Finite Group Databasebeta

← #35159752

Subgroups — #35159752

Order 20224.

2444 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099113C211yesmaximal, characteristic, complemented
2C2×#19099113C211yesmaximal, characteristic, complemented
3#23774397C214yesmaximal, complemented
4#23774389C214yesmaximal, complemented
5#23774335C214yesmaximal, complemented
6#23774327C212yesmaximal, complemented
7#23774320C212yesmaximal, complemented
8#23773852C212yesmaximal, complemented
9#23773794C212yesmaximal, complemented
10#23772866C214yesmaximal, complemented
11#23772654C214yesmaximal, complemented
12C79×#2920C211yesmaximal, characteristic, complemented
13C22×#11929624—21no—
14C22×#11929624C2212yes—
15C2×#14579189C2218yescomplemented
16#19099113—21no—
17#19099113—21no—
18#19099113—21no—
19#19099113—21no—
20#19099113—21no—
21#19099113—21no—
22#19099113—21no—
23#19099113—21no—
24#19099113C2212yes—
25#19099113C2212yes—
26#19099113C2212yes—
27#19099113C2212yes—
28#19099113C2212yescomplemented
29#19099113C2212yescomplemented
30#19099113C2212yescomplemented
31#19099113C2212yescomplemented
32C2×#14579161C2211yescharacteristic, complemented
33C2×#14579161C2211yescharacteristic, complemented
34C2×#14579158C2211yescharacteristic, complemented
35C2×#14579158C2211yescharacteristic, complemented
36C2×#14579149—21no—
37C2×#14579149C2212yescomplemented
38C2×#14579135—21no—
39C2×#14579135—21no—
40C2×#14579135—21no—
41C2×#14579135C2212yes—
42C2×C4×D316—21no—
43C2×C4×D316—21no—
44C2×C4×D316—21no—
45C2×C4×D316C2212yescomplemented
46#19098952C2218yescomplemented
47#19098940C2214yescomplemented
48#19098936C2214yescomplemented
49#19098923C2218yescomplemented
50#19098914C2214yescomplemented
51#19098910C2214yescomplemented
52#19098779C22116yescomplemented
53#19098769C2218yescomplemented
54#19098759C2218yescomplemented
55#19098710C22116yescomplemented
56#19098704C2218yescomplemented
57#19098699C2218yescomplemented
58#19098565C2218yescomplemented
59C22×C42×C79C2211yescharacteristic
60#432×C79C2212yescomplemented
61#432×C79C2212yescomplemented
62#431×C79C2212yescomplemented
63#431×C79C2212yescomplemented
64#423×C79C2212yescomplemented
65#407×C79C2212yes—
66C4×M16×C79C2212yescomplemented
67C2×#11929624—22no—
68C2×#11929624—22no—
69C2×#11929624—22no—
70C2×#11929624—22no—
71C2×#11929624—22no—
72C2×#11929624—22no—
73C2×#11929624—48no—
74C2×#11929624—48no—
75C2×#11929624C2314yes—
76C2×#11929624C2314yes—
77C22×Dic158—21no—
78C22×Dic158C2312yes—
79C22×D316—21no—
80C22×D316—21no—
81C22×D316—21no—
82C22×D316—21no—
83C22×D316C2312yes—
84C22×D316C2312yes—
85C22×C22⋊D79—22no—
86C22×C22⋊D79—22no—
87C22×C4×D79—22no—
88C22×C4×D79—22no—
89#14579189—416no—
90C2×#11929613C23116yes—
91C2×D632C23116yes—
92#14579161—21no—
93#14579161—21no—
94#14579161—21no—
95#14579161—21no—
96#14579161C2312yes—
97#14579161C2312yes—
98#14579161C2312yes—
99#14579161C2312yes—
100#14579158—21no—
101#14579158—21no—
102#14579158—21no—
103#14579158—21no—
104#14579158C2312yes—
105#14579158C2312yes—
106#14579158C2312yes—
107#14579158C2312yes—
108#14579149—22no—
109#14579149—22no—
110#14579149—22no—
111#14579149—22no—
112#14579149—22no—
113#14579149—22no—
114#14579149C2314yes—
115#14579149C2314yes—
116#14579135—22no—
117#14579135—22no—
118#14579135—22no—
119#14579135—22no—
120#14579135—22no—
121#14579135—22no—
122#14579135—22no—
123#14579135—22no—
124#14579135—22no—
125#14579135—22no—
126#14579135—22no—
127#14579135—22no—
128#14579135—22no—
129#14579135—22no—
130#14579135C2314yes—
131#14579135C2314yes—
132C4×D316—22no—
133C4×D316—22no—
134C4×D316—22no—
135C4×D316—22no—
136C4×D316—22no—
137C4×D316—22no—
138C4×D316—22no—
139C4×D316—22no—
140C4×D316—22no—
141C4×D316—22no—
142C4×D316—22no—
143C4×D316—22no—
144C4×D316—22no—
145C4×D316—22no—
146C4×D316C2314yes—
147C4×D316C2314yes—
148C2×C4⋊Dic79—21no—
149C2×C4⋊Dic79—21no—
150C2×C4⋊Dic79—21no—
151C2×C4⋊Dic79C2312yes—
152C2×(C2×D79)⋊C4—22no—
153C2×(C2×D79)⋊C4—22no—
154C2×(C2×D79)⋊C4—22no—
155C2×(C2×D79)⋊C4—22no—
156#14579086C23116yes—
157#14579083C23116yes—
158C23×C4×C79D411yescharacteristic
159C23×C4×C79D411yescharacteristic
160C23×C4×C79C2311yescharacteristic
161C2×M16×C79C2314yes—
162C2×C42×C79D411yescharacteristic
163C2×C42×C79D411yescharacteristic
164C2×C42×C79D411yescharacteristic
165C2×C42×C79D411yescharacteristic
166C2×C42×C79D411yescharacteristic
167C2×C42×C79D411yescharacteristic
168C2×C42×C79C2311yescharacteristic
169C2×C42×C79C2311yescharacteristic
170C2×C42×C79C2311yescharacteristic
171C2×C42×C79C2311yescharacteristic
172C2×C42×C79C2311yescharacteristic
173C2×C42×C79C2311yescharacteristic
174C4⋊C8×C79C2314yes—
175C4⋊C8×C79C2314yes—
176C22⋊C8×C79C2314yes—
177C22⋊C8×C79C2314yes—
178#97×C79C2314yes—
179C4×C8×C79C2314yes—
180C23×D79—22no—
181C23×D79—22no—
182#11929624—216no—
183#11929624—48no—
184#11929624—48no—
185#11929624—48no—
186#11929624—48no—
187#11929624—48no—
188#11929624—48no—
189#11929624—48no—
190C2×Dic158—22no—
191C2×Dic158—22no—
192C2×Dic158—22no—
193C2×Dic158—44no—
194C2×Dic158—44no—
195C2×Dic158C2414yes—
196C2×D316—22no—
197C2×D316—22no—
198C2×D316—22no—
199C2×D316—22no—
200C2×D316—22no—
201C2×D316—22no—
202C2×D316—22no—
203C2×D316—22no—
204C2×D316—22no—
205C2×D316—22no—
206C2×D316—28no—
207C2×D316—44no—
208C2×D316—44no—
209C2×D316—44no—
210C2×D316—44no—
211C2×D316—44no—
212C2×D316C2414yes—
213C2×D316C2414yes—
214C2×C22⋊D79—24no—
215C2×C22⋊D79—24no—
216C2×C22⋊D79—24no—
217C2×C22⋊D79—24no—
218C2×C22⋊D79—48no—
219C2×C22⋊D79—48no—
220C22×Dic79—22no—
221C22×Dic79—22no—
222C2×C4×D79—24no—
223C2×C4×D79—24no—
224C2×C4×D79—24no—
225C2×C4×D79—24no—
226C2×C4×D79—48no—
227C2×C4×D79—48no—
228#11929613—416no—
229D632—416no—
230C4⋊Dic79—22no—
231C4⋊Dic79—22no—
232C4⋊Dic79—22no—
233C4⋊Dic79—22no—
234C4⋊Dic79—22no—
235C4⋊Dic79—22no—
236C4⋊Dic79—22no—
237C4⋊Dic79C2414yes—
238(C2×D79)⋊C4—24no—
239(C2×D79)⋊C4—24no—
240(C2×D79)⋊C4—24no—
241(C2×D79)⋊C4—24no—
242(C2×D79)⋊C4—24no—
243(C2×D79)⋊C4—24no—
244(C2×D79)⋊C4—24no—
245(C2×D79)⋊C4—24no—
246C24×C79C2×D411yescharacteristic
247C22×C4×C79—24no—
248C22×C4×C79—24no—
249C22×C4×C79—42no—
250C22×C4×C79C2×D411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C22×C4×C79C2×D411yescharacteristic
258C22×C4×C79C2×D411yescharacteristic
259C22×C4×C79C2×D411yescharacteristic
260C22×C4×C79C2×D411yescharacteristic
261C22×C4×C79C2×D411yescharacteristic
262C22×C4×C79C2×D411yescharacteristic
263C22×C4×C79C2×D411yescharacteristic
264C22×C4×C79C2×D411yescharacteristic
265C22×C4×C79C2411yescharacteristic
266C22×C4×C79C2411yescharacteristic
267C22×C4×C79C2411yescharacteristic
268M16×C79—28no—
269C2×C8×C79C2418yes—
270C42×C79C2×D411yescharacteristic
271C42×C79C2×D411yescharacteristic
272C42×C79C2×D411yescharacteristic
273C42×C79C2×D411yescharacteristic
274C42×C79C2×D411yescharacteristic
275C42×C79C2×D411yescharacteristic
276C42×C79C2×D411yescharacteristic
277C42×C79C2×D411yescharacteristic
278C42×C79C2×D411yescharacteristic
279C42×C79C2×D411yescharacteristic
280C42×C79C2×D411yescharacteristic
281C42×C79C2×D411yescharacteristic
282C42×C79C2411yescharacteristic
283C42×C79C2411yescharacteristic
284C42×C79C2411yescharacteristic
285C42×C79C2411yescharacteristic
286C23×C79—22no—
287C23×C79—22no—
288C23×C79—41no—
289C23×C79C22×D411yescharacteristic
290C23×C79C22×D411yescharacteristic
291C23×C79C22×D411yescharacteristic
292C22×D79—24no—
293C22×D79—24no—
294C22×D79—44no—
295C22×D79—44no—
296C22×D79—44no—
297C22×D79—44no—
298C22×D79—44no—
299C22×D79—44no—
300C2×C4×C79—22no—
301C2×C4×C79—22no—
302C2×C4×C79—22no—
303C2×C4×C79—22no—
304C2×C4×C79—22no—
305C2×C4×C79—22no—
306C2×C4×C79—22no—
307C2×C4×C79—22no—
308C2×C4×C79—22no—
309C2×C4×C79—22no—
310C2×C4×C79—22no—
311C2×C4×C79—22no—
312C2×C4×C79—22no—
313C2×C4×C79—41no—
314C2×C4×C79—41no—
315C2×C4×C79—41no—
316C2×C4×C79AGL(1,ℤ/8)14yescomplemented
317C2×C4×C79C22×D411yescharacteristic
318C2×C4×C79C22×D411yescharacteristic
319C2×C4×C79C22×D411yescharacteristic
320C2×C4×C79C22×D411yescharacteristic
321C2×C4×C79C22×D411yescharacteristic
322C2×C4×C79C22×D411yescharacteristic
323C2×C4×C79C22×D411yescharacteristic
324C2×C4×C79C22×D411yescharacteristic
325C2×C4×C79C22×D411yescharacteristic
326C2×C4×C79C22×D411yescharacteristic
327C2×C4×C79C22×D411yescharacteristic
328C2×C4×C79H(5,𝔽2)14yes—
329C2×C4×C79C2511yescharacteristic
330C22⋊D79—48no—
331C22⋊D79—48no—
332C22⋊D79—48no—
333C22⋊D79—48no—
334C2×Dic79—24no—
335C2×Dic79—24no—
336C2×Dic79—44no—
337C2×Dic79—44no—
338D316—28no—
339D316—28no—
340D316—44no—
341D316—44no—
342D316—44no—
343D316—44no—
344D316—44no—
345D316—44no—
346D316—44no—
347D316—44no—
348D316—44no—
349D316—44no—
350C4×D79—48no—
351C4×D79—48no—
352C4×D79—48no—
353C4×D79—48no—
354Dic158—28no—
355Dic158—44no—
356Dic158—44no—
357Dic158—44no—
358C8×C79—28no—
359C22×C79—21no—
360C22×C79—21no—
361C22×C79—21no—
362C22×C79—21no—
363C22×C79—21no—
364C22×C79—21no—
365C22×C79—21no—
366C22×C79—44no—
367C22×C79#53512yes—
368C22×C79C2×AGL(1,ℤ/8)12yes—
369C22×C79C23×D411yescharacteristic
370C2×D79—44no—
371C2×D79—44no—
372C2×D79—44no—
373C2×D79—44no—
374C2×D79—44no—
375C2×D79—44no—
376C2×D79—88no—
377C2×D79—88no—
378C4×C79—21no—
379C4×C79—21no—
380C4×C79—21no—
381C4×C79—21no—
382C4×C79—21no—
383C4×C79—21no—
384C4×C79—21no—
385C4×C79#53512yes—
386C4×C79C2×AGL(1,ℤ/8)12yes—
387C4×C79C2×AGL(1,ℤ/8)12yes—
388C4×C79#57512yes—
389C4×C79C2×H(5,𝔽2)12yes—
390Dic79—44no—
391Dic79—44no—
392#60803—791nomaximal, Sylow
393C2×C79—22no—
394C2×C79—22no—
395C2×C79—41no—
396C2×C79C2×#53511yescharacteristic
397C2×C79C22×AGL(1,ℤ/8)11yescharacteristic
398C2×C79C2×#57511yescharacteristic
399D79—84no—
400D79—84no—
401C2×#532—791no—
402C2×#532—791no—
403#3214—794no—
404#3213—794no—
405#3207—794no—
406#3206—792no—
407#3205—792no—
408#3151—792no—
409#3141—792no—
410#3036—794no—
411#3006—794no—
412#2920D7911yescharacteristic, complemented
413C79#6080311yescharacteristic, complemented, Sylow
414C22×#41—792no—
415C22×#41—1581no—
416C2×AGL(1,ℤ/8)—798no—
417#532—792no—
418#532—792no—
419#532—792no—
420#532—792no—
421#532—792no—
422#532—792no—
423#532—792no—
424#532—792no—
425#532—1581no—
426#532—1581no—
427#532—1581no—
428#532—1581no—
429#532—1581no—
430#532—1581no—
431#532—1581no—
432#532—1581no—
433C2×C4⋊Q8—791no—
434C2×C4⋊Q8—791no—
435C2×#127—791no—
436C2×#127—791no—
437C2×#124—792no—
438C2×#124—1581no—
439C2×#121—792no—
440C2×#121—1581no—
441C2×#121—1581no—
442C2×#121—1581no—
443C2×C4×D4—792no—
444C2×C4×D4—1581no—
445C2×C4×D4—1581no—
446C2×C4×D4—1581no—
447C22×C42C2×D7911yescharacteristic
448#496—798no—
449#493—794no—
450#492—794no—
451#489—798no—
452#487—794no—
453#486—794no—
454#463—7916no—
455#461—798no—
456#459—798no—
457#449—7916no—
458#448—798no—
459#447—798no—
460#432C2×D7912yescomplemented
461#432C2×D7912yescomplemented
462#431C2×D7912yescomplemented
463#431C2×D7912yescomplemented
464#423C2×D7912yescomplemented
465#417—798no—
466#407C2×D7912yes—
467C4×M16C2×D7912yescomplemented
468C2×#41—3168no—
469C2×#41—3168no—
470C2×#41—794no—
471C2×#41—794no—
472C2×#41—1582no—
473C2×#41—1582no—
474C2×#41—1582no—
475C2×#41—1582no—
476C2×#41—1582no—
477C2×#41—1582no—
478C22×Q8—792no—
479C22×Q8—1581no—
480C22×D4—792no—
481C22×D4—792no—
482C22×D4—1582no—
483C22×D4—1582no—
484C22×D4—1581no—
485C22×D4—1581no—
486C22×D4—1581no—
487C22×D4—1581no—
488C23×C4—1582no—
489C23×C4—1582no—
490C23×C4D31611yescharacteristic
491C23×C4D31611yescharacteristic
492C23×C4C22×D7911yescharacteristic
493AGL(1,ℤ/8)—31616no—
494C2×SD16—7916no—
495C2×D8—7916no—
496C2×M16C22×D7914yes—
497C4⋊Q8—792no—
498C4⋊Q8—792no—
499C4⋊Q8—792no—
500C4⋊Q8—792no—
501C4⋊Q8—1581no—
502C4⋊Q8—1581no—
503C4⋊Q8—1581no—
504C4⋊Q8—1581no—
505#127—792no—
506#127—792no—
507#127—792no—
508#127—792no—
509#127—1581no—
510#127—1581no—
511#127—1581no—
512#127—1581no—
513#124—794no—
514#124—794no—
515#124—1582no—
516#124—1582no—
517#124—1582no—
518#124—1582no—
519#124—1582no—
520#124—1582no—
521#121—794no—
522#121—794no—
523#121—1582no—
524#121—1582no—
525#121—1582no—
526#121—1582no—
527#121—1582no—
528#121—1582no—
529#121—1582no—
530#121—1582no—
531#121—1582no—
532#121—1582no—
533#121—1582no—
534#121—1582no—
535#121—1582no—
536#121—1582no—
537C4×D4—794no—
538C4×D4—794no—
539C4×D4—1582no—
540C4×D4—1582no—
541C4×D4—1582no—
542C4×D4—1582no—
543C4×D4—1582no—
544C4×D4—1582no—
545C4×D4—1582no—
546C4×D4—1582no—
547C4×D4—1582no—
548C4×D4—1582no—
549C4×D4—1582no—
550C4×D4—1582no—
551C4×D4—1582no—
552C4×D4—1582no—
553C2×C4⋊C4—792no—
554C2×C4⋊C4—1581no—
555C2×C4⋊C4—1581no—
556C2×C4⋊C4—1581no—
557C2×C22⋊C4—1582no—
558C2×C22⋊C4—1582no—
559C2×C22⋊C4—1582no—
560C2×C22⋊C4—1582no—
561C2×C42D31611yescharacteristic
562C2×C42D31611yescharacteristic
563C2×C42D31611yescharacteristic
564C2×C42D31611yescharacteristic
565C2×C42D31611yescharacteristic
566C2×C42D31611yescharacteristic
567C2×C42C22×D7911yescharacteristic
568C2×C42C22×D7911yescharacteristic
569C2×C42C22×D7911yescharacteristic
570C2×C42C22×D7911yescharacteristic
571C2×C42C22×D7911yescharacteristic
572C2×C42C22×D7911yescharacteristic
573C4⋊C8C22×D7914yes—
574C4⋊C8C22×D7914yes—
575#103—7916no—
576#102—7916no—
577C22⋊C8C22×D7914yes—
578C22⋊C8C22×D7914yes—
579#97C22×D7914yes—
580C4×C8C22×D7914yes—
581C24—1582no—
582C24—1582no—
583C24C2×D31611yescharacteristic
584#41—3168no—
585#41—3168no—
586#41—3168no—
587#41—3168no—
588#41—3168no—
589#41—3168no—
590#41—3168no—
591#41—15816no—
592C2×Q8—3164no—
593C2×Q8—3164no—
594C2×Q8—794no—
595C2×Q8—1582no—
596C2×Q8—1582no—
597C2×Q8—1582no—
598C2×D4—3164no—
599C2×D4—3164no—
600C2×D4—3164no—
601C2×D4—3164no—
602C2×D4—3168no—
603C2×D4—3168no—
604C2×D4—3164no—
605C2×D4—794no—
606C2×D4—794no—
607C2×D4—1584no—
608C2×D4—1584no—
609C2×D4—1584no—
610C2×D4—1584no—
611C2×D4—1588no—
612C2×D4—1582no—
613C2×D4—1582no—
614C2×D4—1582no—
615C2×D4—1582no—
616C2×D4—1582no—
617C2×D4—1582no—
618C2×D4—1582no—
619C2×D4—1582no—
620C2×D4—1582no—
621C2×D4—1582no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—42no—
625C22×C4—3168no—
626C22×C4—3168no—
627C22×C4—1582no—
628C22×C4—1582no—
629C22×C4—1584no—
630C22×C4—1584no—
631C22×C4—1584no—
632C22×C4—1584no—
633C22×C4C2×D31611yescharacteristic
634C22×C4C2×D31611yescharacteristic
635C22×C4C2×D31611yescharacteristic
636C22×C4C2×D31611yescharacteristic
637C22×C4C2×D31611yescharacteristic
638C22×C4C2×D31611yescharacteristic
639C22×C4C2×D31611yescharacteristic
640C22×C4C2×D31611yescharacteristic
641C22×C4C2×D31611yescharacteristic
642C22×C4C2×D31611yescharacteristic
643C22×C4C2×D31611yescharacteristic
644C22×C4C2×D31611yescharacteristic
645C22×C4C2×D31611yescharacteristic
646C22×C4C2×D31611yescharacteristic
647C22×C4C2×D31611yescharacteristic
648C22×C4C23×D7911yescharacteristic
649C22×C4C23×D7911yescharacteristic
650C22×C4C23×D7911yescharacteristic
651SD16—31616no—
652D8—31616no—
653M16—28no—
654C2×C8C23×D7918yes—
655C4⋊C4—794no—
656C4⋊C4—1582no—
657C4⋊C4—1582no—
658C4⋊C4—1582no—
659C4⋊C4—1582no—
660C4⋊C4—1582no—
661C4⋊C4—1582no—
662C4⋊C4—1582no—
663C22⋊C4—1584no—
664C22⋊C4—1584no—
665C22⋊C4—1584no—
666C22⋊C4—1584no—
667C22⋊C4—1584no—
668C22⋊C4—1584no—
669C22⋊C4—1584no—
670C22⋊C4—1584no—
671C42C2×D31611yescharacteristic
672C42C2×D31611yescharacteristic
673C42C2×D31611yescharacteristic
674C42C2×D31611yescharacteristic
675C42C2×D31611yescharacteristic
676C42C2×D31611yescharacteristic
677C42C2×D31611yescharacteristic
678C42C2×D31611yescharacteristic
679C42C2×D31611yescharacteristic
680C42C2×D31611yescharacteristic
681C42C2×D31611yescharacteristic
682C42C2×D31611yescharacteristic
683C42C23×D7911yescharacteristic
684C42C23×D7911yescharacteristic
685C42C23×D7911yescharacteristic
686C42C23×D7911yescharacteristic
687C23—22no—
688C23—22no—
689C23—41no—
690C23—3164no—
691C23—3164no—
692C23—3164no—
693C23—3164no—
694C23—3164no—
695C23—3164no—
696C23—1584no—
697C23—1584no—
698C23C22×D31611yescharacteristic
699C23C22×D31611yescharacteristic
700C23C22×D31611yescharacteristic
701Q8—3164no—
702Q8—3164no—
703Q8—3164no—
704Q8—1588no—
705D4—3164no—
706D4—3164no—
707D4—3164no—
708D4—3164no—
709D4—3168no—
710D4—3168no—
711D4—3168no—
712D4—3168no—
713D4—3164no—
714D4—3164no—
715D4—3164no—
716D4—3164no—
717D4—3164no—
718D4—3164no—
719D4—1588no—
720D4—1588no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—3168no—
738C2×C4—3168no—
739C2×C4—3164no—
740C2×C4—3164no—
741C2×C4—3168no—
742C2×C4—3168no—
743C2×C4—1584no—
744C2×C4—1584no—
745C2×C4#1457918914yescomplemented
746C2×C4C22×D31611yescharacteristic
747C2×C4C22×D31611yescharacteristic
748C2×C4C22×D31611yescharacteristic
749C2×C4C22×D31611yescharacteristic
750C2×C4C22×D31611yescharacteristic
751C2×C4C22×D31611yescharacteristic
752C2×C4C22×D31611yescharacteristic
753C2×C4C22×D31611yescharacteristic
754C2×C4C22×D31611yescharacteristic
755C2×C4C22×D31611yescharacteristic
756C2×C4C22×D31611yescharacteristic
757C2×C4#1457920714yes—
758C2×C4C24×D7911yescharacteristic
759C8—28no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—44no—
768C22—3164no—
769C22—3164no—
770C22—3164no—
771C22—3164no—
772C22—3164no—
773C22—3164no—
774C22—6328no—
775C22—6328no—
776C22#1909913212yes—
777C22C2×#1457918912yes—
778C22C23×D31611yescharacteristic
779C4—21no—
780C4—21no—
781C4—21no—
782C4—21no—
783C4—21no—
784C4—21no—
785C4—21no—
786C4—3164no—
787C4—3164no—
788C4#1909913212yes—
789C4C2×#1457918912yes—
790C4C2×#1457918912yes—
791C4#1909936312yes—
792C4C2×#1457920712yes—
793C2—22no—
794C2—22no—
795C2—41no—
796C2—6324no—
797C2—6324no—
798C2C2×#1909913211yescharacteristic
799C2C22×#1457918911yescharacteristic
800C2C2×#1909936311yescharacteristic
subgroupG/H
centerC22C23×D316
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC79×#2920C2
socleC22×C79C23×D4
hypercenter#2920D79
hypocenterC79#60803
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
1. C2×#19099113C2semidirect
2. C2×#19099113C2semidirect
3. #23774397C2semidirect
4. #23774389C2semidirect
5. #23774335C2semidirect
6. #23774327C2semidirect
7. #23774320C2semidirect
8. #23773852C2semidirect
9. #23773794C2semidirect
10. #23772866C2semidirect
11. #23772654C2semidirect
12. C79×#2920C2semidirect
15. C2×#14579189C22semidirect
28. #19099113C22semidirect
29. #19099113C22semidirect
30. #19099113C22semidirect
31. #19099113C22semidirect
32. C2×#14579161C22semidirect
33. C2×#14579161C22semidirect
34. C2×#14579158C22semidirect
35. C2×#14579158C22semidirect
37. C2×#14579149C22semidirect
45. C2×C4×D316C22semidirect
46. #19098952C22semidirect
47. #19098940C22semidirect
48. #19098936C22semidirect
49. #19098923C22semidirect
50. #19098914C22semidirect
51. #19098910C22semidirect
52. #19098779C22semidirect
53. #19098769C22semidirect
54. #19098759C22semidirect
55. #19098710C22semidirect
56. #19098704C22semidirect
57. #19098699C22semidirect
58. #19098565C22semidirect
60. #432×C79C22semidirect
61. #432×C79C22semidirect
62. #431×C79C22semidirect
63. #431×C79C22semidirect
64. #423×C79C22semidirect
66. C4×M16×C79C22semidirect
316. C2×C4×C79AGL(1,ℤ/8)semidirect
412. #2920D79semidirect
413. C79#60803semidirect
460. #432C2×D79semidirect
461. #432C2×D79semidirect
462. #431C2×D79semidirect
463. #431C2×D79semidirect
464. #423C2×D79semidirect
467. C4×M16C2×D79semidirect
745. C2×C4#14579189semidirect

Maximal subgroups

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

subgroupindex
C2×#190991132
#237743972
#237743892
#237743352
#237743272
#237743202
#237738522
#237737942
#237728662
#237726542
C79×#29202
#6080379