Finite Group Databasebeta

← C2×#23773932 #35157894

Subgroups — C2×#23773932 #35157894

Order 20224.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099191C212yesmaximal
2#23773932C2116yesmaximal, direct product factor
3C2×#19098971C214yesmaximal, complemented
4C2×#19098963C212yesmaximal, complemented
5C2×#19098960C212yesmaximal, complemented
6C2×#19098606C212yesmaximal
7C22×#14579093C211yesmaximal, characteristic
8C2×#19098518C211yesmaximal, characteristic
9C2×#427×C79C211yesmaximal, characteristic
10C22×#11929608C2211yescharacteristic
11#19099191—28no—
12#19099191C22116yes—
13C2×#14579161—22no—
14C2×#14579160C2214yes—
15C2×#14579153—22no—
16C2×#14579152C2214yes—
17C2×#14579138—24no—
18C2×#14579120C2211yescharacteristic
19C22×C4⋊Dic79C2212yes—
20#19098971C22132yescomplemented
21#19098963C22116yescomplemented
22#19098960C22116yescomplemented
23#19098606C22116yes—
24C2×#14579094C2214yes—
25C2×#14579093C2212yes—
26C2×#14579093C2212yes—
27C2×#14579093C2218yes—
28C2×#14579092C2214yes—
29#19098518C2218yes—
30C2×#14579071C2212yes—
31C2×C8×Dic79C2212yes—
32C23×C8×C79C2211yescharacteristic
33C2×#117×C79C2212yes—
34#427×C79C2218yes—
35C2×#107×C79C2212yes—
36C2×#106×C79C2211yescharacteristic
37C2×#106×C79C2211yescharacteristic
38C22×Dic158—24no—
39C23×Dic79—22no—
40C2×#11929608Q818yescomplemented
41C2×#11929608C2314yes—
42C22×C79⋊C8C2312yes—
43#14579161—216no—
44#14579160—28no—
45#14579160C23116yes—
46#14579153—216no—
47#14579152—28no—
48#14579152C23116yes—
49#14579138—232no—
50#14579120D414yes—
51#14579120C2314yes—
52C2×C4⋊Dic79—24no—
53C2×C4⋊Dic79—22no—
54C2×C4⋊Dic79—24no—
55C2×C4⋊Dic79D412yes—
56C2×C4⋊Dic79C2318yes—
57C2×C4⋊Dic79C2314yes—
58C2×Dic79⋊C4—24no—
59C2×Dic79⋊C4—24no—
60C2×C22⋊Dic79D412yes—
61C2×C4×Dic79C2312yes—
62#14579094C23116yes—
63#14579093C2318yes—
64#14579093C2318yes—
65#14579092C23116yes—
66#14579071C2318yes—
67C8×Dic79C2318yes—
68C23×C4×C79C2311yescharacteristic
69C22×C8×C79Q818yescomplemented
70C22×C8×C79C2311yescharacteristic
71C22×C8×C79C2311yescharacteristic
72C22×C8×C79C2314yes—
73#117×C79—24no—
74#117×C79C2318yes—
75C2×C4⋊C4×C79C2312yes—
76C2×C4⋊C4×C79C2312yes—
77C2×C22⋊C4×C79—22no—
78C2×C42×C79—22no—
79#107×C79C2318yes—
80#106×C79C2314yes—
81#106×C79C2314yes—
82C2×Dic158—216no—
83C2×Dic158—88no—
84C22×Dic79—24no—
85C22×Dic79—28no—
86C22×Dic79—84no—
87C22×Dic79C2×D414yes—
88#11929608C2×Q8116yescomplemented
89C2×C79⋊C8C2×Q818yes—
90C2×C79⋊C8C2414yes—
91C4⋊Dic79—216no—
92C4⋊Dic79—24no—
93C4⋊Dic79—28no—
94C4⋊Dic79C2×D418yes—
95C4⋊Dic79C2418yes—
96Dic79⋊C4—216no—
97Dic79⋊C4—216no—
98C22⋊Dic79C2×D418yes—
99C4×Dic79C2×D414yes—
100C4×Dic79C2414yes—
101C24×C79C2×D411yescharacteristic
102C22×C4×C79—22no—
103C22×C4×C79—22no—
104C22×C4×C79C2×D411yescharacteristic
105C22×C4×C79C2×D412yes—
106C22×C4×C79C2×Q814yes—
107C22×C4×C79C2×Q814yes—
108C22×C4×C79C2411yescharacteristic
109C22×C4×C79C2412yes—
110C2×C8×C79C2×Q814yes—
111C2×C8×C79C2×Q814yes—
112C2×C8×C79C2×Q8116yescomplemented
113C2×C8×C79C2412yes—
114C2×C8×C79C2412yes—
115C4⋊C4×C79—22no—
116C4⋊C4×C79—22no—
117C4⋊C4×C79C2414yes—
118C4⋊C4×C79C2414yes—
119C22⋊C4×C79—28no—
120C42×C79—28no—
121C23×C79—24no—
122C23×C79C4⋊Q814yes—
123C23×C79C22×D412yes—
124C23×C79C22×D411yescharacteristic
125C2×C4×C79—24no—
126C2×C4×C79—24no—
127C2×C4×C79—44no—
128C2×C4×C79—44no—
129C2×C4×C79C4⋊Q818yes—
130C2×C4×C79C4⋊Q814yes—
131C2×C4×C79C22×D411yescharacteristic
132C2×C4×C79C22×D412yes—
133C2×C4×C79C22×Q812yes—
134C2×C4×C79C22×Q814yes—
135C2×C4×C79C22×Q812yes—
136C2×C4×C79C22×Q814yes—
137C2×C4×C79C2511yescharacteristic
138C2×Dic79—28no—
139C2×Dic79—28no—
140C2×Dic79—48no—
141C2×Dic79—88no—
142C2×Dic79C22×D418yes—
143Dic158—816no—
144C8×C79C22×Q814yes—
145C8×C79C22×Q814yes—
146C79⋊C8C22×Q818yes—
147C22×C79—28no—
148C22×C79—24no—
149C22×C79C2×C4⋊Q814yes—
150C22×C79C2×C4⋊Q812yes—
151C22×C79#57714yes—
152C22×C79C23×D411yescharacteristic
153C4×C79—44no—
154C4×C79—44no—
155C4×C79C2×C4⋊Q812yes—
156C4×C79C2×C4⋊Q814yes—
157C4×C79C23×Q811yescharacteristic
158C4×C79C23×Q811yescharacteristic
159Dic79—28no—
160Dic79—48no—
161C2×#3163—791nomaximal, Sylow
162C2×C79—24no—
163C2×C79#316314yescomplemented
164C2×C79C22×C4⋊Q811yescharacteristic
165C2×C79C2×#57712yes—
166C2×#544—792no—
167#3163—7916no—
168C2×#501—794no—
169C2×#499—792no—
170C2×#498—792no—
171C2×#428—792no—
172C2×#427D7911yescharacteristic
173C22×#106—791no—
174C2×#405—791no—
175C79C2×#316311yescharacteristic, complemented, Sylow
176C22×M16—791no—
177C23×C8C2×D7911yescharacteristic
178#544—7916no—
179#544—1588no—
180C2×C4⋊Q8—794no—
181C2×C4⋊Q8—1582no—
182C2×#125—794no—
183C2×#125—1582no—
184C2×C22⋊Q8—1584no—
185C2×#117—791no—
186C2×#117C2×D7912yes—
187C22×C4⋊C4—792no—
188#501—7932no—
189#499—7916no—
190#498—7916no—
191#428—7916no—
192#427C2×D7918yes—
193C2×#107—794no—
194C2×#107C2×D7912yes—
195C2×#106—792no—
196C2×#106—792no—
197C2×#106—798no—
198C2×#106—794no—
199C2×#106C2×D7911yescharacteristic
200C2×#106C2×D7911yescharacteristic
201#405—798no—
202C2×#97—792no—
203C2×C4×C8—792no—
204C22×Q8—1584no—
205C23×C4—1582no—
206C23×C4C22×D7911yescharacteristic
207C2×M16—798no—
208C2×M16—794no—
209C22×C8—792no—
210C22×C8Dic15818yescomplemented
211C22×C8C22×D7911yescharacteristic
212C22×C8C22×D7911yescharacteristic
213C22×C8C22×D7914yes—
214C4⋊Q8—7916no—
215C4⋊Q8—15816no—
216C4⋊Q8—1588no—
217#125—7916no—
218#125—15816no—
219#125—1588no—
220C22⋊Q8—15832no—
221#117—24no—
222#117—794no—
223#117—794no—
224#117C22×D7918yes—
225C2×C4⋊C4—792no—
226C2×C4⋊C4—794no—
227C2×C4⋊C4—798no—
228C2×C4⋊C4—1584no—
229C2×C4⋊C4—1584no—
230C2×C4⋊C4—1584no—
231C2×C4⋊C4—1582no—
232C2×C4⋊C4—1584no—
233C2×C4⋊C4C22×D7912yes—
234C2×C4⋊C4C22×D7912yes—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—792no—
237C2×C42—22no—
238C2×C42—792no—
239#107—7916no—
240#107C22×D7918yes—
241#106—798no—
242#106—798no—
243#106—7916no—
244#106C22×D7914yes—
245#106C22×D7914yes—
246#97—798no—
247C4×C8—798no—
248C24D4×D7911yescharacteristic
249C2×Q8—6328no—
250C2×Q8—15816no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—794no—
254C22×C4—6324no—
255C22×C4—1584no—
256C22×C4—1588no—
257C22×C4D4×D7912yes—
258C22×C4D4×D7911yescharacteristic
259C22×C4Q8×D7914yes—
260C22×C4C2×Dic15814yes—
261C22×C4C23×D7912yes—
262C22×C4C23×D7911yescharacteristic
263M16—7916no—
264C2×C8—798no—
265C2×C8—794no—
266C2×C8C2×Dic15814yes—
267C2×C8C2×Dic15814yes—
268C2×C8C2×Dic158116yescomplemented
269C2×C8C23×D7912yes—
270C2×C8C23×D7912yes—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—798no—
274C4⋊C4—798no—
275C4⋊C4—15816no—
276C4⋊C4—15816no—
277C4⋊C4—15816no—
278C4⋊C4—1588no—
279C4⋊C4—1584no—
280C4⋊C4C23×D7914yes—
281C4⋊C4C23×D7914yes—
282C22⋊C4—28no—
283C22⋊C4—798no—
284C42—28no—
285C42—794no—
286C42—794no—
287C23—24no—
288C23#1457916014yes—
289C23C2×D4×D7912yes—
290C23C2×D4×D7911yescharacteristic
291Q8—63216no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—3168no—
297C2×C4—798no—
298C2×C4—6328no—
299C2×C4—1588no—
300C2×C4—1588no—
301C2×C4#1457916018yes—
302C2×C4#1457916014yes—
303C2×C4C2×D4×D7912yes—
304C2×C4C2×D4×D7911yescharacteristic
305C2×C4C2×Q8×D7912yes—
306C2×C4C2×Q8×D7914yes—
307C2×C4C22×Dic15812yes—
308C2×C4C22×Dic15814yes—
309C2×C4C24×D7911yescharacteristic
310C8—798no—
311C8C22×Dic15814yes—
312C8C22×Dic15814yes—
313C22—24no—
314C22—28no—
315C22C2×#1457916014yes—
316C22C2×#1457916012yes—
317C22#1909937014yes—
318C22C22×D4×D7911yescharacteristic
319C4—44no—
320C4—44no—
321C4—3168no—
322C4—1588no—
323C4C2×#1457916012yes—
324C4C2×#1457916014yes—
325C4C22×Q8×D7911yescharacteristic
326C4C23×Dic15811yescharacteristic
327C2—24no—
328C2#2377393214yesdirect product factor
329C2C22×#1457916011yescharacteristic
330C2C2×#1909937012yes—
subgroupG/H
centerC23C2×D4×D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC2×#427×C79C2
socleC23×C79C22×D4
prime radicalC24×C79C2×D4
hypercenterC2×#427D79
hypocenterC79C2×#3163
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #23773932C2direct (N × H)
3. C2×#19098971C2semidirect
4. C2×#19098963C2semidirect
5. C2×#19098960C2semidirect
20. #19098971C22semidirect
21. #19098963C22semidirect
22. #19098960C22semidirect
40. C2×#11929608Q8semidirect
69. C22×C8×C79Q8semidirect
88. #11929608C2×Q8semidirect
112. C2×C8×C79C2×Q8semidirect
163. C2×C79#3163semidirect
175. C79C2×#3163semidirect
210. C22×C8Dic158semidirect
268. C2×C8C2×Dic158semidirect
328. C2#23773932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190991912
#237739322
C2×#190989712
C2×#190989632
C2×#190989602
C2×#190986062
C22×#145790932
C2×#190985182
C2×#427×C792
C2×#316379