Finite Group Databasebeta

← C2×#26025910 #36725142

Subgroups — C2×#26025910 #36725142

Order 22784.

1966 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26025910C2116yesmaximal, direct product factor
2C2×#19151532C212yesmaximal
3C2×#19151530C212yesmaximal
4C2×#19151495C212yesmaximal
5C2×#19151495C212yesmaximal
6C2×#19151485C212yesmaximal
7C2×#19151481C212yesmaximal
8C2×C4×C4⋊Dic89C211yesmaximal, characteristic
9C2×#19151444C211yesmaximal, characteristic
10C2×#383×C89C211yesmaximal, characteristic
11C22×C4⋊Dic89C2212yes—
12C22×C4⋊Dic89C2212yes—
13C22×C4⋊Dic89C2212yes—
14C22×#13083553C2212yes—
15C22×#13083553C2212yes—
16C22×#13083553C2212yes—
17C22×#13083553C2212yes—
18C22×C4×Dic89C2212yes—
19C22×C4×Dic89C2211yescharacteristic
20C22×C4×Dic89C2211yescharacteristic
21#19151532C22116yes—
22#19151530C22116yes—
23#19151495C22116yes—
24#19151495C22116yes—
25#19151485C22116yes—
26#19151481C22116yes—
27C4×C4⋊Dic89C2218yes—
28#19151444C2218yes—
29C2×#15667919C2212yes—
30C2×#15667919C2212yes—
31C2×#15667919C2212yes—
32C2×#15667919C2212yes—
33C2×#15667919C2211yescharacteristic
34C2×#15667919C2211yescharacteristic
35C22×C42×C89C2211yescharacteristic
36#383×C89C2218yes—
37C2×#95×C89C2211yescharacteristic
38C2×#95×C89C2212yes—
39C2×#95×C89C2211yescharacteristic
40C2×#95×C89C2212yes—
41C23×Dic89C2312yes—
42C23×Dic89C2312yes—
43C23×Dic89C2312yes—
44C23×Dic89C2312yes—
45C2×C4⋊Dic89—28no—
46C2×C4⋊Dic89—28no—
47C2×C4⋊Dic89—44no—
48C2×C4⋊Dic89C2318yes—
49C2×C4⋊Dic89C2318yes—
50C2×C4⋊Dic89C2318yes—
51C2×#13083553—28no—
52C2×#13083553—28no—
53C2×#13083553—28no—
54C2×#13083553—44no—
55C2×#13083553C2318yes—
56C2×#13083553C2318yes—
57C2×#13083553C2318yes—
58C2×#13083553C2318yes—
59C2×C4×Dic89—28no—
60C2×C4×Dic89—42no—
61C2×C4×Dic89—42no—
62C2×C4×Dic89C2318yes—
63C2×C4×Dic89C2314yes—
64C2×C4×Dic89C2314yes—
65#15667919C2318yes—
66#15667919C2314yes—
67#15667919C2314yes—
68#15667919C2318yes—
69#15667919C2318yes—
70#15667919C2318yes—
71C23×C4×C89C2312yes—
72C23×C4×C89C2312yes—
73C23×C4×C89C2311yescharacteristic
74C23×C4×C89C2311yescharacteristic
75C23×C4×C89C2311yescharacteristic
76C2×C42×C89Q818yes—
77C2×C42×C89C2314yes—
78#95×C89C2314yes—
79#95×C89C2318yes—
80#95×C89C2314yes—
81#95×C89C2318yes—
82C22×Dic89—24no—
83C22×Dic89—24no—
84C22×Dic89—24no—
85C22×Dic89—24no—
86C22×Dic89—24no—
87C22×Dic89—24no—
88C22×Dic89—24no—
89C22×Dic89—24no—
90C22×Dic89—24no—
91C22×Dic89—24no—
92C22×Dic89#4118yes—
93C22×Dic89#4118yes—
94C22×Dic89C2414yes—
95C22×Dic89C2414yes—
96C22×Dic89C2414yes—
97C22×Dic89C2414yes—
98C4⋊Dic89—216no—
99C4⋊Dic89—216no—
100C4⋊Dic89—48no—
101#13083553—216no—
102#13083553—216no—
103#13083553—216no—
104#13083553—48no—
105C4×Dic89—216no—
106C4×Dic89—44no—
107C4×Dic89—44no—
108C24×C89C2411yescharacteristic
109C22×C4×C89—24no—
110C22×C4×C89—24no—
111C22×C4×C89—22no—
112C22×C4×C89—22no—
113C22×C4×C89—24no—
114C22×C4×C89—24no—
115C22×C4×C89—24no—
116C22×C4×C89—24no—
117C22×C4×C89—24no—
118C22×C4×C89—24no—
119C22×C4×C89C2×Q814yes—
120C22×C4×C89C2×Q814yes—
121C22×C4×C89C2×Q814yes—
122C22×C4×C89C2414yes—
123C22×C4×C89C2414yes—
124C22×C4×C89C2412yes—
125C22×C4×C89C2412yes—
126C22×C4×C89C2412yes—
127C42×C89C2×Q8116yes—
128C23×C89C22×Q812yes—
129C23×C89C2×#4114yes—
130C23×C89C2×#4114yes—
131C23×C89H(5,𝔽2)12yes—
132C23×C892−1+412yes—
133C23×C89C2511yescharacteristic
134C2×C4×C89—28no—
135C2×C4×C89—28no—
136C2×C4×C89—28no—
137C2×C4×C89—24no—
138C2×C4×C89—24no—
139C2×C4×C89—22no—
140C2×C4×C89—22no—
141C2×C4×C89—24no—
142C2×C4×C89—24no—
143C2×C4×C89—24no—
144C2×C4×C89—24no—
145C2×C4×C89—24no—
146C2×C4×C89—24no—
147C2×C4×C89—48no—
148C2×C4×C89—48no—
149C2×C4×C89C22×Q814yes—
150C2×C4×C89C22×Q814yes—
151C2×C4×C89C22×Q814yes—
152C2×Dic89—216no—
153C2×Dic89—216no—
154C2×Dic89—24no—
155C2×Dic89—24no—
156C2×Dic89—24no—
157C2×Dic89—24no—
158C2×Dic89—24no—
159C2×Dic89—24no—
160C2×Dic89—24no—
161C2×Dic89—24no—
162C2×Dic89—24no—
163C2×Dic89—24no—
164C2×Dic89—48no—
165C2×Dic89—48no—
166C2×Dic89C2×#4118yes—
167C2×Dic89C2×#4118yes—
168C22×C89#53314yes—
169C22×C89#53314yes—
170C22×C89#54414yes—
171C22×C89#55218yes—
172C22×C89#55318yes—
173C22×C89C23×Q811yescharacteristic
174C22×C89C22×#4112yes—
175C22×C89C22×#4112yes—
176C22×C89C2×H(5,𝔽2)11yescharacteristic
177C22×C89C2×2−1+411yescharacteristic
178C4×C89—24no—
179C4×C89—24no—
180C4×C89—24no—
181C4×C89—44no—
182C4×C89—44no—
183Dic89—28no—
184Dic89—28no—
185Dic89—44no—
186Dic89—44no—
187C2×#2606—891nomaximal, Sylow
188C2×C89#260618yescomplemented
189C2×C89C2×#53311yescharacteristic
190C2×C89C2×#53311yescharacteristic
191C2×C89C2×#54411yescharacteristic
192C2×C89C2×#55212yes—
193C2×C89C2×#55312yes—
194#2606—8916no—
195C2×#398—892no—
196C2×#398—892no—
197C2×#389—892no—
198C2×#389—892no—
199C2×#387—892no—
200C2×#387—892no—
201C2×#383D8911yescharacteristic
202C2×C4×C4⋊C4—891no—
203C2×#376—891no—
204C89C2×#260611yescharacteristic, complemented, Sylow
205C22×C4⋊C4—892no—
206C22×C4⋊C4—892no—
207C22×C4⋊C4—892no—
208C22×C4⋊C4—892no—
209C22×C4⋊C4—892no—
210C22×C4⋊C4—892no—
211C22×C4⋊C4—892no—
212C22×C42—891no—
213C22×C42—891no—
214C22×C42—892no—
215C22×C42C2×D8911yescharacteristic
216#398—8916no—
217#398—8916no—
218#389—8916no—
219#389—8916no—
220#387—8916no—
221#387—8916no—
222#383C2×D8918yes—
223C4×C4⋊C4—898no—
224#376—898no—
225C2×#95—891no—
226C2×#95—891no—
227C2×#95—892no—
228C2×#95—892no—
229C2×#95—892no—
230C2×#95—892no—
231C2×#95C2×D8912yes—
232C2×#95C2×D8911yescharacteristic
233C2×#95C2×D8912yes—
234C2×#95C2×D8911yescharacteristic
235C23×C4—892no—
236C23×C4—892no—
237C23×C4—892no—
238C23×C4—892no—
239C23×C4C22×D8912yes—
240C23×C4C22×D8912yes—
241C23×C4C22×D8911yescharacteristic
242C23×C4C22×D8911yescharacteristic
243C23×C4C22×D8911yescharacteristic
244C2×C4⋊C4—898no—
245C2×C4⋊C4—898no—
246C2×C4⋊C4—898no—
247C2×C4⋊C4—898no—
248C2×C4⋊C4—898no—
249C2×C4⋊C4—898no—
250C2×C4⋊C4—898no—
251C2×C4⋊C4—3564no—
252C2×C4⋊C4—3564no—
253C2×C4⋊C4—1788no—
254C2×C4⋊C4—1788no—
255C2×C4⋊C4—1788no—
256C2×C4⋊C4—1788no—
257C2×C4⋊C4—1788no—
258C2×C42—894no—
259C2×C42—894no—
260C2×C42—898no—
261C2×C42—3562no—
262C2×C42—3562no—
263C2×C42—1788no—
264C2×C42Dic17818yes—
265C2×C42C22×D8914yes—
266#95—898no—
267#95—894no—
268#95—894no—
269#95—898no—
270#95—898no—
271#95—898no—
272#95C22×D8914yes—
273#95C22×D8918yes—
274#95C22×D8914yes—
275#95C22×D8918yes—
276C24C23×D8911yescharacteristic
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—24no—
286C22×C4—24no—
287C22×C4—898no—
288C22×C4—898no—
289C22×C4—894no—
290C22×C4—894no—
291C22×C4—894no—
292C22×C4—894no—
293C22×C4—1784no—
294C22×C4—1784no—
295C22×C4—1784no—
296C22×C4—1784no—
297C22×C4—1784no—
298C22×C4—1784no—
299C22×C4—1784no—
300C22×C4—1784no—
301C22×C4—1784no—
302C22×C4—1784no—
303C22×C4C2×Dic17814yes—
304C22×C4C2×Dic17814yes—
305C22×C4C2×Dic17814yes—
306C22×C4C23×D8914yes—
307C22×C4C23×D8914yes—
308C22×C4C23×D8912yes—
309C22×C4C23×D8912yes—
310C22×C4C23×D8912yes—
311C4⋊C4—3568no—
312C4⋊C4—3568no—
313C4⋊C4—17816no—
314C4⋊C4—17816no—
315C4⋊C4—17816no—
316C4⋊C4—17816no—
317C4⋊C4—17816no—
318C42—3564no—
319C42—3564no—
320C42—17816no—
321C42C2×Dic178116yes—
322C23C22×Dic17812yes—
323C23#41×D8914yes—
324C23#41×D8914yes—
325C23#1566805812yes—
326C23#1566805912yes—
327C23C24×D8911yescharacteristic
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—24no—
331C2×C4—24no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—28no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—48no—
342C2×C4—48no—
343C2×C4—898no—
344C2×C4—898no—
345C2×C4—3568no—
346C2×C4—3568no—
347C2×C4—1784no—
348C2×C4—1784no—
349C2×C4—1784no—
350C2×C4—1784no—
351C2×C4—1784no—
352C2×C4—1784no—
353C2×C4—1784no—
354C2×C4—1784no—
355C2×C4—1784no—
356C2×C4—1784no—
357C2×C4—17816no—
358C2×C4—17816no—
359C2×C4C22×Dic17814yes—
360C2×C4C22×Dic17814yes—
361C2×C4C22×Dic17814yes—
362C22#1915215114yes—
363C22#1915215114yes—
364C22#1915222614yes—
365C22#1915228418yes—
366C22#1915229918yes—
367C22C23×Dic17811yescharacteristic
368C22C2×#41×D8912yes—
369C22C2×#41×D8912yes—
370C22C2×#1566805811yescharacteristic
371C22C2×#1566805911yescharacteristic
372C4—24no—
373C4—24no—
374C4—24no—
375C4—44no—
376C4—44no—
377C4—3564no—
378C4—3564no—
379C4—1788no—
380C4—1788no—
381C2#2602591018yesdirect product factor
382C2C2×#1915215111yescharacteristic
383C2C2×#1915215111yescharacteristic
384C2C2×#1915222611yescharacteristic
385C2C2×#1915228412yes—
386C2C2×#1915229912yes—
subgroupG/H
centerC24C23×D89
commutator, cosocleC23×C89C25
FrattiniC23C24×D89
FittingC2×#383×C89C2
socle, prime radicalC24×C89C24
hypercenterC2×#383D89
hypocenterC89C2×#2606
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C24 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. #26025910C2direct (N × H)
188. C2×C89#2606semidirect
204. C89C2×#2606semidirect
381. C2#26025910direct (N × H)

Maximal subgroups

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

subgroupindex
#260259102
C2×#191515322
C2×#191515302
C2×#191514952
C2×#191514852
C2×#191514812
C2×C4×C4⋊Dic892
C2×#191514442
C2×#383×C892
C2×#260689