Finite Group Databasebeta

← C2×#10589125 #11796831

Subgroups — C2×#10589125 #11796831

Order 1152.

597 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic
2C2×C3×#817C211yesmaximal, characteristic, complemented
3C2×C3×#812C211yesmaximal, characteristic, complemented
4#10589125C214yesmaximal, direct product factor
5C2×#4518—31nomaximal
6C2×#4488—31nomaximal
7C2×#3828—21no—
8C22×C32×C8C2211yescharacteristic
9C2×#3746C411yescharacteristic, complemented
10#64113—21no—
11#64113—21no—
12#64113C412yescomplemented
13#64113C2212yes—
14C2×#3745C411yescharacteristic, complemented
15C2×#3744—21no—
16C2×C3×C4⋊Dic3—21no—
17C3×#817—21no—
18C3×#817C2212yescomplemented
19C3×#812—21no—
20C3×#812C2212yescomplemented
21C2×C3×C3⋊C16—21no—
22C2×#904—31no—
23C2×#904—31no—
24C2×#904—61no—
25C2×C3×M32—31no—
26C2×C3×#106—31no—
27C2×#817D311yescharacteristic, complemented
28C2×#812D311yescharacteristic, complemented
29#4518—34no—
30#4488—34no—
31C22×C32×C4D411yescharacteristic
32C2×#638—41no—
33#3828—22no—
34#3828—22no—
35#3828—41no—
36#3828—41no—
37C2×C4⋊(C3⋊D3)—21no—
38C2×C4×C3⋊D3—41no—
39C2×#634—21no—
40C22×C3×Dic3—41no—
41C2×C32×C8C2×C411yescharacteristic
42C2×C32×C8C2×C411yescharacteristic
43C2×C32×C8D411yescharacteristic
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C2×C32×C8C2311yescharacteristic
47#3746—21no—
48#3746C2×C412yescomplemented
49#3745—21no—
50#3745C2×C412yescomplemented
51#3744—22no—
52#3744—22no—
53C3×C4⋊Dic3—22no—
54C3×C4⋊Dic3—41no—
55C3×C3⋊C16—22no—
56C2×#360—91noSylow
57C2×#235—62no—
58C2×#235—61no—
59C2×#235—61no—
60C22×C3×C8—21no—
61C22×C3×C8C2×D311yescharacteristic
62C22×C3×C8C2×D311yescharacteristic
63C2×C3×C4⋊C4—61no—
64C2×C4⋊Dic3—21no—
65C2×Dic12—31no—
66C2×Dic12—31no—
67C2×Dic12—61no—
68#904—32no—
69#904—32no—
70#904—32no—
71#904—32no—
72#904—62no—
73#904—62no—
74#904—62no—
75#904—62no—
76#904—61no—
77#904—61no—
78#904—61no—
79#904—61no—
80C2×D24—31no—
81C2×D24—31no—
82C2×D24—61no—
83C2×#204—62no—
84C2×#204—61no—
85C2×#204—61no—
86C3×M32—32no—
87C3×M32—61no—
88C2×C3×C16—61no—
89C3×#106—32no—
90C3×#106—61no—
91#817—21no—
92#817C2×D312yescomplemented
93#812—21no—
94#812C2×D312yescomplemented
95C2×C3⋊C16—21no—
96C23×C32D811yescharacteristic
97C22×C3⋊D3—41no—
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4D811yescharacteristic
101C2×C32×C4SD1611yescharacteristic
102C2×C32×C4SD1611yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104#638—42no—
105#638—42no—
106C2×C3⋊Dic3—41no—
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)—41no—
109C4×C3⋊D3—42no—
110C4×C3⋊D3—42no—
111#634—22no—
112#634—41no—
113C2×C3×Dic3—42no—
114C2×C3×Dic3—82no—
115C32×C8C22⋊C411yescharacteristic
116C32×C8C22⋊C411yescharacteristic
117C32×C8C22×C411yescharacteristic
118C32×C8C2×D411yescharacteristic
119C2×#135—91no—
120C2×M32—31no—
121C2×#106—31no—
122#360—94no—
123C22×C3×C4—21no—
124C22×C3×C4—121no—
125C22×C3×C4D1211yescharacteristic
126C22×C3×C4#6711yescharacteristic
127C2×#67—122no—
128C2×#67—121no—
129C2×#67—121no—
130C22×Dic3—41no—
131#235—64no—
132#235—64no—
133#235—62no—
134#235—62no—
135#235—62no—
136#235—62no—
137#235—122no—
138#235—122no—
139#235—121no—
140#235—121no—
141#235—121no—
142#235—121no—
143C2×D12—62no—
144C2×D12—61no—
145C2×D12—61no—
146C2×C4×D3—122no—
147C2×C4×D3—121no—
148C2×C4×D3—121no—
149C2×Dic6—62no—
150C2×Dic6—61no—
151C2×Dic6—61no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8—21no—
155C2×C3×C8—21no—
156C2×C3×C8—21no—
157C2×C3×C8—21no—
158C2×C3×C8C4×D311yescharacteristic
159C2×C3×C8C4×D311yescharacteristic
160C2×C3×C8C4×D311yescharacteristic
161C2×C3×C8C4×D311yescharacteristic
162C2×C3×C8D1211yescharacteristic
163C2×C3×C8D1211yescharacteristic
164C2×C3×C8D1211yescharacteristic
165C2×C3×C8#6711yescharacteristic
166C2×C3×C8#6711yescharacteristic
167C2×C3×C8#6711yescharacteristic
168C2×C3×C8C22×D311yescharacteristic
169C2×C3×C8C22×D311yescharacteristic
170C3×C4⋊C4—62no—
171C3×C4⋊C4—121no—
172C4⋊Dic3—22no—
173C4⋊Dic3—41no—
174Dic12—32no—
175Dic12—32no—
176Dic12—62no—
177Dic12—62no—
178Dic12—61no—
179Dic12—61no—
180D24—32no—
181D24—32no—
182D24—62no—
183D24—62no—
184D24—61no—
185D24—61no—
186#204—64no—
187#204—64no—
188#204—62no—
189#204—62no—
190#204—62no—
191#204—62no—
192C3×C16—62no—
193C3⋊C16—22no—
194C22×C32—22no—
195C22×C32#10211yescharacteristic
196C22×C32#10211yescharacteristic
197C22×C32C2×D811yescharacteristic
198C2×C3⋊D3—42no—
199C2×C3⋊D3—82no—
200C32×C4#10211yescharacteristic
201C32×C4#10211yescharacteristic
202C32×C4C2×C22⋊C411yescharacteristic
203C32×C4C2×SD1611yescharacteristic
204C3⋊Dic3—42no—
205C3×Dic3—82no—
206C2×#41—181no—
207#135—92no—
208#135—92no—
209#135—181no—
210#135—181no—
211C2×Q16—91no—
212C2×SD16—181no—
213C2×D8—91no—
214C22×C8D3211yescharacteristic
215C2×C4⋊C4—61no—
216M32—32no—
217M32—61no—
218C2×C16—61no—
219#106—32no—
220#106—61no—
221C23×C3—21no—
222C23×C3D2411yescharacteristic
223C23×C3#21311yescharacteristic
224C22×D3—122no—
225C22×D3—121no—
226C22×D3—121no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—122no—
234C2×C3×C4—242no—
235C2×C3×C4#20411yescharacteristic
236C2×C3×C4#20411yescharacteristic
237C2×C3×C4D2411yescharacteristic
238C2×C3×C4(C2×D3)⋊C411yescharacteristic
239C2×C3×C4(C2×D3)⋊C411yescharacteristic
240C2×C3×C4(C2×D3)⋊C411yescharacteristic
241C2×C3×C4(C2×D3)⋊C411yescharacteristic
242C2×C3×C4#21311yescharacteristic
243C2×C3×C4#21511yescharacteristic
244C2×C3×C4#21511yescharacteristic
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247#67—124no—
248#67—124no—
249#67—122no—
250#67—122no—
251#67—122no—
252#67—122no—
253C2×Dic3—42no—
254C2×Dic3—82no—
255C2×Dic3—122no—
256C2×Dic3—121no—
257C2×Dic3—121no—
258D12—64no—
259D12—62no—
260D12—62no—
261D12—122no—
262D12—121no—
263D12—121no—
264C4×D3—124no—
265C4×D3—124no—
266C4×D3—122no—
267C4×D3—122no—
268C4×D3—122no—
269C4×D3—122no—
270Dic6—64no—
271Dic6—62no—
272Dic6—62no—
273Dic6—122no—
274Dic6—121no—
275Dic6—121no—
276C3×C8—21no—
277C3×C8—21no—
278C3×C8—21no—
279C3×C8—21no—
280C3×C8(C2×D3)⋊C411yescharacteristic
281C3×C8(C2×D3)⋊C411yescharacteristic
282C3×C8(C2×D3)⋊C411yescharacteristic
283C3×C8(C2×D3)⋊C411yescharacteristic
284C3×C8C2×C4×D311yescharacteristic
285C3×C8C2×C4×D311yescharacteristic
286C3×C8C2×D1211yescharacteristic
287C3×C8C2×#6711yescharacteristic
288C2×C32—21no—
289C2×C32—21no—
290C2×C32#36012yescomplemented
291C2×C32C2×#10211yescharacteristic
292C3⋊D3—82no—
293#41—182no—
294#41—182no—
295#41—361no—
296#41—361no—
297C2×Q8—181no—
298C2×D4—181no—
299C2×D4—361no—
300C22×C4—121no—
301C22×C4—361no—
302C22×C4#62611yescharacteristic
303Q16—92no—
304Q16—181no—
305SD16—182no—
306SD16—182no—
307D8—92no—
308D8—181no—
309C2×C8#62411yescharacteristic
310C2×C8#62411yescharacteristic
311C2×C8#62611yescharacteristic
312C2×C8#62611yescharacteristic
313C2×C8#62611yescharacteristic
314C2×C8C2×D3211yescharacteristic
315C4⋊C4—62no—
316C4⋊C4—121no—
317C16—62no—
318C22×C3—22no—
319C22×C3—22no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—42no—
324C22×C3#80911yescharacteristic
325C22×C3#80911yescharacteristic
326C22×C3#82111yescharacteristic
327C22×C3#82111yescharacteristic
328C22×C3C2×D2411yescharacteristic
329C22×C3C2×#21311yescharacteristic
330C2×D3—124no—
331C2×D3—122no—
332C2×D3—122no—
333C2×D3—244no—
334C2×D3—242no—
335C2×D3—242no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—242no—
341C3×C4#80911yescharacteristic
342C3×C4#80911yescharacteristic
343C3×C4#82111yescharacteristic
344C3×C4#82111yescharacteristic
345C3×C4C2×#20411yescharacteristic
346C3×C4C2×(C2×D3)⋊C411yescharacteristic
347C3×C4C2×(C2×D3)⋊C411yescharacteristic
348C3×C4C2×#21511yescharacteristic
349Dic3—82no—
350Dic3—124no—
351Dic3—122no—
352Dic3—122no—
353C32C2×#36011yescharacteristic, complemented, Sylow
354C23—361no—
355C23#371411yescharacteristic
356Q8—182no—
357Q8—361no—
358D4—182no—
359D4—362no—
360D4—362no—
361D4—361no—
362C2×C4—122no—
363C2×C4—242no—
364C2×C4—361no—
365C2×C4—362no—
366C2×C4—362no—
367C2×C4#371411yescharacteristic
368C2×C4#371711yescharacteristic
369C2×C4#371711yescharacteristic
370C2×C4#372211yescharacteristic
371C2×C4#372211yescharacteristic
372C2×C4C2×#62611yescharacteristic
373C8#372211yescharacteristic
374C8#372211yescharacteristic
375C8C2×#62411yescharacteristic
376C8C2×#62611yescharacteristic
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—22no—
383C2×C3—41no—
384C2×C3—41no—
385C2×C3#448812yescomplemented
386C2×C3#451812yescomplemented
387C2×C3C2×#80911yescharacteristic
388C2×C3C2×#82111yescharacteristic
389D3—244no—
390D3—242no—
391D3—242no—
392C22—22no—
393C22—362no—
394C22—722no—
395C22#6356411yescharacteristic
396C22#6356411yescharacteristic
397C22C2×#371411yescharacteristic
398C4—242no—
399C4—362no—
400C4#6356411yescharacteristic
401C4#6356411yescharacteristic
402C4C2×#371711yescharacteristic
403C4C2×#372211yescharacteristic
404C3—21no—
405C3C2×#448811yescharacteristic, complemented
406C3C2×#451811yescharacteristic, complemented
407C2—21no—
408C2—21no—
409C2—722no—
410C2#1058912512yesdirect product factor
411C2C2×#6356411yescharacteristic
subgroupG/H
centerC22#63564
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC22×C32×C8C22
socleC22×C32#102
prime radicalC2×#64113C2
cosocleC2×C32×C8C23
hypercenterC22×C8D32
hypocenterC32C2×#360
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#817C2semidirect
3. C2×C3×#812C2semidirect
4. #10589125C2direct (N × H)
9. C2×#3746C4semidirect
12. #64113C4semidirect
14. C2×#3745C4semidirect
18. C3×#817C22semidirect
20. C3×#812C22semidirect
27. C2×#817D3semidirect
28. C2×#812D3semidirect
48. #3746C2×C4semidirect
50. #3745C2×C4semidirect
92. #817C2×D3semidirect
94. #812C2×D3semidirect
290. C2×C32#360semidirect
353. C32C2×#360semidirect
385. C2×C3#4488semidirect
386. C2×C3#4518semidirect
405. C3C2×#4488semidirect
406. C3C2×#4518semidirect
410. C2#10589125direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641132
C2×C3×#8172
C2×C3×#8122
#105891252
C2×#45183
C2×#44883