Finite Group Databasebeta

← C2×#21425238 #28615972

Subgroups — C2×#21425238 #28615972

Order 15104.

1518 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273727C211yesmaximal, characteristic
2C22×#14273652C212yesmaximal
3C2×#16837308C211yesmaximal, characteristic
4#21425238C218yesmaximal, direct product factor
5C2×#16837165C212yesmaximal
6C2×C59×#336C211yesmaximal, characteristic
7C23×Dic118—21no—
8C23×Dic118C2211yescharacteristic
9C2×#14273727—28no—
10C2×#14273727—22no—
11C2×#14273727C2214yes—
12C22×C4⋊Dic59—21no—
13C22×C4⋊Dic59C2211yescharacteristic
14C22×C4⋊Dic59C2212yes—
15C2×#14273652—28no—
16C2×#14273652C2218yes—
17#16837308—22no—
18#16837308C2214yes—
19C2×C59⋊#95—21no—
20C2×C59⋊#95—21no—
21#16837165C2218yes—
22C23×C8×C59C2212yes—
23C22×C42×C59C2211yescharacteristic
24C59×#336C2214yes—
25C22×Dic118—24no—
26C22×Dic118—24no—
27C22×Dic118—28no—
28C22×Dic118—24no—
29C22×Dic118—21no—
30C22×Dic118—22no—
31C22×Dic118—44no—
32C22×Dic118—44no—
33C22×Dic118Q814yescomplemented
34C22×Dic118C2312yes—
35C23×Dic59—22no—
36C23×Dic59—21no—
37C23×Dic59—21no—
38#14273727—216no—
39#14273727—216no—
40C2×C4⋊Dic59—28no—
41C2×C4⋊Dic59—22no—
42C2×C4⋊Dic59—24no—
43C2×C4⋊Dic59—24no—
44C2×C4⋊Dic59—24no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59D418yes—
47C2×C4⋊Dic59C2312yes—
48C2×C4⋊Dic59C2314yes—
49#14273652—216no—
50C59⋊#95—24no—
51C59⋊#95—24no—
52C23×C4×C59D411yescharacteristic
53C23×C4×C59D411yescharacteristic
54C23×C4×C59C2311yescharacteristic
55C22×C8×C59—24no—
56C22×C8×C59—24no—
57C22×C8×C59—24no—
58C22×C8×C59C2314yes—
59C2×C42×C59—24no—
60C2×C42×C59D412yes—
61C2×C42×C59C2312yes—
62C24×C59C2×D411yescharacteristic
63C22×C4×C59—22no—
64C22×C4×C59—22no—
65C22×C4×C59—22no—
66C22×C4×C59—22no—
67C22×C4×C59SD1614yes—
68C22×C4×C59Q1614yes—
69C22×C4×C59C2×D412yes—
70C22×C4×C59C2×D412yes—
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D414yes—
73C22×C4×C59C2×Q812yes—
74C22×C4×C59#4114yes—
75C22×C4×C59#4112yes—
76C22×C4×C59C2411yescharacteristic
77C22×Dic59—28no—
78C22×Dic59—24no—
79C22×Dic59—22no—
80C22×Dic59—24no—
81C22×Dic59—22no—
82C22×Dic59—42no—
83C22×Dic59—42no—
84C22×Dic59—44no—
85C22×Dic59—44no—
86C22×Dic59—42no—
87C22×Dic59—42no—
88C22×Dic59—42no—
89C2×Dic118—216no—
90C2×Dic118—24no—
91C2×Dic118—24no—
92C2×Dic118—216no—
93C2×Dic118—24no—
94C2×Dic118—22no—
95C2×Dic118—48no—
96C2×Dic118—432no—
97C2×Dic118—42no—
98C2×Dic118—48no—
99C2×Dic118—42no—
100C2×Dic118—48no—
101C2×Dic118C2×Q814yescomplemented
102C2×C8×C59—24no—
103C2×C8×C59—24no—
104C2×C8×C59—24no—
105C2×C8×C59—48no—
106C42×C59—24no—
107C42×C59—24no—
108C4⋊Dic59—216no—
109C4⋊Dic59—28no—
110C4⋊Dic59—24no—
111C4⋊Dic59—24no—
112C4⋊Dic59—42no—
113C4⋊Dic59C2×D418yes—
114C23×C59#12012yes—
115C23×C59C22⋊Q812yes—
116C23×C59#12412yes—
117C23×C59C2×SD1612yes—
118C23×C59C2×Q1612yes—
119C23×C59AGL(1,ℤ/8)12yes—
120C23×C59#13712yes—
121C23×C59C22×D411yescharacteristic
122C2×C4×C59—22no—
123C2×C4×C59—22no—
124C2×C4×C59—22no—
125C2×C4×C59—22no—
126C2×C4×C59—28no—
127C2×C4×C59—28no—
128C2×C4×C59#12012yes—
129C2×C4×C59C22⋊Q818yes—
130C2×C4×C59C22⋊Q812yes—
131C2×C4×C59#12418yes—
132C2×C4×C59#12412yes—
133C2×C4×C59C2×SD1614yes—
134C2×C4×C59C2×Q1614yes—
135C2×C4×C59C22×D412yes—
136C2×C4×C59C22×Q811yescharacteristic
137C2×C4×C59C2×#4111yescharacteristic
138C2×C4×C59C2×#4112yes—
139C2×Dic59—28no—
140C2×Dic59—24no—
141C2×Dic59—42no—
142C2×Dic59—42no—
143C2×Dic59—44no—
144C2×Dic59—44no—
145C2×Dic59—48no—
146C2×Dic59—416no—
147C2×Dic59—42no—
148C2×Dic59—42no—
149C2×Dic59—42no—
150C2×Dic59—84no—
151Dic118—28no—
152Dic118—432no—
153Dic118—44no—
154Dic118—48no—
155C8×C59—44no—
156C2×#2024—591nomaximal, Sylow
157C22×C59#39314yes—
158C22×C59#45014yes—
159C22×C59#45114yes—
160C22×C59#47514yes—
161C22×C59#47714yes—
162C22×C59#48714yes—
163C22×C59#48914yes—
164C22×C59C2×#12011yescharacteristic
165C22×C59C2×C22⋊Q811yescharacteristic
166C22×C59C2×#12411yescharacteristic
167C22×C59C22×SD1611yescharacteristic
168C22×C59C22×Q1611yescharacteristic
169C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
170C22×C59C2×#13711yescharacteristic
171C4×C59—24no—
172C4×C59—24no—
173C4×C59#39314yes—
174C4×C59C2×C22⋊Q812yes—
175C4×C59C2×#12412yes—
176Dic59—44no—
177Dic59—48no—
178Dic59—82no—
179C22×C4⋊Q8—591no—
180C22×#103—592no—
181C2×#391—591no—
182#2024—598no—
183C2×#340—592no—
184C2×#336D5911yescharacteristic
185C2×C59#202418yescomplemented
186C2×C59C2×#39311yescharacteristic
187C2×C59C2×#45011yescharacteristic
188C2×C59C2×#45111yescharacteristic
189C2×C59C2×#47511yescharacteristic
190C2×C59C2×#47711yescharacteristic
191C2×C59C2×#48711yescharacteristic
192C2×C59C2×#48911yescharacteristic
193C23×Q8—591no—
194C23×Q8—1181no—
195C23×C8C2×D5912yes—
196C2×C4⋊Q8—594no—
197C2×C4⋊Q8—1188no—
198C2×C4⋊Q8—1182no—
199C22×C4⋊C4—592no—
200C22×C4⋊C4—591no—
201C22×C4⋊C4—1181no—
202C22×C42C2×D5911yescharacteristic
203C2×#103—598no—
204C2×#103—1188no—
205#391—594no—
206#391—1182no—
207C2×#95—1181no—
208C2×#95—1181no—
209#340—598no—
210#336C2×D5914yes—
211C59C2×#202411yescharacteristic, complemented, Sylow
212C22×Q8—594no—
213C22×Q8—592no—
214C22×Q8—1188no—
215C22×Q8—1184no—
216C22×Q8—1181no—
217C22×Q8—1182no—
218C22×Q8—1184no—
219C22×Q8—1184no—
220C22×Q8—2364no—
221C22×Q8—2364no—
222C23×C4—1182no—
223C23×C4—1181no—
224C23×C4—1181no—
225C23×C4D23611yescharacteristic
226C23×C4D23611yescharacteristic
227C23×C4C22×D5911yescharacteristic
228C22×C8—24no—
229C22×C8—24no—
230C22×C8—24no—
231C22×C8C22×D5914yes—
232C4⋊Q8—11816no—
233C4⋊Q8—11816no—
234C2×C4⋊C4—598no—
235C2×C4⋊C4—594no—
236C2×C4⋊C4—592no—
237C2×C4⋊C4—1188no—
238C2×C4⋊C4—1182no—
239C2×C4⋊C4—1184no—
240C2×C4⋊C4—1184no—
241C2×C4⋊C4—1184no—
242C2×C4⋊C4—1181no—
243C2×C42—24no—
244C2×C42D23612yes—
245C2×C42C22×D5912yes—
246#103—11816no—
247#95—1184no—
248#95—1184no—
249C24C2×D23611yescharacteristic
250C2×Q8—594no—
251C2×Q8—11816no—
252C2×Q8—1184no—
253C2×Q8—1182no—
254C2×Q8—11816no—
255C2×Q8—1184no—
256C2×Q8—1184no—
257C2×Q8—2368no—
258C2×Q8—23632no—
259C2×Q8—2362no—
260C2×Q8—2368no—
261C2×Q8—2362no—
262C2×Q8—2368no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—1188no—
268C22×C4—1184no—
269C22×C4—1182no—
270C22×C4—1184no—
271C22×C4—1182no—
272C22×C4—2362no—
273C22×C4—2362no—
274C22×C4—2362no—
275C22×C4—2362no—
276C22×C4—2362no—
277C22×C4—2364no—
278C22×C4—2364no—
279C22×C4#1174566014yes—
280C22×C4Dic23614yes—
281C22×C4C2×D23612yes—
282C22×C4C2×D23612yes—
283C22×C4C2×D23611yescharacteristic
284C22×C4#1174568514yes—
285C22×C4D4×D5914yes—
286C22×C4#1174568712yes—
287C22×C4Q8×D5912yes—
288C22×C4C23×D5911yescharacteristic
289C2×C8—24no—
290C2×C8—24no—
291C2×C8—24no—
292C2×C8—48no—
293C4⋊C4—598no—
294C4⋊C4—11816no—
295C4⋊C4—1188no—
296C4⋊C4—1184no—
297C4⋊C4—1184no—
298C4⋊C4—2362no—
299C42—24no—
300C42—24no—
301C23#1427369712yes—
302C23#1427370712yes—
303C23#1427371512yes—
304C23C2×#1174566012yes—
305C23C2×Dic23612yes—
306C23#1427375512yes—
307C23#1427376012yes—
308C23C22×D23611yescharacteristic
309Q8—1188no—
310Q8—23632no—
311Q8—2364no—
312Q8—2368no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—28no—
318C2×C4—28no—
319C2×C4—1188no—
320C2×C4—1184no—
321C2×C4—4724no—
322C2×C4—2362no—
323C2×C4—2362no—
324C2×C4—2362no—
325C2×C4—2362no—
326C2×C4—2362no—
327C2×C4—2364no—
328C2×C4—2364no—
329C2×C4—23616no—
330C2×C4—2368no—
331C2×C4#1427369712yes—
332C2×C4#1427370518yes—
333C2×C4#1427370712yes—
334C2×C4#1427371318yes—
335C2×C4#1427371512yes—
336C2×C4C2×#1174566014yes—
337C2×C4C2×Dic23614yes—
338C2×C4C2×D4×D5912yes—
339C2×C4C2×Q8×D5911yescharacteristic
340C2×C4C2×#1174568711yescharacteristic
341C2×C4C2×#1174568512yes—
342C8—44no—
343C22#1683731514yes—
344C22#1683755514yes—
345C22#1683756014yes—
346C22#1683768814yes—
347C22#1683769814yes—
348C22#1683775314yes—
349C22#1683776214yes—
350C22C2×#1427369711yescharacteristic
351C22C2×#1427370711yescharacteristic
352C22C2×#1427371511yescharacteristic
353C22C22×#1174566011yescharacteristic
354C22C22×Dic23611yescharacteristic
355C22C2×#1427375511yescharacteristic
356C22C2×#1427376011yescharacteristic
357C4—24no—
358C4—24no—
359C4—4722no—
360C4—2364no—
361C4—2368no—
362C4#1683731514yes—
363C4C2×#1427370512yes—
364C4C2×#1427371312yes—
365C2#2142523818yesdirect product factor
366C2C2×#1683731511yescharacteristic
367C2C2×#1683755511yescharacteristic
368C2C2×#1683756011yescharacteristic
369C2C2×#1683768811yescharacteristic
370C2C2×#1683769811yescharacteristic
371C2C2×#1683775311yescharacteristic
372C2C2×#1683776211yescharacteristic
subgroupG/H
centerC24C2×D236
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#336C2
socle, prime radicalC24×C59C2×D4
hypercenterC2×#336D59
hypocenterC59C2×#2024
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. #21425238C2direct (N × H)
33. C22×Dic118Q8semidirect
101. C2×Dic118C2×Q8semidirect
185. C2×C59#2024semidirect
211. C59C2×#2024semidirect
365. C2#21425238direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737272
C22×#142736522
C2×#168373082
#214252382
C2×#168371652
C2×C59×#3362
C2×#202459