Finite Group Databasebeta

← C2×#10590308 #11868353

Subgroups — C2×#10590308 #11868353

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×C3×#870C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4C2×#63575C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C2×#63564C211yesmaximal, characteristic
8#10590308C218yesmaximal, direct product factor
9C2×#5066—31nomaximal
10C2×#4847—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×C32×C42C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C4×C4⋊(C3⋊D3)—22no—
17C4×C4⋊(C3⋊D3)C2214yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×Dic3⋊C4—21no—
21C2×C3×Dic3⋊C4—21no—
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#870—22no—
25C3×#870C2214yescomplemented
26C3×C4⋊(C3⋊C8)C2214yescomplemented
27#63575C2214yescomplemented
28#63573C2214yescomplemented
29#63564C2214yes—
30#63564C2214yes—
31C2×C3×#125—31no—
32C2×C4×D12—31no—
33C2×C4×D12—31no—
34C2×C4×D12—61no—
35C2×#870D311yescharacteristic, complemented
36C2×C3×C4⋊C8—31no—
37C2×#821—31no—
38C2×#821—31no—
39C2×#818—31no—
40C2×#817—31no—
41#5066—38no—
42C2×#809—31no—
43C2×#809—31no—
44C2×#808—31no—
45C2×#807—31no—
46C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
47#4847—38no—
48C23×C3⋊D3—21no—
49C22×C32×C4D411yescharacteristic
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)Q814yes—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4×C3⋊D3—24no—
58C2×C4×C3⋊D3—44no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C32×C42D412yes—
62C32×C42C2312yes—
63#3752—24no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2312yes—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—24no—
71C3×Dic3⋊C4—24no—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76C2×#478—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C22×C4×D3—62no—
81C22×C4×D3—61no—
82C22×C4×D3—61no—
83C22×C3×C8—31no—
84C22×C3×C8—31no—
85C3×#125—34no—
86C3×#125—62no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—61no—
90C2×C3×C4⋊C4—61no—
91C2×C3×C42—21no—
92C2×C3×C42C2×D311yescharacteristic
93C2×C3×C42C2×D311yescharacteristic
94C2×(C2×D3)⋊C4—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—21no—
103C2×Dic3⋊C4—21no—
104C22×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C4×D12—34no—
107C4×D12—34no—
108C4×D12—64no—
109C4×D12—64no—
110C4×D12—62no—
111C4×D12—62no—
112#870—22no—
113#870C2×D314yescomplemented
114C3×C4⋊C8—34no—
115#821—34no—
116#821—34no—
117#818—34no—
118#817—34no—
119#809—34no—
120#809—34no—
121#808—34no—
122#807—34no—
123C4⋊(C3⋊C8)C2×D314yescomplemented
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—24no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—42no—
128C22×C3⋊D3—42no—
129C2×C32×C4—22no—
130C2×C32×C4—22no—
131C2×C32×C4C2×D412yes—
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×Q812yes—
135C2×C32×C4#4112yes—
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—42no—
139C4⋊(C3⋊D3)—24no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)C2×Q814yes—
142C4×C3⋊D3—48no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—22no—
149C2×#125—31no—
150C2×C4×D4—91no—
151#478—98no—
152C2×#107—91no—
153C2×#106—91no—
154C2×C4⋊C8—31no—
155C2×#102—91no—
156C2×#102—91no—
157C23×D3—62no—
158C23×D3—61no—
159C23×D3—61no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4D1211yescharacteristic
166C22×C3×C4D1211yescharacteristic
167C22×C3×C4#6711yescharacteristic
168C22×C3×C4#6711yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—62no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C2×D12—34no—
177C2×D12—34no—
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—62no—
181C2×D12—64no—
182C2×D12—62no—
183C2×D12—64no—
184C2×D12—61no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12—61no—
188C2×C4×D3—68no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—128no—
192C2×C4×D3—124no—
193C2×C4×D3—124no—
194C2×C3×C8—32no—
195C2×C3×C8—32no—
196C2×C3×C8—62no—
197C2×C3×C8—62no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—64no—
201C3×C4⋊C4—64no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C42—22no—
205C3×C42—22no—
206C3×C42D1212yes—
207C3×C42#6712yes—
208C3×C42C22×D312yes—
209C3×C42C22×D312yes—
210(C2×D3)⋊C4—68no—
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—64no—
213C4⋊Dic3—21no—
214C4⋊Dic3—21no—
215C4⋊Dic3—32no—
216C4⋊Dic3—32no—
217C4⋊Dic3—62no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3C22×D312yes—
222C4⋊Dic3C22×D312yes—
223Dic3⋊C4—24no—
224Dic3⋊C4—24no—
225C2×C3⋊C8—22no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8C22×D312yes—
228C2×C3⋊C8C22×D312yes—
229C22×C32C22⋊Q812yes—
230C22×C32#13512yes—
231C22×C32AGL(1,ℤ/8)12yes—
232C22×C32C22×D411yescharacteristic
233C2×C3⋊D3—24no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3—48no—
237C32×C4—22no—
238C32×C4—22no—
239C32×C4C22⋊Q812yes—
240C32×C4C22×Q811yescharacteristic
241C32×C4C2×#4111yescharacteristic
242C3⋊Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C22×D4—91no—
246C23×C4—181no—
247C22×C8—31no—
248C22×C8—31no—
249#125—34no—
250#125—62no—
251C4×D4—94no—
252C4×D4—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—61no—
256C2×C4⋊C4—61no—
257C2×C4⋊C4—91no—
258C2×C22⋊C4—181no—
259C2×C42D3211yescharacteristic
260#107—94no—
261#106—94no—
262C4⋊C8—34no—
263#102—94no—
264#102—94no—
265C23×C3—21no—
266C23×C3C2×D1211yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C22×D3—64no—
269C22×D3—68no—
270C22×D3—64no—
271C22×D3—64no—
272C22×D3—62no—
273C22×D3—62no—
274C22×D3—124no—
275C22×D3—124no—
276C22×D3—122no—
277C22×D3—122no—
278C22×D3—122no—
279C22×D3—122no—
280C2×C3×C4—24no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—42no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—122no—
295C2×C3×C4—122no—
296C2×C3×C4C2×D1212yes—
297C2×C3×C4C2×D1212yes—
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4#23712yes—
300C2×C3×C4D3×Q812yes—
301C2×C3×C4D3×Q812yes—
302C2×C3×C4#23912yes—
303C2×C3×C4C2×#6712yes—
304C2×C3×C4C2×#6712yes—
305C2×C3×C4C2×#6711yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×C3×C4C23×D311yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—64no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—124no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318D12—34no—
319D12—34no—
320D12—64no—
321D12—64no—
322D12—68no—
323D12—64no—
324D12—64no—
325D12—62no—
326D12—62no—
327C4×D3—1216no—
328C4×D3—128no—
329C4×D3—128no—
330C3×C8—62no—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—22no—
334C2×C32#47814yescomplemented
335C2×C32C2×C22⋊Q811yescharacteristic
336C2×C32C2×#13511yescharacteristic
337C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
338C3⋊D3—44no—
339C24—181no—
340C2×D4—92no—
341C2×D4—94no—
342C2×D4—182no—
343C2×D4—181no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—181no—
347C22×C4—184no—
348C22×C4—364no—
349C22×C4#62611yescharacteristic
350C22×C4#62611yescharacteristic
351C22×C4C2×D3211yescharacteristic
352C2×C8—32no—
353C2×C8—32no—
354C2×C8—62no—
355C2×C8—62no—
356C4⋊C4—32no—
357C4⋊C4—32no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—64no—
361C4⋊C4—64no—
362C4⋊C4—92no—
363C4⋊C4—181no—
364C22⋊C4—184no—
365C42#62612yes—
366C42C2×D3212yes—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3#89712yes—
372C22×C3#90412yes—
373C22×C3#90812yes—
374C22×C3#94612yes—
375C22×C3#94912yes—
376C22×C3#95012yes—
377C22×C3C22×D1211yescharacteristic
378C22×C3C22×#6711yescharacteristic
379C2×D3—68no—
380C2×D3—64no—
381C2×D3—64no—
382C2×D3—124no—
383C2×D3—1216no—
384C2×D3—124no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—128no—
390C2×D3—128no—
391C3×C4—24no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—22no—
395C3×C4—22no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—22no—
399C3×C4—42no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4#89712yes—
403C3×C4#94612yes—
404C3×C4C2×#23711yescharacteristic
405C3×C4C2×D3×Q811yescharacteristic
406C3×C4C2×D3×Q811yescharacteristic
407C3×C4C2×#23911yescharacteristic
408Dic3—42no—
409Dic3—42no—
410Dic3—124no—
411Dic3—122no—
412Dic3—122no—
413C32C2×#47811yescharacteristic, complemented, Sylow
414C23—182no—
415C23—184no—
416C23—362no—
417C23—362no—
418C23C2×#62611yescharacteristic
419D4—94no—
420D4—182no—
421D4—184no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—122no—
427C2×C4—122no—
428C2×C4—182no—
429C2×C4—368no—
430C2×C4—362no—
431C2×C4#379612yes—
432C2×C4#379712yes—
433C2×C4C2×#62612yes—
434C2×C4C2×#62612yes—
435C2×C4C2×#62611yescharacteristic
436C2×C4C22×D3211yescharacteristic
437C8—62no—
438C8—62no—
439C2×C3—21no—
440C2×C3—24no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3#484714yescomplemented
444C2×C3#506614yescomplemented
445C2×C3C2×#89711yescharacteristic
446C2×C3C2×#90411yescharacteristic
447C2×C3C2×#90811yescharacteristic
448C2×C3C2×#94611yescharacteristic
449C2×C3C2×#94911yescharacteristic
450C2×C3C2×#95011yescharacteristic
451D3—128no—
452D3—124no—
453D3—124no—
454C22—184no—
455C22—368no—
456C22—362no—
457C22—362no—
458C22#6382512yes—
459C22#6382912yes—
460C22#6387112yes—
461C22C22×#62611yescharacteristic
462C4—22no—
463C4—22no—
464C4—122no—
465C4—122no—
466C4—362no—
467C4#6387112yes—
468C4C2×#379611yescharacteristic
469C4C2×#379711yescharacteristic
470C3—21no—
471C3C2×#484711yescharacteristic, complemented
472C3C2×#506611yescharacteristic, complemented
473C2—364no—
474C2#1059030814yesdirect product factor
475C2C2×#6382511yescharacteristic
476C2C2×#6382911yescharacteristic
477C2C2×#6387111yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#870C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. C2×#63575C2semidirect
5. C2×#63573C2semidirect
8. #10590308C2direct (N × H)
25. C3×#870C22semidirect
26. C3×C4⋊(C3⋊C8)C22semidirect
27. #63575C22semidirect
28. #63573C22semidirect
35. C2×#870D3semidirect
46. C2×C4⋊(C3⋊C8)D3semidirect
113. #870C2×D3semidirect
123. C4⋊(C3⋊C8)C2×D3semidirect
334. C2×C32#478semidirect
413. C32C2×#478semidirect
443. C2×C3#4847semidirect
444. C2×C3#5066semidirect
471. C3C2×#4847semidirect
472. C3C2×#5066semidirect
474. C2#10590308direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×#8702
C2×C3×C4⋊(C3⋊C8)2
C2×#635752
C2×#635732
C2×#635642
#105903082
C2×#50663
C2×#48473