Finite Group Databasebeta

← #34308732

Subgroups — #34308732

Order 20224.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098697C211yesmaximal, characteristic
2C2×#19098673C211yesmaximal, characteristic, complemented
3C2×#19098568C211yesmaximal, characteristic, complemented
4#23766436C211yesmaximal, characteristic, complemented
5#23764265C211yesmaximal, characteristic, complemented
6#23764100C211yesmaximal, characteristic, complemented
7#23764024C211yesmaximal, characteristic, complemented
8#23763836C211yesmaximal, characteristic, complemented
9#23763751C211yesmaximal, characteristic, complemented
10#23763748C211yesmaximal, characteristic, complemented
11#23763647C211yesmaximal, characteristic, complemented
12#23763597C211yesmaximal, characteristic, complemented
13C4×#14579082C211yesmaximal, characteristic, complemented
14#23763184C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C79C211yesmaximal, characteristic, complemented
16C22×#11929609C2211yescharacteristic
17C22×#11929609C2211yescharacteristic
18C22×#11929608C2211yescharacteristic
19C2×#14579135C2211yescharacteristic
20C2×C4×D316C2211yescharacteristic, complemented
21C2×#14579120C2211yescharacteristic
22#19098697C418yescomplemented
23#19098673—24no—
24C2×#14579094C2211yescharacteristic, complemented
25C2×#14579092C2211yescharacteristic, complemented
26#19098568—24no—
27C2×#14579082C2211yescharacteristic
28C2×#14579082C2211yescharacteristic
29C2×#14579082C2211yescharacteristic
30C2×#14579082C2211yescharacteristic
31C2×#14579082C2211yescharacteristic
32C2×#14579082C2211yescharacteristic
33C2×#14579081C2211yescharacteristic, complemented
34C2×#14579081C2211yescharacteristic, complemented
35C2×C22⋊(C79⋊C8)C2211yescharacteristic
36C2×#14579072C2211yescharacteristic, complemented
37C2×C4×C79⋊C8C2211yescharacteristic, complemented
38#19098465C2211yescharacteristic, complemented
39#19098463—21no—
40#19098461C2211yescharacteristic, complemented
41#19098452—21no—
42#19098439—21no—
43C4×C4⋊Dic79C2211yescharacteristic, complemented
44#19098410—21no—
45#19098325C2211yescharacteristic, complemented
46#19098325C2211yescharacteristic, complemented
47#19098325C2211yescharacteristic, complemented
48#19098325C2211yescharacteristic, complemented
49#19098318C2211yescharacteristic, complemented
50#19098318C2211yescharacteristic, complemented
51C23×D4×C79C2211yescharacteristic
52C2×C4×D4×C79C2211yescharacteristic
53C2×C4×D4×C79C2211yescharacteristic
54C22×C22⋊C4×C79—21no—
55#390×C79C2211yescharacteristic
56#390×C79C2211yescharacteristic
57#386×C79—21no—
58#386×C79—21no—
59#380×C79C2211yescharacteristic
60#379×C79—21no—
61C4×C22⋊C4×C79C2211yescharacteristic
62C22×D316C2311yescharacteristic
63C22×C22⋊D79—21no—
64C22×C4×D79—21no—
65C2×#11929609—22no—
66C2×#11929609—22no—
67C2×#11929609—41no—
68C2×#11929609—41no—
69C2×#11929609C2×C414yes—
70C2×#11929609C2×C414yescomplemented
71C2×#11929608—22no—
72C2×#11929608—22no—
73C2×#11929608—41no—
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77C22×C79⋊C8C2311yescharacteristic
78#14579135—22no—
79#14579135C2×C414yescomplemented
80C4×D316—22no—
81C4×D316—41no—
82#14579120—22no—
83#14579120—41no—
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C4⋊Dic79C2311yescharacteristic
87C2×Dic79⋊C4—21no—
88C2×C22⋊Dic79—21no—
89C2×(C2×D79)⋊C4—21no—
90C2×(C2×D79)⋊C4—21no—
91C2×(C2×D79)⋊C4—21no—
92C2×(C2×D79)⋊C4—21no—
93C2×C4×Dic79—21no—
94C2×C4×Dic79—21no—
95#14579094—41no—
96#14579092—22no—
97#14579082—22no—
98#14579082—22no—
99#14579082—22no—
100#14579082C2×C414yescomplemented
101#14579082C2×C414yescomplemented
102#14579082D414yescomplemented
103#14579081—22no—
104#14579081—41no—
105C22⋊(C79⋊C8)C2×C414yescomplemented
106#14579072—22no—
107C4×C79⋊C8—41no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C25×C79—21no—
111C22×D4×C79—22no—
112C22×D4×C79—22no—
113C22×D4×C79—21no—
114C22×D4×C79—22no—
115C22×D4×C79—41no—
116C22×D4×C79—41no—
117C22×D4×C79C2×C414yescomplemented
118C22×D4×C79C2311yescharacteristic
119C22×D4×C79C2311yescharacteristic
120C23×C4×C79—21no—
121C23×C4×C79—21no—
122C23×C4×C79C2311yescharacteristic
123C4×D4×C79—22no—
124C4×D4×C79—22no—
125C4×D4×C79—41no—
126C4×D4×C79—41no—
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C4⋊C4×C79C2311yescharacteristic
129C2×C22⋊C4×C79—21no—
130C2×C22⋊C4×C79—21no—
131C2×C22⋊C4×C79—21no—
132C2×C22⋊C4×C79—21no—
133C2×C22⋊C4×C79—21no—
134C2×C22⋊C4×C79—21no—
135C2×C22⋊C4×C79—21no—
136C2×C22⋊C4×C79—44no—
137C2×C22⋊C4×C79D411yescharacteristic
138C2×C22⋊C4×C79D411yescharacteristic
139C2×C42×C79C2311yescharacteristic
140C2×C42×C79C2311yescharacteristic
141#95×C79—21no—
142#95×C79D411yescharacteristic
143#95×C79D411yescharacteristic
144C23×D79—21no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316—21no—
150C2×D316C22×C412yes—
151C2×C22⋊D79—24no—
152C2×C22⋊D79—81no—
153C2×C22⋊D79—81no—
154C22×Dic79—21no—
155C22×Dic79—21no—
156C22×Dic79—21no—
157C2×C4×D79—42no—
158C2×C4×D79—42no—
159C2×C4×D79—81no—
160#11929609—28no—
161#11929609—44no—
162#11929608—44no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
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⋊C8C22×C412yes—
173C2×C79⋊C8C22×C412yes—
174C2×C79⋊C8C2×D412yes—
175C4⋊Dic79—21no—
176C4⋊Dic79—21no—
177C4⋊Dic79—21no—
178C4⋊Dic79—21no—
179C4⋊Dic79C22×C412yes—
180C4⋊Dic79C2×D412yes—
181Dic79⋊C4—81no—
182C22⋊Dic79—42no—
183(C2×D79)⋊C4—24no—
184(C2×D79)⋊C4—42no—
185(C2×D79)⋊C4—42no—
186(C2×D79)⋊C4—81no—
187C4×Dic79—42no—
188C4×Dic79—81no—
189C24×C79—21no—
190C24×C79—21no—
191C24×C79—24no—
192C24×C79—42no—
193C24×C79—42no—
194C24×C79—42no—
195C24×C79—42no—
196C24×C79—81no—
197C24×C79—81no—
198C24×C79C2×D411yescharacteristic
199C2×D4×C79—28no—
200C2×D4×C79—24no—
201C2×D4×C79—21no—
202C2×D4×C79—21no—
203C2×D4×C79—21no—
204C2×D4×C79—21no—
205C2×D4×C79—21no—
206C2×D4×C79—21no—
207C2×D4×C79—21no—
208C2×D4×C79—21no—
209C2×D4×C79—44no—
210C2×D4×C79—44no—
211C2×D4×C79—44no—
212C2×D4×C79—42no—
213C2×D4×C79—42no—
214C2×D4×C79C22×C412yes—
215C2×D4×C79C22×C412yes—
216C2×D4×C79C2×D412yes—
217C2×D4×C79#4112yes—
218C22×C4×C79—21no—
219C22×C4×C79—21no—
220C22×C4×C79—21no—
221C22×C4×C79—21no—
222C22×C4×C79—21no—
223C22×C4×C79—21no—
224C22×C4×C79—42no—
225C22×C4×C79—42no—
226C22×C4×C79—42no—
227C22×C4×C79—42no—
228C22×C4×C79—81no—
229C22×C4×C79—81no—
230C22×C4×C79C22×C412yes—
231C22×C4×C79C2×D411yescharacteristic
232C22×C4×C79C2×D411yescharacteristic
233C22×C4×C79C2×D411yescharacteristic
234C22×C4×C79C2×D411yescharacteristic
235C22×C4×C79C2×D411yescharacteristic
236C22×C4×C79#4112yes—
237C22×C4×C79C2411yescharacteristic
238C4⋊C4×C79—21no—
239C4⋊C4×C79—21no—
240C4⋊C4×C79—21no—
241C4⋊C4×C79—21no—
242C22⋊C4×C79—22no—
243C22⋊C4×C79—41no—
244C22⋊C4×C79—42no—
245C22⋊C4×C79—42no—
246C22⋊C4×C79—42no—
247C22⋊C4×C79—42no—
248C22⋊C4×C79—42no—
249C22⋊C4×C79—81no—
250C22⋊C4×C79—81no—
251C42×C79—21no—
252C42×C79—21no—
253C42×C79—21no—
254C42×C79—21no—
255C23×C79—22no—
256C23×C79—21no—
257C23×C79—22no—
258C23×C79—22no—
259C23×C79—21no—
260C23×C79—21no—
261C23×C79—21no—
262C23×C79—21no—
263C23×C79—21no—
264C23×C79—22no—
265C23×C79—48no—
266C23×C79—48no—
267C23×C79—41no—
268C23×C79—41no—
269C23×C79—41no—
270C23×C79—41no—
271C23×C79—41no—
272C23×C79—41no—
273C23×C79—41no—
274C23×C79—41no—
275C23×C79—41no—
276C23×C79—41no—
277C23×C79—84no—
278C23×C79—84no—
279C23×C79—84no—
280C23×C79—84no—
281C23×C79—84no—
282C23×C79C4×D412yes—
283C23×C79C22×D411yescharacteristic
284C22×D79—22no—
285C22×D79—41no—
286C22×D79—41no—
287C22×D79—41no—
288C22×D79—41no—
289C22×D79—41no—
290C22×D79—41no—
291D4×C79—22no—
292D4×C79—22no—
293D4×C79—22no—
294D4×C79—22no—
295D4×C79—22no—
296D4×C79—48no—
297D4×C79—41no—
298D4×C79—41no—
299D4×C79C4×D414yes—
300C2×C4×C79—21no—
301C2×C4×C79—21no—
302C2×C4×C79—21no—
303C2×C4×C79—21no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—21no—
309C2×C4×C79—21no—
310C2×C4×C79—21no—
311C2×C4×C79—21no—
312C2×C4×C79—21no—
313C2×C4×C79—21no—
314C2×C4×C79—21no—
315C2×C4×C79—21no—
316C2×C4×C79—21no—
317C2×C4×C79—41no—
318C2×C4×C79—41no—
319C2×C4×C79—41no—
320C2×C4×C79—41no—
321C2×C4×C79—41no—
322C2×C4×C79—41no—
323C2×C4×C79—84no—
324C2×C4×C79—84no—
325C2×C4×C79C4×D412yes—
326C2×C4×C79AGL(1,ℤ/8)12yes—
327C2×C4×C79C23×C411yescharacteristic
328C2×C4×C79C22×D411yescharacteristic
329C2×C4×C79C2×#4111yescharacteristic
330C2×C4×C79C2×#4111yescharacteristic
331C2×C4×C79H(5,𝔽2)11yescharacteristic
332C2×C4×C79H(5,𝔽2)11yescharacteristic
333C22⋊D79—84no—
334C2×Dic79—22no—
335C2×Dic79—22no—
336C2×Dic79—41no—
337C2×Dic79—41no—
338C2×Dic79—41no—
339C2×Dic79—41no—
340C2×Dic79—41no—
341C2×Dic79—41no—
342C2×Dic79—41no—
343D316—22no—
344D316—22no—
345D316—41no—
346D316—41no—
347C4×D79—84no—
348C79⋊C8—22no—
349C79⋊C8—22no—
350C79⋊C8—22no—
351C79⋊C8—41no—
352C22×C79—22no—
353C22×C79—24no—
354C22×C79—22no—
355C22×C79—22no—
356C22×C79—42no—
357C22×C79—42no—
358C22×C79—41no—
359C22×C79—42no—
360C22×C79—42no—
361C22×C79—41no—
362C22×C79—42no—
363C22×C79—41no—
364C22×C79—41no—
365C22×C79—42no—
366C22×C79—42no—
367C22×C79—42no—
368C22×C79—42no—
369C22×C79—816no—
370C22×C79—81no—
371C22×C79—81no—
372C22×C79—81no—
373C22×C79—81no—
374C22×C79C2×C4×D411yescharacteristic
375C22×C79D4211yescharacteristic
376C22×C79#54611yescharacteristic
377C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C79#57511yescharacteristic
379C22×C79#57611yescharacteristic
380C22×C79#57611yescharacteristic
381C2×D79—42no—
382C2×D79—42no—
383C2×D79—42no—
384C2×D79—81no—
385C2×D79—81no—
386C2×D79—81no—
387C2×D79—81no—
388C4×C79—22no—
389C4×C79—22no—
390C4×C79—41no—
391C4×C79—41no—
392C4×C79—41no—
393C4×C79—81no—
394C4×C79—81no—
395C4×C79C2×C4×D411yescharacteristic
396C4×C79#51811yescharacteristic
397C4×C79#54611yescharacteristic
398C4×C79#55111yescharacteristic
399Dic79—42no—
400Dic79—42no—
401Dic79—81no—
402#22868—791nomaximal, Sylow
403C2×C79—42no—
404C2×C79—44no—
405C2×C79—82no—
406C2×C79#235811yescharacteristic
407C2×C79C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C79#294811yescharacteristic
409C2×C79#327311yescharacteristic
410C2×C79#327411yescharacteristic
411C2×C79#331811yescharacteristic
412C2×C79#331911yescharacteristic
413D79—82no—
414C2×#447—791no—
415C2×#442—791no—
416C2×#418—791no—
417#2363—791no—
418D4×C22⋊C4D7911yescharacteristic, complemented
419#1970—791no—
420#1936—791no—
421#1926—791no—
422#1895—791no—
423#1879—791no—
424#1879—791no—
425#1862—791no—
426#1854—791no—
427C4×#102—791no—
428#1753—791no—
429C79#2286811yescharacteristic, complemented, Sylow
430C23×D4C2×D7911yescharacteristic
431C22×D8—791no—
432C22×D8—791no—
433C22×M16—791no—
434C2×#121—791no—
435C2×C4×D4—791no—
436C2×C4×D4C2×D7911yescharacteristic
437C2×C4×D4C2×D7911yescharacteristic
438C2×#117—791no—
439C22×C22⋊C4—21no—
440#447—798no—
441#442—1584no—
442C2×#107—791no—
443C2×#106—791no—
444#418—1584no—
445C2×#102—791no—
446C2×#102—791no—
447C2×#102—791no—
448C2×#102—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×#102—791no—
453C2×C22⋊C8—791no—
454C2×#97—791no—
455C2×C4×C8—791no—
456#390—791no—
457#390—1581no—
458#390C2×D7911yescharacteristic
459#390C2×D7911yescharacteristic
460#389—791no—
461#388—1581no—
462#386—21no—
463#386—21no—
464#386—1581no—
465#380C2×D7911yescharacteristic
466#379—21no—
467C4×C4⋊C4—791no—
468C4×C22⋊C4—1581no—
469C4×C22⋊C4C2×D7911yescharacteristic
470#340—791no—
471#340—791no—
472#340—791no—
473#340—791no—
474#336—791no—
475#336—791no—
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—41no—
482C22×D4—41no—
483C22×D4—791no—
484C22×D4—1581no—
485C22×D4C4×D7914yescomplemented
486C22×D4C22×D7911yescharacteristic
487C22×D4C22×D7911yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—1581no—
491C23×C4C22×D7911yescharacteristic
492C2×D8—3161no—
493C2×D8—3161no—
494C2×D8—794no—
495C2×D8—794no—
496C2×D8—1582no—
497C2×D8—1582no—
498C2×M16—3161no—
499C2×M16—1582no—
500C2×M16—1582no—
501C22×C8—791no—
502C22×C8—791no—
503C22×C8—791no—
504C22×C8—791no—
505#121—794no—
506#121—1582no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—41no—
510C4×D4—41no—
511C4×D4—3161no—
512C4×D4—1582no—
513#117—3161no—
514#117—1582no—
515C2×C4⋊C4—791no—
516C2×C4⋊C4—791no—
517C2×C4⋊C4—791no—
518C2×C4⋊C4—1581no—
519C2×C4⋊C4C22×D7911yescharacteristic
520C2×C4⋊C4C22×D7911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—44no—
529C2×C22⋊C4—1581no—
530C2×C22⋊C4—1581no—
531C2×C22⋊C4—1581no—
532C2×C22⋊C4—1581no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4C22⋊D7911yescharacteristic
535C2×C22⋊C4C22⋊D7911yescharacteristic
536C2×C42—1581no—
537C2×C42—1581no—
538C2×C42C22×D7911yescharacteristic
539C2×C42C22×D7911yescharacteristic
540#107—3161no—
541#106—1582no—
542#102—3161no—
543#102—794no—
544#102—794no—
545#102—794no—
546#102—1582no—
547#102—1582no—
548#102—1582no—
549#102—1582no—
550C22⋊C8—794no—
551#97—1582no—
552C4×C8—3161no—
553#95—21no—
554#95—1581no—
555#95—1581no—
556#95C22⋊D7911yescharacteristic
557#95C22⋊D7911yescharacteristic
558C24—21no—
559C24—21no—
560C24—24no—
561C24—42no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—81no—
566C24—81no—
567C24—1581no—
568C24C2×C22⋊D7911yescharacteristic
569C2×D4—28no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—24no—
578C2×D4—21no—
579C2×D4—44no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—792no—
585C2×D4—6321no—
586C2×D4—6321no—
587C2×D4—1584no—
588C2×D4—1581no—
589C2×D4—1581no—
590C2×D4—1581no—
591C2×D4—1581no—
592C2×D4—1581no—
593C2×D4C2×C4×D7912yes—
594C2×D4C2×C4×D7912yes—
595C2×D4D4×D7912yes—
596C2×D4#1192962312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4—3162no—
610C22×C4—3162no—
611C22×C4—6321no—
612C22×C4—1581no—
613C22×C4—1581no—
614C22×C4—1581no—
615C22×C4C2×C4×D7912yes—
616C22×C4C2×C22⋊D7911yescharacteristic
617C22×C4C2×C22⋊D7911yescharacteristic
618C22×C4C2×C22⋊D7911yescharacteristic
619C22×C4C2×C22⋊D7911yescharacteristic
620C22×C4C2×C22⋊D7911yescharacteristic
621C22×C4#1192962412yes—
622C22×C4C23×D7911yescharacteristic
623D8—3164no—
624D8—1588no—
625M16—3164no—
626C2×C8—792no—
627C2×C8—792no—
628C2×C8—792no—
629C2×C8—1581no—
630C2×C8—1581no—
631C2×C8—1581no—
632C2×C8—1581no—
633C2×C8—1581no—
634C2×C8—1581no—
635C2×C8—1581no—
636C2×C8—1581no—
637C2×C8—1581no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—792no—
643C4⋊C4—792no—
644C4⋊C4—6321no—
645C4⋊C4—1581no—
646C4⋊C4—1581no—
647C4⋊C4—1581no—
648C4⋊C4—1581no—
649C22⋊C4—22no—
650C22⋊C4—41no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C22⋊C4—3162no—
659C22⋊C4—3162no—
660C22⋊C4—3162no—
661C22⋊C4—6321no—
662C22⋊C4—1584no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—3162no—
668C42—6321no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—48no—
680C23—48no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—84no—
692C23—84no—
693C23—84no—
694C23—84no—
695C23—84no—
696C23—3161no—
697C23—3161no—
698C23—3161no—
699C23—3161no—
700C23—3161no—
701C23—3161no—
702C23—1582no—
703C23C4×C22⋊D7912yes—
704C23C22×C22⋊D7911yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—3161no—
714D4—3161no—
715D4—6324no—
716D4—1582no—
717D4—1582no—
718D4(C22⋊D79)⋊C414yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—3161no—
745C2×C4—3161no—
746C2×C4—3161no—
747C2×C4—3161no—
748C2×C4—3161no—
749C2×C4—3161no—
750C2×C4—3161no—
751C2×C4—6324no—
752C2×C4—1582no—
753C2×C4—1582no—
754C2×C4C4×C22⋊D7912yes—
755C2×C4#1457918712yes—
756C2×C4C22×C4×D7911yescharacteristic
757C2×C4C2×D4×D7911yescharacteristic
758C2×C4C2×#1192962311yescharacteristic
759C2×C4C2×#1192962411yescharacteristic
760C2×C4#1457920611yescharacteristic
761C2×C4#1457920611yescharacteristic
762C8—3161no—
763C8—1582no—
764C8—1582no—
765C8—1582no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—24no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—816no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—3162no—
789C22—3162no—
790C22—3162no—
791C22—6321no—
792C22—6321no—
793C22—6321no—
794C22—6321no—
795C22C2×C4×C22⋊D7911yescharacteristic
796C22D4×C22⋊D7911yescharacteristic
797C22#1909920711yescharacteristic
798C22C2×#1457918711yescharacteristic
799C22#1909936111yescharacteristic
800C22#1909936611yescharacteristic
801C22#1909936611yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—81no—
808C4—81no—
809C4—3162no—
810C4—3162no—
811C4—6321no—
812C4C2×(C22⋊D79)⋊C411yescharacteristic
813C4#1909903611yescharacteristic
814C4#1909920311yescharacteristic
815C4#1909923911yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—6322no—
820C2#2376637911yescharacteristic
821C2C4×#1457918711yescharacteristic
822C2#2377225011yescharacteristic
823C2#2377500711yescharacteristic
824C2#2377501611yescharacteristic
825C2#2377554111yescharacteristic
826C2#2377555611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingD4×C22⋊C4×C79C2
socleC23×C79C22×D4
prime radicalC2×#19098697C2
cosocleC22×C4×C79C24
hypercenterD4×C22⋊C4D79
hypocenterC79#22868
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#19098673C2semidirect
3. C2×#19098568C2semidirect
4. #23766436C2semidirect
5. #23764265C2semidirect
6. #23764100C2semidirect
7. #23764024C2semidirect
8. #23763836C2semidirect
9. #23763751C2semidirect
10. #23763748C2semidirect
11. #23763647C2semidirect
12. #23763597C2semidirect
13. C4×#14579082C2semidirect
14. #23763184C2semidirect
15. D4×C22⋊C4×C79C2semidirect
20. C2×C4×D316C22semidirect
22. #19098697C4semidirect
24. C2×#14579094C22semidirect
25. C2×#14579092C22semidirect
33. C2×#14579081C22semidirect
34. C2×#14579081C22semidirect
36. C2×#14579072C22semidirect
37. C2×C4×C79⋊C8C22semidirect
38. #19098465C22semidirect
40. #19098461C22semidirect
43. C4×C4⋊Dic79C22semidirect
45. #19098325C22semidirect
46. #19098325C22semidirect
47. #19098325C22semidirect
48. #19098325C22semidirect
49. #19098318C22semidirect
50. #19098318C22semidirect
70. C2×#11929609C2×C4semidirect
79. #14579135C2×C4semidirect
100. #14579082C2×C4semidirect
101. #14579082C2×C4semidirect
102. #14579082D4semidirect
105. C22⋊(C79⋊C8)C2×C4semidirect
117. C22×D4×C79C2×C4semidirect
418. D4×C22⋊C4D79semidirect
429. C79#22868semidirect
485. C22×D4C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190986972
C2×#190986732
C2×#190985682
#237664362
#237642652
#237641002
#237640242
#237638362
#237637512
#237637482
#237636472
#237635972
C4×#145790822
#237631842
D4×C22⋊C4×C792
#2286879