Finite Group Databasebeta

← C2×#10590533 #11873449

Subgroups — C2×#10590533 #11873449

Order 1152.

905 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#890C211yesmaximal, characteristic, complemented
2C2×#63860C211yesmaximal, characteristic
3C2×#63637C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590533C218yesmaximal, direct product factor
9C2×#5068—31nomaximal
10C2×#4768—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3—21no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#890—22no—
21C3×#890C2214yescomplemented
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63860—22no—
25#63860C2214yes—
26#63637C2214yescomplemented
27C3×#809C2214yes—
28#63567C2214yescomplemented
29#63562C2214yes—
30Dic3×C3⋊C8C2214yescomplemented
31C2×C3×#125—31no—
32C2×#936—31no—
33C2×#890D311yescharacteristic, complemented
34C2×#875—31no—
35C2×C3×#102—31no—
36C2×#832—31no—
37C2×#816—31no—
38C2×C8×Dic3—31no—
39#5068—38no—
40C2×#810—31no—
41C2×#810—31no—
42C2×#810—31no—
43C2×#810—61no—
44C2×#809—31no—
45C2×#809D311yescharacteristic
46C2×C4×C3⋊C8—31no—
47#4768—38no—
48C23×C3×D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C2×#634—22no—
53C2×#634—22no—
54C2×#634—21no—
55C2×#634C2312yes—
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—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—24no—
69C3×C4⋊Dic3C2312yes—
70C3×Dic3⋊C4—24no—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75(C2×D3)⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77C2×#488—91noSylow
78C22×C3×D4—31no—
79C22×D12C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C22×C3×C8—31no—
84C3×#125—34no—
85C3×#125—62no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—61no—
89C2×C3×C4⋊C4—61no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C42—31no—
93C2×#217—61no—
94C2×#217—61no—
95#936—34no—
96#936—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×C4⋊Dic3—21no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—21no—
102C2×C4×Dic3C2×D311yescharacteristic
103C22×C3⋊C8—31no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107#890—22no—
108#890C2×D314yescomplemented
109#875—34no—
110#875—62no—
111C3×#102—34no—
112#832—34no—
113#816—34no—
114C8×Dic3—34no—
115#810—34no—
116#810—34no—
117#810—34no—
118#810—64no—
119#809—34no—
120#809C2×D314yes—
121C4×C3⋊C8—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—42no—
125C22×C3×D3—42no—
126C22×C3×D3—42no—
127C2×C32×C4—22no—
128C2×C32×C4—42no—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4112yes—
131C2×C32×C4#4112yes—
132C2×C32×C4C2411yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—42no—
135#634—22no—
136#634—22no—
137#634—42no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3C2×D412yes—
143C2×C3×Dic3C2×D412yes—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—42no—
147C3⋊(C3⋊C8)—22no—
148C3×C3⋊C8—22no—
149C2×#125—31no—
150C2×#124—91no—
151#488—98no—
152C2×#103—91no—
153C2×#103—91no—
154C2×#102—31no—
155C2×#102—91no—
156C2×C4×C8—91no—
157C24×C3—61no—
158C23×D3—21no—
159C2×C3×D4—32no—
160C2×C3×D4—62no—
161C2×C3×D4—62no—
162C2×C3×D4—61no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—41no—
169C22×C3×C4—61no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C22×Dic3#6711yescharacteristic
177C22×Dic3#6711yescharacteristic
178C2×D12—22no—
179C2×D12—22no—
180C2×D12—21no—
181C2×D12C22×D312yes—
182C2×Dic6—32no—
183C2×Dic6—32no—
184C2×Dic6—62no—
185C2×Dic6—64no—
186C2×Dic6—62no—
187C2×Dic6—62no—
188C2×Dic6—62no—
189C2×Dic6—62no—
190C2×Dic6—61no—
191C2×Dic6—61no—
192C2×Dic6—121no—
193C2×Dic6—122no—
194C2×C3×C8—32no—
195C2×C3×C8—62no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—41no—
201C3×C4⋊C4—64no—
202C3×C4⋊C4—64no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4C22×D312yes—
205C3×C4⋊C4C22×D312yes—
206C3×C42—32no—
207C3×C42—32no—
208#217—64no—
209#217—64no—
210(C2×D3)⋊C4—64no—
211(C2×D3)⋊C4—64no—
212C4⋊Dic3—21no—
213C4⋊Dic3—24no—
214C4⋊Dic3C22×D312yes—
215Dic3⋊C4—24no—
216C4×Dic3#6712yes—
217C4×Dic3C22×D312yes—
218C2×C3⋊C8—22no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C2×C3⋊C8—122no—
225C2×C3⋊C8C22×D312yes—
226C22×C32#12412yes—
227C22×C32#13512yes—
228C22×C32#13512yes—
229C22×C32C22×D411yescharacteristic
230C2×C3×D3—42no—
231C2×C3×D3—42no—
232C2×C3×D3—42no—
233C2×C3×D3—84no—
234C32×C4—42no—
235C32×C4#12412yes—
236C32×C4C2×#4111yescharacteristic
237C32×C4C2×#4111yescharacteristic
238C3⋊Dic3—42no—
239C3×Dic3—22no—
240C3×Dic3—22no—
241C3×Dic3—42no—
242C22×Q8—91no—
243C22×D4—31no—
244C22×C8—31no—
245C22×C8—91no—
246#125—34no—
247#125—62no—
248#124—94no—
249#124—182no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—61no—
252C2×C4⋊C4—61no—
253C2×C4⋊C4D3211yescharacteristic
254C2×C22⋊C4—181no—
255C2×C22⋊C4—181no—
256C2×C42—31no—
257#103—94no—
258#103—94no—
259#102—34no—
260#102—94no—
261C4×C8—94no—
262C23×C3—21no—
263C23×C3—62no—
264C23×C3—122no—
265C23×C3—122no—
266C23×C3—122no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—22no—
270C22×D3—42no—
271C22×D3—42no—
272C22×D3—42no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—122no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—21no—
282C2×C3×C4—32no—
283C2×C3×C4—32no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—82no—
291C2×C3×C4—122no—
292C2×C3×C4#23512yes—
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4#23712yes—
295C2×C3×C4#23912yes—
296C2×C3×C4#23912yes—
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C23×D311yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—42no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—122no—
307C2×Dic3—124no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3C2×#6712yes—
311C2×Dic3C2×#6712yes—
312D12—22no—
313D12—22no—
314D12—42no—
315Dic6—64no—
316Dic6—62no—
317Dic6—62no—
318Dic6—62no—
319Dic6—62no—
320Dic6—122no—
321Dic6—124no—
322Dic6—122no—
323Dic6—122no—
324C3×C8—62no—
325C3⋊C8—22no—
326C3⋊C8—62no—
327C3⋊C8—62no—
328C3⋊C8—122no—
329C2×C32#48814yescomplemented
330C2×C32C2×#12411yescharacteristic
331C2×C32C2×#13511yescharacteristic
332C2×C32C2×#13511yescharacteristic
333C3×D3—82no—
334C24—61no—
335C2×Q8—92no—
336C2×Q8—181no—
337C2×Q8—182no—
338C2×Q8—182no—
339C2×D4—32no—
340C2×D4—62no—
341C2×D4—62no—
342C2×D4—61no—
343C22×C4—21no—
344C22×C4—31no—
345C22×C4—31no—
346C22×C4—61no—
347C22×C4—181no—
348C22×C4C2×D3211yescharacteristic
349C2×C8—32no—
350C2×C8—62no—
351C2×C8—92no—
352C2×C8—182no—
353C4⋊C4—21no—
354C4⋊C4—32no—
355C4⋊C4—64no—
356C4⋊C4—64no—
357C4⋊C4—61no—
358C4⋊C4C2×D3212yes—
359C22⋊C4—184no—
360C22⋊C4—184no—
361C42—32no—
362C42—32no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—122no—
368C22×C3—122no—
369C22×C3—122no—
370C22×C3—244no—
371C22×C3#88512yes—
372C22×C3#91212yes—
373C22×C3#91612yes—
374C22×C3#94712yes—
375C22×C3#95012yes—
376C22×C3#95012yes—
377C22×C3C2×D3×D411yescharacteristic
378C22×C3C22×#6711yescharacteristic
379C2×D3—42no—
380C2×D3—42no—
381C2×D3—42no—
382C2×D3—84no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—22no—
386C3×C4—42no—
387C3×C4—42no—
388C3×C4—62no—
389C3×C4—62no—
390C3×C4—82no—
391C3×C4—122no—
392C3×C4#88512yes—
393C3×C4#94712yes—
394C3×C4C2×#23511yescharacteristic
395C3×C4C2×#23711yescharacteristic
396C3×C4C2×#23911yescharacteristic
397C3×C4C2×#23911yescharacteristic
398Dic3—22no—
399Dic3—22no—
400Dic3—42no—
401Dic3—124no—
402Dic3—122no—
403Dic3—122no—
404C32C2×#48811yescharacteristic, complemented, Sylow
405C23—62no—
406C23—122no—
407C23—122no—
408C23—122no—
409C23D3×#6711yescharacteristic
410Q8—182no—
411Q8—182no—
412Q8—362no—
413D4—62no—
414D4—62no—
415D4—122no—
416C2×C4—22no—
417C2×C4—32no—
418C2×C4—32no—
419C2×C4—42no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—122no—
424C2×C4—182no—
425C2×C4—362no—
426C2×C4#379612yes—
427C2×C4#379912yes—
428C2×C4D3×#6711yescharacteristic
429C2×C4C22×D3211yescharacteristic
430C8—62no—
431C8—182no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—24no—
435C2×C3—21no—
436C2×C3—242no—
437C2×C3#476814yescomplemented
438C2×C3#506814yescomplemented
439C2×C3C2×#88511yescharacteristic
440C2×C3C2×#91211yescharacteristic
441C2×C3C2×#91611yescharacteristic
442C2×C3C2×#94711yescharacteristic
443C2×C3C2×#95011yescharacteristic
444C2×C3C2×#95011yescharacteristic
445D3—82no—
446C22—122no—
447C22—122no—
448C22—122no—
449C22—244no—
450C22#6390712yes—
451C22#6393312yes—
452C22#6394712yes—
453C22C2×D3×#6711yescharacteristic
454C4—42no—
455C4—62no—
456C4—62no—
457C4—122no—
458C4—362no—
459C4#6390712yes—
460C4C2×#379611yescharacteristic
461C4C2×#379911yescharacteristic
462C3—21no—
463C3C2×#476811yescharacteristic, complemented
464C3C2×#506811yescharacteristic, complemented
465C2—242no—
466C2#1059053314yesdirect product factor
467C2C2×#6390711yescharacteristic
468C2C2×#6393311yescharacteristic
469C2C2×#6394711yescharacteristic
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×#488
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
1. C2×C3×#890C2semidirect
3. C2×#63637C2semidirect
5. C2×#63567C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590533C2direct (N × H)
21. C3×#890C22semidirect
26. #63637C22semidirect
28. #63567C22semidirect
30. Dic3×C3⋊C8C22semidirect
33. C2×#890D3semidirect
108. #890C2×D3semidirect
329. C2×C32#488semidirect
404. C32C2×#488semidirect
437. C2×C3#4768semidirect
438. C2×C3#5068semidirect
463. C3C2×#4768semidirect
464. C3C2×#5068semidirect
466. C2#10590533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8902
C2×#638602
C2×#636372
C2×C3×#8092
C2×#635672
C2×#635622
C2×Dic3×C3⋊C82
#105905332
C2×#50683
C2×#47683