Finite Group Databasebeta

← C2×#21432277 #28795061

Subgroups — C2×#21432277 #28795061

Order 15104.

1718 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432277C2116yesmaximal, direct product factor
2C2×C59⋊#401C212yesmaximal
3C2×#16837344C212yesmaximal
4C2×#16837341C212yesmaximal
5C2×#16837334C212yesmaximal
6C2×#16837332C211yesmaximal, characteristic
7C2×#16837323C212yesmaximal
8C2×#16837307C211yesmaximal, characteristic
9C2×#16837284C212yesmaximal
10C2×C59×#400C211yesmaximal, characteristic
11C23×Dic118C2211yescharacteristic
12C22×C4⋊Dic59C2212yes—
13C22×C4⋊Dic59C2212yes—
14C22×C4⋊Dic59C2211yescharacteristic
15C22×Dic59⋊C4C2212yes—
16C22×Dic59⋊C4C2212yes—
17C22×C4×Dic59C2211yescharacteristic
18C59⋊#401C22116yes—
19#16837344C22116yes—
20#16837341C22116yes—
21#16837334C22116yes—
22#16837332C2218yes—
23#16837323C22116yes—
24#16837307C2218yes—
25#16837284C22116yes—
26C2×C59⋊#95C2212yes—
27C2×C59⋊#95C2212yes—
28C2×C59⋊#95C2212yes—
29C2×C59⋊#95C2212yes—
30C2×C59⋊#95C2212yes—
31C2×C59⋊#95C2212yes—
32C2×C59⋊#95C2211yescharacteristic
33C2×C59⋊#95C2212yes—
34C2×C59⋊#95C2212yes—
35C22×C4⋊C4×C59C2211yescharacteristic
36C22×C4⋊C4×C59C2211yescharacteristic
37C59×#400C2218yes—
38C2×#95×C59C2212yes—
39C2×#95×C59C2212yes—
40C2×#95×C59C2211yescharacteristic
41C22×Dic118—24no—
42C22×Dic118—42no—
43C22×Dic118—42no—
44C22×Dic118C2314yes—
45C23×Dic59C2312yes—
46C23×Dic59C2312yes—
47C23×Dic59C2312yes—
48C23×Dic59C2312yes—
49C2×C4⋊Dic59—44no—
50C2×C4⋊Dic59—42no—
51C2×C4⋊Dic59—44no—
52C2×C4⋊Dic59C2318yes—
53C2×C4⋊Dic59C2318yes—
54C2×C4⋊Dic59C2314yes—
55C2×Dic59⋊C4—28no—
56C2×Dic59⋊C4—44no—
57C2×Dic59⋊C4C2318yes—
58C2×Dic59⋊C4C2318yes—
59C2×C4×Dic59—42no—
60C2×C4×Dic59C2314yes—
61C59⋊#95C2318yes—
62C59⋊#95C2318yes—
63C59⋊#95C2318yes—
64C59⋊#95C2318yes—
65C59⋊#95C2318yes—
66C59⋊#95C2318yes—
67C59⋊#95C2318yes—
68C59⋊#95C2318yes—
69C59⋊#95C2314yes—
70C23×C4×C59C2312yes—
71C23×C4×C59C2312yes—
72C23×C4×C59C2311yescharacteristic
73C23×C4×C59C2311yescharacteristic
74C23×C4×C59C2311yescharacteristic
75C2×C4⋊C4×C59—42no—
76C2×C4⋊C4×C59—42no—
77C2×C4⋊C4×C59C2314yes—
78C2×C4⋊C4×C59C2314yes—
79#95×C59C2318yes—
80#95×C59C2318yes—
81#95×C59C2314yes—
82C24×C59C2411yescharacteristic
83C22×C4×C59—22no—
84C22×C4×C59—22no—
85C22×C4×C59—22no—
86C22×C4×C59—24no—
87C22×C4×C59—22no—
88C22×C4×C59—24no—
89C22×C4×C59—24no—
90C22×C4×C59—24no—
91C22×C4×C59—28no—
92C22×C4×C59—24no—
93C22×C4×C59—24no—
94C22×C4×C59#4114yes—
95C22×C4×C59C2414yes—
96C22×C4×C59C2414yes—
97C22×C4×C59C2412yes—
98C22×C4×C59C2412yes—
99C22×C4×C59C2412yes—
100C22×Dic59—24no—
101C22×Dic59—24no—
102C22×Dic59—24no—
103C22×Dic59—24no—
104C22×Dic59—24no—
105C22×Dic59—24no—
106C22×Dic59—24no—
107C22×Dic59—24no—
108C22×Dic59—24no—
109C22×Dic59—24no—
110C22×Dic59—24no—
111C22×Dic59—24no—
112C22×Dic59C2414yes—
113C22×Dic59C2414yes—
114C22×Dic59C2414yes—
115C22×Dic59C2414yes—
116C2×Dic118—28no—
117C2×Dic118—44no—
118C2×Dic118—44no—
119C2×Dic118—416no—
120C4⋊C4×C59—44no—
121C4⋊C4×C59—44no—
122C4⋊Dic59—48no—
123C4⋊Dic59—44no—
124C4⋊Dic59—48no—
125Dic59⋊C4—216no—
126Dic59⋊C4—48no—
127C4×Dic59—44no—
128C23×C59C2×#4112yes—
129C23×C59H(5,𝔽2)12yes—
130C23×C59H(5,𝔽2)12yes—
131C23×C592−1+414yes—
132C23×C592−1+414yes—
133C23×C59C2511yescharacteristic
134C2×C4×C59—28no—
135C2×C4×C59—22no—
136C2×C4×C59—22no—
137C2×C4×C59—24no—
138C2×C4×C59—24no—
139C2×C4×C59—22no—
140C2×C4×C59—22no—
141C2×C4×C59—24no—
142C2×C4×C59—24no—
143C2×C4×C59—28no—
144C2×C4×C59—24no—
145C2×C4×C59—24no—
146C2×C4×C59—48no—
147C2×C4×C59—48no—
148C2×C4×C59—44no—
149C2×C4×C59—44no—
150C2×C4×C59C2×#4114yes—
151C2×Dic59—24no—
152C2×Dic59—24no—
153C2×Dic59—24no—
154C2×Dic59—24no—
155C2×Dic59—24no—
156C2×Dic59—24no—
157C2×Dic59—24no—
158C2×Dic59—24no—
159C2×Dic59—24no—
160C2×Dic59—24no—
161C2×Dic59—24no—
162C2×Dic59—24no—
163C2×Dic59—48no—
164C2×Dic59—48no—
165C2×Dic59—48no—
166C2×Dic59—48no—
167Dic118—416no—
168C2×#2833—591nomaximal, Sylow
169C22×C59#53814yes—
170C22×C59#54118yes—
171C22×C59#56314yes—
172C22×C59#56318yes—
173C22×C59#56314yes—
174C22×C59C22×#4111yescharacteristic
175C22×C59C2×H(5,𝔽2)11yescharacteristic
176C22×C59C2×H(5,𝔽2)11yescharacteristic
177C22×C59C2×2−1+412yes—
178C22×C59C2×2−1+412yes—
179C4×C59—24no—
180C4×C59—44no—
181C4×C59—44no—
182C4×C59—42no—
183C4×C59—42no—
184Dic59—44no—
185Dic59—44no—
186Dic59—44no—
187Dic59—44no—
188#2833—5916no—
189C2×#401—592no—
190C2×#400—592no—
191C2×#400—592no—
192C2×#400D5911yescharacteristic
193C2×#398—592no—
194C2×#398—591no—
195C2×#395—592no—
196C2×#391—591no—
197C2×#387—592no—
198C2×C59#283318yescomplemented
199C2×C59C2×#53811yescharacteristic
200C2×C59C2×#54112yes—
201C2×C59C2×#56311yescharacteristic
202C2×C59C2×#56312yes—
203C2×C59C2×#56311yescharacteristic
204C23×Q8—591no—
205C22×C4⋊C4—592no—
206C22×C4⋊C4—592no—
207C22×C4⋊C4—592no—
208C22×C4⋊C4—591no—
209C22×C4⋊C4—592no—
210C22×C4⋊C4C2×D5911yescharacteristic
211C22×C4⋊C4C2×D5911yescharacteristic
212C22×C42—591no—
213#401—5916no—
214#400—5916no—
215#400—5916no—
216#400C2×D5918yes—
217#398—598no—
218#398—5916no—
219#395—5916no—
220#391—598no—
221#387—5916no—
222C2×#95—592no—
223C2×#95—592no—
224C2×#95—592no—
225C2×#95—592no—
226C2×#95—591no—
227C2×#95—592no—
228C2×#95—592no—
229C2×#95—592no—
230C2×#95—592no—
231C2×#95C2×D5912yes—
232C2×#95C2×D5912yes—
233C2×#95C2×D5911yescharacteristic
234C59C2×#283311yescharacteristic, complemented, Sylow
235C22×Q8—594no—
236C22×Q8—1184no—
237C22×Q8—2362no—
238C22×Q8—2362no—
239C23×C4—592no—
240C23×C4—592no—
241C23×C4—592no—
242C23×C4—592no—
243C23×C4C22×D5912yes—
244C23×C4C22×D5912yes—
245C23×C4C22×D5911yescharacteristic
246C23×C4C22×D5911yescharacteristic
247C23×C4C22×D5911yescharacteristic
248C2×C4⋊C4—42no—
249C2×C4⋊C4—42no—
250C2×C4⋊C4—598no—
251C2×C4⋊C4—598no—
252C2×C4⋊C4—598no—
253C2×C4⋊C4—598no—
254C2×C4⋊C4—594no—
255C2×C4⋊C4—1188no—
256C2×C4⋊C4—2364no—
257C2×C4⋊C4—2362no—
258C2×C4⋊C4—2364no—
259C2×C4⋊C4—2364no—
260C2×C4⋊C4C22×D5914yes—
261C2×C4⋊C4C22×D5914yes—
262C2×C42—594no—
263C2×C42—2362no—
264#95—598no—
265#95—598no—
266#95—598no—
267#95—598no—
268#95—598no—
269#95—598no—
270#95—598no—
271#95—598no—
272#95—594no—
273#95C22×D5918yes—
274#95C22×D5918yes—
275#95C22×D5914yes—
276C24C23×D5911yescharacteristic
277C2×Q8—1188no—
278C2×Q8—2364no—
279C2×Q8—2364no—
280C2×Q8—23616no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—28no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—594no—
293C22×C4—594no—
294C22×C4—594no—
295C22×C4—594no—
296C22×C4—1184no—
297C22×C4—1184no—
298C22×C4—1184no—
299C22×C4—1184no—
300C22×C4—1184no—
301C22×C4—1184no—
302C22×C4—1184no—
303C22×C4—1184no—
304C22×C4—1184no—
305C22×C4—1184no—
306C22×C4—1184no—
307C22×C4—1184no—
308C22×C4#1174568914yes—
309C22×C4C23×D5912yes—
310C22×C4C23×D5914yes—
311C22×C4C23×D5912yes—
312C22×C4C23×D5914yes—
313C22×C4C23×D5912yes—
314C4⋊C4—44no—
315C4⋊C4—44no—
316C4⋊C4—11816no—
317C4⋊C4—2368no—
318C4⋊C4—2364no—
319C4⋊C4—2368no—
320C4⋊C4—2368no—
321C42—2364no—
322C23C2×#1174568912yes—
323C23#1427377212yes—
324C23#1427377312yes—
325C23#1427377414yes—
326C23#1427377414yes—
327C23C24×D5911yescharacteristic
328Q8—23616no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—22no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—24no—
336C2×C4—28no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—48no—
342C2×C4—48no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—1184no—
346C2×C4—1184no—
347C2×C4—1184no—
348C2×C4—1184no—
349C2×C4—1184no—
350C2×C4—1184no—
351C2×C4—1184no—
352C2×C4—1184no—
353C2×C4—1184no—
354C2×C4—1184no—
355C2×C4—1184no—
356C2×C4—1184no—
357C2×C4—2368no—
358C2×C4—2368no—
359C2×C4—2368no—
360C2×C4—2368no—
361C2×C4C2×#1174568914yes—
362C22#1683799214yes—
363C22#1683801518yes—
364C22#1683815214yes—
365C22#1683815418yes—
366C22#1683815514yes—
367C22C22×#1174568911yescharacteristic
368C22C2×#1427377211yescharacteristic
369C22C2×#1427377311yescharacteristic
370C22C2×#1427377412yes—
371C22C2×#1427377412yes—
372C4—24no—
373C4—44no—
374C4—44no—
375C4—42no—
376C4—42no—
377C4—2364no—
378C4—2364no—
379C4—2364no—
380C4—2364no—
381C2#2143227718yesdirect product factor
382C2C2×#1683799211yescharacteristic
383C2C2×#1683801512yes—
384C2C2×#1683815211yescharacteristic
385C2C2×#1683815412yes—
386C2C2×#1683815511yescharacteristic
subgroupG/H
centerC24C23×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC2×C59×#400C2
socle, prime radicalC24×C59C24
hypercenterC2×#400D59
hypocenterC59C2×#2833
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #21432277C2direct (N × H)
198. C2×C59#2833semidirect
234. C59C2×#2833semidirect
381. C2#21432277direct (N × H)

Maximal subgroups

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

subgroupindex
#214322772
C2×C59⋊#4012
C2×#168373442
C2×#168373412
C2×#168373342
C2×#168373322
C2×#168373232
C2×#168373072
C2×#168372842
C2×C59×#4002
C2×#283359