Finite Group Databasebeta

← C2×#10591405 #11860069

Subgroups — C2×#10591405 #11860069

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3754C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic
5#10591405C218yesmaximal, direct product factor
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5018—31nomaximal
10C2×#4757—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C23×C3×Dic3—21no—
14C2×#3754C418yescomplemented
15C2×#3754C2214yes—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#217—21no—
18C3×D4×Dic3—22no—
19C3×D4×Dic3C2214yes—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3724—21no—
25C2×Dic32—21no—
26#63844—22no—
27#63844C2214yescomplemented
28C3×#832C2214yes—
29#63576C2214yescomplemented
30#63567C2214yescomplemented
31#63554C2214yescomplemented
32C2×C3×C4×D4—31no—
33C2×D4×Dic3D311yescharacteristic
34C22×#214—31no—
35C22×#214—31no—
36C22×#214—61no—
37C2×#887—31no—
38C2×C4×Dic6—31no—
39C2×C3×#102—31no—
40C2×#832D311yescharacteristic
41C2×#816—31no—
42C2×#815—31no—
43#5018—38no—
44C2×#810—31no—
45C2×#807—31no—
46C2×#807—31no—
47C2×#803—31no—
48#4757—38no—
49C24×C32—21no—
50C2×C32×D4—21no—
51C2×C32×D4—22no—
52C2×C32×D4C2×C414yes—
53C2×C32×D4C2312yes—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634C2×C414yescomplemented
59C2×#634C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—24no—
63C22×C3×Dic3—44no—
64C22×C3×Dic3D411yescharacteristic
65C22×C3×Dic3D411yescharacteristic
66#3754C2×C4116yescomplemented
67C2×C3⋊(C3⋊C8)C2×C414yescomplemented
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×#217—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3D412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2312yes—
78#3724—24no—
79Dic32—24no—
80C2×#440—91noSylow
81C22×C3×D4—21no—
82C22×C3×D4C2×D311yescharacteristic
83C22×C3×D4C2×D311yescharacteristic
84C23×C3×C4—61no—
85C23×Dic3—21no—
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C22×C3×C8—31no—
90C3×C4×D4—34no—
91C3×C4×D4—62no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—31no—
96C2×#217—21no—
97D4×Dic3—22no—
98D4×Dic3C2×D314yes—
99C2×#214—38no—
100C2×#214—38no—
101C2×#214—34no—
102C2×#214—34no—
103C2×#214—68no—
104C2×#214—64no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×Dic3⋊C4—61no—
108C2×Dic3⋊C4—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3C2×D311yescharacteristic
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116#887—34no—
117#887—62no—
118C4×Dic6—34no—
119C4×Dic6—62no—
120C3×#102—34no—
121#832C2×D314yes—
122#816—34no—
123#815—34no—
124#810—34no—
125#807—34no—
126#807—34no—
127#803—34no—
128C23×C32—24no—
129C23×C32—22no—
130C23×C32—42no—
131C23×C32—42no—
132C23×C32C2×D411yescharacteristic
133C32×D4—24no—
134C32×D4—22no—
135C32×D4C22×C414yes—
136C2×C32×C4C22×C412yes—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—24no—
141C2×C3⋊Dic3—22no—
142#634—24no—
143#634—22no—
144#634C22×C414yescomplemented
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—48no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3—42no—
152C2×C3×Dic3C2×D412yes—
153C2×C3×Dic3C2×D412yes—
154C3⋊(C3⋊C8)C22×C414yescomplemented
155C3×C3⋊C8—22no—
156C22×SD16—91no—
157C2×C4×Q8—91no—
158C2×C4×D4—31no—
159#440—98no—
160C2×#107—91no—
161C2×#103—91no—
162C2×#102—31no—
163C2×#97—91no—
164C24×C3—21no—
165C24×C3—21no—
166C24×C3—41no—
167C2×C3×D4—22no—
168C2×C3×D4—21no—
169C2×C3×D4—22no—
170C2×C3×D4—21no—
171C2×C3×D4—24no—
172C2×C3×D4—22no—
173C2×C3×D4—42no—
174C2×C3×D4—41no—
175C2×C3×D4C4×D314yes—
176C2×C3×D4C4×D314yes—
177C2×C3×D4C22×D312yes—
178C2×C3×D4C22×D312yes—
179C22×C3×C4—21no—
180C22×C3×C4—31no—
181C22×C3×C4—31no—
182C22×C3×C4—64no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—124no—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—24no—
191C22×Dic3—44no—
192C22×Dic3—61no—
193C22×Dic3—61no—
194C22×Dic3—121no—
195C22×Dic3#6711yescharacteristic
196C22×Dic3#6711yescharacteristic
197C2×Dic6—34no—
198C2×Dic6—34no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—64no—
202C2×Dic6—62no—
203C2×Dic6—62no—
204C2×Dic6—61no—
205C2×Dic6—62no—
206C2×Dic6—61no—
207C2×Dic6—122no—
208C2×Dic6—121no—
209C2×C3×C8—32no—
210C2×C3×C8—62no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—61no—
214C3×C4⋊C4—61no—
215C3×C22⋊C4—64no—
216C3×C42—32no—
217C3×C42—32no—
218#217—24no—
219#214—316no—
220#214—316no—
221#214—616no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3C22×D312yes—
225C4⋊Dic3C22×D312yes—
226Dic3⋊C4—64no—
227Dic3⋊C4—64no—
228C4×Dic3—64no—
229C4×Dic3—64no—
230C4×Dic3#6712yes—
231C4×Dic3C22×D312yes—
232C2×C3⋊C8—22no—
233C2×C3⋊C8—34no—
234C2×C3⋊C8—34no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—64no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8C22×D312yes—
240C22×C32—24no—
241C22×C32—42no—
242C22×C32—42no—
243C22×C32—48no—
244C22×C32C4×D412yes—
245C22×C32AGL(1,ℤ/8)12yes—
246C22×C32#13712yes—
247C22×C32C22×D411yescharacteristic
248C32×C4C4×D412yes—
249C32×C4C23×C411yescharacteristic
250C32×C4C2×#4111yescharacteristic
251C3⋊Dic3—24no—
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—42no—
255C3×Dic3—42no—
256C22×Q8—91no—
257C22×D4D3211yescharacteristic
258C23×C4—61no—
259C2×SD16—98no—
260C2×SD16—94no—
261C22×C8—31no—
262C22×C8—91no—
263C4×Q8—94no—
264C4×Q8—182no—
265C4×D4—34no—
266C4×D4—62no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—181no—
270C2×C22⋊C4—61no—
271C2×C42—31no—
272C2×C42—181no—
273#107—94no—
274#103—94no—
275#102—34no—
276#97—94no—
277C23×C3—24no—
278C23×C3—24no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—21no—
282C23×C3—42no—
283C23×C3—44no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—82no—
289C23×C3—82no—
290C23×C3D3×D411yescharacteristic
291C23×C3C2×#6711yescharacteristic
292C3×D4—24no—
293C3×D4—24no—
294C3×D4—22no—
295C3×D4—22no—
296C3×D4—24no—
297C3×D4—42no—
298C3×D4—44no—
299C3×D4C2×C4×D314yes—
300C3×D4C2×C4×D314yes—
301C2×C3×C4—21no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—32no—
306C2×C3×C4—32no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—62no—
311C2×C3×C4—128no—
312C2×C3×C4—122no—
313C2×C3×C4—122no—
314C2×C3×C4C2×C4×D312yes—
315C2×C3×C4C2×C4×D312yes—
316C2×C3×C4#23512yes—
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4#23712yes—
319C2×C3×C4C2×#6711yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—48no—
327C2×Dic3—42no—
328C2×Dic3—42no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—124no—
335C2×Dic3C2×#6712yes—
336C2×Dic3C2×#6712yes—
337Dic6—34no—
338Dic6—34no—
339Dic6—64no—
340Dic6—64no—
341Dic6—64no—
342Dic6—62no—
343Dic6—62no—
344Dic6—122no—
345Dic6—124no—
346C3×C8—62no—
347C3⋊C8—22no—
348C3⋊C8—34no—
349C3⋊C8—34no—
350C3⋊C8—64no—
351C2×C32—44no—
352C2×C32#44014yescomplemented
353C2×C32C2×C4×D411yescharacteristic
354C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
355C2×C32C2×#13711yescharacteristic
356C24—21no—
357C2×Q8—92no—
358C2×Q8—94no—
359C2×Q8—182no—
360C2×Q8—181no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4#62414yes—
364C2×D4C2×D3212yes—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—64no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—124no—
371C22×C4—181no—
372C22×C4C2×D3211yescharacteristic
373SD16—916no—
374C2×C8—32no—
375C2×C8—62no—
376C2×C8—92no—
377C2×C8—94no—
378C4⋊C4—32no—
379C4⋊C4—32no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—184no—
383C22⋊C4—64no—
384C42—32no—
385C42—32no—
386C42—184no—
387C22×C3—24no—
388C22×C3—24no—
389C22×C3—21no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—44no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—48no—
397C22×C3—48no—
398C22×C3—42no—
399C22×C3—42no—
400C22×C3—82no—
401C22×C3—82no—
402C22×C3—88no—
403C22×C3#67⋊C412yes—
404C22×C3#91112yes—
405C22×C3#91512yes—
406C22×C3C4×#6712yes—
407C22×C3#93212yes—
408C22×C3#95112yes—
409C22×C3C2×D3×D411yescharacteristic
410C22×C3C22×#6711yescharacteristic
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—22no—
414C3×C4—62no—
415C3×C4—62no—
416C3×C4—122no—
417C3×C4—122no—
418C3×C4#67⋊C412yes—
419C3×C4C4×#6712yes—
420C3×C4C22×C4×D311yescharacteristic
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C2×#23511yescharacteristic
423C3×C4C2×#23711yescharacteristic
424Dic3—22no—
425Dic3—22no—
426Dic3—42no—
427Dic3—42no—
428Dic3—64no—
429Dic3—64no—
430Dic3—124no—
431C32C2×#44011yescharacteristic, complemented, Sylow
432C23—22no—
433C23—24no—
434C23—42no—
435C23—42no—
436C23D3×#6711yescharacteristic
437Q8—94no—
438Q8—182no—
439Q8—184no—
440D4—22no—
441D4—24no—
442D4C2×#62414yes—
443C2×C4—32no—
444C2×C4—32no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—128no—
450C2×C4—122no—
451C2×C4—122no—
452C2×C4—182no—
453C2×C4—184no—
454C2×C4#380412yes—
455C2×C4C2×#62412yes—
456C2×C4D3×#6711yescharacteristic
457C2×C4C22×D3211yescharacteristic
458C8—62no—
459C8—94no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—24no—
464C2×C3—44no—
465C2×C3—44no—
466C2×C3—84no—
467C2×C3#475714yescomplemented
468C2×C3#501814yescomplemented
469C2×C3C2×#67⋊C411yescharacteristic
470C2×C3C2×#91111yescharacteristic
471C2×C3C2×#91511yescharacteristic
472C2×C3C2×C4×#6711yescharacteristic
473C2×C3C2×#93211yescharacteristic
474C2×C3C2×#95111yescharacteristic
475C22—24no—
476C22—42no—
477C22—42no—
478C22—48no—
479C22#6392912yes—
480C22#6393212yes—
481C22#6395212yes—
482C22C2×D3×#6711yescharacteristic
483C4—62no—
484C4—62no—
485C4—122no—
486C4—122no—
487C4—184no—
488C4#6395212yes—
489C4C2×#380411yescharacteristic
490C4C22×#62411yescharacteristic
491C3—21no—
492C3C2×#475711yescharacteristic, complemented
493C3C2×#501811yescharacteristic, complemented
494C2—44no—
495C2#1059140514yesdirect product factor
496C2C2×#6392911yescharacteristic
497C2C2×#6393211yescharacteristic
498C2C2×#6395211yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32C2×#440
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
3. C2×#63844C2semidirect
5. #10591405C2direct (N × H)
6. C2×#63576C2semidirect
7. C2×#63567C2semidirect
8. C2×#63554C2semidirect
14. C2×#3754C4semidirect
27. #63844C22semidirect
29. #63576C22semidirect
30. #63567C22semidirect
31. #63554C22semidirect
58. C2×#634C2×C4semidirect
66. #3754C2×C4semidirect
67. C2×C3⋊(C3⋊C8)C2×C4semidirect
144. #634C22×C4semidirect
154. C3⋊(C3⋊C8)C22×C4semidirect
352. C2×C32#440semidirect
431. C32C2×#440semidirect
467. C2×C3#4757semidirect
468. C2×C3#5018semidirect
492. C3C2×#4757semidirect
493. C3C2×#5018semidirect
495. C2#10591405direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×D4×Dic32
C2×#638442
C2×C3×#8322
#105914052
C2×#635762
C2×#635672
C2×#635542
C2×#50183
C2×#47573