Finite Group Databasebeta

← #34308767

Subgroups — #34308767

Order 20224.

1398 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098696C211yesmaximal, characteristic
2C2×C4×#11929609C211yesmaximal, characteristic, complemented
3C22×#14579081C211yesmaximal, characteristic, complemented
4C22⋊C4×D316C211yesmaximal, characteristic, complemented
5#23764265C211yesmaximal, characteristic, complemented
6#23764082C211yesmaximal, characteristic, complemented
7#23764020C211yesmaximal, characteristic, complemented
8#23763829C211yesmaximal, characteristic, complemented
9#23763751C211yesmaximal, characteristic, complemented
10#23763748C211yesmaximal, characteristic, complemented
11#23763646C211yesmaximal, characteristic, complemented
12#23763588C211yesmaximal, characteristic, complemented
13C4×#14579081C211yesmaximal, characteristic, complemented
14C22⋊C4×C79⋊C8C211yesmaximal, characteristic, complemented
15C79×#2361C211yesmaximal, characteristic, complemented
16C23×D316C2211yescharacteristic
17C22×#11929609C2211yescharacteristic
18C22×#11929609C2211yescharacteristic
19C23×C79⋊C8C2211yescharacteristic
20C2×C4×D316C2211yescharacteristic
21C2×C4×D316C2211yescharacteristic
22C2×C22⋊C4×D79—21no—
23#19098696C418yescomplemented
24C4×#11929609—24no—
25C2×#14579094C2211yescharacteristic, complemented
26C2×#14579094C2211yescharacteristic, complemented
27C2×#14579082C2211yescharacteristic, complemented
28C2×#14579082C2211yescharacteristic, complemented
29C2×#14579081—24no—
30C2×#14579081C2211yescharacteristic
31C2×#14579081C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37C2×C4×C79⋊C8C2211yescharacteristic, complemented
38C2×C4×C79⋊C8C2211yescharacteristic, complemented
39#19098465C2211yescharacteristic
40#19098465C2211yescharacteristic
41#19098441—21no—
42#19098441—21no—
43#19098423C2211yescharacteristic
44#19098418—21no—
45#19098325C2211yescharacteristic, complemented
46#19098325C2211yescharacteristic, complemented
47#19098325C2211yescharacteristic, complemented
48#19098325C2211yescharacteristic, complemented
49#19098318C2211yescharacteristic, complemented
50#19098318C2211yescharacteristic, complemented
51C2×#121×C79C2211yescharacteristic
52C2×C4×D4×C79—21no—
53C2×C4×D4×C79C2211yescharacteristic, complemented
54C22×C4⋊C4×C79C2211yescharacteristic
55#390×C79C2211yescharacteristic, complemented
56#389×C79C2211yescharacteristic, complemented
57#388×C79—21no—
58#386×C79—21no—
59#385×C79—21no—
60C4×C4⋊C4×C79C2211yescharacteristic, complemented
61C4×C22⋊C4×C79C2211yescharacteristic
62C24×D79—21no—
63C22×D316—22no—
64C22×D316—22no—
65C22×D316—21no—
66C22×D316—22no—
67C22×D316—41no—
68C22×D316—41no—
69C22×D316C2×C414yescomplemented
70C22×D316C2311yescharacteristic
71C22×D316C2311yescharacteristic
72C22×C4×D79—21no—
73C22×C4×D79—21no—
74C2×#11929609—22no—
75C2×#11929609—22no—
76C2×#11929609—41no—
77C2×#11929609—41no—
78C2×#11929609C2×C414yescomplemented
79C2×#11929609C2×C414yescomplemented
80C22×C79⋊C8—22no—
81C22×C79⋊C8—22no—
82C22×C79⋊C8—41no—
83C22×C79⋊C8C2311yescharacteristic
84C22×C79⋊C8C2311yescharacteristic
85C22×C79⋊C8C2311yescharacteristic
86C22×C79⋊C8C2311yescharacteristic
87C4×D316—22no—
88C4×D316—22no—
89C4×D316—41no—
90C4×D316—41no—
91C2×C4⋊Dic79C2311yescharacteristic
92C2×C4⋊Dic79C2311yescharacteristic
93C2×C22⋊Dic79—21no—
94C2×(C2×D79)⋊C4—21no—
95C2×(C2×D79)⋊C4—21no—
96C2×(C2×D79)⋊C4—21no—
97C2×(C2×D79)⋊C4—21no—
98C2×(C2×D79)⋊C4—21no—
99C2×(C2×D79)⋊C4—21no—
100C22⋊C4×D79—44no—
101#14579094—22no—
102#14579094—41no—
103#14579082—22no—
104#14579082—41no—
105#14579081—22no—
106#14579081—22no—
107#14579081—22no—
108#14579081C2×C414yescomplemented
109#14579081C2×C414yescomplemented
110#14579081D414yescomplemented
111C22⋊(C79⋊C8)C2×C414yescomplemented
112C4×C79⋊C8—22no—
113C4×C79⋊C8—41no—
114C79⋊#95—21no—
115C22×D4×C79—21no—
116C22×D4×C79C2311yescharacteristic
117C23×C4×C79—21no—
118C23×C4×C79—21no—
119C23×C4×C79C2311yescharacteristic
120#121×C79—22no—
121#121×C79C2×C414yescomplemented
122C4×D4×C79—22no—
123C4×D4×C79—41no—
124C4×D4×C79—44no—
125C2×C4⋊C4×C79—22no—
126C2×C4⋊C4×C79—21no—
127C2×C4⋊C4×C79—21no—
128C2×C4⋊C4×C79—41no—
129C2×C4⋊C4×C79C2311yescharacteristic
130C2×C4⋊C4×C79C2311yescharacteristic
131C2×C4⋊C4×C79C2311yescharacteristic
132C2×C22⋊C4×C79—21no—
133C2×C22⋊C4×C79—21no—
134C2×C22⋊C4×C79—21no—
135C2×C22⋊C4×C79—21no—
136C2×C22⋊C4×C79D411yescharacteristic
137C2×C22⋊C4×C79D411yescharacteristic
138C2×C42×C79—21no—
139C2×C42×C79C2311yescharacteristic
140C2×C42×C79C2311yescharacteristic
141#95×C79—21no—
142#95×C79—21no—
143#95×C79D411yescharacteristic
144#95×C79D411yescharacteristic
145C23×D79—21no—
146C23×D79—21no—
147C23×D79—24no—
148C23×D79—42no—
149C23×D79—42no—
150C23×D79—42no—
151C23×D79—42no—
152C23×D79—81no—
153C23×D79—81no—
154C2×D316—28no—
155C2×D316—24no—
156C2×D316—21no—
157C2×D316—21no—
158C2×D316—21no—
159C2×D316—21no—
160C2×D316—21no—
161C2×D316—21no—
162C2×D316—21no—
163C2×D316—21no—
164C2×D316—42no—
165C2×D316—42no—
166C2×D316—44no—
167C2×D316—44no—
168C2×D316—44no—
169C2×D316C22×C412yes—
170C2×D316C22×C412yes—
171C2×D316C2×D412yes—
172C2×D316#4112yes—
173C22×Dic79—21no—
174C22×Dic79—21no—
175C2×C4×D79—42no—
176C2×C4×D79—42no—
177C2×C4×D79—42no—
178C2×C4×D79—42no—
179C2×C4×D79—81no—
180C2×C4×D79—81no—
181#11929609—28no—
182#11929609—44no—
183C2×C79⋊C8—21no—
184C2×C79⋊C8—21no—
185C2×C79⋊C8—21no—
186C2×C79⋊C8—21no—
187C2×C79⋊C8—21no—
188C2×C79⋊C8—21no—
189C2×C79⋊C8—21no—
190C2×C79⋊C8—21no—
191C2×C79⋊C8—21no—
192C2×C79⋊C8—44no—
193C2×C79⋊C8C22×C412yes—
194C2×C79⋊C8C22×C412yes—
195C2×C79⋊C8C2×D412yes—
196C4⋊Dic79—21no—
197C4⋊Dic79—21no—
198C4⋊Dic79—21no—
199C4⋊Dic79—21no—
200C22⋊Dic79—42no—
201(C2×D79)⋊C4—42no—
202(C2×D79)⋊C4—42no—
203(C2×D79)⋊C4—42no—
204(C2×D79)⋊C4—42no—
205(C2×D79)⋊C4—81no—
206(C2×D79)⋊C4—81no—
207C24×C79—21no—
208C24×C79C2×D411yescharacteristic
209C2×D4×C79—24no—
210C2×D4×C79—21no—
211C2×D4×C79—21no—
212C2×D4×C79—21no—
213C2×D4×C79—21no—
214C2×D4×C79—21no—
215C2×D4×C79—42no—
216C2×D4×C79—42no—
217C2×D4×C79C22×C412yes—
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—21no—
225C22×C4×C79—42no—
226C22×C4×C79—42no—
227C22×C4×C79—42no—
228C22×C4×C79—42no—
229C22×C4×C79—81no—
230C22×C4×C79—81no—
231C22×C4×C79C22×C412yes—
232C22×C4×C79C2×D411yescharacteristic
233C22×C4×C79C2×D411yescharacteristic
234C22×C4×C79C2×D411yescharacteristic
235C22×C4×C79C2×D411yescharacteristic
236C22×C4×C79C2×D411yescharacteristic
237C22×C4×C79#4112yes—
238C22×C4×C79C2411yescharacteristic
239C4⋊C4×C79—21no—
240C4⋊C4×C79—21no—
241C4⋊C4×C79—21no—
242C4⋊C4×C79—21no—
243C4⋊C4×C79—42no—
244C4⋊C4×C79—42no—
245C4⋊C4×C79C22×C412yes—
246C4⋊C4×C79C2×D412yes—
247C22⋊C4×C79—22no—
248C22⋊C4×C79—24no—
249C22⋊C4×C79—42no—
250C22⋊C4×C79—42no—
251C22⋊C4×C79—81no—
252C22⋊C4×C79D814yescomplemented
253C42×C79—21no—
254C42×C79—21no—
255C42×C79—21no—
256C42×C79—21no—
257C42×C79—42no—
258C23×C79—21no—
259C23×C79—21no—
260C23×C79—21no—
261C23×C79—21no—
262C23×C79—22no—
263C23×C79—41no—
264C23×C79—41no—
265C23×C79—41no—
266C23×C79—41no—
267C23×C79—41no—
268C23×C79—41no—
269C23×C79C4×D412yes—
270C23×C79C2×D812yes—
271C23×C79#13512yes—
272C23×C79C22×D411yescharacteristic
273C22×D79—22no—
274C22×D79—22no—
275C22×D79—22no—
276C22×D79—22no—
277C22×D79—48no—
278C22×D79—41no—
279C22×D79—41no—
280C22×D79—41no—
281C22×D79—41no—
282C22×D79—41no—
283C22×D79—41no—
284C22×D79—41no—
285C22×D79—41no—
286C22×D79—41no—
287C22×D79—41no—
288C22×D79—48no—
289C22×D79—84no—
290C22×D79—84no—
291C22×D79—84no—
292C22×D79—84no—
293C22×D79—84no—
294D4×C79—22no—
295D4×C79—22no—
296D4×C79—48no—
297D4×C79—41no—
298D4×C79—41no—
299C2×C4×C79—21no—
300C2×C4×C79—21no—
301C2×C4×C79—21no—
302C2×C4×C79—21no—
303C2×C4×C79—21no—
304C2×C4×C79—21no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—21no—
311C2×C4×C79—22no—
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—41no—
324C2×C4×C79—84no—
325C2×C4×C79—84no—
326C2×C4×C79C4×D412yes—
327C2×C4×C79C2×D812yes—
328C2×C4×C79C2×D812yes—
329C2×C4×C79C23×C411yescharacteristic
330C2×C4×C79C22×D411yescharacteristic
331C2×C4×C79C2×#4111yescharacteristic
332C2×C4×C79C2×#4111yescharacteristic
333C2×C4×C79H(5,𝔽2)11yescharacteristic
334C2×C4×C79H(5,𝔽2)11yescharacteristic
335C2×Dic79—41no—
336C2×Dic79—41no—
337C2×Dic79—41no—
338C2×Dic79—41no—
339C2×Dic79—41no—
340C2×Dic79—41no—
341D316—22no—
342D316—22no—
343D316—22no—
344D316—22no—
345D316—22no—
346D316—48no—
347D316—41no—
348D316—41no—
349D316C4×D414yescomplemented
350C4×D79—84no—
351C4×D79—84no—
352C79⋊C8—22no—
353C79⋊C8—22no—
354C79⋊C8—22no—
355C79⋊C8—41no—
356C22×C79—22no—
357C22×C79—22no—
358C22×C79—22no—
359C22×C79—22no—
360C22×C79—22no—
361C22×C79—22no—
362C22×C79—42no—
363C22×C79—42no—
364C22×C79—42no—
365C22×C79—81no—
366C22×C79—81no—
367C22×C79—81no—
368C22×C79—81no—
369C22×C79C4×D814yescomplemented
370C22×C79C2×C4×D411yescharacteristic
371C22×C79D4211yescharacteristic
372C22×C79#54611yescharacteristic
373C22×C79C22×D811yescharacteristic
374C22×C79C2×#13511yescharacteristic
375C22×C79#57611yescharacteristic
376C22×C79#57711yescharacteristic
377C2×D79—24no—
378C2×D79—42no—
379C2×D79—42no—
380C2×D79—42no—
381C2×D79—42no—
382C2×D79—42no—
383C2×D79—42no—
384C2×D79—42no—
385C2×D79—42no—
386C2×D79—42no—
387C2×D79—816no—
388C2×D79—81no—
389C2×D79—81no—
390C2×D79—81no—
391C2×D79—81no—
392C4×C79—22no—
393C4×C79—22no—
394C4×C79—22no—
395C4×C79—42no—
396C4×C79—42no—
397C4×C79—41no—
398C4×C79—41no—
399C4×C79—81no—
400C4×C79C2×C4×D411yescharacteristic
401C4×C79#51811yescharacteristic
402C4×C79#54611yescharacteristic
403C4×C79#55111yescharacteristic
404Dic79—81no—
405Dic79—81no—
406#22870—791nomaximal, Sylow
407C2×C79—24no—
408C2×C79—82no—
409C2×C79#235811yescharacteristic
410C2×C79C2×C4×D811yescharacteristic
411C2×C79#294611yescharacteristic
412C2×C79D4×D811yescharacteristic
413C2×C79#328211yescharacteristic
414C2×C79#329411yescharacteristic
415C2×C79#329711yescharacteristic
416D79—44no—
417D79—82no—
418C2×#447—791no—
419C2×C4×D8—791no—
420C22×#102—791no—
421#2361D7911yescharacteristic, complemented
422D4×C22⋊C4—791no—
423#1970—791no—
424#1934—791no—
425#1925—791no—
426#1893—791no—
427#1879—791no—
428#1879—791no—
429#1862—791no—
430#1852—791no—
431C4×#102—791no—
432C8×C22⋊C4—791no—
433C79#2287011yescharacteristic, complemented, Sylow
434C23×D4—791no—
435C22×D8—791no—
436C22×D8—791no—
437C23×C8—791no—
438C2×#121C2×D7911yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4—791no—
441C2×C4×D4—791no—
442C2×C4×D4C2×D7911yescharacteristic, complemented
443C22×C4⋊C4C2×D7911yescharacteristic
444C22×C22⋊C4—1581no—
445#447—798no—
446C4×D8—1584no—
447C2×#107—791no—
448C2×#107—791no—
449C2×#102—791no—
450C2×#102—791no—
451C2×#102—791no—
452C2×#102—791no—
453C2×#102—791no—
454C2×#102—791no—
455C2×#102—791no—
456C2×#102—791no—
457C2×#102—1584no—
458C2×C22⋊C8—791no—
459C2×C4×C8—791no—
460C2×C4×C8—791no—
461#390—791no—
462#390—791no—
463#390C2×D7911yescharacteristic, complemented
464#389C2×D7911yescharacteristic, complemented
465#388—21no—
466#386—21no—
467#386—1581no—
468#386—1581no—
469#385—21no—
470#380—791no—
471#379—1581no—
472C4×C4⋊C4C2×D7911yescharacteristic, complemented
473C4×C22⋊C4C2×D7911yescharacteristic
474#340—791no—
475#340—791no—
476#340—791no—
477#340—791no—
478#336—791no—
479#336—791no—
480C25—1581no—
481C22×D4—21no—
482C22×D4—3161no—
483C22×D4—3161no—
484C22×D4—794no—
485C22×D4—791no—
486C22×D4—791no—
487C22×D4—1582no—
488C22×D4—1582no—
489C22×D4—1581no—
490C22×D4—1582no—
491C22×D4C22×D7911yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1581no—
495C23×C4—1581no—
496C23×C4C22×D7911yescharacteristic
497C2×D8—3161no—
498C2×D8—3161no—
499C2×D8—794no—
500C2×D8—794no—
501C2×D8—1582no—
502C2×D8—1582no—
503C22×C8—3161no—
504C22×C8—791no—
505C22×C8—791no—
506C22×C8—791no—
507C22×C8—791no—
508C22×C8—1582no—
509C22×C8—1582no—
510#121—22no—
511#121C4×D7914yescomplemented
512C4×D4—22no—
513C4×D4—41no—
514C4×D4—44no—
515C4×D4—3161no—
516C4×D4—3161no—
517C4×D4—1582no—
518C4×D4—1582no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—791no—
524C2×C4⋊C4—791no—
525C2×C4⋊C4C22×D7911yescharacteristic
526C2×C4⋊C4C22×D7911yescharacteristic
527C2×C4⋊C4C22×D7911yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—3164no—
533C2×C22⋊C4—1581no—
534C2×C22⋊C4—1581no—
535C2×C22⋊C4—1581no—
536C2×C22⋊C4—1581no—
537C2×C22⋊C4—1581no—
538C2×C22⋊C4—1581no—
539C2×C22⋊C4—1581no—
540C2×C22⋊C4C22⋊D7911yescharacteristic
541C2×C22⋊C4C22⋊D7911yescharacteristic
542C2×C42—21no—
543C2×C42C22×D7911yescharacteristic
544C2×C42C22×D7911yescharacteristic
545#107—3161no—
546#107—1582no—
547#102—3161no—
548#102—794no—
549#102—794no—
550#102—794no—
551#102—1582no—
552#102—1582no—
553#102—1582no—
554#102—1582no—
555C22⋊C8—794no—
556C4×C8—3161no—
557C4×C8—1582no—
558#95—21no—
559#95—21no—
560#95—1581no—
561#95C22⋊D7911yescharacteristic
562#95C22⋊D7911yescharacteristic
563C24—21no—
564C24—3162no—
565C24—3162no—
566C24—3162no—
567C24—3162no—
568C24—6321no—
569C24—6321no—
570C24—1581no—
571C24—1584no—
572C24—1581no—
573C24C2×C22⋊D7911yescharacteristic
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—3162no—
583C2×D4—3162no—
584C2×D4—3164no—
585C2×D4—3164no—
586C2×D4—3164no—
587C2×D4—792no—
588C2×D4—792no—
589C2×D4—792no—
590C2×D4—792no—
591C2×D4—1588no—
592C2×D4—1581no—
593C2×D4—1581no—
594C2×D4—1581no—
595C2×D4—1581no—
596C2×D4—1581no—
597C2×D4—1581no—
598C2×D4—1581no—
599C2×D4—1584no—
600C2×D4—1581no—
601C2×D4C2×C4×D7912yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—3162no—
616C22×C4—3162no—
617C22×C4—3162no—
618C22×C4—3162no—
619C22×C4—6321no—
620C22×C4—6321no—
621C22×C4—1581no—
622C22×C4—1581no—
623C22×C4C2×C4×D7912yes—
624C22×C4C2×C22⋊D7911yescharacteristic
625C22×C4C2×C22⋊D7911yescharacteristic
626C22×C4C2×C22⋊D7911yescharacteristic
627C22×C4C2×C22⋊D7911yescharacteristic
628C22×C4C2×C22⋊D7911yescharacteristic
629C22×C4#1192962412yes—
630C22×C4C23×D7911yescharacteristic
631D8—3164no—
632D8—1588no—
633C2×C8—3164no—
634C2×C8—792no—
635C2×C8—792no—
636C2×C8—792no—
637C2×C8—1581no—
638C2×C8—1581no—
639C2×C8—1581no—
640C2×C8—1581no—
641C2×C8—1581no—
642C2×C8—1581no—
643C2×C8—1581no—
644C2×C8—1581no—
645C2×C8—1581no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—1581no—
653C4⋊C4—1581no—
654C4⋊C4—1581no—
655C4⋊C4—1581no—
656C4⋊C4C2×C4×D7912yes—
657C4⋊C4D4×D7912yes—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—81no—
663C22⋊C4—3162no—
664C22⋊C4—3162no—
665C22⋊C4—3162no—
666C22⋊C4—3162no—
667C22⋊C4—3162no—
668C22⋊C4—6321no—
669C22⋊C4—6321no—
670C22⋊C4#1192960914yescomplemented
671C42—21no—
672C42—21no—
673C42—21no—
674C42—21no—
675C42—42no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—22no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—3168no—
688C23—3161no—
689C23—3161no—
690C23—3161no—
691C23—3161no—
692C23—3168no—
693C23—3161no—
694C23—3161no—
695C23—3161no—
696C23—3161no—
697C23—3161no—
698C23—3161no—
699C23—6324no—
700C23—6324no—
701C23—6324no—
702C23—6324no—
703C23—6324no—
704C23—1582no—
705C23—1582no—
706C23—1582no—
707C23—1582no—
708C23C4×C22⋊D7912yes—
709C23C2×#1192960912yes—
710C23#1457918112yes—
711C23C22×C22⋊D7911yescharacteristic
712D4—22no—
713D4—22no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—3168no—
718D4—3161no—
719D4—3161no—
720D4—794no—
721D4—1582no—
722D4—1582no—
723D4—1582no—
724D4—1582no—
725D4—1582no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—3161no—
754C2×C4—3161no—
755C2×C4—3161no—
756C2×C4—3161no—
757C2×C4—3161no—
758C2×C4—3161no—
759C2×C4—6324no—
760C2×C4—6324no—
761C2×C4C4×C22⋊D7912yes—
762C2×C4C2×#1192960912yes—
763C2×C4C2×#1192960912yes—
764C2×C4C22×C4×D7911yescharacteristic
765C2×C4C2×D4×D7911yescharacteristic
766C2×C4#41×D7911yescharacteristic
767C2×C4C2×#1192962411yescharacteristic
768C2×C4#1457920611yescharacteristic
769C2×C4#1457920711yescharacteristic
770C8—3161no—
771C8—1582no—
772C8—1582no—
773C8—1582no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—3162no—
788C22—3162no—
789C22—3162no—
790C22—3162no—
791C22—3162no—
792C22—3162no—
793C22—3162no—
794C22—3162no—
795C22—3162no—
796C22—63216no—
797C22—6321no—
798C22—6321no—
799C22—6321no—
800C22—6321no—
801C22—1584no—
802C22C4×#1192960914yescomplemented
803C22C2×C4×C22⋊D7911yescharacteristic
804C22D4×C22⋊D7911yescharacteristic
805C22#1909920111yescharacteristic
806C22C22×#1192960911yescharacteristic
807C22C2×#1457918111yescharacteristic
808C22#1909936611yescharacteristic
809C22#1909937111yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—41no—
814C4—42no—
815C4—41no—
816C4—42no—
817C4—81no—
818C4—6321no—
819C4—6321no—
820C4C4×D4×D7911yescharacteristic
821C4#1909903511yescharacteristic
822C4#1909920911yescharacteristic
823C4#1909924211yescharacteristic
824C2—24no—
825C2—82no—
826C2—3164no—
827C2—6322no—
828C2#2376637711yescharacteristic
829C2C2×C4×#1192960911yescharacteristic
830C2#2377222811yescharacteristic
831C2D4×#1192960911yescharacteristic
832C2#2377510811yescharacteristic
833C2#2377520711yescharacteristic
834C2#2377524411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2361C2
socleC23×C79C22×D4
prime radicalC2×#19098696C2
cosocleC22×C4×C79C24
hypercenter#2361D79
hypocenterC79#22870
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11929609C2semidirect
3. C22×#14579081C2semidirect
4. C22⋊C4×D316C2semidirect
5. #23764265C2semidirect
6. #23764082C2semidirect
7. #23764020C2semidirect
8. #23763829C2semidirect
9. #23763751C2semidirect
10. #23763748C2semidirect
11. #23763646C2semidirect
12. #23763588C2semidirect
13. C4×#14579081C2semidirect
14. C22⋊C4×C79⋊C8C2semidirect
15. C79×#2361C2semidirect
23. #19098696C4semidirect
25. C2×#14579094C22semidirect
26. C2×#14579094C22semidirect
27. C2×#14579082C22semidirect
28. C2×#14579082C22semidirect
37. C2×C4×C79⋊C8C22semidirect
38. C2×C4×C79⋊C8C22semidirect
45. #19098325C22semidirect
46. #19098325C22semidirect
47. #19098325C22semidirect
48. #19098325C22semidirect
49. #19098318C22semidirect
50. #19098318C22semidirect
53. C2×C4×D4×C79C22semidirect
55. #390×C79C22semidirect
56. #389×C79C22semidirect
60. C4×C4⋊C4×C79C22semidirect
69. C22×D316C2×C4semidirect
78. C2×#11929609C2×C4semidirect
79. C2×#11929609C2×C4semidirect
108. #14579081C2×C4semidirect
109. #14579081C2×C4semidirect
110. #14579081D4semidirect
111. C22⋊(C79⋊C8)C2×C4semidirect
121. #121×C79C2×C4semidirect
252. C22⋊C4×C79D8semidirect
349. D316C4×D4semidirect
369. C22×C79C4×D8semidirect
421. #2361D79semidirect
433. C79#22870semidirect
442. C2×C4×D4C2×D79semidirect
463. #390C2×D79semidirect
464. #389C2×D79semidirect
472. C4×C4⋊C4C2×D79semidirect
511. #121C4×D79semidirect
670. C22⋊C4#11929609semidirect
802. C22C4×#11929609semidirect

Maximal subgroups

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

subgroupindex
C2×#190986962
C2×C4×#119296092
C22×#145790812
C22⋊C4×D3162
#237642652
#237640822
#237640202
#237638292
#237637512
#237637482
#237636462
#237635882
C4×#145790812
C22⋊C4×C79⋊C82
C79×#23612
#2287079