Finite Group Databasebeta

← C2×#10590866 #11873543

Subgroups — C2×#10590866 #11873543

Order 1152.

945 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63919C211yesmaximal, characteristic, complemented
2C2×#63863C211yesmaximal, characteristic
3C2×#63642C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#10590866C218yesmaximal, direct product factor
9C2×#4794—31nomaximal
10C2×#4765—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×#627—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×#3724—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63919—22no—
23#63919C2214yescomplemented
24#63863—22no—
25#63863C2214yes—
26#63642C2214yescomplemented
27C3×#821C2214yes—
28C3×#816C2214yescomplemented
29#63565C2214yescomplemented
30#63562C2214yes—
31C2×#947—31no—
32C2×#936—31no—
33C2×#888—31no—
34C2×#888—31no—
35C2×C3×#103—31no—
36C2×C3×#102—31no—
37C2×#835—31no—
38C2×#832—31no—
39C2×#821D311yescharacteristic
40C2×#816D311yescharacteristic, complemented
41C2×#815—31no—
42C2×#815—31no—
43C2×#815—61no—
44C2×#810—31no—
45C2×#809—31no—
46#4794—38no—
47#4765—38no—
48C23×C3×D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×D12—22no—
56C2×C3×D12—22no—
57C2×C3×D12—21no—
58C2×C3×D12C2312yes—
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⋊Dic3D412yes—
68C4×C3⋊Dic3C2312yes—
69C2×C3⋊(C3⋊C8)—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4⋊Dic3C2312yes—
75#3724—24no—
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×Dic6C2×D311yescharacteristic
85C22×C3×C8—21no—
86C22×C3×C8C2×D311yescharacteristic
87C22×C3×C8C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—31no—
90C2×#217—61no—
91C2×#217—61no—
92#947—34no—
93#947—62no—
94#936—34no—
95#936—62no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×Dic3⋊C4—61no—
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—31no—
104C2×C4×Dic3—61no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—61no—
108#888—34no—
109#888—34no—
110#888—62no—
111#888—62no—
112C3×#103—34no—
113C3×#102—34no—
114#835—34no—
115#832—34no—
116#821C2×D314yes—
117#816C2×D314yescomplemented
118#815—34no—
119#815—34no—
120#815—64no—
121#810—34no—
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—22no—
134C2×C3⋊Dic3C2×D412yes—
135C2×C3⋊Dic3C2×D412yes—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C3×D12—22no—
143C3×D12—22no—
144C3×D12—42no—
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—31no—
157C2×#102—91no—
158C2×#97—91no—
159C24×C3—61no—
160C23×D3—21no—
161C2×C3×Q8—32no—
162C2×C3×Q8—61no—
163C2×C3×Q8—62no—
164C2×C3×Q8—62no—
165C2×C3×D4—32no—
166C2×C3×D4—62no—
167C2×C3×D4—61no—
168C2×C3×D4—62no—
169C22×C3×C4—21no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4—61no—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—21no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C2×D12—22no—
185C2×D12—22no—
186C2×D12—21no—
187C2×D12C22×D312yes—
188C2×Dic6—22no—
189C2×Dic6—22no—
190C2×Dic6—21no—
191C2×Dic6—64no—
192C2×Dic6—64no—
193C2×Dic6—124no—
194C2×Dic6—124no—
195C2×Dic6C22×D312yes—
196C2×C3×C8—24no—
197C2×C3×C8—22no—
198C2×C3×C8—22no—
199C2×C3×C8—22no—
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⋊Dic3C22×D312yes—
213C4⋊Dic3C22×D312yes—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—64no—
226C2×C3⋊C8—62no—
227C2×C3⋊C8—62no—
228C22×C32#12412yes—
229C22×C32AGL(1,ℤ/8)12yes—
230C22×C32#13712yes—
231C22×C32C22×D411yescharacteristic
232C2×C3×D3—42no—
233C2×C3×D3—42no—
234C2×C3×D3—42no—
235C2×C3×D3—84no—
236C32×C4#12412yes—
237C32×C4C2×#4111yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—22no—
240C3⋊Dic3—22no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C22×Q8—31no—
245C22×Q8—181no—
246C22×D4—31no—
247C22×C8—91no—
248C22×C8D3211yescharacteristic
249C4⋊Q8—94no—
250C4⋊Q8—182no—
251#124—94no—
252#124—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—181no—
256C2×C22⋊C4—181no—
257C2×C22⋊C4—181no—
258C2×C42—91no—
259#103—34no—
260#103—94no—
261#102—34no—
262#102—94no—
263#97—94no—
264C23×C3—21no—
265C23×C3—62no—
266C23×C3—122no—
267C23×C3—122no—
268C23×C3—122no—
269C23×C3D3×D411yescharacteristic
270C23×C3D3×D411yescharacteristic
271C22×D3—22no—
272C22×D3—42no—
273C22×D3—42no—
274C22×D3—42no—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×Q8—122no—
278C3×D4—62no—
279C3×D4—62no—
280C3×D4—122no—
281C2×C3×C4—21no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—22no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—122no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4#23512yes—
292C2×C3×C4#23512yes—
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4#23712yes—
296C2×C3×C4#23712yes—
297C2×C3×C4C23×D311yescharacteristic
298C2×C3×C4C23×D311yescharacteristic
299C2×Dic3—22no—
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—32no—
303C2×Dic3—32no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—42no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317D12—22no—
318D12—22no—
319D12—42no—
320Dic6—22no—
321Dic6—22no—
322Dic6—42no—
323Dic6—128no—
324Dic6—128no—
325C3×C8—24no—
326C3×C8—22no—
327C3×C8—22no—
328C3⋊C8—64no—
329C3⋊C8—62no—
330C3⋊C8—62no—
331C2×C32#48914yescomplemented
332C2×C32C2×#12411yescharacteristic
333C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
334C2×C32C2×#13711yescharacteristic
335C3×D3—82no—
336C24—61no—
337C2×Q8—32no—
338C2×Q8—61no—
339C2×Q8—62no—
340C2×Q8—62no—
341C2×Q8—184no—
342C2×Q8—364no—
343C2×D4—32no—
344C2×D4—62no—
345C2×D4—61no—
346C2×D4—62no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4C2×D3211yescharacteristic
353C2×C8—22no—
354C2×C8—92no—
355C2×C8—182no—
356C2×C8C2×D3212yes—
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—184no—
362C22⋊C4—184no—
363C22⋊C4—184no—
364C42—92no—
365C42—92no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—122no—
371C22×C3—122no—
372C22×C3—122no—
373C22×C3—244no—
374C22×C3#88512yes—
375C22×C3#88512yes—
376C22×C3#91112yes—
377C22×C3#91412yes—
378C22×C3#91512yes—
379C22×C3#91812yes—
380C22×C3C2×D3×D411yescharacteristic
381C22×C3C2×D3×D411yescharacteristic
382C2×D3—42no—
383C2×D3—42no—
384C2×D3—42no—
385C2×D3—84no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—22no—
389C3×C4—122no—
390C3×C4—122no—
391C3×C4—122no—
392C3×C4#88512yes—
393C3×C4#88512yes—
394C3×C4C2×#23511yescharacteristic
395C3×C4C2×#23511yescharacteristic
396C3×C4C2×#23711yescharacteristic
397C3×C4C2×#23711yescharacteristic
398Dic3—42no—
399Dic3—42no—
400Dic3—42no—
401Dic3—62no—
402Dic3—62no—
403Dic3—62no—
404Dic3—62no—
405Dic3—122no—
406Dic3—122no—
407C32C2×#48911yescharacteristic, complemented, Sylow
408C23—62no—
409C23—122no—
410C23—122no—
411C23—122no—
412C23#380211yescharacteristic
413Q8—62no—
414Q8—62no—
415Q8—122no—
416Q8—368no—
417D4—62no—
418D4—62no—
419D4—122no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—92no—
424C2×C4—92no—
425C2×C4—122no—
426C2×C4—122no—
427C2×C4—122no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4#379812yes—
431C2×C4#380211yescharacteristic
432C2×C4#380512yes—
433C2×C4C22×D3211yescharacteristic
434C8—22no—
435C8—182no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—24no—
439C2×C3—21no—
440C2×C3—242no—
441C2×C3#476514yescomplemented
442C2×C3#479414yescomplemented
443C2×C3C2×#88511yescharacteristic
444C2×C3C2×#88511yescharacteristic
445C2×C3C2×#91111yescharacteristic
446C2×C3C2×#91411yescharacteristic
447C2×C3C2×#91511yescharacteristic
448C2×C3C2×#91811yescharacteristic
449D3—82no—
450C22—122no—
451C22—122no—
452C22—122no—
453C22—244no—
454C22#6379812yes—
455C22#6381112yes—
456C22#6391512yes—
457C22C2×#380211yescharacteristic
458C4—122no—
459C4—122no—
460C4—122no—
461C4—182no—
462C4—182no—
463C4#6391512yes—
464C4C2×#379811yescharacteristic
465C4C2×#380511yescharacteristic
466C3—21no—
467C3C2×#476511yescharacteristic, complemented
468C3C2×#479411yescharacteristic, complemented
469C2—242no—
470C2#1059086614yesdirect product factor
471C2C2×#6379811yescharacteristic
472C2C2×#6381111yescharacteristic
473C2C2×#6391511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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×#63919C2semidirect
3. C2×#63642C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63565C2semidirect
8. #10590866C2direct (N × H)
23. #63919C22semidirect
26. #63642C22semidirect
28. C3×#816C22semidirect
29. #63565C22semidirect
40. C2×#816D3semidirect
117. #816C2×D3semidirect
331. C2×C32#489semidirect
407. C32C2×#489semidirect
441. C2×C3#4765semidirect
442. C2×C3#4794semidirect
467. C3C2×#4765semidirect
468. C3C2×#4794semidirect
470. C2#10590866direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#638632
C2×#636422
C2×C3×#8212
C2×C3×#8162
C2×#635652
C2×#635622
#105908662
C2×#47943
C2×#47653