Finite Group Databasebeta

← C2×#21448037 #29834902

Subgroups — C2×#21448037 #29834902

Order 15616.

552 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840017C211yesmaximal, characteristic
2C2×#16839809C211yesmaximal, characteristic
3#21448037C218yesmaximal, direct product factor
4C2×#16839586C211yesmaximal, characteristic, complemented
5C2×#16839585C211yesmaximal, characteristic, complemented
6C2×#16839578C211yesmaximal, characteristic, complemented
7C2×#16839543C211yesmaximal, characteristic
8C2×C61×#362C211yesmaximal, characteristic, complemented
9C22×#11758189C2211yescharacteristic
10C2×M16×D61—21no—
11C2×#14519753—21no—
12C2×#14519717C2211yescharacteristic
13#16840017—22no—
14#16840017C2214yes—
15#16839809—22no—
16#16839809C2214yes—
17C2×#14519713C2211yescharacteristic
18C2×#14519712—21no—
19C2×#14519709C2211yescharacteristic
20C2×#14519701—21no—
21#16839586C2214yescomplemented
22#16839585C2214yescomplemented
23#16839578C2214yescomplemented
24#16839543C2214yes—
25C22×Q16×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C61×#362C2214yescomplemented
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31C2×#11758189—21no—
32C2×#11758189—21no—
33C2×#11758189—21no—
34C2×#11758189—21no—
35C2×#11758189—41no—
36C2×#11758189D412yes—
37C2×#11758189C2312yes—
38M16×D61—24no—
39M16×D61—42no—
40C22×#92418D411yescharacteristic
41C2×C8×D61—41no—
42#14519753—24no—
43#14519753—42no—
44C2×C4⋊Dic61—21no—
45C2×#11758196—41no—
46C2×#11758198—41no—
47#14519717—21no—
48#14519717C2312yes—
49C2×#11758185—21no—
50#14519713—21no—
51#14519713C2312yes—
52#14519712—24no—
53#14519709—21no—
54#14519709C2312yes—
55#14519701—24no—
56C22×Q8×C61—21no—
57C2×Q16×C61—21no—
58C2×Q16×C61—21no—
59C2×Q16×C61—21no—
60C2×Q16×C61—21no—
61C2×Q16×C61—21no—
62C2×Q16×C61C2312yes—
63C2×M16×C61—21no—
64C22×C8×C61C2311yescharacteristic
65M32×C61—21no—
66M32×C61C2312yes—
67C2×C16×C61—21no—
68#108×C61—21no—
69#108×C61C2312yes—
70C23×D61SD1611yescharacteristic
71C2×Q8×C61—22no—
72C2×Q8×C61—41no—
73C2×Q8×C61—41no—
74C2×Q8×C61—41no—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—41no—
80C22×Dic61SD1611yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61SD1612yes—
86C2×C4×D61C2×D412yes—
87Q16×C61—22no—
88Q16×C61—22no—
89Q16×C61—41no—
90Q16×C61—41no—
91M16×C61—22no—
92M16×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61#4111yescharacteristic
96C2×C8×C61#4111yescharacteristic
97C2×C8×C61#4111yescharacteristic
98C2×C8×C61#4111yescharacteristic
99C2×C8×C61C2411yescharacteristic
100#11758198—44no—
101C4⋊Dic61—22no—
102C4⋊Dic61—41no—
103#11758196—44no—
104#11758194—22no—
105#11758194—41no—
106C2×#92418—21no—
107C2×#92418—21no—
108C2×#92418—41no—
109C2×#92418C2×D412yes—
110#11758189—22no—
111#11758189—22no—
112#11758189—22no—
113#11758189—22no—
114#11758189—44no—
115C8×D61—44no—
116C16×C61—22no—
117#11758185—22no—
118C23×C61C2×SD1611yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—42no—
122C22×D61C2×SD1612yes—
123Q8×C61—42no—
124Q8×C61—42no—
125Q8×C61—81no—
126Q8×C61—81no—
127C2×C4×C61—42no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61#12311yescharacteristic
131C2×C4×C61#12311yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C61C22×D411yescharacteristic
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—82no—
140C2×Dic61C2×SD1612yes—
141C4×D61—22no—
142C4×D61—22no—
143C4×D61—22no—
144C4×D61—22no—
145C8×C61—42no—
146C8×C61#12311yescharacteristic
147C8×C61#12311yescharacteristic
148C8×C61C2×#4111yescharacteristic
149C8×C61C2×#4111yescharacteristic
150#92418—22no—
151#92418—42no—
152C2×#2239—611nomaximal, Sylow
153C22×C61—22no—
154C22×C61#48111yescharacteristic
155C22×C61#48111yescharacteristic
156C22×C61C22×SD1611yescharacteristic
157C2×D61—22no—
158C2×D61—42no—
159C2×D61—42no—
160C2×D61—81no—
161C4×C61—82no—
162C4×C61#48111yescharacteristic
163C4×C61#48111yescharacteristic
164C4×C61C2×#12311yescharacteristic
165C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
166Dic61—22no—
167Dic61—82no—
168C2×#470—611no—
169C2×#430—611no—
170#2239—618no—
171C2×#365—611no—
172C2×#365—611no—
173C2×#362—611no—
174C2×#362D6111yescharacteristic, complemented
175C2×#349—611no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61#223912yescomplemented
179C2×C61C2×#48111yescharacteristic
180D61—42no—
181C22×Q16C2×D6111yescharacteristic
182C22×M16—611no—
183C22×M16—1221no—
184C2×C22⋊Q8—1221no—
185C2×M32—611no—
186C2×M32C2×D6111yescharacteristic
187#470—614no—
188#470—1222no—
189#430—614no—
190#430—1222no—
191C2×#108—611no—
192C2×#108—1221no—
193C2×#108C2×D6111yescharacteristic
194C2×#106—611no—
195C2×#103—1221no—
196#365—614no—
197#365—614no—
198#362—614no—
199#362C2×D6114yescomplemented
200#349—614no—
201C61C2×#223911yescharacteristic, complemented, Sylow
202C22×Q8—21no—
203C23×C4—611no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16C22×D6112yes—
210C2×M16—21no—
211C2×M16—612no—
212C2×M16—612no—
213C2×M16—1221no—
214C2×M16—1221no—
215C2×M16—1221no—
216C2×M16—1221no—
217C2×M16—1224no—
218C2×M16—1221no—
219C2×M16—2441no—
220C2×M16—2442no—
221C22×C8—611no—
222C22×C8—2441no—
223C22×C8C22×D6111yescharacteristic
224C22⋊Q8—1224no—
225C22⋊Q8—2442no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—2441no—
228C2×C22⋊C4—2441no—
229M32—21no—
230M32—612no—
231M32—1221no—
232M32C22×D6112yes—
233C2×C16—21no—
234C2×C16—1221no—
235#108—21no—
236#108—612no—
237#108—1224no—
238#108—1221no—
239#108C22×D6112yes—
240#106—612no—
241#106—1221no—
242#103—1224no—
243C24—611no—
244C2×Q8—22no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C22×C4—41no—
251C22×C4—611no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—2441no—
259C22×C4D4×D6111yescharacteristic
260Q16—22no—
261Q16—22no—
262Q16—41no—
263Q16—41no—
264M16—22no—
265M16—41no—
266M16—1222no—
267M16—1222no—
268M16—1222no—
269M16—1222no—
270M16—1222no—
271M16—2444no—
272M16—2441no—
273C2×C8—41no—
274C2×C8—612no—
275C2×C8—1221no—
276C2×C8—1221no—
277C2×C8—2444no—
278C2×C8—2441no—
279C2×C8#1175822211yescharacteristic
280C2×C8#1175822211yescharacteristic
281C2×C8D4×D6111yescharacteristic
282C2×C8#1175822411yescharacteristic
283C2×C8#1175822411yescharacteristic
284C2×C8C23×D6111yescharacteristic
285C4⋊C4—1222no—
286C4⋊C4—2444no—
287C4⋊C4—2441no—
288C22⋊C4—2444no—
289C16—22no—
290C16—1222no—
291C23—612no—
292C23—1221no—
293C23—1221no—
294C23—2442no—
295C23SD16×D6111yescharacteristic
296Q8—42no—
297Q8—42no—
298Q8—81no—
299Q8—81no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—612no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1222no—
307C2×C4—1222no—
308C2×C4—1222no—
309C2×C4—1222no—
310C2×C4—4882no—
311C2×C4—2442no—
312C2×C4#1451975911yescharacteristic
313C2×C4#1451975911yescharacteristic
314C2×C4SD16×D6111yescharacteristic
315C2×C4#1451980111yescharacteristic
316C2×C4#1451980111yescharacteristic
317C2×C4C2×D4×D6111yescharacteristic
318C8—42no—
319C8—1222no—
320C8—2442no—
321C8#1451975911yescharacteristic
322C8#1451975911yescharacteristic
323C8C2×#1175822411yescharacteristic
324C8C2×#1175822211yescharacteristic
325C22—22no—
326C22—1222no—
327C22—4881no—
328C22—2442no—
329C22—2442no—
330C22#1684007911yescharacteristic
331C22#1684007911yescharacteristic
332C22C2×SD16×D6111yescharacteristic
333C4—82no—
334C4—1222no—
335C4—4882no—
336C4#1684007911yescharacteristic
337C4#1684007911yescharacteristic
338C4C2×#1451975911yescharacteristic
339C4C2×#1451980111yescharacteristic
340C2—21no—
341C2—21no—
342C2—2442no—
343C2#2144803712yesdirect product factor
344C2C2×#1684007911yescharacteristic
subgroupG/H
centerC22#16840079
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC2×C61×#362C2
socleC22×C61#481
prime radicalC23×D61SD16
hypercenterC2×#362D61
hypocenterC61C2×#2239
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

Complements

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

NH ≅ G/Ntype
3. #21448037C2direct (N × H)
4. C2×#16839586C2semidirect
5. C2×#16839585C2semidirect
6. C2×#16839578C2semidirect
8. C2×C61×#362C2semidirect
21. #16839586C22semidirect
22. #16839585C22semidirect
23. #16839578C22semidirect
28. C61×#362C22semidirect
174. C2×#362D61semidirect
178. C2×C61#2239semidirect
199. #362C2×D61semidirect
201. C61C2×#2239semidirect
343. C2#21448037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168400172
C2×#168398092
#214480372
C2×#168395862
C2×#168395852
C2×#168395782
C2×#168395432
C2×C61×#3622
C2×#223961