Finite Group Databasebeta

← C2×#10590548 #11873370

Subgroups — C2×#10590548 #11873370

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#888C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×Dic3×C3⋊C8C211yesmaximal, characteristic, complemented
8#10590548C218yesmaximal, direct product factor
9C2×#5088—31nomaximal
10C2×#4760—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6—21no—
14C22×#626—21no—
15C22×#626—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×Dic3⋊C4—21no—
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#888—22no—
23C3×#888C2214yescomplemented
24#63911—22no—
25#63911C2214yes—
26#63636C2214yescomplemented
27C3×#809C2214yescomplemented
28#63564C2214yescomplemented
29#63562C2214yescomplemented
30Dic3×C3⋊C8C2214yescomplemented
31C2×C3×C4⋊Q8—31no—
32C2×#940—31no—
33C2×#888D311yescharacteristic, complemented
34C2×#874—31no—
35C2×C3×#102—31no—
36C2×#832—31no—
37C2×#821—31no—
38C2×C8×Dic3—31no—
39#5088—38no—
40C2×#809—31no—
41C2×#809—31no—
42C2×#809—31no—
43C2×#809—31no—
44C2×#809—61no—
45C2×#809D311yescharacteristic, complemented
46C2×C4×C3⋊C8—31no—
47#4760—38no—
48C23×C3⋊D3—21no—
49C23×C3×D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12C2312yes—
63C2×C3×Dic6—24no—
64C2×C3×Dic6—44no—
65C2×#626—24no—
66C2×#626—24no—
67C2×#626—44no—
68C2×#626—44no—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C2×C3⋊(C3⋊C8)—22no—
72C2×C3⋊(C3⋊C8)C2312yes—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×Dic3⋊C4—24no—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80C2×#486—91noSylow
81C22×C3×Q8—61no—
82C22×C3×D4—31no—
83C22×#67—61no—
84C22×#67—61no—
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×D12—61no—
89C22×D12—61no—
90C22×D12C2×D311yescharacteristic
91C22×Dic6—21no—
92C22×C3×C8—31no—
93C3×C4⋊Q8—34no—
94C3×C4⋊Q8—62no—
95C2×C3×C4⋊C4—21no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—61no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C42—31no—
101#940—34no—
102#940—62no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—21no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#888—22no—
111#888C2×D314yescomplemented
112#874—34no—
113#874—62no—
114C3×#102—34no—
115#832—34no—
116#821—34no—
117C8×Dic3—34no—
118#809—34no—
119#809—34no—
120#809—34no—
121#809—34no—
122#809—64no—
123#809C2×D314yescomplemented
124C4×C3⋊C8—34no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—22no—
127C22×C3⋊D3—42no—
128C22×C3⋊D3—42no—
129C22×C3⋊D3—42no—
130C22×C3×D3—22no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—42no—
134C2×C32×C4—22no—
135C2×C32×C4—42no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4112yes—
138C2×C32×C4#4112yes—
139C2×C32×C4C2411yescharacteristic
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—22no—
142C4⋊(C3⋊D3)—42no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—42no—
145C2×C3×Dic3D814yes—
146C2×C3×Dic3SD1614yes—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×D412yes—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—42no—
152C3×Dic6—48no—
153#626—48no—
154#626—48no—
155C3⋊(C3⋊C8)—22no—
156C3×C3⋊C8—22no—
157C2×C4⋊Q8—31no—
158C2×#127—91no—
159#486—98no—
160C2×#102—31no—
161C2×#102—91no—
162C2×#102—91no—
163C2×#102—91no—
164C2×C4×C8—91no—
165C24×C3—61no—
166C23×D3—21no—
167C23×D3—61no—
168C23×D3—61no—
169C23×D3—121no—
170C2×C3×Q8—64no—
171C2×C3×Q8—124no—
172C2×C3×D4—32no—
173C2×C3×D4—62no—
174C2×C3×D4—62no—
175C2×C3×D4—61no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—41no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—64no—
186C2×#67—64no—
187C2×#67—124no—
188C2×#67—124no—
189C22×Dic3—21no—
190C22×Dic3#6711yescharacteristic
191C22×Dic3#6711yescharacteristic
192C2×D12—22no—
193C2×D12—22no—
194C2×D12—21no—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×D12—64no—
199C2×D12—62no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—64no—
204C2×D12—64no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—122no—
208C2×D12—121no—
209C2×D12—124no—
210C2×D12—124no—
211C2×D12C22×D312yes—
212C2×Dic6—24no—
213C2×Dic6—44no—
214C2×C3×C8—32no—
215C2×C3×C8—62no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—41no—
221C3×C4⋊C4—64no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4C22×D312yes—
224C3×C4⋊C4C22×D312yes—
225C3×C42—32no—
226C3×C42—32no—
227C4⋊Dic3—21no—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—24no—
230C4×Dic3#6712yes—
231C4×Dic3C22×D312yes—
232C2×C3⋊C8—22no—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—62no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—122no—
239C2×C3⋊C8C22×D312yes—
240C22×C32#12412yes—
241C22×C32C2×D812yes—
242C22×C32C2×SD1612yes—
243C22×C32C22×D411yescharacteristic
244C2×C3⋊D3—42no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3—42no—
247C2×C3⋊D3—84no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—42no—
251C2×C3×D3—84no—
252C32×C4—42no—
253C32×C4#12412yes—
254C32×C4C2×#4111yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3×Dic3—42no—
257C3×Dic3C2×D814yes—
258C3×Dic3C2×SD1614yes—
259C22×Q8—61no—
260C22×D4—31no—
261C22×D4—91no—
262C22×D4—181no—
263C22×D4—181no—
264C22×C8—31no—
265C22×C8—91no—
266C4⋊Q8—34no—
267C4⋊Q8—62no—
268#127—94no—
269#127—182no—
270C2×C4⋊C4—31no—
271C2×C4⋊C4—61no—
272C2×C4⋊C4D3211yescharacteristic
273C2×C42—31no—
274#102—34no—
275#102—94no—
276#102—94no—
277#102—94no—
278C4×C8—94no—
279C23×C3—21no—
280C23×C3—62no—
281C23×C3—122no—
282C23×C3—122no—
283C23×C3—122no—
284C23×C3D3×D411yescharacteristic
285C23×C3C2×#6711yescharacteristic
286C22×D3—22no—
287C22×D3—42no—
288C22×D3—42no—
289C22×D3—42no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—122no—
293C22×D3—124no—
294C22×D3—122no—
295C22×D3—122no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—122no—
299C22×D3—122no—
300C22×D3—242no—
301C22×D3—242no—
302C3×Q8—128no—
303C3×D4—62no—
304C3×D4—62no—
305C3×D4—122no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—34no—
313C2×C3×C4—34no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—62no—
320C2×C3×C4—82no—
321C2×C3×C4—122no—
322C2×C3×C4#23512yes—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4#23712yes—
325C2×C3×C4#23912yes—
326C2×C3×C4#23912yes—
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330#67—128no—
331#67—128no—
332C2×Dic3—22no—
333C2×Dic3—42no—
334C2×Dic3#21314yes—
335C2×Dic3#21514yes—
336C2×Dic3C2×#6712yes—
337C2×Dic3C2×#6712yes—
338D12—22no—
339D12—22no—
340D12—42no—
341D12—64no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—122no—
347D12—124no—
348D12—128no—
349D12—128no—
350D12—122no—
351D12—122no—
352Dic6—48no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C2×C32#48614yescomplemented
359C2×C32C2×#12411yescharacteristic
360C2×C32C22×D811yescharacteristic
361C2×C32C22×SD1611yescharacteristic
362C3⋊D3—82no—
363C3×D3—82no—
364C24—61no—
365C24—181no—
366C2×Q8—64no—
367C2×Q8—124no—
368C2×D4—32no—
369C2×D4—62no—
370C2×D4—62no—
371C2×D4—61no—
372C2×D4—92no—
373C2×D4—184no—
374C2×D4—184no—
375C2×D4—182no—
376C2×D4—182no—
377C2×D4—181no—
378C2×D4—364no—
379C2×D4—364no—
380C22×C4—21no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—61no—
384C22×C4C2×D3211yescharacteristic
385C2×C8—32no—
386C2×C8—62no—
387C2×C8—92no—
388C2×C8—182no—
389C4⋊C4—21no—
390C4⋊C4—32no—
391C4⋊C4—64no—
392C4⋊C4—61no—
393C4⋊C4C2×D3212yes—
394C42—32no—
395C42—32no—
396C22×C3—21no—
397C22×C3—22no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—244no—
404C22×C3#88512yes—
405C22×C3D3×D812yes—
406C22×C3D3×SD1612yes—
407C22×C3C2×#21312yes—
408C22×C3C2×#21512yes—
409C22×C3#94712yes—
410C22×C3C2×D3×D411yescharacteristic
411C22×C3C22×#6711yescharacteristic
412C2×D3—42no—
413C2×D3—42no—
414C2×D3—42no—
415C2×D3—84no—
416C2×D3—124no—
417C2×D3—122no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—242no—
424C2×D3—242no—
425C2×D3—248no—
426C2×D3—244no—
427C2×D3—244no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—22no—
431C3×C4—34no—
432C3×C4—34no—
433C3×C4—42no—
434C3×C4—42no—
435C3×C4—82no—
436C3×C4—122no—
437C3×C4#88512yes—
438C3×C4#94712yes—
439C3×C4C2×#23511yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4C2×#23911yescharacteristic
442C3×C4C2×#23911yescharacteristic
443Dic3—42no—
444Dic3C2×#21314yes—
445Dic3C2×#21514yes—
446C32C2×#48611yescharacteristic, complemented, Sylow
447C23—62no—
448C23—122no—
449C23—122no—
450C23—122no—
451C23—182no—
452C23—362no—
453C23—362no—
454C23—362no—
455C23D3×#6711yescharacteristic
456Q8—128no—
457D4—62no—
458D4—62no—
459D4—122no—
460D4—182no—
461D4—182no—
462D4—368no—
463D4—368no—
464D4—362no—
465C2×C4—22no—
466C2×C4—32no—
467C2×C4—32no—
468C2×C4—34no—
469C2×C4—34no—
470C2×C4—42no—
471C2×C4—62no—
472C2×C4—122no—
473C2×C4#379612yes—
474C2×C4#379912yes—
475C2×C4D3×#6711yescharacteristic
476C2×C4C22×D3211yescharacteristic
477C8—62no—
478C8—182no—
479C2×C3—21no—
480C2×C3—24no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—242no—
484C2×C3#476014yescomplemented
485C2×C3#508814yescomplemented
486C2×C3C2×#88511yescharacteristic
487C2×C3C2×D3×D811yescharacteristic
488C2×C3C2×D3×SD1611yescharacteristic
489C2×C3C22×#21311yescharacteristic
490C2×C3C22×#21511yescharacteristic
491C2×C3C2×#94711yescharacteristic
492D3—82no—
493D3—244no—
494D3—242no—
495D3—242no—
496C22—122no—
497C22—122no—
498C22—122no—
499C22—244no—
500C22—362no—
501C22—362no—
502C22—362no—
503C22—724no—
504C22#6390712yes—
505C22D3×#21312yes—
506C22D3×#21512yes—
507C22C2×D3×#6711yescharacteristic
508C4—34no—
509C4—34no—
510C4—42no—
511C4—122no—
512C4#6390712yes—
513C4C2×#379611yescharacteristic
514C4C2×#379911yescharacteristic
515C3—21no—
516C3C2×#476011yescharacteristic, complemented
517C3C2×#508811yescharacteristic, complemented
518C2—242no—
519C2—722no—
520C2#1059054814yesdirect product factor
521C2C2×#6390711yescharacteristic
522C2C2×D3×#21311yescharacteristic
523C2C2×D3×#21511yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#486
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×C3×#888C2semidirect
3. C2×#63636C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63564C2semidirect
6. C2×#63562C2semidirect
7. C2×Dic3×C3⋊C8C2semidirect
8. #10590548C2direct (N × H)
23. C3×#888C22semidirect
26. #63636C22semidirect
27. C3×#809C22semidirect
28. #63564C22semidirect
29. #63562C22semidirect
30. Dic3×C3⋊C8C22semidirect
33. C2×#888D3semidirect
45. C2×#809D3semidirect
111. #888C2×D3semidirect
123. #809C2×D3semidirect
358. C2×C32#486semidirect
446. C32C2×#486semidirect
484. C2×C3#4760semidirect
485. C2×C3#5088semidirect
516. C3C2×#4760semidirect
517. C3C2×#5088semidirect
520. C2#10590548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8882
C2×#639112
C2×#636362
C2×C3×#8092
C2×#635642
C2×#635622
C2×Dic3×C3⋊C82
#105905482
C2×#50883
C2×#47603