Finite Group Databasebeta

← #34304581

Subgroups — #34304581

Order 20224.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099259C211yesmaximal, characteristic
2C2×#19098635C211yesmaximal, characteristic, complemented
3#23764368C211yesmaximal, characteristic, complemented
4#23764357C211yesmaximal, characteristic, complemented
5#23763836C211yesmaximal, characteristic, complemented
6#23763826C211yesmaximal, characteristic, complemented
7#23763717C211yesmaximal, characteristic, complemented
8#23763717C211yesmaximal, characteristic, complemented
9#23763492C211yesmaximal, characteristic, complemented
10#23763488C211yesmaximal, characteristic, complemented
11#23763397C211yesmaximal, characteristic, complemented
12#23763228C211yesmaximal, characteristic, complemented
13#23763119C211yesmaximal, characteristic, complemented
14C2×#19098325C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C79C211yesmaximal, characteristic, complemented
16C22×#11929608C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18#19099259—24no—
19#19099259C418yescomplemented
20C2×#14579156—21no—
21C2×#14579153C2211yescharacteristic
22C2×#14579143—21no—
23C2×#14579135C2211yescharacteristic
24C2×#14579135C2211yescharacteristic
25C2×#14579133—21no—
26C2×C4×D316C2211yescharacteristic
27C2×(C22⋊D79)⋊C4—21no—
28C2×#14579120C2211yescharacteristic
29C22×C4⋊Dic79C2211yescharacteristic
30#19098635—24no—
31C2×C4⋊(C79⋊C8)C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37C2×C22⋊(C79⋊C8)C2211yescharacteristic
38C2×#14579072C2211yescharacteristic
39#19098325C2211yescharacteristic
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51C2×C4×D4×C79—21no—
52C2×C4×D4×C79C2211yescharacteristic
53C22×C4⋊C4×C79C2211yescharacteristic
54C22×C4⋊C4×C79C2211yescharacteristic
55#389×C79—21no—
56#385×C79—21no—
57#385×C79—21no—
58#384×C79C2211yescharacteristic
59#380×C79C2211yescharacteristic
60#380×C79C2211yescharacteristic
61C4×C4⋊C4×C79C2211yescharacteristic
62C22×D316C2311yescharacteristic
63C22×C22⋊D79—21no—
64C22×C22⋊D79—21no—
65C23×Dic79—21no—
66C22×C4×D79—21no—
67C2×#11929608—22no—
68C2×#11929608—22no—
69C2×#11929608—41no—
70C22×C79⋊C8—22no—
71C22×C79⋊C8—22no—
72C22×C79⋊C8—41no—
73C22×C79⋊C8C2311yescharacteristic
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77#14579156—28no—
78#14579153—22no—
79#14579153C2×C414yescomplemented
80#14579143—28no—
81#14579135—22no—
82#14579135—22no—
83#14579135C2×C414yescomplemented
84#14579135C2×C414yescomplemented
85#14579133—28no—
86C4×D316—22no—
87C4×D316C2×C414yescomplemented
88(C22⋊D79)⋊C4—28no—
89#14579120—22no—
90#14579120C2×C414yescomplemented
91C2×C4⋊Dic79—22no—
92C2×C4⋊Dic79—21no—
93C2×C4⋊Dic79C2×C414yescomplemented
94C2×C4⋊Dic79C2311yescharacteristic
95C2×C4⋊Dic79C2311yescharacteristic
96C2×C4⋊Dic79C2311yescharacteristic
97C2×Dic79⋊C4—21no—
98C2×Dic79⋊C4—21no—
99C2×C22⋊Dic79—21no—
100C2×(C2×D79)⋊C4—21no—
101C2×(C2×D79)⋊C4—21no—
102C2×(C2×D79)⋊C4—21no—
103C2×C4×Dic79—21no—
104C4⋊(C79⋊C8)—22no—
105#14579081—22no—
106#14579081—22no—
107#14579081—41no—
108#14579081—41no—
109C22⋊(C79⋊C8)—22no—
110C22⋊(C79⋊C8)—22no—
111#14579072—22no—
112C22×D4×C79D411yescharacteristic
113C23×C4×C79—21no—
114C23×C4×C79—21no—
115C23×C4×C79C2311yescharacteristic
116C23×C4×C79C2311yescharacteristic
117C4×D4×C79—44no—
118C4×D4×C79C2×C414yes—
119C4×D4×C79D414yes—
120C2×C4⋊C4×C79—22no—
121C2×C4⋊C4×C79—22no—
122C2×C4⋊C4×C79—21no—
123C2×C4⋊C4×C79—21no—
124C2×C4⋊C4×C79—21no—
125C2×C4⋊C4×C79—21no—
126C2×C4⋊C4×C79—41no—
127C2×C4⋊C4×C79—41no—
128C2×C4⋊C4×C79D411yescharacteristic
129C2×C4⋊C4×C79C2311yescharacteristic
130C2×C4⋊C4×C79C2311yescharacteristic
131C2×C4⋊C4×C79C2311yescharacteristic
132C2×C4⋊C4×C79C2311yescharacteristic
133C2×C22⋊C4×C79—21no—
134C2×C22⋊C4×C79—21no—
135C2×C22⋊C4×C79D411yescharacteristic
136C2×C22⋊C4×C79D411yescharacteristic
137C2×C42×C79—21no—
138C2×C42×C79C2311yescharacteristic
139#95×C79—21no—
140#95×C79—21no—
141#95×C79—21no—
142C23×D79—21no—
143C2×D316—21no—
144C2×D316—21no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316C22×C412yes—
149C2×C22⋊D79—24no—
150C2×C22⋊D79—24no—
151C2×C22⋊D79—42no—
152C2×C22⋊D79—42no—
153C2×C22⋊D79—81no—
154C2×C22⋊D79—81no—
155C22×Dic79—24no—
156C22×Dic79—21no—
157C22×Dic79—21no—
158C22×Dic79—21no—
159C22×Dic79—81no—
160C22×Dic79—81no—
161C2×C4×D79—24no—
162C2×C4×D79—81no—
163C2×C4×D79—81no—
164#11929608—44no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8—21no—
168C2×C79⋊C8—21no—
169C2×C79⋊C8—21no—
170C2×C79⋊C8—21no—
171C2×C79⋊C8—21no—
172C2×C79⋊C8—21no—
173C2×C79⋊C8—21no—
174C2×C79⋊C8—21no—
175C2×C79⋊C8—21no—
176C2×C79⋊C8—44no—
177C2×C79⋊C8#4112yes—
178C4⋊Dic79—24no—
179C4⋊Dic79—21no—
180C4⋊Dic79—21no—
181C4⋊Dic79—21no—
182C4⋊Dic79C22×C412yes—
183C4⋊Dic79C22×C412yes—
184C4⋊Dic79C22×C412yes—
185Dic79⋊C4—24no—
186Dic79⋊C4—24no—
187C22⋊Dic79—24no—
188(C2×D79)⋊C4—24no—
189(C2×D79)⋊C4—24no—
190(C2×D79)⋊C4—24no—
191C4×Dic79—24no—
192C24×C79C2×D411yescharacteristic
193C24×C79C2×D411yescharacteristic
194C2×D4×C79—22no—
195C2×D4×C79—22no—
196C2×D4×C79C22⋊C414yes—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—21no—
209C22×C4×C79—42no—
210C22×C4×C79—42no—
211C22×C4×C79—42no—
212C22×C4×C79—42no—
213C22×C4×C79—81no—
214C22×C4×C79—81no—
215C22×C4×C79C22×C412yes—
216C22×C4×C79C22×C412yes—
217C22×C4×C79C2×D411yescharacteristic
218C22×C4×C79C2×D411yescharacteristic
219C22×C4×C79C2×D411yescharacteristic
220C22×C4×C79C2×D411yescharacteristic
221C22×C4×C79C2×D412yes—
222C22×C4×C79C2×D412yes—
223C22×C4×C79C2411yescharacteristic
224C4⋊C4×C79—21no—
225C4⋊C4×C79—21no—
226C4⋊C4×C79—21no—
227C4⋊C4×C79—21no—
228C4⋊C4×C79—21no—
229C4⋊C4×C79—21no—
230C4⋊C4×C79—21no—
231C4⋊C4×C79—42no—
232C4⋊C4×C79—42no—
233C4⋊C4×C79—42no—
234C4⋊C4×C79—81no—
235C4⋊C4×C79C22⋊C414yes—
236C4⋊C4×C79#4112yes—
237C22⋊C4×C79—42no—
238C22⋊C4×C79—42no—
239C22⋊C4×C79C22⋊C414yes—
240C22⋊C4×C79C22⋊C414yes—
241C42×C79—42no—
242C42×C79C22×C412yes—
243C42×C79C2×D412yes—
244C23×C79—21no—
245C23×C79—21no—
246C23×C79—21no—
247C23×C79—21no—
248C23×C79—21no—
249C23×C79—21no—
250C23×C79—21no—
251C23×C79—21no—
252C23×C79—21no—
253C23×C79—21no—
254C23×C79C2×C22⋊C412yes—
255C23×C79C2×C22⋊C412yes—
256C23×C79AGL(1,ℤ/8)12yes—
257C23×C79#13712yes—
258C23×C79C22×D411yescharacteristic
259C22×D79—22no—
260C22×D79—41no—
261C22×D79—41no—
262C22×D79—41no—
263C22×D79—41no—
264C22×D79—41no—
265C22×D79—41no—
266D4×C79—28no—
267C2×C4×C79—21no—
268C2×C4×C79—21no—
269C2×C4×C79—21no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—22no—
280C2×C4×C79—22no—
281C2×C4×C79—22no—
282C2×C4×C79—22no—
283C2×C4×C79—22no—
284C2×C4×C79—41no—
285C2×C4×C79—41no—
286C2×C4×C79—41no—
287C2×C4×C79—41no—
288C2×C4×C79—41no—
289C2×C4×C79—41no—
290C2×C4×C79—41no—
291C2×C4×C79—41no—
292C2×C4×C79—41no—
293C2×C4×C79—41no—
294C2×C4×C79—41no—
295C2×C4×C79—84no—
296C2×C4×C79—84no—
297C2×C4×C79C2×C22⋊C412yes—
298C2×C4×C79C2×C22⋊C412yes—
299C2×C4×C79C2×C22⋊C412yes—
300C2×C4×C79C2×C22⋊C412yes—
301C2×C4×C79C23×C411yescharacteristic
302C2×C4×C79C22×D411yescharacteristic
303C2×C4×C79C2×#4111yescharacteristic
304C2×C4×C79C2×#4111yescharacteristic
305C2×C4×C79H(5,𝔽2)11yescharacteristic
306C2×C4×C792−1+411yescharacteristic
307C22⋊D79—48no—
308C22⋊D79—84no—
309C2×Dic79—22no—
310C2×Dic79—22no—
311C2×Dic79—22no—
312C2×Dic79—41no—
313C2×Dic79—41no—
314C2×Dic79—41no—
315C2×Dic79—41no—
316C2×Dic79—41no—
317C2×Dic79—41no—
318C2×Dic79—84no—
319D316—22no—
320D316—22no—
321D316—41no—
322D316—41no—
323C4×D79—84no—
324C79⋊C8—22no—
325C79⋊C8—41no—
326C79⋊C8—41no—
327C79⋊C8—41no—
328C22×C79—22no—
329C22×C79—22no—
330C22×C79—22no—
331C22×C79—22no—
332C22×C79—22no—
333C22×C79—22no—
334C22×C79—22no—
335C22×C79—22no—
336C22×C79—22no—
337C22×C79—41no—
338C22×C79—41no—
339C22×C79—41no—
340C22×C79—41no—
341C22×C79#41714yes—
342C22×C79C22×C22⋊C411yescharacteristic
343C22×C79#54611yescharacteristic
344C22×C79#54711yescharacteristic
345C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C79C2×#13711yescharacteristic
347C22×C79#57611yescharacteristic
348C22×C79#57711yescharacteristic
349C2×D79—42no—
350C2×D79—42no—
351C2×D79—42no—
352C2×D79—81no—
353C2×D79—81no—
354C2×D79—81no—
355C2×D79—81no—
356C4×C79—22no—
357C4×C79—22no—
358C4×C79—22no—
359C4×C79—22no—
360C4×C79—42no—
361C4×C79—81no—
362C4×C79—81no—
363C4×C79—81no—
364C4×C79C4×#4111yescharacteristic
365C4×C79#52011yescharacteristic
366C4×C79#54611yescharacteristic
367C4×C79#54711yescharacteristic
368Dic79—42no—
369Dic79—42no—
370Dic79—42no—
371#22493—791nomaximal, Sylow
372C2×C79—24no—
373C2×C79—42no—
374C2×C79#233911yescharacteristic
375C2×C79C2×#41711yescharacteristic
376C2×C79#289711yescharacteristic
377C2×C79#331811yescharacteristic
378C2×C79#332011yescharacteristic
379C2×C79#334511yescharacteristic
380C2×C79#334611yescharacteristic
381D79—82no—
382C2×#553—791no—
383C2×#435—791no—
384D4×C4⋊C4D7911yescharacteristic, complemented
385#1992—791no—
386#1989—791no—
387#1895—791no—
388#1893—791no—
389#1874—791no—
390#1874—791no—
391#1825—791no—
392#1824—791no—
393#1802—791no—
394#1762—791no—
395#1736—791no—
396C2×#340—791no—
397C79#2249311yescharacteristic, complemented, Sylow
398C22×M16—791no—
399C23×C8—791no—
400#553—798no—
401#553—1584no—
402C2×#126—1581no—
403C2×#125—791no—
404C2×#123—1581no—
405C2×#121—791no—
406C2×#121—791no—
407C2×#121—1581no—
408C2×C4×D4—21no—
409C2×C4×D4—791no—
410C2×C4×D4—1581no—
411C2×C4×D4C2×D7911yescharacteristic
412C2×#117—791no—
413C22×C4⋊C4—791no—
414C22×C4⋊C4C2×D7911yescharacteristic
415C22×C4⋊C4C2×D7911yescharacteristic
416#435—1584no—
417C2×C4⋊C8—791no—
418C2×#102—791no—
419C2×#102—791no—
420C2×#102—791no—
421C2×#102—791no—
422C2×C22⋊C8—791no—
423C2×C22⋊C8—791no—
424C2×#97—791no—
425#389—21no—
426#385—21no—
427#385—21no—
428#384C2×D7911yescharacteristic
429#380C2×D7911yescharacteristic
430#380C2×D7911yescharacteristic
431C4×C4⋊C4C2×D7911yescharacteristic
432#340—791no—
433#340—791no—
434#340—791no—
435#340—791no—
436#340—791no—
437#340—791no—
438#340—791no—
439#340—791no—
440#340—791no—
441#340—791no—
442#340—791no—
443#340—791no—
444C22×D4—791no—
445C22×D4—1581no—
446C22×D4—1581no—
447C22×D4C22⋊D7911yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—1581no—
451C23×C4—1581no—
452C23×C4C22×D7911yescharacteristic
453C23×C4C22×D7911yescharacteristic
454C2×M16—3161no—
455C2×M16—1582no—
456C2×M16—1582no—
457C22×C8—3161no—
458C22×C8—791no—
459C22×C8—791no—
460C22×C8—791no—
461C22×C8—791no—
462C22×C8—1582no—
463C22×C8—1582no—
464#126—1588no—
465#125—794no—
466#125—1582no—
467#123—1588no—
468#121—794no—
469#121—794no—
470#121—1588no—
471#121—1582no—
472#121—1582no—
473C4×D4—44no—
474C4×D4—794no—
475C4×D4—1588no—
476C4×D4—1582no—
477C4×D4C4×D7914yes—
478C4×D4D31614yes—
479#117—794no—
480#117—1582no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—41no—
488C2×C4⋊C4—41no—
489C2×C4⋊C4—794no—
490C2×C4⋊C4—791no—
491C2×C4⋊C4—791no—
492C2×C4⋊C4—791no—
493C2×C4⋊C4—1581no—
494C2×C4⋊C4—1581no—
495C2×C4⋊C4—1581no—
496C2×C4⋊C4—1582no—
497C2×C4⋊C4C22⋊D7911yescharacteristic
498C2×C4⋊C4C22×D7911yescharacteristic
499C2×C4⋊C4C22×D7911yescharacteristic
500C2×C4⋊C4C22×D7911yescharacteristic
501C2×C4⋊C4C22×D7911yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1581no—
505C2×C22⋊C4—1581no—
506C2×C22⋊C4—1581no—
507C2×C22⋊C4—1581no—
508C2×C22⋊C4C22⋊D7911yescharacteristic
509C2×C22⋊C4C22⋊D7911yescharacteristic
510C2×C42—21no—
511C2×C42—1581no—
512C2×C42C22×D7911yescharacteristic
513C4⋊C8—1582no—
514#102—3161no—
515#102—3161no—
516#102—1582no—
517#102—1582no—
518C22⋊C8—1582no—
519C22⋊C8—1582no—
520#97—1582no—
521#95—21no—
522#95—21no—
523#95—21no—
524C24—1581no—
525C24C2×C22⋊D7911yescharacteristic
526C24C2×C22⋊D7911yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—3162no—
530C2×D4—3162no—
531C2×D4—792no—
532C2×D4—6321no—
533C2×D4—6321no—
534C2×D4—1584no—
535C2×D4—1584no—
536C2×D4—1581no—
537C2×D4—1581no—
538C2×D4—1581no—
539C2×D4—1581no—
540C2×D4—1581no—
541C2×D4(C2×D79)⋊C414yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—6321no—
561C22×C4—6321no—
562C22×C4—6321no—
563C22×C4—6321no—
564C22×C4—1581no—
565C22×C4—1581no—
566C22×C4—1581no—
567C22×C4—1584no—
568C22×C4—1584no—
569C22×C4C2×C4×D7912yes—
570C22×C4C2×C4×D7912yes—
571C22×C4C2×C22⋊D7911yescharacteristic
572C22×C4C2×C22⋊D7911yescharacteristic
573C22×C4C2×C22⋊D7911yescharacteristic
574C22×C4C2×C22⋊D7911yescharacteristic
575C22×C4C2×D31612yes—
576C22×C4C2×D31612yes—
577C22×C4C23×D7911yescharacteristic
578M16—3164no—
579C2×C8—3164no—
580C2×C8—792no—
581C2×C8—1581no—
582C2×C8—1581no—
583C2×C8—1581no—
584C2×C8—1581no—
585C2×C8—1581no—
586C2×C8—1581no—
587C2×C8—1581no—
588C2×C8—1581no—
589C2×C8—1581no—
590C2×C8—1581no—
591C2×C8—1581no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—42no—
600C4⋊C4—42no—
601C4⋊C4—42no—
602C4⋊C4—81no—
603C4⋊C4—792no—
604C4⋊C4—792no—
605C4⋊C4—792no—
606C4⋊C4—1584no—
607C4⋊C4—1584no—
608C4⋊C4—1584no—
609C4⋊C4—1581no—
610C4⋊C4—1581no—
611C4⋊C4—1581no—
612C4⋊C4(C2×D79)⋊C414yes—
613C4⋊C4#1192962312yes—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—1584no—
617C22⋊C4—1584no—
618C22⋊C4—1584no—
619C22⋊C4—1584no—
620C22⋊C4(C2×D79)⋊C414yes—
621C22⋊C4(C2×D79)⋊C414yes—
622C42—42no—
623C42—1584no—
624C42C2×C4×D7912yes—
625C42C2×D31612yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—3161no—
637C23—3161no—
638C23—3161no—
639C23—3161no—
640C23—3161no—
641C23—3161no—
642C23—1582no—
643C23C2×(C2×D79)⋊C412yes—
644C23C2×(C2×D79)⋊C412yes—
645C23#1457918712yes—
646C23#1457919212yes—
647C23C22×C22⋊D7911yescharacteristic
648D4—28no—
649D4—3168no—
650D4—3161no—
651D4—3161no—
652D4—6324no—
653D4—1582no—
654D4—1582no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—84no—
684C2×C4—84no—
685C2×C4—3161no—
686C2×C4—3161no—
687C2×C4—3161no—
688C2×C4—3161no—
689C2×C4—3161no—
690C2×C4—3161no—
691C2×C4—6324no—
692C2×C4—6324no—
693C2×C4—1582no—
694C2×C4—1582no—
695C2×C4—1582no—
696C2×C4C2×(C2×D79)⋊C412yes—
697C2×C4C2×(C2×D79)⋊C412yes—
698C2×C4C2×(C2×D79)⋊C412yes—
699C2×C4C2×(C2×D79)⋊C412yes—
700C2×C4C22×C4×D7911yescharacteristic
701C2×C4C22×D31611yescharacteristic
702C2×C4#41×D7911yescharacteristic
703C2×C4C2×#1192962311yescharacteristic
704C2×C4#1457920611yescharacteristic
705C2×C4#1457920811yescharacteristic
706C8—3161no—
707C8—3161no—
708C8—3161no—
709C8—1582no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—3162no—
724C22—3162no—
725C22—3162no—
726C22—6321no—
727C22—6321no—
728C22—6321no—
729C22—6321no—
730C22#1909856214yes—
731C22C22×(C2×D79)⋊C411yescharacteristic
732C22#1909920711yescharacteristic
733C22#1909921211yescharacteristic
734C22C2×#1457918711yescharacteristic
735C22C2×#1457919211yescharacteristic
736C22#1909936611yescharacteristic
737C22#1909937111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—3162no—
747C4—3162no—
748C4—3162no—
749C4C4×#1192962311yescharacteristic
750C4#1909904211yescharacteristic
751C4#1909920811yescharacteristic
752C4#1909921711yescharacteristic
753C2—24no—
754C2—42no—
755C2—6322no—
756C2#2376622511yescharacteristic
757C2C2×#1909856211yescharacteristic
758C2#2377192311yescharacteristic
759C2#2377554111yescharacteristic
760C2#2377557111yescharacteristic
761C2#2377587011yescharacteristic
762C2#2377587911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingD4×C4⋊C4×C79C2
socleC23×C79C22×D4
prime radicalC2×#19099259C2
cosocleC22×C4×C79C24
hypercenterD4×C4⋊C4D79
hypocenterC79#22493
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19098635C2semidirect
3. #23764368C2semidirect
4. #23764357C2semidirect
5. #23763836C2semidirect
6. #23763826C2semidirect
7. #23763717C2semidirect
8. #23763717C2semidirect
9. #23763492C2semidirect
10. #23763488C2semidirect
11. #23763397C2semidirect
12. #23763228C2semidirect
13. #23763119C2semidirect
14. C2×#19098325C2semidirect
15. D4×C4⋊C4×C79C2semidirect
19. #19099259C4semidirect
79. #14579153C2×C4semidirect
83. #14579135C2×C4semidirect
84. #14579135C2×C4semidirect
87. C4×D316C2×C4semidirect
90. #14579120C2×C4semidirect
93. C2×C4⋊Dic79C2×C4semidirect
384. D4×C4⋊C4D79semidirect
397. C79#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#190992592
C2×#190986352
#237643682
#237643572
#237638362
#237638262
#237637172
#237634922
#237634882
#237633972
#237632282
#237631192
C2×#190983252
D4×C4⋊C4×C792
#2249379