Finite Group Databasebeta

← C2×#10591056 #11858795

Subgroups — C2×#10591056 #11858795

Order 1152.

925 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×#926C211yesmaximal, characteristic
2C2×#63657C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63554C211yesmaximal, characteristic, complemented
7#10591056C218yesmaximal, direct product factor
8C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
9C2×#5000—31nomaximal
10C2×#4720—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217C411yescharacteristic
15C2×C3×#217C411yescharacteristic
16C3×#926C414yes—
17C3×#926C2214yes—
18C2×C3×C4⋊Dic3C411yescharacteristic
19C2×C3×C4⋊Dic3C411yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24#63657C2214yes—
25C3×#830C2214yes—
26Dic3⋊(C3⋊C8)C2214yescomplemented
27Dic3⋊(C3⋊C8)C2214yescomplemented
28#63554C2214yescomplemented
29Dic3×C3⋊C8C2214yescomplemented
30C2×C3×#117—31no—
31C2×#926D311yescharacteristic
32C2×C3×C22⋊C8—31no—
33C2×#830—31no—
34C2×#830—31no—
35C2×#830—61no—
36C2×#830D311yescharacteristic
37C2×#815—31no—
38C2×Dic3⋊C8—31no—
39C2×Dic3⋊C8—31no—
40C2×C8×Dic3—31no—
41#5000—38no—
42C2×C4⋊(C3⋊C8)—31no—
43C2×C4⋊(C3⋊C8)—31no—
44C2×#803—31no—
45C2×C4×C3⋊C8—31no—
46#4720—38no—
47C24×C32C2×C411yescharacteristic
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4C2×C411yescharacteristic
51C22×C32×C4C2×C412yes—
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C22×C3×Dic3C2×C411yescharacteristic
56C22×C3×Dic3C2×C411yescharacteristic
57C22×C3×Dic3C2×C411yescharacteristic
58C2×C3⋊(C3⋊C8)—22no—
59C2×C3⋊(C3⋊C8)—22no—
60C2×C3⋊(C3⋊C8)C2312yes—
61C2×C3⋊(C3⋊C8)C2312yes—
62C3×#217C2×C414yes—
63C3×#217C2×C414yes—
64C3×C4⋊Dic3C2×C414yes—
65C3×C4⋊Dic3C2×C414yes—
66C3×C4×Dic3C2×C412yes—
67C3×C4×Dic3C2×C412yes—
68C3×C4×Dic3C2312yes—
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—21no—
76C23×C3×C4C2×D311yescharacteristic
77C23×C3×C4C2×D311yescharacteristic
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C3×#117—34no—
81C3×#117—34no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C22⋊C4—31no—
85C2×C3×C22⋊C4—31no—
86C2×C3×C42—31no—
87C2×C3×C42—31no—
88C2×#217Dic311yescharacteristic
89C2×#217Dic311yescharacteristic
90#926Dic314yes—
91#926C2×D314yes—
92C2×C4⋊Dic3Dic311yescharacteristic
93C2×C4⋊Dic3Dic311yescharacteristic
94C2×C4×Dic3C2×D311yescharacteristic
95C2×C4×Dic3C2×D311yescharacteristic
96C22×C3⋊C8—31no—
97C22×C3⋊C8—31no—
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C22×C3⋊C8—61no—
102C22×C3⋊C8C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104C3×C22⋊C8—34no—
105#830—34no—
106#830—34no—
107#830—64no—
108#830C2×D314yes—
109#815—34no—
110Dic3⋊C8—34no—
111Dic3⋊C8—34no—
112C8×Dic3—34no—
113C4⋊(C3⋊C8)—34no—
114C4⋊(C3⋊C8)—34no—
115#803—34no—
116C4×C3⋊C8—34no—
117C23×C32—22no—
118C23×C32—22no—
119C23×C32—22no—
120C23×C32C22×C412yes—
121C23×C32C22×C411yescharacteristic
122C2×C32×C4—22no—
123C2×C32×C4—24no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4C22×C412yes—
127C2×C32×C4C22×C411yescharacteristic
128C2×C32×C4#4112yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3C22×C412yes—
136C2×C3×Dic3C22×C412yes—
137C2×C3×Dic3C22×C412yes—
138C2×C3×Dic3C22×C412yes—
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—91no—
146C2×C4⋊C8—91no—
147C2×C22⋊C8—31no—
148C2×C22⋊C8—91no—
149C2×#97—91no—
150C2×C4×C8—91no—
151C24×C3—21no—
152C24×C3C4×D311yescharacteristic
153C24×C3C2×Dic311yescharacteristic
154C22×C3×C4—22no—
155C22×C3×C4—22no—
156C22×C3×C4—22no—
157C22×C3×C4—22no—
158C22×C3×C4—21no—
159C22×C3×C4—22no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—42no—
167C22×C3×C4—42no—
168C22×C3×C4C4×D311yescharacteristic
169C22×C3×C4C4×D312yes—
170C22×C3×C4C2×Dic311yescharacteristic
171C22×C3×C4C2×Dic312yes—
172C22×C3×C4C22×D312yes—
173C22×C3×C4C22×D312yes—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3C2×Dic311yescharacteristic
177C22×Dic3C2×Dic311yescharacteristic
178C22×Dic3C2×Dic311yescharacteristic
179C22×Dic3C2×Dic311yescharacteristic
180C2×C3×C8—32no—
181C2×C3×C8—32no—
182C2×C3×C8—62no—
183C2×C3×C8—62no—
184C3×C4⋊C4—34no—
185C3×C4⋊C4—34no—
186C3×C22⋊C4—34no—
187C3×C22⋊C4—34no—
188C3×C42—32no—
189C3×C42—32no—
190C3×C42—32no—
191C3×C42—32no—
192#217C2×Dic314yes—
193#217C2×Dic314yes—
194C4⋊Dic3C2×Dic314yes—
195C4⋊Dic3C2×Dic314yes—
196C4×Dic3C2×Dic312yes—
197C4×Dic3C2×Dic312yes—
198C4×Dic3C22×D312yes—
199C4×Dic3C22×D312yes—
200C2×C3⋊C8—22no—
201C2×C3⋊C8—22no—
202C2×C3⋊C8—32no—
203C2×C3⋊C8—32no—
204C2×C3⋊C8—32no—
205C2×C3⋊C8—32no—
206C2×C3⋊C8—62no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—62no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—62no—
212C2×C3⋊C8—122no—
213C2×C3⋊C8—122no—
214C2×C3⋊C8C22×D312yes—
215C2×C3⋊C8C22×D312yes—
216C22×C32—22no—
217C22×C32—22no—
218C22×C32—22no—
219C22×C32—44no—
220C22×C32#11712yes—
221C22×C32#13112yes—
222C22×C32#13112yes—
223C22×C32C23×C411yescharacteristic
224C32×C4—22no—
225C32×C4#11712yes—
226C32×C4C2×#4111yescharacteristic
227C32×C4C2×#4111yescharacteristic
228C3×Dic3—22no—
229C3×Dic3—22no—
230C3×Dic3—22no—
231C3×Dic3—22no—
232C23×C4D3211yescharacteristic
233C22×C8—31no—
234C22×C8—31no—
235C22×C8—91no—
236C22×C8—91no—
237#117—34no—
238#117—34no—
239C2×C4⋊C4—31no—
240C2×C4⋊C4—31no—
241C2×C22⋊C4—31no—
242C2×C22⋊C4—31no—
243C2×C42—31no—
244C2×C42—31no—
245C4⋊C8—94no—
246C4⋊C8—94no—
247C22⋊C8—34no—
248C22⋊C8—94no—
249#97—94no—
250C4×C8—94no—
251C23×C3—24no—
252C23×C3—22no—
253C23×C3—22no—
254C23×C3—22no—
255C23×C3—22no—
256C23×C3—22no—
257C23×C3—22no—
258C23×C3—21no—
259C23×C3—22no—
260C23×C3—42no—
261C23×C3—42no—
262C23×C3C2×C4×D312yes—
263C23×C3C2×C4×D311yescharacteristic
264C23×C3C22×Dic312yes—
265C23×C3C22×Dic311yescharacteristic
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—24no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—32no—
280C2×C3×C4—32no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—44no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4C2×C4×D312yes—
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4#23512yes—
294C2×C3×C4#23512yes—
295C2×C3×C4#23712yes—
296C2×C3×C4#23712yes—
297C2×C3×C4C22×Dic312yes—
298C2×C3×C4C22×Dic311yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300C2×C3×C4C23×D311yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—22no—
305C2×Dic3C22×Dic312yes—
306C2×Dic3C22×Dic312yes—
307C2×Dic3C22×Dic312yes—
308C2×Dic3C22×Dic312yes—
309C3×C8—62no—
310C3×C8—62no—
311C3⋊C8—22no—
312C3⋊C8—22no—
313C3⋊C8—62no—
314C3⋊C8—62no—
315C3⋊C8—62no—
316C3⋊C8—62no—
317C3⋊C8—122no—
318C3⋊C8—122no—
319C2×C32—42no—
320C2×C32#43314yescomplemented
321C2×C32C2×#11711yescharacteristic
322C2×C32C2×#13111yescharacteristic
323C2×C32C2×#13111yescharacteristic
324C24D3×Dic311yescharacteristic
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—31no—
328C22×C4—31no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4D3×Dic311yescharacteristic
332C22×C4D3×Dic312yes—
333C22×C4C2×D3212yes—
334C22×C4C2×D3211yescharacteristic
335C2×C8—32no—
336C2×C8—32no—
337C2×C8—62no—
338C2×C8—62no—
339C2×C8—92no—
340C2×C8—92no—
341C2×C8—182no—
342C2×C8—182no—
343C4⋊C4—34no—
344C4⋊C4—34no—
345C22⋊C4—34no—
346C22⋊C4—34no—
347C42—32no—
348C42—32no—
349C42—32no—
350C42—32no—
351C22×C3—24no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—42no—
363C22×C3—42no—
364C22×C3—48no—
365C22×C3—44no—
366C22×C3—44no—
367C22×C3#87712yes—
368C22×C3#90112yes—
369C22×C3#90712yes—
370C22×C3#92612yes—
371C22×C3#94812yes—
372C22×C3#94812yes—
373C22×C3C22×C4×D311yescharacteristic
374C22×C3C23×Dic311yescharacteristic
375C3×C4—22no—
376C3×C4—22no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—22no—
380C3×C4—42no—
381C3×C4—62no—
382C3×C4—62no—
383C3×C4—62no—
384C3×C4—62no—
385C3×C4#87712yes—
386C3×C4#92612yes—
387C3×C4C2×#23511yescharacteristic
388C3×C4C2×#23511yescharacteristic
389C3×C4C2×#23711yescharacteristic
390C3×C4C2×#23711yescharacteristic
391Dic3—22no—
392Dic3—22no—
393Dic3—22no—
394Dic3—22no—
395C32C2×#43311yescharacteristic, complemented, Sylow
396C23—22no—
397C23—22no—
398C23—22no—
399C23C2×D3×Dic312yes—
400C23C2×D3×Dic311yescharacteristic
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—32no—
406C2×C4—32no—
407C2×C4—32no—
408C2×C4—32no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4C2×D3×Dic312yes—
414C2×C4C2×D3×Dic311yescharacteristic
415C2×C4#380412yes—
416C2×C4#380412yes—
417C2×C4C22×D3211yescharacteristic
418C8—62no—
419C8—62no—
420C8—182no—
421C8—182no—
422C2×C3—24no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—44no—
427C2×C3—42no—
428C2×C3—42no—
429C2×C3#472014yescomplemented
430C2×C3#500014yescomplemented
431C2×C3C2×#87711yescharacteristic
432C2×C3C2×#90111yescharacteristic
433C2×C3C2×#90711yescharacteristic
434C2×C3C2×#92611yescharacteristic
435C2×C3C2×#94811yescharacteristic
436C2×C3C2×#94811yescharacteristic
437C22—22no—
438C22—22no—
439C22—22no—
440C22—44no—
441C22#6381412yes—
442C22#6381512yes—
443C22#6395512yes—
444C22C22×D3×Dic311yescharacteristic
445C4—22no—
446C4—62no—
447C4—62no—
448C4—62no—
449C4—62no—
450C4#6395512yes—
451C4C2×#380411yescharacteristic
452C4C2×#380411yescharacteristic
453C3—21no—
454C3C2×#472011yescharacteristic, complemented
455C3C2×#500011yescharacteristic, complemented
456C2—42no—
457C2#1059105614yesdirect product factor
458C2C2×#6381411yescharacteristic
459C2C2×#6381511yescharacteristic
460C2C2×#6395511yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#433
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×Dic3⋊(C3⋊C8)C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C2×#63554C2semidirect
7. #10591056C2direct (N × H)
8. C2×Dic3×C3⋊C8C2semidirect
26. Dic3⋊(C3⋊C8)C22semidirect
27. Dic3⋊(C3⋊C8)C22semidirect
28. #63554C22semidirect
29. Dic3×C3⋊C8C22semidirect
320. C2×C32#433semidirect
395. C32C2×#433semidirect
429. C2×C3#4720semidirect
430. C2×C3#5000semidirect
454. C3C2×#4720semidirect
455. C3C2×#5000semidirect
457. C2#10591056direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C2×#636572
C2×C3×#8302
C2×Dic3⋊(C3⋊C8)2
C2×#635542
#105910562
C2×Dic3×C3⋊C82
C2×#50003
C2×#47203