Finite Group Databasebeta

← #28484772

Subgroups — #28484772

Order 15104.

478 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433884C211yesmaximal, characteristic
2#21424116C211yesmaximal, characteristic
3#21422596C211yesmaximal, characteristic, complemented
4#21422552C211yesmaximal, characteristic, complemented
5#21421992C211yesmaximal, characteristic, complemented
6#21421936C211yesmaximal, characteristic, complemented
7C8×#41×C59C211yesmaximal, characteristic
8#16837959C2211yescharacteristic
9#16837709—21no—
10#16837702—21no—
11#16837697C411yescharacteristic, complemented
12#16837692C411yescharacteristic, complemented
13#16837687C411yescharacteristic, complemented
14#16837682C411yescharacteristic, complemented
15#16837438—21no—
16#16837426C2211yescharacteristic
17C2×C4⋊(C59⋊C8)C2211yescharacteristic
18C2×#14273654—21no—
19#16837398—21no—
20C4×C4⋊Dic59C2211yescharacteristic
21#16837161—21no—
22#16837140—22no—
23#16837134—21no—
24#16837134—21no—
25C4×#41×C59C2211yescharacteristic
26C8×Q8×C59—21no—
27C8×D4×C59—21no—
28C8×D4×C59—22no—
29C59×#431—21no—
30C59×#431C2211yescharacteristic
31C2×C4×C8×C59—21no—
32C2×C4×C8×C59C2211yescharacteristic
33C2×#11745664—21no—
34C22×C59⋊C8—21no—
35#14273727C2×C411yescharacteristic
36#14273727C2×C411yescharacteristic
37#14273719—21no—
38#14273706—21no—
39#14273706—21no—
40C4×Dic118—21no—
41C4×Dic118—21no—
42#14273686—21no—
43C2×C4⋊Dic59—21no—
44C2×C4×Dic59—21no—
45#14273660—21no—
46#14273660—21no—
47#14273658—21no—
48#14273658—21no—
49C4⋊(C59⋊C8)—21no—
50C4⋊(C59⋊C8)—21no—
51C4⋊(C59⋊C8)—21no—
52C4⋊(C59⋊C8)C2×C411yescharacteristic
53C4⋊(C59⋊C8)C2×C411yescharacteristic
54#14273654—42no—
55#14273651—21no—
56#14273651—21no—
57#14273648—21no—
58#14273648—21no—
59C59⋊#95—21no—
60C2×#41×C59D411yescharacteristic
61C22×C8×C59—22no—
62C22×C8×C59—21no—
63C4×Q8×C59C2×C411yescharacteristic
64C4×Q8×C59D411yescharacteristic
65C4×D4×C59—21no—
66C4×D4×C59—21no—
67C4×D4×C59C2×C411yescharacteristic
68C4×D4×C59D411yescharacteristic
69#117×C59—21no—
70#117×C59D411yescharacteristic
71C2×C42×C59—21no—
72C2×C42×C59C2311yescharacteristic
73C4⋊C8×C59—22no—
74C4⋊C8×C59—21no—
75C22⋊C8×C59—22no—
76C22⋊C8×C59D412yes—
77C4×C8×C59—22no—
78C4×C8×C59—21no—
79C4×C8×C59—21no—
80C4×C8×C59D411yescharacteristic
81C4×C8×C59D411yescharacteristic
82#41×C59—21no—
83#41×C59—21no—
84#41×C59SD1612yes—
85#41×C59Q1612yes—
86C2×Q8×C59C22⋊C411yescharacteristic
87C2×D4×C59—21no—
88C2×D4×C59C22⋊C411yescharacteristic
89C22×C4×C59—21no—
90C22×C4×C59—21no—
91C22×C4×C59—21no—
92C22×C4×C59C2×D411yescharacteristic
93C22×C4×C59C2×D411yescharacteristic
94C22×C4×C59#4111yescharacteristic
95C22×Dic59—41no—
96C2×Dic118—21no—
97C2×Dic118—21no—
98C2×C8×C59—21no—
99C2×C8×C59—22no—
100C2×C8×C59—21no—
101C2×C8×C59—42no—
102C2×C8×C59—44no—
103C4⋊C4×C59—21no—
104C4⋊C4×C59—21no—
105C4⋊C4×C59C22⋊C411yescharacteristic
106C4⋊C4×C59C22⋊C411yescharacteristic
107C22⋊C4×C59—21no—
108C22⋊C4×C59—21no—
109C22⋊C4×C59—21no—
110C42×C59—21no—
111C42×C59—21no—
112C42×C59—21no—
113C42×C59C22×C411yescharacteristic
114C42×C59C2×D411yescharacteristic
115C42×C59C2×D411yescharacteristic
116C42×C59#4111yescharacteristic
117C22⋊Dic59—41no—
118C4⋊Dic59—22no—
119C4⋊Dic59—21no—
120C4⋊Dic59—21no—
121C4⋊Dic59—21no—
122C4⋊Dic59—21no—
123C4⋊Dic59—41no—
124Dic59⋊C4—41no—
125Dic59⋊C4—41no—
126C4×Dic59—41no—
127C4×Dic59—41no—
128C4×Dic59—41no—
129#11745664—41no—
130#11745664—41no—
131C2×C59⋊C8—21no—
132C2×C59⋊C8—21no—
133C2×C59⋊C8—41no—
134C2×C59⋊C8—41no—
135C2×C59⋊C8—41no—
136C23×C59—21no—
137C23×C59#12111yescharacteristic
138Q8×C59—21no—
139Q8×C59#10312yes—
140D4×C59—22no—
141D4×C59—22no—
142D4×C59—21no—
143D4×C59#10312yes—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—22no—
148C2×C4×C59—22no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—41no—
152C2×C4×C59—42no—
153C2×C4×C59—41no—
154C2×C4×C59—41no—
155C2×C4×C59C2×C22⋊C411yescharacteristic
156C2×C4×C59C4×D411yescharacteristic
157C2×C4×C59C4×D411yescharacteristic
158C2×C4×C59#12011yescharacteristic
159C2×C4×C59#12111yescharacteristic
160C2×C4×C59#12311yescharacteristic
161C2×C4×C59C2×SD1611yescharacteristic
162C2×C4×C59C2×Q1611yescharacteristic
163C2×C4×C59#13511yescharacteristic
164C2×C4×C59#13511yescharacteristic
165C2×Dic59—42no—
166C2×Dic59—41no—
167C2×Dic59—41no—
168C2×Dic59—81no—
169C2×Dic59—81no—
170Dic118—41no—
171Dic118—41no—
172Dic118—81no—
173C8×C59—22no—
174C8×C59—42no—
175C8×C59—41no—
176C59⋊C8—41no—
177C59⋊C8—41no—
178C59⋊C8—81no—
179#9207—591nomaximal, Sylow
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—22no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59#38611yescharacteristic
186C22×C59#46511yescharacteristic
187C22×C59#46711yescharacteristic
188C4×C59—21no—
189C4×C59—22no—
190C4×C59—21no—
191C4×C59—21no—
192C4×C59—41no—
193C4×C59—41no—
194C4×C59C2×#10311yescharacteristic
195C4×C59#41611yescharacteristic
196C4×C59#44311yescharacteristic
197C4×C59#44411yescharacteristic
198C4×C59#46511yescharacteristic
199C4×C59#46711yescharacteristic
200Dic59—82no—
201Dic59—81no—
202Dic59—81no—
203#3076—591no—
204C8×#41D5911yescharacteristic
205#1806—591no—
206#1503—591no—
207#1493—591no—
208#1301—591no—
209#1279—591no—
210C2×C59—21no—
211C2×C59—21no—
212C2×C59—42no—
213C2×C59#187611yescharacteristic
214C2×C59#189211yescharacteristic
215C2×C59#190611yescharacteristic
216#533—591no—
217C4×#41C2×D5911yescharacteristic
218#479—1181no—
219#478—1181no—
220#477—591no—
221#476—591no—
222#475—591no—
223#474—591no—
224C8×Q8—21no—
225C8×D4—21no—
226C8×D4—22no—
227#431—21no—
228#431C2×D5911yescharacteristic
229#427—1181no—
230#423—591no—
231C2×C4⋊C8—591no—
232C2×#104—1181no—
233#416—1181no—
234C2×C4×C8—21no—
235C2×C4×C8C2×D5911yescharacteristic
236C4×C4⋊C4—591no—
237#339—1181no—
238#328—1182no—
239Q8⋊C8—1181no—
240Q8⋊C8—1181no—
241C59#920711yescharacteristic, complemented, Sylow
242C2×#41D23611yescharacteristic
243C2×M16—1181no—
244C22×C8—22no—
245C22×C8—21no—
246C22×C8—1181no—
247C4⋊Q8—591no—
248C4⋊Q8—591no—
249#125—1181no—
250C22⋊Q8—1181no—
251C22⋊Q8—1181no—
252C4×Q8—1181no—
253C4×Q8—1181no—
254C4×Q8C4×D5911yescharacteristic
255C4×Q8C22⋊D5911yescharacteristic
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C4×D5911yescharacteristic
259C4×D4C22⋊D5911yescharacteristic
260#117—21no—
261#117—1181no—
262#117D23611yescharacteristic
263C2×C4⋊C4—1181no—
264C2×C42—21no—
265C2×C42—1181no—
266C2×C42C22×D5911yescharacteristic
267#107—1181no—
268#107—1181no—
269#106—1181no—
270#106—1181no—
271C4⋊C8—22no—
272C4⋊C8—21no—
273C4⋊C8—591no—
274C4⋊C8—591no—
275C4⋊C8—1181no—
276C4⋊C8—1181no—
277C4⋊C8—1181no—
278#104—2362no—
279#103—1181no—
280#103—1181no—
281#102—1181no—
282#102—1181no—
283C22⋊C8—22no—
284C22⋊C8C22⋊D5912yes—
285C4×C8—22no—
286C4×C8—21no—
287C4×C8—21no—
288C4×C8C22⋊D5911yescharacteristic
289C4×C8C22⋊D5911yescharacteristic
290#95—1181no—
291#41—21no—
292#41—21no—
293#41#1174566012yes—
294#41Dic23612yes—
295C2×Q8—1181no—
296C2×Q8—1181no—
297C2×Q8(C2×D59)⋊C411yescharacteristic
298C2×D4—21no—
299C2×D4(C2×D59)⋊C411yescharacteristic
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—2361no—
304C22×C4C2×D23611yescharacteristic
305C22×C4#1174568511yescharacteristic
306C22×C4C2×C22⋊D5911yescharacteristic
307M16—2361no—
308M16—2361no—
309C2×C8—21no—
310C2×C8—22no—
311C2×C8—21no—
312C2×C8—42no—
313C2×C8—44no—
314C2×C8—1181no—
315C2×C8—1181no—
316C2×C8—2361no—
317C2×C8—2361no—
318C2×C8—2361no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—1182no—
322C4⋊C4—1181no—
323C4⋊C4—1181no—
324C4⋊C4—1181no—
325C4⋊C4—1181no—
326C4⋊C4—2361no—
327C4⋊C4—2361no—
328C4⋊C4—2361no—
329C4⋊C4(C2×D59)⋊C411yescharacteristic
330C4⋊C4(C2×D59)⋊C411yescharacteristic
331C22⋊C4—21no—
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—2361no—
335C42—21no—
336C42—21no—
337C42—21no—
338C42—2361no—
339C42—2361no—
340C42—2361no—
341C42C2×C4×D5911yescharacteristic
342C42#1174568511yescharacteristic
343C42C2×C22⋊D5911yescharacteristic
344C42C2×C22⋊D5911yescharacteristic
345C23—21no—
346C23#1427370111yescharacteristic
347Q8—21no—
348Q8—4721no—
349Q8—2361no—
350Q8—2361no—
351Q8#1427365212yes—
352D4—22no—
353D4—22no—
354D4—21no—
355D4#1427365212yes—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—4721no—
368C2×C4—4721no—
369C2×C4—2362no—
370C2×C4—2361no—
371C2×C4—2361no—
372C2×C4C2×(C2×D59)⋊C411yescharacteristic
373C2×C4C4×C22⋊D5911yescharacteristic
374C2×C4C4×C22⋊D5911yescharacteristic
375C2×C4#1427369611yescharacteristic
376C2×C4#1427370111yescharacteristic
377C2×C4#1427371011yescharacteristic
378C2×C4C2×#1174566011yescharacteristic
379C2×C4C2×Dic23611yescharacteristic
380C2×C4#1427374911yescharacteristic
381C2×C4#1427374911yescharacteristic
382C8—22no—
383C8—42no—
384C8—41no—
385C8—4721no—
386C8—2361no—
387C8—2361no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22#1683728111yescharacteristic
394C22#1683763111yescharacteristic
395C22#1683764311yescharacteristic
396C4—21no—
397C4—22no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—4722no—
403C4—4721no—
404C4—4721no—
405C4C2×#1427365211yescharacteristic
406C4#1683739911yescharacteristic
407C4#1683751711yescharacteristic
408C4#1683752211yescharacteristic
409C4#1683763111yescharacteristic
410C4#1683764311yescharacteristic
411C2—21no—
412C2—21no—
413C2—42no—
414C2#2142442311yescharacteristic
415C2#2142451911yescharacteristic
416C2#2142459711yescharacteristic
subgroupG/H
centerC2×C4#14273701
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC8×#41×C59C2
socleC22×C59#386
prime radicalC2×#41×C59D4
cosocleC2×C42×C59C23
hypercenterC8×#41D59
hypocenterC59#9207
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
3. #21422596C2semidirect
4. #21422552C2semidirect
5. #21421992C2semidirect
6. #21421936C2semidirect
11. #16837697C4semidirect
12. #16837692C4semidirect
13. #16837687C4semidirect
14. #16837682C4semidirect
241. C59#9207semidirect

Maximal subgroups

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

subgroupindex
#214338842
#214241162
#214225962
#214225522
#214219922
#214219362
C8×#41×C592
#920759