Finite Group Databasebeta

← C2×#24908904 #35433295

Subgroups — C2×#24908904 #35433295

Order 21248.

950 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127700C212yesmaximal
2C2×#19127667C211yesmaximal, characteristic
3#24908904C218yesmaximal, direct product factor
4C2×#19127470C212yesmaximal, complemented
5C2×#19127466C211yesmaximal, characteristic, complemented
6C22×#107×C83C211yesmaximal, characteristic, complemented
7C22×#13050590C2211yescharacteristic
8C22×#13050574C2212yes—
9C22×#13050574C2211yescharacteristic
10#19127700—24no—
11#19127700C2218yes—
12C2×#14581715—22no—
13C2×#14581712—22no—
14#19127667—22no—
15#19127667C2214yes—
16C2×(C2×D83)⋊C8—22no—
17#19127470C2218yescomplemented
18#19127466C2214yescomplemented
19C23×C8×C83C2211yescharacteristic
20C22×C4⋊C4×C83C2212yes—
21C2×#107×C83—22no—
22C2×#107×C83—22no—
23C2×#107×C83C2214yescomplemented
24C2×#13050590—21no—
25C2×#13050590—21no—
26C2×#13050590—24no—
27C2×#13050590—24no—
28C2×#13050590D412yes—
29C2×#13050590C2312yes—
30C22×Dic166D411yescharacteristic
31C22×D332D411yescharacteristic
32C22×C22⋊D83—21no—
33C22×C4×D83—21no—
34C2×#13050574—21no—
35C2×#13050574—22no—
36C2×#13050574—24no—
37C2×#13050574—24no—
38C2×#13050574—24no—
39C2×#13050574C2312yes—
40C2×#13050574C2314yes—
41C22×C83⋊C8—21no—
42C22×C83⋊C8—22no—
43#14581715—28no—
44#14581712—28no—
45(C2×D83)⋊C8—28no—
46C23×C4×C83—22no—
47C23×C4×C83C2311yescharacteristic
48C22×C8×C83—24no—
49C22×C8×C83D412yes—
50C22×C8×C83D412yes—
51C22×C8×C83C2312yes—
52C2×C4⋊C4×C83—22no—
53C2×C4⋊C4×C83—22no—
54C2×C4⋊C4×C83—22no—
55C2×C4⋊C4×C83—22no—
56C2×C4⋊C4×C83—22no—
57C2×C4⋊C4×C83C2314yes—
58#107×C83—28no—
59C23×D83—21no—
60#13050590—28no—
61#13050590—24no—
62#13050590—24no—
63#13050590—42no—
64#13050590—42no—
65#13050590—44no—
66C2×Dic166—24no—
67C2×Dic166—21no—
68C2×Dic166C2×D412yes—
69C2×D332—24no—
70C2×D332—21no—
71C2×D332C2×D412yes—
72C2×C22⋊D83—22no—
73C2×C22⋊D83—22no—
74C2×C22⋊D83—44no—
75C22×Dic83—21no—
76C2×C4×D83—22no—
77C2×C4×D83—22no—
78C2×C4×D83—42no—
79C2×C4×D83—42no—
80#13050574—24no—
81#13050574—24no—
82#13050574—24no—
83#13050574—44no—
84#13050574—42no—
85C2×C83⋊C8—22no—
86C2×C83⋊C8—24no—
87C2×C83⋊C8—44no—
88C2×C83⋊C8—42no—
89C24×C83#4111yescharacteristic
90C22×C4×C83—24no—
91C22×C4×C83—42no—
92C22×C4×C83—42no—
93C22×C4×C83—84no—
94C22×C4×C83C2×D411yescharacteristic
95C22×C4×C83C2×D411yescharacteristic
96C22×C4×C83C2×D411yescharacteristic
97C22×C4×C83C2×D411yescharacteristic
98C22×C4×C83#4111yescharacteristic
99C22×C4×C83#4114yes—
100C22×C4×C83#4114yes—
101C22×C4×C83C2411yescharacteristic
102C2×C8×C83—24no—
103C2×C8×C83—24no—
104C2×C8×C83—24no—
105C2×C8×C83C2×D414yes—
106C4⋊C4×C83—24no—
107C4⋊C4×C83—24no—
108C4⋊C4×C83—42no—
109C4⋊C4×C83—42no—
110C23×C83—22no—
111C23×C83—22no—
112C23×C83#12111yescharacteristic
113C23×C83#12111yescharacteristic
114C23×C83#12614yes—
115C23×C83C2×#4111yescharacteristic
116C22×D83—22no—
117C22×D83—42no—
118C22×D83—42no—
119C22×D83—42no—
120C2×C4×C83—44no—
121C2×C4×C83—84no—
122C2×C4×C83—84no—
123C2×C4×C83—84no—
124C2×C4×C83#12111yescharacteristic
125C2×C4×C83#12111yescharacteristic
126C2×C4×C83#12312yes—
127C2×C4×C83#12312yes—
128C2×C4×C83#12314yes—
129C2×C4×C83#12314yes—
130C2×C4×C83#12412yes—
131C2×C4×C83#12412yes—
132C2×C4×C83#12614yes—
133C2×C4×C83C22×D411yescharacteristic
134C2×C4×C83C22×D411yescharacteristic
135C2×C4×C83C2×#4112yes—
136C2×C4×C83C2×#4112yes—
137C22⋊D83—44no—
138C22⋊D83—44no—
139C2×Dic83—22no—
140C2×Dic83—42no—
141D332—24no—
142D332—42no—
143C4×D83—42no—
144C4×D83—42no—
145C4×D83—44no—
146Dic166—24no—
147Dic166—42no—
148C8×C83—24no—
149C83⋊C8—44no—
150C83⋊C8—42no—
151C22×C83—28no—
152C22×C83—21no—
153C22×C83—21no—
154C22×C83—21no—
155C22×C83—21no—
156C22×C83#39712yes—
157C22×C83#39712yes—
158C22×C83#47212yes—
159C22×C83#47312yes—
160C22×C83C2×#12111yescharacteristic
161C22×C83C2×#12612yes—
162C2×D83—42no—
163C2×D83—42no—
164C2×D83—42no—
165C2×D83—84no—
166C4×C83—84no—
167C4×C83#39712yes—
168C4×C83#39712yes—
169C4×C83C2×#12311yescharacteristic
170C4×C83C2×#12312yes—
171C4×C83C2×#12411yescharacteristic
172Dic83—42no—
173C2×#2078—831nomaximal, Sylow
174C2×C83—22no—
175C2×C83—22no—
176C2×C83#207814yescomplemented
177C2×C83C2×#39711yescharacteristic
178C2×C83C2×#47211yescharacteristic
179C2×C83C2×#47311yescharacteristic
180D83—82no—
181C22×#107D8311yescharacteristic, complemented
182C2×#417—832no—
183C2×#408—831no—
184#2078—838no—
185C2×#343—832no—
186C2×#341—831no—
187C83C2×#207811yescharacteristic, complemented, Sylow
188C22×#41—831no—
189C22×M16—831no—
190C22×M16—832no—
191C23×C8C2×D8311yescharacteristic
192C22×C4⋊C4C2×D8312yes—
193C2×#107—22no—
194C2×#107—22no—
195C2×#107C2×D8314yescomplemented
196#417—838no—
197#417—1664no—
198C2×#103—1662no—
199C2×#102—1662no—
200#408—834no—
201#408—1662no—
202C2×C22⋊C8—1662no—
203#343—838no—
204#341—834no—
205C2×#41—832no—
206C2×#41—832no—
207C2×#41—1664no—
208C2×#41—1664no—
209C2×#41—1661no—
210C2×#41—1661no—
211C22×Q8—831no—
212C22×D4—831no—
213C22×D4—1661no—
214C23×C4—22no—
215C23×C4—1661no—
216C23×C4C22×D8311yescharacteristic
217C2×M16—834no—
218C2×M16—832no—
219C2×M16—1664no—
220C2×M16—1664no—
221C2×M16—1664no—
222C2×M16—1662no—
223C2×M16—1661no—
224C22×C8—24no—
225C22×C8—1662no—
226C22×C8—1661no—
227C22×C8C22⋊D8312yes—
228C22×C8C22⋊D8312yes—
229C22×C8C22×D8312yes—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4C22×D8314yes—
236#107—28no—
237#103—1668no—
238#102—1668no—
239C22⋊C8—1668no—
240C24—1661no—
241C24#1305058911yescharacteristic
242#41—3322no—
243#41—3322no—
244#41—3324no—
245#41—1668no—
246#41—1664no—
247#41—1664no—
248C2×Q8—832no—
249C2×Q8—1664no—
250C2×Q8—1661no—
251C2×D4—3324no—
252C2×D4—832no—
253C2×D4—1662no—
254C2×D4—1662no—
255C2×D4—1661no—
256C2×D4—1664no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—84no—
261C22×C4—3322no—
262C22×C4—3322no—
263C22×C4—1661no—
264C22×C4—1662no—
265C22×C4—1662no—
266C22×C4D4×D8311yescharacteristic
267C22×C4D4×D8311yescharacteristic
268C22×C4C2×C22⋊D8311yescharacteristic
269C22×C4C2×C22⋊D8311yescharacteristic
270C22×C4#1305058911yescharacteristic
271C22×C4#1305059014yes—
272C22×C4#1305059114yes—
273C22×C4C23×D8311yescharacteristic
274M16—3324no—
275M16—3322no—
276M16—1664no—
277M16—1664no—
278M16—1664no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—3324no—
283C2×C8—3322no—
284C2×C8—1664no—
285C2×C8—1662no—
286C2×C8C2×C22⋊D8314yes—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C23—22no—
292C23—22no—
293C23—3322no—
294C23—3322no—
295C23—3322no—
296C23—1662no—
297C23#1458176311yescharacteristic
298C23#1458176311yescharacteristic
299C23#1458178714yes—
300C23C2×#1305058911yescharacteristic
301Q8—3322no—
302Q8—1664no—
303D4—3324no—
304D4—3324no—
305D4—3322no—
306D4—1664no—
307C2×C4—44no—
308C2×C4—84no—
309C2×C4—84no—
310C2×C4—84no—
311C2×C4—3322no—
312C2×C4—3324no—
313C2×C4—3322no—
314C2×C4—3322no—
315C2×C4—1662no—
316C2×C4#1458176311yescharacteristic
317C2×C4#1458176311yescharacteristic
318C2×C4#1458177512yes—
319C2×C4#1458177512yes—
320C2×C4#1458177714yes—
321C2×C4#1458177714yes—
322C2×C4#1458178112yes—
323C2×C4#1458178112yes—
324C2×C4#1458178714yes—
325C2×C4C2×D4×D8311yescharacteristic
326C2×C4C22×C22⋊D8311yescharacteristic
327C2×C4C2×#1305059012yes—
328C2×C4C2×#1305059112yes—
329C8—24no—
330C8—3324no—
331C8—3322no—
332C22—28no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—3322no—
338C22—3322no—
339C22—3322no—
340C22—6644no—
341C22#1912762712yes—
342C22#1912762712yes—
343C22#1912796812yes—
344C22#1912797312yes—
345C22C2×#1458176311yescharacteristic
346C22C2×#1458178712yes—
347C4—84no—
348C4—3322no—
349C4#1912762712yes—
350C4#1912762712yes—
351C4C2×#1458177511yescharacteristic
352C4C2×#1458177712yes—
353C4C2×#1458178111yescharacteristic
354C2—22no—
355C2—22no—
356C2—6642no—
357C2#2490890414yesdirect product factor
358C2C2×#1912762711yescharacteristic
359C2C2×#1912796811yescharacteristic
360C2C2×#1912797311yescharacteristic
subgroupG/H
centerC23#14581763
commutator, cosocleC22×C4×C83C24
FrattiniC22×C4C23×D83
FittingC22×#107×C83C2
socleC23×C83#121
prime radicalC22×#13050590C22
hypercenterC22×#107D83
hypocenterC83C2×#2078
LCSG ▷ C22×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
3. #24908904C2direct (N × H)
4. C2×#19127470C2semidirect
5. C2×#19127466C2semidirect
6. C22×#107×C83C2semidirect
17. #19127470C22semidirect
18. #19127466C22semidirect
23. C2×#107×C83C22semidirect
176. C2×C83#2078semidirect
181. C22×#107D83semidirect
187. C83C2×#2078semidirect
195. C2×#107C2×D83semidirect
357. C2#24908904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191277002
C2×#191276672
#249089042
C2×#191274702
C2×#191274662
C22×#107×C832
C2×#207883