Finite Group Databasebeta

← #34306453

Subgroups — #34306453

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×#19098605C211yesmaximal, characteristic, complemented
2C22×#14579095C211yesmaximal, characteristic, complemented
3#23766329C211yesmaximal, characteristic
4D4×C4⋊Dic79C211yesmaximal, characteristic
5#23764170C211yesmaximal, characteristic, complemented
6#23764159C211yesmaximal, characteristic, complemented
7#23763601C211yesmaximal, characteristic, complemented
8#23763595C211yesmaximal, characteristic, complemented
9#23763590C211yesmaximal, characteristic, complemented
10#23763590C211yesmaximal, characteristic, complemented
11#23763568C211yesmaximal, characteristic, complemented
12#23763433C211yesmaximal, characteristic, complemented
13#23763425C211yesmaximal, characteristic, complemented
14#23763297C211yesmaximal, characteristic, complemented
15C2×#435×C79C211yesmaximal, characteristic
16C2×D4×Dic79—21no—
17C2×#14579120C2211yescharacteristic
18C22×C4⋊Dic79C2211yescharacteristic
19C22×C4⋊Dic79C2211yescharacteristic
20C22×C4⋊Dic79C2211yescharacteristic
21#19098605—24no—
22C2×#14579095—24no—
23C2×#14579095C2211yescharacteristic
24C2×#14579095C2211yescharacteristic
25C2×#14579095C2211yescharacteristic
26C2×#14579095C2211yescharacteristic
27C2×#14579095C2211yescharacteristic
28C2×#14579095C2211yescharacteristic
29C2×#14579093C2211yescharacteristic
30C2×#14579093C2211yescharacteristic
31C2×#14579093C2211yescharacteristic
32C2×#14579093C2211yescharacteristic
33#19098462—21no—
34#19098456—21no—
35#19098449—21no—
36#19098443—21no—
37#19098438—21no—
38#19098438—21no—
39#19098433C2211yescharacteristic
40#19098429C2211yescharacteristic
41#19098423C2211yescharacteristic
42#19098423C2211yescharacteristic
43#19098423C2211yescharacteristic
44#19098423C2211yescharacteristic
45C4×C4⋊Dic79C2211yescharacteristic
46C4×C4⋊Dic79C2211yescharacteristic
47C22⋊C4×Dic79—21no—
48#19098326C2211yescharacteristic
49#19098326C2211yescharacteristic
50#19098326C2211yescharacteristic
51#19098326C2211yescharacteristic
52#19098326C2211yescharacteristic
53#19098326C2211yescharacteristic
54C22×M16×C79C2211yescharacteristic
55C23×C8×C79C2211yescharacteristic
56C2×C4×D4×C79C2211yescharacteristic
57#435×C79C418yescomplemented
58C2×C4⋊C8×C79C2211yescharacteristic
59C2×C22⋊C8×C79C2211yescharacteristic
60C2×C22⋊C8×C79C2211yescharacteristic
61C2×#97×C79C2211yescharacteristic
62C23×Dic79—21no—
63C23×Dic79—21no—
64C23×Dic79—21no—
65D4×Dic79—44no—
66#14579120—22no—
67#14579120—41no—
68C2×C4⋊Dic79—22no—
69C2×C4⋊Dic79—22no—
70C2×C4⋊Dic79—22no—
71C2×C4⋊Dic79—21no—
72C2×C4⋊Dic79—21no—
73C2×C4⋊Dic79—21no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79—21no—
76C2×C4⋊Dic79—41no—
77C2×C4⋊Dic79—41no—
78C2×C4⋊Dic79—41no—
79C2×C4⋊Dic79C2311yescharacteristic
80C2×C4⋊Dic79C2311yescharacteristic
81C2×C4⋊Dic79C2311yescharacteristic
82C2×C4⋊Dic79C2311yescharacteristic
83C2×C4⋊Dic79C2311yescharacteristic
84C2×C4⋊Dic79C2311yescharacteristic
85C2×C4⋊Dic79C2311yescharacteristic
86C2×C4⋊Dic79C2311yescharacteristic
87C2×C22⋊Dic79—21no—
88C2×C22⋊Dic79—21no—
89C2×C22⋊Dic79—21no—
90C2×C22⋊Dic79—21no—
91C2×C22⋊Dic79—21no—
92C2×C4×Dic79—21no—
93C2×C4×Dic79—21no—
94C2×C4×Dic79—21no—
95#14579095—22no—
96#14579095—22no—
97#14579095—22no—
98#14579095—22no—
99#14579095—41no—
100#14579095D414yescomplemented
101#14579093—22no—
102#14579093—22no—
103#14579093—22no—
104#14579093—41no—
105C79⋊#95—21no—
106C79⋊#95—21no—
107C79⋊#95—21no—
108C79⋊#95—21no—
109C79⋊#95—21no—
110C79⋊#95—21no—
111C79⋊#95—21no—
112C79⋊#95—21no—
113C22×D4×C79D411yescharacteristic
114C23×C4×C79C2311yescharacteristic
115C23×C4×C79C2311yescharacteristic
116C2×M16×C79—22no—
117C2×M16×C79—22no—
118C2×M16×C79C2×C414yescomplemented
119C22×C8×C79—22no—
120C22×C8×C79—22no—
121C22×C8×C79C2×C414yescomplemented
122C22×C8×C79C2311yescharacteristic
123C22×C8×C79C2311yescharacteristic
124C22×C8×C79C2311yescharacteristic
125C22×C8×C79C2311yescharacteristic
126C4×D4×C79C2×C414yes—
127C4×D4×C79Q814yes—
128C2×C4⋊C4×C79D411yescharacteristic
129C2×C22⋊C4×C79D411yescharacteristic
130C2×C22⋊C4×C79D411yescharacteristic
131C2×C42×C79C2311yescharacteristic
132C4⋊C8×C79C2×C414yescomplemented
133C22⋊C8×C79C2×C414yescomplemented
134C22⋊C8×C79C2×C414yescomplemented
135#97×C79C2×C414yescomplemented
136C22×Dic79—21no—
137C22×Dic79—21no—
138C22×Dic79—21no—
139C22×Dic79—21no—
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—42no—
149C22×Dic79—42no—
150C22×Dic79—81no—
151C22×Dic79—81no—
152C22×Dic79—81no—
153C4⋊Dic79—21no—
154C4⋊Dic79—21no—
155C4⋊Dic79—21no—
156C4⋊Dic79—21no—
157C4⋊Dic79—21no—
158C4⋊Dic79—21no—
159C4⋊Dic79—21no—
160C4⋊Dic79—21no—
161C4⋊Dic79—21no—
162C4⋊Dic79—21no—
163C4⋊Dic79—21no—
164C4⋊Dic79—21no—
165C4⋊Dic79—21no—
166C4⋊Dic79—21no—
167C4⋊Dic79—42no—
168C4⋊Dic79—42no—
169C4⋊Dic79—42no—
170C4⋊Dic79—42no—
171C4⋊Dic79—81no—
172C4⋊Dic79C2×D412yes—
173C4⋊Dic79C2×D412yes—
174C22⋊Dic79—42no—
175C22⋊Dic79—42no—
176C22⋊Dic79—42no—
177C22⋊Dic79—42no—
178C22⋊Dic79—81no—
179C4×Dic79—42no—
180C4×Dic79—42no—
181C4×Dic79—81no—
182C24×C79C2×D411yescharacteristic
183C24×C79C2×D411yescharacteristic
184C2×D4×C79—22no—
185C2×D4×C79—22no—
186C2×D4×C79C4⋊C414yes—
187C22×C4×C79—21no—
188C22×C4×C79—21no—
189C22×C4×C79—21no—
190C22×C4×C79—21no—
191C22×C4×C79—21no—
192C22×C4×C79—21no—
193C22×C4×C79—21no—
194C22×C4×C79—21no—
195C22×C4×C79C22×C412yes—
196C22×C4×C79C22×C412yes—
197C22×C4×C79C2×D411yescharacteristic
198C22×C4×C79C2×D411yescharacteristic
199C22×C4×C79C2×D411yescharacteristic
200C22×C4×C79C2×D411yescharacteristic
201C22×C4×C79C2×Q812yes—
202C22×C4×C79C2×Q812yes—
203C22×C4×C79C2411yescharacteristic
204M16×C79—28no—
205C2×C8×C79—28no—
206C2×C8×C79—21no—
207C2×C8×C79—21no—
208C2×C8×C79—21no—
209C2×C8×C79—21no—
210C2×C8×C79—21no—
211C2×C8×C79—21no—
212C2×C8×C79C22×C412yes—
213C2×C8×C79C22×C412yes—
214C2×C8×C79C22×C412yes—
215C2×C8×C79C22×C412yes—
216C2×C8×C79C2×D412yes—
217C2×C8×C79#4112yes—
218C4⋊C4×C79C4⋊C414yes—
219C22⋊C4×C79C4⋊C414yes—
220C22⋊C4×C79C4⋊C414yes—
221C42×C79C22×C412yes—
222C42×C79C2×Q812yes—
223C23×C79—21no—
224C23×C79—21no—
225C23×C79—21no—
226C23×C79—21no—
227C23×C79—21no—
228C23×C79—21no—
229C23×C79—21no—
230C23×C79—21no—
231C23×C79—21no—
232C23×C79—21no—
233C23×C79C2×C4⋊C412yes—
234C23×C79C2×C4⋊C412yes—
235C23×C79AGL(1,ℤ/8)12yes—
236C23×C79#13712yes—
237C23×C79C22×D411yescharacteristic
238D4×C79—28no—
239C2×C4×C79—21no—
240C2×C4×C79—21no—
241C2×C4×C79—21no—
242C2×C4×C79—21no—
243C2×C4×C79—21no—
244C2×C4×C79—21no—
245C2×C4×C79—21no—
246C2×C4×C79—21no—
247C2×C4×C79—22no—
248C2×C4×C79—22no—
249C2×C4×C79—22no—
250C2×C4×C79—22no—
251C2×C4×C79—22no—
252C2×C4×C79—22no—
253C2×C4×C79—22no—
254C2×C4×C79—22no—
255C2×C4×C79C2×C4⋊C412yes—
256C2×C4×C79C2×C4⋊C412yes—
257C2×C4×C79C2×C4⋊C412yes—
258C2×C4×C79C2×C4⋊C412yes—
259C2×C4×C79C23×C411yescharacteristic
260C2×C4×C79C22×D411yescharacteristic
261C2×C4×C79C22×Q811yescharacteristic
262C2×C4×C79C2×#4111yescharacteristic
263C2×C4×C79H(5,𝔽2)11yescharacteristic
264C2×C4×C792−1+411yescharacteristic
265C2×Dic79—22no—
266C2×Dic79—22no—
267C2×Dic79—41no—
268C2×Dic79—41no—
269C2×Dic79—41no—
270C2×Dic79—41no—
271C2×Dic79—41no—
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—41no—
283C2×Dic79—41no—
284C2×Dic79—41no—
285C2×Dic79—41no—
286C2×Dic79—41no—
287C2×Dic79—41no—
288C2×Dic79—41no—
289C2×Dic79—84no—
290C2×Dic79—84no—
291C2×Dic79—84no—
292C8×C79—22no—
293C8×C79—22no—
294C8×C79—22no—
295C8×C79C4×D414yescomplemented
296C22×C79—22no—
297C22×C79—22no—
298C22×C79—22no—
299C22×C79—22no—
300C22×C79—22no—
301C22×C79—22no—
302C22×C79—22no—
303C22×C79—22no—
304C22×C79—22no—
305C22×C79—41no—
306C22×C79—41no—
307C22×C79—41no—
308C22×C79—41no—
309C22×C79#42814yescomplemented
310C22×C79C22×C4⋊C411yescharacteristic
311C22×C79D4211yescharacteristic
312C22×C79#54711yescharacteristic
313C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C79C2×#13711yescharacteristic
315C22×C79#57611yescharacteristic
316C22×C79#57811yescharacteristic
317C4×C79—22no—
318C4×C79—22no—
319C4×C79—22no—
320C4×C79—22no—
321C4×C79C2×C4×D411yescharacteristic
322C4×C79#52011yescharacteristic
323C4×C79D4×Q811yescharacteristic
324C4×C79#55411yescharacteristic
325Dic79—42no—
326Dic79—42no—
327Dic79—81no—
328Dic79—81no—
329Dic79—81no—
330Dic79—81no—
331Dic79—81no—
332Dic79—81no—
333#22661—791nomaximal, Sylow
334C2×C79—24no—
335C2×C79—42no—
336C2×C79D4×C4⋊C411yescharacteristic
337C2×C79C2×#42811yescharacteristic
338C2×C79#291311yescharacteristic
339C2×C79#326411yescharacteristic
340C2×C79#327011yescharacteristic
341C2×C79#334311yescharacteristic
342C2×C79#334611yescharacteristic
343C2×#435D7911yescharacteristic
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#1807—791no—
357#1776—791no—
358C79#2266111yescharacteristic, complemented, Sylow
359C22×M16C2×D7911yescharacteristic
360C23×C8C2×D7911yescharacteristic
361C2×C4×D4—1581no—
362C2×C4×D4C2×D7911yescharacteristic
363C2×#117—791no—
364C22×C4⋊C4—791no—
365C22×C4⋊C4—791no—
366C22×C4⋊C4—791no—
367#435Dic7918yescomplemented
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×#106—791no—
379C2×#106—791no—
380C2×C4⋊C8C2×D7911yescharacteristic
381C2×C22⋊C8C2×D7911yescharacteristic
382C2×C22⋊C8C2×D7911yescharacteristic
383C2×#97C2×D7911yescharacteristic
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#380—791no—
395#380—791no—
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#340—791no—
404#340—791no—
405C22×D4D31611yescharacteristic
406C23×C4—1581no—
407C23×C4—1581no—
408C23×C4—1581no—
409C23×C4C22×D7911yescharacteristic
410C23×C4C22×D7911yescharacteristic
411C2×M16—22no—
412C2×M16—22no—
413C2×M16C2×Dic7914yescomplemented
414C22×C8—22no—
415C22×C8—22no—
416C22×C8C2×Dic7914yescomplemented
417C22×C8C22×D7911yescharacteristic
418C22×C8C22×D7911yescharacteristic
419C22×C8C22×D7911yescharacteristic
420C22×C8C22×D7911yescharacteristic
421C4×D4—3164no—
422C4×D4Dic15814yes—
423C4×D4C2×Dic7914yes—
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—791no—
435C2×C4⋊C4—791no—
436C2×C4⋊C4—791no—
437C2×C4⋊C4—1581no—
438C2×C4⋊C4—1581no—
439C2×C4⋊C4—1581no—
440C2×C4⋊C4—1581no—
441C2×C4⋊C4—1582no—
442C2×C4⋊C4—1582no—
443C2×C4⋊C4—1582no—
444C2×C4⋊C4—1581no—
445C2×C4⋊C4D31611yescharacteristic
446C2×C22⋊C4—1581no—
447C2×C22⋊C4—1581no—
448C2×C22⋊C4—1581no—
449C2×C22⋊C4—1581no—
450C2×C22⋊C4—1581no—
451C2×C22⋊C4D31611yescharacteristic
452C2×C22⋊C4D31611yescharacteristic
453C2×C42—1581no—
454C2×C42—1581no—
455C2×C42—1581no—
456C2×C42C22×D7911yescharacteristic
457#107—3161no—
458#107—794no—
459#107—1582no—
460#107—1582no—
461#107—1582no—
462#107—1582no—
463#106—3161no—
464#106—1582no—
465#106—1582no—
466#106—1582no—
467C4⋊C8C2×Dic7914yescomplemented
468C22⋊C8C2×Dic7914yescomplemented
469C22⋊C8C2×Dic7914yescomplemented
470#97C2×Dic7914yescomplemented
471#95—1581no—
472#95—1581no—
473#95—1581no—
474#95—1581no—
475#95—1581no—
476#95—1581no—
477#95—1581no—
478#95—1581no—
479C24C2×D31611yescharacteristic
480C24C2×D31611yescharacteristic
481C2×D4—22no—
482C2×D4—22no—
483C2×D4C4⋊Dic7914yes—
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—6321no—
499C22×C4—6321no—
500C22×C4—6321no—
501C22×C4—1581no—
502C22×C4—1581no—
503C22×C4—1581no—
504C22×C4—1581no—
505C22×C4—1581no—
506C22×C4—1581no—
507C22×C4—1581no—
508C22×C4—1581no—
509C22×C4C22×Dic7912yes—
510C22×C4C22×Dic7912yes—
511C22×C4C2×D31611yescharacteristic
512C22×C4C2×D31611yescharacteristic
513C22×C4C2×D31611yescharacteristic
514C22×C4C2×D31611yescharacteristic
515C22×C4C2×Dic15812yes—
516C22×C4C2×Dic15812yes—
517C22×C4C23×D7911yescharacteristic
518M16—28no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—28no—
526C2×C8C22×Dic7912yes—
527C2×C8C22×Dic7912yes—
528C2×C8C22×Dic7912yes—
529C2×C8C22×Dic7912yes—
530C2×C8D4×D7912yes—
531C2×C8#1192962312yes—
532C4⋊C4—3162no—
533C4⋊C4—3162no—
534C4⋊C4—3162no—
535C4⋊C4—3162no—
536C4⋊C4—792no—
537C4⋊C4—792no—
538C4⋊C4—6321no—
539C4⋊C4—1581no—
540C4⋊C4—1581no—
541C4⋊C4—1581no—
542C4⋊C4—1581no—
543C4⋊C4—1581no—
544C4⋊C4—1581no—
545C4⋊C4—1581no—
546C4⋊C4—1581no—
547C4⋊C4—1581no—
548C4⋊C4—1581no—
549C4⋊C4—1581no—
550C4⋊C4—1581no—
551C4⋊C4—1581no—
552C4⋊C4—1581no—
553C4⋊C4C4⋊Dic7914yes—
554C22⋊C4—3162no—
555C22⋊C4—3162no—
556C22⋊C4—3162no—
557C22⋊C4—3162no—
558C22⋊C4—6321no—
559C22⋊C4C4⋊Dic7914yes—
560C22⋊C4C4⋊Dic7914yes—
561C42—3162no—
562C42—3162no—
563C42—6321no—
564C42C22×Dic7912yes—
565C42C2×Dic15812yes—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C4⋊Dic7912yes—
577C23C2×C4⋊Dic7912yes—
578C23#1457918912yes—
579C23#1457919412yes—
580C23C22×D31611yescharacteristic
581D4—28no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—3161no—
599C2×C4—3161no—
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—3161no—
611C2×C4—3161no—
612C2×C4—3161no—
613C2×C4—3161no—
614C2×C4—3161no—
615C2×C4—3161no—
616C2×C4—3161no—
617C2×C4—3161no—
618C2×C4—3161no—
619C2×C4—3161no—
620C2×C4—6324no—
621C2×C4—6324no—
622C2×C4—6324no—
623C2×C4—1582no—
624C2×C4—1582no—
625C2×C4C2×C4⋊Dic7912yes—
626C2×C4C2×C4⋊Dic7912yes—
627C2×C4C2×C4⋊Dic7912yes—
628C2×C4C2×C4⋊Dic7912yes—
629C2×C4C23×Dic7911yescharacteristic
630C2×C4C2×D4×D7911yescharacteristic
631C2×C4C22×Dic15811yescharacteristic
632C2×C4C2×#1192962311yescharacteristic
633C2×C4#1457920711yescharacteristic
634C2×C4#1457920811yescharacteristic
635C8—22no—
636C8—22no—
637C8—22no—
638C8D4×Dic7914yescomplemented
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22#1909860514yescomplemented
653C22C22×C4⋊Dic7911yescharacteristic
654C22D4×D31611yescharacteristic
655C22#1909921711yescharacteristic
656C22C2×#1457918911yescharacteristic
657C22C2×#1457919411yescharacteristic
658C22#1909936811yescharacteristic
659C22#1909938011yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—22no—
664C4—3162no—
665C4—3162no—
666C4—6321no—
667C4—6321no—
668C4—6321no—
669C4—6321no—
670C4—6321no—
671C4—6321no—
672C4C2×D4×Dic7911yescharacteristic
673C4#1909904611yescharacteristic
674C4D4×Dic15811yescharacteristic
675C4#1909927011yescharacteristic
676C2—24no—
677C2—42no—
678C2D4×C4⋊Dic7911yescharacteristic
679C2C2×#1909860511yescharacteristic
680C2#2377200011yescharacteristic
681C2#2377488511yescharacteristic
682C2#2377497511yescharacteristic
683C2#2377584211yescharacteristic
684C2#2377588711yescharacteristic
subgroupG/H
centerC23C22×D316
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC2×#435×C79C2
socleC23×C79C22×D4
prime radicalC22×D4×C79D4
cosocleC22×C4×C79C24
hypercenterC2×#435D79
hypocenterC79#22661
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#19098605C2semidirect
2. C22×#14579095C2semidirect
5. #23764170C2semidirect
6. #23764159C2semidirect
7. #23763601C2semidirect
8. #23763595C2semidirect
9. #23763590C2semidirect
10. #23763590C2semidirect
11. #23763568C2semidirect
12. #23763433C2semidirect
13. #23763425C2semidirect
14. #23763297C2semidirect
57. #435×C79C4semidirect
100. #14579095D4semidirect
118. C2×M16×C79C2×C4semidirect
121. C22×C8×C79C2×C4semidirect
132. C4⋊C8×C79C2×C4semidirect
133. C22⋊C8×C79C2×C4semidirect
134. C22⋊C8×C79C2×C4semidirect
135. #97×C79C2×C4semidirect
295. C8×C79C4×D4semidirect
309. C22×C79#428semidirect
358. C79#22661semidirect
367. #435Dic79semidirect
413. C2×M16C2×Dic79semidirect
416. C22×C8C2×Dic79semidirect
467. C4⋊C8C2×Dic79semidirect
468. C22⋊C8C2×Dic79semidirect
469. C22⋊C8C2×Dic79semidirect
470. #97C2×Dic79semidirect
638. C8D4×Dic79semidirect
652. C22#19098605semidirect

Maximal subgroups

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

subgroupindex
C2×#190986052
C22×#145790952
#237663292
D4×C4⋊Dic792
#237641702
#237641592
#237636012
#237635952
#237635902
#237635682
#237634332
#237634252
#237632972
C2×#435×C792
#2266179