Finite Group Databasebeta

← #34305633

Subgroups — #34305633

Order 20224.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772058C211yesmaximal, characteristic, complemented
2#23771917C211yesmaximal, characteristic
3#23771850C211yesmaximal, characteristic
4#23764112C211yesmaximal, characteristic, complemented
5#23764105C211yesmaximal, characteristic, complemented
6#23764046C211yesmaximal, characteristic, complemented
7#23764046C211yesmaximal, characteristic, complemented
8#23763676C211yesmaximal, characteristic, complemented
9#23763676C211yesmaximal, characteristic, complemented
10#23763440C211yesmaximal, characteristic, complemented
11#23763345C211yesmaximal, characteristic
12#23763241C211yesmaximal, characteristic, complemented
13#23763234C211yesmaximal, characteristic, complemented
14#23763184C211yesmaximal, characteristic, complemented
15C79×#1826C211yesmaximal, characteristic, complemented
16C22×#11929624C2211yescharacteristic
17C2×#14579169C2211yescharacteristic
18C2×#14579169C2211yescharacteristic
19C22×#11929608C2211yescharacteristic
20#19098624—21no—
21#19098624—21no—
22#19098620—21no—
23#19098616—21no—
24C2×#14579096C2211yescharacteristic, complemented
25C2×#14579096C2211yescharacteristic, complemented
26#19098590C2211yescharacteristic, complemented
27#19098590C2211yescharacteristic, complemented
28C2×#14579089C2211yescharacteristic
29C2×#14579089C2211yescharacteristic
30C2×#14579089C2211yescharacteristic
31C2×#14579089C2211yescharacteristic
32#19098571C411yescharacteristic, complemented
33#19098571C411yescharacteristic, complemented
34#19098567C411yescharacteristic, complemented
35#19098567C411yescharacteristic, complemented
36#19098562C411yescharacteristic, complemented
37#19098562C411yescharacteristic, complemented
38#19098562C411yescharacteristic, complemented
39#19098562C411yescharacteristic, complemented
40#19098557C2211yescharacteristic
41#19098557C2211yescharacteristic
42#19098557C2211yescharacteristic
43#19098557C2211yescharacteristic
44#19098531C2211yescharacteristic
45#19098531C2211yescharacteristic
46#19098528—21no—
47#19098528—21no—
48#19098527C2211yescharacteristic
49#19098525—21no—
50C2×C22⋊(C79⋊C8)C2211yescharacteristic
51C22⋊C8×D79—21no—
52#19098519C2211yescharacteristic, complemented
53#19098519C2211yescharacteristic, complemented
54C2×#14579072C2211yescharacteristic, complemented
55C2×C4×C79⋊C8C2211yescharacteristic, complemented
56#19098327C2211yescharacteristic, complemented
57#19098327C2211yescharacteristic, complemented
58#19098318C2211yescharacteristic, complemented
59#19098318C2211yescharacteristic, complemented
60C2×#117×C79C2211yescharacteristic
61#407×C79C2211yescharacteristic
62C4×C22⋊C4×C79C2211yescharacteristic
63#339×C79C2211yescharacteristic, complemented
64#339×C79C2211yescharacteristic, complemented
65#339×C79C2211yescharacteristic, complemented
66#339×C79C2211yescharacteristic, complemented
67C2×#11929624—21no—
68C2×#11929624—21no—
69C2×#11929624—22no—
70C2×#11929624—22no—
71C2×#11929624—41no—
72C2×#11929624—41no—
73C2×#11929624C2×C411yescharacteristic
74C2×#11929624C2×C411yescharacteristic
75C2×#11929624C2311yescharacteristic
76C2×#11929624C2311yescharacteristic
77C22×Dic158C2×C411yescharacteristic
78C22×D316C2×C411yescharacteristic
79C22×C22⋊D79—21no—
80C22×C4×D79—21no—
81#14579169—22no—
82#14579169—22no—
83#14579169—41no—
84#14579169—41no—
85C2×#11929608—41no—
86C2×#11929608—41no—
87C2×#11929608C2×C411yescharacteristic
88C2×#11929608C2×C411yescharacteristic
89C2×#11929608C2×C411yescharacteristic
90C2×#11929608C2×C411yescharacteristic
91C2×#11929608C2311yescharacteristic
92C2×#11929608C2311yescharacteristic
93C2×#11929607—21no—
94C2×#11929607—21no—
95C22×C79⋊C8C2311yescharacteristic
96C22×C79⋊C8C2311yescharacteristic
97C22×C79⋊C8C2311yescharacteristic
98C22×C79⋊C8C2311yescharacteristic
99C2×C8×D79—21no—
100C2×C8×D79—21no—
101#14579096—41no—
102#14579096—41no—
103C4⋊(C79⋊C8)—21no—
104C4⋊(C79⋊C8)—21no—
105C4⋊(C79⋊C8)—21no—
106C4⋊(C79⋊C8)—21no—
107#14579089—22no—
108#14579089—22no—
109#14579089—41no—
110#14579089—41no—
111#14579084C2×C411yescharacteristic
112#14579084C2×C411yescharacteristic
113#14579084C2×C411yescharacteristic
114#14579084C2×C411yescharacteristic
115#14579084C2×C411yescharacteristic
116#14579084C2×C411yescharacteristic
117#14579084C2×C411yescharacteristic
118#14579084C2×C411yescharacteristic
119#14579081C2×C411yescharacteristic
120#14579081C2×C411yescharacteristic
121#14579081C2×C411yescharacteristic
122#14579081C2×C411yescharacteristic
123#14579081C2×C411yescharacteristic
124#14579081C2×C411yescharacteristic
125#14579081C2×C411yescharacteristic
126#14579081C2×C411yescharacteristic
127C22⋊(C79⋊C8)—21no—
128C22⋊(C79⋊C8)—21no—
129C22⋊(C79⋊C8)D411yescharacteristic
130C22⋊(C79⋊C8)D411yescharacteristic
131C22⋊(C79⋊C8)D411yescharacteristic
132C22⋊(C79⋊C8)D411yescharacteristic
133(C2×D79)⋊C8—21no—
134(C2×D79)⋊C8—21no—
135(C2×D79)⋊C8—21no—
136(C2×D79)⋊C8—21no—
137#14579072—21no—
138#14579072—21no—
139#14579072—41no—
140C4×C79⋊C8—21no—
141C4×C79⋊C8—21no—
142C4×C79⋊C8—41no—
143C23×C4×C79C2311yescharacteristic
144C2×M16×C79C2311yescharacteristic
145C2×M16×C79C2311yescharacteristic
146#117×C79—21no—
147#117×C79—21no—
148#117×C79C2×C411yescharacteristic
149#117×C79C2×C411yescharacteristic
150#117×C79C2311yescharacteristic
151#117×C79C2311yescharacteristic
152C2×C4⋊C4×C79C2×C411yescharacteristic
153C2×C4⋊C4×C79C2×C411yescharacteristic
154C2×C22⋊C4×C79—21no—
155C2×C22⋊C4×C79—21no—
156C2×C42×C79—21no—
157C2×C42×C79C2311yescharacteristic
158C2×C42×C79C2311yescharacteristic
159C22⋊C8×C79—21no—
160C22⋊C8×C79—21no—
161#95×C79—21no—
162C23×D79—21no—
163#11929624—21no—
164#11929624—21no—
165#11929624—22no—
166#11929624—22no—
167#11929624—21no—
168#11929624—21no—
169#11929624—21no—
170#11929624—21no—
171#11929624—42no—
172#11929624—42no—
173#11929624—41no—
174#11929624—41no—
175#11929624—42no—
176#11929624—42no—
177#11929624#4112yes—
178#11929624#4112yes—
179C2×Dic158—22no—
180C2×Dic158—21no—
181C2×Dic158—41no—
182C2×Dic158C22×C411yescharacteristic
183C2×Dic158C22×C411yescharacteristic
184C2×D316—22no—
185C2×D316—21no—
186C2×D316—41no—
187C2×D316C22×C411yescharacteristic
188C2×D316C22×C411yescharacteristic
189C2×C22⋊D79—21no—
190C2×C22⋊D79—21no—
191C2×C22⋊D79—21no—
192C2×C22⋊D79—21no—
193C2×C22⋊D79—42no—
194C2×C22⋊D79—42no—
195C22×Dic79—21no—
196C2×C4×D79—21no—
197C2×C4×D79—21no—
198C2×C4×D79—21no—
199C2×C4×D79—21no—
200C2×C4×D79—42no—
201C2×C4×D79—42no—
202#11929608—21no—
203#11929608—21no—
204#11929608—21no—
205#11929608—21no—
206#11929608—41no—
207#11929608—41no—
208#11929608—41no—
209#11929608—41no—
210#11929607—42no—
211#11929607—42no—
212C2×C79⋊C8—21no—
213C2×C79⋊C8—21no—
214C2×C79⋊C8—21no—
215C2×C79⋊C8—21no—
216C2×C79⋊C8—21no—
217C2×C79⋊C8—21no—
218C2×C79⋊C8—21no—
219C2×C79⋊C8—21no—
220C2×C79⋊C8—21no—
221C2×C79⋊C8—21no—
222C2×C79⋊C8C22×C411yescharacteristic
223C2×C79⋊C8C22×C411yescharacteristic
224C2×C79⋊C8C22×C411yescharacteristic
225C2×C79⋊C8C22×C411yescharacteristic
226C2×C79⋊C8C2×D411yescharacteristic
227C2×C79⋊C8C2×D411yescharacteristic
228C2×C79⋊C8C2×D411yescharacteristic
229C2×C79⋊C8C2×D411yescharacteristic
230C8×D79—42no—
231C8×D79—42no—
232C24×C79#4111yescharacteristic
233C22×C4×C79—21no—
234C22×C4×C79—21no—
235C22×C4×C79—21no—
236C22×C4×C79—21no—
237C22×C4×C79—21no—
238C22×C4×C79—21no—
239C22×C4×C79—21no—
240C22×C4×C79—21no—
241C22×C4×C79C22×C411yescharacteristic
242C22×C4×C79C22×C411yescharacteristic
243C22×C4×C79C2×D411yescharacteristic
244C22×C4×C79C2×D411yescharacteristic
245C22×C4×C79#4111yescharacteristic
246C22×C4×C79C2411yescharacteristic
247M16×C79—21no—
248M16×C79—21no—
249M16×C79—21no—
250M16×C79—21no—
251C2×C8×C79—21no—
252C2×C8×C79—21no—
253C4⋊C4×C79—21no—
254C4⋊C4×C79—21no—
255C4⋊C4×C79C22×C411yescharacteristic
256C4⋊C4×C79C22×C411yescharacteristic
257C4⋊C4×C79C22×C411yescharacteristic
258C4⋊C4×C79C22×C411yescharacteristic
259C22⋊C4×C79—21no—
260C22⋊C4×C79—21no—
261C22⋊C4×C79—21no—
262C22⋊C4×C79—21no—
263C22⋊C4×C79—42no—
264C42×C79—21no—
265C42×C79—21no—
266C42×C79—21no—
267C42×C79—21no—
268C42×C79—21no—
269C42×C79—21no—
270C42×C79—21no—
271C42×C79—21no—
272C23×C79—21no—
273C23×C79—21no—
274C23×C79—41no—
275C23×C79—41no—
276C23×C79C4×D411yescharacteristic
277C23×C79C4×D411yescharacteristic
278C23×C79C2×#4111yescharacteristic
279C22×D79—21no—
280C22×D79—21no—
281C22×D79—42no—
282C22×D79—42no—
283C22×D79—81no—
284C2×C4×C79—21no—
285C2×C4×C79—21no—
286C2×C4×C79—21no—
287C2×C4×C79—21no—
288C2×C4×C79—21no—
289C2×C4×C79—21no—
290C2×C4×C79—21no—
291C2×C4×C79—21no—
292C2×C4×C79—21no—
293C2×C4×C79—21no—
294C2×C4×C79—22no—
295C2×C4×C79—21no—
296C2×C4×C79—21no—
297C2×C4×C79—21no—
298C2×C4×C79—21no—
299C2×C4×C79—41no—
300C2×C4×C79—42no—
301C2×C4×C79—41no—
302C2×C4×C79—41no—
303C2×C4×C79—41no—
304C2×C4×C79—41no—
305C2×C4×C79—81no—
306C2×C4×C79C4×D411yescharacteristic
307C2×C4×C79C4×D411yescharacteristic
308C2×C4×C79C23×C411yescharacteristic
309C2×C4×C79C22×D411yescharacteristic
310C2×C4×C79C2×#4111yescharacteristic
311C2×C4×C79C2×#4111yescharacteristic
312C2×C4×C79H(5,𝔽2)11yescharacteristic
313C2×C4×C79H(5,𝔽2)11yescharacteristic
314C22⋊D79—22no—
315C22⋊D79—22no—
316C22⋊D79—42no—
317C22⋊D79—42no—
318C22⋊D79—41no—
319C22⋊D79—41no—
320C2×Dic79—21no—
321C2×Dic79—21no—
322C2×Dic79—42no—
323D316—21no—
324D316—21no—
325D316—21no—
326D316—42no—
327D316#11712yes—
328C4×D79—22no—
329C4×D79—22no—
330C4×D79—42no—
331C4×D79—42no—
332C4×D79—41no—
333C4×D79—41no—
334Dic158—21no—
335Dic158—21no—
336Dic158—21no—
337Dic158—42no—
338Dic158#11712yes—
339C8×C79—41no—
340C8×C79—41no—
341C79⋊C8—21no—
342C79⋊C8—21no—
343C79⋊C8—21no—
344C79⋊C8—21no—
345C79⋊C8—21no—
346C79⋊C8—21no—
347C79⋊C8—21no—
348C79⋊C8—21no—
349C79⋊C8—41no—
350C79⋊C8—41no—
351C22×C79—21no—
352C22×C79—21no—
353C22×C79—21no—
354C22×C79—21no—
355C22×C79—21no—
356C22×C79—21no—
357C22×C79—21no—
358C22×C79—21no—
359C22×C79—81no—
360C22×C79—81no—
361C22×C79C2×C4×D411yescharacteristic
362C22×C79#55111yescharacteristic
363C22×C79#55111yescharacteristic
364C2×D79—22no—
365C2×D79—41no—
366C2×D79—41no—
367C2×D79—41no—
368C2×D79—41no—
369C2×D79—41no—
370C2×D79—84no—
371C4×C79—21no—
372C4×C79—21no—
373C4×C79—42no—
374C4×C79—41no—
375C4×C79—41no—
376C4×C79—41no—
377C4×C79—41no—
378C4×C79—81no—
379C4×C79C2×#11711yescharacteristic
380C4×C79#51811yescharacteristic
381C4×C79#54611yescharacteristic
382C4×C79#54611yescharacteristic
383Dic79—22no—
384Dic79—41no—
385#22588—791nomaximal, Sylow
386C2×C79—21no—
387C2×C79—21no—
388C2×C79—41no—
389C2×C79—41no—
390C2×C79#234211yescharacteristic
391C2×C79#295511yescharacteristic
392C2×C79#295611yescharacteristic
393D79—42no—
394D79—81no—
395#2924—791no—
396#2896—791no—
397#2880—791no—
398#1938—791no—
399#1937—791no—
400#1929—791no—
401#1929—791no—
402#1866—791no—
403#1866—791no—
404#1826D7911yescharacteristic, complemented
405#1811—791no—
406#1789—791no—
407#1765—791no—
408#1764—791no—
409#1753—791no—
410C79#2258811yescharacteristic, complemented, Sylow
411C22×#41—791no—
412C2×#131—791no—
413C2×#131—791no—
414C22×M16—791no—
415C2×#117C2×D7911yescharacteristic
416#433—1581no—
417#433—1581no—
418#432—1581no—
419#431—1581no—
420C2×#108—791no—
421C2×#108—791no—
422#424—791no—
423#424—791no—
424C2×#104—791no—
425C2×#104—791no—
426C2×#104—791no—
427C2×#104—791no—
428#419—791no—
429#419—791no—
430#418—791no—
431#418—791no—
432#417—791no—
433#417—791no—
434#417—791no—
435#417—791no—
436#416—791no—
437#416—791no—
438#416—791no—
439#416—791no—
440#408—791no—
441#408—791no—
442#408—1581no—
443#408—1581no—
444#407—791no—
445#407—1581no—
446#407C2×D7911yescharacteristic
447C2×C22⋊C8—791no—
448C2×C22⋊C8—1581no—
449#405—791no—
450#405—791no—
451C2×#97—791no—
452C2×C4×C8—791no—
453C4×C22⋊C4C2×D7911yescharacteristic
454#341—791no—
455#341—791no—
456#339C2×D7911yescharacteristic, complemented
457#339C2×D7911yescharacteristic, complemented
458#339C2×D7911yescharacteristic, complemented
459#339C2×D7911yescharacteristic, complemented
460#336—791no—
461#336—791no—
462C2×#41—3161no—
463C2×#41—3161no—
464C2×#41—791no—
465C2×#41—791no—
466C2×#41—791no—
467C2×#41—791no—
468C2×#41—1582no—
469C2×#41—1582no—
470C2×#41—1581no—
471C2×#41—1581no—
472C22×Q8—791no—
473C22×D4—791no—
474C22×D4—1581no—
475C23×C4—1581no—
476C23×C4C22×D7911yescharacteristic
477#131—3161no—
478#131—3161no—
479#131—1582no—
480#131—1582no—
481C2×M16—3161no—
482C2×M16—3161no—
483C2×M16—791no—
484C2×M16—791no—
485C2×M16—791no—
486C2×M16—791no—
487C2×M16—791no—
488C2×M16—791no—
489C2×M16—1581no—
490C2×M16—1581no—
491C2×M16C22×D7911yescharacteristic
492C2×M16C22×D7911yescharacteristic
493C22×C8—791no—
494C22×C8—791no—
495C22×C8—791no—
496C22×C8—791no—
497C22×C8—1581no—
498C22×C8—1581no—
499#117—21no—
500#117—21no—
501#117C4×D7911yescharacteristic
502#117C4×D7911yescharacteristic
503#117C22×D7911yescharacteristic
504#117C22×D7911yescharacteristic
505C2×C4⋊C4C4×D7911yescharacteristic
506C2×C4⋊C4C4×D7911yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C22×D7911yescharacteristic
511C2×C42C22×D7911yescharacteristic
512#108—3161no—
513#108—3161no—
514C4⋊C8—1581no—
515C4⋊C8—1581no—
516C4⋊C8—1581no—
517C4⋊C8—1581no—
518#104—3161no—
519#104—3161no—
520#104—1582no—
521#104—1582no—
522#103—791no—
523#103—791no—
524#103—791no—
525#103—791no—
526#103—791no—
527#103—791no—
528#103—791no—
529#103—791no—
530#102—791no—
531#102—791no—
532#102—791no—
533#102—791no—
534#102—791no—
535#102—791no—
536#102—791no—
537#102—791no—
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—791no—
541C22⋊C8—791no—
542C22⋊C8—791no—
543C22⋊C8—791no—
544C22⋊C8—1581no—
545C22⋊C8—1581no—
546C22⋊C8—1581no—
547C22⋊C8—1581no—
548C22⋊C8—1581no—
549C22⋊C8—1581no—
550#97—3161no—
551#97—1581no—
552#97—1581no—
553C4×C8—3161no—
554C4×C8—1581no—
555C4×C8—1581no—
556#95—21no—
557C24—1581no—
558C24#1192962311yescharacteristic
559#41—3162no—
560#41—3162no—
561#41—3161no—
562#41—3161no—
563#41—3162no—
564#41—3162no—
565#41—792no—
566#41—792no—
567#41—1582no—
568#41—1582no—
569#41—1581no—
570#41—1581no—
571#41—1581no—
572#41—1581no—
573#41—1581no—
574#41—1581no—
575C2×Q8—3161no—
576C2×Q8—791no—
577C2×Q8—791no—
578C2×Q8—1582no—
579C2×Q8—1581no—
580C2×D4—3161no—
581C2×D4—3162no—
582C2×D4—3162no—
583C2×D4—791no—
584C2×D4—791no—
585C2×D4—1582no—
586C2×D4—1581no—
587C2×D4—1581no—
588C2×D4—1581no—
589C2×D4—1581no—
590C2×D4—1581no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—3162no—
600C22×C4—3162no—
601C22×C4—1581no—
602C22×C4—1581no—
603C22×C4—1581no—
604C22×C4—1581no—
605C22×C4—1581no—
606C22×C4C2×C4×D7911yescharacteristic
607C22×C4C2×C4×D7911yescharacteristic
608C22×C4D4×D7911yescharacteristic
609C22×C4D4×D7911yescharacteristic
610C22×C4#1192962311yescharacteristic
611C22×C4C23×D7911yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—3162no—
617M16—3162no—
618M16—3161no—
619M16—3161no—
620M16—3161no—
621M16—3161no—
622M16—1581no—
623M16—1581no—
624M16—1581no—
625M16—1581no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—3162no—
629C2×C8—3162no—
630C2×C8—791no—
631C2×C8—791no—
632C2×C8—791no—
633C2×C8—791no—
634C2×C8—791no—
635C2×C8—791no—
636C2×C8—791no—
637C2×C8—791no—
638C2×C8—1581no—
639C2×C8—1581no—
640C2×C8—1581no—
641C2×C8—1581no—
642C2×C8—1581no—
643C2×C8—1581no—
644C2×C8—1581no—
645C2×C8—1581no—
646C2×C8—1581no—
647C2×C8—1581no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C2×C4×D7911yescharacteristic
651C4⋊C4C2×C4×D7911yescharacteristic
652C4⋊C4C2×C4×D7911yescharacteristic
653C4⋊C4C2×C4×D7911yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—3162no—
672C23—3162no—
673C23—6321no—
674C23—1581no—
675C23—1581no—
676C23(C22⋊D79)⋊C411yescharacteristic
677C23(C22⋊D79)⋊C411yescharacteristic
678C23C2×#1192962311yescharacteristic
679Q8—3162no—
680Q8—792no—
681Q8—1581no—
682Q8—1581no—
683Q8—1581no—
684D4—3162no—
685D4—3162no—
686D4—3161no—
687D4—3161no—
688D4—3162no—
689D4—792no—
690D4—1582no—
691D4—1582no—
692D4—1581no—
693D4—1581no—
694D4—1581no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—81no—
717C2×C4—3162no—
718C2×C4—3162no—
719C2×C4—3162no—
720C2×C4—3161no—
721C2×C4—3161no—
722C2×C4—1581no—
723C2×C4—1581no—
724C2×C4—1582no—
725C2×C4—1582no—
726C2×C4(C22⋊D79)⋊C411yescharacteristic
727C2×C4(C22⋊D79)⋊C411yescharacteristic
728C2×C4C22×C4×D7911yescharacteristic
729C2×C4C2×D4×D7911yescharacteristic
730C2×C4#41×D7911yescharacteristic
731C2×C4#41×D7911yescharacteristic
732C2×C4#1457920711yescharacteristic
733C2×C4#1457920711yescharacteristic
734C8—41no—
735C8—41no—
736C8—3161no—
737C8—3161no—
738C8—1581no—
739C8—1581no—
740C8—1581no—
741C8—1581no—
742C8—1581no—
743C8—1581no—
744C8—1581no—
745C8—1581no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—3161no—
757C22—3161no—
758C22—3161no—
759C22—3161no—
760C22—3161no—
761C22—6324no—
762C22—1582no—
763C22C2×(C22⋊D79)⋊C411yescharacteristic
764C22#1909923611yescharacteristic
765C22#1909923611yescharacteristic
766C4—21no—
767C4—21no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—81no—
774C4—3161no—
775C4—1582no—
776C4#117×D7911yescharacteristic
777C4#1909903711yescharacteristic
778C4#1909920511yescharacteristic
779C4#1909920511yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—3162no—
785C2—6321no—
786C2#2376624211yescharacteristic
787C2#2377229911yescharacteristic
788C2#2377230611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#1826C2
socleC22×C79C2×C4×D4
prime radicalC22×#11929624C22
cosocleC22×C4×C79C24
hypercenter#1826D79
hypocenterC79#22588
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
1. #23772058C2semidirect
4. #23764112C2semidirect
5. #23764105C2semidirect
6. #23764046C2semidirect
7. #23764046C2semidirect
8. #23763676C2semidirect
9. #23763676C2semidirect
10. #23763440C2semidirect
12. #23763241C2semidirect
13. #23763234C2semidirect
14. #23763184C2semidirect
15. C79×#1826C2semidirect
24. C2×#14579096C22semidirect
25. C2×#14579096C22semidirect
26. #19098590C22semidirect
27. #19098590C22semidirect
32. #19098571C4semidirect
33. #19098571C4semidirect
34. #19098567C4semidirect
35. #19098567C4semidirect
36. #19098562C4semidirect
37. #19098562C4semidirect
38. #19098562C4semidirect
39. #19098562C4semidirect
52. #19098519C22semidirect
53. #19098519C22semidirect
54. C2×#14579072C22semidirect
55. C2×C4×C79⋊C8C22semidirect
56. #19098327C22semidirect
57. #19098327C22semidirect
58. #19098318C22semidirect
59. #19098318C22semidirect
63. #339×C79C22semidirect
64. #339×C79C22semidirect
65. #339×C79C22semidirect
66. #339×C79C22semidirect
404. #1826D79semidirect
410. C79#22588semidirect
456. #339C2×D79semidirect
457. #339C2×D79semidirect
458. #339C2×D79semidirect
459. #339C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237720582
#237719172
#237718502
#237641122
#237641052
#237640462
#237636762
#237634402
#237633452
#237632412
#237632342
#237631842
C79×#18262
#2258879