Finite Group Databasebeta

← C2×#21433035 #29453060

Subgroups — C2×#21433035 #29453060

Order 15104.

1894 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837955C211yesmaximal, characteristic
2#21433035C2116yesmaximal, direct product factor
3C2×#16837531C214yesmaximal, complemented
4C2×#16837529C214yesmaximal, complemented
5C2×#16837428C211yesmaximal, characteristic
6C2×#16837425C211yesmaximal, characteristic
7C2×#16837360C211yesmaximal, characteristic
8C2×#16837358C211yesmaximal, characteristic
9C22×#14273637C211yesmaximal, characteristic
10C2×C59×#424C211yesmaximal, characteristic
11C22×#11745664C2211yescharacteristic
12C23×C59⋊C8C2211yescharacteristic
13#16837955C418yes—
14#16837955C2218yes—
15C2×#14273726C412yes—
16C2×#14273718C412yes—
17C2×#14273704C414yes—
18C2×C4×Dic118C2214yes—
19C2×#14273686C2211yescharacteristic
20C22×C4×Dic59C2211yescharacteristic
21#16837531C22132yescomplemented
22#16837529C22132yescomplemented
23#16837428C2218yes—
24#16837425C2218yes—
25C2×Dic59⋊C8C2214yes—
26C2×Dic59⋊C8C2214yes—
27#16837360C2218yes—
28#16837358C2218yes—
29C2×#14273638C2212yes—
30C2×#14273637C2212yes—
31C2×#14273637C2212yes—
32C2×#14273637C2218yes—
33C2×#14273637C2212yes—
34C2×C4×C59⋊C8C2212yes—
35C2×C8×Dic59C2212yes—
36C22×M16×C59C2211yescharacteristic
37C23×C8×C59C2211yescharacteristic
38C2×#117×C59C2211yescharacteristic
39C59×#424C2218yes—
40C2×C4⋊C8×C59C2214yes—
41C22×Dic118C2×C414yes—
42C23×Dic59C2×C412yes—
43C2×#11745664—24no—
44C2×#11745664C2314yes—
45C22×C59⋊C8Q818yescomplemented
46C22×C59⋊C8C2312yes—
47C22×C59⋊C8C2311yescharacteristic
48C22×C59⋊C8C2311yescharacteristic
49C22×C59⋊C8C2314yes—
50#14273726C2×C4116yes—
51#14273718C2×C4116yes—
52#14273704C2×C4132yes—
53C4×Dic118C2×C4116yes—
54C4×Dic118C23116yes—
55#14273686C2×C414yes—
56#14273686C2314yes—
57C2×C4⋊Dic59C2×C414yes—
58C2×C4⋊Dic59C2×C412yes—
59C2×Dic59⋊C4C2×C414yes—
60C2×Dic59⋊C4C2×C414yes—
61C2×C22⋊Dic59C2×C412yes—
62C2×C4×Dic59C2×C411yescharacteristic
63C2×C4×Dic59C2×C411yescharacteristic
64C2×C4×Dic59C2×C414yes—
65C2×C4×Dic59C2312yes—
66C2×C4×Dic59C2312yes—
67C2×C4×Dic59C2314yes—
68Dic59⋊C8C23116yes—
69Dic59⋊C8C23116yes—
70#14273638C2318yes—
71#14273637C2318yes—
72#14273637C2318yes—
73#14273637C2318yes—
74C4×C59⋊C8C2318yes—
75C8×Dic59C2318yes—
76C23×C4×C59C2311yescharacteristic
77C2×M16×C59—24no—
78C2×M16×C59C2314yes—
79C22×C8×C59—24no—
80C22×C8×C59C2312yes—
81C22×C8×C59C2312yes—
82C22×C8×C59C2314yes—
83#117×C59C2×C414yes—
84#117×C59C2314yes—
85C2×C4⋊C4×C59C2×C412yes—
86C2×C22⋊C4×C59C2×C412yes—
87C2×C42×C59C2312yes—
88C4⋊C8×C59C23116yes—
89C24×C59C22×C411yescharacteristic
90C22×C4×C59C22×C414yes—
91C22×C4×C59C22×C411yescharacteristic
92C22×C4×C59C22×C412yes—
93C22×C4×C59C2×Q814yes—
94C22×C4×C59#4114yes—
95C22×C4×C59C2412yes—
96C22×C4×C59C2411yescharacteristic
97C22×Dic59—44no—
98C22×Dic59C22×C412yes—
99C22×Dic59C22×C412yes—
100C22×Dic59C22×C414yes—
101C22×Dic59C22×C418yes—
102C2×Dic118—48no—
103C2×Dic118C22×C4116yes—
104M16×C59—28no—
105C2×C8×C59—24no—
106C2×C8×C59—28no—
107C2×C8×C59—24no—
108C2×C8×C59C2414yes—
109C2×C8×C59C2414yes—
110C4⋊C4×C59C22×C418yes—
111C22⋊C4×C59C22×C418yes—
112C42×C59C22×C414yes—
113C42×C59C2414yes—
114C22⋊Dic59C22×C418yes—
115C4⋊Dic59C22×C418yes—
116C4⋊Dic59C22×C4116yes—
117Dic59⋊C4C22×C4116yes—
118Dic59⋊C4C22×C4116yes—
119C4×Dic59C22×C414yes—
120C4×Dic59C22×C414yes—
121C4×Dic59C22×C414yes—
122C4×Dic59C22×C414yes—
123C4×Dic59C2414yes—
124C4×Dic59C2414yes—
125#11745664—28no—
126C2×C59⋊C8—24no—
127C2×C59⋊C8C2×Q814yes—
128C2×C59⋊C8C2×Q814yes—
129C2×C59⋊C8C2×Q8116yescomplemented
130C2×C59⋊C8C2414yes—
131C2×C59⋊C8C2412yes—
132C2×C59⋊C8C2412yes—
133C23×C59—24no—
134C23×C59C4×Q814yes—
135C23×C59C23×C412yes—
136C23×C59C23×C411yescharacteristic
137C2×C4×C59—28no—
138C2×C4×C59C4×Q818yes—
139C2×C4×C59C4×Q814yes—
140C2×C4×C59C23×C418yes—
141C2×C4×C59C23×C411yescharacteristic
142C2×C4×C59C23×C412yes—
143C2×C4×C59C22×Q812yes—
144C2×C4×C59C22×Q814yes—
145C2×C4×C59C2×#4112yes—
146C2×C4×C59C2×#4114yes—
147C2×C4×C59C2511yescharacteristic
148C2×Dic59—24no—
149C2×Dic59—28no—
150C2×Dic59—24no—
151C2×Dic59—48no—
152C2×Dic59C23×C414yes—
153C2×Dic59C23×C414yes—
154C2×Dic59C23×C418yes—
155Dic118—416no—
156C8×C59—24no—
157C8×C59—24no—
158C59⋊C8—24no—
159C59⋊C8C22×Q814yes—
160C59⋊C8C22×Q814yes—
161C2×#2961—591nomaximal, Sylow
162C22×C59—28no—
163C22×C59—24no—
164C22×C59C2×C4×Q814yes—
165C22×C59C2×C4×Q812yes—
166C22×C59#56814yes—
167C22×C59C24×C411yescharacteristic
168C4×C59—28no—
169C4×C59C2×C4×Q812yes—
170C4×C59C2×C4×Q814yes—
171C4×C59C23×Q811yescharacteristic
172C4×C59C22×#4111yescharacteristic
173Dic59—24no—
174Dic59—28no—
175Dic59—24no—
176C2×#533—591no—
177#2961—5916no—
178C2×#446—594no—
179C2×#446—594no—
180C2×#424—591no—
181C2×#424D5911yescharacteristic
182C2×#423—591no—
183C2×#405—591no—
184C2×#405—591no—
185C22×#97—591no—
186C2×C59—24no—
187C2×C59#296114yescomplemented
188C2×C59C22×C4×Q811yescharacteristic
189C2×C59C2×#56812yes—
190C22×M16—591no—
191C22×M16C2×D5911yescharacteristic
192C23×C8—591no—
193C23×C8C2×D5911yescharacteristic
194#533—598no—
195#533—598no—
196C2×C4⋊Q8—592no—
197C2×#125—592no—
198C2×C22⋊Q8—594no—
199C2×C4×Q8—594no—
200C2×#117—591no—
201C2×#117C2×D5911yescharacteristic
202C22×C42—591no—
203#446—5932no—
204#446—5932no—
205#424—598no—
206#424C2×D5918yes—
207#423—598no—
208C2×C4⋊C8—594no—
209C2×C4⋊C8—594no—
210C2×C4⋊C8C2×D5914yes—
211#405—598no—
212#405—598no—
213C2×#97—592no—
214C2×#97—592no—
215C2×#97—598no—
216C2×#97—592no—
217C2×#97—592no—
218C2×C4×C8—592no—
219C2×C4×C8—592no—
220C59C2×#296111yescharacteristic, complemented, Sylow
221C22×Q8—594no—
222C23×C4—592no—
223C23×C4C22×D5911yescharacteristic
224C2×M16—24no—
225C2×M16—594no—
226C2×M16—1184no—
227C2×M16C22×D5914yes—
228C22×C8—24no—
229C22×C8—598no—
230C22×C8—594no—
231C22×C8—591no—
232C22×C8—591no—
233C22×C8—592no—
234C22×C8C22×D5914yes—
235C22×C8C22×D5912yes—
236C22×C8C22×D5912yes—
237C4⋊Q8—5916no—
238#125—5916no—
239C22⋊Q8—5932no—
240C4×Q8—5916no—
241C4×Q8—5916no—
242#117—594no—
243#117—594no—
244#117C4×D5914yes—
245#117C22×D5914yes—
246C2×C4⋊C4—592no—
247C2×C4⋊C4—594no—
248C2×C4⋊C4—594no—
249C2×C4⋊C4—594no—
250C2×C4⋊C4C4×D5912yes—
251C2×C22⋊C4—592no—
252C2×C22⋊C4C4×D5912yes—
253C2×C42—591no—
254C2×C42—591no—
255C2×C42—594no—
256C2×C42—594no—
257C2×C42—592no—
258C2×C42—592no—
259C2×C42C22×D5912yes—
260C4⋊C8—5916no—
261C4⋊C8—5916no—
262C4⋊C8C22×D59116yes—
263#97—598no—
264#97—598no—
265#97—598no—
266#97—598no—
267C4×C8—598no—
268C4×C8—598no—
269C24C2×C4×D5911yescharacteristic
270C2×Q8—5916no—
271C2×Q8—2368no—
272C22×C4—592no—
273C22×C4—592no—
274C22×C4—594no—
275C22×C4—598no—
276C22×C4—2364no—
277C22×C4C2×C4×D5914yes—
278C22×C4C2×C4×D5911yescharacteristic
279C22×C4C2×C4×D5912yes—
280C22×C4#1174568714yes—
281C22×C4Q8×D5914yes—
282C22×C4C23×D5912yes—
283C22×C4C23×D5911yescharacteristic
284M16—28no—
285M16—1188no—
286C2×C8—24no—
287C2×C8—28no—
288C2×C8—24no—
289C2×C8—594no—
290C2×C8—594no—
291C2×C8—5916no—
292C2×C8—592no—
293C2×C8—592no—
294C2×C8—594no—
295C2×C8—1184no—
296C2×C8C23×D5914yes—
297C2×C8C23×D5914yes—
298C4⋊C4—598no—
299C4⋊C4—5916no—
300C4⋊C4—5916no—
301C4⋊C4—5916no—
302C4⋊C4C2×C4×D5918yes—
303C22⋊C4—598no—
304C22⋊C4C2×C4×D5918yes—
305C42—594no—
306C42—594no—
307C42—594no—
308C42—594no—
309C42—594no—
310C42—594no—
311C42C2×C4×D5914yes—
312C42C23×D5914yes—
313C23—24no—
314C23#1427369214yes—
315C23C22×C4×D5912yes—
316C23C22×C4×D5911yescharacteristic
317Q8—23616no—
318C2×C4—28no—
319C2×C4—594no—
320C2×C4—594no—
321C2×C4—598no—
322C2×C4—1184no—
323C2×C4—1184no—
324C2×C4—1188no—
325C2×C4—2368no—
326C2×C4#1427369218yes—
327C2×C4#1427369214yes—
328C2×C4C22×C4×D5918yes—
329C2×C4C22×C4×D5911yescharacteristic
330C2×C4C22×C4×D5912yes—
331C2×C4C2×Q8×D5914yes—
332C2×C4C2×Q8×D5912yes—
333C2×C4C2×#1174568712yes—
334C2×C4C2×#1174568714yes—
335C2×C4C24×D5911yescharacteristic
336C8—24no—
337C8—24no—
338C8—594no—
339C8—594no—
340C8—1184no—
341C22—24no—
342C22—28no—
343C22C2×#1427369214yes—
344C22C2×#1427369212yes—
345C22#1683816714yes—
346C22C23×C4×D5911yescharacteristic
347C4—28no—
348C4—1184no—
349C4—1184no—
350C4—1188no—
351C4C2×#1427369212yes—
352C4C2×#1427369214yes—
353C4C22×Q8×D5911yescharacteristic
354C4C22×#1174568711yescharacteristic
355C2—24no—
356C2#2143303514yesdirect product factor
357C2C22×#1427369211yescharacteristic
358C2C2×#1683816712yes—
subgroupG/H
centerC22×C4C23×D59
commutatorC22×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#424C2
socleC23×C59C23×C4
prime radicalC24×C59C22×C4
cosocleC2×C4×C59C25
hypercenterC2×#424D59
hypocenterC59C2×#2961
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
2. #21433035C2direct (N × H)
3. C2×#16837531C2semidirect
4. C2×#16837529C2semidirect
21. #16837531C22semidirect
22. #16837529C22semidirect
45. C22×C59⋊C8Q8semidirect
129. C2×C59⋊C8C2×Q8semidirect
187. C2×C59#2961semidirect
220. C59C2×#2961semidirect
356. C2#21433035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379552
#214330352
C2×#168375312
C2×#168375292
C2×#168374282
C2×#168374252
C2×#168373602
C2×#168373582
C22×#142736372
C2×C59×#4242
C2×#296159