Finite Group Databasebeta

← #28505600

Subgroups — #28505600

Order 15104.

456 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437199C211yesmaximal, characteristic, complemented
2#21425724C211yesmaximal, characteristic, complemented
3#21425724C211yesmaximal, characteristic, complemented
4#21425717C211yesmaximal, characteristic, complemented
5#21422180C211yesmaximal, characteristic, complemented
6#21422176C211yesmaximal, characteristic, complemented
7C2×C59×#444C211yesmaximal, characteristic
8#16837819—22no—
9#16837819—22no—
10C2×#14273667—22no—
11C2×#14273667C2211yescharacteristic
12C2×#14273667C2211yescharacteristic
13C2×#14273667C2211yescharacteristic
14C2×#14273667C2211yescharacteristic
15#16837186—22no—
16#16837186—22no—
17#16837184—22no—
18C2×#135×C59C411yescharacteristic
19C2×#131×C59C2211yescharacteristic
20C2×#131×C59C2211yescharacteristic
21C59×#444—22no—
22C59×#444—22no—
23C2×#108×C59C411yescharacteristic
24C2×#104×C59C411yescharacteristic
25C2×#104×C59C411yescharacteristic
26C2×#97×C59C2211yescharacteristic
27#14273667—24no—
28#14273667—21no—
29#14273667—21no—
30#14273667—21no—
31#14273667—21no—
32#14273667—21no—
33#14273667—21no—
34#14273667—21no—
35#14273667D412yes—
36C2×C59⋊C16—24no—
37C2×C59⋊C16—21no—
38C2×C59⋊C16—21no—
39C2×C59⋊C16—21no—
40C2×C59⋊C16D412yes—
41C2×#41×C59C2×C411yescharacteristic
42C2×#41×C59C2×C411yescharacteristic
43#135×C59—22no—
44#135×C59—22no—
45C2×Q16×C59C811yescharacteristic
46C2×SD16×C59C811yescharacteristic
47C2×SD16×C59C811yescharacteristic
48C2×D8×C59C811yescharacteristic
49#131×C59—21no—
50#131×C59—21no—
51#131×C59—21no—
52#131×C59—21no—
53#131×C59—21no—
54#131×C59—21no—
55#131×C59D412yes—
56#131×C59D412yes—
57C2×M16×C59—21no—
58C2×M16×C59—21no—
59C2×M16×C59C2×C411yescharacteristic
60C2×M16×C59C2×C411yescharacteristic
61C22×C8×C59—21no—
62C22×C8×C59—21no—
63C22×C8×C59C2×C411yescharacteristic
64C22×C8×C59C2311yescharacteristic
65C2×C42×C59C2×C411yescharacteristic
66#108×C59—22no—
67#104×C59—22no—
68#104×C59—22no—
69#97×C59—21no—
70#97×C59—21no—
71#41×C59—21no—
72#41×C59—21no—
73#41×C59—21no—
74#41×C59—21no—
75#41×C59—21no—
76#41×C59—21no—
77#41×C59C22⋊C412yes—
78#41×C59M1612yes—
79C2×Q8×C59C2×C811yescharacteristic
80C2×Q8×C59C2×C811yescharacteristic
81C2×D4×C59—21no—
82C2×D4×C59—21no—
83C2×D4×C59C2×C811yescharacteristic
84C2×D4×C59C2×C811yescharacteristic
85C22×C4×C59—21no—
86C22×C4×C59—21no—
87C22×C4×C59—21no—
88C22×C4×C59C22×C411yescharacteristic
89Q16×C59—22no—
90SD16×C59—22no—
91SD16×C59—22no—
92D8×C59—22no—
93M16×C59—21no—
94M16×C59—22no—
95M16×C59—22no—
96M16×C59—21no—
97M16×C59—21no—
98M16×C59—41no—
99M16×C59—41no—
100M16×C59C22⋊C412yes—
101C2×C8×C59—21no—
102C2×C8×C59—21no—
103C2×C8×C59—21no—
104C2×C8×C59—22no—
105C2×C8×C59—22no—
106C2×C8×C59—21no—
107C2×C8×C59—41no—
108C2×C8×C59—41no—
109C2×C8×C59C2×C811yescharacteristic
110C2×C8×C59C2×C811yescharacteristic
111C2×C8×C59C2×D411yescharacteristic
112C2×C8×C59C2×D411yescharacteristic
113C2×C8×C59C2×D411yescharacteristic
114C2×C8×C59C2×D411yescharacteristic
115C2×C8×C59#4111yescharacteristic
116C2×C8×C59#4111yescharacteristic
117C42×C59—21no—
118C42×C59—21no—
119C59⋊C16—22no—
120C59⋊C16—22no—
121C59⋊C16—41no—
122C59⋊C16—41no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59#13111yescharacteristic
126Q8×C59—21no—
127Q8×C59—21no—
128Q8×C59—21no—
129Q8×C59C22⋊C812yes—
130D4×C59—22no—
131D4×C59—22no—
132D4×C59—21no—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—41no—
136D4×C59—41no—
137D4×C59C22⋊C812yes—
138C2×C4×C59—21no—
139C2×C4×C59—22no—
140C2×C4×C59—22no—
141C2×C4×C59—21no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—81no—
146C2×C4×C59C2×C22⋊C411yescharacteristic
147C2×C4×C59C4×D411yescharacteristic
148C2×C4×C59C4×D411yescharacteristic
149C2×C4×C59C22×C811yescharacteristic
150C2×C4×C59C2×M1611yescharacteristic
151C2×C4×C59#13111yescharacteristic
152C8×C59—22no—
153C8×C59—21no—
154C8×C59—21no—
155C8×C59—41no—
156C8×C59#12011yescharacteristic
157C8×C59#12111yescharacteristic
158C8×C59#12111yescharacteristic
159C8×C59#12311yescharacteristic
160#12986—591nomaximal, Sylow
161C22×C59—22no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59—81no—
165C22×C59—81no—
166C22×C59#40811yescharacteristic
167C22×C59C8×D411yescharacteristic
168C22×C59#43511yescharacteristic
169C4×C59—22no—
170C4×C59—41no—
171C4×C59—81no—
172C4×C59#38611yescharacteristic
173C4×C59C2×C22⋊C811yescharacteristic
174C4×C59C8×D411yescharacteristic
175C4×C59#43511yescharacteristic
176#3407—591no—
177C2×#444D5911yescharacteristic
178#2117—591no—
179#2117—591no—
180#2115—591no—
181#1377—591no—
182#1375—591no—
183C2×C59—21no—
184C2×C59—21no—
185C2×C59—21no—
186C2×C59—42no—
187C2×C59—81no—
188C2×C59#186911yescharacteristic
189C2×#135Dic5911yescharacteristic
190C2×#131C2×D5911yescharacteristic
191C2×#131C2×D5911yescharacteristic
192#504—1182no—
193#504—1182no—
194C2×M32—591no—
195C2×M32—591no—
196C2×M32—591no—
197C2×M32—591no—
198C2×M32—1182no—
199#444—22no—
200#444—22no—
201C2×#108Dic5911yescharacteristic
202C2×#104Dic5911yescharacteristic
203C2×#104Dic5911yescharacteristic
204C2×#97C2×D5911yescharacteristic
205#350—1182no—
206#350—1182no—
207#349—1182no—
208C59#1298611yescharacteristic, complemented, Sylow
209C2×#41C2×Dic5911yescharacteristic
210C2×#41C2×Dic5911yescharacteristic
211#135—22no—
212#135—22no—
213C2×Q16C59⋊C811yescharacteristic
214C2×SD16C59⋊C811yescharacteristic
215C2×SD16C59⋊C811yescharacteristic
216C2×D8C59⋊C811yescharacteristic
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221#131—21no—
222#131—21no—
223#131C22⋊D5912yes—
224#131C22⋊D5912yes—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16C2×Dic5911yescharacteristic
228C2×M16C2×Dic5911yescharacteristic
229C22×C8—21no—
230C22×C8—21no—
231C22×C8C2×Dic5911yescharacteristic
232C22×C8C22×D5911yescharacteristic
233C2×C42C2×Dic5911yescharacteristic
234M32—592no—
235M32—1184no—
236M32—1181no—
237M32—1181no—
238M32—1181no—
239M32—1181no—
240M32—1181no—
241M32—1181no—
242M32—1181no—
243C2×C16—592no—
244C2×C16—1184no—
245C2×C16—1181no—
246C2×C16—1181no—
247C2×C16—1181no—
248#108—22no—
249#104—22no—
250#104—22no—
251#97—21no—
252#97—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41#1174566412yes—
260#41C22⋊Dic5912yes—
261C2×Q8C2×C59⋊C811yescharacteristic
262C2×Q8C2×C59⋊C811yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4C2×C59⋊C811yescharacteristic
266C2×D4C2×C59⋊C811yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4C22×Dic5911yescharacteristic
271Q16—22no—
272SD16—22no—
273SD16—22no—
274D8—22no—
275M16—21no—
276M16—22no—
277M16—22no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16C22⋊Dic5912yes—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8C2×C59⋊C811yescharacteristic
292C2×C8C2×C59⋊C811yescharacteristic
293C2×C8D4×D5911yescharacteristic
294C2×C8D4×D5911yescharacteristic
295C2×C8#1174568711yescharacteristic
296C2×C8#1174568711yescharacteristic
297C2×C8C2×C22⋊D5911yescharacteristic
298C2×C8C2×C22⋊D5911yescharacteristic
299C42—21no—
300C42—21no—
301C16—1182no—
302C16—1182no—
303C16—2361no—
304C16—2361no—
305C23—21no—
306C23—21no—
307C23#1427373411yescharacteristic
308Q8—21no—
309Q8—21no—
310Q8—21no—
311Q8C22⋊(C59⋊C8)12yes—
312D4—22no—
313D4—22no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—41no—
318D4—41no—
319D4C22⋊(C59⋊C8)12yes—
320C2×C4—21no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4C2×C22⋊Dic5911yescharacteristic
329C2×C4D4×Dic5911yescharacteristic
330C2×C4D4×Dic5911yescharacteristic
331C2×C4C22×C59⋊C811yescharacteristic
332C2×C4C2×#1174566411yescharacteristic
333C2×C4#1427373411yescharacteristic
334C8—22no—
335C8—21no—
336C8—21no—
337C8—41no—
338C8#1427369511yescharacteristic
339C8#1427369911yescharacteristic
340C8#1427369911yescharacteristic
341C8#1427370811yescharacteristic
342C22—22no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22#1683736911yescharacteristic
348C22D4×C59⋊C811yescharacteristic
349C22#1683747411yescharacteristic
350C4—22no—
351C4—41no—
352C4—81no—
353C4#1683728211yescharacteristic
354C4C2×C22⋊(C59⋊C8)11yescharacteristic
355C4D4×C59⋊C811yescharacteristic
356C4#1683747411yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—81no—
362C2#2142438911yescharacteristic
subgroupG/H
centerC4#16837282
commutatorC2×C4×C59C22×C8
FrattiniC22×C8C22×D59
FittingC2×C59×#444C2
socleC2×C59#1869
prime radicalC2×#135×C59C4
cosocleC22×C8×C59C23
hypercenterC2×#444D59
hypocenterC59#12986
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
1. #21437199C2semidirect
2. #21425724C2semidirect
3. #21425724C2semidirect
4. #21425717C2semidirect
5. #21422180C2semidirect
6. #21422176C2semidirect
208. C59#12986semidirect

Maximal subgroups

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

subgroupindex
#214371992
#214257242
#214257172
#214221802
#214221762
C2×C59×#4442
#1298659