Finite Group Databasebeta

← #34448746

Subgroups — #34448746

Order 20224.

2094 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D79C211yesmaximal, characteristic
2#23766499C214yesmaximal, complemented
3#23766493C214yesmaximal, complemented
4#23766276C214yesmaximal
5#23766274C214yesmaximal
6#23766142C211yesmaximal, characteristic, complemented
7#23766141C211yesmaximal, characteristic, complemented
8#23766139C211yesmaximal, characteristic, complemented
9#23766015C212yesmaximal
10#23765959C212yesmaximal, complemented
11C4×#14579152C212yesmaximal, complemented
12#23765805C211yesmaximal, characteristic
13#23765754C212yesmaximal
14#23765739C211yesmaximal, characteristic
15C79×#2330C211yesmaximal, characteristic, complemented
16C2×#14579153C2211yescharacteristic
17C2×#14579152C2212yes—
18C2×#14579151C2214yes—
19#125×D79C4116yescomplemented
20C2×#14579119C2212yes—
21C2×#14579118C2211yescharacteristic
22C2×#14579118C2211yescharacteristic
23C2×C4⋊C4×D79C2214yes—
24C2×C4⋊C4×D79C2212yes—
25C2×C42×D79C2211yescharacteristic
26#19098462C2214yes—
27#19098462C2212yes—
28#19098461C2212yes—
29#19098460C2214yes—
30#19098460C2214yes—
31#19098459C2212yes—
32#19098458C2214yes—
33#19098458C2214yes—
34#19098450C2214yes—
35#19098450C2214yes—
36#19098449C2214yes—
37#19098448C2214yes—
38#19098446C2214yes—
39#19098444C2214yes—
40#19098444C2214yes—
41#19098433C2211yescharacteristic
42#19098428C2212yes—
43#19098422C2214yes—
44#19098420C2214yes—
45#19098420C2214yes—
46C4⋊C4×Dic79C2214yes—
47C4⋊C4×Dic79C2214yes—
48C4⋊C4×Dic79C2212yes—
49C4⋊C4×Dic79C2212yes—
50C4×Dic79⋊C4C2214yes—
51C4×Dic79⋊C4C2214yes—
52C4×C4⋊Dic79C2214yes—
53C4×C4⋊Dic79C2212yes—
54#19098414C2214yes—
55#19098414C2212yes—
56#19098414C2214yes—
57#19098414C2212yes—
58C4×(C2×D79)⋊C4C2214yes—
59#19098410C2212yes—
60#19098410C2214yes—
61#19098410C2212yes—
62#19098409C2211yescharacteristic
63C42×Dic79C2211yescharacteristic
64C42×Dic79C2211yescharacteristic
65C2×#125×C79C2211yescharacteristic
66#389×C79C2214yes—
67#389×C79C2212yes—
68#387×C79C2214yes—
69#384×C79C2211yescharacteristic
70C4×C4⋊C4×C79C2212yes—
71#376×C79C2211yescharacteristic
72C22×C4×D79C2312yes—
73C22×C4×D79C2314yes—
74C22×C4×D79C2311yescharacteristic
75#14579153C2×C418yes—
76#14579152C2×C4116yes—
77#14579151C2×C4132yes—
78#14579119—28no—
79#14579118—24no—
80#14579118Q818yes—
81C2×C4⋊Dic79C2312yes—
82C2×C4⋊Dic79C2314yes—
83C2×C4⋊Dic79C2314yes—
84C2×C4⋊Dic79C2314yes—
85C2×C4⋊Dic79C2312yes—
86C2×Dic79⋊C4C2311yescharacteristic
87C2×Dic79⋊C4C2311yescharacteristic
88C2×Dic79⋊C4C2314yes—
89C2×Dic79⋊C4C2314yes—
90C2×Dic79⋊C4C2314yes—
91C2×Dic79⋊C4C2314yes—
92C2×Dic79⋊C4C2314yes—
93C2×Dic79⋊C4C2312yes—
94C4⋊C4×D79C2×C4116yes—
95C4⋊C4×D79C2×C4132yes—
96C2×(C2×D79)⋊C4C2311yescharacteristic
97C2×(C2×D79)⋊C4C2311yescharacteristic
98C2×(C2×D79)⋊C4C2314yes—
99C2×(C2×D79)⋊C4C2312yes—
100C2×C4×Dic79C2311yescharacteristic
101C2×C4×Dic79C2314yes—
102C2×C4×Dic79C2312yes—
103C2×C4×Dic79C2312yes—
104C2×C4×Dic79C2312yes—
105C2×C4×Dic79C2312yes—
106C2×C4×Dic79C2314yes—
107C2×C4×Dic79C2314yes—
108C2×C4×Dic79C2314yes—
109C2×C4×Dic79C2311yescharacteristic
110C2×C4×Dic79C2312yes—
111C2×C4×Dic79C2311yescharacteristic
112C42×D79C2×C418yes—
113C79⋊#95C2312yes—
114C79⋊#95C2312yes—
115C79⋊#95C2314yes—
116C79⋊#95C2314yes—
117C79⋊#95C2314yes—
118C79⋊#95C2314yes—
119C79⋊#95C2314yes—
120C79⋊#95C2314yes—
121C79⋊#95C2314yes—
122C79⋊#95C2314yes—
123#125×C79C2×C418yes—
124C2×C4⋊C4×C79C2312yes—
125C2×C4⋊C4×C79C2314yes—
126C2×C4⋊C4×C79C2314yes—
127C2×C4⋊C4×C79C2312yes—
128C2×C4⋊C4×C79C2314yes—
129C2×C42×C79C2311yescharacteristic
130C2×C42×C79C2314yes—
131C2×C42×C79C2311yescharacteristic
132C2×C42×C79C2311yescharacteristic
133#95×C79C2314yes—
134#95×C79C2312yes—
135#95×C79C2312yes—
136#95×C79C2314yes—
137C23×D79C2411yescharacteristic
138C22×Dic79C2411yescharacteristic
139C22×Dic79C2411yescharacteristic
140C22×Dic79C2414yes—
141C22×Dic79C2412yes—
142C22×Dic79C2414yes—
143C22×Dic79C2412yes—
144C22×Dic79C2411yescharacteristic
145C2×C4×D79—44no—
146C2×C4×D79—42no—
147C2×C4×D79—44no—
148C2×C4×D79—42no—
149C2×C4×D79C22×C418yes—
150C2×C4×D79C22×C4116yes—
151C2×C4×D79C22×C414yes—
152C2×C4×D79C2×Q814yes—
153C2×C4×D79#4114yes—
154C4⋊Dic79—24no—
155C4⋊Dic79—44no—
156C4⋊Dic79—44no—
157C4⋊Dic79C22×C4116yes—
158C4⋊Dic79C22×C418yes—
159Dic79⋊C4—22no—
160Dic79⋊C4—22no—
161Dic79⋊C4—44no—
162Dic79⋊C4—44no—
163Dic79⋊C4C22×C4116yes—
164Dic79⋊C4C22×C4116yes—
165Dic79⋊C4C22×C4116yes—
166Dic79⋊C4C2×Q818yes—
167(C2×D79)⋊C4—22no—
168(C2×D79)⋊C4—22no—
169(C2×D79)⋊C4—28no—
170(C2×D79)⋊C4C2×Q818yes—
171C4×Dic79—28no—
172C4×Dic79—22no—
173C4×Dic79—42no—
174C4×Dic79—44no—
175C4×Dic79—44no—
176C4×Dic79—42no—
177C4×Dic79—42no—
178C4×Dic79—44no—
179C4×Dic79—42no—
180C4×Dic79C22×C418yes—
181C4×Dic79C22×C414yes—
182C4×Dic79C2×Q814yes—
183C22×C4×C79C2411yescharacteristic
184C22×C4×C79C2414yes—
185C22×C4×C79C2411yescharacteristic
186C22×C4×C79C2414yes—
187C22×C4×C79C2412yes—
188C22×C4×C79C2412yes—
189C22×C4×C79C2411yescharacteristic
190C4⋊C4×C79—24no—
191C4⋊C4×C79—44no—
192C4⋊C4×C79—44no—
193C4⋊C4×C79C22×C4116yes—
194C4⋊C4×C79C22×C418yes—
195C42×C79—22no—
196C42×C79—44no—
197C42×C79C22×C414yes—
198C42×C79C2×Q814yes—
199C23×C79C2511yescharacteristic
200C22×D79—22no—
201C22×D79—22no—
202C22×D79C23×C412yes—
203C22×D79C22×Q812yes—
204C22×D79C2×#4112yes—
205C2×C4×C79—22no—
206C2×C4×C79—24no—
207C2×C4×C79—22no—
208C2×C4×C79—22no—
209C2×C4×C79—24no—
210C2×C4×C79—22no—
211C2×C4×C79—24no—
212C2×C4×C79—21no—
213C2×C4×C79—21no—
214C2×C4×C79—22no—
215C2×C4×C79—24no—
216C2×C4×C79—22no—
217C2×C4×C79—24no—
218C2×C4×C79C23×C414yes—
219C2×C4×C79C23×C418yes—
220C2×C4×C79C23×C412yes—
221C2×C4×C79C22×Q814yes—
222C2×C4×C79C22×Q812yes—
223C2×C4×C79C2×#4112yes—
224C2×Dic79—22no—
225C2×Dic79—22no—
226C2×Dic79—22no—
227C2×Dic79—22no—
228C2×Dic79—24no—
229C2×Dic79—24no—
230C2×Dic79—21no—
231C2×Dic79—21no—
232C2×Dic79—24no—
233C2×Dic79—24no—
234C2×Dic79—22no—
235C2×Dic79—22no—
236C2×Dic79—24no—
237C2×Dic79C23×C414yes—
238C2×Dic79C23×C418yes—
239C2×Dic79C23×C412yes—
240C2×Dic79C22×Q814yes—
241C2×Dic79C22×Q812yes—
242C2×Dic79C2×#4112yes—
243C4×D79—48no—
244C4×D79—416no—
245C4×D79C4×Q8116yes—
246C22×C79C24×C411yescharacteristic
247C22×C79C23×Q811yescharacteristic
248C22×C79C22×#4111yescharacteristic
249C22×C79#58512yes—
250C22×C79#58512yes—
251C2×D79—24no—
252C2×D79—24no—
253C2×D79—22no—
254C2×D79—22no—
255C2×D79C2×C4×Q814yes—
256C4×C79—28no—
257C4×C79—24no—
258C4×C79—24no—
259C4×C79—44no—
260C4×C79—41no—
261C4×C79—41no—
262C4×C79C2×C4×Q814yes—
263Dic79—24no—
264Dic79—28no—
265Dic79—24no—
266Dic79—41no—
267Dic79—41no—
268Dic79—44no—
269Dic79C2×C4×Q814yes—
270#34217—791nomaximal, Sylow
271C2×C79C22×C4×Q811yescharacteristic
272C2×C79#342812yes—
273C2×C79#350412yes—
274C2×C79#351211yescharacteristic
275C2×C79#351211yescharacteristic
276D79—24no—
277C22×#125—791no—
278#2370—794no—
279#2370—794no—
280#2345—794no—
281#2345—794no—
282#2330—791no—
283#2330—791no—
284#2330—791no—
285#2330D7911yescharacteristic, complemented
286#2316—792no—
287C4×#125—792no—
288C4×#125—792no—
289#2285—791no—
290#2274—792no—
291C4×#117—791no—
292C79#3421711yescharacteristic, complemented, Sylow
293C2×#125—7916no—
294C2×#125—792no—
295C2×#125—794no—
296C2×#125—791no—
297C2×#125C2×D7911yescharacteristic
298C2×#117—792no—
299C2×#117—791no—
300C2×#117—791no—
301C22×C4⋊C4—792no—
302C22×C4⋊C4—794no—
303C22×C42—791no—
304#389—792no—
305#389—792no—
306#389—794no—
307#389—794no—
308#389—794no—
309#389—792no—
310#389—794no—
311#389—794no—
312#389C2×D7912yes—
313#389C2×D7914yes—
314#387—794no—
315#387—794no—
316#387—794no—
317#387—794no—
318#387—794no—
319#387—794no—
320#387—794no—
321#387C2×D7914yes—
322#384—791no—
323#384C2×D7911yescharacteristic
324#382—792no—
325#380—794no—
326#380—794no—
327#380—794no—
328C4×C4⋊C4—792no—
329C4×C4⋊C4—792no—
330C4×C4⋊C4—794no—
331C4×C4⋊C4—794no—
332C4×C4⋊C4—792no—
333C4×C4⋊C4—794no—
334C4×C4⋊C4—794no—
335C4×C4⋊C4—794no—
336C4×C4⋊C4—794no—
337C4×C4⋊C4—792no—
338C4×C4⋊C4—792no—
339C4×C4⋊C4—794no—
340C4×C4⋊C4C2×D7912yes—
341C4×C22⋊C4—794no—
342C4×C22⋊C4—792no—
343C4×C22⋊C4—792no—
344C4×C22⋊C4—794no—
345#376—791no—
346#376C2×D7911yescharacteristic
347C43—791no—
348C43—791no—
349C23×C4—794no—
350C23×C4—792no—
351C23×C4—791no—
352#125—7932no—
353#125—7916no—
354#125—798no—
355#125C4×D7918yes—
356#117—798no—
357#117—1584no—
358#117—1588no—
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—792no—
367C2×C4⋊C4—794no—
368C2×C4⋊C4—792no—
369C2×C4⋊C4—7932no—
370C2×C4⋊C4—7916no—
371C2×C4⋊C4—792no—
372C2×C4⋊C4—791no—
373C2×C4⋊C4—791no—
374C2×C4⋊C4C22×D7912yes—
375C2×C4⋊C4C22×D7914yes—
376C2×C4⋊C4C22×D7914yes—
377C2×C4⋊C4C22×D7912yes—
378C2×C4⋊C4C22×D7914yes—
379C2×C22⋊C4—792no—
380C2×C22⋊C4—794no—
381C2×C22⋊C4—791no—
382C2×C22⋊C4—791no—
383C2×C42—792no—
384C2×C42—792no—
385C2×C42—792no—
386C2×C42—792no—
387C2×C42—794no—
388C2×C42—794no—
389C2×C42—794no—
390C2×C42—791no—
391C2×C42—791no—
392C2×C42—792no—
393C2×C42—798no—
394C2×C42—791no—
395C2×C42—794no—
396C2×C42C22×D7911yescharacteristic
397C2×C42C22×D7914yes—
398C2×C42C22×D7911yescharacteristic
399C2×C42C22×D7911yescharacteristic
400#95—792no—
401#95—792no—
402#95—794no—
403#95—794no—
404#95—794no—
405#95—794no—
406#95—794no—
407#95—794no—
408#95—794no—
409#95—794no—
410#95C22×D7912yes—
411#95C22×D7912yes—
412#95C22×D7914yes—
413#95C22×D7914yes—
414C24—791no—
415C22×C4—3164no—
416C22×C4—3162no—
417C22×C4—3164no—
418C22×C4—3162no—
419C22×C4—798no—
420C22×C4—7916no—
421C22×C4—791no—
422C22×C4—794no—
423C22×C4—794no—
424C22×C4—794no—
425C22×C4—792no—
426C22×C4—792no—
427C22×C4—794no—
428C22×C4—791no—
429C22×C4—794no—
430C22×C4—791no—
431C22×C4C23×D7914yes—
432C22×C4C23×D7911yescharacteristic
433C22×C4C23×D7911yescharacteristic
434C22×C4C23×D7912yes—
435C22×C4C23×D7914yes—
436C22×C4C23×D7912yes—
437C22×C4C23×D7911yescharacteristic
438C4⋊C4—24no—
439C4⋊C4—44no—
440C4⋊C4—44no—
441C4⋊C4—3164no—
442C4⋊C4—3164no—
443C4⋊C4—3164no—
444C4⋊C4—3164no—
445C4⋊C4—798no—
446C4⋊C4—7916no—
447C4⋊C4—7916no—
448C4⋊C4—7916no—
449C4⋊C4—7916no—
450C4⋊C4—798no—
451C4⋊C4—1582no—
452C4⋊C4—1582no—
453C4⋊C4—1584no—
454C4⋊C4C2×C4×D79116yes—
455C4⋊C4C2×C4×D7918yes—
456C22⋊C4—798no—
457C22⋊C4—1582no—
458C22⋊C4—1582no—
459C22⋊C4—1588no—
460C42—22no—
461C42—44no—
462C42—3162no—
463C42—3164no—
464C42—3162no—
465C42—3164no—
466C42—3164no—
467C42—3162no—
468C42—3162no—
469C42—794no—
470C42—798no—
471C42—794no—
472C42—1588no—
473C42—1582no—
474C42C2×C4×D7914yes—
475C42Q8×D7914yes—
476C23—792no—
477C23—792no—
478C23—792no—
479C23—1582no—
480C23—1582no—
481C23C24×D7911yescharacteristic
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—24no—
495C2×C4—3168no—
496C2×C4—31616no—
497C2×C4—792no—
498C2×C4—792no—
499C2×C4—792no—
500C2×C4—7916no—
501C2×C4—794no—
502C2×C4—798no—
503C2×C4—794no—
504C2×C4—1582no—
505C2×C4—1584no—
506C2×C4—1582no—
507C2×C4—1584no—
508C2×C4—1581no—
509C2×C4—1584no—
510C2×C4—1581no—
511C2×C4—1582no—
512C2×C4—1582no—
513C2×C4—1584no—
514C2×C4—1582no—
515C2×C4—1582no—
516C2×C4—1584no—
517C2×C4C22×C4×D7914yes—
518C2×C4C22×C4×D7918yes—
519C2×C4C22×C4×D7912yes—
520C2×C4C2×Q8×D7914yes—
521C2×C4C2×Q8×D7912yes—
522C2×C4#41×D7912yes—
523C22—794no—
524C22—1582no—
525C22—1582no—
526C22—1584no—
527C22—1584no—
528C22C23×C4×D7911yescharacteristic
529C22C22×Q8×D7911yescharacteristic
530C22C2×#41×D7911yescharacteristic
531C22#1909939812yes—
532C22#1909940012yes—
533C4—28no—
534C4—24no—
535C4—24no—
536C4—44no—
537C4—41no—
538C4—41no—
539C4—3161no—
540C4—3164no—
541C4—3161no—
542C4—794no—
543C4—1584no—
544C4—1588no—
545C4—1584no—
546C4C4×Q8×D7914yes—
547C2—1584no—
548C2C2×C4×Q8×D7911yescharacteristic
549C2#2377660012yes—
550C2#2377722312yes—
551C2#2377731911yescharacteristic
552C2#2377732311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2330C2
socle, cosocleC23×C79C25
prime radicalC23×D79C24
hypercenter#2330D79
hypocenterC79#34217
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2330

Complements

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

NH ≅ G/Ntype
2. #23766499C2semidirect
3. #23766493C2semidirect
6. #23766142C2semidirect
7. #23766141C2semidirect
8. #23766139C2semidirect
10. #23765959C2semidirect
11. C4×#14579152C2semidirect
15. C79×#2330C2semidirect
19. #125×D79C4semidirect
285. #2330D79semidirect
292. C79#34217semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D792
#237664992
#237664932
#237662762
#237662742
#237661422
#237661412
#237661392
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C4×#145791522
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C79×#23302
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