Finite Group Databasebeta

← #28504989

Subgroups — #28504989

Order 15104.

404 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D59C211yesmaximal, characteristic
2C2×(C2×D59)⋊C16C211yesmaximal, characteristic
3#21424131C211yesmaximal, characteristic
4#21422193C211yesmaximal, characteristic, complemented
5#21422192C211yesmaximal, characteristic, complemented
6#21422191C211yesmaximal, characteristic, complemented
7C59×#1382C211yesmaximal, characteristic, complemented
8C22×C8×D59C2211yescharacteristic
9#117×D59—21no—
10C22×C59⋊C16C2211yescharacteristic
11C2×#14273663C2211yescharacteristic
12#16837440C2211yescharacteristic
13#16837439C411yescharacteristic
14#16837439C411yescharacteristic
15#16837438—21no—
16#16837437—21no—
17#107×D59C411yescharacteristic
18#107×D59C411yescharacteristic
19#106×D59—21no—
20#16837365—21no—
21(C2×D59)⋊C16—21no—
22(C2×D59)⋊C16—21no—
23#16837166—21no—
24C22×C16×C59C2211yescharacteristic
25C2×#108×C59C2211yescharacteristic
26C59×#427C2211yescharacteristic
27C22×C4×D59D411yescharacteristic
28C2×#11745664—21no—
29C22×C59⋊C8D411yescharacteristic
30C2×C8×D59—21no—
31C2×C8×D59—21no—
32C2×C8×D59—21no—
33C2×C8×D59—21no—
34C2×C8×D59C2×C411yescharacteristic
35C2×C8×D59C2×C411yescharacteristic
36C2×C8×D59D411yescharacteristic
37C2×C8×D59D411yescharacteristic
38#14273686—21no—
39#14273685—21no—
40#14273685—21no—
41#14273684—41no—
42#14273683—41no—
43C4⋊C4×D59—21no—
44C4⋊C4×D59—21no—
45C22⋊C4×D59—41no—
46C42×D59—41no—
47C2×C59⋊C16—21no—
48C2×C59⋊C16—21no—
49C2×C59⋊C16—21no—
50#14273663—21no—
51#14273663—21no—
52#14273661C2×C411yescharacteristic
53#14273661C2×C411yescharacteristic
54#14273660—21no—
55#14273660—21no—
56#14273659—21no—
57#14273658—21no—
58#14273658—21no—
59(C2×D59)⋊C8—41no—
60(C2×D59)⋊C8—41no—
61C2×M16×C59—21no—
62C22×C8×C59C2311yescharacteristic
63#117×C59—21no—
64C2×C16×C59—21no—
65C2×C16×C59—21no—
66C2×C16×C59—21no—
67#108×C59—21no—
68#108×C59—21no—
69#107×C59C2×C411yescharacteristic
70#107×C59C2×C411yescharacteristic
71#106×C59—21no—
72C23×D59SD1611yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×Dic59SD1611yescharacteristic
75C2×C4×D59—21no—
76C2×C4×D59—21no—
77C2×C4×D59—21no—
78C2×C4×D59—21no—
79C2×C4×D59—41no—
80C2×C4×D59—41no—
81C2×C4×D59C22⋊C411yescharacteristic
82C2×C4×D59C22⋊C411yescharacteristic
83C2×C4×D59D811yescharacteristic
84C2×C4×D59D811yescharacteristic
85M16×C59—41no—
86M16×C59—41no—
87C2×C8×C59—41no—
88C2×C8×C59C22×C411yescharacteristic
89C2×C8×C59C2×D411yescharacteristic
90C2×C8×C59#4111yescharacteristic
91C2×C8×C59#4111yescharacteristic
92C2×C8×C59#4111yescharacteristic
93C2×C8×C59#4111yescharacteristic
94C4⋊C4×C59—21no—
95C4⋊C4×C59—21no—
96C22⋊C4×C59—41no—
97C42×C59—41no—
98C22⋊Dic59—41no—
99(C2×D59)⋊C4—41no—
100(C2×D59)⋊C4—41no—
101C4⋊Dic59—21no—
102C4⋊Dic59—21no—
103Dic59⋊C4—41no—
104Dic59⋊C4—41no—
105C4×Dic59—41no—
106C4×Dic59—41no—
107C4×Dic59—41no—
108#11745664—41no—
109#11745664—41no—
110C2×C59⋊C8—21no—
111C2×C59⋊C8—21no—
112C2×C59⋊C8—41no—
113C2×C59⋊C8C22⋊C411yescharacteristic
114C2×C59⋊C8C22⋊C411yescharacteristic
115C8×D59—21no—
116C8×D59—21no—
117C8×D59—21no—
118C8×D59—21no—
119C8×D59—21no—
120C8×D59—21no—
121C8×D59—21no—
122C8×D59—21no—
123C16×C59—41no—
124C59⋊C16—41no—
125C23×C59C2×SD1611yescharacteristic
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—22no—
129C22×D59—41no—
130C22×D59#10211yescharacteristic
131C22×D59#10211yescharacteristic
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59C2×C22⋊C411yescharacteristic
135C2×C4×C59#12311yescharacteristic
136C2×C4×C59#12311yescharacteristic
137C2×C4×C59C2×D811yescharacteristic
138C2×C4×C59#13711yescharacteristic
139C2×C4×C59#13711yescharacteristic
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59#10211yescharacteristic
145C2×Dic59#10211yescharacteristic
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—21no—
149C4×D59—21no—
150C4×D59—21no—
151C4×D59—21no—
152C4×D59—21no—
153C4×D59—21no—
154C4×D59—82no—
155C4×D59—82no—
156C8×C59—81no—
157C8×C59#11711yescharacteristic
158C8×C59#11711yescharacteristic
159C8×C59#12311yescharacteristic
160C8×C59#12311yescharacteristic
161C59⋊C8—21no—
162C59⋊C8—21no—
163C59⋊C8—81no—
164#12869—591nomaximal, Sylow
165C22×C59—21no—
166C22×C59—21no—
167C22×C59C2×#10211yescharacteristic
168C22×C59#48311yescharacteristic
169C22×C59#48311yescharacteristic
170C2×D59—21no—
171C2×D59—21no—
172C2×D59—21no—
173C2×D59—21no—
174C2×D59—21no—
175C2×D59—42no—
176C2×D59—42no—
177C2×D59#35912yes—
178C4×C59—81no—
179C4×C59—81no—
180C4×C59#38111yescharacteristic
181C4×C59#41911yescharacteristic
182C4×C59#48011yescharacteristic
183C4×C59#48011yescharacteristic
184Dic59—21no—
185Dic59—21no—
186Dic59—81no—
187Dic59—81no—
188C2×#427—591no—
189C2×C22⋊C16—591no—
190#1810—591no—
191#1382—591no—
192#1382—591no—
193#1382—591no—
194#1382D5911yescharacteristic, complemented
195C2×C59—21no—
196C2×C59—21no—
197C2×C59#182311yescharacteristic
198C2×C59C2×#35911yescharacteristic
199C2×C59#214311yescharacteristic
200D59—22no—
201D59—41no—
202C23×C8—591no—
203C2×#117—1181no—
204C22×C16—591no—
205C22×C16C2×D5911yescharacteristic
206C2×#108—591no—
207C2×#108C2×D5911yescharacteristic
208#427—591no—
209#427—591no—
210#427—591no—
211#427—1181no—
212#427—1181no—
213#427C2×D5911yescharacteristic
214C2×#107—591no—
215C2×#107—591no—
216C2×#106—1181no—
217#407—1181no—
218C22⋊C16—1181no—
219C22⋊C16—1181no—
220#341—1181no—
221C59#1286911yescharacteristic, complemented, Sylow
222C23×C4—591no—
223C2×M16—21no—
224C2×M16—1181no—
225C22×C8—591no—
226C22×C8—591no—
227C22×C8—591no—
228C22×C8—591no—
229C22×C8—591no—
230C22×C8—1181no—
231C22×C8—1181no—
232C22×C8—1181no—
233C22×C8—1181no—
234C22×C8C22×D5911yescharacteristic
235#117—21no—
236#117—1181no—
237#117—1181no—
238#117—1181no—
239#117—2361no—
240#117—2361no—
241C2×C4⋊C4—1181no—
242C2×C4⋊C4—1181no—
243C2×C22⋊C4—2361no—
244C2×C42—2361no—
245C2×C16—21no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—1181no—
249C2×C16—1181no—
250C2×C16—1181no—
251#108—21no—
252#108—21no—
253#108—1181no—
254#108—1181no—
255#107—591no—
256#107—591no—
257#107—1181no—
258#107—1181no—
259#107C4×D5911yescharacteristic
260#107C4×D5911yescharacteristic
261#106—21no—
262#106—1181no—
263#106—1181no—
264#106—1181no—
265C22⋊C8—2361no—
266C22⋊C8—2361no—
267C24—591no—
268C22×C4—591no—
269C22×C4—591no—
270C22×C4—591no—
271C22×C4—591no—
272C22×C4—591no—
273C22×C4—1181no—
274C22×C4—1181no—
275C22×C4—1181no—
276C22×C4—1181no—
277C22×C4—2361no—
278C22×C4—2361no—
279C22×C4D4×D5911yescharacteristic
280M16—41no—
281M16—41no—
282M16—2361no—
283M16—2361no—
284C2×C8—41no—
285C2×C8—591no—
286C2×C8—591no—
287C2×C8—1181no—
288C2×C8—1181no—
289C2×C8—1181no—
290C2×C8—1181no—
291C2×C8—1181no—
292C2×C8—1181no—
293C2×C8—1181no—
294C2×C8—1181no—
295C2×C8—1181no—
296C2×C8—1181no—
297C2×C8—2361no—
298C2×C8C2×C4×D5911yescharacteristic
299C2×C8#1174568511yescharacteristic
300C2×C8#1174568511yescharacteristic
301C2×C8D4×D5911yescharacteristic
302C2×C8#1174568711yescharacteristic
303C2×C8#1174568911yescharacteristic
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—1181no—
307C4⋊C4—1181no—
308C4⋊C4—2361no—
309C4⋊C4—2361no—
310C22⋊C4—41no—
311C22⋊C4—2361no—
312C22⋊C4—2361no—
313C22⋊C4—2361no—
314C42—41no—
315C42—2361no—
316C42—2361no—
317C42—2361no—
318C16—41no—
319C16—2361no—
320C23—591no—
321C23—591no—
322C23—1182no—
323C23—1181no—
324C23—1181no—
325C23—2361no—
326C23SD16×D5911yescharacteristic
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—591no—
330C2×C4—591no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—4722no—
342C2×C4—4722no—
343C2×C4—2361no—
344C2×C4—2361no—
345C2×C4C22⋊C4×D5911yescharacteristic
346C2×C4#1427370911yescharacteristic
347C2×C4#1427371211yescharacteristic
348C2×C4D8×D5911yescharacteristic
349C2×C4#1427375611yescharacteristic
350C2×C4#1427375911yescharacteristic
351C8—81no—
352C8—1181no—
353C8—1181no—
354C8—4721no—
355C8#1427368411yescharacteristic
356C8#1427368511yescharacteristic
357C8#1427370911yescharacteristic
358C8#1427371211yescharacteristic
359C22—21no—
360C22—21no—
361C22—592no—
362C22—1181no—
363C22—1181no—
364C22—1181no—
365C22—1181no—
366C22—1181no—
367C22—2362no—
368C22—2362no—
369C22#102×D5911yescharacteristic
370C22#1683773111yescharacteristic
371C22#1683773411yescharacteristic
372C4—81no—
373C4—81no—
374C4—1181no—
375C4—1181no—
376C4—4721no—
377C4—4721no—
378C4#1683726411yescharacteristic
379C4#1683740911yescharacteristic
380C4#1683771411yescharacteristic
381C4#1683771711yescharacteristic
382C2—21no—
383C2—21no—
384C2—1182no—
385C2—2361no—
386C2#2142418111yescharacteristic
387C2#359×D5911yescharacteristic
388C2#2142582211yescharacteristic
subgroupG/H
centerC2×C4D8×D59
commutatorC2×C8×C59C22×C4
FrattiniC22×C8C22×D59
FittingC59×#1382C2
socleC22×C59C2×#102
prime radicalC23×D59SD16
cosocleC22×C8×C59C23
hypercenter#1382D59
hypocenterC59#12869
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
4. #21422193C2semidirect
5. #21422192C2semidirect
6. #21422191C2semidirect
7. C59×#1382C2semidirect
194. #1382D59semidirect
221. C59#12869semidirect

Maximal subgroups

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

subgroupindex
#427×D592
C2×(C2×D59)⋊C162
#214241312
#214221932
#214221922
#214221912
C59×#13822
#1286959