Finite Group Databasebeta

← C2×#10590253 #11858803

Subgroups — C2×#10590253 #11858803

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#872C211yesmaximal, characteristic
2C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
5C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
6C2×#63554C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590253C218yesmaximal, direct product factor
9C2×#5000—31nomaximal
10C2×#4840—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4C411yescharacteristic
16C2×C3×(C2×D3)⋊C4C411yescharacteristic
17C2×C3×Dic3⋊C4C411yescharacteristic
18C2×C3×Dic3⋊C4C411yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#872C414yes—
23C3×#872C2214yes—
24C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
25C3×C4⋊(C3⋊C8)C2214yescomplemented
26(C2×D3)⋊(C3⋊C8)C2214yes—
27(C2×D3)⋊(C3⋊C8)C2214yes—
28#63554C2214yescomplemented
29Dic3×C3⋊C8C2214yescomplemented
30C2×C3×#117—31no—
31C2×#872D311yescharacteristic
32C2×C3×C4⋊C8—31no—
33C2×#830—31no—
34C2×#830—31no—
35C2×(C2×D3)⋊C8—31no—
36C2×(C2×D3)⋊C8—31no—
37C2×#815—31no—
38C2×C8×Dic3—31no—
39#5000—38no—
40C2×C4⋊(C3⋊C8)—31no—
41C2×C4⋊(C3⋊C8)—31no—
42C2×C4⋊(C3⋊C8)—61no—
43C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
44C2×#803—31no—
45C2×C4×C3⋊C8—31no—
46#4840—38no—
47C23×C3×D3C2×C411yescharacteristic
48C22×C32×C4C2×C411yescharacteristic
49C22×C32×C4C2×C411yescharacteristic
50C22×C32×C4C2311yescharacteristic
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—
58C32×C42C2×C412yes—
59C32×C42C2312yes—
60C2×C3⋊(C3⋊C8)—22no—
61C2×C3⋊(C3⋊C8)—22no—
62C2×C3⋊(C3⋊C8)C2312yes—
63C2×C3⋊(C3⋊C8)C2312yes—
64C3×(C2×D3)⋊C4C2×C414yes—
65C3×(C2×D3)⋊C4C2×C414yes—
66C3×Dic3⋊C4C2×C414yes—
67C3×Dic3⋊C4C2×C414yes—
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—
74C2×#433—91noSylow
75C23×C3×C4—31no—
76C22×C4×D3C2×D311yescharacteristic
77C22×C3×C8—31no—
78C22×C3×C8—31no—
79C3×#117—34no—
80C3×#117—34no—
81C2×C3×C4⋊C4—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C22⋊C4—31no—
84C2×C3×C22⋊C4—31no—
85C2×C3×C42—21no—
86C2×C3×C42—31no—
87C2×C3×C42C2×D311yescharacteristic
88C2×C3×C42C2×D311yescharacteristic
89C2×(C2×D3)⋊C4Dic311yescharacteristic
90C2×(C2×D3)⋊C4Dic311yescharacteristic
91C2×Dic3⋊C4Dic311yescharacteristic
92C2×Dic3⋊C4Dic311yescharacteristic
93C2×C4×Dic3C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—31no—
97C22×C3⋊C8—31no—
98C22×C3⋊C8—61no—
99C22×C3⋊C8—61no—
100C22×C3⋊C8C2×D311yescharacteristic
101C22×C3⋊C8C2×D311yescharacteristic
102#872Dic314yes—
103#872C2×D314yes—
104C3×C4⋊C8—34no—
105#830—34no—
106#830—34no—
107(C2×D3)⋊C8—34no—
108(C2×D3)⋊C8—34no—
109#815—34no—
110C8×Dic3—34no—
111C4⋊(C3⋊C8)—34no—
112C4⋊(C3⋊C8)—34no—
113C4⋊(C3⋊C8)—64no—
114C4⋊(C3⋊C8)C2×D314yescomplemented
115#803—34no—
116C4×C3⋊C8—34no—
117C23×C32C22×C411yescharacteristic
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—22no—
121C22×C3×D3C22×C412yes—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C22×C412yes—
125C2×C32×C4C22×C412yes—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4#4112yes—
128C2×C32×C4#4112yes—
129C2×C32×C4C2411yescharacteristic
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3C22×C412yes—
134C2×C3×Dic3C22×C412yes—
135C2×C3×Dic3C22×C412yes—
136C3×C4×D3—24no—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3⋊(C3⋊C8)—22no—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—22no—
143C2×#117—31no—
144#433—98no—
145C2×C4⋊C8—31no—
146C2×C4⋊C8—91no—
147C2×C22⋊C8—91no—
148C2×C22⋊C8—91no—
149C2×#97—91no—
150C2×C4×C8—91no—
151C24×C3—31no—
152C23×D3C2×Dic311yescharacteristic
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—32no—
160C22×C3×C4—32no—
161C22×C3×C4—62no—
162C22×C3×C4—62no—
163C22×C3×C4C4×D311yescharacteristic
164C22×C3×C4C4×D311yescharacteristic
165C22×C3×C4C2×Dic311yescharacteristic
166C22×C3×C4C2×Dic311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3C2×Dic311yescharacteristic
170C22×Dic3C2×Dic311yescharacteristic
171C22×Dic3C2×Dic311yescharacteristic
172C2×C4×D3—22no—
173C2×C4×D3—22no—
174C2×C4×D3C2×Dic312yes—
175C2×C4×D3C22×D312yes—
176C2×C3×C8—32no—
177C2×C3×C8—32no—
178C2×C3×C8—62no—
179C2×C3×C8—62no—
180C3×C4⋊C4—34no—
181C3×C4⋊C4—34no—
182C3×C22⋊C4—34no—
183C3×C22⋊C4—34no—
184C3×C42—22no—
185C3×C42—22no—
186C3×C42—32no—
187C3×C42—32no—
188C3×C42C4×D312yes—
189C3×C42C2×Dic312yes—
190C3×C42C22×D312yes—
191C3×C42C22×D312yes—
192(C2×D3)⋊C4C2×Dic314yes—
193(C2×D3)⋊C4C2×Dic314yes—
194Dic3⋊C4C2×Dic314yes—
195Dic3⋊C4C2×Dic314yes—
196C4×Dic3C2×Dic312yes—
197C4×Dic3C22×D312yes—
198C2×C3⋊C8—22no—
199C2×C3⋊C8—22no—
200C2×C3⋊C8—32no—
201C2×C3⋊C8—32no—
202C2×C3⋊C8—32no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—62no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—62no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—62no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—122no—
211C2×C3⋊C8—122no—
212C2×C3⋊C8C22×D312yes—
213C2×C3⋊C8C22×D312yes—
214C22×C32#11712yes—
215C22×C32#13112yes—
216C22×C32#13112yes—
217C22×C32C23×C411yescharacteristic
218C2×C3×D3—22no—
219C2×C3×D3—22no—
220C2×C3×D3—22no—
221C2×C3×D3—44no—
222C32×C4—22no—
223C32×C4—22no—
224C32×C4#11712yes—
225C32×C4C2×#4111yescharacteristic
226C32×C4C2×#4111yescharacteristic
227C3×Dic3—22no—
228C3×Dic3—22no—
229C3×Dic3—22no—
230C23×C4—31no—
231C22×C8—31no—
232C22×C8—31no—
233C22×C8—91no—
234C22×C8—91no—
235#117—34no—
236#117—34no—
237C2×C4⋊C4—31no—
238C2×C4⋊C4—31no—
239C2×C22⋊C4—31no—
240C2×C22⋊C4—31no—
241C2×C42—31no—
242C2×C42D3211yescharacteristic
243C4⋊C8—34no—
244C4⋊C8—94no—
245C22⋊C8—94no—
246C22⋊C8—94no—
247#97—94no—
248C4×C8—94no—
249C23×C3—21no—
250C23×C3—32no—
251C23×C3—62no—
252C23×C3—62no—
253C23×C3—62no—
254C23×C3C2×C4×D311yescharacteristic
255C23×C3C22×Dic311yescharacteristic
256C22×D3—22no—
257C22×D3—22no—
258C22×D3—22no—
259C22×D3C22×Dic312yes—
260C2×C3×C4—24no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—21no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—32no—
272C2×C3×C4—32no—
273C2×C3×C4—32no—
274C2×C3×C4—42no—
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×D312yes—
282C2×C3×C4C2×C4×D312yes—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4#23512yes—
285C2×C3×C4#23512yes—
286C2×C3×C4#23712yes—
287C2×C3×C4#23912yes—
288C2×C3×C4C22×Dic312yes—
289C2×C3×C4C22×Dic312yes—
290C2×C3×C4C22×Dic311yescharacteristic
291C2×C3×C4C23×D311yescharacteristic
292C2×C3×C4C23×D311yescharacteristic
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3C22×Dic312yes—
297C2×Dic3C22×Dic312yes—
298C2×Dic3C22×Dic312yes—
299C4×D3—24no—
300C4×D3—22no—
301C4×D3—22no—
302C3×C8—62no—
303C3×C8—62no—
304C3⋊C8—22no—
305C3⋊C8—22no—
306C3⋊C8—62no—
307C3⋊C8—62no—
308C3⋊C8—62no—
309C3⋊C8—62no—
310C3⋊C8—122no—
311C3⋊C8—122no—
312C2×C32#43314yescomplemented
313C2×C32C2×#11711yescharacteristic
314C2×C32C2×#13111yescharacteristic
315C2×C32C2×#13111yescharacteristic
316C3×D3—42no—
317C24—31no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—31no—
321C22×C4—32no—
322C22×C4—32no—
323C22×C4—62no—
324C22×C4—62no—
325C22×C4D3×Dic311yescharacteristic
326C22×C4D3×Dic311yescharacteristic
327C22×C4C2×D3211yescharacteristic
328C2×C8—32no—
329C2×C8—32no—
330C2×C8—62no—
331C2×C8—62no—
332C2×C8—92no—
333C2×C8—92no—
334C2×C8—182no—
335C2×C8—182no—
336C4⋊C4—34no—
337C4⋊C4—34no—
338C22⋊C4—34no—
339C22⋊C4—34no—
340C42—32no—
341C42—32no—
342C42D3×Dic312yes—
343C42C2×D3212yes—
344C22×C3—21no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—62no—
349C22×C3—62no—
350C22×C3—62no—
351C22×C3—124no—
352C22×C3#89212yes—
353C22×C3#90112yes—
354C22×C3#90712yes—
355C22×C3#92612yes—
356C22×C3#94812yes—
357C22×C3#94812yes—
358C22×C3C22×C4×D311yescharacteristic
359C22×C3C23×Dic311yescharacteristic
360C2×D3—22no—
361C2×D3—22no—
362C2×D3—22no—
363C2×D3—44no—
364C3×C4—24no—
365C3×C4—22no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—22no—
372C3×C4—42no—
373C3×C4—62no—
374C3×C4—62no—
375C3×C4—62no—
376C3×C4#89212yes—
377C3×C4#92612yes—
378C3×C4C2×#23511yescharacteristic
379C3×C4C2×#23511yescharacteristic
380C3×C4C2×#23711yescharacteristic
381C3×C4C2×#23911yescharacteristic
382Dic3—22no—
383Dic3—22no—
384Dic3—22no—
385C32C2×#43311yescharacteristic, complemented, Sylow
386C23—32no—
387C23—62no—
388C23—62no—
389C23—62no—
390C23C2×D3×Dic311yescharacteristic
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—32no—
394C2×C4—32no—
395C2×C4—32no—
396C2×C4—62no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—64no—
402C2×C4#379512yes—
403C2×C4#379912yes—
404C2×C4C2×D3×Dic312yes—
405C2×C4C2×D3×Dic312yes—
406C2×C4C2×D3×Dic311yescharacteristic
407C2×C4C22×D3211yescharacteristic
408C8—62no—
409C8—62no—
410C8—182no—
411C8—182no—
412C2×C3—24no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—122no—
417C2×C3#484014yescomplemented
418C2×C3#500014yescomplemented
419C2×C3C2×#89211yescharacteristic
420C2×C3C2×#90111yescharacteristic
421C2×C3C2×#90711yescharacteristic
422C2×C3C2×#92611yescharacteristic
423C2×C3C2×#94811yescharacteristic
424C2×C3C2×#94811yescharacteristic
425D3—42no—
426C22—62no—
427C22—62no—
428C22—62no—
429C22—124no—
430C22#6381412yes—
431C22#6381512yes—
432C22#6384112yes—
433C22C22×D3×Dic311yescharacteristic
434C4—22no—
435C4—22no—
436C4—62no—
437C4—62no—
438C4—62no—
439C4#6384112yes—
440C4C2×#379511yescharacteristic
441C4C2×#379911yescharacteristic
442C3—21no—
443C3C2×#484011yescharacteristic, complemented
444C3C2×#500011yescharacteristic, complemented
445C2—122no—
446C2#1059025314yesdirect product factor
447C2C2×#6381411yescharacteristic
448C2C2×#6381511yescharacteristic
449C2C2×#6384111yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
6. C2×#63554C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590253C2direct (N × H)
24. C4⋊(C3⋊(C3⋊C8))C22semidirect
25. C3×C4⋊(C3⋊C8)C22semidirect
28. #63554C22semidirect
29. Dic3×C3⋊C8C22semidirect
43. C2×C4⋊(C3⋊C8)D3semidirect
114. C4⋊(C3⋊C8)C2×D3semidirect
312. C2×C32#433semidirect
385. C32C2×#433semidirect
417. C2×C3#4840semidirect
418. C2×C3#5000semidirect
443. C3C2×#4840semidirect
444. C3C2×#5000semidirect
446. C2#10590253direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8722
C2×C4⋊(C3⋊(C3⋊C8))2
C2×C3×C4⋊(C3⋊C8)2
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635542
C2×Dic3×C3⋊C82
#105902532
C2×#50003
C2×#48403