Finite Group Databasebeta

← C2×#10590541 #11873547

Subgroups — C2×#10590541 #11873547

Order 1152.

1017 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2C2×#63863C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C2×#63566C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C2×#63555C211yesmaximal, characteristic, complemented
8#10590541C218yesmaximal, direct product factor
9C2×#4794—31nomaximal
10C2×#4765—31nomaximal
11C22×#634—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64097—22no—
19#64097C2214yescomplemented
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63863—22no—
25#63863C2214yes—
26C3×#810C2214yescomplemented
27C3×#809C2214yes—
28#63566C2214yescomplemented
29#63563C2214yes—
30#63555C2214yescomplemented
31C2×#947—31no—
32C2×#936—31no—
33C2×#888—31no—
34C2×#888—31no—
35C2×#888—61no—
36C2×C3×#103—31no—
37C2×C3×#102—31no—
38C2×#835—31no—
39C2×#832—31no—
40C2×#821—31no—
41C2×#816—31no—
42C2×#815—31no—
43C2×#815—31no—
44C2×#810D311yescharacteristic, complemented
45C2×#809D311yescharacteristic
46#4794—38no—
47#4765—38no—
48C23×C3×D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C2×#634—24no—
55C2×#634—44no—
56C22×C3×Dic3—21no—
57C2×C3×D12—22no—
58C2×C3×D12—22no—
59C2×C3×D12—21no—
60C2×C3×D12C2312yes—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69#3750—24no—
70C4×C3⋊Dic3D412yes—
71C4×C3⋊Dic3C2312yes—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76(C2×D3)⋊Dic3—24no—
77(C2×D3)⋊Dic3—24no—
78C2×#489—91noSylow
79C22×C3×Q8—31no—
80C22×C3×D4—31no—
81C22×D12C2×D311yescharacteristic
82C22×Dic6—61no—
83C22×Dic6—61no—
84C22×Dic6—62no—
85C22×Dic6C2×D311yescharacteristic
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×#217—61no—
92C2×#217—61no—
93#947—34no—
94#947—62no—
95#936—34no—
96#936—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—61no—
104C2×Dic3⋊C4—62no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110#888—34no—
111#888—34no—
112#888—64no—
113#888—62no—
114#888—62no—
115#888—64no—
116C3×#103—34no—
117C3×#102—34no—
118#835—34no—
119#832—34no—
120#821—34no—
121#816—34no—
122#815—34no—
123#815—34no—
124#810C2×D314yescomplemented
125#809C2×D314yes—
126C23×C32C2×D411yescharacteristic
127C22×C3×D3—22no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C22×C3×D3—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—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—42no—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D412yes—
143#634—48no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C3×D12—22no—
147C3×D12—22no—
148C3×D12—42no—
149C3×Dic6—22no—
150C3×Dic6—22no—
151C3×Dic6—42no—
152C3×C3⋊C8—22no—
153C3×C3⋊C8—22no—
154C2×C4⋊Q8—91no—
155C2×#124—91no—
156#489—98no—
157C2×#103—31no—
158C2×#103—91no—
159C2×#102—31no—
160C2×#102—91no—
161C2×#97—91no—
162C24×C3—61no—
163C23×D3—21no—
164C2×C3×Q8—32no—
165C2×C3×Q8—61no—
166C2×C3×Q8—62no—
167C2×C3×Q8—62no—
168C2×C3×D4—32no—
169C2×C3×D4—62no—
170C2×C3×D4—61no—
171C2×C3×D4—62no—
172C22×C3×C4—22no—
173C22×C3×C4—21no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—62no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C2×D12—22no—
190C2×D12—22no—
191C2×D12—21no—
192C2×D12C22×D312yes—
193C2×Dic6—22no—
194C2×Dic6—22no—
195C2×Dic6—21no—
196C2×Dic6—64no—
197C2×Dic6—64no—
198C2×Dic6—68no—
199C2×Dic6—128no—
200C2×Dic6—124no—
201C2×Dic6—124no—
202C2×Dic6C22×D312yes—
203C2×C3×C8—32no—
204C2×C3×C8—32no—
205C2×C3×C8—62no—
206C2×C3×C8—62no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—22no—
211C3×C4⋊C4C22×D312yes—
212C3×C4⋊C4C22×D312yes—
213#217—64no—
214#217—64no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—62no—
220C4⋊Dic3—62no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223Dic3⋊C4—64no—
224Dic3⋊C4—64no—
225Dic3⋊C4—68no—
226C4×Dic3—32no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—32no—
230C4×Dic3—62no—
231C4×Dic3—62no—
232C2×C3⋊C8—22no—
233C2×C3⋊C8—22no—
234C2×C3⋊C8C22×D312yes—
235C2×C3⋊C8C22×D312yes—
236C22×C32#12412yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32#13712yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—84no—
244C32×C4—42no—
245C32×C4#12412yes—
246C32×C4C2×#4111yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3⋊Dic3—22no—
249C3⋊Dic3—22no—
250C3⋊Dic3—42no—
251C3×Dic3—42no—
252C22×Q8—31no—
253C22×Q8—181no—
254C22×D4—31no—
255C22×C8—31no—
256C22×C8—31no—
257C4⋊Q8—94no—
258C4⋊Q8—182no—
259#124—94no—
260#124—182no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—181no—
263C2×C4⋊C4D3211yescharacteristic
264C2×C22⋊C4—181no—
265C2×C22⋊C4—181no—
266C2×C42—91no—
267#103—34no—
268#103—94no—
269#102—34no—
270#102—94no—
271#97—94no—
272C23×C3—21no—
273C23×C3—62no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3—122no—
277C23×C3D3×D411yescharacteristic
278C23×C3D3×D411yescharacteristic
279C22×D3—22no—
280C22×D3—42no—
281C22×D3—42no—
282C22×D3—42no—
283C3×Q8—62no—
284C3×Q8—62no—
285C3×Q8—122no—
286C3×D4—62no—
287C3×D4—62no—
288C3×D4—122no—
289C2×C3×C4—24no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—44no—
297C2×C3×C4—42no—
298C2×C3×C4—42no—
299C2×C3×C4—62no—
300C2×C3×C4—122no—
301C2×C3×C4#23512yes—
302C2×C3×C4#23512yes—
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23712yes—
306C2×C3×C4#23712yes—
307C2×C3×C4C23×D311yescharacteristic
308C2×C3×C4C23×D311yescharacteristic
309C2×Dic3—22no—
310C2×Dic3—32no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—42no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—64no—
318C2×Dic3—64no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—64no—
324C2×Dic3—62no—
325C2×Dic3—62no—
326C2×Dic3—124no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329D12—22no—
330D12—22no—
331D12—42no—
332Dic6—22no—
333Dic6—22no—
334Dic6—42no—
335Dic6—1216no—
336Dic6—128no—
337Dic6—128no—
338C3×C8—62no—
339C3×C8—62no—
340C3⋊C8—22no—
341C3⋊C8—22no—
342C2×C32#48914yescomplemented
343C2×C32C2×#12411yescharacteristic
344C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
345C2×C32C2×#13711yescharacteristic
346C3×D3—82no—
347C24—61no—
348C2×Q8—32no—
349C2×Q8—61no—
350C2×Q8—62no—
351C2×Q8—62no—
352C2×Q8—184no—
353C2×Q8—364no—
354C2×D4—32no—
355C2×D4—62no—
356C2×D4—62no—
357C2×D4—61no—
358C22×C4—21no—
359C22×C4—61no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—181no—
363C22×C4C2×D3211yescharacteristic
364C2×C8—32no—
365C2×C8—32no—
366C2×C8—62no—
367C2×C8—62no—
368C4⋊C4—21no—
369C4⋊C4—92no—
370C4⋊C4—184no—
371C4⋊C4—181no—
372C4⋊C4C2×D3212yes—
373C22⋊C4—184no—
374C22⋊C4—184no—
375C42—92no—
376C42—92no—
377C22×C3—21no—
378C22×C3—22no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—122no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—244no—
385C22×C3#88512yes—
386C22×C3#88512yes—
387C22×C3#91112yes—
388C22×C3#91412yes—
389C22×C3#91512yes—
390C22×C3#91812yes—
391C22×C3C2×D3×D411yescharacteristic
392C22×C3C2×D3×D411yescharacteristic
393C2×D3—42no—
394C2×D3—42no—
395C2×D3—42no—
396C2×D3—84no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—22no—
400C3×C4—44no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—122no—
404C3×C4#88512yes—
405C3×C4#88512yes—
406C3×C4C2×#23511yescharacteristic
407C3×C4C2×#23511yescharacteristic
408C3×C4C2×#23711yescharacteristic
409C3×C4C2×#23711yescharacteristic
410Dic3—42no—
411Dic3—64no—
412Dic3—64no—
413Dic3—62no—
414Dic3—62no—
415Dic3—62no—
416Dic3—62no—
417Dic3—124no—
418Dic3—122no—
419Dic3—122no—
420C32C2×#48911yescharacteristic, complemented, Sylow
421C23—62no—
422C23—122no—
423C23—122no—
424C23—122no—
425C23#381111yescharacteristic
426Q8—62no—
427Q8—62no—
428Q8—122no—
429Q8—368no—
430D4—62no—
431D4—62no—
432D4—122no—
433C2×C4—22no—
434C2×C4—42no—
435C2×C4—62no—
436C2×C4—92no—
437C2×C4—92no—
438C2×C4—122no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—362no—
443C2×C4#379512yes—
444C2×C4#379512yes—
445C2×C4#381111yescharacteristic
446C2×C4C22×D3211yescharacteristic
447C8—62no—
448C8—62no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—24no—
452C2×C3—21no—
453C2×C3—242no—
454C2×C3#476514yescomplemented
455C2×C3#479414yescomplemented
456C2×C3C2×#88511yescharacteristic
457C2×C3C2×#88511yescharacteristic
458C2×C3C2×#91111yescharacteristic
459C2×C3C2×#91411yescharacteristic
460C2×C3C2×#91511yescharacteristic
461C2×C3C2×#91811yescharacteristic
462D3—82no—
463C22—122no—
464C22—122no—
465C22—122no—
466C22—244no—
467C22#6391312yes—
468C22#6393712yes—
469C22#6395112yes—
470C22C2×#381111yescharacteristic
471C4—42no—
472C4—122no—
473C4—182no—
474C4—182no—
475C4—362no—
476C4#6391312yes—
477C4C2×#379511yescharacteristic
478C4C2×#379511yescharacteristic
479C3—21no—
480C3C2×#476511yescharacteristic, complemented
481C3C2×#479411yescharacteristic, complemented
482C2—242no—
483C2#1059054114yesdirect product factor
484C2C2×#6391311yescharacteristic
485C2C2×#6393711yescharacteristic
486C2C2×#6395111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#489
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×#64097C2semidirect
3. C2×C3×#810C2semidirect
5. C2×#63566C2semidirect
7. C2×#63555C2semidirect
8. #10590541C2direct (N × H)
19. #64097C22semidirect
26. C3×#810C22semidirect
28. #63566C22semidirect
30. #63555C22semidirect
44. C2×#810D3semidirect
124. #810C2×D3semidirect
342. C2×C32#489semidirect
420. C32C2×#489semidirect
454. C2×C3#4765semidirect
455. C2×C3#4794semidirect
480. C3C2×#4765semidirect
481. C3C2×#4794semidirect
483. C2#10590541direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640972
C2×#638632
C2×C3×#8102
C2×C3×#8092
C2×#635662
C2×#635632
C2×#635552
#105905412
C2×#47943
C2×#47653