Finite Group Databasebeta

← C2×#21447265 #29708910

Subgroups — C2×#21447265 #29708910

Order 15616.

950 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839761C212yesmaximal
2C2×#16839728C211yesmaximal, characteristic
3#21447265C218yesmaximal, direct product factor
4C2×#16839531C212yesmaximal, complemented
5C2×#16839527C211yesmaximal, characteristic, complemented
6C22×#106×C61C211yesmaximal, characteristic, complemented
7C22×#11758222C2211yescharacteristic
8C22×#11758194C2212yes—
9C22×#11758194C2211yescharacteristic
10#16839761—24no—
11#16839761C2218yes—
12C2×#14519700—22no—
13C2×#14519697—22no—
14#16839728—22no—
15#16839728C2214yes—
16C2×#14519689—22no—
17#16839531C2218yescomplemented
18#16839527C2214yescomplemented
19C23×C8×C61C2211yescharacteristic
20C22×C4⋊C4×C61C2212yes—
21C2×#106×C61—22no—
22C2×#106×C61—22no—
23C2×#106×C61C2214yescomplemented
24C2×#11758222—21no—
25C2×#11758222—21no—
26C2×#11758222—24no—
27C2×#11758222—24no—
28C2×#11758222D412yes—
29C2×#11758222C2312yes—
30C22×Dic122D411yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C22×C4×D61—21no—
34C2×#11758194—21no—
35C2×#11758194—22no—
36C2×#11758194—24no—
37C2×#11758194—24no—
38C2×#11758194—24no—
39C2×#11758194C2312yes—
40C2×#11758194C2314yes—
41C22×#92418—21no—
42C22×#92418—22no—
43#14519700—28no—
44#14519697—28no—
45#14519689—28no—
46C23×C4×C61—22no—
47C23×C4×C61C2311yescharacteristic
48C22×C8×C61—24no—
49C22×C8×C61D412yes—
50C22×C8×C61D412yes—
51C22×C8×C61C2312yes—
52C2×C4⋊C4×C61—22no—
53C2×C4⋊C4×C61—22no—
54C2×C4⋊C4×C61—22no—
55C2×C4⋊C4×C61—22no—
56C2×C4⋊C4×C61—22no—
57C2×C4⋊C4×C61C2314yes—
58#106×C61—28no—
59C24×C61#4111yescharacteristic
60C23×D61—21no—
61C22×C4×C61—24no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61—84no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×C4×C61#4114yes—
71C22×C4×C61#4114yes—
72C22×C4×C61C2411yescharacteristic
73C2×C22⋊D61—22no—
74C2×C22⋊D61—22no—
75C2×C22⋊D61—44no—
76C22×Dic61—21no—
77#11758222—28no—
78#11758222—24no—
79#11758222—24no—
80#11758222—42no—
81#11758222—42no—
82#11758222—44no—
83C2×D244—24no—
84C2×D244—21no—
85C2×D244C2×D412yes—
86C2×C4×D61—22no—
87C2×C4×D61—22no—
88C2×C4×D61—42no—
89C2×C4×D61—42no—
90C2×Dic122—24no—
91C2×Dic122—21no—
92C2×Dic122C2×D412yes—
93C2×C8×C61—24no—
94C2×C8×C61—24no—
95C2×C8×C61—24no—
96C2×C8×C61C2×D414yes—
97C4⋊C4×C61—24no—
98C4⋊C4×C61—24no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—42no—
101#11758194—24no—
102#11758194—24no—
103#11758194—24no—
104#11758194—44no—
105#11758194—42no—
106C2×#92418—22no—
107C2×#92418—24no—
108C2×#92418—44no—
109C2×#92418—42no—
110C23×C61—24no—
111C23×C61#12111yescharacteristic
112C23×C61#12111yescharacteristic
113C23×C61#12614yes—
114C23×C61C2×#4111yescharacteristic
115C22×D61—22no—
116C22×D61—42no—
117C22×D61—44no—
118C2×C4×C61—44no—
119C2×C4×C61—84no—
120C2×C4×C61—84no—
121C2×C4×C61—84no—
122C2×C4×C61#12111yescharacteristic
123C2×C4×C61#12111yescharacteristic
124C2×C4×C61#12312yes—
125C2×C4×C61#12312yes—
126C2×C4×C61#12314yes—
127C2×C4×C61#12314yes—
128C2×C4×C61#12412yes—
129C2×C4×C61#12412yes—
130C2×C4×C61#12614yes—
131C2×C4×C61C22×D411yescharacteristic
132C2×C4×C61C22×D411yescharacteristic
133C2×C4×C61C2×#4112yes—
134C2×C4×C61C2×#4112yes—
135C22⋊D61—44no—
136C22⋊D61—44no—
137C2×Dic61—22no—
138C2×Dic61—42no—
139D244—24no—
140D244—42no—
141C4×D61—42no—
142C4×D61—42no—
143C4×D61—44no—
144Dic122—24no—
145Dic122—42no—
146C8×C61—24no—
147#92418—44no—
148#92418—42no—
149C2×#2079—611nomaximal, Sylow
150C22×C61—28no—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61#39712yes—
154C22×C61#39712yes—
155C22×C61#47114yes—
156C22×C61C2×#12111yescharacteristic
157C22×C61C2×#12612yes—
158C2×D61—42no—
159C2×D61—44no—
160C2×D61—84no—
161C4×C61—84no—
162C4×C61#39712yes—
163C4×C61#39712yes—
164C4×C61C2×#12311yescharacteristic
165C4×C61C2×#12312yes—
166C4×C61C2×#12411yescharacteristic
167Dic61—42no—
168C22×#106D6111yescharacteristic, complemented
169C2×#417—612no—
170C2×#408—611no—
171#2079—618no—
172C2×#343—612no—
173C2×#341—611no—
174C2×C61—22no—
175C2×C61—22no—
176C2×C61#207914yescomplemented
177C2×C61C2×#39711yescharacteristic
178C2×C61C2×#47112yes—
179D61—82no—
180C22×#41—611no—
181C22×M16—611no—
182C22×M16—612no—
183C23×C8C2×D6111yescharacteristic
184C22×C4⋊C4C2×D6112yes—
185C2×#106—22no—
186C2×#106—22no—
187C2×#106C2×D6114yescomplemented
188#417—618no—
189#417—1224no—
190C2×#103—1222no—
191C2×#102—1222no—
192#408—614no—
193#408—1222no—
194C2×C22⋊C8—1222no—
195#343—618no—
196#341—614no—
197C61C2×#207911yescharacteristic, complemented, Sylow
198C2×#41—612no—
199C2×#41—612no—
200C2×#41—1221no—
201C2×#41—1221no—
202C2×#41—1224no—
203C2×#41—1224no—
204C22×Q8—611no—
205C22×D4—611no—
206C22×D4—1221no—
207C23×C4—22no—
208C23×C4—1221no—
209C23×C4C22×D6111yescharacteristic
210C2×M16—614no—
211C2×M16—612no—
212C2×M16—1222no—
213C2×M16—1221no—
214C2×M16—1224no—
215C2×M16—1224no—
216C2×M16—1224no—
217C22×C8—24no—
218C22×C8—1222no—
219C22×C8—1221no—
220C22×C8C22⋊D6112yes—
221C22×C8C22⋊D6112yes—
222C22×C8C22×D6112yes—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4C22×D6114yes—
229#106—28no—
230#103—1228no—
231#102—1228no—
232C22⋊C8—1228no—
233C24—1221no—
234C24#1175822411yescharacteristic
235#41—1224no—
236#41—1224no—
237#41—1228no—
238#41—2442no—
239#41—2442no—
240#41—2444no—
241C2×Q8—612no—
242C2×Q8—1221no—
243C2×Q8—1224no—
244C2×D4—612no—
245C2×D4—1222no—
246C2×D4—1222no—
247C2×D4—1221no—
248C2×D4—1224no—
249C2×D4—2444no—
250C22×C4—24no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—84no—
254C22×C4—1221no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—2442no—
258C22×C4—2442no—
259C22×C4#1175822214yes—
260C22×C4D4×D6111yescharacteristic
261C22×C4D4×D6111yescharacteristic
262C22×C4#1175822411yescharacteristic
263C22×C4#1175822614yes—
264C22×C4C2×C22⋊D6111yescharacteristic
265C22×C4C2×C22⋊D6111yescharacteristic
266C22×C4C23×D6111yescharacteristic
267M16—1224no—
268M16—1224no—
269M16—1224no—
270M16—2444no—
271M16—2442no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—1224no—
276C2×C8—1222no—
277C2×C8—2444no—
278C2×C8—2442no—
279C2×C8C2×C22⋊D6114yes—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C23—24no—
285C23—1222no—
286C23—2442no—
287C23—2444no—
288C23#1451974811yescharacteristic
289C23#1451974811yescharacteristic
290C23#1451977214yes—
291C23C2×#1175822411yescharacteristic
292Q8—1224no—
293Q8—2442no—
294D4—1224no—
295D4—2444no—
296D4—2444no—
297D4—2442no—
298C2×C4—44no—
299C2×C4—84no—
300C2×C4—84no—
301C2×C4—84no—
302C2×C4—1222no—
303C2×C4—2442no—
304C2×C4—2444no—
305C2×C4—2442no—
306C2×C4—2442no—
307C2×C4#1451974811yescharacteristic
308C2×C4#1451974811yescharacteristic
309C2×C4#1451976012yes—
310C2×C4#1451976012yes—
311C2×C4#1451976214yes—
312C2×C4#1451976214yes—
313C2×C4#1451976612yes—
314C2×C4#1451976612yes—
315C2×C4#1451977214yes—
316C2×C4C2×D4×D6111yescharacteristic
317C2×C4C22×C22⋊D6111yescharacteristic
318C2×C4C2×#1175822212yes—
319C2×C4C2×#1175822612yes—
320C8—24no—
321C8—2444no—
322C8—2442no—
323C22—28no—
324C22—22no—
325C22—22no—
326C22—4884no—
327C22—2442no—
328C22—2444no—
329C22#1683968812yes—
330C22#1683968812yes—
331C22#1684002214yes—
332C22C2×#1451974811yescharacteristic
333C22C2×#1451977212yes—
334C4—84no—
335C4—2442no—
336C4#1683968812yes—
337C4#1683968812yes—
338C4C2×#1451976011yescharacteristic
339C4C2×#1451976212yes—
340C4C2×#1451976611yescharacteristic
341C2—22no—
342C2—22no—
343C2—4882no—
344C2#2144726514yesdirect product factor
345C2C2×#1683968811yescharacteristic
346C2C2×#1684002212yes—
subgroupG/H
centerC23#14519748
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#106×C61C2
socleC23×C61#121
prime radicalC22×#11758222C22
hypercenterC22×#106D61
hypocenterC61C2×#2079
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #21447265C2direct (N × H)
4. C2×#16839531C2semidirect
5. C2×#16839527C2semidirect
6. C22×#106×C61C2semidirect
17. #16839531C22semidirect
18. #16839527C22semidirect
23. C2×#106×C61C22semidirect
168. C22×#106D61semidirect
176. C2×C61#2079semidirect
187. C2×#106C2×D61semidirect
197. C61C2×#2079semidirect
344. C2#21447265direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168397612
C2×#168397282
#214472652
C2×#168395312
C2×#168395272
C22×#106×C612
C2×#207961