Finite Group Databasebeta

← C2×#10590555 #11868261

Subgroups — C2×#10590555 #11868261

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3C2×#63634C211yesmaximal, characteristic, complemented
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C2×#63562C211yesmaximal, characteristic
8#10590555C218yesmaximal, direct product factor
9C2×#5007—31nomaximal
10C2×#4890—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C22×#627—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893—22no—
22C3×#893C2214yes—
23C2×Dic3⋊Dic3—21no—
24#63918—22no—
25#63918C2214yescomplemented
26#63634C2214yescomplemented
27C3×#807C2214yescomplemented
28Dic3⋊(C3⋊C8)C2214yescomplemented
29#63563C2214yes—
30#63562C2214yes—
31C2×C3×C4×D4—31no—
32C2×#893D311yescharacteristic
33C2×#888—31no—
34C2×#869—31no—
35C2×C3×#107—31no—
36C2×#832—31no—
37C2×#832—31no—
38C2×#821—31no—
39C2×Dic3⋊C8—31no—
40#5007—38no—
41C2×#809—31no—
42C2×#807—31no—
43C2×#807—31no—
44C2×#807—61no—
45C2×#807D311yescharacteristic, complemented
46C2×C4⋊(C3⋊C8)—31no—
47#4890—38no—
48C23×C3×D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—22no—
57C2×C3×D12Q814yescomplemented
58C2×C3×D12C2312yes—
59C2×C3×C4×D3—24no—
60C2×C3×C4×D3—44no—
61C2×#627—24no—
62C2×#627—44no—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4×Dic3D412yes—
73C3×C4×Dic3C2312yes—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76Dic3⋊Dic3—24no—
77C2×#474—91noSylow
78C22×C3×D4—31no—
79C23×C3×C4—61no—
80C22×D12C2×D311yescharacteristic
81C22×C4×D3—21no—
82C22×Dic6—61no—
83C22×Dic6—61no—
84C22×C3×C8—31no—
85C3×C4×D4—34no—
86C3×C4×D4—62no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C22⋊C4—61no—
92C2×C3×C42—31no—
93C2×(C2×D3)⋊C4—21no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×C4×Dic3C2×D311yescharacteristic
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—61no—
104C22×C3⋊C8C2×D311yescharacteristic
105#893—22no—
106#893C2×D314yes—
107#888—34no—
108#888—62no—
109#869—34no—
110#869—62no—
111C3×#107—34no—
112#832—34no—
113#832—34no—
114#821—34no—
115Dic3⋊C8—34no—
116#809—34no—
117#807—34no—
118#807—34no—
119#807—64no—
120#807C2×D314yescomplemented
121C4⋊(C3⋊C8)—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—24no—
124C22×C3×D3—22no—
125C22×C3×D3—42no—
126C22×C3×D3—42no—
127C2×C32×C4—22no—
128C2×C32×C4—42no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×Q812yes—
131C2×C32×C4#4112yes—
132C2×C32×C4C2411yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—42no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3D814yes—
139C2×C3×Dic3C2×D412yes—
140C2×C3×Dic3C2×D412yes—
141C3×D12—24no—
142C3×D12—22no—
143C3×D12C2×Q814yescomplemented
144C3×C4×D3—48no—
145#627—48no—
146C3⋊(C3⋊C8)—22no—
147C3×C3⋊C8—22no—
148C2×C4⋊Q8—91no—
149C2×C4×D4—31no—
150#474—98no—
151C2×#107—31no—
152C2×#107—91no—
153C2×C4⋊C8—91no—
154C2×#102—91no—
155C2×#102—91no—
156C24×C3—61no—
157C23×D3—21no—
158C2×C3×D4—34no—
159C2×C3×D4—32no—
160C2×C3×D4—62no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—41no—
168C22×C3×C4—64no—
169C22×C3×C4—61no—
170C22×C3×C4—124no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—121no—
177C22×Dic3#6711yescharacteristic
178C22×Dic3#6711yescharacteristic
179C2×D12—22no—
180C2×D12—21no—
181C2×D12Dic614yescomplemented
182C2×D12C22×D312yes—
183C2×C4×D3—24no—
184C2×C4×D3—44no—
185C2×Dic6—64no—
186C2×Dic6—64no—
187C2×Dic6—124no—
188C2×Dic6—124no—
189C2×C3×C8—32no—
190C2×C3×C8—62no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—22no—
194C3×C4⋊C4—32no—
195C3×C4⋊C4—41no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4C22×D312yes—
198C3×C4⋊C4C22×D312yes—
199C3×C22⋊C4—64no—
200C3×C42—32no—
201C3×C42—32no—
202(C2×D3)⋊C4—24no—
203C4⋊Dic3—21no—
204C4⋊Dic3—32no—
205C4⋊Dic3—32no—
206C4⋊Dic3—62no—
207C4⋊Dic3—64no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—121no—
211C4⋊Dic3C22×D312yes—
212Dic3⋊C4—64no—
213C4×Dic3#6712yes—
214C4×Dic3C22×D312yes—
215C2×C3⋊C8—22no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—64no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8C22×D312yes—
223C22×C32C22⋊Q812yes—
224C22×C32C2×D812yes—
225C22×C32#13712yes—
226C22×C32C22×D411yescharacteristic
227C2×C3×D3—24no—
228C2×C3×D3—42no—
229C2×C3×D3—42no—
230C2×C3×D3—48no—
231C32×C4—42no—
232C32×C4C22⋊Q812yes—
233C32×C4C22×Q811yescharacteristic
234C32×C4C2×#4111yescharacteristic
235C3⋊Dic3—42no—
236C3×Dic3—22no—
237C3×Dic3—42no—
238C3×Dic3C2×D814yes—
239C22×Q8—181no—
240C22×D4—31no—
241C23×C4—61no—
242C22×C8—31no—
243C22×C8—91no—
244C4⋊Q8—94no—
245C4⋊Q8—182no—
246C4×D4—34no—
247C4×D4—62no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—181no—
251C2×C4⋊C4D3211yescharacteristic
252C2×C22⋊C4—61no—
253C2×C42—31no—
254#107—34no—
255#107—94no—
256C4⋊C8—94no—
257#102—94no—
258#102—94no—
259C23×C3—21no—
260C23×C3—64no—
261C23×C3—62no—
262C23×C3—122no—
263C23×C3—122no—
264C23×C3D3×D411yescharacteristic
265C23×C3C2×#6711yescharacteristic
266C22×D3—24no—
267C22×D3—22no—
268C22×D3—42no—
269C22×D3—42no—
270C3×D4—34no—
271C3×D4—64no—
272C3×D4—62no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—34no—
280C2×C3×C4—32no—
281C2×C3×C4—32no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—82no—
288C2×C3×C4—128no—
289C2×C3×C4—122no—
290C2×C3×C4C2×Dic612yes—
291C2×C3×C4#23512yes—
292C2×C3×C4#23512yes—
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×Q812yes—
295C2×C3×C4C2×#6711yescharacteristic
296C2×C3×C4C23×D311yescharacteristic
297C2×C3×C4C23×D311yescharacteristic
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—42no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—242no—
307C2×Dic3#21314yes—
308C2×Dic3C2×#6712yes—
309C2×Dic3C2×#6712yes—
310D12—24no—
311D12—22no—
312D12C2×Dic614yescomplemented
313C4×D3—48no—
314Dic6—128no—
315Dic6—128no—
316C3×C8—62no—
317C3⋊C8—22no—
318C3⋊C8—64no—
319C3⋊C8—62no—
320C3⋊C8—62no—
321C2×C32#47414yescomplemented
322C2×C32C2×C22⋊Q811yescharacteristic
323C2×C32C22×D811yescharacteristic
324C2×C32C2×#13711yescharacteristic
325C3×D3—44no—
326C24—61no—
327C2×Q8—184no—
328C2×Q8—364no—
329C2×D4—32no—
330C2×D4—34no—
331C2×D4—62no—
332C2×D4—61no—
333C22×C4—21no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—64no—
337C22×C4—61no—
338C22×C4—124no—
339C22×C4—181no—
340C22×C4C2×D3211yescharacteristic
341C2×C8—32no—
342C2×C8—62no—
343C2×C8—92no—
344C2×C8—182no—
345C4⋊C4—21no—
346C4⋊C4—32no—
347C4⋊C4—61no—
348C4⋊C4—92no—
349C4⋊C4—184no—
350C4⋊C4—181no—
351C4⋊C4C2×D3212yes—
352C22⋊C4—64no—
353C42—32no—
354C42—32no—
355C22×C3—21no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—22no—
359C22×C3—64no—
360C22×C3—128no—
361C22×C3—122no—
362C22×C3—122no—
363C22×C3#89612yes—
364C22×C3D3×D812yes—
365C22×C3#91812yes—
366C22×C3#92412yes—
367C22×C3C2×#21312yes—
368C22×C3#95112yes—
369C22×C3C2×D3×D411yescharacteristic
370C22×C3C22×#6711yescharacteristic
371C2×D3—24no—
372C2×D3—48no—
373C2×D3—42no—
374C2×D3—42no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—22no—
378C3×C4—34no—
379C3×C4—42no—
380C3×C4—42no—
381C3×C4—62no—
382C3×C4—82no—
383C3×C4—122no—
384C3×C4#89612yes—
385C3×C4#92412yes—
386C3×C4C22×Dic611yescharacteristic
387C3×C4C2×#23511yescharacteristic
388C3×C4C2×#23511yescharacteristic
389C3×C4C2×D3×Q811yescharacteristic
390Dic3—22no—
391Dic3—42no—
392Dic3—122no—
393Dic3—122no—
394Dic3—242no—
395Dic3C2×#21314yes—
396C32C2×#47411yescharacteristic, complemented, Sylow
397C23—62no—
398C23—64no—
399C23—122no—
400C23—122no—
401C23D3×#6711yescharacteristic
402Q8—368no—
403D4—34no—
404D4—62no—
405D4—64no—
406C2×C4—22no—
407C2×C4—32no—
408C2×C4—34no—
409C2×C4—32no—
410C2×C4—42no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—128no—
414C2×C4—122no—
415C2×C4—182no—
416C2×C4—362no—
417C2×C4D3×Dic612yes—
418C2×C4#379812yes—
419C2×C4D3×#6711yescharacteristic
420C2×C4C22×D3211yescharacteristic
421C8—62no—
422C8—182no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—24no—
426C2×C3—21no—
427C2×C3—124no—
428C2×C3#489014yescomplemented
429C2×C3#500714yescomplemented
430C2×C3C2×#89611yescharacteristic
431C2×C3C2×D3×D811yescharacteristic
432C2×C3C2×#91811yescharacteristic
433C2×C3C2×#92411yescharacteristic
434C2×C3C22×#21311yescharacteristic
435C2×C3C2×#95111yescharacteristic
436D3—44no—
437C22—64no—
438C22—122no—
439C22—128no—
440C22—122no—
441C22#6385112yes—
442C22D3×#21312yes—
443C22#6394312yes—
444C22C2×D3×#6711yescharacteristic
445C4—34no—
446C4—42no—
447C4—62no—
448C4—122no—
449C4—362no—
450C4#6385112yes—
451C4C2×D3×Dic611yescharacteristic
452C4C2×#379811yescharacteristic
453C3—21no—
454C3C2×#489011yescharacteristic, complemented
455C3C2×#500711yescharacteristic, complemented
456C2—124no—
457C2#1059055514yesdirect product factor
458C2C2×#6385111yescharacteristic
459C2C2×D3×#21311yescharacteristic
460C2C2×#6394311yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#474
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63918C2semidirect
3. C2×#63634C2semidirect
4. C2×C3×#807C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590555C2direct (N × H)
25. #63918C22semidirect
26. #63634C22semidirect
27. C3×#807C22semidirect
28. Dic3⋊(C3⋊C8)C22semidirect
45. C2×#807D3semidirect
57. C2×C3×D12Q8semidirect
120. #807C2×D3semidirect
143. C3×D12C2×Q8semidirect
181. C2×D12Dic6semidirect
312. D12C2×Dic6semidirect
321. C2×C32#474semidirect
396. C32C2×#474semidirect
428. C2×C3#4890semidirect
429. C2×C3#5007semidirect
454. C3C2×#4890semidirect
455. C3C2×#5007semidirect
457. C2#10590555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#639182
C2×#636342
C2×C3×#8072
C2×Dic3⋊(C3⋊C8)2
C2×#635632
C2×#635622
#105905552
C2×#50073
C2×#48903