Finite Group Databasebeta

← #34446047

Subgroups — #34446047

Order 20224.

480 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23776413C211yesmaximal, characteristic
2#23765643C211yesmaximal, characteristic
3#23765639C211yesmaximal, characteristic, complemented
4#23765634C211yesmaximal, characteristic, complemented
5#23765561C211yesmaximal, characteristic, complemented
6#23765554C211yesmaximal, characteristic, complemented
7#23765544C211yesmaximal, characteristic, complemented
8#23765462C211yesmaximal, characteristic, complemented
9#23765462C211yesmaximal, characteristic, complemented
10#23765440C211yesmaximal, characteristic
11#23765309C211yesmaximal, characteristic, complemented
12#23765269C211yesmaximal, characteristic, complemented
13#23765262C211yesmaximal, characteristic, complemented
14C4×#14579104C211yesmaximal, characteristic, complemented
15C79×#3383C211yesmaximal, characteristic, complemented
16#19099298—21no—
17C2×#14579107C2211yescharacteristic
18C2×#14579104C2211yescharacteristic
19C2×#14579104C2211yescharacteristic
20#19098947C2211yescharacteristic
21#19098947C2211yescharacteristic
22#19098940C2211yescharacteristic
23#19098779—21no—
24#19098779—21no—
25#19098764—21no—
26C4×Dic316C2211yescharacteristic
27C4×D632C2211yescharacteristic
28C4×D632C2211yescharacteristic
29#19098390C2211yescharacteristic
30#19098390C2211yescharacteristic
31#19098388C2211yescharacteristic
32C4⋊(C79⋊C16)C2211yescharacteristic
33C4⋊(C79⋊C16)C2211yescharacteristic
34C4⋊(C79⋊C16)C2211yescharacteristic
35#19098367C2211yescharacteristic
36#19098366C2211yescharacteristic
37#19098366C2211yescharacteristic
38#19098366C2211yescharacteristic
39#19098363C2211yescharacteristic
40#19098363C2211yescharacteristic
41#19098363C2211yescharacteristic
42#19098363C2211yescharacteristic
43#19098363C2211yescharacteristic
44#19098363C2211yescharacteristic
45#19098339C2211yescharacteristic
46#19098339C2211yescharacteristic
47C4×C79⋊C16C2211yescharacteristic
48#557×C79—21no—
49#500×C79C2211yescharacteristic
50#499×C79C2211yescharacteristic
51#499×C79C2211yescharacteristic
52#479×C79—21no—
53#479×C79—21no—
54#475×C79—21no—
55C8×Q8×C79C2211yescharacteristic
56C4×Q16×C79C2211yescharacteristic
57C4×Q16×C79C2211yescharacteristic
58C4×Q16×C79C2211yescharacteristic
59C2×Dic316C2311yescharacteristic
60C2×#11929613—21no—
61C2×#11929613—21no—
62C2×D632—21no—
63C2×D632C2311yescharacteristic
64C2×D632C2311yescharacteristic
65#14579158—21no—
66#14579150—41no—
67#14579149—21no—
68#14579149—21no—
69#14579146—41no—
70#14579146—41no—
71C4×Dic158—21no—
72C4×D316—21no—
73C4×D316—21no—
74#14579123—41no—
75#14579107—22no—
76#14579104—22no—
77#14579104—22no—
78C2×C79⋊C16C2311yescharacteristic
79C2×C79⋊C16C2311yescharacteristic
80C2×C79⋊C16C2311yescharacteristic
81C2×C79⋊C16C2311yescharacteristic
82#14579095C2311yescharacteristic
83#14579086—21no—
84#14579083—21no—
85#14579083—21no—
86C2×Q16×C79C2311yescharacteristic
87C4⋊Q8×C79—21no—
88C4⋊Q8×C79—41no—
89#125×C79—21no—
90#125×C79—21no—
91#125×C79—41no—
92#125×C79—41no—
93C4×Q8×C79—21no—
94C4×Q8×C79—21no—
95C4×Q8×C79—21no—
96C4×Q8×C79—41no—
97C4×Q8×C79D411yescharacteristic
98#107×C79—21no—
99#107×C79C2311yescharacteristic
100#107×C79C2311yescharacteristic
101#107×C79C2311yescharacteristic
102#106×C79—21no—
103#106×C79—21no—
104C4⋊C8×C79D411yescharacteristic
105C4⋊C8×C79D411yescharacteristic
106C4⋊C8×C79D411yescharacteristic
107#103×C79—21no—
108#103×C79—21no—
109#103×C79—21no—
110C4×C8×C79C2311yescharacteristic
111C4×C8×C79C2311yescharacteristic
112C4×C8×C79C2311yescharacteristic
113C2×Dic158—21no—
114C2×D316—21no—
115C2×D316—21no—
116C2×D316—41no—
117C2×D316—41no—
118C2×C4×D79—41no—
119C2×C4×D79—41no—
120Dic316—21no—
121Dic316—21no—
122#11929613—81no—
123#11929613—81no—
124D632—21no—
125D632—21no—
126D632—21no—
127D632—21no—
128D632—81no—
129C4⋊Dic79—21no—
130Dic79⋊C4—41no—
131(C2×D79)⋊C4—41no—
132(C2×D79)⋊C4—41no—
133(C2×D79)⋊C4—41no—
134(C2×D79)⋊C4—41no—
135(C2×D79)⋊C4—41no—
136(C2×D79)⋊C4—41no—
137C4×Dic79—41no—
138C79⋊C16—21no—
139C79⋊C16—21no—
140C79⋊C16—21no—
141C79⋊C16—21no—
142C2×Q8×C79—21no—
143C2×Q8×C79—41no—
144C2×Q8×C79D811yescharacteristic
145Q16×C79—21no—
146Q16×C79#4112yes—
147C2×C8×C79C2×D411yescharacteristic
148C2×C8×C79C2×D411yescharacteristic
149C2×C8×C79C2×D411yescharacteristic
150C2×C8×C79C2411yescharacteristic
151C4⋊C4×C79—21no—
152C4⋊C4×C79—21no—
153C4⋊C4×C79—21no—
154C4⋊C4×C79—41no—
155C4⋊C4×C79—41no—
156C4⋊C4×C79—41no—
157C4⋊C4×C79—41no—
158C4⋊C4×C79—41no—
159C4⋊C4×C79—41no—
160C4⋊C4×C79—41no—
161C4⋊C4×C79—41no—
162C4⋊C4×C79D811yescharacteristic
163C4⋊C4×C79D811yescharacteristic
164C4⋊C4×C79D811yescharacteristic
165C42×C79—41no—
166C42×C79—41no—
167C42×C79—41no—
168C42×C79C2×D411yescharacteristic
169C42×C79C2×D411yescharacteristic
170C42×C79C2×D411yescharacteristic
171C22×D79—41no—
172C22×D79—41no—
173Q8×C79—22no—
174Q8×C79—41no—
175Q8×C79—41no—
176Q8×C79—82no—
177C2×C4×C79—41no—
178C2×C4×C79—41no—
179C2×C4×C79—41no—
180C2×C4×C79—41no—
181C2×C4×C79C2×D811yescharacteristic
182C2×C4×C79C2×D811yescharacteristic
183C2×C4×C79C2×D811yescharacteristic
184C2×C4×C79C2×D811yescharacteristic
185C2×C4×C79C2×D811yescharacteristic
186C2×C4×C79C2×D811yescharacteristic
187C2×C4×C79C22×D411yescharacteristic
188C2×Dic79—41no—
189C2×Dic79—41no—
190D316—41no—
191D316—41no—
192D316—41no—
193D316—41no—
194D316—82no—
195D316—161no—
196C4×D79—161no—
197C4×D79—161no—
198Dic158—41no—
199Dic158—41no—
200C8×C79—21no—
201C8×C79—21no—
202C8×C79—21no—
203C8×C79C2×#4111yescharacteristic
204C8×C792−1+411yescharacteristic
205C22×C79C22×D811yescharacteristic
206C2×D79—81no—
207C2×D79—81no—
208C2×D79—81no—
209C2×D79—81no—
210C2×D79—81no—
211C2×D79—81no—
212C4×C79—21no—
213C4×C79—21no—
214C4×C79—21no—
215C4×C79—21no—
216C4×C79—21no—
217C4×C79—21no—
218C4×C79—42no—
219C4×C79—81no—
220C4×C79—81no—
221C4×C79—81no—
222C4×C79#54811yescharacteristic
223C4×C79#57711yescharacteristic
224Dic79—81no—
225Dic79—81no—
226#33938—791nomaximal, Sylow
227C2×C79#335811yescharacteristic
228C2×C79#341411yescharacteristic
229C2×C79#341611yescharacteristic
230D79—161no—
231D79—161no—
232#3396—791no—
233#3383D7911yescharacteristic, complemented
234#2244—791no—
235#2243—791no—
236#2242—791no—
237#2229—791no—
238#2228—791no—
239#2226—791no—
240#2211—791no—
241#2211—791no—
242#2207—791no—
243#2183—791no—
244#2176—791no—
245#2175—791no—
246C4×SD32—791no—
247C79#3393811yescharacteristic, complemented, Sylow
248#559—1581no—
249#557—21no—
250C2×Q32—791no—
251C2×SD32—791no—
252C2×SD32—791no—
253#500C2×D7911yescharacteristic
254#499C2×D7911yescharacteristic
255#499C2×D7911yescharacteristic
256#495—791no—
257#495—791no—
258#493—791no—
259#479—21no—
260#479—21no—
261#475—21no—
262#463—1581no—
263#463—1581no—
264#460—1581no—
265C8×Q8C2×D7911yescharacteristic
266C4×Q16—791no—
267C4×Q16C2×D7911yescharacteristic
268C4×Q16C2×D7911yescharacteristic
269C4×Q16C2×D7911yescharacteristic
270C4×D8—791no—
271C4×D8—791no—
272#367—791no—
273#367—791no—
274#366—791no—
275C4⋊C16—791no—
276C4⋊C16—791no—
277C4⋊C16—791no—
278#358—791no—
279#358—791no—
280#358—791no—
281#358—791no—
282#357—791no—
283#357—791no—
284#357—791no—
285#357—791no—
286#357—791no—
287#357—791no—
288#346—791no—
289#346—791no—
290C4×C16—791no—
291C2×Q16—791no—
292C2×Q16C22×D7911yescharacteristic
293C2×SD16—1581no—
294C2×SD16—1581no—
295C2×D8—791no—
296C2×D8—791no—
297C2×D8—1581no—
298C4⋊Q8—21no—
299C4⋊Q8—41no—
300#127—1581no—
301#125—21no—
302#125—21no—
303#125—41no—
304#125—41no—
305#124—3161no—
306#124—1581no—
307#124—1581no—
308#123—3161no—
309#123—3161no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×Q8—41no—
314C4×Q8—1581no—
315C4×Q8C22⋊D7911yescharacteristic
316C4×D4—3161no—
317C4×D4—1581no—
318C4×D4—1581no—
319Q32—1582no—
320SD32—1582no—
321SD32—1582no—
322C2×C16—791no—
323C2×C16—791no—
324C2×C16—791no—
325C2×C16—791no—
326#107—21no—
327#107—791no—
328#107C22×D7911yescharacteristic
329#107C22×D7911yescharacteristic
330#107C22×D7911yescharacteristic
331#106—21no—
332#106—21no—
333C4⋊C8C22⋊D7911yescharacteristic
334C4⋊C8C22⋊D7911yescharacteristic
335C4⋊C8C22⋊D7911yescharacteristic
336#103—21no—
337#103—21no—
338#103—21no—
339#103—1581no—
340#102—1581no—
341#102—1581no—
342C4×C8C22×D7911yescharacteristic
343C4×C8C22×D7911yescharacteristic
344C4×C8C22×D7911yescharacteristic
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—1581no—
348C2×Q8#1192960911yescharacteristic
349C2×D4—3161no—
350C2×D4—3161no—
351C2×D4—1581no—
352C2×D4—1581no—
353C22×C4—3161no—
354C22×C4—3161no—
355Q16—21no—
356Q16—1581no—
357Q16—1581no—
358Q16#1192962512yes—
359SD16—6321no—
360SD16—6321no—
361D8—6321no—
362D8—1581no—
363D8—1581no—
364D8—1581no—
365D8—1581no—
366C2×C8C2×C22⋊D7911yescharacteristic
367C2×C8C2×C22⋊D7911yescharacteristic
368C2×C8C2×C22⋊D7911yescharacteristic
369C2×C8C23×D7911yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—3161no—
382C4⋊C4—1581no—
383C4⋊C4#1192960911yescharacteristic
384C4⋊C4#1192960911yescharacteristic
385C4⋊C4#1192960911yescharacteristic
386C22⋊C4—3161no—
387C22⋊C4—3161no—
388C22⋊C4—3161no—
389C22⋊C4—3161no—
390C22⋊C4—3161no—
391C22⋊C4—3161no—
392C42—41no—
393C42—41no—
394C42—41no—
395C42—3161no—
396C42C2×C22⋊D7911yescharacteristic
397C42C2×C22⋊D7911yescharacteristic
398C42C2×C22⋊D7911yescharacteristic
399C16—1581no—
400C16—1581no—
401C16—1581no—
402C16—1581no—
403C23—3161no—
404C23—3161no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—82no—
409Q8—3161no—
410Q8—3161no—
411D4—3161no—
412D4—3161no—
413D4—3161no—
414D4—3161no—
415D4—6322no—
416D4—12641no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—3161no—
422C2×C4—3161no—
423C2×C4—12641no—
424C2×C4—12641no—
425C2×C4C2×#1192960911yescharacteristic
426C2×C4C2×#1192960911yescharacteristic
427C2×C4C2×#1192960911yescharacteristic
428C2×C4C2×#1192960911yescharacteristic
429C2×C4C2×#1192960911yescharacteristic
430C2×C4C2×#1192960911yescharacteristic
431C2×C4C22×C22⋊D7911yescharacteristic
432C8—21no—
433C8—21no—
434C8—21no—
435C8C2×#1192962511yescharacteristic
436C8#1457920911yescharacteristic
437C22—6321no—
438C22—6321no—
439C22—6321no—
440C22—6321no—
441C22—6321no—
442C22—6321no—
443C22C22×#1192960911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—42no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—6321no—
455C4—6321no—
456C4#1909922411yescharacteristic
457C4#1909937111yescharacteristic
458C2—12641no—
459C2—12641no—
460C2#2377603511yescharacteristic
461C2#2377653411yescharacteristic
462C2#2377654411yescharacteristic
subgroupG/H
centerC22C22×#11929609
commutator, cosocleC2×C8×C79C24
FrattiniC2×C8C23×D79
FittingC79×#3383C2
socleC22×C79C22×D8
prime radical#19098940C22
hypercenter#3383D79
hypocenterC79#33938
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3383

Complements

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

NH ≅ G/Ntype
3. #23765639C2semidirect
4. #23765634C2semidirect
5. #23765561C2semidirect
6. #23765554C2semidirect
7. #23765544C2semidirect
8. #23765462C2semidirect
9. #23765462C2semidirect
11. #23765309C2semidirect
12. #23765269C2semidirect
13. #23765262C2semidirect
14. C4×#14579104C2semidirect
15. C79×#3383C2semidirect
233. #3383D79semidirect
247. C79#33938semidirect

Maximal subgroups

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

subgroupindex
#237764132
#237656432
#237656392
#237656342
#237655612
#237655542
#237655442
#237654622
#237654402
#237653092
#237652692
#237652622
C4×#145791042
C79×#33832
#3393879