Finite Group Databasebeta

← C2×#10590660 #11858754

Subgroups — C2×#10590660 #11858754

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×Dic3C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×C3×#815C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590660C218yesmaximal, direct product factor
9C2×#4719—31nomaximal
10C2×#4705—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3C411yescharacteristic
13C22×D3×Dic3C411yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×Dic32C411yescharacteristic
21C2×Dic32C411yescharacteristic
22C4×D3×Dic3C414yes—
23C4×D3×Dic3C2214yes—
24#63641C2214yescomplemented
25C3×(C2×D3)⋊C8C2214yes—
26C3×#815C2214yescomplemented
27#63572C2214yescomplemented
28(C2×D3)⋊(C3⋊C8)C2214yes—
29#63554C2214yescomplemented
30C22×C4×Dic3—31no—
31C2×C42×D3—31no—
32C2×C3×C22⋊C8—31no—
33C2×C3×#97—31no—
34C2×#830—31no—
35C2×(C2×D3)⋊C8—31no—
36C2×(C2×D3)⋊C8D311yescharacteristic
37C2×#815—31no—
38C2×#815D311yescharacteristic, complemented
39C2×Dic3⋊C8—31no—
40C2×Dic3⋊C8—31no—
41C2×Dic3⋊C8—31no—
42C2×Dic3⋊C8—31no—
43C2×Dic3⋊C8—61no—
44C2×#803—31no—
45#4719—38no—
46#4705—38no—
47C23×C3×D3C2×C411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3C2×C411yescharacteristic
50C22×C3⋊Dic3C2×C411yescharacteristic
51C22×C3×Dic3C2×C411yescharacteristic
52C22×C3×Dic3C2×C411yescharacteristic
53C22×C3×Dic3C2×C411yescharacteristic
54C2×C3×C4×D3—22no—
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3C2×C412yes—
57C2×C3×C4×D3C2312yes—
58C2×D3×Dic3—24no—
59C2×D3×Dic3—24no—
60C2×D3×Dic3C2×C414yes—
61C2×D3×Dic3C2×C414yes—
62C2×C32×C8—22no—
63C2×C32×C8C2312yes—
64C4×C3⋊Dic3C2×C412yes—
65C4×C3⋊Dic3C2312yes—
66C2×C3⋊(C3⋊C8)—22no—
67C2×C3⋊(C3⋊C8)C2312yes—
68C3×C4×Dic3C2×C412yes—
69C3×C4×Dic3C2312yes—
70C2×C3×C3⋊C8—22no—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8C2312yes—
73C2×C3×C3⋊C8C2312yes—
74Dic32C2×C414yes—
75Dic32C2×C414yes—
76C2×#432—91noSylow
77C23×C3×C4—31no—
78C23×Dic3—31no—
79C23×Dic3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—31no—
82C22×C4×D3C2×D311yescharacteristic
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8—31no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C42—31no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—34no—
96C2×C4×Dic3—34no—
97C2×C4×Dic3—61no—
98C2×C4×Dic3C2×D311yescharacteristic
99C22×C3⋊C8—31no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—61no—
102C22×C3⋊C8C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104C42×D3—34no—
105C42×D3—34no—
106C3×C22⋊C8—34no—
107C3×#97—34no—
108#830—34no—
109(C2×D3)⋊C8—34no—
110(C2×D3)⋊C8C2×D314yes—
111#815—34no—
112#815C2×D314yescomplemented
113Dic3⋊C8—34no—
114Dic3⋊C8—34no—
115Dic3⋊C8—34no—
116Dic3⋊C8—34no—
117Dic3⋊C8—64no—
118#803—34no—
119C23×C32C22×C411yescharacteristic
120C22×C3×D3—22no—
121C22×C3×D3—22no—
122C22×C3×D3M1614yes—
123C22×C3×D3C22×C412yes—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4#4112yes—
126C2×C32×C4#4112yes—
127C2×C32×C4C2411yescharacteristic
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3M1614yes—
130C2×C3⋊Dic3C22×C412yes—
131C2×C3⋊Dic3C22×C412yes—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3C22×C412yes—
136C2×C3×Dic3C22×C412yes—
137C2×C3×Dic3C22×C412yes—
138C3×C4×D3—24no—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141D3×Dic3—28no—
142D3×Dic3—28no—
143C32×C8—22no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—22no—
147C22×C42—91no—
148#432—98no—
149C2×C4⋊C8—91no—
150C2×C4⋊C8—91no—
151C2×C22⋊C8—31no—
152C2×C22⋊C8—91no—
153C2×#97—31no—
154C2×#97—91no—
155C24×C3—31no—
156C23×D3C4×D311yescharacteristic
157C22×C3×C4—21no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—32no—
162C22×C3×C4—32no—
163C22×C3×C4—62no—
164C22×C3×C4—62no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C22×Dic3—31no—
168C22×Dic3—31no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—34no—
172C22×Dic3—34no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—64no—
176C22×Dic3—64no—
177C22×Dic3C4×D311yescharacteristic
178C22×Dic3C4×D311yescharacteristic
179C22×Dic3C4×D311yescharacteristic
180C2×C4×D3—22no—
181C2×C4×D3—22no—
182C2×C4×D3—34no—
183C2×C4×D3—34no—
184C2×C4×D3—64no—
185C2×C4×D3—64no—
186C2×C4×D3C4×D312yes—
187C2×C4×D3C22×D312yes—
188C2×C3×C8—22no—
189C2×C3×C8—22no—
190C2×C3×C8—22no—
191C2×C3×C8—32no—
192C2×C3×C8—32no—
193C2×C3×C8—42no—
194C2×C3×C8—62no—
195C2×C3×C8—62no—
196C2×C3×C8C22×D312yes—
197C2×C3×C8C22×D312yes—
198C3×C42—32no—
199C3×C42—32no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—32no—
203C4×Dic3—32no—
204C4×Dic3—34no—
205C4×Dic3—34no—
206C4×Dic3—34no—
207C4×Dic3—34no—
208C4×Dic3—62no—
209C4×Dic3—62no—
210C4×Dic3C4×D312yes—
211C4×Dic3C22×D312yes—
212C2×C3⋊C8—22no—
213C2×C3⋊C8—22no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—32no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—62no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—122no—
220C2×C3⋊C8C22×D312yes—
221C2×C3⋊C8C22×D312yes—
222C22×C32#11712yes—
223C22×C32C2×M1612yes—
224C22×C32C2×M1612yes—
225C22×C32C23×C411yescharacteristic
226C2×C3×D3—22no—
227C2×C3×D3—22no—
228C2×C3×D3—28no—
229C2×C3×D3C2×M1614yes—
230C32×C4#11712yes—
231C32×C4C2×#4111yescharacteristic
232C32×C4C2×#4111yescharacteristic
233C3⋊Dic3—22no—
234C3⋊Dic3C2×M1614yes—
235C3×Dic3—22no—
236C3×Dic3—22no—
237C3×Dic3—22no—
238C23×C4—31no—
239C23×C4—91no—
240C23×C4—91no—
241C22×C8—31no—
242C22×C8—31no—
243C22×C8—91no—
244C22×C8D3211yescharacteristic
245C2×C42—31no—
246C2×C42—94no—
247C2×C42—94no—
248C2×C42—91no—
249C2×C42—91no—
250C2×C42—91no—
251C4⋊C8—94no—
252C4⋊C8—94no—
253C22⋊C8—34no—
254C22⋊C8—94no—
255#97—34no—
256#97—94no—
257C23×C3—21no—
258C23×C3—34no—
259C23×C3—32no—
260C23×C3—62no—
261C23×C3—62no—
262C23×C3C2×C4×D311yescharacteristic
263C23×C3C2×C4×D311yescharacteristic
264C22×D3—22no—
265C22×D3—22no—
266C22×D3ΓL(1,𝔽25)14yes—
267C22×D3C2×C4×D312yes—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—22no—
272C2×C3×C4—32no—
273C2×C3×C4—32no—
274C2×C3×C4—32no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—64no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4#23512yes—
284C2×C3×C4#23512yes—
285C2×C3×C4#23712yes—
286C2×C3×C4#23712yes—
287C2×C3×C4C23×D311yescharacteristic
288C2×C3×C4C23×D311yescharacteristic
289C2×Dic3—22no—
290C2×Dic3—22no—
291C2×Dic3—22no—
292C2×Dic3—34no—
293C2×Dic3—34no—
294C2×Dic3—32no—
295C2×Dic3—32no—
296C2×Dic3—32no—
297C2×Dic3—32no—
298C2×Dic3—64no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—68no—
302C2×Dic3—68no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—122no—
306C2×Dic3C2×C4×D312yes—
307C2×Dic3C2×C4×D312yes—
308C2×Dic3C2×C4×D312yes—
309C4×D3—24no—
310C4×D3—22no—
311C4×D3—22no—
312C4×D3—68no—
313C4×D3—68no—
314C3×C8—22no—
315C3×C8—22no—
316C3×C8—42no—
317C3×C8—62no—
318C3×C8—62no—
319C3⋊C8—22no—
320C3⋊C8—22no—
321C3⋊C8—62no—
322C3⋊C8—62no—
323C3⋊C8—122no—
324C2×C32#43214yescomplemented
325C2×C32C2×#11711yescharacteristic
326C2×C32C22×M1611yescharacteristic
327C2×C32C22×M1611yescharacteristic
328C3×D3—24no—
329C24—31no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—32no—
334C22×C4—32no—
335C22×C4—62no—
336C22×C4—62no—
337C22×C4—94no—
338C22×C4—94no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—184no—
342C22×C4—184no—
343C22×C4C2×D3211yescharacteristic
344C2×C8—22no—
345C2×C8—32no—
346C2×C8—32no—
347C2×C8—62no—
348C2×C8—62no—
349C2×C8—92no—
350C2×C8—182no—
351C2×C8C2×D3212yes—
352C42—32no—
353C42—32no—
354C42—94no—
355C42—94no—
356C42—92no—
357C42—92no—
358C22×C3—22no—
359C22×C3—21no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—34no—
363C22×C3—62no—
364C22×C3—68no—
365C22×C3—62no—
366C22×C3#87212yes—
367C22×C3#87712yes—
368C22×C3C2×ΓL(1,𝔽25)12yes—
369C22×C3D3×M1612yes—
370C22×C3D3×M1612yes—
371C22×C3D3×M1612yes—
372C22×C3C22×C4×D311yescharacteristic
373C22×C3C22×C4×D311yescharacteristic
374C2×D3—22no—
375C2×D3—28no—
376C2×D3—22no—
377C2×D3C2×ΓL(1,𝔽25)14yes—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—22no—
381C3×C4—62no—
382C3×C4—62no—
383C3×C4—62no—
384C3×C4#87212yes—
385C3×C4#87712yes—
386C3×C4C2×#23511yescharacteristic
387C3×C4C2×#23511yescharacteristic
388C3×C4C2×#23711yescharacteristic
389C3×C4C2×#23711yescharacteristic
390Dic3—22no—
391Dic3—22no—
392Dic3—22no—
393Dic3—34no—
394Dic3—34no—
395Dic3—64no—
396Dic3—62no—
397Dic3—62no—
398Dic3—122no—
399C32C2×#43211yescharacteristic, complemented, Sylow
400C23—34no—
401C23—32no—
402C23—62no—
403C23—62no—
404C23C4×D3211yescharacteristic
405C2×C4—32no—
406C2×C4—32no—
407C2×C4—32no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—64no—
414C2×C4—92no—
415C2×C4—94no—
416C2×C4—92no—
417C2×C4—188no—
418C2×C4—188no—
419C2×C4—182no—
420C2×C4#379512yes—
421C2×C4C4×D3211yescharacteristic
422C2×C4#380412yes—
423C2×C4C22×D3211yescharacteristic
424C8—22no—
425C8—62no—
426C8—62no—
427C8—182no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—24no—
432C2×C3—64no—
433C2×C3#470514yescomplemented
434C2×C3#471914yescomplemented
435C2×C3C2×#87211yescharacteristic
436C2×C3C2×#87711yescharacteristic
437C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
438C2×C3C2×D3×M1611yescharacteristic
439C2×C3C2×D3×M1611yescharacteristic
440C2×C3C2×D3×M1611yescharacteristic
441D3—24no—
442C22—34no—
443C22—62no—
444C22—62no—
445C22—68no—
446C22D3×ΓL(1,𝔽25)12yes—
447C22#6379112yes—
448C22#6387712yes—
449C22C2×C4×D3211yescharacteristic
450C4—62no—
451C4—62no—
452C4—62no—
453C4—94no—
454C4—182no—
455C4#6387712yes—
456C4C2×#379511yescharacteristic
457C4C2×#380411yescharacteristic
458C3—21no—
459C3C2×#470511yescharacteristic, complemented
460C3C2×#471911yescharacteristic, complemented
461C2—64no—
462C2#1059066014yesdirect product factor
463C2C2×D3×ΓL(1,𝔽25)11yescharacteristic
464C2C2×#6379111yescharacteristic
465C2C2×#6387711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#432
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63641C2semidirect
4. C2×C3×#815C2semidirect
5. C2×#63572C2semidirect
7. C2×#63554C2semidirect
8. #10590660C2direct (N × H)
24. #63641C22semidirect
26. C3×#815C22semidirect
27. #63572C22semidirect
29. #63554C22semidirect
38. C2×#815D3semidirect
112. #815C2×D3semidirect
324. C2×C32#432semidirect
399. C32C2×#432semidirect
433. C2×C3#4705semidirect
434. C2×C3#4719semidirect
459. C3C2×#4705semidirect
460. C3C2×#4719semidirect
462. C2#10590660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D3×Dic32
C2×#636412
C2×C3×(C2×D3)⋊C82
C2×C3×#8152
C2×#635722
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635542
#105906602
C2×#47193
C2×#47053