Finite Group Databasebeta

← #34306457

Subgroups — #34306457

Order 20224.

1042 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098634C211yesmaximal, characteristic
2C2×#19098602C211yesmaximal, characteristic, complemented
3C22×#14579095C211yesmaximal, characteristic, complemented
4#23766331C211yesmaximal, characteristic
5#23766296C211yesmaximal, characteristic
6#23764171C211yesmaximal, characteristic, complemented
7#23764157C211yesmaximal, characteristic, complemented
8#23763602C211yesmaximal, characteristic, complemented
9#23763592C211yesmaximal, characteristic, complemented
10#23763589C211yesmaximal, characteristic, complemented
11#23763587C211yesmaximal, characteristic, complemented
12#23763565C211yesmaximal, characteristic, complemented
13#23763430C211yesmaximal, characteristic, complemented
14#23763300C211yesmaximal, characteristic, complemented
15C79×#1807C211yesmaximal, characteristic, complemented
16C22×#11929607C2211yescharacteristic
17C2×C4×C22⋊D79C2211yescharacteristic
18C2×(C22⋊D79)⋊C4—21no—
19C2×#14579119C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21C22×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊C4×D79C2211yescharacteristic
23#19098634C418yescomplemented
24#19098602—24no—
25C2×#14579095—24no—
26C2×#14579095C2211yescharacteristic
27C2×#14579095C2211yescharacteristic
28C2×#14579095C2211yescharacteristic
29C2×#14579095C2211yescharacteristic
30C2×#14579094C2211yescharacteristic
31C2×#14579094C2211yescharacteristic
32C2×#14579092C2211yescharacteristic
33C2×#14579092C2211yescharacteristic
34C2×Dic79⋊C8C2211yescharacteristic
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36C2×(C2×D79)⋊C8C2211yescharacteristic
37C2×#14579071C2211yescharacteristic
38#19098460—21no—
39#19098455—21no—
40#19098450—21no—
41#19098440—21no—
42#19098437—21no—
43#19098435—21no—
44#19098432C2211yescharacteristic
45#19098428C2211yescharacteristic
46#19098420C2211yescharacteristic
47#19098420C2211yescharacteristic
48C4⋊C4×Dic79C2211yescharacteristic
49C4⋊C4×Dic79C2211yescharacteristic
50C22⋊C4×Dic79—21no—
51#19098325C2211yescharacteristic
52#19098325C2211yescharacteristic
53#19098325C2211yescharacteristic
54#19098325C2211yescharacteristic
55C23×C8×C79C2211yescharacteristic
56C2×#106×C79C2211yescharacteristic
57C2×#106×C79C2211yescharacteristic
58#380×C79C2211yescharacteristic
59#380×C79C2211yescharacteristic
60#340×C79C2211yescharacteristic
61#340×C79C2211yescharacteristic
62C22×C22⋊D79D411yescharacteristic
63C23×Dic79—21no—
64C23×Dic79—21no—
65C22×C4×D79—21no—
66C22×C4×D79C2311yescharacteristic
67C2×#11929607—22no—
68C2×#11929607—22no—
69C2×#11929607C2×C414yescomplemented
70C22×C79⋊C8C2311yescharacteristic
71C22×C79⋊C8C2311yescharacteristic
72C4×C22⋊D79C2×C414yes—
73C4×C22⋊D79Q814yes—
74(C22⋊D79)⋊C4—44no—
75#14579119—22no—
76#14579119—41no—
77C2×C4⋊Dic79—22no—
78C2×C4⋊Dic79—22no—
79C2×C4⋊Dic79—21no—
80C2×C4⋊Dic79—21no—
81C2×C4⋊Dic79—41no—
82C2×C4⋊Dic79—41no—
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C4⋊Dic79C2311yescharacteristic
87C2×Dic79⋊C4—21no—
88C2×Dic79⋊C4—21no—
89C2×Dic79⋊C4—21no—
90C2×Dic79⋊C4D411yescharacteristic
91C4⋊C4×D79—22no—
92C4⋊C4×D79—41no—
93C2×C22⋊Dic79D411yescharacteristic
94C2×(C2×D79)⋊C4—21no—
95C2×(C2×D79)⋊C4—21no—
96C2×(C2×D79)⋊C4—21no—
97C2×(C2×D79)⋊C4D411yescharacteristic
98C2×C4×Dic79—21no—
99C2×C4×Dic79—21no—
100C2×C4×Dic79—21no—
101C2×C4×Dic79C2311yescharacteristic
102#14579095—22no—
103#14579095—22no—
104#14579095—22no—
105#14579095D414yescomplemented
106#14579094—22no—
107#14579094—41no—
108#14579092—22no—
109#14579092—41no—
110Dic79⋊C8C2×C414yescomplemented
111C22⋊(C79⋊C8)C2×C414yescomplemented
112(C2×D79)⋊C8C2×C414yescomplemented
113#14579071C2×C414yescomplemented
114C79⋊#95—21no—
115C79⋊#95—21no—
116C79⋊#95—21no—
117C79⋊#95—21no—
118C79⋊#95—21no—
119C79⋊#95—21no—
120C23×C4×C79C2311yescharacteristic
121C22×C8×C79—22no—
122C22×C8×C79—22no—
123C22×C8×C79C2×C414yescomplemented
124C22×C8×C79C2311yescharacteristic
125C22×C8×C79C2311yescharacteristic
126C2×C4⋊C4×C79C2311yescharacteristic
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C4⋊C4×C79C2311yescharacteristic
129C2×C4⋊C4×C79C2311yescharacteristic
130C2×C22⋊C4×C79—21no—
131C2×C22⋊C4×C79—21no—
132#106×C79—22no—
133#106×C79—22no—
134#95×C79—21no—
135#95×C79—21no—
136C23×D79C2×D411yescharacteristic
137C2×C22⋊D79—22no—
138C2×C22⋊D79—22no—
139C2×C22⋊D79C4⋊C414yes—
140C22×Dic79—21no—
141C22×Dic79—21no—
142C22×Dic79—21no—
143C22×Dic79—21no—
144C22×Dic79—42no—
145C22×Dic79—42no—
146C22×Dic79—42no—
147C22×Dic79—42no—
148C22×Dic79—81no—
149C22×Dic79—81no—
150C22×Dic79C2×D411yescharacteristic
151C22×Dic79C2×D411yescharacteristic
152C22×Dic79C2×D411yescharacteristic
153C2×C4×D79—21no—
154C2×C4×D79—21no—
155C2×C4×D79—21no—
156C2×C4×D79—21no—
157C2×C4×D79—42no—
158C2×C4×D79—42no—
159C2×C4×D79—81no—
160C2×C4×D79C22×C412yes—
161C2×C4×D79C2×Q812yes—
162#11929607—28no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8C22×C412yes—
168C2×C79⋊C8C22×C412yes—
169C4⋊Dic79—21no—
170C4⋊Dic79—21no—
171C4⋊Dic79—21no—
172C4⋊Dic79—21no—
173C4⋊Dic79—21no—
174C4⋊Dic79—21no—
175C4⋊Dic79—42no—
176C4⋊Dic79—42no—
177C4⋊Dic79C2×D412yes—
178C4⋊Dic79C2×D412yes—
179Dic79⋊C4—42no—
180Dic79⋊C4—42no—
181Dic79⋊C4—81no—
182Dic79⋊C4C4⋊C414yes—
183C22⋊Dic79C4⋊C414yes—
184(C2×D79)⋊C4—42no—
185(C2×D79)⋊C4—42no—
186(C2×D79)⋊C4—81no—
187(C2×D79)⋊C4C4⋊C414yes—
188C4×Dic79—42no—
189C4×Dic79—42no—
190C4×Dic79—81no—
191C4×Dic79C22×C412yes—
192C4×Dic79C2×Q812yes—
193C24×C79C2×D411yescharacteristic
194C22×C4×C79—21no—
195C22×C4×C79—21no—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79C22×C412yes—
203C22×C4×C79C2×D411yescharacteristic
204C22×C4×C79C2×Q812yes—
205C22×C4×C79C2411yescharacteristic
206C2×C8×C79—28no—
207C2×C8×C79—21no—
208C2×C8×C79—21no—
209C2×C8×C79C22×C412yes—
210C2×C8×C79C22×C412yes—
211C2×C8×C79C2×D412yes—
212C2×C8×C79#4112yes—
213C4⋊C4×C79—21no—
214C4⋊C4×C79—21no—
215C4⋊C4×C79—21no—
216C4⋊C4×C79—21no—
217C4⋊C4×C79—21no—
218C4⋊C4×C79—21no—
219C4⋊C4×C79—21no—
220C4⋊C4×C79—21no—
221C22⋊C4×C79—42no—
222C22⋊C4×C79—42no—
223C23×C79—21no—
224C23×C79—21no—
225C23×C79—21no—
226C23×C79—21no—
227C23×C79C2×C4⋊C412yes—
228C23×C79AGL(1,ℤ/8)12yes—
229C23×C79#13712yes—
230C23×C79C22×D411yescharacteristic
231C22×D79—21no—
232C22×D79—21no—
233C22×D79—21no—
234C22×D79—21no—
235C22×D79—21no—
236C22×D79—21no—
237C22×D79C2×C4⋊C412yes—
238C2×C4×C79—21no—
239C2×C4×C79—21no—
240C2×C4×C79—22no—
241C2×C4×C79—22no—
242C2×C4×C79—22no—
243C2×C4×C79—22no—
244C2×C4×C79—41no—
245C2×C4×C79—41no—
246C2×C4×C79—41no—
247C2×C4×C79—41no—
248C2×C4×C79—41no—
249C2×C4×C79—41no—
250C2×C4×C79—41no—
251C2×C4×C79—41no—
252C2×C4×C79—41no—
253C2×C4×C79—41no—
254C2×C4×C79—41no—
255C2×C4×C79—41no—
256C2×C4×C79C2×C4⋊C412yes—
257C2×C4×C79C23×C411yescharacteristic
258C2×C4×C79C22×D411yescharacteristic
259C2×C4×C79C22×Q811yescharacteristic
260C2×C4×C79C2×#4111yescharacteristic
261C2×C4×C79H(5,𝔽2)11yescharacteristic
262C2×C4×C792−1+411yescharacteristic
263C22⋊D79—28no—
264C2×Dic79—21no—
265C2×Dic79—21no—
266C2×Dic79—21no—
267C2×Dic79—21no—
268C2×Dic79—21no—
269C2×Dic79—21no—
270C2×Dic79—22no—
271C2×Dic79—22no—
272C2×Dic79—41no—
273C2×Dic79—41no—
274C2×Dic79—41no—
275C2×Dic79—41no—
276C2×Dic79—41no—
277C2×Dic79—41no—
278C2×Dic79—41no—
279C2×Dic79—41no—
280C2×Dic79—41no—
281C2×Dic79—41no—
282C2×Dic79—84no—
283C2×Dic79—84no—
284C2×Dic79C2×C4⋊C412yes—
285C2×Dic79C2×C4⋊C412yes—
286C2×Dic79C2×C4⋊C412yes—
287C4×D79—22no—
288C4×D79—22no—
289C4×D79—22no—
290C4×D79—22no—
291C4×D79—84no—
292C8×C79—22no—
293C8×C79C4×D414yescomplemented
294C79⋊C8—22no—
295C79⋊C8—22no—
296C22×C79—22no—
297C22×C79—22no—
298C22×C79—22no—
299C22×C79—22no—
300C22×C79—22no—
301C22×C79—22no—
302C22×C79#42814yescomplemented
303C22×C79C22×C4⋊C411yescharacteristic
304C22×C79D4211yescharacteristic
305C22×C79#54711yescharacteristic
306C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C79C2×#13711yescharacteristic
308C22×C79#57611yescharacteristic
309C22×C79#57811yescharacteristic
310C2×D79—22no—
311C2×D79—22no—
312C2×D79—22no—
313C2×D79—41no—
314C2×D79—41no—
315C2×D79—41no—
316C2×D79—41no—
317C4×C79—22no—
318C4×C79—81no—
319C4×C79—81no—
320C4×C79—81no—
321C4×C79—81no—
322C4×C79C2×C4×D411yescharacteristic
323C4×C79#52011yescharacteristic
324C4×C79D4×Q811yescharacteristic
325C4×C79#55411yescharacteristic
326Dic79—22no—
327Dic79—22no—
328Dic79—22no—
329Dic79—42no—
330Dic79—42no—
331Dic79—81no—
332Dic79—81no—
333#22661—791nomaximal, Sylow
334C2×C79—24no—
335C2×C79D4×C4⋊C411yescharacteristic
336C2×C79C2×#42811yescharacteristic
337C2×C79#291311yescharacteristic
338C2×C79#326411yescharacteristic
339C2×C79#327011yescharacteristic
340C2×C79#334311yescharacteristic
341C2×C79#334611yescharacteristic
342D79—42no—
343C2×#435—791no—
344C2×#428—791no—
345C22×#107—791no—
346#2352—791no—
347D4×C4⋊C4—791no—
348#1949—791no—
349#1947—791no—
350#1854—791no—
351#1853—791no—
352#1852—791no—
353#1852—791no—
354#1847—791no—
355#1809—791no—
356#1807D7911yescharacteristic, complemented
357#1776—791no—
358C79#2266111yescharacteristic, complemented, Sylow
359C22×M16—791no—
360C23×C8C2×D7911yescharacteristic
361C2×C4×D4—791no—
362C2×C4×D4—1581no—
363C2×#117—791no—
364C22×C4⋊C4—791no—
365C22×C4⋊C4—791no—
366C22×C4⋊C4—791no—
367#435—798no—
368#428—1584no—
369C2×#107—791no—
370C2×#107—791no—
371C2×#107—791no—
372C2×#107—791no—
373C2×#107—791no—
374C2×#107—791no—
375C2×#107—1584no—
376C2×#106—791no—
377C2×#106—791no—
378C2×#106C2×D7911yescharacteristic
379C2×#106C2×D7911yescharacteristic
380C2×C4⋊C8—791no—
381C2×C22⋊C8—791no—
382C2×C22⋊C8—791no—
383C2×#97—791no—
384#389—1581no—
385#388—1581no—
386#387—1581no—
387#386—1581no—
388#385—1581no—
389#385—1581no—
390#384—791no—
391#382—791no—
392#380—791no—
393#380—791no—
394#380C2×D7911yescharacteristic
395#380C2×D7911yescharacteristic
396C4×C4⋊C4—791no—
397C4×C4⋊C4—791no—
398C4×C22⋊C4—1581no—
399#340—791no—
400#340—791no—
401#340—791no—
402#340—791no—
403#340C2×D7911yescharacteristic
404#340C2×D7911yescharacteristic
405C22×D4—791no—
406C23×C4—791no—
407C23×C4—1581no—
408C23×C4—1581no—
409C23×C4—1581no—
410C23×C4C22×D7911yescharacteristic
411C2×M16—794no—
412C2×M16—1582no—
413C2×M16—1582no—
414C22×C8—22no—
415C22×C8—22no—
416C22×C8—791no—
417C22×C8—791no—
418C22×C8C4×D7914yescomplemented
419C22×C8C22×D7911yescharacteristic
420C22×C8C22×D7911yescharacteristic
421C4×D4—3164no—
422C4×D4—794no—
423C4×D4—794no—
424#117—3161no—
425#117—1582no—
426C2×C4⋊C4—3161no—
427C2×C4⋊C4—3161no—
428C2×C4⋊C4—3161no—
429C2×C4⋊C4—791no—
430C2×C4⋊C4—791no—
431C2×C4⋊C4—791no—
432C2×C4⋊C4—791no—
433C2×C4⋊C4—791no—
434C2×C4⋊C4—1582no—
435C2×C4⋊C4—1581no—
436C2×C4⋊C4—1581no—
437C2×C4⋊C4—1581no—
438C2×C4⋊C4—1581no—
439C2×C4⋊C4—1582no—
440C2×C4⋊C4—1582no—
441C2×C4⋊C4—1581no—
442C2×C4⋊C4C22×D7911yescharacteristic
443C2×C4⋊C4C22×D7911yescharacteristic
444C2×C4⋊C4C22×D7911yescharacteristic
445C2×C4⋊C4C22×D7911yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—791no—
449C2×C22⋊C4—791no—
450C2×C22⋊C4—1581no—
451C2×C22⋊C4—1581no—
452C2×C22⋊C4—1581no—
453C2×C42—791no—
454C2×C42—1581no—
455C2×C42—1581no—
456C2×C42—1581no—
457#107—3161no—
458#107—794no—
459#107—1582no—
460#107—1582no—
461#107—1582no—
462#107—1582no—
463#106—22no—
464#106—22no—
465#106—3161no—
466#106—1582no—
467C4⋊C8—794no—
468C22⋊C8—794no—
469C22⋊C8—794no—
470#97—794no—
471#95—21no—
472#95—21no—
473#95—1581no—
474#95—1581no—
475#95—1581no—
476#95—1581no—
477#95—1581no—
478#95—1581no—
479C24—791no—
480C24D4×D7911yescharacteristic
481C2×D4—794no—
482C2×D4—1582no—
483C2×D4—1582no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—3162no—
493C22×C4—3162no—
494C22×C4—3162no—
495C22×C4—3162no—
496C22×C4—3162no—
497C22×C4—3162no—
498C22×C4—791no—
499C22×C4—791no—
500C22×C4—791no—
501C22×C4—792no—
502C22×C4—792no—
503C22×C4—6321no—
504C22×C4—6321no—
505C22×C4—6321no—
506C22×C4—1581no—
507C22×C4—1581no—
508C22×C4—1581no—
509C22×C4—1581no—
510C22×C4—1581no—
511C22×C4—1581no—
512C22×C4—1581no—
513C22×C4—1581no—
514C22×C4C2×C4×D7912yes—
515C22×C4D4×D7911yescharacteristic
516C22×C4Q8×D7912yes—
517C22×C4C23×D7911yescharacteristic
518M16—1588no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—28no—
522C2×C8—792no—
523C2×C8—792no—
524C2×C8—1581no—
525C2×C8—1581no—
526C2×C8—1581no—
527C2×C8—1581no—
528C2×C8C2×C4×D7912yes—
529C2×C8C2×C4×D7912yes—
530C2×C8D4×D7912yes—
531C2×C8#1192962312yes—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—3162no—
541C4⋊C4—3162no—
542C4⋊C4—3162no—
543C4⋊C4—3162no—
544C4⋊C4—794no—
545C4⋊C4—792no—
546C4⋊C4—792no—
547C4⋊C4—6321no—
548C4⋊C4—1581no—
549C4⋊C4—1581no—
550C4⋊C4—1581no—
551C4⋊C4—1581no—
552C4⋊C4—1581no—
553C4⋊C4—1581no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—3162no—
557C22⋊C4—3162no—
558C22⋊C4—794no—
559C22⋊C4—794no—
560C22⋊C4—6321no—
561C42—3162no—
562C42—3162no—
563C42—792no—
564C42—792no—
565C42—6321no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—792no—
571C23—1581no—
572C23—1581no—
573C23—1581no—
574C23—1581no—
575C23—1581no—
576C23—1581no—
577C23C4⋊C4×D7912yes—
578C23#1457918812yes—
579C23#1457919012yes—
580C23C2×D4×D7911yescharacteristic
581D4—1588no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—3161no—
601C2×C4—3161no—
602C2×C4—3161no—
603C2×C4—3161no—
604C2×C4—3161no—
605C2×C4—3161no—
606C2×C4—3161no—
607C2×C4—3161no—
608C2×C4—3161no—
609C2×C4—3161no—
610C2×C4—792no—
611C2×C4—792no—
612C2×C4—792no—
613C2×C4—6324no—
614C2×C4—6324no—
615C2×C4—6324no—
616C2×C4—1582no—
617C2×C4—1582no—
618C2×C4—1581no—
619C2×C4—1581no—
620C2×C4—1581no—
621C2×C4—1581no—
622C2×C4—1581no—
623C2×C4—1581no—
624C2×C4—1582no—
625C2×C4—1582no—
626C2×C4—1582no—
627C2×C4—1582no—
628C2×C4C4⋊C4×D7912yes—
629C2×C4C22×C4×D7911yescharacteristic
630C2×C4C2×D4×D7911yescharacteristic
631C2×C4C2×Q8×D7911yescharacteristic
632C2×C4C2×#1192962311yescharacteristic
633C2×C4#1457920711yescharacteristic
634C2×C4#1457920811yescharacteristic
635C8—22no—
636C8—1582no—
637C8—1582no—
638C8(C22⋊D79)⋊C414yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—3161no—
646C22—3161no—
647C22—3161no—
648C22—3161no—
649C22—1582no—
650C22—1582no—
651C22—1582no—
652C22#1909860214yescomplemented
653C22C2×C4⋊C4×D7911yescharacteristic
654C22#1909919711yescharacteristic
655C22#1909921311yescharacteristic
656C22C2×#1457918811yescharacteristic
657C22C2×#1457919011yescharacteristic
658C22#1909936511yescharacteristic
659C22#1909937711yescharacteristic
660C4—22no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—3162no—
666C4—3162no—
667C4—6321no—
668C4—6321no—
669C4—1582no—
670C4—1582no—
671C4—1582no—
672C4C2×(C22⋊D79)⋊C411yescharacteristic
673C4#1909904311yescharacteristic
674C4#1909922611yescharacteristic
675C4#1909927111yescharacteristic
676C2—24no—
677C2—3162no—
678C2#2376629611yescharacteristic
679C2C2×#1909860211yescharacteristic
680C2#2377199711yescharacteristic
681C2#2377487711yescharacteristic
682C2#2377496711yescharacteristic
683C2#2377584611yescharacteristic
684C2#2377589111yescharacteristic
subgroupG/H
centerC23C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1807C2
socleC23×C79C22×D4
prime radicalC22×C22⋊D79D4
cosocleC22×C4×C79C24
hypercenter#1807D79
hypocenterC79#22661
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1807

Complements

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

NH ≅ G/Ntype
2. C2×#19098602C2semidirect
3. C22×#14579095C2semidirect
6. #23764171C2semidirect
7. #23764157C2semidirect
8. #23763602C2semidirect
9. #23763592C2semidirect
10. #23763589C2semidirect
11. #23763587C2semidirect
12. #23763565C2semidirect
13. #23763430C2semidirect
14. #23763300C2semidirect
15. C79×#1807C2semidirect
23. #19098634C4semidirect
69. C2×#11929607C2×C4semidirect
105. #14579095D4semidirect
110. Dic79⋊C8C2×C4semidirect
111. C22⋊(C79⋊C8)C2×C4semidirect
112. (C2×D79)⋊C8C2×C4semidirect
113. #14579071C2×C4semidirect
123. C22×C8×C79C2×C4semidirect
293. C8×C79C4×D4semidirect
302. C22×C79#428semidirect
356. #1807D79semidirect
358. C79#22661semidirect
418. C22×C8C4×D79semidirect
638. C8(C22⋊D79)⋊C4semidirect
652. C22#19098602semidirect

Maximal subgroups

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

subgroupindex
C2×#190986342
C2×#190986022
C22×#145790952
#237663312
#237662962
#237641712
#237641572
#237636022
#237635922
#237635892
#237635872
#237635652
#237634302
#237633002
C79×#18072
#2266179