Finite Group Databasebeta

← C2×#10590893 #11873542

Subgroups — C2×#10590893 #11873542

Order 1152.

973 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63918C211yesmaximal, characteristic, complemented
2C2×#63864C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590893C218yesmaximal, direct product factor
9C2×#4794—31nomaximal
10C2×#4714—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#627—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C2×#3722—21no—
21C2×#3722—21no—
22#63918—22no—
23#63918C2214yescomplemented
24#63864—22no—
25#63864C2214yes—
26#63648C2214yes—
27C3×#816C2214yescomplemented
28C3×#815C2214yescomplemented
29#63566C2214yescomplemented
30#63564C2214yes—
31C2×#947—31no—
32C2×#888—31no—
33C2×#875—31no—
34C2×#869—31no—
35C2×C3×#103—31no—
36C2×C3×#97—31no—
37C2×#835—31no—
38C2×#821—31no—
39C2×#821—31no—
40C2×#821—31no—
41C2×#821—61no—
42C2×#816—31no—
43C2×#816D311yescharacteristic, complemented
44C2×#815D311yescharacteristic, complemented
45C2×#809—31no—
46#4794—38no—
47#4714—38no—
48C23×C3⋊D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×#627—24no—
64C2×#627—44no—
65C2×C32×C8—22no—
66C2×C32×C8C2312yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75Dic3⋊Dic3—24no—
76#3722—24no—
77#3722—24no—
78C2×#489—91noSylow
79C22×C3×Q8—31no—
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C22×Dic6—61no—
84C22×Dic6—61no—
85C22×Dic6C2×D311yescharacteristic
86C22×C3×C8—21no—
87C22×C3×C8—31no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C2×D311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C42—31no—
92#947—34no—
93#947—62no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×Dic3⋊C4—61no—
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106#888—34no—
107#888—62no—
108#875—34no—
109#875—62no—
110#869—34no—
111#869—62no—
112C3×#103—34no—
113C3×#97—34no—
114#835—34no—
115#821—34no—
116#821—34no—
117#821—34no—
118#821—64no—
119#816—34no—
120#816C2×D314yescomplemented
121#815C2×D314yescomplemented
122#809—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—42no—
126C22×C3⋊D3—42no—
127C22×C3⋊D3—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4112yes—
130C2×C32×C4#4112yes—
131C2×C32×C4C2411yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—42no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—42no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C2×C3×Dic3C2×D412yes—
145C3×Dic6—22no—
146C3×Dic6—22no—
147C3×Dic6—42no—
148#627—48no—
149C32×C8—22no—
150C3×C3⋊C8—22no—
151C2×C4⋊Q8—91no—
152C2×#124—91no—
153#489—98no—
154C2×#103—31no—
155C2×#103—91no—
156C2×#102—91no—
157C2×#102—91no—
158C2×#97—31no—
159C23×D3—61no—
160C23×D3—61no—
161C23×D3—121no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—62no—
165C2×C3×Q8—62no—
166C22×C3×C4—21no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
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—121no—
178C22×Dic3D1211yescharacteristic
179C22×Dic3D1211yescharacteristic
180C2×D12—32no—
181C2×D12—32no—
182C2×D12—62no—
183C2×D12—64no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12—62no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—121no—
191C2×D12—122no—
192C2×Dic6—22no—
193C2×Dic6—22no—
194C2×Dic6—21no—
195C2×Dic6—64no—
196C2×Dic6—64no—
197C2×Dic6—124no—
198C2×Dic6—124no—
199C2×Dic6C22×D312yes—
200C2×C3×C8—22no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—32no—
204C2×C3×C8—42no—
205C2×C3×C8—62no—
206C2×C3×C8C22×D312yes—
207C2×C3×C8C22×D312yes—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—61no—
210C3×C42—32no—
211C3×C42—32no—
212(C2×D3)⋊C4—64no—
213(C2×D3)⋊C4—64no—
214(C2×D3)⋊C4—64no—
215(C2×D3)⋊C4—64no—
216C4⋊Dic3—21no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—62no—
220C4⋊Dic3—64no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—121no—
224C4⋊Dic3C22×D312yes—
225Dic3⋊C4—64no—
226C4×Dic3D1212yes—
227C4×Dic3C22×D312yes—
228C2×C3⋊C8—22no—
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#12412yes—
239C32×C4C2×#4111yescharacteristic
240C32×C4C2×#4111yescharacteristic
241C3⋊Dic3—42no—
242C3×Dic3—22no—
243C3×Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C22×Q8—31no—
247C22×Q8—181no—
248C22×D4—91no—
249C22×C8—31no—
250C22×C8D3211yescharacteristic
251C4⋊Q8—94no—
252C4⋊Q8—182no—
253#124—94no—
254#124—182no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—181no—
258C2×C22⋊C4—181no—
259C2×C22⋊C4—181no—
260C2×C42—31no—
261#103—34no—
262#103—94no—
263#102—94no—
264#102—94no—
265#97—34no—
266C23×C3—21no—
267C23×C3C2×D1211yescharacteristic
268C23×C3D3×D411yescharacteristic
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—122no—
272C22×D3—124no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—122no—
276C22×D3—122no—
277C22×D3—122no—
278C22×D3—122no—
279C22×D3—242no—
280C22×D3—242no—
281C3×Q8—62no—
282C3×Q8—62no—
283C3×Q8—122no—
284C2×C3×C4—21no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—22no—
288C2×C3×C4—32no—
289C2×C3×C4—32no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—122no—
295C2×C3×C4—122no—
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4#23512yes—
298C2×C3×C4#23512yes—
299C2×C3×C4#23512yes—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23712yes—
302C2×C3×C4C23×D311yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3—242no—
316C2×Dic3C2×D1212yes—
317C2×Dic3C2×D1212yes—
318D12—64no—
319D12—62no—
320D12—62no—
321D12—62no—
322D12—62no—
323D12—122no—
324D12—124no—
325D12—122no—
326D12—122no—
327Dic6—22no—
328Dic6—22no—
329Dic6—42no—
330Dic6—128no—
331Dic6—128no—
332C3×C8—22no—
333C3×C8—22no—
334C3×C8—42no—
335C3×C8—62no—
336C3⋊C8—22no—
337C2×C32#48914yescomplemented
338C2×C32C2×#12411yescharacteristic
339C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
340C2×C32C2×#13711yescharacteristic
341C3⋊D3—82no—
342C24—181no—
343C2×Q8—32no—
344C2×Q8—61no—
345C2×Q8—62no—
346C2×Q8—62no—
347C2×Q8—184no—
348C2×Q8—364no—
349C2×D4—92no—
350C2×D4—182no—
351C2×D4—181no—
352C2×D4—182no—
353C22×C4—31no—
354C22×C4—31no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4—181no—
358C22×C4C2×D3211yescharacteristic
359C2×C8—22no—
360C2×C8—32no—
361C2×C8—62no—
362C2×C8C2×D3212yes—
363C4⋊C4—32no—
364C4⋊C4—61no—
365C4⋊C4—92no—
366C4⋊C4—184no—
367C4⋊C4—181no—
368C22⋊C4—184no—
369C22⋊C4—184no—
370C42—32no—
371C42—32no—
372C22×C3—21no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—22no—
376C22×C3#87512yes—
377C22×C3#88512yes—
378C22×C3#90812yes—
379C22×C3#90912yes—
380C22×C3#91412yes—
381C22×C3#91812yes—
382C22×C3C22×D1211yescharacteristic
383C22×C3C2×D3×D411yescharacteristic
384C2×D3—124no—
385C2×D3—122no—
386C2×D3—122no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—122no—
391C2×D3—242no—
392C2×D3—242no—
393C2×D3—248no—
394C2×D3—244no—
395C2×D3—244no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—22no—
399C3×C4—62no—
400C3×C4—62no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4#87512yes—
404C3×C4#88512yes—
405C3×C4C2×#23511yescharacteristic
406C3×C4C2×#23511yescharacteristic
407C3×C4C2×#23511yescharacteristic
408C3×C4C2×#23711yescharacteristic
409Dic3—22no—
410Dic3—22no—
411Dic3—42no—
412Dic3—42no—
413Dic3—122no—
414Dic3—122no—
415Dic3—242no—
416C32C2×#48911yescharacteristic, complemented, Sylow
417C23—182no—
418C23—362no—
419C23—362no—
420C23—362no—
421C23D3×D1211yescharacteristic
422Q8—62no—
423Q8—62no—
424Q8—122no—
425Q8—368no—
426D4—182no—
427D4—182no—
428D4—362no—
429C2×C4—32no—
430C2×C4—32no—
431C2×C4—62no—
432C2×C4—62no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—122no—
436C2×C4—122no—
437C2×C4—182no—
438C2×C4—362no—
439C2×C4#379812yes—
440C2×C4D3×D1211yescharacteristic
441C2×C4#380412yes—
442C2×C4C22×D3211yescharacteristic
443C8—22no—
444C8—62no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—24no—
449C2×C3#471414yescomplemented
450C2×C3#479414yescomplemented
451C2×C3C2×#87511yescharacteristic
452C2×C3C2×#88511yescharacteristic
453C2×C3C2×#90811yescharacteristic
454C2×C3C2×#90911yescharacteristic
455C2×C3C2×#91411yescharacteristic
456C2×C3C2×#91811yescharacteristic
457D3—244no—
458D3—242no—
459D3—242no—
460C22—362no—
461C22—362no—
462C22—362no—
463C22—724no—
464C22#6379412yes—
465C22#6380112yes—
466C22#6385212yes—
467C22C2×D3×D1211yescharacteristic
468C4—62no—
469C4—62no—
470C4—122no—
471C4—122no—
472C4—362no—
473C4#6385212yes—
474C4C2×#379811yescharacteristic
475C4C2×#380411yescharacteristic
476C3—21no—
477C3C2×#471411yescharacteristic, complemented
478C3C2×#479411yescharacteristic, complemented
479C2—722no—
480C2#1059089314yesdirect product factor
481C2C2×#6379411yescharacteristic
482C2C2×#6380111yescharacteristic
483C2C2×#6385211yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32C2×#489
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
1. C2×#63918C2semidirect
4. C2×C3×#816C2semidirect
5. C2×C3×#815C2semidirect
6. C2×#63566C2semidirect
8. #10590893C2direct (N × H)
23. #63918C22semidirect
27. C3×#816C22semidirect
28. C3×#815C22semidirect
29. #63566C22semidirect
43. C2×#816D3semidirect
44. C2×#815D3semidirect
120. #816C2×D3semidirect
121. #815C2×D3semidirect
337. C2×C32#489semidirect
416. C32C2×#489semidirect
449. C2×C3#4714semidirect
450. C2×C3#4794semidirect
477. C3C2×#4714semidirect
478. C3C2×#4794semidirect
480. C2#10590893direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639182
C2×#638642
C2×#636482
C2×C3×#8162
C2×C3×#8152
C2×#635662
C2×#635642
#105908932
C2×#47943
C2×#47143