Finite Group Databasebeta

← C2×#10590242 #11899525

Subgroups — C2×#10590242 #11899525

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic, complemented
2C2×#63807C211yesmaximal, characteristic, complemented
3C2×#63627C211yesmaximal, characteristic, complemented
4C2×C3×#800C211yesmaximal, characteristic, complemented
5C2×C3×D3×C16C211yesmaximal, characteristic, complemented
6C2×#63551C211yesmaximal, characteristic, complemented
7C2×#63546C211yesmaximal, characteristic, complemented
8#10590242C218yesmaximal, direct product factor
9C2×#4916—31nomaximal
10C2×#4904—31nomaximal
11C2×#3799—21no—
12C2×#3795—21no—
13C2×#3746C2211yescharacteristic
14C2×#3745C2211yescharacteristic
15C2×C3×Dic12C2211yescharacteristic
16C2×C3×D24C2211yescharacteristic
17C2×C3×D3×C8C2211yescharacteristic
18C2×#3717—21no—
19C2×#3716—21no—
20#63808—22no—
21#63808C2214yescomplemented
22#63807—22no—
23#63807C2214yescomplemented
24C2×C32×C16C2211yescharacteristic
25#63627C2214yescomplemented
26C2×C3×C3⋊C16C2211yescharacteristic
27C3×#800C2214yescomplemented
28C3×D3×C16C2214yescomplemented
29#63551C2214yescomplemented
30#63546C2214yescomplemented
31C2×#919—31no—
32C2×#912—31no—
33C2×#904—31no—
34C2×#904—31no—
35C2×C3×SD32—31no—
36C22×C3×C16—31no—
37C2×#829—31no—
38C2×#826—31no—
39#4916—38no—
40C2×Dic24—31no—
41#4904—38no—
42C2×#800—31no—
43C2×#800—31no—
44C2×#800—61no—
45C2×#800D311yescharacteristic, complemented
46C2×D48—31no—
47C2×D3×C16D311yescharacteristic, complemented
48C2×C4⋊(C3⋊D3)—21no—
49C2×#634—21no—
50C2×C3×D12—21no—
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×#626—41no—
54C2×#625—41no—
55C2×#624—41no—
56C2×D3×Dic3—41no—
57#3799—24no—
58#3799—42no—
59#3795—24no—
60#3795—42no—
61C2×C32×C8C2311yescharacteristic
62#3746—21no—
63#3746C2312yes—
64#3745—21no—
65#3745C2312yes—
66C2×C3×C3⋊C8D411yescharacteristic
67C3×Dic12—21no—
68C3×Dic12C2312yes—
69C3×D24—21no—
70C3×D24C2312yes—
71C3×D3×C8D412yes—
72C3×D3×C8C2312yes—
73#3717—24no—
74#3716—24no—
75C32×C16C2312yes—
76C3×C3⋊C16C2312yes—
77C2×#508—91noSylow
78C2×#239—61no—
79C2×#237—61no—
80C2×#235—61no—
81C2×#235—61no—
82C2×C3×Q16—31no—
83C2×C3×D8—31no—
84C22×C3×C8—31no—
85C2×#215—61no—
86C2×#214—61no—
87#919—34no—
88#919—62no—
89#912—34no—
90#912—62no—
91C2×Dic12—31no—
92C2×Dic12—31no—
93C2×Dic12—61no—
94C2×Dic12C2×D311yescharacteristic
95#904—34no—
96#904—34no—
97#904—62no—
98#904—62no—
99C2×D24—31no—
100C2×D24—31no—
101C2×D24—61no—
102C2×D24C2×D311yescharacteristic
103C2×#204—61no—
104C2×#204—61no—
105C2×D3×C8C2×D311yescharacteristic
106C3×SD32—34no—
107C2×C3×C16—21no—
108C2×C3×C16—31no—
109C2×C3×C16—34no—
110C2×C3×C16C2×D311yescharacteristic
111C2×C3×C16C2×D311yescharacteristic
112#829—34no—
113#826—34no—
114C2×C3⋊C16C2×D311yescharacteristic
115Dic24—34no—
116#800—34no—
117#800—34no—
118#800—64no—
119#800C2×D314yescomplemented
120D48—34no—
121D3×C16C2×D314yescomplemented
122C22×C3⋊D3—41no—
123C22×C3×D3—41no—
124C22×C3×D3D811yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C3⋊Dic3—41no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—41no—
129#634—22no—
130#634—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3D811yescharacteristic
133C3×D12—22no—
134C3×D12—41no—
135C3×C4×D3D812yes—
136C3×C4×D3C2×D412yes—
137C3×Dic6—22no—
138C3×Dic6—41no—
139#626—44no—
140#625—44no—
141#624—44no—
142D3×Dic3—44no—
143C32×C8C2×D411yescharacteristic
144C32×C8C2411yescharacteristic
145C3×C3⋊C8C2×D412yes—
146C2×#135—91no—
147C2×#135—91no—
148#508—98no—
149C2×Q32—91no—
150C2×SD32—31no—
151C2×SD32—91no—
152C2×D16—91no—
153C22×C16—31no—
154C2×C3×Q8—61no—
155C2×C3×D4—61no—
156C22×C3×C4—31no—
157C2×#67—121no—
158C2×#67—121no—
159C2×#67—121no—
160C22×Dic3—121no—
161#239—64no—
162#239—122no—
163#237—64no—
164#237—122no—
165#235—64no—
166#235—64no—
167#235—122no—
168#235—122no—
169C2×D12—21no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—121no—
173C2×D12—121no—
174C2×C4×D3—121no—
175C2×C4×D3—121no—
176C2×C4×D3—121no—
177C2×C4×D3D1211yescharacteristic
178C2×Dic6—21no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—121no—
182C3×Q16—32no—
183C3×Q16—61no—
184C3×D8—32no—
185C3×D8—61no—
186C2×C3×C8—21no—
187C2×C3×C8—31no—
188C2×C3×C8—32no—
189C2×C3×C8—32no—
190C2×C3×C8C22×D311yescharacteristic
191C2×C3×C8C22×D311yescharacteristic
192#215—64no—
193#214—64no—
194C2×C3⋊C8D1211yescharacteristic
195Dic12—21no—
196Dic12—32no—
197Dic12—32no—
198Dic12—62no—
199Dic12—61no—
200Dic12—61no—
201Dic12—121no—
202Dic12C22×D312yes—
203D24—21no—
204D24—32no—
205D24—32no—
206D24—62no—
207D24—61no—
208D24—61no—
209D24—121no—
210D24C22×D312yes—
211#204—64no—
212#204—64no—
213D3×C8D1212yes—
214D3×C8C22×D312yes—
215C3×C16—22no—
216C3×C16—32no—
217C3×C16C22×D312yes—
218C3×C16C22×D312yes—
219C3⋊C16C22×D312yes—
220C22×C32C2×D811yescharacteristic
221C2×C3⋊D3—42no—
222C2×C3⋊D3—82no—
223C2×C3×D3—22no—
224C2×C3×D3—42no—
225C2×C3×D3—82no—
226C2×C3×D3C2×D812yes—
227C32×C4C2×D811yescharacteristic
228C32×C4C22×D411yescharacteristic
229C3⋊Dic3—42no—
230C3×Dic3—42no—
231C3×Dic3C2×D812yes—
232C2×#41—181no—
233C2×#41—181no—
234#135—94no—
235#135—94no—
236#135—182no—
237#135—182no—
238C2×Q16—31no—
239C2×Q16—91no—
240C2×SD16—181no—
241C2×SD16—181no—
242C2×D8—31no—
243C2×D8—91no—
244C22×C8—31no—
245Q32—94no—
246SD32—34no—
247SD32—94no—
248D16—94no—
249C2×C16—31no—
250C2×C16—34no—
251C2×C16D3211yescharacteristic
252C23×C3—31no—
253C23×C3—121no—
254C22×D3—41no—
255C22×D3—121no—
256C22×D3—121no—
257C22×D3—241no—
258C22×D3D2411yescharacteristic
259C3×Q8—62no—
260C3×Q8—121no—
261C3×D4—62no—
262C3×D4—121no—
263C2×C3×C4—21no—
264C2×C3×C4—31no—
265C2×C3×C4—32no—
266C2×C3×C4—32no—
267C2×C3×C4—121no—
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270#67—124no—
271#67—124no—
272#67—124no—
273C2×Dic3—41no—
274C2×Dic3—121no—
275C2×Dic3—121no—
276C2×Dic3—124no—
277C2×Dic3—241no—
278C2×Dic3D2411yescharacteristic
279D12—22no—
280D12—41no—
281D12—62no—
282D12—62no—
283D12—122no—
284D12—124no—
285D12—121no—
286D12—121no—
287D12—241no—
288C4×D3—124no—
289C4×D3—124no—
290C4×D3—124no—
291C4×D3D2412yes—
292C4×D3C2×D1212yes—
293Dic6—22no—
294Dic6—41no—
295Dic6—62no—
296Dic6—62no—
297Dic6—122no—
298Dic6—121no—
299Dic6—121no—
300Dic6—241no—
301C3×C8—21no—
302C3×C8—21no—
303C3×C8—32no—
304C3×C8C2×D1211yescharacteristic
305C3×C8D3×D411yescharacteristic
306C3×C8C23×D311yescharacteristic
307C3×C8C23×D311yescharacteristic
308C3⋊C8C2×D1212yes—
309C2×C32#50812yescomplemented
310C2×C32C22×D811yescharacteristic
311C3⋊D3—82no—
312C3×D3—22no—
313C3×D3—82no—
314#41—184no—
315#41—184no—
316#41—362no—
317#41—362no—
318C2×Q8—61no—
319C2×Q8—181no—
320C2×D4—61no—
321C2×D4—181no—
322C2×D4—361no—
323C2×D4—361no—
324C22×C4—31no—
325C22×C4—361no—
326C22×C4—361no—
327Q16—32no—
328Q16—61no—
329Q16—92no—
330Q16—181no—
331SD16—184no—
332SD16—184no—
333D8—32no—
334D8—61no—
335D8—92no—
336D8—181no—
337C2×C8—31no—
338C2×C8—32no—
339C2×C8—32no—
340C2×C8C2×D3211yescharacteristic
341C16—32no—
342C16C2×D3212yes—
343C22×C3—21no—
344C22×C3—32no—
345C22×C3—62no—
346C22×C3—122no—
347C22×C3—242no—
348C22×C3C2×D2411yescharacteristic
349C22×C3D3×D811yescharacteristic
350C2×D3—22no—
351C2×D3—42no—
352C2×D3—82no—
353C2×D3—122no—
354C2×D3—122no—
355C2×D3—242no—
356C2×D3—242no—
357C2×D3—242no—
358C2×D3—482no—
359C2×D3C2×D2412yes—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—32no—
363C3×C4—122no—
364C3×C4C2×D2411yescharacteristic
365C3×C4D3×D811yescharacteristic
366C3×C4C22×D1211yescharacteristic
367C3×C4C2×D3×D411yescharacteristic
368Dic3—42no—
369Dic3—122no—
370Dic3—122no—
371Dic3—242no—
372Dic3C2×D2412yes—
373C32C2×#50811yescharacteristic, complemented, Sylow
374C23—31no—
375C23—121no—
376C23—361no—
377Q8—62no—
378Q8—121no—
379Q8—182no—
380Q8—361no—
381D4—62no—
382D4—121no—
383D4—182no—
384D4—364no—
385D4—364no—
386D4—361no—
387C2×C4—31no—
388C2×C4—32no—
389C2×C4—32no—
390C2×C4—121no—
391C2×C4—364no—
392C2×C4—364no—
393C2×C4—361no—
394C2×C4D3×D1211yescharacteristic
395C8—32no—
396C8D3×D1211yescharacteristic
397C8C22×D3211yescharacteristic
398C2×C3—22no—
399C2×C3—21no—
400C2×C3—62no—
401C2×C3—242no—
402C2×C3#490412yescomplemented
403C2×C3#491612yescomplemented
404C2×C3C22×D2411yescharacteristic
405C2×C3C2×D3×D811yescharacteristic
406D3—22no—
407D3—82no—
408D3—242no—
409D3—242no—
410D3—482no—
411C22—32no—
412C22—62no—
413C22—122no—
414C22—242no—
415C22—362no—
416C22—722no—
417C22D3×D2411yescharacteristic
418C4—32no—
419C4—122no—
420C4—362no—
421C4D3×D2411yescharacteristic
422C4C2×D3×D1211yescharacteristic
423C3—21no—
424C3C2×#490411yescharacteristic, complemented
425C3C2×#491611yescharacteristic, complemented
426C2—62no—
427C2—242no—
428C2—722no—
429C2#1059024212yesdirect product factor
430C2C2×D3×D2411yescharacteristic
subgroupG/H
centerC22D3×D24
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
hypercenterC2×C16D32
hypocenterC32C2×#508
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×#63808C2semidirect
2. C2×#63807C2semidirect
3. C2×#63627C2semidirect
4. C2×C3×#800C2semidirect
5. C2×C3×D3×C16C2semidirect
6. C2×#63551C2semidirect
7. C2×#63546C2semidirect
8. #10590242C2direct (N × H)
21. #63808C22semidirect
23. #63807C22semidirect
25. #63627C22semidirect
27. C3×#800C22semidirect
28. C3×D3×C16C22semidirect
29. #63551C22semidirect
30. #63546C22semidirect
45. C2×#800D3semidirect
47. C2×D3×C16D3semidirect
119. #800C2×D3semidirect
121. D3×C16C2×D3semidirect
309. C2×C32#508semidirect
373. C32C2×#508semidirect
402. C2×C3#4904semidirect
403. C2×C3#4916semidirect
424. C3C2×#4904semidirect
425. C3C2×#4916semidirect
429. C2#10590242direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638082
C2×#638072
C2×#636272
C2×C3×#8002
C2×C3×D3×C162
C2×#635512
C2×#635462
#105902422
C2×#49163
C2×#49043