no—
84C22×C22⋊D79—21no—
85C22×C22⋊D79—21no—
86C22×C22⋊D79—21no—
87C23×Dic79—21no—
88C23×Dic79D411yescharacteristic
89C22×C4×D79—42no—
90C22×C4×D79—42no—
91C22×C4×D79D411yescharacteristic
92C22×C4×D79D411yescharacteristic
93C22×C4×D79D414yes—
94C22×C4×D79C2311yescharacteristic
95C22×C4×D79C2311yescharacteristic
96C22×C4×D79C2314yes—
97C2×#11929614—42no—
98C2×#11929614C2314yescomplemented
99C2×#11929612—42no—
100C2×#11929612C2314yescomplemented
101C2×#11929607—42no—
102C2×#11929607—42no—
103C2×#11929607C2314yes—
104C2×#11929607C2314yes—
105C22×C79⋊C8C2311yescharacteristic
106C22×C79⋊C8C2311yescharacteristic
107#14579143—28no—
108#14579142—28no—
109#14579141—22no—
110#14579141C2314yes—
111#14579140—22no—
112#14579140C2314yes—
113#14579137—22no—
114#14579137—22no—
115#14579137C2314yes—
116#14579137C2314yes—
117#14579132—22no—
118#14579132—22no—
119#14579132—22no—
120#14579132C2314yes—
121#14579132C2314yes—
122#14579132C2314yes—
123#14579129—28no—
124#14579129—28no—
125D4×Dic79—28no—
126C4×C22⋊D79—28no—
127C4×C22⋊D79—28no—
128(C22⋊D79)⋊C4—28no—
129#14579120—22no—
130#14579120C2314yes—
131#14579119—22no—
132#14579119C2314yes—
133C2×C4⋊Dic79—21no—
134C2×C4⋊Dic79C2311yescharacteristic
135C2×C4⋊Dic79C2311yescharacteristic
136C2×C4⋊Dic79C2311yescharacteristic
137C2×Dic79⋊C4—21no—
138C2×Dic79⋊C4—21no—
139C2×Dic79⋊C4—21no—
140C2×C22⋊Dic79—21no—
141C2×C22⋊Dic79—21no—
142C2×C22⋊Dic79—21no—
143C2×C22⋊Dic79—21no—
144C2×C22⋊Dic79—21no—
145C2×(C2×D79)⋊C4—21no—
146C2×(C2×D79)⋊C4—21no—
147C2×(C2×D79)⋊C4—21no—
148C2×(C2×D79)⋊C4—21no—
149C2×C4×Dic79—21no—
150C2×C4×Dic79—21no—
151#14579095C2314yescomplemented
152#14579094C2314yescomplemented
153#14579093C2314yescomplemented
154#14579092C2314yescomplemented
155#14579086C2314yescomplemented
156#14579086C2314yescomplemented
157#14579085C2314yescomplemented
158#14579082C2314yescomplemented
159#14579082C2314yescomplemented
160#14579082C2314yescomplemented
161C22⋊(C79⋊C8)C2314yes—
162(C2×D79)⋊C8C2314yes—
163(C2×D79)⋊C8C2314yes—
164C2×#41×C79—22no—
165C2×#41×C79—42no—
166C2×#41×C79—42no—
167C2×#41×C79C2314yes—
168C22×Q8×C79C2311yescharacteristic
169C22×D4×C79—21no—
170C22×D4×C79—21no—
171C22×D4×C79C2311yescharacteristic
172C22×D4×C79C2311yescharacteristic
173C23×C4×C79—21no—
174C23×C4×C79C2311yescharacteristic
175C2×SD16×C79—42no—
176C2×SD16×C79C2314yescomplemented
177C2×D8×C79—42no—
178C2×D8×C79C2314yescomplemented
179C22×C8×C79C2311yescharacteristic
180C22×C8×C79C2311yescharacteristic
181#121×C79—22no—
182#121×C79C2314yes—
183C2×C4⋊C4×C79C2311yescharacteristic
184C2×C22⋊C4×C79—21no—
185#103×C79C2314yescomplemented
186#102×C79C2314yescomplemented
187C22⋊C8×C79C2314yes—
188C23×D79—42no—
189C23×D79—42no—
190C23×D79—42no—
191C23×D79C2×D411yescharacteristic
192C23×D79C2×D411yescharacteristic
193C23×D79C2×D414yes—
194#11929623—44no—
195#11929623—44no—
196#11929623—48no—
197C2×Dic158—21no—
198C2×Dic158—22no—
199C2×Dic158—22no—
200C2×Dic158C2412yes—
201C2×C22⋊D79—24no—
202C2×C22⋊D79—24no—
203C2×C22⋊D79—24no—
204C2×C22⋊D79—24no—
205C2×C22⋊D79—44no—
206C2×C22⋊D79—44no—
207C2×C22⋊D79—44no—
208C2×C22⋊D79—44no—
209C22×Dic79—24no—
210C22×Dic79—21no—
211C22×Dic79—21no—
212C22×Dic79—21no—
213C22×Dic79—21no—
214C22×Dic79—42no—
215C22×Dic79—44no—
216C22×Dic79C2×D411yescharacteristic
217C22×Dic79C2×D411yescharacteristic
218C22×Dic79C2×D414yes—
219C2×C4×D79—22no—
220C2×C4×D79—22no—
221C2×C4×D79—22no—
222C2×C4×D79—22no—
223C2×C4×D79—42no—
224C2×C4×D79—42no—
225C2×C4×D79—48no—
226C2×C4×D79—44no—
227C2×C4×D79—44no—
228C2×C4×D79C2×D412yes—
229C2×C4×D79C2×D412yes—
230C2×C4×D79C2×D414yes—
231C2×C4×D79C2×D414yes—
232C2×C4×D79C2412yes—
233C2×C4×D79C2412yes—
234#11929614—44no—
235#11929612—44no—
236#11929607—44no—
237#11929607—44no—
238C2×C79⋊C8—22no—
239C2×C79⋊C8—22no—
240C2×C79⋊C8C2412yes—
241C2×C79⋊C8C2412yes—
242C4⋊Dic79—24no—
243C4⋊Dic79—21no—
244C4⋊Dic79—21no—
245C4⋊Dic79—21no—
246C4⋊Dic79C2412yes—
247C4⋊Dic79C2412yes—
248C4⋊Dic79C2412yes—
249Dic79⋊C4—24no—
250Dic79⋊C4—24no—
251Dic79⋊C4—24no—
252C22⋊Dic79—24no—
253C22⋊Dic79—24no—
254C22⋊Dic79—24no—
255C22⋊Dic79—24no—
256C22⋊Dic79—24no—
257(C2×D79)⋊C4—24no—
258(C2×D79)⋊C4—24no—
259(C2×D79)⋊C4—24no—
260(C2×D79)⋊C4—24no—
261C4×Dic79—24no—
262C4×Dic79—24no—
263C24×C79—21no—
264C24×C79—21no—
265C24×C79C2×D411yescharacteristic
266#41×C79—44no—
267#41×C79—44no—
268#41×C79—48no—
269C2×Q8×C79—21no—
270C2×Q8×C79—22no—
271C2×Q8×C79—22no—
272C2×Q8×C79C2412yes—
273C2×D4×C79—24no—
274C2×D4×C79—24no—
275C2×D4×C79—21no—
276C2×D4×C79—21no—
277C2×D4×C79—22no—
278C2×D4×C79—22no—
279C2×D4×C79—22no—
280C2×D4×C79—22no—
281C2×D4×C79—44no—
282C2×D4×C79—44no—
283C2×D4×C79C2412yes—
284C2×D4×C79C2412yes—
285C22×C4×C79—22no—
286C22×C4×C79—22no—
287C22×C4×C79—21no—
288C22×C4×C79—21no—
289C22×C4×C79—24no—
290C22×C4×C79—44no—
291C22×C4×C79C2×D411yescharacteristic
292C22×C4×C79C2×D412yes—
293C22×C4×C79C2412yes—
294C22×C4×C79C2411yescharacteristic
295SD16×C79—44no—
296D8×C79—44no—
297C2×C8×C79—22no—
298C2×C8×C79—22no—
299C2×C8×C79C2412yes—
300C2×C8×C79C2412yes—
301C4⋊C4×C79—21no—
302C4⋊C4×C79C2412yes—
303C22⋊C4×C79—24no—
304C23×C79—22no—
305C23×C79—22no—
306C23×C79—22no—
307C23×C79—22no—
308C23×C79—22no—
309C23×C79—42no—
310C23×C79—42no—
311C23×C79—42no—
312C23×C79—42no—
313C23×C79—42no—
314C23×C79—42no—
315C23×C79C22×D412yes—
316C23×C79C22×D411yescharacteristic
317C22×D79—22no—
318C22×D79—22no—
319C22×D79—22no—
320C22×D79—22no—
321C22×D79—22no—
322C22×D79—22no—
323C22×D79—44no—
324C22×D79—44no—
325C22×D79—44no—
326C22×D79—416no—
327C22×D79C22×D412yes—
328C22×D79C22×D412yes—
329Q8×C79—22no—
330Q8×C79—22no—
331Q8×C79—42no—
332D4×C79—22no—
333D4×C79—22no—
334D4×C79—22no—
335D4×C79—22no—
336D4×C79—48no—
337D4×C79—48no—
338D4×C79—42no—
339D4×C79—42no—
340C2×C4×C79—22no—
341C2×C4×C79—24no—
342C2×C4×C79—22no—
343C2×C4×C79—22no—
344C2×C4×C79—22no—
345C2×C4×C79—22no—
346C2×C4×C79—48no—
347C2×C4×C79—42no—
348C2×C4×C79—42no—
349C2×C4×C79C22×D412yes—
350C2×C4×C79C22×D411yescharacteristic
351C2×C4×C79H(5,𝔽2)12yes—
352C2×C4×C79H(5,𝔽2)12yes—
353C2×C4×C79C2511yescharacteristic
354C22⋊D79—48no—
355C22⋊D79—48no—
356C22⋊D79—48no—
357C22⋊D79—48no—
358C2×Dic79—22no—
359C2×Dic79—22no—
360C2×Dic79—22no—
361C2×Dic79—22no—
362C2×Dic79—22no—
363C2×Dic79—22no—
364C2×Dic79—44no—
365C2×Dic79—48no—
366C2×Dic79—42no—
367C2×Dic79—42no—
368C2×Dic79—42no—
369C2×Dic79—42no—
370C2×Dic79C22×D412yes—
371C2×Dic79C22×D412yes—
372C4×D79—24no—
373C4×D79—24no—
374C4×D79—22no—
375C4×D79—22no—
376C4×D79—22no—
377C4×D79—22no—
378C4×D79—44no—
379C4×D79—44no—
380Dic158—22no—
381Dic158—22no—
382Dic158—42no—
383C8×C79—22no—
384C8×C79—22no—
385C79⋊C8—22no—
386C79⋊C8—22no—
387C22×C79—22no—
388C22×C79—22no—
389C22×C79—22no—
390C22×C79—44no—
391C22×C79—42no—
392C22×C79—42no—
393C22×C79—42no—
394C22×C79—42no—
395C22×C79—42no—
396C22×C79—42no—
397C22×C79—84no—
398C22×C79—84no—
399C22×C79#53412yes—
400C22×C79#57512yes—
401C22×C79#57512yes—
402C22×C79C23×D411yescharacteristic
403C2×D79—22no—
404C2×D79—22no—
405C2×D79—22no—
406C2×D79—22no—
407C2×D79—22no—
408C2×D79—22no—
409C2×D79—416no—
410C2×D79—44no—
411C2×D79—44no—
412C4×C79—22no—
413C4×C79—42no—
414C4×C79—42no—
415C4×C79#53412yes—
416C4×C79C2×H(5,𝔽2)11yescharacteristic
417C4×C79C2×H(5,𝔽2)11yescharacteristic
418Dic79—22no—
419Dic79—22no—
420Dic79—42no—
421Dic79—42no—
422Dic79—42no—
423Dic79—42no—
424C2×#3197—791nomaximal, Sylow
425C2×C79—42no—
426C2×C79—82no—
427C2×C79—82no—
428C2×C79#319714yescomplemented
429C2×C79C2×#53411yescharacteristic
430C2×C79C2×#57511yescharacteristic
431C2×C79C2×#57511yescharacteristic
432D79—42no—
433D79—42no—
434C2×#525—791no—
435C2×#525—791no—
436#3197—7916no—
437C2×#485—791no—
438C2×#485—791no—
439C2×#482—791no—
440C2×#482—791no—
441C2×#470—791no—
442C2×#469—791no—
443C2×#468—791no—
444C2×#468—791no—
445C2×#452—791no—
446C2×#452—791no—
447C2×#449—791no—
448C2×#449D7911yescharacteristic, complemented
449C2×#407—791no—
450C79C2×#319711yescharacteristic, complemented, Sylow
451C22×#41—791no—
452C22×#41C2×D7911yescharacteristic
453C24×C4—791no—
454C22×Q16—791no—
455C22×SD16—791no—
456C22×SD16C2×D7911yescharacteristic, complemented
457C22×D8C2×D7911yescharacteristic, complemented
458C22×M16—791no—
459C22×M16—791no—
460#525—798no—
461#525—798no—
462#525—1584no—
463#525—1584no—
464C2×#123—1581no—
465C2×#123—1581no—
466C2×C22⋊Q8—791no—
467C2×C22⋊Q8—791no—
468C2×C22⋊Q8—791no—
469C2×C22⋊Q8—791no—
470C2×#121—791no—
471C2×#121—791no—
472C2×#121—791no—
473C2×#121C2×D7911yescharacteristic
474C2×#120—1581no—
475C2×#120—1581no—
476C2×C4×D4—1581no—
477C2×C4×D4—1581no—
478C2×C4×D4—1581no—
479C2×C4×D4—1581no—
480C2×#117—791no—
481C2×#117—791no—
482#485—798no—
483#485—798no—
484#482—798no—
485#482—798no—
486#470—798no—
487#469—798no—
488#468—798no—
489#468—798no—
490#452—798no—
491#452—798no—
492#449—798no—
493#449C2×D7918yescomplemented
494C2×#107—791no—
495C2×#107—791no—
496C2×#106—791no—
497C2×#106—791no—
498C2×#103—791no—
499C2×#103—791no—
500C2×#103—791no—
501C2×#103C2×D7911yescharacteristic, complemented
502C2×#102—791no—
503C2×#102—791no—
504C2×#102—791no—
505C2×#102C2×D7911yescharacteristic, complemented
506#407—798no—
507C2×C22⋊C8—791no—
508C2×C22⋊C8—791no—
509C2×C22⋊C8—791no—
510C2×C22⋊C8C2×D7911yescharacteristic
511C25—791no—
512C2×#41—22no—
513C2×#41—42no—
514C2×#41—42no—
515C2×#41—3162no—
516C2×#41—3162no—
517C2×#41—794no—
518C2×#41—1582no—
519C2×#41C22×D7914yes—
520C22×Q8—791no—
521C22×Q8C22×D7911yescharacteristic
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—1581no—
525C22×D4—1581no—
526C22×D4—1581no—
527C22×D4—1581no—
528C22×D4C22×D7911yescharacteristic
529C22×D4C22×D7911yescharacteristic
530C23×C4—21no—
531C23×C4—3162no—
532C23×C4—3162no—
533C23×C4—791no—
534C23×C4—791no—
535C23×C4—791no—
536C23×C4—794no—
537C23×C4—794no—
538C23×C4—791no—
539C23×C4—791no—
540C23×C4—1581no—
541C23×C4C22×D7911yescharacteristic
542C2×Q16—3162no—
543C2×Q16—794no—
544C2×SD16—42no—
545C2×SD16—3162no—
546C2×SD16—794no—
547C2×SD16C22×D7914yescomplemented
548C2×D8—42no—
549C2×D8C22×D7914yescomplemented
550C2×M16—3162no—
551C2×M16—3162no—
552C2×M16—794no—
553C2×M16—794no—
554C22×C8—791no—
555C22×C8—791no—
556C22×C8C22×D7911yescharacteristic
557C22×C8C22×D7911yescharacteristic
558#123—1588no—
559#123—1588no—
560C22⋊Q8—794no—
561C22⋊Q8—794no—
562C22⋊Q8—794no—
563C22⋊Q8—794no—
564C22⋊Q8—1582no—
565C22⋊Q8—1582no—
566C22⋊Q8—1582no—
567C22⋊Q8—1582no—
568#121—22no—
569#121—794no—
570#121—794no—
571#121—794no—
572#121—1582no—
573#121—1582no—
574#121—1582no—
575#121C22×D7914yes—
576#120—1588no—
577#120—1588no—
578C4×D4—1588no—
579C4×D4—1588no—
580C4×D4—1588no—
581C4×D4—1588no—
582#117—794no—
583#117—794no—
584#117—1582no—
585#117—1582no—
586C2×C4⋊C4—791no—
587C2×C4⋊C4—791no—
588C2×C4⋊C4—791no—
589C2×C4⋊C4—1581no—
590C2×C4⋊C4—1581no—
591C2×C4⋊C4—1581no—
592C2×C4⋊C4—1581no—
593C2×C4⋊C4C22×D7911yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—1581no—
596C2×C22⋊C4—1581no—
597C2×C22⋊C4—1581no—
598C2×C22⋊C4—1581no—
599C2×C22⋊C4—1581no—
600C2×C22⋊C4—1581no—
601C2×C22⋊C4—1581no—
602C2×C22⋊C4—1581no—
603C2×C22⋊C4—1581no—
604C2×C42—1581no—
605C2×C42—1581no—
606#107—794no—
607#107—794no—
608#106—794no—
609#106—794no—
610#103—794no—
611#103—794no—
612#103—794no—
613#103C22×D7914yescomplemented
614#102—794no—
615#102—794no—
616#102—794no—
617#102C22×D7914yescomplemented
618C22⋊C8—794no—
619C22⋊C8—794no—
620C22⋊C8—794no—
621C22⋊C8C22×D7914yes—
622C24—21no—
623C24—21no—
624C24—3162no—
625C24—3162no—
626C24—3162no—
627C24—794no—
628C24—791no—
629C24—791no—
630C24D4×D7911yescharacteristic
631#41—44no—
632#41—44no—
633#41—48no—
634#41—3164no—
635#41—3164no—
636#41—3168no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—792no—
641C2×Q8—1582no—
642C2×Q8—1582no—
643C2×Q8—1581no—
644C2×Q8C23×D7912yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—22no—
648C2×D4—22no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—44no—
654C2×D4—44no—
655C2×D4—3164no—
656C2×D4—3164no—
657C2×D4—3164no—
658C2×D4—3164no—
659C2×D4—1584no—
660C2×D4—1584no—
661C2×D4—1584no—
662C2×D4—1584no—
663C2×D4C23×D7912yes—
664C2×D4C23×D7912yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—44no—
671C22×C4—3162no—
672C22×C4—3162no—
673C22×C4—3164no—
674C22×C4—3164no—
675C22×C4—3168no—
676C22×C4—3164no—
677C22×C4—3162no—
678C22×C4—794no—
679C22×C4—794no—
680C22×C4—794no—
681C22×C4—791no—
682C22×C4—791no—
683C22×C4—792no—
684C22×C4—792no—
685C22×C4—792no—
686C22×C4—792no—
687C22×C4—1584no—
688C22×C4—1581no—
689C22×C4—1581no—
690C22×C4—1581no—
691C22×C4—1581no—
692C22×C4—1582no—
693C22×C4—1582no—
694C22×C4—1582no—
695C22×C4—1582no—
696C22×C4D4×D7912yes—
697C22×C4D4×D7911yescharacteristic
698C22×C4C23×D7912yes—
699C22×C4C23×D7911yescharacteristic
700Q16—3164no—
701SD16—44no—
702SD16—3164no—
703D8—44no—
704M16—3164no—
705M16—3164no—
706C2×C8—22no—
707C2×C8—22no—
708C2×C8—792no—
709C2×C8—792no—
710C2×C8—1582no—
711C2×C8—1582no—
712C2×C8C23×D7912yes—
713C2×C8C23×D7912yes—
714C4⋊C4—21no—
715C4⋊C4—792no—
716C4⋊C4—792no—
717C4⋊C4—792no—
718C4⋊C4—1584no—
719C4⋊C4—1584no—
720C4⋊C4—1584no—
721C4⋊C4—1584no—
722C4⋊C4—1581no—
723C4⋊C4—1581no—
724C4⋊C4—1581no—
725C4⋊C4C23×D7912yes—
726C22⋊C4—24no—
727C22⋊C4—1584no—
728C22⋊C4—1584no—
729C22⋊C4—1584no—
730C22⋊C4—1584no—
731C22⋊C4—1584no—
732C22⋊C4—1584no—
733C22⋊C4—1584no—
734C22⋊C4—1584no—
735C22⋊C4—1584no—
736C42—1584no—
737C42—1584no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—3164no—
750C23—3164no—
751C23—3164no—
752C23—31616no—
753C23—792no—
754C23—792no—
755C23—1582no—
756C23—1582no—
757C23—1582no—
758C23—1582no—
759C23—1582no—
760C23—1582no—
761C23C2×D4×D7912yes—
762C23C2×D4×D7911yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—42no—
766Q8—3162no—
767Q8—1582no—
768Q8—1582no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—3168no—
778D4—3168no—
779D4—3168no—
780D4—3168no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—48no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—3164no—
791C2×C4—3164no—
792C2×C4—3162no—
793C2×C4—3162no—
794C2×C4—3162no—
795C2×C4—3162no—
796C2×C4—3168no—
797C2×C4—3164no—
798C2×C4—792no—
799C2×C4—792no—
800C2×C4—1582no—
801C2×C4—1582no—
802C2×C4—1582no—
803C2×C4—1582no—
804C2×C4—1582no—
805C2×C4—1582no—
806C2×C4—1582no—
807C2×C4—1582no—
808C2×C4—1582no—
809C2×C4—1582no—
810C2×C4—1584no—
811C2×C4—1584no—
812C2×C4C2×D4×D7912yes—
813C2×C4C2×D4×D7911yescharacteristic
814C2×C4#1457920612yes—
815C2×C4#1457920612yes—
816C2×C4C24×D7911yescharacteristic
817C8—22no—
818C8—22no—
819C8—1582no—
820C8—1582no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—84no—
832C22—84no—
833C22—31616no—
834C22—3164no—
835C22—3164no—
836C22—1582no—
837C22—1582no—
838C22—1582no—
839C22—1582no—
840C22—1582no—
841C22—1582no—
842C22#1909912312yes—
843C22#1909935912yes—
844C22#1909936012yes—
845C22C22×D4×D7911yescharacteristic
846C4—22no—
847C4—42no—
848C4—42no—
849C4—3162no—
850C4—3162no—
851C4—3162no—
852C4—3162no—
853C4—1582no—
854C4—1582no—
855C4#1909912312yes—
856C4C2×#1457920611yescharacteristic
857C4C2×#1457920611yescharacteristic
858C2—42no—
859C2—82no—
860C2—82no—
861C2—3162no—
862C2—3162no—
863C2#2377423914yesdirect product factor
864C2C2×#1909912311yescharacteristic
865C2C2×#1909935911yescharacteristic
866C2C2×#1909936011yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#449×C79C2
socleC23×C79C22×D4
hypercenterC2×#449D79
hypocenterC79C2×#3197
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#19099073C2semidirect
2. C2×#19099070C2semidirect
3. #23774239C2direct (N × H)
4. C2×#19098905C2semidirect
5. C2×#19098902C2semidirect
6. C2×#19098885C2semidirect
7. C2×#19098884C2semidirect
8. C2×#19098820C2semidirect
9. C2×#19098813C2semidirect
10. C2×#19098808C2semidirect
11. C2×#19098806C2semidirect
12. C2×#19098725C2semidirect
13. C2×#19098722C2semidirect
14. C2×#19098705C2semidirect
15. C2×#19098525C2semidirect
16. C2×#449×C79C2semidirect
19. C22×#11929614C22semidirect
20. C22×#11929612C22semidirect
24. #19099073C22semidirect
26. #19099070C22semidirect
44. #19098905C22semidirect
45. #19098902C22semidirect
46. #19098885C22semidirect
47. #19098884C22semidirect
48. #19098820C22semidirect
49. #19098813C22semidirect
50. #19098808C22semidirect
51. #19098806C22semidirect
52. #19098725C22semidirect
53. #19098722C22semidirect
54. #19098705C22semidirect
55. C2×#14579095C22semidirect
56. C2×#14579094C22semidirect
57. C2×#14579093C22semidirect
58. C2×#14579092C22semidirect
59. C2×#14579086C22semidirect
60. C2×#14579086C22semidirect
61. C2×#14579085C22semidirect
62. C2×#14579082C22semidirect
63. C2×#14579082C22semidirect
64. C2×#14579082C22semidirect
65. #19098525C22semidirect
70. C22×SD16×C79C22semidirect
71. C22×D8×C79C22semidirect
73. #449×C79C22semidirect
74. C2×#103×C79C22semidirect
75. C2×#102×C79C22semidirect
98. C2×#11929614C23semidirect
100. C2×#11929612C23semidirect
151. #14579095C23semidirect
152. #14579094C23semidirect
153. #14579093C23semidirect
154. #14579092C23semidirect
155. #14579086C23semidirect
156. #14579086C23semidirect
157. #14579085C23semidirect
158. #14579082C23semidirect
159. #14579082C23semidirect
160. #14579082C23semidirect
176. C2×SD16×C79C23semidirect
178. C2×D8×C79C23semidirect
185. #103×C79C23semidirect
186. #102×C79C23semidirect
428. C2×C79#3197semidirect
448. C2×#449D79semidirect
450. C79C2×#3197semidirect
456. C22×SD16C2×D79semidirect
457. C22×D8C2×D79semidirect
493. #449C2×D79semidirect
501. C2×#103C2×D79semidirect
505. C2×#102C2×D79semidirect
547. C2×SD16C22×D79semidirect
549. C2×D8C22×D79semidirect
613. #103C22×D79semidirect
617. #102C22×D79semidirect
863. C2#23774239direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190990732
C2×#190990702
#237742392
C2×#190989052
C2×#190989022
C2×#190988852
C2×#190988842
C2×#190988202
C2×#190988132
C2×#190988082
C2×#190988062
C2×#190987252
C2×#190987222
C2×#190987052
C2×#190985252
C2×#449×C792
C2×#319779