Finite Group Databasebeta

← C2×#10590616 #11863792

Subgroups — C2×#10590616 #11863792

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C22×#3718C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic, complemented
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590616C218yesmaximal, direct product factor
9C2×#5047—31nomaximal
10C2×#4808—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×#624—21no—
17C2×#3799—24no—
18C2×#3799—22no—
19C2×#3799—24no—
20C2×#3799C2214yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4—21no—
24C2×C3×C4⋊Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#897—22no—
27C3×#897C2214yescomplemented
28C2×#3718—24no—
29C2×#3718C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32#63636C2214yescomplemented
33C3×#810C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×#239—31no—
36C22×#235—31no—
37C2×C3×C22⋊Q8—31no—
38C22×#216—31no—
39C22×#216—31no—
40C22×#215—31no—
41C22×#204—31no—
42C2×#897D311yescharacteristic, complemented
43C2×C3×#103—31no—
44C2×#830—31no—
45C2×(C2×D3)⋊C8—31no—
46#5047—38no—
47C2×#810D311yescharacteristic, complemented
48C2×#809—31no—
49C2×#809—31no—
50C2×#809—61no—
51#4808—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)D414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D414yes—
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×#624—28no—
78C2×#624—24no—
79#3799—216no—
80#3799—28no—
81#3799—28no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—24no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90#3718—28no—
91#3717—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C22×#67—61no—
97C2×#239—34no—
98C2×#239—64no—
99C2×#239—64no—
100C2×#239—62no—
101C2×#235—34no—
102C2×#235—64no—
103C2×#235—62no—
104C2×#235—64no—
105C22×D12—31no—
106C22×D12—31no—
107C22×D12—61no—
108C22×D12—61no—
109C22×C4×D3—61no—
110C22×C4×D3—61no—
111C22×C4×D3C2×D311yescharacteristic
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C22×C3×C8—31no—
115C3×C22⋊Q8—34no—
116C3×C22⋊Q8—62no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—61no—
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4—61no—
122C2×#216—34no—
123C2×#216—34no—
124C2×#216—64no—
125C2×#216—64no—
126C2×#215—34no—
127C2×#215—64no—
128C2×(C2×D3)⋊C4—21no—
129C2×C4⋊Dic3—21no—
130C22×C3⋊C8—31no—
131C22×C3⋊C8—31no—
132C22×C3⋊C8—61no—
133C22×C3⋊C8C2×D311yescharacteristic
134C2×#204—34no—
135C2×#204—64no—
136#897—22no—
137#897C2×D314yescomplemented
138C3×#103—34no—
139#830—34no—
140(C2×D3)⋊C8—34no—
141#810C2×D314yescomplemented
142#809—34no—
143#809—34no—
144#809—64no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—24no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—42no—
149C22×C3⋊D3—42no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3C2×D412yes—
154C2×C32×C4—22no—
155C2×C32×C4—42no—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2411yescharacteristic
160C4⋊(C3⋊D3)—24no—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)C2×D414yes—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D412yes—
169C3×C4×D3—24no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172C3×Dic6—24no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C3×Dic6—42no—
177C3×Dic6C2×D414yes—
178#626—216no—
179#624—216no—
180C3⋊(C3⋊C8)—22no—
181C3×C3⋊C8—22no—
182C22×#41—91no—
183C22×Q16—91no—
184C22×SD16—91no—
185C2×C22⋊Q8—31no—
186#452—98no—
187C2×#103—31no—
188C2×#102—91no—
189C2×C22⋊C8—91no—
190C24×C3—31no—
191C23×D3—61no—
192C23×D3—61no—
193C23×D3—121no—
194C23×D3#6711yescharacteristic
195C2×C3×Q8—34no—
196C2×C3×Q8—32no—
197C2×C3×Q8—32no—
198C2×C3×Q8—62no—
199C2×C3×Q8—61no—
200C2×C3×Q8—61no—
201C2×C3×Q8—62no—
202C2×C3×Q8—62no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—41no—
210C22×C3×C4—61no—
211C22×C3×C4—62no—
212C22×C3×C4—62no—
213C22×C3×C4—61no—
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C2×#67—64no—
217C2×#67—68no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3#6711yescharacteristic
221#239—68no—
222#239—68no—
223#239—616no—
224#235—68no—
225#235—616no—
226#235—68no—
227C2×D12—34no—
228C2×D12—34no—
229C2×D12—32no—
230C2×D12—32no—
231C2×D12—62no—
232C2×D12—64no—
233C2×D12—68no—
234C2×D12—64no—
235C2×D12—62no—
236C2×D12—61no—
237C2×D12—62no—
238C2×D12—61no—
239C2×D12—122no—
240C2×D12—121no—
241C2×C4×D3—22no—
242C2×C4×D3—22no—
243C2×C4×D3—64no—
244C2×C4×D3—68no—
245C2×C4×D3—68no—
246C2×C4×D3—64no—
247C2×C4×D3#6712yes—
248C2×C4×D3C22×D312yes—
249C2×Dic6—22no—
250C2×Dic6—21no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6D1214yes—
255C2×Dic6C22×D312yes—
256C2×Dic6C22×D312yes—
257C2×C3×C8—32no—
258C2×C3×C8—62no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—41no—
263C3×C4⋊C4—64no—
264C3×C4⋊C4C22×D312yes—
265C3×C4⋊C4C22×D312yes—
266C3×C22⋊C4—64no—
267#216—68no—
268#216—68no—
269#215—68no—
270(C2×D3)⋊C4—24no—
271C4⋊Dic3—24no—
272C2×C3⋊C8—22no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—122no—
279C2×C3⋊C8C22×D312yes—
280#204—68no—
281C22×C32#12012yes—
282C22×C32#13512yes—
283C22×C32#13712yes—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—24no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—48no—
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C2×C3×D3—44no—
293C32×C4—42no—
294C32×C4#12012yes—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3×Dic3—22no—
298C3×Dic3—24no—
299C3×Dic3—42no—
300C2×#41—94no—
301C2×#41—182no—
302C2×#41—184no—
303C2×#41—184no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×D4—91no—
307C22×D4—181no—
308C23×C4—31no—
309C23×C4—181no—
310C2×Q16—94no—
311C2×Q16—184no—
312C2×SD16—94no—
313C2×SD16—184no—
314C22×C8—31no—
315C22×C8—91no—
316C22⋊Q8—34no—
317C22⋊Q8—62no—
318C2×C4⋊C4—61no—
319C2×C4⋊C4D3211yescharacteristic
320C2×C22⋊C4—61no—
321#103—34no—
322#102—94no—
323C22⋊C8—94no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3D3×D411yescharacteristic
330C23×C3C2×#6711yescharacteristic
331C22×D3—22no—
332C22×D3—22no—
333C22×D3—22no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—122no—
339C22×D3—124no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—242no—
345C22×D3—242no—
346C22×D3C2×#6712yes—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—32no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—62no—
364C2×C3×C4—64no—
365C2×C3×C4—62no—
366C2×C3×C4—64no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—82no—
371C2×C3×C4—122no—
372C2×C3×C4C2×D1212yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4D3×D412yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380#67—616no—
381C2×Dic3—24no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—42no—
386C2×Dic3C2×#6712yes—
387D12—34no—
388D12—34no—
389D12—64no—
390D12—616no—
391D12—64no—
392D12—64no—
393D12—62no—
394D12—62no—
395D12—122no—
396D12—124no—
397C4×D3—24no—
398C4×D3—22no—
399C4×D3—22no—
400C4×D3—616no—
401C4×D3—616no—
402Dic6—24no—
403Dic6—22no—
404Dic6—22no—
405Dic6—22no—
406Dic6—42no—
407Dic6C2×D1214yes—
408C3×C8—62no—
409C3⋊C8—22no—
410C3⋊C8—62no—
411C3⋊C8—62no—
412C3⋊C8—122no—
413C2×C32#45214yescomplemented
414C2×C32C2×#12011yescharacteristic
415C2×C32C2×#13511yescharacteristic
416C2×C32C2×#13711yescharacteristic
417C3⋊D3—44no—
418C3×D3—42no—
419C24—31no—
420C24—181no—
421#41—188no—
422#41—188no—
423#41—1816no—
424C2×Q8—32no—
425C2×Q8—32no—
426C2×Q8—34no—
427C2×Q8—62no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—62no—
431C2×Q8—62no—
432C2×D4—92no—
433C2×D4—94no—
434C2×D4—184no—
435C2×D4—188no—
436C2×D4—182no—
437C2×D4—181no—
438C22×C4—21no—
439C22×C4—31no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—61no—
443C22×C4—62no—
444C22×C4—62no—
445C22×C4—61no—
446C22×C4—184no—
447C22×C4—188no—
448C22×C4C2×D3211yescharacteristic
449Q16—188no—
450SD16—188no—
451C2×C8—32no—
452C2×C8—62no—
453C2×C8—92no—
454C2×C8—182no—
455C4⋊C4—21no—
456C4⋊C4—64no—
457C4⋊C4C2×D3212yes—
458C22⋊C4—64no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—124no—
467C22×C3#88212yes—
468C22×C3#91612yes—
469C22×C3#91812yes—
470C22×C3#93712yes—
471C22×C3#94212yes—
472C22×C3#95012yes—
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C22×#6711yescharacteristic
475C2×D3—22no—
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—44no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—124no—
482C2×D3—122no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—128no—
486C2×D3—122no—
487C2×D3—128no—
488C2×D3—242no—
489C2×D3—242no—
490C2×D3—248no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—42no—
495C3×C4—42no—
496C3×C4—62no—
497C3×C4—64no—
498C3×C4—82no—
499C3×C4—122no—
500C3×C4#88212yes—
501C3×C4#93712yes—
502C3×C4C22×D1211yescharacteristic
503C3×C4C2×D3×D411yescharacteristic
504C3×C4C2×D3×D411yescharacteristic
505C3×C4C2×D3×D411yescharacteristic
506Dic3—24no—
507Dic3—22no—
508Dic3—42no—
509C32C2×#45211yescharacteristic, complemented, Sylow
510C23—32no—
511C23—62no—
512C23—62no—
513C23—62no—
514C23—182no—
515C23—184no—
516C23—362no—
517C23—362no—
518C23D3×#6711yescharacteristic
519Q8—34no—
520Q8—62no—
521Q8—64no—
522Q8—62no—
523Q8—62no—
524Q8—122no—
525D4—94no—
526D4—1816no—
527D4—182no—
528D4—184no—
529C2×C4—22no—
530C2×C4—32no—
531C2×C4—42no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—64no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—64no—
538C2×C4—62no—
539C2×C4—122no—
540C2×C4—1816no—
541C2×C4D3×D1212yes—
542C2×C4#380212yes—
543C2×C4D3×#6711yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—62no—
546C8—182no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—24no—
550C2×C3—21no—
551C2×C3—122no—
552C2×C3#480814yescomplemented
553C2×C3#504714yescomplemented
554C2×C3C2×#88211yescharacteristic
555C2×C3C2×#91611yescharacteristic
556C2×C3C2×#91811yescharacteristic
557C2×C3C2×#93711yescharacteristic
558C2×C3C2×#94211yescharacteristic
559C2×C3C2×#95011yescharacteristic
560D3—42no—
561D3—124no—
562D3—124no—
563D3—244no—
564C22—62no—
565C22—62no—
566C22—62no—
567C22—124no—
568C22—184no—
569C22—362no—
570C22—362no—
571C22—368no—
572C22#6392212yes—
573C22#6393512yes—
574C22#6394812yes—
575C22C2×D3×#6711yescharacteristic
576C4—42no—
577C4—62no—
578C4—64no—
579C4—122no—
580C4#6392212yes—
581C4C2×D3×D1211yescharacteristic
582C4C2×#380211yescharacteristic
583C3—21no—
584C3C2×#480811yescharacteristic, complemented
585C3C2×#504711yescharacteristic, complemented
586C2—122no—
587C2—364no—
588C2#1059061614yesdirect product factor
589C2C2×#6392211yescharacteristic
590C2C2×#6393511yescharacteristic
591C2C2×#6394811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3799C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#452
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×C3×#897C2semidirect
3. C22×#3718C2semidirect
4. C22×#3717C2semidirect
5. C2×#63636C2semidirect
6. C2×C3×#810C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590616C2direct (N × H)
27. C3×#897C22semidirect
29. C2×#3718C22semidirect
31. C2×#3717C22semidirect
32. #63636C22semidirect
33. C3×#810C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
42. C2×#897D3semidirect
47. C2×#810D3semidirect
137. #897C2×D3semidirect
141. #810C2×D3semidirect
413. C2×C32#452semidirect
509. C32C2×#452semidirect
552. C2×C3#4808semidirect
553. C2×C3#5047semidirect
584. C3C2×#4808semidirect
585. C3C2×#5047semidirect
588. C2#10590616direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C2×C3×#8972
C22×#37182
C22×#37172
C2×#636362
C2×C3×#8102
C2×(C2×D3)⋊(C3⋊C8)2
#105906162
C2×#50473
C2×#48083