Finite Group Databasebeta

← C2×#23762975 #34270842

Subgroups — C2×#23762975 #34270842

Order 20224.

694 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19098914C211yesmaximal, characteristic, complemented
2C2×#19098853C211yesmaximal, characteristic
3C2×#19098843C211yesmaximal, characteristic
4#23762975C218yesmaximal, direct product factor
5C2×#19098314C211yesmaximal, characteristic, complemented
6C2×#19098311C211yesmaximal, characteristic, complemented
7C2×#19098310C211yesmaximal, characteristic, complemented
8C2×#436×C79C211yesmaximal, characteristic
9C2×#14579161C2211yescharacteristic
10C2×#14579161C2211yescharacteristic
11#19098914—22no—
12#19098914C2214yescomplemented
13#19098853—22no—
14#19098853C2214yes—
15#19098843—22no—
16#19098843C2214yes—
17C2×#14579094—21no—
18C2×#14579092—21no—
19C2×C4⋊(C79⋊C8)C2211yescharacteristic
20C2×C4⋊(C79⋊C8)C2211yescharacteristic
21C2×#14579086—21no—
22C2×#14579086—21no—
23C2×#14579082—21no—
24C2×#14579082—21no—
25#19098314C2214yescomplemented
26#19098311C2214yescomplemented
27#19098310C2214yescomplemented
28C22×M16×C79—21no—
29C2×C4×D4×C79C2211yescharacteristic
30#436×C79—22no—
31#436×C79C2214yes—
32C2×C4⋊C8×C79C2211yescharacteristic
33C2×C22⋊C8×C79—21no—
34C2×C4×C8×C79C2211yescharacteristic
35C22×Dic158—21no—
36C22×Dic158—21no—
37C22×C79⋊C8—21no—
38C22×C79⋊C8—21no—
39#14579161—21no—
40#14579161—21no—
41#14579161—21no—
42#14579161—21no—
43#14579161—21no—
44#14579161—21no—
45#14579161C2312yes—
46#14579161C2312yes—
47C2×C4⋊Dic79—21no—
48C2×C4⋊Dic79—21no—
49C2×C4⋊Dic79—21no—
50C2×C4⋊Dic79—21no—
51#14579094—24no—
52#14579092—24no—
53C4⋊(C79⋊C8)—21no—
54C4⋊(C79⋊C8)—21no—
55C4⋊(C79⋊C8)C2312yes—
56C4⋊(C79⋊C8)C2312yes—
57#14579086—24no—
58#14579086—24no—
59#14579082—24no—
60#14579082—24no—
61C22×D4×C79D411yescharacteristic
62C23×C4×C79—21no—
63C2×M16×C79—24no—
64C2×M16×C79—44no—
65C22×C8×C79—21no—
66C22×C8×C79D411yescharacteristic
67C22×C8×C79D411yescharacteristic
68C4×D4×C79—21no—
69C4×D4×C79—21no—
70C4×D4×C79D412yes—
71C4×D4×C79C2312yes—
72C2×C4⋊C4×C79D411yescharacteristic
73C2×C22⋊C4×C79—21no—
74C2×C42×C79C2311yescharacteristic
75C4⋊C8×C79—21no—
76C4⋊C8×C79C2312yes—
77C22⋊C8×C79—24no—
78C4×C8×C79D412yes—
79C4×C8×C79C2312yes—
80C2×Dic158—22no—
81C2×Dic158—22no—
82C2×Dic158—41no—
83C2×Dic158—41no—
84C2×Dic158—42no—
85C2×Dic158—42no—
86C2×Dic158—82no—
87C22×Dic79—41no—
88C22×Dic79—41no—
89C2×C79⋊C8—22no—
90C2×C79⋊C8—22no—
91C2×C79⋊C8—42no—
92C2×C79⋊C8—42no—
93C4⋊Dic79—22no—
94C4⋊Dic79—22no—
95C4⋊Dic79—22no—
96C4⋊Dic79—22no—
97C4⋊Dic79—41no—
98C4⋊Dic79—41no—
99C4⋊Dic79—41no—
100C4⋊Dic79—41no—
101C24×C79—21no—
102C2×D4×C79—21no—
103C2×D4×C79—22no—
104C2×D4×C79—22no—
105C2×D4×C79C2×D412yes—
106C22×C4×C79—21no—
107C22×C4×C79—22no—
108C22×C4×C79—22no—
109C22×C4×C79—42no—
110C22×C4×C79—42no—
111C22×C4×C79C2×D411yescharacteristic
112C22×C4×C79C2×D411yescharacteristic
113C22×C4×C79#4111yescharacteristic
114M16×C79—48no—
115C2×C8×C79—22no—
116C2×C8×C79—22no—
117C2×C8×C79—22no—
118C2×C8×C79—42no—
119C2×C8×C79C2×D412yes—
120C2×C8×C79C2×D412yes—
121C4⋊C4×C79—21no—
122C4⋊C4×C79C2×D412yes—
123C22⋊C4×C79—22no—
124C22⋊C4×C79—22no—
125C42×C79C2×D411yescharacteristic
126C42×C79C2×D411yescharacteristic
127C42×C79#4111yescharacteristic
128C42×C79C2411yescharacteristic
129C23×C79—22no—
130C23×C79—42no—
131C23×C79—42no—
132C23×C79—42no—
133C23×C79#12111yescharacteristic
134D4×C79—22no—
135D4×C79—22no—
136D4×C79—42no—
137C2×C4×C79—22no—
138C2×C4×C79—22no—
139C2×C4×C79—42no—
140C2×C4×C79—42no—
141C2×C4×C79—42no—
142C2×C4×C79—44no—
143C2×C4×C79#12111yescharacteristic
144C2×C4×C79#12111yescharacteristic
145C2×C4×C79#12111yescharacteristic
146C2×C4×C79#13512yes—
147C2×C4×C79AGL(1,ℤ/8)12yes—
148C2×C4×C79#13712yes—
149C2×C4×C79#13712yes—
150C2×C4×C79C22×D411yescharacteristic
151C2×C4×C79C22×D411yescharacteristic
152C2×C4×C79C2×#4111yescharacteristic
153C2×Dic79—42no—
154C2×Dic79—42no—
155C2×Dic79—82no—
156C2×Dic79—82no—
157Dic158—42no—
158Dic158—42no—
159Dic158—82no—
160Dic158—82no—
161Dic158—82no—
162C8×C79—22no—
163C8×C79—22no—
164C8×C79—42no—
165C79⋊C8—42no—
166C79⋊C8—42no—
167C22×C79—42no—
168C22×C79—42no—
169C22×C79—42no—
170C22×C79—84no—
171C22×C79#46312yes—
172C22×C79#47012yes—
173C22×C79#47112yes—
174C22×C79C2×#12111yescharacteristic
175C4×C79—21no—
176C4×C79—21no—
177C4×C79—42no—
178C4×C79#46312yes—
179C4×C79#47012yes—
180C4×C79C2×#13511yescharacteristic
181C4×C79C2×AGL(1,ℤ/8)11yescharacteristic
182C4×C79C2×#13711yescharacteristic
183C4×C79C2×#13711yescharacteristic
184Dic79—82no—
185Dic79—82no—
186C2×#1703—791nomaximal, Sylow
187C2×C79—82no—
188C2×C79#170314yescomplemented
189C2×C79C2×#46311yescharacteristic
190C2×C79C2×#47011yescharacteristic
191C2×C79C2×#47111yescharacteristic
192C2×#487—791no—
193C2×#476—791no—
194C2×#474—791no—
195C2×#436D7911yescharacteristic
196#1703—798no—
197C2×#334—791no—
198C2×#333—791no—
199C2×#332—791no—
200C79C2×#170311yescharacteristic, complemented, Sylow
201C22×M16—21no—
202C2×C4⋊Q8—791no—
203C2×C4⋊Q8—791no—
204C2×C4×D4C2×D7911yescharacteristic
205#487—794no—
206#487—1582no—
207#476—794no—
208#476—1582no—
209#474—794no—
210#474—1582no—
211#436—22no—
212#436C2×D7914yes—
213C2×#107—1581no—
214C2×#106—1581no—
215C2×C4⋊C8—791no—
216C2×C4⋊C8—791no—
217C2×C4⋊C8C2×D7911yescharacteristic
218C2×#103—1581no—
219C2×#103—1581no—
220C2×#102—1581no—
221C2×#102—1581no—
222C2×C22⋊C8—21no—
223C2×C4×C8C2×D7911yescharacteristic
224#334—794no—
225#333—794no—
226#332—794no—
227C22×Q8—1581no—
228C22×Q8—1581no—
229C22×D4D31611yescharacteristic
230C23×C4—21no—
231C2×M16—24no—
232C2×M16—44no—
233C22×C8—21no—
234C22×C8—1581no—
235C22×C8—1581no—
236C22×C8C22⋊D7911yescharacteristic
237C22×C8C22⋊D7911yescharacteristic
238C4⋊Q8—792no—
239C4⋊Q8—792no—
240C4⋊Q8—1581no—
241C4⋊Q8—1581no—
242C4⋊Q8—1581no—
243C4⋊Q8—1581no—
244C4⋊Q8—1581no—
245C4⋊Q8—1581no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4D31612yes—
249C4×D4C22×D7912yes—
250C2×C4⋊C4—1581no—
251C2×C4⋊C4—1581no—
252C2×C4⋊C4—1581no—
253C2×C4⋊C4—1581no—
254C2×C4⋊C4D31611yescharacteristic
255C2×C22⋊C4—21no—
256C2×C42C22×D7911yescharacteristic
257#107—1584no—
258#106—1584no—
259C4⋊C8—21no—
260C4⋊C8—792no—
261C4⋊C8—792no—
262C4⋊C8—1581no—
263C4⋊C8—1581no—
264C4⋊C8C22×D7912yes—
265#103—1584no—
266#103—1584no—
267#102—1584no—
268#102—1584no—
269C22⋊C8—24no—
270C4×C8C22⋊D7912yes—
271C4×C8C22×D7912yes—
272C24—21no—
273C2×Q8—3161no—
274C2×Q8—3161no—
275C2×Q8—3162no—
276C2×Q8—3162no—
277C2×Q8—6322no—
278C2×Q8—1582no—
279C2×Q8—1582no—
280C2×D4—21no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4C2×D31612yes—
284C22×C4—21no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—3161no—
290C22×C4—3161no—
291C22×C4C2×C22⋊D7911yescharacteristic
292C22×C4C2×D31611yescharacteristic
293C22×C4#1192962411yescharacteristic
294M16—48no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—42no—
299C2×C8—3162no—
300C2×C8—3162no—
301C2×C8—1582no—
302C2×C8—1582no—
303C2×C8C2×C22⋊D7912yes—
304C2×C8C2×C22⋊D7912yes—
305C4⋊C4—21no—
306C4⋊C4—3161no—
307C4⋊C4—3161no—
308C4⋊C4—3161no—
309C4⋊C4—3161no—
310C4⋊C4—1582no—
311C4⋊C4—1582no—
312C4⋊C4—1582no—
313C4⋊C4—1582no—
314C4⋊C4C2×D31612yes—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C42C2×C22⋊D7911yescharacteristic
318C42C2×D31611yescharacteristic
319C42#1192962411yescharacteristic
320C42C23×D7911yescharacteristic
321C23—22no—
322C23—42no—
323C23—42no—
324C23—42no—
325C23#1457913511yescharacteristic
326Q8—3162no—
327Q8—3162no—
328Q8—6322no—
329Q8—6322no—
330Q8—6322no—
331D4—22no—
332D4—22no—
333D4—42no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—3162no—
341C2×C4—3162no—
342C2×C4—6322no—
343C2×C4—6322no—
344C2×C4#1457913511yescharacteristic
345C2×C4#1457913511yescharacteristic
346C2×C4#1457913511yescharacteristic
347C2×C4#1457918112yes—
348C2×C4#1457918712yes—
349C2×C4#1457919412yes—
350C2×C4#1457919412yes—
351C2×C4C22×C22⋊D7911yescharacteristic
352C2×C4C22×D31611yescharacteristic
353C2×C4C2×#1192962411yescharacteristic
354C8—22no—
355C8—22no—
356C8—42no—
357C8—3162no—
358C8—3162no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—84no—
363C22#1909877812yes—
364C22#1909882112yes—
365C22#1909882612yes—
366C22C2×#1457913511yescharacteristic
367C4—21no—
368C4—21no—
369C4—42no—
370C4—6322no—
371C4—6322no—
372C4#1909877812yes—
373C4#1909882112yes—
374C4C2×#1457918111yescharacteristic
375C4C2×#1457918711yescharacteristic
376C4C2×#1457919411yescharacteristic
377C4C2×#1457919411yescharacteristic
378C2—82no—
379C2#2376297514yesdirect product factor
380C2C2×#1909877811yescharacteristic
381C2C2×#1909882111yescharacteristic
382C2C2×#1909882611yescharacteristic
subgroupG/H
centerC23#14579135
commutator, cosocleC42×C79C24
FrattiniC42C23×D79
FittingC2×#436×C79C2
socleC23×C79#121
prime radicalC22×D4×C79D4
hypercenterC2×#436D79
hypocenterC79C2×#1703
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#19098914C2semidirect
4. #23762975C2direct (N × H)
5. C2×#19098314C2semidirect
6. C2×#19098311C2semidirect
7. C2×#19098310C2semidirect
12. #19098914C22semidirect
25. #19098314C22semidirect
26. #19098311C22semidirect
27. #19098310C22semidirect
188. C2×C79#1703semidirect
200. C79C2×#1703semidirect
379. C2#23762975direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#190989142
C2×#190988532
C2×#190988432
#237629752
C2×#190983142
C2×#190983112
C2×#190983102
C2×#436×C792
C2×#170379