Finite Group Databasebeta

← C2×#10590378 #11865700

Subgroups — C2×#10590378 #11865700

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×#875C211yesmaximal, characteristic
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic
5C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590378C218yesmaximal, direct product factor
9C2×#5054—31nomaximal
10C2×#4845—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×C4×C3⋊Dic3—21no—
18C4×#634—22no—
19C4×#634C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×(C2×D3)⋊C4—21no—
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×#875—22no—
25C3×#875C2214yes—
26C2×#3719—24no—
27C2×#3719C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yes—
30C3×C4⋊(C3⋊C8)C2214yescomplemented
31#63566C2214yescomplemented
32#63563C2214yes—
33C2×C3×#124—31no—
34C22×#216—31no—
35C22×#214—31no—
36C22×Dic12—31no—
37C22×#204—31no—
38C2×#875D311yescharacteristic
39C2×C4×Dic6—31no—
40C2×C4×Dic6—31no—
41C2×C4×Dic6—61no—
42C2×C3×C4⋊C8—31no—
43C2×#835—31no—
44C2×#832—31no—
45C2×#821—31no—
46C2×#816—31no—
47#5054—38no—
48C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
49#4845—38no—
50C23×C3×D3—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634D414yes—
59C2×#634C2312yes—
60C22×C3×Dic3—21no—
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C32×C42D412yes—
70C32×C42C2312yes—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73#3750—24no—
74C4×C3⋊Dic3—24no—
75C3×(C2×D3)⋊C4—24no—
76C3×(C2×D3)⋊C4—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81#3719—28no—
82#3716—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—31no—
86C22×D12C2×D311yescharacteristic
87C22×Dic6—31no—
88C22×Dic6—31no—
89C22×Dic6—61no—
90C22×Dic6C2×D311yescharacteristic
91C22×C3×C8—31no—
92C22×C3×C8—31no—
93C3×#124—34no—
94C3×#124—62no—
95C2×C3×C22⋊C4—61no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C42—21no—
98C2×C3×C42C2×D311yescharacteristic
99C2×C3×C42C2×D311yescharacteristic
100C2×#216—34no—
101C2×#216—64no—
102C2×#214—34no—
103C2×#214—64no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—61no—
109C2×Dic3⋊C4—62no—
110C2×Dic3⋊C4—61no—
111C2×Dic3⋊C4—61no—
112C2×C4×Dic3—62no—
113C2×C4×Dic3—61no—
114C2×C4×Dic3—61no—
115C22×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117C2×Dic12—34no—
118C2×Dic12—64no—
119C2×#204—34no—
120C2×#204—64no—
121#875—22no—
122#875C2×D314yes—
123C4×Dic6—34no—
124C4×Dic6—34no—
125C4×Dic6—64no—
126C4×Dic6—64no—
127C4×Dic6—62no—
128C4×Dic6—62no—
129C3×C4⋊C8—34no—
130#835—34no—
131#832—34no—
132#821—34no—
133#816—34no—
134C4⋊(C3⋊C8)C2×D314yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4C2×D412yes—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D412yes—
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—24no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—42no—
152#634—24no—
153#634—22no—
154#634C2×D414yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—42no—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—42no—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—22no—
165C22×Q16—91no—
166C22×SD16—91no—
167C2×#124—31no—
168C2×C4×Q8—91no—
169#464—98no—
170C2×C4⋊C8—31no—
171C2×#103—91no—
172C2×#102—91no—
173C24×C3—61no—
174C23×D3—21no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8—62no—
178C2×C3×Q8—62no—
179C2×C3×D4—32no—
180C2×C3×D4—61no—
181C2×C3×D4—62no—
182C2×C3×D4—62no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4D1211yescharacteristic
188C22×C3×C4D1211yescharacteristic
189C22×C3×C4#6711yescharacteristic
190C22×C3×C4#6711yescharacteristic
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—21no—
194C22×Dic3—62no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—62no—
198C22×Dic3—61no—
199C22×Dic3—61no—
200C2×D12—22no—
201C2×D12—22no—
202C2×D12—21no—
203C2×D12C22×D312yes—
204C2×Dic6—22no—
205C2×Dic6—22no—
206C2×Dic6—21no—
207C2×Dic6—34no—
208C2×Dic6—34no—
209C2×Dic6—32no—
210C2×Dic6—32no—
211C2×Dic6—62no—
212C2×Dic6—64no—
213C2×Dic6—62no—
214C2×Dic6—64no—
215C2×Dic6—61no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—61no—
219C2×Dic6C22×D312yes—
220C2×C3×C8—32no—
221C2×C3×C8—32no—
222C2×C3×C8—62no—
223C2×C3×C8—62no—
224C3×C22⋊C4—64no—
225C3×C22⋊C4—64no—
226C3×C42—22no—
227C3×C42—22no—
228C3×C42D1212yes—
229C3×C42#6712yes—
230C3×C42C22×D312yes—
231C3×C42C22×D312yes—
232#216—68no—
233#214—68no—
234(C2×D3)⋊C4—24no—
235(C2×D3)⋊C4—24no—
236C4⋊Dic3—32no—
237C4⋊Dic3—32no—
238C4⋊Dic3—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242Dic3⋊C4—68no—
243Dic3⋊C4—64no—
244Dic3⋊C4—64no—
245C4×Dic3—68no—
246C4×Dic3—64no—
247C4×Dic3—64no—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—22no—
250C2×C3⋊C8C22×D312yes—
251C2×C3⋊C8C22×D312yes—
252Dic12—68no—
253#204—68no—
254C22×C32#12112yes—
255C22×C32#13512yes—
256C22×C32#13712yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—84no—
262C32×C4—22no—
263C32×C4—22no—
264C32×C4#12112yes—
265C32×C4C22×D411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—24no—
268C3⋊Dic3—42no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×Q8—91no—
272C22×D4—31no—
273C2×Q16—94no—
274C2×Q16—184no—
275C2×SD16—94no—
276C2×SD16—184no—
277C22×C8—31no—
278C22×C8—31no—
279#124—34no—
280#124—62no—
281C4×Q8—94no—
282C4×Q8—182no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—181no—
285C2×C22⋊C4—61no—
286C2×C22⋊C4—61no—
287C2×C42—181no—
288C2×C42D3211yescharacteristic
289C4⋊C8—34no—
290#103—94no—
291#102—94no—
292C23×C3—21no—
293C23×C3—62no—
294C23×C3—122no—
295C23×C3—122no—
296C23×C3—122no—
297C23×C3C2×D1211yescharacteristic
298C23×C3C2×#6711yescharacteristic
299C22×D3—22no—
300C22×D3—42no—
301C22×D3—42no—
302C22×D3—42no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C3×D4—62no—
307C3×D4—62no—
308C3×D4—122no—
309C2×C3×C4—24no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—21no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—42no—
321C2×C3×C4—62no—
322C2×C3×C4—122no—
323C2×C3×C4C2×D1212yes—
324C2×C3×C4C2×D1212yes—
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4D3×D412yes—
327C2×C3×C4D3×D412yes—
328C2×C3×C4#23712yes—
329C2×C3×C4#23912yes—
330C2×C3×C4C2×#6712yes—
331C2×C3×C4C2×#6712yes—
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×Dic3—22no—
336C2×Dic3—42no—
337C2×Dic3—64no—
338C2×Dic3—68no—
339C2×Dic3—64no—
340C2×Dic3—64no—
341C2×Dic3—62no—
342C2×Dic3—62no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—124no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349D12—22no—
350D12—22no—
351D12—42no—
352Dic6—22no—
353Dic6—22no—
354Dic6—34no—
355Dic6—34no—
356Dic6—42no—
357Dic6—64no—
358Dic6—64no—
359Dic6—68no—
360Dic6—64no—
361Dic6—64no—
362Dic6—62no—
363Dic6—62no—
364C3×C8—62no—
365C3×C8—62no—
366C3⋊C8—22no—
367C3⋊C8—22no—
368C2×C32#46414yescomplemented
369C2×C32C2×#12111yescharacteristic
370C2×C32C2×#13511yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C3×D3—82no—
373C24—61no—
374C2×Q8—32no—
375C2×Q8—61no—
376C2×Q8—62no—
377C2×Q8—62no—
378C2×Q8—92no—
379C2×Q8—94no—
380C2×Q8—182no—
381C2×Q8—181no—
382C2×D4—32no—
383C2×D4—62no—
384C2×D4—62no—
385C2×D4—61no—
386C22×C4—61no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4#62611yescharacteristic
390C22×C4#62611yescharacteristic
391C22×C4C2×D3211yescharacteristic
392Q16—188no—
393SD16—188no—
394C2×C8—32no—
395C2×C8—32no—
396C2×C8—62no—
397C2×C8—62no—
398C4⋊C4—92no—
399C4⋊C4—181no—
400C4⋊C4—184no—
401C22⋊C4—64no—
402C22⋊C4—64no—
403C42—184no—
404C42#62612yes—
405C42C2×D3212yes—
406C22×C3—21no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3—122no—
413C22×C3—244no—
414C22×C3#89512yes—
415C22×C3#90412yes—
416C22×C3#90912yes—
417C22×C3#93812yes—
418C22×C3#95012yes—
419C22×C3#95112yes—
420C22×C3C22×D1211yescharacteristic
421C22×C3C22×#6711yescharacteristic
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—84no—
426C3×C4—24no—
427C3×C4—22no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—42no—
435C3×C4—122no—
436C3×C4#89512yes—
437C3×C4#93812yes—
438C3×C4C2×D3×D411yescharacteristic
439C3×C4C2×D3×D411yescharacteristic
440C3×C4C2×#23711yescharacteristic
441C3×C4C2×#23911yescharacteristic
442Dic3—42no—
443Dic3—68no—
444Dic3—64no—
445Dic3—64no—
446Dic3—124no—
447Dic3—122no—
448Dic3—122no—
449C32C2×#46411yescharacteristic, complemented, Sylow
450C23—62no—
451C23—122no—
452C23—122no—
453C23—122no—
454C23C2×#62611yescharacteristic
455Q8—62no—
456Q8—62no—
457Q8—94no—
458Q8—122no—
459Q8—182no—
460Q8—184no—
461D4—62no—
462D4—62no—
463D4—122no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—62no—
467C2×C4—122no—
468C2×C4—182no—
469C2×C4—184no—
470C2×C4—182no—
471C2×C4—362no—
472C2×C4#379612yes—
473C2×C4#380212yes—
474C2×C4C2×#62612yes—
475C2×C4C2×#62612yes—
476C2×C4C2×#62611yescharacteristic
477C2×C4C22×D3211yescharacteristic
478C8—62no—
479C8—62no—
480C2×C3—24no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—242no—
485C2×C3#484514yescomplemented
486C2×C3#505414yescomplemented
487C2×C3C2×#89511yescharacteristic
488C2×C3C2×#90411yescharacteristic
489C2×C3C2×#90911yescharacteristic
490C2×C3C2×#93811yescharacteristic
491C2×C3C2×#95011yescharacteristic
492C2×C3C2×#95111yescharacteristic
493D3—82no—
494C22—122no—
495C22—122no—
496C22—122no—
497C22—244no—
498C22#6382912yes—
499C22#6383112yes—
500C22#6391612yes—
501C22C22×#62611yescharacteristic
502C4—22no—
503C4—22no—
504C4—122no—
505C4—184no—
506C4—362no—
507C4#6391612yes—
508C4C2×#379611yescharacteristic
509C4C2×#380211yescharacteristic
510C3—21no—
511C3C2×#484511yescharacteristic, complemented
512C3C2×#505411yescharacteristic, complemented
513C2—242no—
514C2#1059037814yesdirect product factor
515C2C2×#6382911yescharacteristic
516C2C2×#6383111yescharacteristic
517C2C2×#6391611yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C22×#3719C2semidirect
5. C2×C3×C4⋊(C3⋊C8)C2semidirect
6. C2×#63566C2semidirect
8. #10590378C2direct (N × H)
19. C4×#634C22semidirect
27. C2×#3719C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63566C22semidirect
48. C2×C4⋊(C3⋊C8)D3semidirect
134. C4⋊(C3⋊C8)C2×D3semidirect
368. C2×C32#464semidirect
449. C32C2×#464semidirect
485. C2×C3#4845semidirect
486. C2×C3#5054semidirect
511. C3C2×#4845semidirect
512. C3C2×#5054semidirect
514. C2#10590378direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8752
C22×#37192
C22×#37162
C2×C3×C4⋊(C3⋊C8)2
C2×#635662
C2×#635632
#105903782
C2×#50543
C2×#48453