Finite Group Databasebeta

← C2×#10590506 #11866934

Subgroups — C2×#10590506 #11866934

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic, complemented
4C22×#3712C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590506C218yesmaximal, direct product factor
9C2×#4886—31nomaximal
10C2×#4780—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×#626—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)—21no—
18#64106—22no—
19#64106C2214yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C2×(C2×D3)⋊Dic3—21no—
24#63916—22no—
25#63916C2214yes—
26C2×#3716—24no—
27C2×#3716C2214yescomplemented
28C2×#3712—24no—
29C2×#3712C2214yescomplemented
30C3×#809C2214yescomplemented
31C3×#807C2214yescomplemented
32#63567C2214yescomplemented
33C2×#938—31no—
34C22×#214—31no—
35C22×#204—31no—
36C22×ΓL(1,𝔽25)—31no—
37C22×ΓL(1,𝔽25)—31no—
38C2×#897—31no—
39C2×#897—31no—
40C2×#897—61no—
41C2×#895—31no—
42C2×C3×#107—31no—
43C2×C3×#102—31no—
44C2×#816—31no—
45C2×#810—31no—
46C2×#809D311yescharacteristic, complemented
47C2×#807D311yescharacteristic, complemented
48#4886—38no—
49#4780—38no—
50C23×C3⋊D3D411yescharacteristic
51C23×C3×D3—21no—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D411yescharacteristic
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3D412yes—
59C2×C4×C3⋊D3C2312yes—
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C22×C3×Dic3—21no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×#626—24no—
70C2×#626—44no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73#3752—24no—
74C4⋊(C3⋊Dic3)—24no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8D414yescomplemented
79C2×C3×C3⋊C8C2312yes—
80C2×C3×C3⋊C8C2312yes—
81(C2×D3)⋊Dic3—24no—
82#3716—28no—
83#3712—28no—
84C2×#468—91noSylow
85C22×C3×D4—31no—
86C22×#67—61no—
87C22×D12—61no—
88C22×D12C2×D311yescharacteristic
89C22×C4×D3—31no—
90C22×C4×D3—31no—
91C22×C4×D3—61no—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×#217—61no—
102#938—34no—
103#938—62no—
104C2×#214—34no—
105C2×#214—64no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—62no—
110C2×C4⋊Dic3—61no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3—62no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115C22×C3⋊C8C2×D311yescharacteristic
116C2×#204—34no—
117C2×#204—64no—
118C2×ΓL(1,𝔽25)—34no—
119C2×ΓL(1,𝔽25)—34no—
120C2×ΓL(1,𝔽25)—64no—
121C2×ΓL(1,𝔽25)—64no—
122#897—34no—
123#897—34no—
124#897—64no—
125#897—62no—
126#897—62no—
127#897—64no—
128#895—34no—
129#895—62no—
130C3×#107—34no—
131C3×#102—34no—
132#816—34no—
133#810—34no—
134#809C2×D314yescomplemented
135#807C2×D314yescomplemented
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3C2×D412yes—
141C22×C3×D3—22no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C2×C32×C4—22no—
146C2×C32×C4—42no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—42no—
154C2×C3⋊Dic3C2×D412yes—
155C4×C3⋊D3—24no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158#634—22no—
159#634—22no—
160#634—42no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—42no—
166#626—48no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8C2×D414yescomplemented
169C22×SD16—91no—
170C22×M16—91no—
171C2×C22⋊Q8—91no—
172C2×#121—91no—
173#468—98no—
174C2×#107—31no—
175C2×#103—91no—
176C2×#102—31no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—31no—
180C23×D3—31no—
181C23×D3—61no—
182C2×C3×D4—32no—
183C2×C3×D4—62no—
184C2×C3×D4—61no—
185C2×C3×D4—62no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—64no—
194C2×#67—124no—
195C22×Dic3—21no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—61no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C2×D12—22no—
203C2×D12—22no—
204C2×D12—21no—
205C2×D12—64no—
206C2×D12—124no—
207C2×D12C22×D312yes—
208C2×C4×D3—32no—
209C2×C4×D3—32no—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—122no—
219C2×C4×D3—122no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—122no—
231C2×Dic6—122no—
232C2×C3×C8—34no—
233C2×C3×C8—32no—
234C2×C3×C8—32no—
235C2×C3×C8—62no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4C22×D312yes—
243C3×C4⋊C4C22×D312yes—
244#217—64no—
245#214—68no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—68no—
250C4⋊Dic3—21no—
251C4⋊Dic3—64no—
252C4⋊Dic3—64no—
253C4⋊Dic3—68no—
254C4⋊Dic3C22×D312yes—
255C2×C3⋊C8—22no—
256C2×C3⋊C8D1214yescomplemented
257C2×C3⋊C8C22×D312yes—
258C2×C3⋊C8C22×D312yes—
259#204—68no—
260ΓL(1,𝔽25)—68no—
261ΓL(1,𝔽25)—68no—
262C22×C32#12112yes—
263C22×C32AGL(1,ℤ/8)12yes—
264C22×C32#13712yes—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3—22no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—44no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—84no—
274C32×C4—42no—
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—22no—
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C22×Q8—91no—
282C22×D4—31no—
283C22×D4—181no—
284C23×C4—91no—
285C2×SD16—94no—
286C2×SD16—184no—
287C2×M16—94no—
288C2×M16—184no—
289C22×C8—31no—
290C22×C8—31no—
291C22⋊Q8—94no—
292C22⋊Q8—182no—
293#121—94no—
294#121—182no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—181no—
297C2×C4⋊C4D3211yescharacteristic
298C2×C22⋊C4—181no—
299C2×C22⋊C4—181no—
300#107—34no—
301#103—94no—
302#102—34no—
303C23×C3—21no—
304C23×C3—62no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3—122no—
308C23×C3D3×D411yescharacteristic
309C23×C3D3×D411yescharacteristic
310C22×D3—22no—
311C22×D3—32no—
312C22×D3—32no—
313C22×D3—42no—
314C22×D3—42no—
315C22×D3—42no—
316C22×D3—62no—
317C22×D3—64no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—122no—
325C22×D3—122no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—122no—
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—44no—
337C2×C3×C4—42no—
338C2×C3×C4—42no—
339C2×C3×C4—62no—
340C2×C3×C4—122no—
341C2×C3×C4C2×D1212yes—
342C2×C3×C4#23512yes—
343C2×C3×C4D3×D412yes—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23912yes—
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—128no—
350C2×Dic3—22no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—42no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—64no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—124no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364D12—22no—
365D12—22no—
366D12—42no—
367D12—128no—
368C4×D3—64no—
369C4×D3—64no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3—124no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—122no—
383Dic6—124no—
384Dic6—122no—
385Dic6—122no—
386C3×C8—34no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8C2×D1214yescomplemented
390C2×C32#46814yescomplemented
391C2×C32C2×#12111yescharacteristic
392C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
393C2×C32C2×#13711yescharacteristic
394C3⋊D3—42no—
395C3×D3—82no—
396C24—61no—
397C24—91no—
398C2×Q8—92no—
399C2×Q8—181no—
400C2×Q8—182no—
401C2×Q8—182no—
402C2×D4—32no—
403C2×D4—62no—
404C2×D4—62no—
405C2×D4—61no—
406C2×D4—184no—
407C2×D4—364no—
408C22×C4—21no—
409C22×C4—61no—
410C22×C4—91no—
411C22×C4—92no—
412C22×C4—92no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417SD16—188no—
418M16—188no—
419C2×C8—32no—
420C2×C8—34no—
421C2×C8—32no—
422C2×C8—62no—
423C4⋊C4—21no—
424C4⋊C4—32no—
425C4⋊C4—61no—
426C4⋊C4—184no—
427C4⋊C4C2×D3212yes—
428C22⋊C4—184no—
429C22⋊C4—184no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—122no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—244no—
438C22×C3#88412yes—
439C22×C3#89512yes—
440C22×C3#91112yes—
441C22×C3#91112yes—
442C22×C3#91512yes—
443C22×C3#91812yes—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—42no—
449C2×D3—64no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—84no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—128no—
460C2×D3—124no—
461C2×D3—124no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—44no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—122no—
469C3×C4#88412yes—
470C3×C4#89512yes—
471C3×C4C22×D1211yescharacteristic
472C3×C4C2×#23511yescharacteristic
473C3×C4C2×D3×D411yescharacteristic
474C3×C4C2×#23911yescharacteristic
475Dic3—42no—
476Dic3—62no—
477Dic3—62no—
478Dic3—122no—
479Dic3—124no—
480Dic3—122no—
481Dic3—122no—
482C32C2×#46811yescharacteristic, complemented, Sylow
483C23—62no—
484C23—92no—
485C23—122no—
486C23—122no—
487C23—122no—
488C23—182no—
489C23—182no—
490C23—182no—
491C23#381111yescharacteristic
492Q8—182no—
493Q8—182no—
494Q8—362no—
495D4—62no—
496D4—62no—
497D4—122no—
498D4—368no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—122no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—184no—
508C2×C4—182no—
509C2×C4—362no—
510C2×C4#379912yes—
511C2×C4D3×D1212yes—
512C2×C4#381111yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—34no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—24no—
519C2×C3—21no—
520C2×C3—242no—
521C2×C3#478014yescomplemented
522C2×C3#488614yescomplemented
523C2×C3C2×#88411yescharacteristic
524C2×C3C2×#89511yescharacteristic
525C2×C3C2×#91111yescharacteristic
526C2×C3C2×#91111yescharacteristic
527C2×C3C2×#91511yescharacteristic
528C2×C3C2×#91811yescharacteristic
529D3—82no—
530D3—124no—
531D3—122no—
532D3—122no—
533C22—122no—
534C22—122no—
535C22—122no—
536C22—182no—
537C22—182no—
538C22—182no—
539C22—244no—
540C22—364no—
541C22#6391012yes—
542C22#6392712yes—
543C22#6395112yes—
544C22C2×#381111yescharacteristic
545C4—42no—
546C4—122no—
547C4—182no—
548C4—362no—
549C4#6391012yes—
550C4C2×#379911yescharacteristic
551C4C2×D3×D1211yescharacteristic
552C3—21no—
553C3C2×#478011yescharacteristic, complemented
554C3C2×#488611yescharacteristic, complemented
555C2—242no—
556C2—362no—
557C2#1059050614yesdirect product factor
558C2C2×#6391011yescharacteristic
559C2C2×#6392711yescharacteristic
560C2C2×#6395111yescharacteristic
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×#468
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×#64106C2semidirect
3. C22×#3716C2semidirect
4. C22×#3712C2semidirect
5. C2×C3×#809C2semidirect
6. C2×C3×#807C2semidirect
7. C2×#63567C2semidirect
8. #10590506C2direct (N × H)
19. #64106C22semidirect
27. C2×#3716C22semidirect
29. C2×#3712C22semidirect
30. C3×#809C22semidirect
31. C3×#807C22semidirect
32. #63567C22semidirect
46. C2×#809D3semidirect
47. C2×#807D3semidirect
78. C2×C3×C3⋊C8D4semidirect
134. #809C2×D3semidirect
135. #807C2×D3semidirect
168. C3×C3⋊C8C2×D4semidirect
256. C2×C3⋊C8D12semidirect
389. C3⋊C8C2×D12semidirect
390. C2×C32#468semidirect
482. C32C2×#468semidirect
521. C2×C3#4780semidirect
522. C2×C3#4886semidirect
553. C3C2×#4780semidirect
554. C3C2×#4886semidirect
557. C2#10590506direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641062
C2×#639162
C22×#37162
C22×#37122
C2×C3×#8092
C2×C3×#8072
C2×#635672
#105905062
C2×#48863
C2×#47803