Finite Group Databasebeta

← C2×#23762898 #34270789

Subgroups — C2×#23762898 #34270789

Order 20224.

726 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
1C2×#19098959C211yesmaximal, characteristic, complemented
2C2×#19098854C211yesmaximal, characteristic
3C2×#19098765C211yesmaximal, characteristic
4C2×#19098640C211yesmaximal, characteristic
5#23762898C218yesmaximal, direct product factor
6C2×#19098315C211yesmaximal, characteristic, complemented
7C2×#19098311C211yesmaximal, characteristic, complemented
8C2×#332×C79C211yesmaximal, characteristic, complemented
9C22×#11929611—21no—
10C22×#11929607—21no—
11C2×#14579161C2211yescharacteristic
12C2×C4×D316C2211yescharacteristic
13#19098959—22no—
14#19098959C2214yescomplemented
15#19098854—22no—
16#19098854C2214yes—
17#19098765—22no—
18#19098765C2214yes—
19#19098640—22no—
20#19098640C2214yes—
21C2×#14579093—21no—
22C2×#14579092—21no—
23C2×#14579092—21no—
24C2×C4⋊(C79⋊C8)C2211yescharacteristic
25C2×#14579085—21no—
26C2×#14579083—21no—
27C2×(C2×D79)⋊C8—21no—
28C2×C4×C79⋊C8C2211yescharacteristic
29#19098315C2214yescomplemented
30#19098311C2214yescomplemented
31C2×C4⋊Q8×C79C2211yescharacteristic
32C2×C4⋊C8×C79C2211yescharacteristic
33C2×C4⋊C8×C79C2211yescharacteristic
34#332×C79C2214yescomplemented
35C22×Dic158—21no—
36C22×D316D411yescharacteristic
37C22×C4×D79—21no—
38C2×#11929611—24no—
39C2×#11929611—44no—
40C2×#11929607—24no—
41C2×#11929607—44no—
42C22×C79⋊C8—21no—
43C22×C79⋊C8D411yescharacteristic
44C22×C79⋊C8D411yescharacteristic
45#14579161—21no—
46#14579161—21no—
47#14579161—21no—
48#14579161C2312yes—
49C4×D316—21no—
50C4×D316—21no—
51C4×D316D412yes—
52C4×D316C2312yes—
53C2×C4⋊Dic79—21no—
54C2×C4⋊Dic79—21no—
55C2×C4⋊Dic79D411yescharacteristic
56C2×(C2×D79)⋊C4—21no—
57#14579093—24no—
58#14579092—24no—
59#14579092—24no—
60C4⋊(C79⋊C8)—21no—
61C4⋊(C79⋊C8)C2312yes—
62#14579085—24no—
63#14579083—24no—
64(C2×D79)⋊C8—24no—
65C4×C79⋊C8D412yes—
66C4×C79⋊C8C2312yes—
67C22×Q8×C79—21no—
68C22×C8×C79—21no—
69C22×C8×C79—21no—
70C4⋊Q8×C79—21no—
71C4⋊Q8×C79—21no—
72C4⋊Q8×C79—21no—
73C4⋊Q8×C79C2312yes—
74C2×C4⋊C4×C79—21no—
75C2×C4⋊C4×C79—21no—
76C2×C42×C79C2311yescharacteristic
77C4⋊C8×C79—21no—
78C4⋊C8×C79—21no—
79C4⋊C8×C79C2312yes—
80C4⋊C8×C79C2312yes—
81C23×D79—21no—
82C2×Dic158—22no—
83C2×Dic158—41no—
84C2×Dic158—82no—
85C2×D316—21no—
86C2×D316—22no—
87C2×D316—22no—
88C2×D316C2×D412yes—
89C22×Dic79—21no—
90C22×Dic79—41no—
91C2×C4×D79—22no—
92C2×C4×D79—22no—
93C2×C4×D79—42no—
94C2×C4×D79—42no—
95#11929611—48no—
96#11929607—48no—
97C2×C79⋊C8—22no—
98C2×C79⋊C8—22no—
99C2×C79⋊C8—42no—
100C2×C79⋊C8SD1614yescomplemented
101C2×C79⋊C8C2×D412yes—
102C2×C79⋊C8C2×D412yes—
103C4⋊Dic79—21no—
104C4⋊Dic79—22no—
105C4⋊Dic79—22no—
106C4⋊Dic79—41no—
107C4⋊Dic79—41no—
108C4⋊Dic79C2×D412yes—
109(C2×D79)⋊C4—22no—
110(C2×D79)⋊C4—22no—
111C2×Q8×C79—22no—
112C2×Q8×C79—41no—
113C2×Q8×C79—42no—
114C2×Q8×C79—42no—
115C22×C4×C79—41no—
116C22×C4×C79C2×D411yescharacteristic
117C22×C4×C79C2×D411yescharacteristic
118C22×C4×C79#4111yescharacteristic
119C2×C8×C79—22no—
120C2×C8×C79—22no—
121C2×C8×C79—42no—
122C2×C8×C79—42no—
123C4⋊C4×C79—22no—
124C4⋊C4×C79—22no—
125C4⋊C4×C79—41no—
126C4⋊C4×C79—41no—
127C42×C79C2×D411yescharacteristic
128C42×C79C2×D411yescharacteristic
129C42×C79#4111yescharacteristic
130C42×C79C2411yescharacteristic
131C23×C79#12111yescharacteristic
132C22×D79—22no—
133C22×D79—42no—
134C22×D79—42no—
135C22×D79—42no—
136Q8×C79—42no—
137Q8×C79—42no—
138Q8×C79—82no—
139C2×C4×C79—22no—
140C2×C4×C79—42no—
141C2×C4×C79—82no—
142C2×C4×C79#12111yescharacteristic
143C2×C4×C79#12111yescharacteristic
144C2×C4×C79#12111yescharacteristic
145C2×C4×C79C2×SD1612yes—
146C2×C4×C79AGL(1,ℤ/8)12yes—
147C2×C4×C79#13712yes—
148C2×C4×C79#13712yes—
149C2×C4×C79C22×D411yescharacteristic
150C2×C4×C79C22×D411yescharacteristic
151C2×C4×C79C2×#4111yescharacteristic
152C2×Dic79—22no—
153C2×Dic79—42no—
154C2×Dic79—42no—
155C2×Dic79—82no—
156D316—22no—
157D316—22no—
158D316—42no—
159C4×D79—42no—
160C4×D79—42no—
161C4×D79—44no—
162Dic158—82no—
163Dic158—82no—
164C8×C79—42no—
165C8×C79—42no—
166C79⋊C8—22no—
167C79⋊C8—42no—
168C79⋊C8C2×SD1614yescomplemented
169C22×C79#46112yes—
170C22×C79#46812yes—
171C22×C79#47112yes—
172C22×C79C2×#12111yescharacteristic
173C2×D79—42no—
174C2×D79—42no—
175C2×D79—42no—
176C2×D79—84no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—82no—
180C4×C79#46112yes—
181C4×C79#46812yes—
182C4×C79C22×SD1611yescharacteristic
183C4×C79C2×AGL(1,ℤ/8)11yescharacteristic
184C4×C79C2×#13711yescharacteristic
185C4×C79C2×#13711yescharacteristic
186Dic79—42no—
187Dic79—82no—
188C2×#1691—791nomaximal, Sylow
189C2×C79#169114yescomplemented
190C2×C79C2×#46111yescharacteristic
191C2×C79C2×#46811yescharacteristic
192C2×C79C2×#47111yescharacteristic
193D79—82no—
194C2×#498—791no—
195C2×#476—791no—
196C2×#461—791no—
197C2×#436—791no—
198#1691—798no—
199C2×#335—791no—
200C2×#333—791no—
201C2×#332D7911yescharacteristic, complemented
202C79C2×#169111yescharacteristic, complemented, Sylow
203C22×SD16—1581no—
204C22×M16—1581no—
205C2×C4⋊Q8—791no—
206C2×C4⋊Q8C2×D7911yescharacteristic
207C2×C4×D4—791no—
208#498—794no—
209#498—1582no—
210#476—794no—
211#476—1582no—
212#461—794no—
213#461—1582no—
214#436—794no—
215#436—1582no—
216C2×#106—1581no—
217C2×#106—1581no—
218C2×#106—1581no—
219C2×C4⋊C8—791no—
220C2×C4⋊C8C2×D7911yescharacteristic
221C2×C4⋊C8C2×D7911yescharacteristic
222C2×#103—1581no—
223C2×#102—1581no—
224C2×C22⋊C8—1581no—
225C2×C4×C8—791no—
226#335—794no—
227#333—794no—
228#332C2×D7914yescomplemented
229C22×Q8—21no—
230C22×Q8—1581no—
231C22×D4—791no—
232C23×C4—1581no—
233C2×SD16—3164no—
234C2×SD16—1584no—
235C2×M16—3164no—
236C2×M16—1584no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—791no—
240C22×C8—791no—
241C22×C8—1581no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—792no—
246C4⋊Q8—1581no—
247C4⋊Q8—1581no—
248C4⋊Q8—1581no—
249C4⋊Q8C22×D7912yes—
250C4×D4—792no—
251C4×D4—792no—
252C4×D4—1581no—
253C4×D4—1581no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—791no—
257C2×C4⋊C4—1581no—
258C2×C4⋊C4—1581no—
259C2×C22⋊C4—1581no—
260C2×C42C22×D7911yescharacteristic
261#106—1584no—
262#106—1584no—
263#106—1584no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—792no—
267C4⋊C8—1581no—
268C4⋊C8C22×D7912yes—
269C4⋊C8C22×D7912yes—
270#103—1584no—
271#102—1584no—
272C22⋊C8—1584no—
273C4×C8—792no—
274C4×C8—792no—
275C24—1581no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—3161no—
281C2×Q8—6322no—
282C2×Q8—1582no—
283C2×D4—792no—
284C2×D4—1581no—
285C2×D4—1582no—
286C2×D4—1582no—
287C22×C4—41no—
288C22×C4—3162no—
289C22×C4—3162no—
290C22×C4—3161no—
291C22×C4—1581no—
292C22×C4—1582no—
293C22×C4—1582no—
294C22×C4D4×D7911yescharacteristic
295C22×C4D4×D7911yescharacteristic
296C22×C4#1192962411yescharacteristic
297SD16—3168no—
298M16—3168no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—42no—
303C2×C8—3162no—
304C2×C8—794no—
305C2×C8—792no—
306C2×C8—792no—
307C2×C8—1582no—
308C2×C8—1582no—
309C4⋊C4—22no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—3161no—
314C4⋊C4—3161no—
315C4⋊C4—792no—
316C4⋊C4—1582no—
317C4⋊C4—1582no—
318C4⋊C4—1581no—
319C22⋊C4—1582no—
320C22⋊C4—1582no—
321C42D4×D7911yescharacteristic
322C42D4×D7911yescharacteristic
323C42#1192962411yescharacteristic
324C42C23×D7911yescharacteristic
325C23—3162no—
326C23—3162no—
327C23—3162no—
328C23—1582no—
329C23#1457913411yescharacteristic
330Q8—42no—
331Q8—42no—
332Q8—82no—
333Q8—6322no—
334Q8—6322no—
335D4—3162no—
336D4—1582no—
337D4—1582no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—82no—
341C2×C4—3162no—
342C2×C4—3164no—
343C2×C4—3162no—
344C2×C4—3162no—
345C2×C4—3162no—
346C2×C4—6322no—
347C2×C4—1582no—
348C2×C4#1457913411yescharacteristic
349C2×C4#1457913411yescharacteristic
350C2×C4#1457913411yescharacteristic
351C2×C4SD16×D7912yes—
352C2×C4#1457918512yes—
353C2×C4#1457919012yes—
354C2×C4#1457919312yes—
355C2×C4C2×D4×D7911yescharacteristic
356C2×C4C2×D4×D7911yescharacteristic
357C2×C4C2×#1192962411yescharacteristic
358C8—42no—
359C8—42no—
360C8—3162no—
361C8—794no—
362C8—1582no—
363C22—3162no—
364C22—3162no—
365C22—3162no—
366C22—6324no—
367C22#1909876712yes—
368C22#1909880812yes—
369C22#1909882912yes—
370C22C2×#1457913411yescharacteristic
371C4—21no—
372C4—21no—
373C4—82no—
374C4—3162no—
375C4—6322no—
376C4#1909876712yes—
377C4#1909880812yes—
378C4C2×SD16×D7911yescharacteristic
379C4C2×#1457918511yescharacteristic
380C4C2×#1457919011yescharacteristic
381C4C2×#1457919311yescharacteristic
382C2—6322no—
383C2#2376289814yesdirect product factor
384C2C2×#1909876711yescharacteristic
385C2C2×#1909880811yescharacteristic
386C2C2×#1909882911yescharacteristic
subgroupG/H
centerC23#14579134
commutator, cosocleC42×C79C24
FrattiniC42C23×D79
FittingC2×#332×C79C2
socleC23×C79#121
prime radicalC22×D316D4
hypercenterC2×#332D79
hypocenterC79C2×#1691
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#19098959C2semidirect
5. #23762898C2direct (N × H)
6. C2×#19098315C2semidirect
7. C2×#19098311C2semidirect
8. C2×#332×C79C2semidirect
14. #19098959C22semidirect
29. #19098315C22semidirect
30. #19098311C22semidirect
34. #332×C79C22semidirect
100. C2×C79⋊C8SD16semidirect
168. C79⋊C8C2×SD16semidirect
189. C2×C79#1691semidirect
201. C2×#332D79semidirect
202. C79C2×#1691semidirect
228. #332C2×D79semidirect
383. C2#23762898direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190989592
C2×#190988542
C2×#190987652
C2×#190986402
#237628982
C2×#190983152
C2×#190983112
C2×#332×C792
C2×#169179