Finite Group Databasebeta

← C2×#10590522 #11866928

Subgroups — C2×#10590522 #11866928

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C2×#63871C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C22×#3712C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C2×C3×#807C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590522C218yesmaximal, direct product factor
9C2×#4886—31nomaximal
10C2×#4812—31nomaximal
11C22×C4⋊(C3⋊D3)—21no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752—21no—
17#64104—22no—
18#64104C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×#3722—21no—
24#63871—22no—
25#63871C2214yescomplemented
26C2×#3717—24no—
27C2×#3717C2214yescomplemented
28C2×#3712—24no—
29C2×#3712C2214yescomplemented
30C3×#810C2214yescomplemented
31C3×#807C2214yescomplemented
32#63564C2214yescomplemented
33C2×#946—31no—
34C22×#215—31no—
35C22×#204—31no—
36C22×ΓL(1,𝔽25)—31no—
37C22×ΓL(1,𝔽25)—31no—
38C2×#897—31no—
39C2×#895—31no—
40C2×#895—31no—
41C2×#895—61no—
42C2×C3×#107—31no—
43C2×C3×#103—31no—
44C2×#821—31no—
45C2×#810D311yescharacteristic, complemented
46C2×#809—31no—
47C2×#807D311yescharacteristic, complemented
48#4886—38no—
49#4812—38no—
50C23×C3⋊D3—21no—
51C23×C3⋊D3D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—24no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—44no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3—22no—
63C2×C4×C3⋊D3D412yes—
64C2×C4×C3⋊D3C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73#3752—24no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8D414yescomplemented
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80Dic3⋊Dic3—24no—
81#3722—24no—
82#3717—28no—
83#3712—28no—
84C2×#468—91noSylow
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×D12—61no—
90C22×D12—61no—
91C22×D12—62no—
92C22×C4×D3—31no—
93C22×C4×D3—31no—
94C22×C4×D3—61no—
95C22×Dic6C2×D311yescharacteristic
96C22×C3×C8—31no—
97C22×C3×C8—31no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C4⋊C4C2×D311yescharacteristic
102#946—34no—
103#946—62no—
104C2×#215—34no—
105C2×#215—64no—
106C2×(C2×D3)⋊C4—61no—
107C2×(C2×D3)⋊C4—61no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—62no—
111C2×C4⋊Dic3—61no—
112C2×C4⋊Dic3C2×D311yescharacteristic
113C2×Dic3⋊C4—61no—
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—62no—
124#895—34no—
125#895—34no—
126#895—64no—
127#895—62no—
128#895—62no—
129#895—64no—
130C3×#107—34no—
131C3×#103—34no—
132#821—34no—
133#810C2×D314yescomplemented
134#809—34no—
135#807C2×D314yescomplemented
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3—42no—
143C22×C3⋊D3—42no—
144C22×C3⋊D3C2×D412yes—
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⋊Dic3C2×D412yes—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)—22no—
155C4⋊(C3⋊D3)—48no—
156C4⋊(C3⋊D3)—42no—
157C4×C3⋊D3—24no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3—42no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
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—31no—
176C2×#102—91no—
177C23×D3—31no—
178C23×D3—31no—
179C23×D3—61no—
180C23×D3—62no—
181C23×D3—61no—
182C23×D3—61no—
183C2×C3×Q8—32no—
184C2×C3×Q8—61no—
185C2×C3×Q8—62no—
186C2×C3×Q8—62no—
187C22×C3×C4—22no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—61no—
200C2×D12—32no—
201C2×D12—32no—
202C2×D12—62no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—64no—
208C2×D12—64no—
209C2×D12—68no—
210C2×D12—62no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—122no—
214C2×D12—122no—
215C2×D12—128no—
216C2×D12—124no—
217C2×D12—124no—
218C2×C4×D3—32no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×Dic6—22no—
231C2×Dic6—22no—
232C2×Dic6—21no—
233C2×Dic6C22×D312yes—
234C2×C3×C8—34no—
235C2×C3×C8—32no—
236C2×C3×C8—32no—
237C2×C3×C8—62no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—32no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4C22×D312yes—
245C3×C4⋊C4C22×D312yes—
246#215—68no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—68no—
252C4⋊Dic3—21no—
253C4⋊Dic3—64no—
254C4⋊Dic3C22×D312yes—
255Dic3⋊C4—64no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8D1214yescomplemented
258C2×C3⋊C8C22×D312yes—
259C2×C3⋊C8C22×D312yes—
260#204—68no—
261ΓL(1,𝔽25)—68no—
262ΓL(1,𝔽25)—68no—
263C22×C32#12112yes—
264C22×C32AGL(1,ℤ/8)12yes—
265C22×C32#13712yes—
266C22×C32C22×D411yescharacteristic
267C2×C3⋊D3—22no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—44no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—84no—
275C32×C4—42no—
276C32×C4#12112yes—
277C32×C4C22×D411yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3⋊Dic3—22no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×Q8—31no—
283C22×D4—91no—
284C22×D4—181no—
285C23×C4—91no—
286C2×SD16—94no—
287C2×SD16—184no—
288C2×M16—94no—
289C2×M16—184no—
290C22×C8—31no—
291C22×C8—31no—
292C22⋊Q8—94no—
293C22⋊Q8—182no—
294#121—94no—
295#121—182no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—181no—
298C2×C4⋊C4D3211yescharacteristic
299C2×C22⋊C4—181no—
300C2×C22⋊C4—181no—
301#107—34no—
302#103—34no—
303#102—94no—
304C23×C3—21no—
305C23×C3D3×D411yescharacteristic
306C23×C3D3×D411yescharacteristic
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—62no—
310C22×D3—64no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—64no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—122no—
321C22×D3—122no—
322C22×D3—124no—
323C22×D3—124no—
324C22×D3—124no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—122no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—122no—
331C3×Q8—62no—
332C3×Q8—62no—
333C3×Q8—122no—
334C2×C3×C4—24no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—44no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—122no—
347C2×C3×C4—122no—
348C2×C3×C4C2×D1212yes—
349C2×C3×C4#23512yes—
350C2×C3×C4D3×D412yes—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4#23912yes—
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—42no—
361C2×Dic3—42no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—122no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—122no—
371D12—122no—
372D12—124no—
373D12—1216no—
374D12—128no—
375D12—128no—
376D12—122no—
377D12—122no—
378C4×D3—64no—
379C4×D3—64no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—62no—
384C4×D3—122no—
385C4×D3—122no—
386C4×D3—124no—
387Dic6—22no—
388Dic6—22no—
389Dic6—42no—
390C3×C8—34no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8C2×D1214yescomplemented
394C2×C32#46814yescomplemented
395C2×C32C2×#12111yescharacteristic
396C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
397C2×C32C2×#13711yescharacteristic
398C3⋊D3—42no—
399C3⋊D3—82no—
400C24—91no—
401C24—181no—
402C2×Q8—32no—
403C2×Q8—61no—
404C2×Q8—62no—
405C2×Q8—62no—
406C2×D4—92no—
407C2×D4—184no—
408C2×D4—182no—
409C2×D4—182no—
410C2×D4—181no—
411C2×D4—364no—
412C22×C4—21no—
413C22×C4—61no—
414C22×C4—61no—
415C22×C4—91no—
416C22×C4—92no—
417C22×C4—92no—
418C22×C4—182no—
419C22×C4—182no—
420C22×C4C2×D3211yescharacteristic
421SD16—188no—
422M16—188no—
423C2×C8—32no—
424C2×C8—34no—
425C2×C8—32no—
426C2×C8—62no—
427C4⋊C4—21no—
428C4⋊C4—32no—
429C4⋊C4—61no—
430C4⋊C4—184no—
431C4⋊C4C2×D3212yes—
432C22⋊C4—184no—
433C22⋊C4—184no—
434C22×C3—21no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3#88412yes—
439C22×C3#89512yes—
440C22×C3#91112yes—
441C22×C3#91412yes—
442C22×C3#91812yes—
443C22×C3#91812yes—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C2×D3—64no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—62no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—128no—
456C2×D3—124no—
457C2×D3—124no—
458C2×D3—124no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—248no—
468C2×D3—244no—
469C2×D3—244no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—44no—
474C3×C4—42no—
475C3×C4—42no—
476C3×C4—122no—
477C3×C4—122no—
478C3×C4#88412yes—
479C3×C4#89512yes—
480C3×C4C22×D1211yescharacteristic
481C3×C4C2×#23511yescharacteristic
482C3×C4C2×D3×D411yescharacteristic
483C3×C4C2×#23911yescharacteristic
484Dic3—42no—
485Dic3—42no—
486Dic3—62no—
487Dic3—62no—
488Dic3—122no—
489C32C2×#46811yescharacteristic, complemented, Sylow
490C23—92no—
491C23—182no—
492C23—182no—
493C23—182no—
494C23—182no—
495C23—362no—
496C23—362no—
497C23—362no—
498C23#381111yescharacteristic
499Q8—62no—
500Q8—62no—
501Q8—122no—
502D4—182no—
503D4—182no—
504D4—368no—
505D4—362no—
506C2×C4—22no—
507C2×C4—42no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—92no—
511C2×C4—122no—
512C2×C4—122no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—184no—
517C2×C4#379912yes—
518C2×C4D3×D1212yes—
519C2×C4#381111yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—34no—
522C8—62no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—24no—
526C2×C3—21no—
527C2×C3#481214yescomplemented
528C2×C3#488614yescomplemented
529C2×C3C2×#88411yescharacteristic
530C2×C3C2×#89511yescharacteristic
531C2×C3C2×#91111yescharacteristic
532C2×C3C2×#91411yescharacteristic
533C2×C3C2×#91811yescharacteristic
534C2×C3C2×#91811yescharacteristic
535D3—124no—
536D3—122no—
537D3—122no—
538D3—244no—
539D3—242no—
540D3—242no—
541C22—182no—
542C22—182no—
543C22—182no—
544C22—364no—
545C22—362no—
546C22—362no—
547C22—362no—
548C22—724no—
549C22#6391012yes—
550C22#6393712yes—
551C22#6394512yes—
552C22C2×#381111yescharacteristic
553C4—42no—
554C4—122no—
555C4—122no—
556C4—182no—
557C4#6391012yes—
558C4C2×#379911yescharacteristic
559C4C2×D3×D1211yescharacteristic
560C3—21no—
561C3C2×#481211yescharacteristic, complemented
562C3C2×#488611yescharacteristic, complemented
563C2—362no—
564C2—722no—
565C2#1059052214yesdirect product factor
566C2C2×#6391011yescharacteristic
567C2C2×#6393711yescharacteristic
568C2C2×#6394511yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#64104C2
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
2. C2×#63871C2semidirect
3. C22×#3717C2semidirect
4. C22×#3712C2semidirect
5. C2×C3×#810C2semidirect
6. C2×C3×#807C2semidirect
7. C2×#63564C2semidirect
8. #10590522C2direct (N × H)
25. #63871C22semidirect
27. C2×#3717C22semidirect
29. C2×#3712C22semidirect
30. C3×#810C22semidirect
31. C3×#807C22semidirect
32. #63564C22semidirect
45. C2×#810D3semidirect
47. C2×#807D3semidirect
77. C2×C3×C3⋊C8D4semidirect
133. #810C2×D3semidirect
135. #807C2×D3semidirect
168. C3×C3⋊C8C2×D4semidirect
257. C2×C3⋊C8D12semidirect
393. C3⋊C8C2×D12semidirect
394. C2×C32#468semidirect
489. C32C2×#468semidirect
527. C2×C3#4812semidirect
528. C2×C3#4886semidirect
561. C3C2×#4812semidirect
562. C3C2×#4886semidirect
565. C2#10590522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641042
C2×#638712
C22×#37172
C22×#37122
C2×C3×#8102
C2×C3×#8072
C2×#635642
#105905222
C2×#48863
C2×#48123