Finite Group Databasebeta

← C2×#23763038 #34276008

Subgroups — C2×#23763038 #34276008

Order 20224.

966 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098935C211yesmaximal, characteristic, complemented
2C2×#19098914C211yesmaximal, characteristic, complemented
3C2×#19098909C211yesmaximal, characteristic, complemented
4C2×#19098909C211yesmaximal, characteristic, complemented
5C2×#19098909C211yesmaximal, characteristic, complemented
6#23763038C218yesmaximal, direct product factor
7C2×#19098285C211yesmaximal, characteristic, complemented
8C2×#493×C79C211yesmaximal, characteristic
9C22×#11929612—22no—
10C2×#14579161C2211yescharacteristic
11C2×#14579161C2211yescharacteristic
12#19098935—22no—
13#19098935C2214yescomplemented
14#19098914—22no—
15#19098914C2214yescomplemented
16#19098909—22no—
17#19098909—22no—
18#19098909—22no—
19#19098909C2214yescomplemented
20#19098909C2214yescomplemented
21#19098909C2214yescomplemented
22C2×#14579086—22no—
23C2×#14579082—22no—
24C2×#14579082—22no—
25C2×#14579082—22no—
26C2×C4×C79⋊C8C2211yescharacteristic
27C2×C4×C79⋊C8C2211yescharacteristic
28#19098285C2214yescomplemented
29C22×D8×C79—22no—
30C2×#127×C79C2211yescharacteristic
31C2×#127×C79C2211yescharacteristic
32#493×C79—22no—
33#493×C79C2214yes—
34C2×C4×C8×C79C2211yescharacteristic
35C22×Dic158—21no—
36C22×Dic158—21no—
37C2×#11929612—28no—
38C2×#11929612—48no—
39C22×C79⋊C8D412yes—
40C22×C79⋊C8D412yes—
41#14579161—21no—
42#14579161—21no—
43#14579161—21no—
44#14579161—21no—
45#14579161—21no—
46#14579161—21no—
47#14579161C2312yes—
48#14579161C2312yes—
49C2×C4⋊Dic79—21no—
50C2×C4⋊Dic79—21no—
51C2×C4⋊Dic79—21no—
52C2×C4⋊Dic79—21no—
53#14579086—28no—
54#14579082—28no—
55#14579082—28no—
56#14579082—28no—
57C4×C79⋊C8D412yes—
58C4×C79⋊C8D412yes—
59C4×C79⋊C8C2312yes—
60C4×C79⋊C8C2312yes—
61C22×D4×C79—21no—
62C22×D4×C79—21no—
63C22×D4×C79—21no—
64C22×D4×C79—21no—
65C22×D4×C79—21no—
66C22×D4×C79—21no—
67C2×D8×C79—28no—
68C2×D8×C79—48no—
69C22×C8×C79D412yes—
70#127×C79—21no—
71#127×C79—21no—
72#127×C79—21no—
73#127×C79—21no—
74#127×C79—21no—
75#127×C79—21no—
76#127×C79C2312yes—
77#127×C79C2312yes—
78C2×C42×C79C2311yescharacteristic
79C4×C8×C79D412yes—
80C4×C8×C79C2312yes—
81C2×Dic158—22no—
82C2×Dic158—22no—
83C2×Dic158—41no—
84C2×Dic158—41no—
85C2×Dic158—44no—
86C2×Dic158—44no—
87C22×Dic79—41no—
88C22×Dic79—41no—
89#11929612—416no—
90C2×C79⋊C8—24no—
91C2×C79⋊C8—24no—
92C2×C79⋊C8C2×D414yes—
93C2×C79⋊C8C2×D414yes—
94C4⋊Dic79—22no—
95C4⋊Dic79—22no—
96C4⋊Dic79—22no—
97C4⋊Dic79—22no—
98C4⋊Dic79—41no—
99C4⋊Dic79—41no—
100C4⋊Dic79—41no—
101C4⋊Dic79—41no—
102C24×C79—41no—
103C24×C79—41no—
104C2×D4×C79—22no—
105C2×D4×C79—22no—
106C2×D4×C79—22no—
107C2×D4×C79—22no—
108C2×D4×C79—22no—
109C2×D4×C79—22no—
110C2×D4×C79—41no—
111C2×D4×C79—41no—
112C2×D4×C79—41no—
113C2×D4×C79—41no—
114C2×D4×C79—41no—
115C2×D4×C79—41no—
116C2×D4×C79—44no—
117C2×D4×C79—44no—
118C2×D4×C79—44no—
119C2×D4×C79—44no—
120C2×D4×C79—44no—
121C2×D4×C79—44no—
122C22×C4×C79C2×D411yescharacteristic
123C22×C4×C79C2×D411yescharacteristic
124C22×C4×C79C2×D411yescharacteristic
125D8×C79—416no—
126C2×C8×C79—24no—
127C2×C8×C79C2×D414yes—
128C42×C79C2×D411yescharacteristic
129C42×C79C2×D411yescharacteristic
130C42×C79C2×D411yescharacteristic
131C42×C79C2411yescharacteristic
132C23×C79—42no—
133C23×C79—42no—
134C23×C79—82no—
135C23×C79—82no—
136C23×C79—82no—
137C23×C79—82no—
138C23×C79—82no—
139C23×C79—82no—
140C23×C79#12711yescharacteristic
141D4×C79—44no—
142D4×C79—44no—
143D4×C79—44no—
144D4×C79—44no—
145D4×C79—44no—
146D4×C79—44no—
147D4×C79—82no—
148D4×C79—82no—
149D4×C79—82no—
150D4×C79—82no—
151D4×C79—82no—
152D4×C79—82no—
153C2×C4×C79#12711yescharacteristic
154C2×C4×C79#12711yescharacteristic
155C2×C4×C79#12711yescharacteristic
156C2×C4×C79#13514yes—
157C2×C4×C79AGL(1,ℤ/8)14yes—
158C2×C4×C79AGL(1,ℤ/8)14yes—
159C2×C4×C79C22×D411yescharacteristic
160C2×C4×C79C22×D411yescharacteristic
161C2×C4×C79C22×D411yescharacteristic
162C2×Dic79—42no—
163C2×Dic79—42no—
164C2×Dic79—82no—
165C2×Dic79—82no—
166Dic158—44no—
167Dic158—44no—
168Dic158—82no—
169Dic158—82no—
170C8×C79—24no—
171C79⋊C8—24no—
172C79⋊C8—24no—
173C22×C79—82no—
174C22×C79—82no—
175C22×C79—82no—
176C22×C79—82no—
177C22×C79—82no—
178C22×C79—82no—
179C22×C79—164no—
180C22×C79—164no—
181C22×C79#49512yes—
182C22×C79#49612yes—
183C22×C79#49612yes—
184C22×C79C2×#12711yescharacteristic
185C4×C79#49512yes—
186C4×C79#49612yes—
187C4×C79#49612yes—
188C4×C79C2×#13512yes—
189C4×C79C2×AGL(1,ℤ/8)12yes—
190C4×C79C2×AGL(1,ℤ/8)12yes—
191Dic79—82no—
192Dic79—82no—
193C2×#1717—791nomaximal, Sylow
194C2×C79—162no—
195C2×C79—162no—
196C2×C79#171714yescomplemented
197C2×C79C2×#49511yescharacteristic
198C2×C79C2×#49611yescharacteristic
199C2×C79C2×#49611yescharacteristic
200C2×#493D7911yescharacteristic
201C2×#492—791no—
202C2×#487—791no—
203C2×#486—791no—
204C2×#486—791no—
205C2×#486—791no—
206#1717—798no—
207C2×#322—791no—
208C79C2×#171711yescharacteristic, complemented, Sylow
209C22×SD16—1582no—
210C22×D8—22no—
211C2×C4⋊Q8—791no—
212C2×C4⋊Q8—791no—
213C2×#127C2×D7911yescharacteristic
214C2×#127C2×D7911yescharacteristic
215#493—22no—
216#493C2×D7914yes—
217#492—794no—
218#492—1582no—
219#487—794no—
220#487—1582no—
221#486—794no—
222#486—794no—
223#486—794no—
224#486—1582no—
225#486—1582no—
226#486—1582no—
227C2×#103—1582no—
228C2×#102—1582no—
229C2×#102—1582no—
230C2×#102—1582no—
231C2×C4×C8—791no—
232C2×C4×C8—791no—
233C2×C4×C8C2×D7911yescharacteristic
234#322—794no—
235C22×Q8—1581no—
236C22×Q8—1581no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4—21no—
242C22×D4—21no—
243C2×SD16—3168no—
244C2×SD16—1588no—
245C2×D8—28no—
246C2×D8—48no—
247C22×C8—792no—
248C22×C8—792no—
249C22×C8C22⋊D7912yes—
250C4⋊Q8—792no—
251C4⋊Q8—792no—
252C4⋊Q8—1581no—
253C4⋊Q8—1581no—
254C4⋊Q8—1581no—
255C4⋊Q8—1581no—
256C4⋊Q8—1581no—
257C4⋊Q8—1581no—
258#127—21no—
259#127—21no—
260#127—21no—
261#127—21no—
262#127—21no—
263#127—21no—
264#127C22×D7912yes—
265#127C22×D7912yes—
266C2×C4⋊C4—1581no—
267C2×C4⋊C4—1581no—
268C2×C4⋊C4—1581no—
269C2×C4⋊C4—1581no—
270C2×C42C22×D7911yescharacteristic
271#103—1588no—
272#102—1588no—
273#102—1588no—
274#102—1588no—
275C4×C8—792no—
276C4×C8—792no—
277C4×C8—792no—
278C4×C8—792no—
279C4×C8C22⋊D7912yes—
280C4×C8C22×D7912yes—
281C24—41no—
282C24—41no—
283C2×Q8—3161no—
284C2×Q8—3161no—
285C2×Q8—3164no—
286C2×Q8—3164no—
287C2×Q8—1582no—
288C2×Q8—1582no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—44no—
302C2×D4—44no—
303C2×D4—44no—
304C2×D4—44no—
305C2×D4—44no—
306C2×D4—44no—
307C22×C4—3161no—
308C22×C4—3161no—
309C22×C4D4×D7911yescharacteristic
310C22×C4D4×D7911yescharacteristic
311C22×C4C2×C22⋊D7911yescharacteristic
312SD16—31616no—
313D8—416no—
314C2×C8—24no—
315C2×C8—794no—
316C2×C8—794no—
317C2×C8—1584no—
318C2×C8—1584no—
319C2×C8C2×C22⋊D7914yes—
320C4⋊C4—3161no—
321C4⋊C4—3161no—
322C4⋊C4—3161no—
323C4⋊C4—3161no—
324C4⋊C4—1582no—
325C4⋊C4—1582no—
326C4⋊C4—1582no—
327C4⋊C4—1582no—
328C42D4×D7911yescharacteristic
329C42D4×D7911yescharacteristic
330C42C2×C22⋊D7911yescharacteristic
331C42C23×D7911yescharacteristic
332C23—42no—
333C23—42no—
334C23—82no—
335C23—82no—
336C23—82no—
337C23—82no—
338C23—82no—
339C23—82no—
340C23#1457915711yescharacteristic
341Q8—3164no—
342Q8—3164no—
343Q8—6322no—
344Q8—6322no—
345D4—44no—
346D4—44no—
347D4—44no—
348D4—44no—
349D4—44no—
350D4—44no—
351D4—82no—
352D4—82no—
353D4—82no—
354D4—82no—
355D4—82no—
356D4—82no—
357C2×C4—3162no—
358C2×C4—3162no—
359C2×C4—6322no—
360C2×C4—6322no—
361C2×C4#1457915711yescharacteristic
362C2×C4#1457915711yescharacteristic
363C2×C4#1457915711yescharacteristic
364C2×C4#1457918014yes—
365C2×C4#1457918514yes—
366C2×C4#1457918714yes—
367C2×C4C2×D4×D7911yescharacteristic
368C2×C4C2×D4×D7911yescharacteristic
369C2×C4C22×C22⋊D7911yescharacteristic
370C8—24no—
371C8—1584no—
372C8—1584no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—82no—
377C22—82no—
378C22—82no—
379C22—164no—
380C22—164no—
381C22#1909894612yes—
382C22#1909895012yes—
383C22#1909895112yes—
384C22C2×#1457915711yescharacteristic
385C4—6322no—
386C4—6322no—
387C4#1909894612yes—
388C4#1909895012yes—
389C4#1909895112yes—
390C4C2×#1457918012yes—
391C4C2×#1457918512yes—
392C4C2×#1457918712yes—
393C2—162no—
394C2—162no—
395C2#2376303814yesdirect product factor
396C2C2×#1909894611yescharacteristic
397C2C2×#1909895011yescharacteristic
398C2C2×#1909895111yescharacteristic
subgroupG/H
centerC23#14579157
commutator, cosocleC42×C79C24
FrattiniC42C23×D79
Fitting, prime radicalC2×#493×C79C2
socleC23×C79#127
hypercenterC2×#493D79
hypocenterC79C2×#1717
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#19098935C2semidirect
2. C2×#19098914C2semidirect
3. C2×#19098909C2semidirect
4. C2×#19098909C2semidirect
5. C2×#19098909C2semidirect
6. #23763038C2direct (N × H)
7. C2×#19098285C2semidirect
13. #19098935C22semidirect
15. #19098914C22semidirect
19. #19098909C22semidirect
20. #19098909C22semidirect
21. #19098909C22semidirect
28. #19098285C22semidirect
196. C2×C79#1717semidirect
208. C79C2×#1717semidirect
395. C2#23763038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190989352
C2×#190989142
C2×#190989092
#237630382
C2×#190982852
C2×#493×C792
C2×#171779