Finite Group Databasebeta

← C2×#19134135 #25079245

Subgroups — C2×#19134135 #25079245

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583246C211yesmaximal, characteristic
2C2×#14583194C211yesmaximal, characteristic, complemented
3C2×#14583099C211yesmaximal, characteristic
4#19134135C218yesmaximal, direct product factor
5C2×#14582652C211yesmaximal, characteristic, complemented
6C2×#14582647C211yesmaximal, characteristic, complemented
7C2×#14582642C211yesmaximal, characteristic
8C2×C43×#446C211yesmaximal, characteristic, complemented
9C22×#10621884—21no—
10C2×#13063325C2211yescharacteristic
11C2×#13063322C2211yescharacteristic
12#14583246—22no—
13#14583246C2214yes—
14#14583194—22no—
15#14583194C2214yescomplemented
16#14583099—22no—
17#14583099C2214yes—
18C2×#13063258—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21C2×#13063249—21no—
22C2×#13063247—21no—
23C2×#13063247—21no—
24C2×#13063245—21no—
25#14582652C2214yescomplemented
26#14582647C2214yescomplemented
27#14582642C2214yes—
28C2×C4×Q8×C43C2211yescharacteristic
29C43×#446—22no—
30C43×#446C2214yescomplemented
31C2×C4⋊C8×C43—21no—
32C2×C4⋊C8×C43C2211yescharacteristic
33C2×#97×C43—21no—
34C2×C4×C8×C43C2211yescharacteristic
35C22×Dic86—21no—
36C22×D172—21no—
37C22×D172—21no—
38C22×D172—21no—
39C2×#10621884—24no—
40C2×#10621884—44no—
41C22×C43⋊C8—21no—
42C22×C43⋊C8—21no—
43#13063325—21no—
44#13063325—21no—
45#13063325—21no—
46#13063325C2312yes—
47#13063322—21no—
48#13063322—21no—
49#13063322—21no—
50#13063322C2312yes—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—21no—
53#13063258—24no—
54C4⋊(C43⋊C8)—21no—
55C4⋊(C43⋊C8)—21no—
56C4⋊(C43⋊C8)C2312yes—
57C4⋊(C43⋊C8)C2312yes—
58#13063249—24no—
59#13063247—24no—
60#13063247—24no—
61#13063245—24no—
62C22×Q8×C43D411yescharacteristic
63C22×C8×C43—21no—
64C22×C8×C43D411yescharacteristic
65C22×C8×C43D411yescharacteristic
66C4×Q8×C43—21no—
67C4×Q8×C43—21no—
68C4×Q8×C43D412yes—
69C4×Q8×C43C2312yes—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C42×C43—21no—
73C2×C42×C43C2311yescharacteristic
74C4⋊C8×C43—24no—
75C4⋊C8×C43—21no—
76C4⋊C8×C43C2312yes—
77#97×C43—24no—
78C4×C8×C43D412yes—
79C4×C8×C43C2312yes—
80C23×D43—41no—
81C2×Q8×C43—21no—
82C2×Q8×C43—22no—
83C2×Q8×C43—22no—
84C2×Q8×C43C2×D412yes—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43#4111yescharacteristic
90C22×Dic43—41no—
91C2×D172—22no—
92C2×D172—22no—
93C2×D172—22no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—42no—
98C2×D172—42no—
99C2×D172—42no—
100C2×D172—42no—
101C2×D172—82no—
102C2×Dic86—22no—
103C2×Dic86—41no—
104C2×Dic86—82no—
105C2×C8×C43—22no—
106C2×C8×C43—22no—
107C2×C8×C43—22no—
108C2×C8×C43—42no—
109C2×C8×C43C2×D412yes—
110C2×C8×C43C2×D412yes—
111C4⋊C4×C43—22no—
112C4⋊C4×C43—21no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43C2×D412yes—
115C42×C43—22no—
116C42×C43—22no—
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C42×C43C2411yescharacteristic
121#10621884—48no—
122C4⋊Dic43—22no—
123C4⋊Dic43—22no—
124C4⋊Dic43—41no—
125C4⋊Dic43—41no—
126C2×C43⋊C8—22no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—42no—
129C2×C43⋊C8—42no—
130C23×C43#12111yescharacteristic
131C22×D43—42no—
132C22×D43—82no—
133C22×D43—82no—
134C22×D43—82no—
135Q8×C43—22no—
136Q8×C43—22no—
137Q8×C43—42no—
138C2×C4×C43—22no—
139C2×C4×C43—22no—
140C2×C4×C43—22no—
141C2×C4×C43—42no—
142C2×C4×C43—42no—
143C2×C4×C43#12111yescharacteristic
144C2×C4×C43#12111yescharacteristic
145C2×C4×C43#12111yescharacteristic
146C2×C4×C43#13512yes—
147C2×C4×C43AGL(1,ℤ/8)12yes—
148C2×C4×C43#13712yes—
149C2×C4×C43#13712yes—
150C2×C4×C43C22×D411yescharacteristic
151C2×C4×C43C22×D411yescharacteristic
152C2×C4×C43C2×#4111yescharacteristic
153C2×Dic43—42no—
154C2×Dic43—82no—
155D172—42no—
156D172—42no—
157D172—42no—
158D172—42no—
159D172—82no—
160D172—82no—
161D172—82no—
162D172—82no—
163Dic86—82no—
164Dic86—82no—
165C8×C43—22no—
166C8×C43—22no—
167C8×C43—42no—
168C43⋊C8—42no—
169C43⋊C8—42no—
170C2×#1698—431nomaximal, Sylow
171C22×C43#46412yes—
172C22×C43#46812yes—
173C22×C43#47212yes—
174C22×C43C2×#12111yescharacteristic
175C2×D43—82no—
176C2×D43—82no—
177C2×D43—82no—
178C2×D43—164no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43—42no—
183C4×C43#46412yes—
184C4×C43#46812yes—
185C4×C43C2×#13511yescharacteristic
186C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
187C4×C43C2×#13711yescharacteristic
188C4×C43C2×#13711yescharacteristic
189Dic43—82no—
190C2×#486—431no—
191C2×#477—431no—
192C2×#460—431no—
193C2×#446D4311yescharacteristic, complemented
194#1698—438no—
195C2×#335—431no—
196C2×#333—431no—
197C2×#331—431no—
198C2×C43#169814yescomplemented
199C2×C43C2×#46411yescharacteristic
200C2×C43C2×#46811yescharacteristic
201C2×C43C2×#47211yescharacteristic
202D43—162no—
203C22×SD16—861no—
204C2×C4⋊Q8—431no—
205C2×#127—431no—
206C2×C4×Q8C2×D4311yescharacteristic
207#486—434no—
208#486—862no—
209#477—434no—
210#477—862no—
211#460—434no—
212#460—862no—
213#446—22no—
214#446C2×D4314yescomplemented
215C2×#107—861no—
216C2×C4⋊C8—21no—
217C2×C4⋊C8—431no—
218C2×C4⋊C8—431no—
219C2×C4⋊C8C2×D4311yescharacteristic
220C2×#103—861no—
221C2×#102—861no—
222C2×#102—861no—
223C2×#102—861no—
224C2×#97—21no—
225C2×C4×C8C2×D4311yescharacteristic
226#335—434no—
227#333—434no—
228#331—434no—
229C43C2×#169811yescharacteristic, complemented, Sylow
230C22×Q8—861no—
231C22×Q8D17211yescharacteristic
232C22×D4—861no—
233C22×D4—861no—
234C22×D4—861no—
235C2×SD16—864no—
236C2×SD16—1724no—
237C22×C8—21no—
238C22×C8—861no—
239C22×C8—861no—
240C22×C8C22⋊D4311yescharacteristic
241C22×C8C22⋊D4311yescharacteristic
242C4⋊Q8—432no—
243C4⋊Q8—861no—
244C4⋊Q8—861no—
245C4⋊Q8—861no—
246#127—432no—
247#127—861no—
248#127—861no—
249#127—861no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×Q8D17212yes—
253C4×Q8C22×D4312yes—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—861no—
256C2×C4⋊C4—861no—
257C2×C4⋊C4D17211yescharacteristic
258C2×C42—21no—
259C2×C42C22×D4311yescharacteristic
260#107—864no—
261C4⋊C8—24no—
262C4⋊C8—21no—
263C4⋊C8—432no—
264C4⋊C8—432no—
265C4⋊C8—861no—
266C4⋊C8—861no—
267C4⋊C8C22×D4312yes—
268#103—864no—
269#102—864no—
270#102—864no—
271#102—864no—
272#97—24no—
273C4×C8C22⋊D4312yes—
274C4×C8C22×D4312yes—
275C24—1721no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—862no—
280C2×Q8—3442no—
281C2×Q8—1721no—
282C2×Q8C2×D17212yes—
283C2×D4—862no—
284C2×D4—862no—
285C2×D4—862no—
286C2×D4—3442no—
287C2×D4—1721no—
288C2×D4—1721no—
289C2×D4—1721no—
290C2×D4—1722no—
291C2×D4—1722no—
292C2×D4—1722no—
293C2×D4—1722no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—1721no—
297C22×C4C2×D17211yescharacteristic
298C22×C4#1062189811yescharacteristic
299C22×C4C2×C22⋊D4311yescharacteristic
300SD16—1728no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—42no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—1722no—
308C2×C8—1722no—
309C2×C8C2×C22⋊D4312yes—
310C2×C8C2×C22⋊D4312yes—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—862no—
315C4⋊C4—862no—
316C4⋊C4—1721no—
317C4⋊C4—1721no—
318C4⋊C4C2×D17212yes—
319C42—22no—
320C42—22no—
321C42C2×D17211yescharacteristic
322C42#1062189811yescharacteristic
323C42C2×C22⋊D4311yescharacteristic
324C42C23×D4311yescharacteristic
325C23—3442no—
326C23—3442no—
327C23—3442no—
328C23—1722no—
329C23#1306329911yescharacteristic
330Q8—22no—
331Q8—22no—
332Q8—42no—
333Q8—3442no—
334Q8—3442no—
335D4—3442no—
336D4—3442no—
337D4—3442no—
338D4—3442no—
339D4—1722no—
340D4—1722no—
341D4—1722no—
342D4—1722no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—3442no—
349C2×C4—1722no—
350C2×C4#1306329911yescharacteristic
351C2×C4#1306329911yescharacteristic
352C2×C4#1306329911yescharacteristic
353C2×C4#1306334512yes—
354C2×C4#1306335312yes—
355C2×C4#1306335612yes—
356C2×C4#1306335812yes—
357C2×C4C22×C22⋊D4311yescharacteristic
358C2×C4C22×D17211yescharacteristic
359C2×C4C2×#1062189811yescharacteristic
360C8—22no—
361C8—22no—
362C8—42no—
363C8—1722no—
364C8—1722no—
365C22—3442no—
366C22—3442no—
367C22—3442no—
368C22—6884no—
369C22#1458312112yes—
370C22#1458314512yes—
371C22#1458316912yes—
372C22C2×#1306329911yescharacteristic
373C4—21no—
374C4—21no—
375C4—42no—
376C4—42no—
377C4—3442no—
378C4#1458312112yes—
379C4#1458314512yes—
380C4C2×#1306334511yescharacteristic
381C4C2×#1306335311yescharacteristic
382C4C2×#1306335611yescharacteristic
383C4C2×#1306335811yescharacteristic
384C2—6882no—
385C2#1913413514yesdirect product factor
386C2C2×#1458312111yescharacteristic
387C2C2×#1458314511yescharacteristic
388C2C2×#1458316911yescharacteristic
subgroupG/H
centerC23#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#446C2
socleC23×C43#121
prime radicalC2×#13063322C22
hypercenterC2×#446D43
hypocenterC43C2×#1698
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#14583194C2semidirect
4. #19134135C2direct (N × H)
5. C2×#14582652C2semidirect
6. C2×#14582647C2semidirect
8. C2×C43×#446C2semidirect
15. #14583194C22semidirect
25. #14582652C22semidirect
26. #14582647C22semidirect
30. C43×#446C22semidirect
193. C2×#446D43semidirect
198. C2×C43#1698semidirect
214. #446C2×D43semidirect
229. C43C2×#1698semidirect
385. C2#19134135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145832462
C2×#145831942
C2×#145830992
#191341352
C2×#145826522
C2×#145826472
C2×#145826422
C2×C43×#4462
C2×#169843