Finite Group Databasebeta

← C2×#10590710 #11869524

Subgroups — C2×#10590710 #11869524

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63856C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C2×#63645C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590710C218yesmaximal, direct product factor
9C2×#4814—31nomaximal
10C2×#4723—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3724—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×Dic32—21no—
22#63856—22no—
23#63856C2214yes—
24#63841—22no—
25#63841C2214yes—
26#63645C2214yescomplemented
27C3×(C2×D3)⋊C8C2214yes—
28C3×#816C2214yescomplemented
29#63573C2214yescomplemented
30#63566C2214yescomplemented
31C2×#946—31no—
32C2×#926—31no—
33C2×#924—31no—
34C2×#892—31no—
35C2×C3×#103—31no—
36C2×C3×C22⋊C8—31no—
37C2×#835—31no—
38C2×(C2×D3)⋊C8D311yescharacteristic
39C2×#818—31no—
40C2×#818—31no—
41C2×#818—61no—
42C2×#817—31no—
43C2×#816—31no—
44C2×#816D311yescharacteristic, complemented
45C2×#808—31no—
46#4814—38no—
47#4723—38no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C2×C3×C4×D3—22no—
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3D412yes—
58C2×C3×C4×D3C2312yes—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×C32×C8—22no—
64C2×C32×C8C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2312yes—
68C4⋊(C3⋊Dic3)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8C2312yes—
73#3724—24no—
74(C2×D3)⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76Dic32—24no—
77C2×#485—91noSylow
78C22×C3×Q8—31no—
79C23×C3×C4—31no—
80C22×C4×D3C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C22×C3×C8—21no—
83C22×C3×C8—31no—
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C2×D311yescharacteristic
86C2×C3×C4⋊C4—31no—
87C2×#217—61no—
88C2×#217—61no—
89#946—34no—
90#946—62no—
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—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102#924—34no—
103#924—62no—
104C2×Dic3⋊C4—61no—
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109#892—34no—
110#892—62no—
111C3×#103—34no—
112C3×C22⋊C8—34no—
113#835—34no—
114(C2×D3)⋊C8C2×D314yes—
115#818—34no—
116#818—34no—
117#818—64no—
118#817—34no—
119#816—34no—
120#816C2×D314yescomplemented
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—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3C2×D412yes—
141C3×C4×D3—24no—
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—42no—
147C32×C8—22no—
148C3×C3⋊C8—22no—
149C2×C22⋊Q8—91no—
150C2×#117—91no—
151#485—98no—
152C2×#107—91no—
153C2×#106—91no—
154C2×#103—31no—
155C2×#103—91no—
156C2×C22⋊C8—31no—
157C24×C3—31no—
158C23×D3D1211yescharacteristic
159C2×C3×Q8—32no—
160C2×C3×Q8—61no—
161C2×C3×Q8—62no—
162C2×C3×Q8—62no—
163C22×C3×C4—21no—
164C22×C3×C4—31no—
165C22×C3×C4—32no—
166C22×C3×C4—32no—
167C22×C3×C4—62no—
168C22×C3×C4—62no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—121no—
180C22×Dic3—121no—
181C22×Dic3D1211yescharacteristic
182C2×C4×D3—22no—
183C2×C4×D3—22no—
184C2×C4×D3D1212yes—
185C2×C4×D3C22×D312yes—
186C2×Dic6—22no—
187C2×Dic6—22no—
188C2×Dic6—21no—
189C2×Dic6C22×D312yes—
190C2×C3×C8—24no—
191C2×C3×C8—22no—
192C2×C3×C8—22no—
193C2×C3×C8—22no—
194C2×C3×C8—32no—
195C2×C3×C8—62no—
196C2×C3×C8C22×D312yes—
197C2×C3×C8C22×D312yes—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—61no—
200#217—64no—
201#217—64no—
202(C2×D3)⋊C4—64no—
203(C2×D3)⋊C4—64no—
204C4⋊Dic3—21no—
205C4⋊Dic3—32no—
206C4⋊Dic3—32no—
207C4⋊Dic3—32no—
208C4⋊Dic3—32no—
209C4⋊Dic3—62no—
210C4⋊Dic3—62no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—121no—
216C4⋊Dic3—121no—
217C4⋊Dic3C22×D312yes—
218Dic3⋊C4—64no—
219Dic3⋊C4—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8C22×D312yes—
224C22×C32#12312yes—
225C22×C32#13512yes—
226C22×C32#13712yes—
227C22×C32C22×D411yescharacteristic
228C2×C3×D3—22no—
229C2×C3×D3—22no—
230C2×C3×D3—22no—
231C2×C3×D3—44no—
232C32×C4#12312yes—
233C32×C4C2×#4111yescharacteristic
234C32×C4C2×#4111yescharacteristic
235C3⋊Dic3—42no—
236C3⋊Dic3—42no—
237C3×Dic3—22no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C22×Q8—31no—
241C23×C4—31no—
242C22×C8—31no—
243C22×C8D3211yescharacteristic
244C22⋊Q8—94no—
245C22⋊Q8—182no—
246#117—94no—
247#117—182no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—181no—
252C2×C22⋊C4—181no—
253C2×C22⋊C4—181no—
254C2×C42—181no—
255#107—94no—
256#106—94no—
257#103—34no—
258#103—94no—
259C22⋊C8—34no—
260C23×C3—21no—
261C23×C3—32no—
262C23×C3—62no—
263C23×C3—62no—
264C23×C3—62no—
265C23×C3C2×D1211yescharacteristic
266C23×C3D3×D411yescharacteristic
267C22×D3—22no—
268C22×D3—22no—
269C22×D3—22no—
270C22×D3C2×D1212yes—
271C3×Q8—62no—
272C3×Q8—62no—
273C3×Q8—122no—
274C2×C3×C4—21no—
275C2×C3×C4—22no—
276C2×C3×C4—21no—
277C2×C3×C4—22no—
278C2×C3×C4—32no—
279C2×C3×C4—62no—
280C2×C3×C4—64no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—122no—
286C2×C3×C4—122no—
287C2×C3×C4C2×D1211yescharacteristic
288C2×C3×C4#23512yes—
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23712yes—
291C2×C3×C4#23712yes—
292C2×C3×C4#23712yes—
293C2×C3×C4C23×D311yescharacteristic
294C2×C3×C4C23×D311yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—42no—
299C2×Dic3—42no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—122no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3—242no—
311C2×Dic3—242no—
312C2×Dic3C2×D1212yes—
313C4×D3—24no—
314C4×D3—22no—
315C4×D3—22no—
316Dic6—22no—
317Dic6—22no—
318Dic6—42no—
319C3×C8—24no—
320C3×C8—22no—
321C3×C8—22no—
322C3×C8—62no—
323C3⋊C8—22no—
324C2×C32#48514yescomplemented
325C2×C32C2×#12311yescharacteristic
326C2×C32C2×#13511yescharacteristic
327C2×C32C2×#13711yescharacteristic
328C3×D3—42no—
329C24—31no—
330C2×Q8—32no—
331C2×Q8—61no—
332C2×Q8—62no—
333C2×Q8—62no—
334C22×C4—31no—
335C22×C4—32no—
336C22×C4—32no—
337C22×C4—62no—
338C22×C4—62no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—181no—
342C22×C4—181no—
343C22×C4C2×D3211yescharacteristic
344C2×C8—22no—
345C2×C8—32no—
346C2×C8—62no—
347C2×C8C2×D3212yes—
348C4⋊C4—32no—
349C4⋊C4—61no—
350C4⋊C4—92no—
351C4⋊C4—92no—
352C4⋊C4—184no—
353C4⋊C4—181no—
354C4⋊C4—181no—
355C22⋊C4—184no—
356C22⋊C4—184no—
357C42—184no—
358C22×C3—21no—
359C22×C3—22no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—62no—
363C22×C3—62no—
364C22×C3—62no—
365C22×C3—124no—
366C22×C3#88312yes—
367C22×C3#88612yes—
368C22×C3#90412yes—
369C22×C3#90912yes—
370C22×C3#91512yes—
371C22×C3#91912yes—
372C22×C3C22×D1211yescharacteristic
373C22×C3C2×D3×D411yescharacteristic
374C2×D3—22no—
375C2×D3—22no—
376C2×D3—22no—
377C2×D3—44no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—22no—
381C3×C4—62no—
382C3×C4—122no—
383C3×C4—122no—
384C3×C4#88312yes—
385C3×C4#88612yes—
386C3×C4C2×#23511yescharacteristic
387C3×C4C2×#23711yescharacteristic
388C3×C4C2×#23711yescharacteristic
389C3×C4C2×#23711yescharacteristic
390Dic3—22no—
391Dic3—42no—
392Dic3—42no—
393Dic3—122no—
394Dic3—122no—
395Dic3—122no—
396Dic3—122no—
397Dic3—242no—
398Dic3—242no—
399C32C2×#48511yescharacteristic, complemented, Sylow
400C23—32no—
401C23—62no—
402C23—62no—
403C23—62no—
404C23D3×D1211yescharacteristic
405Q8—62no—
406Q8—62no—
407Q8—122no—
408C2×C4—32no—
409C2×C4—62no—
410C2×C4—62no—
411C2×C4—62no—
412C2×C4—64no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—122no—
416C2×C4—122no—
417C2×C4—182no—
418C2×C4—182no—
419C2×C4—362no—
420C2×C4—362no—
421C2×C4#379512yes—
422C2×C4D3×D1211yescharacteristic
423C2×C4#380512yes—
424C2×C4C22×D3211yescharacteristic
425C8—22no—
426C8—62no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—24no—
431C2×C3—122no—
432C2×C3#472314yescomplemented
433C2×C3#481414yescomplemented
434C2×C3C2×#88311yescharacteristic
435C2×C3C2×#88611yescharacteristic
436C2×C3C2×#90411yescharacteristic
437C2×C3C2×#90911yescharacteristic
438C2×C3C2×#91511yescharacteristic
439C2×C3C2×#91911yescharacteristic
440D3—42no—
441C22—62no—
442C22—62no—
443C22—62no—
444C22—124no—
445C22#6380012yes—
446C22#6380812yes—
447C22#6389112yes—
448C22C2×D3×D1211yescharacteristic
449C4—62no—
450C4—122no—
451C4—122no—
452C4—362no—
453C4—362no—
454C4#6389112yes—
455C4C2×#379511yescharacteristic
456C4C2×#380511yescharacteristic
457C3—21no—
458C3C2×#472311yescharacteristic, complemented
459C3C2×#481411yescharacteristic, complemented
460C2—122no—
461C2#1059071014yesdirect product factor
462C2C2×#6380011yescharacteristic
463C2C2×#6380811yescharacteristic
464C2C2×#6389111yescharacteristic
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×#63645C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63573C2semidirect
7. C2×#63566C2semidirect
8. #10590710C2direct (N × H)
26. #63645C22semidirect
28. C3×#816C22semidirect
29. #63573C22semidirect
30. #63566C22semidirect
44. C2×#816D3semidirect
120. #816C2×D3semidirect
324. C2×C32#485semidirect
399. C32C2×#485semidirect
432. C2×C3#4723semidirect
433. C2×C3#4814semidirect
458. C3C2×#4723semidirect
459. C3C2×#4814semidirect
461. C2#10590710direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638562
C2×#638412
C2×#636452
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×#635732
C2×#635662
#105907102
C2×#48143
C2×#47233