Finite Group Databasebeta

← C2×#10590708 #11869525

Subgroups — C2×#10590708 #11869525

Order 1152.

913 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×#63857C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
5C2×C3×#818C211yesmaximal, characteristic, complemented
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590708C218yesmaximal, direct product factor
9C2×#4888—31nomaximal
10C2×#4723—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×Dic3⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×Dic32—21no—
22#63857—22no—
23#63857C2214yes—
24#63841—22no—
25#63841C2214yes—
26#63643C2214yescomplemented
27C3×(C2×D3)⋊C8C2214yes—
28C3×#818C2214yescomplemented
29#63573C2214yescomplemented
30#63567C2214yescomplemented
31C2×#926—31no—
32C2×#924—31no—
33C2×#897—31no—
34C2×#892—31no—
35C2×C3×#107—31no—
36C2×C3×C22⋊C8—31no—
37C2×(C2×D3)⋊C8D311yescharacteristic
38C2×#818D311yescharacteristic, complemented
39C2×#817—31no—
40C2×#816—31no—
41C2×#816—31no—
42C2×#816—31no—
43C2×#816—61no—
44C2×#810—31no—
45C2×#808—31no—
46#4888—38no—
47#4723—38no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C2×#634—22no—
53C2×#634—22no—
54C2×#634—21no—
55C2×#634C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3D412yes—
62C2×C3×C4×D3C2312yes—
63C2×C32×C8—22no—
64C2×C32×C8C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2312yes—
70C3×C4⋊Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8C2312yes—
73Dic3⋊Dic3—24no—
74(C2×D3)⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76Dic32—24no—
77C2×#485—91noSylow
78C23×C3×C4—31no—
79C22×C4×D3C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×#217—61no—
90C2×#217—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
93#926—34no—
94#926—62no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101#924—34no—
102#924—62no—
103C2×Dic3⋊C4—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—61no—
106C22×C3⋊C8C2×D311yescharacteristic
107#897—34no—
108#897—62no—
109#892—34no—
110#892—62no—
111C3×#107—34no—
112C3×C22⋊C8—34no—
113(C2×D3)⋊C8C2×D314yes—
114#818C2×D314yescomplemented
115#817—34no—
116#816—34no—
117#816—34no—
118#816—34no—
119#816—64no—
120#810—34no—
121#808—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3C2×D412yes—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4112yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—42no—
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×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C3×C4×D3—24no—
145C3×C4×D3—22no—
146C3×C4×D3—22no—
147C32×C8—22no—
148C3×C3⋊C8—22no—
149C2×C22⋊Q8—91no—
150C2×#117—91no—
151#485—98no—
152C2×#107—31no—
153C2×#106—91no—
154C2×#103—91no—
155C2×#103—91no—
156C2×C22⋊C8—31no—
157C24×C3—31no—
158C23×D3D1211yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—32no—
162C22×C3×C4—32no—
163C22×C3×C4—62no—
164C22×C3×C4—62no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C22×Dic3—121no—
177C22×Dic3D1211yescharacteristic
178C2×C4×D3—22no—
179C2×C4×D3—22no—
180C2×C4×D3D1212yes—
181C2×C4×D3C22×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—22no—
195C2×C3×C8—22no—
196C2×C3×C8—22no—
197C2×C3×C8—32no—
198C2×C3×C8—42no—
199C2×C3×C8—62no—
200C2×C3×C8C22×D312yes—
201C2×C3×C8C22×D312yes—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206#217—64no—
207#217—64no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3—32no—
213C4⋊Dic3—32no—
214C4⋊Dic3—62no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—64no—
218C4⋊Dic3—121no—
219C4⋊Dic3C22×D312yes—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—64no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C2×C3⋊C8—22no—
225C2×C3⋊C8C22×D312yes—
226C22×C32#12312yes—
227C22×C32#13512yes—
228C22×C32#13712yes—
229C22×C32C22×D411yescharacteristic
230C2×C3×D3—22no—
231C2×C3×D3—22no—
232C2×C3×D3—22no—
233C2×C3×D3—44no—
234C32×C4#12312yes—
235C32×C4C2×#4111yescharacteristic
236C32×C4C2×#4111yescharacteristic
237C3⋊Dic3—42no—
238C3⋊Dic3—42no—
239C3×Dic3—22no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—91no—
243C23×C4—31no—
244C22×C8—31no—
245C22×C8D3211yescharacteristic
246C22⋊Q8—94no—
247C22⋊Q8—182no—
248#117—94no—
249#117—182no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—91no—
253C2×C4⋊C4—181no—
254C2×C22⋊C4—181no—
255C2×C22⋊C4—181no—
256C2×C42—181no—
257#107—34no—
258#106—94no—
259#103—94no—
260#103—94no—
261C22⋊C8—34no—
262C23×C3—21no—
263C23×C3—32no—
264C23×C3—62no—
265C23×C3—62no—
266C23×C3—62no—
267C23×C3C2×D1211yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—22no—
270C22×D3—22no—
271C22×D3—22no—
272C22×D3C2×D1212yes—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—21no—
276C2×C3×C4—22no—
277C2×C3×C4—32no—
278C2×C3×C4—62no—
279C2×C3×C4—64no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—122no—
285C2×C3×C4—122no—
286C2×C3×C4C2×D1211yescharacteristic
287C2×C3×C4#23512yes—
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4#23712yes—
290C2×C3×C4#23712yes—
291C2×C3×C4#23912yes—
292C2×C3×C4C23×D311yescharacteristic
293C2×C3×C4C23×D311yescharacteristic
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—42no—
298C2×Dic3—42no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—122no—
304C2×Dic3—122no—
305C2×Dic3—124no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3—242no—
311C2×Dic3C2×D1212yes—
312C4×D3—24no—
313C4×D3—22no—
314C4×D3—22no—
315Dic6—64no—
316Dic6—62no—
317Dic6—62no—
318Dic6—62no—
319Dic6—62no—
320Dic6—122no—
321Dic6—124no—
322Dic6—122no—
323Dic6—122no—
324C3×C8—22no—
325C3×C8—22no—
326C3×C8—42no—
327C3×C8—62no—
328C3⋊C8—22no—
329C2×C32#48514yescomplemented
330C2×C32C2×#12311yescharacteristic
331C2×C32C2×#13511yescharacteristic
332C2×C32C2×#13711yescharacteristic
333C3×D3—42no—
334C24—31no—
335C2×Q8—92no—
336C2×Q8—181no—
337C2×Q8—182no—
338C2×Q8—182no—
339C22×C4—31no—
340C22×C4—32no—
341C22×C4—32no—
342C22×C4—62no—
343C22×C4—62no—
344C22×C4—61no—
345C22×C4—61no—
346C22×C4—181no—
347C22×C4—181no—
348C22×C4C2×D3211yescharacteristic
349C2×C8—22no—
350C2×C8—32no—
351C2×C8—62no—
352C2×C8C2×D3212yes—
353C4⋊C4—32no—
354C4⋊C4—32no—
355C4⋊C4—61no—
356C4⋊C4—61no—
357C4⋊C4—92no—
358C4⋊C4—184no—
359C4⋊C4—181no—
360C22⋊C4—184no—
361C22⋊C4—184no—
362C42—184no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—62no—
368C22×C3—62no—
369C22×C3—62no—
370C22×C3—124no—
371C22×C3#88612yes—
372C22×C3#89412yes—
373C22×C3#90412yes—
374C22×C3#90912yes—
375C22×C3#91212yes—
376C22×C3#91812yes—
377C22×C3C22×D1211yescharacteristic
378C22×C3C2×D3×D411yescharacteristic
379C2×D3—22no—
380C2×D3—22no—
381C2×D3—22no—
382C2×D3—44no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—22no—
386C3×C4—62no—
387C3×C4—122no—
388C3×C4—122no—
389C3×C4#88612yes—
390C3×C4#89412yes—
391C3×C4C2×#23511yescharacteristic
392C3×C4C2×#23711yescharacteristic
393C3×C4C2×#23711yescharacteristic
394C3×C4C2×#23911yescharacteristic
395Dic3—22no—
396Dic3—42no—
397Dic3—42no—
398Dic3—124no—
399Dic3—122no—
400Dic3—122no—
401Dic3—122no—
402Dic3—122no—
403Dic3—242no—
404C32C2×#48511yescharacteristic, complemented, Sylow
405C23—32no—
406C23—62no—
407C23—62no—
408C23—62no—
409C23D3×D1211yescharacteristic
410Q8—182no—
411Q8—182no—
412Q8—362no—
413C2×C4—32no—
414C2×C4—62no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—64no—
418C2×C4—62no—
419C2×C4—62no—
420C2×C4—122no—
421C2×C4—122no—
422C2×C4—182no—
423C2×C4—182no—
424C2×C4—362no—
425C2×C4—362no—
426C2×C4#379612yes—
427C2×C4D3×D1211yescharacteristic
428C2×C4#380412yes—
429C2×C4C22×D3211yescharacteristic
430C8—22no—
431C8—62no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—24no—
436C2×C3—122no—
437C2×C3#472314yescomplemented
438C2×C3#488814yescomplemented
439C2×C3C2×#88611yescharacteristic
440C2×C3C2×#89411yescharacteristic
441C2×C3C2×#90411yescharacteristic
442C2×C3C2×#90911yescharacteristic
443C2×C3C2×#91211yescharacteristic
444C2×C3C2×#91811yescharacteristic
445D3—42no—
446C22—62no—
447C22—62no—
448C22—62no—
449C22—124no—
450C22#6380112yes—
451C22#6380712yes—
452C22#6389012yes—
453C22C2×D3×D1211yescharacteristic
454C4—62no—
455C4—122no—
456C4—122no—
457C4—362no—
458C4—362no—
459C4#6389012yes—
460C4C2×#379611yescharacteristic
461C4C2×#380411yescharacteristic
462C3—21no—
463C3C2×#472311yescharacteristic, complemented
464C3C2×#488811yescharacteristic, complemented
465C2—122no—
466C2#1059070814yesdirect product factor
467C2C2×#6380111yescharacteristic
468C2C2×#6380711yescharacteristic
469C2C2×#6389011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×C8D32
hypocenterC32C2×#485
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×#63643C2semidirect
5. C2×C3×#818C2semidirect
6. C2×#63573C2semidirect
7. C2×#63567C2semidirect
8. #10590708C2direct (N × H)
26. #63643C22semidirect
28. C3×#818C22semidirect
29. #63573C22semidirect
30. #63567C22semidirect
38. C2×#818D3semidirect
114. #818C2×D3semidirect
329. C2×C32#485semidirect
404. C32C2×#485semidirect
437. C2×C3#4723semidirect
438. C2×C3#4888semidirect
463. C3C2×#4723semidirect
464. C3C2×#4888semidirect
466. C2#10590708direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638572
C2×#638412
C2×#636432
C2×C3×(C2×D3)⋊C82
C2×C3×#8182
C2×#635732
C2×#635672
#105907082
C2×#48883
C2×#47233