Finite Group Databasebeta

← C2×#14530230 #17063221

Subgroups — C2×#14530230 #17063221

Order 4352.

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×#11762808C212yesmaximal
2C2×#11762775C211yesmaximal, characteristic
3#14530230C218yesmaximal, direct product factor
4C2×#11762578C212yesmaximal, complemented
5C2×#11762574C211yesmaximal, characteristic, complemented
6C22×C17×#106C211yesmaximal, characteristic, complemented
7C22×#63252C2211yescharacteristic
8C22×#63223C2211yescharacteristic
9C22×#63223C2212yes—
10#11762808—24no—
11#11762808C2218yes—
12C2×#10587481—22no—
13C2×#10587480—22no—
14#11762775—22no—
15#11762775C2214yes—
16C2×#10587491—22no—
17#11762578C2218yescomplemented
18#11762574C2214yescomplemented
19C23×C8×C17C2211yescharacteristic
20C22×C4⋊C4×C17C2212yes—
21C2×C17×#106—22no—
22C2×C17×#106—22no—
23C2×C17×#106C2214yescomplemented
24C23×C4×C17—22no—
25C23×C4×C17C2311yescharacteristic
26C22×C22⋊D17—21no—
27C2×#63252—21no—
28C2×#63252—21no—
29C2×#63252—24no—
30C2×#63252—24no—
31C2×#63252D412yes—
32C2×#63252C2312yes—
33C22×D68D411yescharacteristic
34C22×C4×D17—21no—
35C22×Dic34D411yescharacteristic
36C22×C8×C17—24no—
37C22×C8×C17D412yes—
38C22×C8×C17D412yes—
39C22×C8×C17C2312yes—
40C2×C4⋊C4×C17—22no—
41C2×C4⋊C4×C17—22no—
42C2×C4⋊C4×C17—22no—
43C2×C4⋊C4×C17—22no—
44C2×C4⋊C4×C17—22no—
45C2×C4⋊C4×C17C2314yes—
46C2×#63223—21no—
47C2×#63223—22no—
48C2×#63223—24no—
49C2×#63223—24no—
50C2×#63223—24no—
51C2×#63223C2312yes—
52C2×#63223C2314yes—
53C22×#3622—21no—
54C22×#3622—22no—
55C17×#106—28no—
56#10587491—28no—
57#10587481—28no—
58#10587480—28no—
59C24×C17#4111yescharacteristic
60C23×D17—21no—
61C22×C4×C17—24no—
62C22×C4×C17—42no—
63C22×C4×C17—42no—
64C22×C4×C17—84no—
65C22×C4×C17C2×D411yescharacteristic
66C22×C4×C17C2×D411yescharacteristic
67C22×C4×C17C2×D411yescharacteristic
68C22×C4×C17C2×D411yescharacteristic
69C22×C4×C17#4114yes—
70C22×C4×C17#4111yescharacteristic
71C22×C4×C17#4114yes—
72C22×C4×C17C2411yescharacteristic
73C2×C22⋊D17—22no—
74C2×C22⋊D17—22no—
75C2×C22⋊D17—44no—
76C22×Dic17—21no—
77#63252—28no—
78#63252—24no—
79#63252—24no—
80#63252—42no—
81#63252—42no—
82#63252—44no—
83C2×D68—24no—
84C2×D68—21no—
85C2×D68C2×D412yes—
86C2×C4×D17—22no—
87C2×C4×D17—22no—
88C2×C4×D17—42no—
89C2×C4×D17—42no—
90C2×Dic34—24no—
91C2×Dic34—21no—
92C2×Dic34C2×D412yes—
93C2×C8×C17—24no—
94C2×C8×C17—24no—
95C2×C8×C17—24no—
96C2×C8×C17C2×D414yes—
97C4⋊C4×C17—24no—
98C4⋊C4×C17—24no—
99C4⋊C4×C17—42no—
100C4⋊C4×C17—42no—
101#63223—24no—
102#63223—24no—
103#63223—24no—
104#63223—44no—
105#63223—42no—
106C2×#3622—24no—
107C2×#3622—22no—
108C2×#3622—44no—
109C2×#3622—42no—
110C2×#2079—171nomaximal, Sylow
111C23×C17—24no—
112C23×C17#12111yescharacteristic
113C23×C17#12111yescharacteristic
114C23×C17#12614yes—
115C23×C17C2×#4111yescharacteristic
116C22×D17—22no—
117C22×D17—42no—
118C22×D17—44no—
119C2×C4×C17—44no—
120C2×C4×C17—84no—
121C2×C4×C17—84no—
122C2×C4×C17—84no—
123C2×C4×C17#12111yescharacteristic
124C2×C4×C17#12111yescharacteristic
125C2×C4×C17#12314yes—
126C2×C4×C17#12314yes—
127C2×C4×C17#12312yes—
128C2×C4×C17#12312yes—
129C2×C4×C17#12412yes—
130C2×C4×C17#12412yes—
131C2×C4×C17#12614yes—
132C2×C4×C17C22×D411yescharacteristic
133C2×C4×C17C22×D411yescharacteristic
134C2×C4×C17C2×#4112yes—
135C2×C4×C17C2×#4112yes—
136C22⋊D17—44no—
137C22⋊D17—44no—
138C2×Dic17—22no—
139C2×Dic17—42no—
140D68—24no—
141D68—42no—
142C4×D17—42no—
143C4×D17—42no—
144C4×D17—44no—
145Dic34—24no—
146Dic34—42no—
147C8×C17—24no—
148#3622—44no—
149#3622—42no—
150C22×#106D1711yescharacteristic, complemented
151C2×#417—172no—
152C2×#408—171no—
153#2079—178no—
154C2×#343—172no—
155C2×#341—171no—
156C22×C17—28no—
157C22×C17—22no—
158C22×C17—22no—
159C22×C17#39712yes—
160C22×C17#39712yes—
161C22×C17#47114yes—
162C22×C17C2×#12111yescharacteristic
163C22×C17C2×#12612yes—
164C2×D17—42no—
165C2×D17—44no—
166C2×D17—84no—
167C4×C17—84no—
168C4×C17#39712yes—
169C4×C17#39712yes—
170C4×C17C2×#12311yescharacteristic
171C4×C17C2×#12312yes—
172C4×C17C2×#12411yescharacteristic
173Dic17—42no—
174C22×#41—171no—
175C22×M16—171no—
176C22×M16—172no—
177C23×C8C2×D1711yescharacteristic
178C22×C4⋊C4C2×D1712yes—
179C2×#106—22no—
180C2×#106—22no—
181C2×#106C2×D1714yescomplemented
182#417—178no—
183#417—344no—
184C2×#103—342no—
185C2×#102—342no—
186#408—174no—
187#408—342no—
188C2×C22⋊C8—342no—
189#343—178no—
190#341—174no—
191C2×C17—22no—
192C2×C17—22no—
193C2×C17#207914yescomplemented
194C2×C17C2×#39711yescharacteristic
195C2×C17C2×#47112yes—
196D17—82no—
197C2×#41—172no—
198C2×#41—172no—
199C2×#41—341no—
200C2×#41—341no—
201C2×#41—344no—
202C2×#41—344no—
203C22×Q8—171no—
204C22×D4—171no—
205C22×D4—341no—
206C23×C4—22no—
207C23×C4—341no—
208C23×C4C22×D1711yescharacteristic
209C2×M16—174no—
210C2×M16—172no—
211C2×M16—342no—
212C2×M16—341no—
213C2×M16—344no—
214C2×M16—344no—
215C2×M16—344no—
216C22×C8—24no—
217C22×C8—342no—
218C22×C8—341no—
219C22×C8C22⋊D1712yes—
220C22×C8C22⋊D1712yes—
221C22×C8C22×D1712yes—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4C22×D1714yes—
228#106—28no—
229#103—348no—
230#102—348no—
231C22⋊C8—348no—
232C17C2×#207911yescharacteristic, complemented, Sylow
233C24—341no—
234C24#6325411yescharacteristic
235#41—344no—
236#41—344no—
237#41—348no—
238#41—684no—
239#41—682no—
240#41—682no—
241C2×Q8—172no—
242C2×Q8—341no—
243C2×Q8—344no—
244C2×D4—172no—
245C2×D4—342no—
246C2×D4—342no—
247C2×D4—344no—
248C2×D4—341no—
249C2×D4—684no—
250C22×C4—24no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—84no—
254C22×C4—341no—
255C22×C4—342no—
256C22×C4—342no—
257C22×C4—682no—
258C22×C4—682no—
259C22×C4#6325214yes—
260C22×C4D4×D1711yescharacteristic
261C22×C4D4×D1711yescharacteristic
262C22×C4#6325411yescharacteristic
263C22×C4#6325614yes—
264C22×C4C2×C22⋊D1711yescharacteristic
265C22×C4C2×C22⋊D1711yescharacteristic
266C22×C4C23×D1711yescharacteristic
267M16—344no—
268M16—344no—
269M16—344no—
270M16—684no—
271M16—682no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8—24no—
275C2×C8—344no—
276C2×C8—342no—
277C2×C8—684no—
278C2×C8—682no—
279C2×C8C2×C22⋊D1714yes—
280C4⋊C4—24no—
281C4⋊C4—24no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C23—24no—
285C23—342no—
286C23—682no—
287C23—684no—
288C23#1058758414yes—
289C23#1058762411yescharacteristic
290C23#1058762411yescharacteristic
291C23C2×#6325411yescharacteristic
292Q8—344no—
293Q8—682no—
294D4—344no—
295D4—684no—
296D4—684no—
297D4—682no—
298C2×C4—44no—
299C2×C4—84no—
300C2×C4—84no—
301C2×C4—84no—
302C2×C4—342no—
303C2×C4—682no—
304C2×C4—684no—
305C2×C4—682no—
306C2×C4—682no—
307C2×C4#1058758014yes—
308C2×C4#1058758014yes—
309C2×C4#1058758414yes—
310C2×C4#1058761512yes—
311C2×C4#1058761512yes—
312C2×C4#1058762411yescharacteristic
313C2×C4#1058762411yescharacteristic
314C2×C4#1058763312yes—
315C2×C4#1058763312yes—
316C2×C4C2×#6325212yes—
317C2×C4C2×D4×D1711yescharacteristic
318C2×C4C2×#6325612yes—
319C2×C4C22×C22⋊D1711yescharacteristic
320C8—24no—
321C8—684no—
322C8—682no—
323C22—28no—
324C22—22no—
325C22—22no—
326C22—682no—
327C22—684no—
328C22—1364no—
329C22#1176273512yes—
330C22#1176273512yes—
331C22#1176306914yes—
332C22C2×#1058762411yescharacteristic
333C22C2×#1058758412yes—
334C4—84no—
335C4—682no—
336C4#1176273512yes—
337C4#1176273512yes—
338C4C2×#1058761511yescharacteristic
339C4C2×#1058758012yes—
340C4C2×#1058763311yescharacteristic
341C2—22no—
342C2—22no—
343C2—1362no—
344C2#1453023014yesdirect product factor
345C2C2×#1176273511yescharacteristic
346C2C2×#1176306912yes—
subgroupG/H
centerC23#10587624
commutator, cosocleC22×C4×C17C24
FrattiniC22×C4C23×D17
FittingC22×C17×#106C2
socleC23×C17#121
prime radicalC22×#63252C22
hypercenterC22×#106D17
hypocenterC17C2×#2079
LCSG ▷ C22×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
3. #14530230C2direct (N × H)
4. C2×#11762578C2semidirect
5. C2×#11762574C2semidirect
6. C22×C17×#106C2semidirect
17. #11762578C22semidirect
18. #11762574C22semidirect
23. C2×C17×#106C22semidirect
150. C22×#106D17semidirect
181. C2×#106C2×D17semidirect
193. C2×C17#2079semidirect
232. C17C2×#2079semidirect
344. C2#14530230direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117628082
C2×#117627752
#145302302
C2×#117625782
C2×#117625742
C22×C17×#1062
C2×#207917