Finite Group Databasebeta

← #34345581

Subgroups — #34345581

Order 20224.

1004 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098848C211yesmaximal, characteristic, complemented
2C2×#19098564C211yesmaximal, characteristic
3#23767102C211yesmaximal, characteristic, complemented
4#23764933C211yesmaximal, characteristic, complemented
5#23764788C211yesmaximal, characteristic, complemented
6#23764774C211yesmaximal, characteristic, complemented
7#23764536C211yesmaximal, characteristic, complemented
8#23763668C211yesmaximal, characteristic, complemented
9#23763654C211yesmaximal, characteristic, complemented
10#23763592C211yesmaximal, characteristic, complemented
11#23763585C211yesmaximal, characteristic, complemented
12#23763431C211yesmaximal, characteristic, complemented
13#23763405C211yesmaximal, characteristic, complemented
14#23763340C211yesmaximal, characteristic
15C79×#2341C211yesmaximal, characteristic
16C22×#11929608C2211yescharacteristic
17C2×#14579161C2211yescharacteristic
18C2×#14579138—21no—
19C22×C4⋊Dic79C2211yescharacteristic
20#19098848—24no—
21C2×#14579094C2211yescharacteristic
22C2×#14579092C2211yescharacteristic
23C2×#14579092C2211yescharacteristic
24C2×#14579092C2211yescharacteristic
25C2×C4⋊(C79⋊C8)C2211yescharacteristic
26C2×C4⋊(C79⋊C8)C2211yescharacteristic
27#19098564—24no—
28C2×#14579085C2211yescharacteristic
29C2×#14579085C2211yescharacteristic
30C2×#14579085C2211yescharacteristic
31C2×#14579085C2211yescharacteristic
32C2×#14579082C2211yescharacteristic
33C2×#14579082C2211yescharacteristic
34C2×#14579082C2211yescharacteristic
35C2×#14579082C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37#19098495—21no—
38#19098484—21no—
39#19098461C2211yescharacteristic
40#19098461C2211yescharacteristic
41#19098438—21no—
42#19098433C2211yescharacteristic
43#19098423C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098318C2211yescharacteristic
49#19098318C2211yescharacteristic
50C22×#41×C79C2211yescharacteristic
51C2×C4×Q8×C79C2211yescharacteristic
52C2×C4×Q8×C79C2211yescharacteristic
53#390×C79—21no—
54#390×C79—21no—
55#390×C79C2211yescharacteristic
56#390×C79C2211yescharacteristic
57#380×C79—21no—
58#380×C79C2211yescharacteristic
59C4×C22⋊C4×C79—21no—
60C4×C22⋊C4×C79C2211yescharacteristic
61C22×Dic158—21no—
62C23×Dic79—21no—
63C2×#11929608—22no—
64C2×#11929608—22no—
65C2×#11929608—41no—
66C22×C79⋊C8C2311yescharacteristic
67C22×C79⋊C8C2311yescharacteristic
68C22×C79⋊C8C2311yescharacteristic
69C22×C79⋊C8C2311yescharacteristic
70#14579161—22no—
71#14579161—41no—
72#14579138—44no—
73C2×C4⋊Dic79—22no—
74C2×C4⋊Dic79—21no—
75C2×C4⋊Dic79—21no—
76C2×C4⋊Dic79—21no—
77C2×C4⋊Dic79—21no—
78C2×C4⋊Dic79—41no—
79C2×C4⋊Dic79C2311yescharacteristic
80C2×C4⋊Dic79C2311yescharacteristic
81C2×C4⋊Dic79C2311yescharacteristic
82C2×C4⋊Dic79C2311yescharacteristic
83C2×Dic79⋊C4—21no—
84C2×Dic79⋊C4—21no—
85C2×C22⋊Dic79—21no—
86#14579094—41no—
87#14579092—22no—
88#14579092—22no—
89#14579092—41no—
90C4⋊(C79⋊C8)—22no—
91C4⋊(C79⋊C8)—41no—
92#14579085—22no—
93#14579085—22no—
94#14579085—22no—
95#14579085D414yes—
96#14579082—22no—
97#14579082—22no—
98#14579082—41no—
99#14579082—41no—
100C22⋊(C79⋊C8)—22no—
101C79⋊#95—21no—
102C79⋊#95—21no—
103C79⋊#95—21no—
104C2×#41×C79—22no—
105C2×#41×C79—22no—
106C2×#41×C79—22no—
107C2×#41×C79—41no—
108C2×#41×C79—41no—
109C2×#41×C79Q814yescomplemented
110C22×Q8×C79C2311yescharacteristic
111C22×D4×C79—21no—
112C22×D4×C79C2311yescharacteristic
113C23×C4×C79—21no—
114C23×C4×C79C2311yescharacteristic
115C4×Q8×C79—22no—
116C4×Q8×C79—22no—
117C4×Q8×C79—41no—
118C4×Q8×C79—41no—
119C2×C4⋊C4×C79—21no—
120C2×C4⋊C4×C79—21no—
121C2×C4⋊C4×C79C2311yescharacteristic
122C2×C4⋊C4×C79C2311yescharacteristic
123C2×C22⋊C4×C79—21no—
124C2×C22⋊C4×C79—21no—
125C2×C22⋊C4×C79—21no—
126C2×C22⋊C4×C79—21no—
127C2×C22⋊C4×C79—21no—
128C2×C22⋊C4×C79D411yescharacteristic
129C2×C22⋊C4×C79D411yescharacteristic
130C2×C42×C79—21no—
131C2×C42×C79—21no—
132C2×C42×C79C2311yescharacteristic
133C2×C42×C79C2311yescharacteristic
134#95×C79—21no—
135#95×C79D411yescharacteristic
136#95×C79D411yescharacteristic
137C2×Dic158—42no—
138C2×Dic158—42no—
139C2×Dic158—81no—
140C22×Dic79—21no—
141C22×Dic79—21no—
142C22×Dic79—21no—
143C22×Dic79—21no—
144C22×Dic79—42no—
145C22×Dic79—42no—
146C22×Dic79—81no—
147#11929608—44no—
148C2×C79⋊C8—21no—
149C2×C79⋊C8—21no—
150C2×C79⋊C8—21no—
151C2×C79⋊C8—21no—
152C2×C79⋊C8—21no—
153C2×C79⋊C8—21no—
154C2×C79⋊C8—21no—
155C2×C79⋊C8—21no—
156C2×C79⋊C8—21no—
157C2×C79⋊C8—21no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8C2×D412yes—
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—81no—
171C4⋊Dic79C2×D412yes—
172Dic79⋊C4—42no—
173Dic79⋊C4—42no—
174C22⋊Dic79—42no—
175C24×C79—21no—
176C24×C79C2×D411yescharacteristic
177#41×C79—28no—
178#41×C79—44no—
179#41×C79—44no—
180#41×C79—44no—
181C2×Q8×C79—21no—
182C2×Q8×C79—21no—
183C2×Q8×C79—21no—
184C2×Q8×C79C2×D412yes—
185C2×Q8×C79C2×Q812yes—
186C2×Q8×C79#4112yes—
187C2×D4×C79—24no—
188C2×D4×C79—21no—
189C2×D4×C79—21no—
190C2×D4×C79—21no—
191C2×D4×C79—21no—
192C2×D4×C79—21no—
193C2×D4×C79—42no—
194C2×D4×C79—42no—
195C2×D4×C79C2×Q812yes—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—24no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—42no—
205C22×C4×C79—42no—
206C22×C4×C79C2×D411yescharacteristic
207C22×C4×C79C2×D411yescharacteristic
208C22×C4×C79C2×D411yescharacteristic
209C22×C4×C79C2×D411yescharacteristic
210C22×C4×C79C2×D411yescharacteristic
211C22×C4×C79C2×Q812yes—
212C22×C4×C79#4112yes—
213C22×C4×C79C2411yescharacteristic
214C4⋊C4×C79—21no—
215C4⋊C4×C79—21no—
216C4⋊C4×C79—21no—
217C4⋊C4×C79—21no—
218C4⋊C4×C79—42no—
219C4⋊C4×C79—42no—
220C22⋊C4×C79—22no—
221C22⋊C4×C79—22no—
222C22⋊C4×C79—42no—
223C22⋊C4×C79—42no—
224C22⋊C4×C79—81no—
225C22⋊C4×C79—81no—
226C22⋊C4×C79—81no—
227C42×C79—21no—
228C42×C79—21no—
229C42×C79—21no—
230C42×C79—21no—
231C42×C79—42no—
232C42×C79—42no—
233C23×C79—21no—
234C23×C79—21no—
235C23×C79—21no—
236C23×C79—21no—
237C23×C79—21no—
238C23×C79—21no—
239C23×C79—22no—
240C23×C79—41no—
241C23×C79—41no—
242C23×C79—41no—
243C23×C79—41no—
244C23×C79—41no—
245C23×C79—41no—
246C23×C79C22⋊Q812yes—
247C23×C79C22×D411yescharacteristic
248Q8×C79—22no—
249Q8×C79—22no—
250Q8×C79—22no—
251Q8×C79C22⋊Q814yescomplemented
252D4×C79—22no—
253D4×C79—22no—
254D4×C79—48no—
255D4×C79—41no—
256D4×C79—41no—
257C2×C4×C79—22no—
258C2×C4×C79—21no—
259C2×C4×C79—21no—
260C2×C4×C79—22no—
261C2×C4×C79—21no—
262C2×C4×C79—22no—
263C2×C4×C79—21no—
264C2×C4×C79—21no—
265C2×C4×C79—21no—
266C2×C4×C79—22no—
267C2×C4×C79—22no—
268C2×C4×C79—22no—
269C2×C4×C79—22no—
270C2×C4×C79—21no—
271C2×C4×C79—21no—
272C2×C4×C79—21no—
273C2×C4×C79—21no—
274C2×C4×C79—21no—
275C2×C4×C79—21no—
276C2×C4×C79—48no—
277C2×C4×C79—41no—
278C2×C4×C79—41no—
279C2×C4×C79—41no—
280C2×C4×C79—41no—
281C2×C4×C79—41no—
282C2×C4×C79—41no—
283C2×C4×C79C22⋊Q812yes—
284C2×C4×C79AGL(1,ℤ/8)12yes—
285C2×C4×C79#13712yes—
286C2×C4×C79C22×D411yescharacteristic
287C2×C4×C79C22×Q811yescharacteristic
288C2×C4×C79C2×#4111yescharacteristic
289C2×C4×C79C2×#4111yescharacteristic
290C2×C4×C79H(5,𝔽2)11yescharacteristic
291C2×C4×C79H(5,𝔽2)11yescharacteristic
292C2×Dic79—22no—
293C2×Dic79—41no—
294C2×Dic79—41no—
295C2×Dic79—41no—
296C2×Dic79—41no—
297C2×Dic79—41no—
298C2×Dic79—41no—
299C2×Dic79—41no—
300C2×Dic79—41no—
301C2×Dic79—41no—
302C2×Dic79—41no—
303C2×Dic79—41no—
304C2×Dic79—84no—
305Dic158—84no—
306C79⋊C8—22no—
307C79⋊C8—41no—
308C79⋊C8—41no—
309C79⋊C8—41no—
310C22×C79—22no—
311C22×C79—22no—
312C22×C79—22no—
313C22×C79—41no—
314C22×C79—41no—
315C22×C79—41no—
316C22×C79—41no—
317C22×C79—42no—
318C22×C79—42no—
319C22×C79—42no—
320C22×C79—81no—
321C22×C79—81no—
322C22×C79—81no—
323C22×C79—81no—
324C22×C79C2×C22⋊Q811yescharacteristic
325C22×C79D4211yescharacteristic
326C22×C79#54611yescharacteristic
327C22×C79C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C79C2×#13711yescharacteristic
329C22×C79#57711yescharacteristic
330C22×C79#57711yescharacteristic
331C4×C79—22no—
332C4×C79—24no—
333C4×C79—22no—
334C4×C79—22no—
335C4×C79—41no—
336C4×C79—41no—
337C4×C79—81no—
338C4×C79—81no—
339C4×C79C2×C22⋊Q811yescharacteristic
340C4×C79#54311yescharacteristic
341C4×C79#54611yescharacteristic
342C4×C79#55111yescharacteristic
343Dic79—42no—
344Dic79—81no—
345Dic79—81no—
346Dic79—81no—
347#25967—791nomaximal, Sylow
348C2×C79—42no—
349C2×C79—82no—
350C2×C79#243711yescharacteristic
351C2×C79#307911yescharacteristic
352C2×C79#308411yescharacteristic
353C2×C79#326511yescharacteristic
354C2×C79#327811yescharacteristic
355C2×C79#331611yescharacteristic
356C2×C79#333211yescharacteristic
357C2×#475—791no—
358C2×#417—791no—
359#2440—791no—
360#2341D7911yescharacteristic
361#2094—791no—
362#2067—791no—
363#2065—791no—
364#2023—791no—
365#1865—791no—
366#1863—791no—
367#1853—791no—
368#1851—791no—
369#1809—791no—
370#1803—791no—
371#1788—791no—
372C79#2596711yescharacteristic, complemented, Sylow
373C22×#41C2×D7911yescharacteristic
374C22×M16—791no—
375C2×C4⋊Q8—791no—
376C2×C22⋊Q8—1581no—
377C2×C4×Q8C2×D7911yescharacteristic
378C2×C4×Q8C2×D7911yescharacteristic
379C22×C4⋊C4—791no—
380#475—1584no—
381C2×#107—791no—
382C2×#106—791no—
383C2×#106—791no—
384C2×#106—791no—
385C2×C4⋊C8—791no—
386C2×C4⋊C8—791no—
387#417—1584no—
388C2×#103—791no—
389C2×#103—791no—
390C2×#103—791no—
391C2×#103—791no—
392C2×#102—791no—
393C2×#102—791no—
394C2×#102—791no—
395C2×#102—791no—
396C2×C22⋊C8—791no—
397#398—1581no—
398#395—1581no—
399#390—21no—
400#390—21no—
401#390C2×D7911yescharacteristic
402#390C2×D7911yescharacteristic
403#389—791no—
404#389—791no—
405#385—1581no—
406#384—791no—
407#380—21no—
408#380—791no—
409#380C2×D7911yescharacteristic
410C4×C22⋊C4—21no—
411C4×C22⋊C4C2×D7911yescharacteristic
412#340—791no—
413#340—791no—
414#340—791no—
415#340—791no—
416#336—791no—
417#336—791no—
418C2×#41—22no—
419C2×#41—22no—
420C2×#41—22no—
421C2×#41—41no—
422C2×#41—41no—
423C2×#41Dic15814yescomplemented
424C22×Q8—1581no—
425C22×Q8C22×D7911yescharacteristic
426C22×D4—21no—
427C22×D4C22×D7911yescharacteristic
428C23×C4—21no—
429C23×C4—1581no—
430C23×C4C22×D7911yescharacteristic
431C2×M16—3161no—
432C2×M16—1582no—
433C2×M16—1582no—
434C22×C8—791no—
435C22×C8—791no—
436C22×C8—791no—
437C22×C8—791no—
438C4⋊Q8—3161no—
439C4⋊Q8—1582no—
440C22⋊Q8—3164no—
441C4×Q8—22no—
442C4×Q8—22no—
443C4×Q8—41no—
444C4×Q8—41no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—3161no—
448C2×C4⋊C4—791no—
449C2×C4⋊C4—791no—
450C2×C4⋊C4—791no—
451C2×C4⋊C4—791no—
452C2×C4⋊C4—1581no—
453C2×C4⋊C4—1581no—
454C2×C4⋊C4—1581no—
455C2×C4⋊C4—1581no—
456C2×C4⋊C4—1581no—
457C2×C4⋊C4—1582no—
458C2×C4⋊C4—1581no—
459C2×C4⋊C4C22×D7911yescharacteristic
460C2×C4⋊C4C22×D7911yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—1581no—
467C2×C22⋊C4C22⋊D7911yescharacteristic
468C2×C22⋊C4C22⋊D7911yescharacteristic
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C22×D7911yescharacteristic
472C2×C42C22×D7911yescharacteristic
473#107—3161no—
474#106—3161no—
475#106—1582no—
476#106—1582no—
477C4⋊C8—3161no—
478C4⋊C8—1582no—
479#103—794no—
480#103—1582no—
481#103—1582no—
482#103—1582no—
483#102—3161no—
484#102—3161no—
485#102—1582no—
486#102—1582no—
487C22⋊C8—1582no—
488#95—21no—
489#95—1581no—
490#95—1581no—
491#95—1581no—
492#95C22⋊D7911yescharacteristic
493#95C22⋊D7911yescharacteristic
494C24—21no—
495C24C2×C22⋊D7911yescharacteristic
496#41—28no—
497#41—44no—
498#41—44no—
499#41—44no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—3162no—
504C2×Q8—3162no—
505C2×Q8—6321no—
506C2×Q8D4×D7912yes—
507C2×Q8C2×Dic15812yes—
508C2×Q8#1192962312yes—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4C2×Dic15812yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—3162no—
529C22×C4—3162no—
530C22×C4—6321no—
531C22×C4—1581no—
532C22×C4—1581no—
533C22×C4—1581no—
534C22×C4—1581no—
535C22×C4C2×C22⋊D7911yescharacteristic
536C22×C4C2×C22⋊D7911yescharacteristic
537C22×C4C2×C22⋊D7911yescharacteristic
538C22×C4C2×C22⋊D7911yescharacteristic
539C22×C4C2×C22⋊D7911yescharacteristic
540C22×C4C2×Dic15812yes—
541C22×C4#1192962412yes—
542C22×C4C23×D7911yescharacteristic
543M16—3164no—
544C2×C8—792no—
545C2×C8—1581no—
546C2×C8—1581no—
547C2×C8—1581no—
548C2×C8—1581no—
549C2×C8—1581no—
550C2×C8—1581no—
551C2×C8—1581no—
552C2×C8—1581no—
553C2×C8—1581no—
554C2×C8—1581no—
555C2×C8—1581no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—3162no—
563C4⋊C4—3162no—
564C4⋊C4—3162no—
565C4⋊C4—3162no—
566C4⋊C4—3162no—
567C4⋊C4—792no—
568C4⋊C4—6321no—
569C4⋊C4—1581no—
570C4⋊C4—1581no—
571C4⋊C4—1581no—
572C4⋊C4—1581no—
573C4⋊C4—1581no—
574C4⋊C4—1581no—
575C4⋊C4—1581no—
576C22⋊C4—22no—
577C22⋊C4—22no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—3162no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—42no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23#1457914012yes—
604C23C22×C22⋊D7911yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—6324no—
609Q8#1457913814yescomplemented
610D4—22no—
611D4—22no—
612D4—48no—
613D4—41no—
614D4—41no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—3161no—
642C2×C4—3161no—
643C2×C4—3161no—
644C2×C4—3161no—
645C2×C4—3161no—
646C2×C4—3161no—
647C2×C4—3161no—
648C2×C4—3161no—
649C2×C4—3161no—
650C2×C4—3161no—
651C2×C4—3161no—
652C2×C4—6324no—
653C2×C4—1582no—
654C2×C4#1457914012yes—
655C2×C4#1457918612yes—
656C2×C4#1457919112yes—
657C2×C4C2×D4×D7911yescharacteristic
658C2×C4C22×Dic15811yescharacteristic
659C2×C4C2×#1192962311yescharacteristic
660C2×C4C2×#1192962411yescharacteristic
661C2×C4#1457920611yescharacteristic
662C2×C4#1457920611yescharacteristic
663C8—3161no—
664C8—3161no—
665C8—3161no—
666C8—1582no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#1457914011yescharacteristic
682C22D4×C22⋊D7911yescharacteristic
683C22#1909920711yescharacteristic
684C22C2×#1457918611yescharacteristic
685C22C2×#1457919111yescharacteristic
686C22#1909937111yescharacteristic
687C22#1909937411yescharacteristic
688C4—22no—
689C4—24no—
690C4—22no—
691C4—22no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—3162no—
697C4—6321no—
698C4—6321no—
699C4—6321no—
700C4C2×#1457913811yescharacteristic
701C4#1909918911yescharacteristic
702C4#1909920311yescharacteristic
703C4#1909923911yescharacteristic
704C2—42no—
705C2—82no—
706C2#2376706111yescharacteristic
707C2#2377321511yescharacteristic
708C2#2377326211yescharacteristic
709C2#2377489611yescharacteristic
710C2#2377506611yescharacteristic
711C2#2377551111yescharacteristic
712C2#2377572711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutator, cosocleC22×C4×C79C24
FrattiniC22×C4C23×D79
FittingC79×#2341C2
socleC23×C79C22×D4
prime radicalC22×#41×C79C22
hypercenter#2341D79
hypocenterC79#25967
LCSG ▷ C22×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C2×#19098848C2semidirect
3. #23767102C2semidirect
4. #23764933C2semidirect
5. #23764788C2semidirect
6. #23764774C2semidirect
7. #23764536C2semidirect
8. #23763668C2semidirect
9. #23763654C2semidirect
10. #23763592C2semidirect
11. #23763585C2semidirect
12. #23763431C2semidirect
13. #23763405C2semidirect
109. C2×#41×C79Q8semidirect
251. Q8×C79C22⋊Q8semidirect
372. C79#25967semidirect
423. C2×#41Dic158semidirect
609. Q8#14579138semidirect

Maximal subgroups

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

subgroupindex
C2×#190988482
C2×#190985642
#237671022
#237649332
#237647882
#237647742
#237645362
#237636682
#237636542
#237635922
#237635852
#237634312
#237634052
#237633402
C79×#23412
#2596779