Finite Group Databasebeta

← C2×#10591624 #11873551

Subgroups — C2×#10591624 #11873551

Order 1152.

953 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×C3×#947C211yesmaximal, characteristic
2C2×#63918C211yesmaximal, characteristic, complemented
3C2×#63662C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591624C218yesmaximal, direct product factor
6C2×#63563C211yesmaximal, characteristic
7C2×#63562C211yesmaximal, characteristic
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5055—31nomaximal
10C2×#4794—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#627—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#947—22no—
17C3×#947C2214yes—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×Dic3⋊Dic3—21no—
24#63918—22no—
25#63918C2214yescomplemented
26#63662C2214yescomplemented
27C3×#835C2214yescomplemented
28#63563C2214yes—
29#63562C2214yes—
30#63554C2214yescomplemented
31C2×C3×#124—31no—
32C2×#947D311yescharacteristic
33C2×#888—31no—
34C2×#869—31no—
35C2×C3×#103—31no—
36C2×#835—31no—
37C2×#835—31no—
38C2×#835—61no—
39C2×#835D311yescharacteristic, complemented
40C2×#832—31no—
41C2×#832—31no—
42C2×#821—31no—
43C2×#815—31no—
44#5055—38no—
45C2×#809—31no—
46C2×#803—31no—
47#4794—38no—
48C23×C3×D3—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—22no—
51C2×C32×Q8—22no—
52C2×C32×Q8C2312yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×#627—24no—
64C2×#627—44no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×(C2×D3)⋊C4—24no—
70C3×(C2×D3)⋊C4—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4×Dic3D412yes—
74C3×C4×Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77Dic3⋊Dic3—24no—
78C2×#489—91noSylow
79C22×C3×Q8—21no—
80C22×C3×Q8C2×D311yescharacteristic
81C22×C3×Q8C2×D311yescharacteristic
82C22×C3×D4—31no—
83C22×D12C2×D311yescharacteristic
84C22×Dic6—61no—
85C22×Dic6—61no—
86C22×C3×C8—31no—
87C3×#124—34no—
88C3×#124—62no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C22⋊C4—61no—
92C2×C3×C42—31no—
93#947—22no—
94#947C2×D314yes—
95C2×(C2×D3)⋊C4—21no—
96C2×(C2×D3)⋊C4—21no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3C2×D311yescharacteristic
104C22×C3⋊C8—31no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108#888—34no—
109#888—62no—
110#869—34no—
111#869—62no—
112C3×#103—34no—
113#835—34no—
114#835—34no—
115#835—64no—
116#835C2×D314yescomplemented
117#832—34no—
118#832—34no—
119#821—34no—
120#815—34no—
121#809—34no—
122#803—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—42no—
126C22×C3×D3—42no—
127C22×C3×D3—42no—
128C32×Q8—22no—
129C32×Q8—22no—
130C32×Q8—42no—
131C2×C32×C4—22no—
132C2×C32×C4—42no—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4112yes—
135C2×C32×C4#4112yes—
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—42no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C2×C3×Dic3C2×D412yes—
145C3×D12—22no—
146C3×D12—22no—
147C3×D12—42no—
148#627—48no—
149C3⋊(C3⋊C8)—22no—
150C3×C3⋊C8—22no—
151C2×C4⋊Q8—91no—
152C2×#124—31no—
153#489—98no—
154C2×#103—31no—
155C2×#103—91no—
156C2×#102—91no—
157C2×#102—91no—
158C2×#97—91no—
159C24×C3—61no—
160C23×D3—21no—
161C2×C3×Q8—21no—
162C2×C3×Q8—21no—
163C2×C3×Q8—24no—
164C2×C3×Q8—22no—
165C2×C3×Q8—22no—
166C2×C3×Q8—22no—
167C2×C3×Q8—22no—
168C2×C3×Q8—22no—
169C2×C3×Q8—41no—
170C2×C3×Q8—42no—
171C2×C3×Q8C22×D312yes—
172C2×C3×Q8C22×D312yes—
173C2×C3×D4—32no—
174C2×C3×D4—62no—
175C2×C3×D4—61no—
176C2×C3×D4—62no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—41no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C22×Dic3#6711yescharacteristic
191C22×Dic3#6711yescharacteristic
192C2×D12—22no—
193C2×D12—22no—
194C2×D12—21no—
195C2×D12C22×D312yes—
196C2×Dic6—64no—
197C2×Dic6—64no—
198C2×Dic6—124no—
199C2×Dic6—124no—
200C2×C3×C8—32no—
201C2×C3×C8—62no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—61no—
204C3×C22⋊C4—64no—
205C3×C22⋊C4—64no—
206C3×C42—32no—
207C3×C42—32no—
208(C2×D3)⋊C4—24no—
209(C2×D3)⋊C4—24no—
210C4⋊Dic3—21no—
211C4⋊Dic3—32no—
212C4⋊Dic3—32no—
213C4⋊Dic3—62no—
214C4⋊Dic3—64no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—121no—
218C4⋊Dic3C22×D312yes—
219Dic3⋊C4—64no—
220C4×Dic3#6712yes—
221C4×Dic3C22×D312yes—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—122no—
229C2×C3⋊C8C22×D312yes—
230C22×C32#12412yes—
231C22×C32AGL(1,ℤ/8)12yes—
232C22×C32#13712yes—
233C22×C32C22×D411yescharacteristic
234C2×C3×D3—42no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—84no—
238C32×C4—42no—
239C32×C4#12412yes—
240C32×C4C2×#4111yescharacteristic
241C32×C4C2×#4111yescharacteristic
242C3⋊Dic3—42no—
243C3×Dic3—22no—
244C3×Dic3—22no—
245C3×Dic3—42no—
246C22×Q8—181no—
247C22×Q8D3211yescharacteristic
248C22×D4—31no—
249C22×C8—31no—
250C22×C8—91no—
251C4⋊Q8—94no—
252C4⋊Q8—182no—
253#124—34no—
254#124—62no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258C2×C22⋊C4—61no—
259C2×C22⋊C4—61no—
260C2×C42—31no—
261#103—34no—
262#103—94no—
263#102—94no—
264#102—94no—
265#97—94no—
266C23×C3—21no—
267C23×C3—62no—
268C23×C3—122no—
269C23×C3—122no—
270C23×C3—122no—
271C23×C3D3×D411yescharacteristic
272C23×C3C2×#6711yescharacteristic
273C22×D3—22no—
274C22×D3—42no—
275C22×D3—42no—
276C22×D3—42no—
277C3×Q8—24no—
278C3×Q8—22no—
279C3×Q8—22no—
280C3×Q8—22no—
281C3×Q8—22no—
282C3×Q8—42no—
283C3×Q8—44no—
284C3×Q8—42no—
285C3×Q8—42no—
286C3×D4—62no—
287C3×D4—62no—
288C3×D4—122no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—22no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—42no—
298C2×C3×C4—44no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—122no—
305C2×C3×C4#23512yes—
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23712yes—
308C2×C3×C4#23712yes—
309C2×C3×C4#23712yes—
310C2×C3×C4C2×#6711yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×C3×C4C23×D311yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—42no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—242no—
323C2×Dic3C2×#6712yes—
324C2×Dic3C2×#6712yes—
325D12—22no—
326D12—22no—
327D12—42no—
328Dic6—128no—
329Dic6—128no—
330C3×C8—62no—
331C3⋊C8—22no—
332C3⋊C8—62no—
333C3⋊C8—62no—
334C3⋊C8—122no—
335C2×C32#48914yescomplemented
336C2×C32C2×#12411yescharacteristic
337C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
338C2×C32C2×#13711yescharacteristic
339C3×D3—82no—
340C24—61no—
341C2×Q8—21no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—184no—
345C2×Q8—364no—
346C2×Q8C2×D3212yes—
347C2×D4—32no—
348C2×D4—62no—
349C2×D4—62no—
350C2×D4—61no—
351C22×C4—21no—
352C22×C4—31no—
353C22×C4—31no—
354C22×C4—61no—
355C22×C4—181no—
356C22×C4C2×D3211yescharacteristic
357C2×C8—32no—
358C2×C8—62no—
359C2×C8—92no—
360C2×C8—182no—
361C4⋊C4—32no—
362C4⋊C4—61no—
363C4⋊C4—92no—
364C4⋊C4—184no—
365C4⋊C4—181no—
366C22⋊C4—64no—
367C22⋊C4—64no—
368C42—32no—
369C42—32no—
370C22×C3—21no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—122no—
375C22×C3—122no—
376C22×C3—122no—
377C22×C3—244no—
378C22×C3#88512yes—
379C22×C3#91412yes—
380C22×C3#91812yes—
381C22×C3#93612yes—
382C22×C3#94912yes—
383C22×C3#95112yes—
384C22×C3C2×D3×D411yescharacteristic
385C22×C3C22×#6711yescharacteristic
386C2×D3—42no—
387C2×D3—42no—
388C2×D3—42no—
389C2×D3—84no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—44no—
394C3×C4—42no—
395C3×C4—42no—
396C3×C4—62no—
397C3×C4—62no—
398C3×C4—122no—
399C3×C4#88512yes—
400C3×C4#93612yes—
401C3×C4C2×#23511yescharacteristic
402C3×C4C2×#23711yescharacteristic
403C3×C4C2×#23711yescharacteristic
404C3×C4C2×#23711yescharacteristic
405Dic3—22no—
406Dic3—22no—
407Dic3—42no—
408Dic3—122no—
409Dic3—122no—
410Dic3—242no—
411C32C2×#48911yescharacteristic, complemented, Sylow
412C23—62no—
413C23—122no—
414C23—122no—
415C23—122no—
416C23D3×#6711yescharacteristic
417Q8—22no—
418Q8—22no—
419Q8—42no—
420Q8—368no—
421D4—62no—
422D4—62no—
423D4—122no—
424C2×C4—22no—
425C2×C4—32no—
426C2×C4—32no—
427C2×C4—42no—
428C2×C4—62no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—122no—
432C2×C4—182no—
433C2×C4—362no—
434C2×C4#380412yes—
435C2×C4#380512yes—
436C2×C4D3×#6711yescharacteristic
437C2×C4C22×D3211yescharacteristic
438C8—62no—
439C8—182no—
440C2×C3—24no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—242no—
445C2×C3#479414yescomplemented
446C2×C3#505514yescomplemented
447C2×C3C2×#88511yescharacteristic
448C2×C3C2×#91411yescharacteristic
449C2×C3C2×#91811yescharacteristic
450C2×C3C2×#93611yescharacteristic
451C2×C3C2×#94911yescharacteristic
452C2×C3C2×#95111yescharacteristic
453D3—82no—
454C22—122no—
455C22—122no—
456C22—122no—
457C22—244no—
458C22#6393912yes—
459C22#6394312yes—
460C22#6395912yes—
461C22C2×D3×#6711yescharacteristic
462C4—42no—
463C4—62no—
464C4—62no—
465C4—122no—
466C4—362no—
467C4#6395912yes—
468C4C2×#380411yescharacteristic
469C4C2×#380511yescharacteristic
470C3—21no—
471C3C2×#479411yescharacteristic, complemented
472C3C2×#505511yescharacteristic, complemented
473C2—242no—
474C2#1059162414yesdirect product factor
475C2C2×#6393911yescharacteristic
476C2C2×#6394311yescharacteristic
477C2C2×#6395911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×Q8D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63918C2semidirect
3. C2×#63662C2semidirect
4. C2×C3×#835C2semidirect
5. #10591624C2direct (N × H)
8. C2×#63554C2semidirect
25. #63918C22semidirect
26. #63662C22semidirect
27. C3×#835C22semidirect
30. #63554C22semidirect
39. C2×#835D3semidirect
116. #835C2×D3semidirect
335. C2×C32#489semidirect
411. C32C2×#489semidirect
445. C2×C3#4794semidirect
446. C2×C3#5055semidirect
471. C3C2×#4794semidirect
472. C3C2×#5055semidirect
474. C2#10591624direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9472
C2×#639182
C2×#636622
C2×C3×#8352
#105916242
C2×#635632
C2×#635622
C2×#635542
C2×#50553
C2×#47943