Finite Group Databasebeta

← C2×#10590513 #11869450

Subgroups — C2×#10590513 #11869450

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C2×C3×#809C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7C2×#63557C211yesmaximal, characteristic, complemented
8#10590513C218yesmaximal, direct product factor
9C2×#4866—31nomaximal
10C2×#4784—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×#626—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4×C3⋊Dic3—21no—
18#64101—22no—
19#64101C2214yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—21no—
24#63916—22no—
25#63916C2214yes—
26C3×#809C2214yescomplemented
27C3×#808C2214yescomplemented
28#63575C2214yescomplemented
29#63563C2214yescomplemented
30#63557C2214yescomplemented
31C2×#938—31no—
32C2×#895—31no—
33C2×#892—31no—
34C2×#892—31no—
35C2×#892—61no—
36C2×C3×#106—31no—
37C2×C3×#102—31no—
38C2×#832—31no—
39C2×#821—31no—
40C2×(C2×D3)⋊C8—31no—
41C2×(C2×D3)⋊C8—31no—
42C2×#818—31no—
43C2×#809D311yescharacteristic, complemented
44C2×#808D311yescharacteristic, complemented
45C2×#807—31no—
46#4866—38no—
47#4784—38no—
48C23×C3⋊D3D411yescharacteristic
49C23×C3×D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3D411yescharacteristic
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—22no—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3C2312yes—
58C22×C3×Dic3—21no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×#626—24no—
64C2×#626—44no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67#3752—24no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)C2312yes—
70C4×C3⋊Dic3—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8—22no—
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2312yes—
77(C2×D3)⋊Dic3—24no—
78C2×#482—91noSylow
79C22×C3×D4—31no—
80C22×#67—61no—
81C22×D12—61no—
82C22×D12C2×D311yescharacteristic
83C22×C4×D3—31no—
84C22×C4×D3—31no—
85C22×C4×D3—61no—
86C22×C3×C8—31no—
87C22×C3×C8—31no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×#217—61no—
93#938—34no—
94#938—62no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—62no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—31no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3—62no—
106C22×C3⋊C8C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108#895—34no—
109#895—62no—
110#892—34no—
111#892—34no—
112#892—64no—
113#892—62no—
114#892—62no—
115#892—64no—
116C3×#106—34no—
117C3×#102—34no—
118#832—34no—
119#821—34no—
120(C2×D3)⋊C8—34no—
121(C2×D3)⋊C8—34no—
122#818—34no—
123#809C2×D314yescomplemented
124#808C2×D314yescomplemented
125#807—34no—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3C2×D412yes—
131C22×C3×D3—22no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C2×C32×C4—22no—
136C2×C32×C4—42no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4112yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—42no—
144C2×C3⋊Dic3C2×D412yes—
145C4×C3⋊D3—24no—
146C4×C3⋊D3—22no—
147C4×C3⋊D3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C3×D12—22no—
151C3×D12—22no—
152C3×D12—42no—
153#626—48no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—22no—
156C2×#121—91no—
157C2×#117—91no—
158#482—98no—
159C2×#107—91no—
160C2×#106—31no—
161C2×#102—31no—
162C2×#102—91no—
163C2×C22⋊C8—91no—
164C24×C3—61no—
165C23×D3—21no—
166C23×D3—31no—
167C23×D3—31no—
168C23×D3—61no—
169C2×C3×D4—32no—
170C2×C3×D4—62no—
171C2×C3×D4—61no—
172C2×C3×D4—62no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C2×#67—64no—
181C2×#67—124no—
182C22×Dic3—21no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—61no—
186C22×Dic3—62no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C2×D12—22no—
190C2×D12—22no—
191C2×D12—21no—
192C2×D12—64no—
193C2×D12—124no—
194C2×D12C22×D312yes—
195C2×C4×D3—32no—
196C2×C4×D3—32no—
197C2×C4×D3—32no—
198C2×C4×D3—32no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×C3×C8—32no—
208C2×C3×C8—32no—
209C2×C3×C8—62no—
210C2×C3×C8—62no—
211C3×C4⋊C4—22no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—22no—
215C3×C4⋊C4—32no—
216C3×C4⋊C4—61no—
217C3×C4⋊C4C22×D312yes—
218C3×C4⋊C4C22×D312yes—
219#217—64no—
220(C2×D3)⋊C4—64no—
221(C2×D3)⋊C4—64no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—68no—
224C4⋊Dic3—21no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3—62no—
229C4⋊Dic3—61no—
230C4⋊Dic3—61no—
231C4⋊Dic3C22×D312yes—
232C4×Dic3—64no—
233C4×Dic3—64no—
234C4×Dic3—68no—
235C2×C3⋊C8—22no—
236C2×C3⋊C8—22no—
237C2×C3⋊C8C22×D312yes—
238C2×C3⋊C8C22×D312yes—
239C22×C32#12312yes—
240C22×C32#13512yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32C22×D411yescharacteristic
243C2×C3⋊D3—22no—
244C2×C3⋊D3—22no—
245C2×C3⋊D3—22no—
246C2×C3⋊D3—44no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—84no—
251C32×C4—42no—
252C32×C4#12312yes—
253C32×C4C2×#4111yescharacteristic
254C32×C4C2×#4111yescharacteristic
255C3⋊Dic3—22no—
256C3⋊Dic3—42no—
257C3×Dic3—42no—
258C22×D4—31no—
259C22×D4—181no—
260C23×C4—91no—
261C22×C8—31no—
262C22×C8—31no—
263#121—94no—
264#121—182no—
265#117—94no—
266#117—182no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4D3211yescharacteristic
270C2×C22⋊C4—181no—
271C2×C22⋊C4—181no—
272C2×C42—181no—
273#107—94no—
274#106—34no—
275#102—34no—
276#102—94no—
277C22⋊C8—94no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—122no—
281C23×C3—122no—
282C23×C3—122no—
283C23×C3D3×D411yescharacteristic
284C23×C3D3×D411yescharacteristic
285C22×D3—22no—
286C22×D3—32no—
287C22×D3—32no—
288C22×D3—42no—
289C22×D3—42no—
290C22×D3—42no—
291C22×D3—62no—
292C22×D3—64no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—122no—
300C22×D3—122no—
301C3×D4—62no—
302C3×D4—62no—
303C3×D4—122no—
304C2×C3×C4—24no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—44no—
312C2×C3×C4—42no—
313C2×C3×C4—42no—
314C2×C3×C4—62no—
315C2×C3×C4—122no—
316C2×C3×C4#23512yes—
317C2×C3×C4#23512yes—
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4#23712yes—
321C2×C3×C4#23912yes—
322C2×C3×C4C23×D311yescharacteristic
323C2×C3×C4C23×D311yescharacteristic
324#67—128no—
325C2×Dic3—22no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—42no—
329C2×Dic3—62no—
330C2×Dic3—64no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—64no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—124no—
337C2×Dic3—122no—
338C2×Dic3—122no—
339D12—22no—
340D12—22no—
341D12—42no—
342D12—128no—
343C4×D3—64no—
344C4×D3—64no—
345C4×D3—68no—
346C4×D3—64no—
347C4×D3—64no—
348C4×D3—62no—
349C4×D3—62no—
350C4×D3—62no—
351C4×D3—62no—
352C3×C8—62no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—22no—
356C2×C32#48214yescomplemented
357C2×C32C2×#12311yescharacteristic
358C2×C32C2×#13511yescharacteristic
359C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
360C3⋊D3—42no—
361C3×D3—82no—
362C24—61no—
363C24—91no—
364C2×D4—32no—
365C2×D4—62no—
366C2×D4—62no—
367C2×D4—61no—
368C2×D4—184no—
369C2×D4—364no—
370C22×C4—21no—
371C22×C4—61no—
372C22×C4—91no—
373C22×C4—92no—
374C22×C4—92no—
375C22×C4—182no—
376C22×C4—182no—
377C22×C4—181no—
378C22×C4C2×D3211yescharacteristic
379C2×C8—32no—
380C2×C8—32no—
381C2×C8—62no—
382C2×C8—62no—
383C4⋊C4—21no—
384C4⋊C4—32no—
385C4⋊C4—61no—
386C4⋊C4—92no—
387C4⋊C4—181no—
388C4⋊C4C2×D3212yes—
389C22⋊C4—184no—
390C22⋊C4—184no—
391C42—184no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—122no—
399C22×C3—244no—
400C22×C3#88312yes—
401C22×C3#89412yes—
402C22×C3#91212yes—
403C22×C3#91412yes—
404C22×C3#91412yes—
405C22×C3#91612yes—
406C22×C3C2×D3×D411yescharacteristic
407C22×C3C2×D3×D411yescharacteristic
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—42no—
411C2×D3—64no—
412C2×D3—62no—
413C2×D3—62no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—84no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—128no—
422C2×D3—124no—
423C2×D3—124no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—22no—
427C3×C4—44no—
428C3×C4—42no—
429C3×C4—42no—
430C3×C4—122no—
431C3×C4#88312yes—
432C3×C4#89412yes—
433C3×C4C2×#23511yescharacteristic
434C3×C4C2×#23511yescharacteristic
435C3×C4C2×#23711yescharacteristic
436C3×C4C2×#23911yescharacteristic
437Dic3—42no—
438Dic3—64no—
439Dic3—62no—
440Dic3—62no—
441Dic3—124no—
442Dic3—122no—
443Dic3—122no—
444C32C2×#48211yescharacteristic, complemented, Sylow
445C23—62no—
446C23—92no—
447C23—122no—
448C23—122no—
449C23—122no—
450C23—182no—
451C23—182no—
452C23—182no—
453C23#381111yescharacteristic
454D4—62no—
455D4—62no—
456D4—122no—
457D4—368no—
458C2×C4—22no—
459C2×C4—42no—
460C2×C4—62no—
461C2×C4—92no—
462C2×C4—122no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—184no—
467C2×C4—182no—
468C2×C4—362no—
469C2×C4#379612yes—
470C2×C4#379812yes—
471C2×C4#381111yescharacteristic
472C2×C4C22×D3211yescharacteristic
473C8—62no—
474C8—62no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—24no—
478C2×C3—21no—
479C2×C3—242no—
480C2×C3#478414yescomplemented
481C2×C3#486614yescomplemented
482C2×C3C2×#88311yescharacteristic
483C2×C3C2×#89411yescharacteristic
484C2×C3C2×#91211yescharacteristic
485C2×C3C2×#91411yescharacteristic
486C2×C3C2×#91411yescharacteristic
487C2×C3C2×#91611yescharacteristic
488D3—82no—
489D3—124no—
490D3—122no—
491D3—122no—
492C22—122no—
493C22—122no—
494C22—122no—
495C22—182no—
496C22—182no—
497C22—182no—
498C22—244no—
499C22—364no—
500C22#6385312yes—
501C22#6393612yes—
502C22#6394112yes—
503C22C2×#381111yescharacteristic
504C4—42no—
505C4—122no—
506C4—182no—
507C4—362no—
508C4#6385312yes—
509C4C2×#379611yescharacteristic
510C4C2×#379811yescharacteristic
511C3—21no—
512C3C2×#478411yescharacteristic, complemented
513C3C2×#486611yescharacteristic, complemented
514C2—242no—
515C2—362no—
516C2#1059051314yesdirect product factor
517C2C2×#6385311yescharacteristic
518C2C2×#6393611yescharacteristic
519C2C2×#6394111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#482
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×#64101C2semidirect
3. C2×C3×#809C2semidirect
4. C2×C3×#808C2semidirect
5. C2×#63575C2semidirect
6. C2×#63563C2semidirect
7. C2×#63557C2semidirect
8. #10590513C2direct (N × H)
19. #64101C22semidirect
26. C3×#809C22semidirect
27. C3×#808C22semidirect
28. #63575C22semidirect
29. #63563C22semidirect
30. #63557C22semidirect
43. C2×#809D3semidirect
44. C2×#808D3semidirect
123. #809C2×D3semidirect
124. #808C2×D3semidirect
356. C2×C32#482semidirect
444. C32C2×#482semidirect
480. C2×C3#4784semidirect
481. C2×C3#4866semidirect
512. C3C2×#4784semidirect
513. C3C2×#4866semidirect
516. C2#10590513direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#639162
C2×C3×#8092
C2×C3×#8082
C2×#635752
C2×#635632
C2×#635572
#105905132
C2×#48663
C2×#47843