Finite Group Databasebeta

← #2647×D79 #34455372

Subgroups — #2647×D79 #34455372

Order 20224.

1854 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23769380C211yesmaximal, characteristic, complemented
2#23769379C211yesmaximal, characteristic, complemented
3#23769378C214yesmaximal, complemented
4#23769377C212yesmaximal, complemented
5#23769376C212yesmaximal, complemented
6#23769375C211yesmaximal, characteristic, complemented
7#23769374C214yesmaximal, complemented
8#400×D79C214yesmaximal
9#398×D79C214yesmaximal
10#389×D79C212yesmaximal
11#389×D79C212yesmaximal
12#384×D79C211yesmaximal, characteristic
13#382×D79C211yesmaximal, characteristic
14#376×D79C211yesmaximal, characteristic
15C79×#2647C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D79C2212yes—
17C2×C4⋊C4×D79C2212yes—
18C2×C4⋊C4×D79C2214yes—
19C2×C4⋊C4×D79C2214yes—
20C2×C4⋊C4×D79C2214yes—
21C2×C42×D79C2211yescharacteristic
22C2×C42×D79C2211yescharacteristic
23C2×C42×D79C2211yescharacteristic
24#19098505C2214yes—
25#19098505C2214yes—
26#19098504C2214yes—
27#19098504C2214yes—
28#19098503C2214yes—
29#19098502C2214yes—
30#19098501C2214yes—
31#19098497C2214yes—
32#19098497C2214yes—
33#19098496C2214yes—
34#19098496C2214yes—
35#19098495C2214yes—
36#19098494C2214yes—
37#19098493C2214yes—
38#19098462C2212yes—
39#19098462C2212yes—
40#19098461C2212yes—
41#19098461C2212yes—
42#19098460C2214yes—
43#19098460C2214yes—
44#19098459C2212yes—
45#19098459C2212yes—
46#19098458C2214yes—
47#19098458C2214yes—
48#19098433C2211yescharacteristic
49#19098432C2214yes—
50#19098432C2212yes—
51#19098429C2211yescharacteristic
52#19098428C2212yes—
53#19098427C2214yes—
54#19098409C2211yescharacteristic
55#19098409C2211yescharacteristic
56#19098409C2211yescharacteristic
57#19098408C2212yes—
58#19098408C2212yes—
59#95×D79C2214yes—
60#95×D79C2214yes—
61#95×D79C2214yes—
62#95×D79C2212yes—
63#95×D79C2212yes—
64#400×C79C2214yes—
65#398×C79C2214yes—
66#389×C79C2212yes—
67#389×C79C2212yes—
68#384×C79C2211yescharacteristic
69#382×C79C2211yescharacteristic
70#376×C79C2211yescharacteristic
71C22×C4×D79C2311yescharacteristic
72C22×C4×D79C2312yes—
73C22×C4×D79C2314yes—
74C22×C4×D79C2311yescharacteristic
75C22×C4×D79C2314yes—
76C22×C4×D79C2312yes—
77C22×C4×D79C2311yescharacteristic
78C2×C4⋊Dic79C2312yes—
79C2×C4⋊Dic79C2312yes—
80C2×C4⋊Dic79C2314yes—
81C2×C4⋊Dic79C2314yes—
82C2×C4⋊Dic79C2314yes—
83C2×Dic79⋊C4C2314yes—
84C2×Dic79⋊C4C2314yes—
85C2×Dic79⋊C4C2314yes—
86C2×Dic79⋊C4C2314yes—
87C2×Dic79⋊C4C2314yes—
88C2×Dic79⋊C4C2314yes—
89C2×Dic79⋊C4C2314yes—
90C2×Dic79⋊C4C2314yes—
91C4⋊C4×D79—28no—
92C4⋊C4×D79—28no—
93C4⋊C4×D79—48no—
94C4⋊C4×D79—48no—
95C4⋊C4×D79—48no—
96C2×C4×Dic79C2311yescharacteristic
97C2×C4×Dic79C2312yes—
98C2×C4×Dic79C2311yescharacteristic
99C2×C4×Dic79C2311yescharacteristic
100C2×C4×Dic79C2311yescharacteristic
101C2×C4×Dic79C2312yes—
102C2×C4×Dic79C2311yescharacteristic
103C42×D79—24no—
104C42×D79—24no—
105C42×D79Q818yes—
106C79⋊#95C2312yes—
107C79⋊#95C2312yes—
108C79⋊#95C2312yes—
109C79⋊#95C2312yes—
110C79⋊#95C2312yes—
111C79⋊#95C2312yes—
112C79⋊#95C2314yes—
113C79⋊#95C2314yes—
114C79⋊#95C2314yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C2×C4⋊C4×C79C2312yes—
122C2×C4⋊C4×C79C2312yes—
123C2×C4⋊C4×C79C2314yes—
124C2×C4⋊C4×C79C2314yes—
125C2×C4⋊C4×C79C2314yes—
126C2×C42×C79C2311yescharacteristic
127C2×C42×C79C2311yescharacteristic
128C2×C42×C79C2311yescharacteristic
129#95×C79C2312yes—
130#95×C79C2312yes—
131#95×C79C2314yes—
132#95×C79C2314yes—
133#95×C79C2314yes—
134C23×D79C2411yescharacteristic
135C22×Dic79C2411yescharacteristic
136C22×Dic79C2412yes—
137C22×Dic79C2414yes—
138C22×Dic79C2411yescharacteristic
139C22×Dic79C2414yes—
140C22×Dic79C2412yes—
141C22×Dic79C2411yescharacteristic
142C2×C4×D79—22no—
143C2×C4×D79—22no—
144C2×C4×D79—24no—
145C2×C4×D79—28no—
146C2×C4×D79—28no—
147C2×C4×D79—24no—
148C2×C4×D79—24no—
149C2×C4×D79—28no—
150C2×C4×D79—24no—
151C2×C4×D79—28no—
152C2×C4×D79—28no—
153C2×C4×D79—24no—
154C2×C4×D79—24no—
155C2×C4×D79—24no—
156C2×C4×D79—28no—
157C2×C4×D79C2×Q818yes—
158C2×C4×D79C2×Q814yes—
159C2×C4×D79#4114yes—
160C2×C4×D79#4114yes—
161C4⋊Dic79—24no—
162C4⋊Dic79—24no—
163C4⋊Dic79—44no—
164C4⋊Dic79—44no—
165C4⋊Dic79—44no—
166Dic79⋊C4—28no—
167Dic79⋊C4—28no—
168Dic79⋊C4—44no—
169Dic79⋊C4—44no—
170Dic79⋊C4—44no—
171Dic79⋊C4—44no—
172Dic79⋊C4—44no—
173Dic79⋊C4—44no—
174C4×Dic79—22no—
175C4×Dic79—24no—
176C4×Dic79—22no—
177C4×Dic79—22no—
178C4×Dic79—22no—
179C4×Dic79C2×Q818yes—
180C4×Dic79C2×Q814yes—
181C22×C4×C79C2411yescharacteristic
182C22×C4×C79C2412yes—
183C22×C4×C79C2414yes—
184C22×C4×C79C2411yescharacteristic
185C22×C4×C79C2414yes—
186C22×C4×C79C2412yes—
187C22×C4×C79C2411yescharacteristic
188C4⋊C4×C79—24no—
189C4⋊C4×C79—24no—
190C4⋊C4×C79—44no—
191C4⋊C4×C79—44no—
192C4⋊C4×C79—44no—
193C42×C79—22no—
194C42×C79—22no—
195C42×C79C2×Q814yes—
196C23×C79C2511yescharacteristic
197C22×D79C22×Q812yes—
198C22×D79C2×#4112yes—
199C22×D79C2×#4112yes—
200C22×D79H(5,𝔽2)14yes—
201C22×D792−1+414yes—
202C2×C4×C79—22no—
203C2×C4×C79—22no—
204C2×C4×C79—21no—
205C2×C4×C79—21no—
206C2×C4×C79—22no—
207C2×C4×C79—24no—
208C2×C4×C79—24no—
209C2×C4×C79—22no—
210C2×C4×C79—24no—
211C2×C4×C79—22no—
212C2×C4×C79—24no—
213C2×C4×C79—24no—
214C2×C4×C79—22no—
215C2×C4×C79—22no—
216C2×C4×C79—24no—
217C2×C4×C79C22×Q814yes—
218C2×C4×C79C22×Q812yes—
219C2×C4×C79C2×#4112yes—
220C2×C4×C79C2×#4112yes—
221C2×Dic79—22no—
222C2×Dic79—22no—
223C2×Dic79—21no—
224C2×Dic79—21no—
225C2×Dic79—22no—
226C2×Dic79—24no—
227C2×Dic79—24no—
228C2×Dic79—24no—
229C2×Dic79—24no—
230C2×Dic79—22no—
231C2×Dic79—24no—
232C2×Dic79—22no—
233C2×Dic79—22no—
234C2×Dic79—22no—
235C2×Dic79—24no—
236C2×Dic79C22×Q814yes—
237C2×Dic79C22×Q812yes—
238C2×Dic79C2×#4112yes—
239C2×Dic79C2×#4112yes—
240C4×D79—216no—
241C4×D79—44no—
242C4×D79—416no—
243C4×D79—44no—
244C4×D79—48no—
245C4×D79—416no—
246C4×D79#125116yes—
247C22×C79C23×Q811yescharacteristic
248C22×C79C22×#4111yescharacteristic
249C22×C79C22×#4111yescharacteristic
250C22×C79C2×H(5,𝔽2)12yes—
251C22×C79C2×2−1+412yes—
252C2×D79C2×#12514yes—
253C2×D79#54014yes—
254C2×D79#54114yes—
255C2×D79#54218yes—
256C2×D79#54418yes—
257C4×C79—24no—
258C4×C79—41no—
259C4×C79—44no—
260C4×C79—41no—
261C4×C79—42no—
262C4×C79—44no—
263C4×C79C2×#12514yes—
264Dic79—24no—
265Dic79—41no—
266Dic79—44no—
267Dic79—41no—
268Dic79—42no—
269Dic79—44no—
270Dic79C2×#12514yes—
271C2×#2647—791nomaximal, Sylow
272C2×C79C22×#12511yescharacteristic
273C2×C79C2×#54011yescharacteristic
274C2×C79C2×#54111yescharacteristic
275C2×C79C2×#54212yes—
276C2×C79C2×#54412yes—
277D79#264718yesdirect product factor
278#2647—794no—
279#2647—794no—
280#2647—792no—
281#2647—792no—
282#2647—791no—
283#2647—791no—
284#2647—791no—
285#2647D7911yescharacteristic, direct product factor
286C2×#400—794no—
287C2×#398—794no—
288C2×#389—792no—
289C2×#389—792no—
290C2×#384—791no—
291C2×#382—791no—
292C2×#376—791no—
293C79C2×#264711yescharacteristic, complemented, Sylow
294C22×C4⋊C4—794no—
295C22×C4⋊C4—794no—
296C22×C4⋊C4—794no—
297C22×C4⋊C4—792no—
298C22×C4⋊C4—792no—
299C22×C42—791no—
300C22×C42—791no—
301C22×C42—791no—
302#400—794no—
303#400—794no—
304#400—794no—
305#400—794no—
306#400—794no—
307#400—794no—
308#400—794no—
309#400C2×D7914yes—
310#398—794no—
311#398—794no—
312#398—794no—
313#398—794no—
314#398—794no—
315#398—794no—
316#398—794no—
317#398C2×D7914yes—
318#389—794no—
319#389—794no—
320#389—792no—
321#389—792no—
322#389—792no—
323#389—792no—
324#389—792no—
325#389—792no—
326#389—794no—
327#389—794no—
328#389C2×D7912yes—
329#389C2×D7912yes—
330#384—792no—
331#384—794no—
332#384—791no—
333#384C2×D7911yescharacteristic
334#382—792no—
335#382—791no—
336#382—794no—
337#382C2×D7911yescharacteristic
338#376—791no—
339#376—791no—
340#376—791no—
341#376—792no—
342#376—792no—
343#376C2×D7911yescharacteristic
344C2×#95—792no—
345C2×#95—794no—
346C2×#95—794no—
347C2×#95—792no—
348C2×#95—794no—
349C23×C4—791no—
350C23×C4—792no—
351C23×C4—794no—
352C23×C4—791no—
353C23×C4—794no—
354C23×C4—792no—
355C23×C4—791no—
356C2×C4⋊C4—3168no—
357C2×C4⋊C4—3168no—
358C2×C4⋊C4—3168no—
359C2×C4⋊C4—794no—
360C2×C4⋊C4—794no—
361C2×C4⋊C4—794no—
362C2×C4⋊C4—794no—
363C2×C4⋊C4—794no—
364C2×C4⋊C4—794no—
365C2×C4⋊C4—794no—
366C2×C4⋊C4—794no—
367C2×C4⋊C4—794no—
368C2×C4⋊C4—794no—
369C2×C4⋊C4—792no—
370C2×C4⋊C4—794no—
371C2×C4⋊C4—792no—
372C2×C4⋊C4—1588no—
373C2×C4⋊C4—1588no—
374C2×C4⋊C4C22×D7912yes—
375C2×C4⋊C4C22×D7912yes—
376C2×C4⋊C4C22×D7914yes—
377C2×C4⋊C4C22×D7914yes—
378C2×C4⋊C4C22×D7914yes—
379C2×C42—792no—
380C2×C42—791no—
381C2×C42—798no—
382C2×C42—791no—
383C2×C42—792no—
384C2×C42—791no—
385C2×C42—791no—
386C2×C42—791no—
387C2×C42—1584no—
388C2×C42—1584no—
389C2×C42C22×D7911yescharacteristic
390C2×C42C22×D7911yescharacteristic
391C2×C42C22×D7911yescharacteristic
392#95—792no—
393#95—792no—
394#95—792no—
395#95—792no—
396#95—792no—
397#95—792no—
398#95—794no—
399#95—794no—
400#95—794no—
401#95—794no—
402#95—794no—
403#95—794no—
404#95—794no—
405#95—794no—
406#95—794no—
407#95C22×D7912yes—
408#95C22×D7912yes—
409#95C22×D7914yes—
410#95C22×D7914yes—
411#95C22×D7914yes—
412C24—791no—
413C22×C4—791no—
414C22×C4—794no—
415C22×C4—794no—
416C22×C4—794no—
417C22×C4—792no—
418C22×C4—798no—
419C22×C4—791no—
420C22×C4—792no—
421C22×C4—794no—
422C22×C4—791no—
423C22×C4—794no—
424C22×C4—1582no—
425C22×C4—1584no—
426C22×C4—1582no—
427C22×C4—1588no—
428C22×C4—1588no—
429C22×C4—1584no—
430C22×C4—1588no—
431C22×C4—1584no—
432C22×C4—1588no—
433C22×C4—1588no—
434C22×C4—1588no—
435C22×C4—1584no—
436C22×C4—1584no—
437C22×C4—1584no—
438C22×C4—1584no—
439C22×C4C23×D7911yescharacteristic
440C22×C4C23×D7912yes—
441C22×C4C23×D7914yes—
442C22×C4C23×D7911yescharacteristic
443C22×C4C23×D7914yes—
444C22×C4C23×D7912yes—
445C22×C4C23×D7911yescharacteristic
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—44no—
449C4⋊C4—44no—
450C4⋊C4—44no—
451C4⋊C4—3164no—
452C4⋊C4—3164no—
453C4⋊C4—3164no—
454C4⋊C4—3164no—
455C4⋊C4—3164no—
456C4⋊C4—3164no—
457C4⋊C4—3164no—
458C4⋊C4—3164no—
459C4⋊C4—3164no—
460C4⋊C4—1588no—
461C4⋊C4—1588no—
462C4⋊C4—1584no—
463C4⋊C4—1584no—
464C42—22no—
465C42—22no—
466C42—798no—
467C42—794no—
468C42—1584no—
469C42—1582no—
470C42—1582no—
471C42—1582no—
472C42—1582no—
473C42Q8×D7914yes—
474C23—794no—
475C23—794no—
476C23—792no—
477C23—792no—
478C23—792no—
479C23C24×D7911yescharacteristic
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—3168no—
496C2×C4—31616no—
497C2×C4—3164no—
498C2×C4—31616no—
499C2×C4—3164no—
500C2×C4—792no—
501C2×C4—792no—
502C2×C4—792no—
503C2×C4—7916no—
504C2×C4—794no—
505C2×C4—15816no—
506C2×C4—1584no—
507C2×C4—1582no—
508C2×C4—1584no—
509C2×C4—1582no—
510C2×C4—1584no—
511C2×C4—1582no—
512C2×C4—1584no—
513C2×C4—1582no—
514C2×C4—1582no—
515C2×C4—1581no—
516C2×C4—1581no—
517C2×C4—1584no—
518C2×C4—1584no—
519C2×C4—1582no—
520C2×C4—1582no—
521C2×C4C2×Q8×D7914yes—
522C2×C4C2×Q8×D7912yes—
523C2×C4#41×D7912yes—
524C2×C4#41×D7912yes—
525C22—798no—
526C22—798no—
527C22—794no—
528C22—794no—
529C22—794no—
530C22C22×Q8×D7911yescharacteristic
531C22C2×#41×D7911yescharacteristic
532C22C2×#41×D7911yescharacteristic
533C22H(5,𝔽2)×D7912yes—
534C222−1+4×D7912yes—
535C4—24no—
536C4—42no—
537C4—44no—
538C4—41no—
539C4—44no—
540C4—41no—
541C4—3162no—
542C4—3164no—
543C4—3161no—
544C4—3164no—
545C4—3161no—
546C4—794no—
547C4—1584no—
548C4#125×D7914yes—
549C2—798no—
550C2C2×#125×D7911yescharacteristic
551C2#540×D7911yescharacteristic
552C2#541×D7911yescharacteristic
553C2#542×D7912yes—
554C2#544×D7912yes—
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2647C2
prime radicalC23×D79C24
hypercenter#2647D79
hypocenterC79C2×#2647
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2647

Complements

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

NH ≅ G/Ntype
1. #23769380C2semidirect
2. #23769379C2semidirect
3. #23769378C2semidirect
4. #23769377C2semidirect
5. #23769376C2semidirect
6. #23769375C2semidirect
7. #23769374C2semidirect
15. C79×#2647C2semidirect
277. D79#2647direct (N × H)
285. #2647D79direct (N × H)
293. C79C2×#2647semidirect

Maximal subgroups

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

subgroupindex
#237693802
#237693792
#237693782
#237693772
#237693762
#237693752
#237693742
#400×D792
#398×D792
#389×D792
#384×D792
#382×D792
#376×D792
C79×#26472
C2×#264779