Finite Group Databasebeta

← C2×#10591657 #11863780

Subgroups — C2×#10591657 #11863780

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C22×#3755C211yesmaximal, characteristic, complemented
3C2×C3×#946C211yesmaximal, characteristic, complemented
4C22×C3×#216C211yesmaximal, characteristic, complemented
5#10591657C218yesmaximal, direct product factor
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5187—31nomaximal
10C2×#5047—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×#624—21no—
17C2×#3799—24no—
18C2×#3799—22no—
19C2×#3799—24no—
20C2×#3799C2214yes—
21C2×#3755—24no—
22C2×#3755C2214yescomplemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#946—22no—
25C3×#946C2214yescomplemented
26C2×C3×#216—24no—
27C2×C3×#216C2214yescomplemented
28C2×C3×(C2×D3)⋊C4—21no—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4—21no—
31C22×C3×C3⋊C8C2211yescharacteristic
32#63565C2214yescomplemented
33#63564C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×#239—31no—
36C22×#235—31no—
37C22×C3×Q16—31no—
38C2×C3×C22⋊Q8—31no—
39C2×#946D311yescharacteristic, complemented
40C22×#216D311yescharacteristic, complemented
41C22×#215—31no—
42C22×#215—31no—
43C22×#215—61no—
44C2×#835—31no—
45C2×#830—31no—
46#5187—38no—
47C2×#821—31no—
48C2×(C2×D3)⋊C8—31no—
49#5047—38no—
50C2×#810—31no—
51C2×#809—31no—
52C23×C3⋊D3—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×Q8—21no—
55C2×C32×Q8—22no—
56C2×C32×Q8—22no—
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)D414yes—
63C2×C4⋊(C3⋊D3)C2312yes—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yes—
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×#624—28no—
78C2×#624—24no—
79#3799—216no—
80#3799—28no—
81#3799—28no—
82#3755—28no—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#216—28no—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—24no—
90C2×C3×C3⋊C8—22no—
91C2×C3×C3⋊C8C2312yes—
92C2×#452—91noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8—31no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C23×C3×C4—31no—
98C22×#67—61no—
99C2×#239—34no—
100C2×#239—64no—
101C2×#239—64no—
102C2×#239—62no—
103C2×#235—34no—
104C2×#235—64no—
105C2×#235—62no—
106C2×#235—64no—
107C22×D12—31no—
108C22×D12—31no—
109C22×D12—61no—
110C22×D12—61no—
111C22×C4×D3—61no—
112C22×C4×D3—61no—
113C22×C4×D3C2×D311yescharacteristic
114C22×Dic6C2×D311yescharacteristic
115C2×C3×Q16—34no—
116C2×C3×Q16—64no—
117C22×C3×C8—31no—
118C3×C22⋊Q8—34no—
119C3×C22⋊Q8—62no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C22⋊C4—61no—
123#946—22no—
124#946C2×D314yescomplemented
125C2×#216—24no—
126C2×#216C2×D314yescomplemented
127C2×#215—34no—
128C2×#215—34no—
129C2×#215—64no—
130C2×#215—64no—
131C2×#215—64no—
132C2×#215—68no—
133C2×(C2×D3)⋊C4—21no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×Dic3⋊C4—21no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—31no—
138C22×C3⋊C8—61no—
139C22×C3⋊C8C2×D311yescharacteristic
140#835—34no—
141#830—34no—
142#821—34no—
143(C2×D3)⋊C8—34no—
144#810—34no—
145#809—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—24no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3C2×D412yes—
155C32×Q8—22no—
156C32×Q8—22no—
157C32×Q8—42no—
158C2×C32×C4—22no—
159C2×C32×C4—42no—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C4⋊(C3⋊D3)—24no—
165C4⋊(C3⋊D3)—22no—
166C4⋊(C3⋊D3)C2×D414yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—24no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—42no—
172C2×C3×Dic3C2×D412yes—
173C3×C4×D3—24no—
174C3×C4×D3—22no—
175C3×C4×D3—22no—
176C3×Dic6—24no—
177C3×Dic6—22no—
178C3×Dic6C2×D414yes—
179#626—216no—
180#624—216no—
181C3⋊(C3⋊C8)—22no—
182C3×C3⋊C8—22no—
183C22×#41—91no—
184C22×Q16—31no—
185C22×SD16—91no—
186C2×C22⋊Q8—31no—
187#452—98no—
188C2×#103—91no—
189C2×#102—91no—
190C2×C22⋊C8—91no—
191C24×C3—31no—
192C23×D3—61no—
193C23×D3—61no—
194C23×D3—121no—
195C23×D3#6711yescharacteristic
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—24no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8—22no—
202C2×C3×Q8—22no—
203C2×C3×Q8—22no—
204C2×C3×Q8—34no—
205C2×C3×Q8—32no—
206C2×C3×Q8—41no—
207C2×C3×Q8—42no—
208C2×C3×Q8—62no—
209C2×C3×Q8—61no—
210C2×C3×Q8C22×D312yes—
211C2×C3×Q8C22×D312yes—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—31no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—41no—
219C22×C3×C4—61no—
220C22×C3×C4—62no—
221C22×C3×C4—62no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—64no—
226C2×#67—68no—
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3#6711yescharacteristic
230#239—68no—
231#239—68no—
232#239—616no—
233#235—68no—
234#235—616no—
235#235—68no—
236C2×D12—34no—
237C2×D12—34no—
238C2×D12—32no—
239C2×D12—32no—
240C2×D12—64no—
241C2×D12—62no—
242C2×D12—68no—
243C2×D12—64no—
244C2×D12—61no—
245C2×D12—62no—
246C2×D12—62no—
247C2×D12—61no—
248C2×D12—122no—
249C2×D12—121no—
250C2×C4×D3—22no—
251C2×C4×D3—22no—
252C2×C4×D3—64no—
253C2×C4×D3—68no—
254C2×C4×D3—68no—
255C2×C4×D3—64no—
256C2×C4×D3#6712yes—
257C2×C4×D3C22×D312yes—
258C2×Dic6—21no—
259C2×Dic6—22no—
260C2×Dic6#6714yes—
261C2×Dic6C22×D312yes—
262C3×Q16—68no—
263C2×C3×C8—32no—
264C2×C3×C8—62no—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—64no—
267C3×C4⋊C4—61no—
268C3×C22⋊C4—64no—
269#216—28no—
270#215—68no—
271#215—68no—
272#215—616no—
273(C2×D3)⋊C4—24no—
274C4⋊Dic3—21no—
275C4⋊Dic3C22×D312yes—
276Dic3⋊C4—24no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—32no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—64no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8C22×D312yes—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—24no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—48no—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C2×C3×D3—44no—
297C32×C4—42no—
298C32×C4#12012yes—
299C32×C4C22×D411yescharacteristic
300C32×C4C22×D411yescharacteristic
301C3×Dic3—22no—
302C3×Dic3—24no—
303C3×Dic3—42no—
304C2×#41—94no—
305C2×#41—182no—
306C2×#41—184no—
307C2×#41—184no—
308C22×Q8—31no—
309C22×Q8D3211yescharacteristic
310C22×D4—91no—
311C22×D4—181no—
312C23×C4—31no—
313C23×C4—181no—
314C2×Q16—34no—
315C2×Q16—64no—
316C2×SD16—94no—
317C2×SD16—184no—
318C22×C8—31no—
319C22×C8—91no—
320C22⋊Q8—34no—
321C22⋊Q8—62no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—61no—
324C2×C22⋊C4—61no—
325#103—94no—
326#102—94no—
327C22⋊C8—94no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3D3×D411yescharacteristic
334C23×C3C2×#6711yescharacteristic
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—64no—
339C22×D3—64no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—122no—
343C22×D3—124no—
344C22×D3—122no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—242no—
349C22×D3—242no—
350C22×D3C2×#6712yes—
351C3×Q8—24no—
352C3×Q8—22no—
353C3×Q8—22no—
354C3×Q8—22no—
355C3×Q8—22no—
356C3×Q8—34no—
357C3×Q8—42no—
358C3×Q8—44no—
359C3×Q8—42no—
360C3×Q8—42no—
361C3×Q8—64no—
362C3×Q8—62no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—22no—
369C2×C3×C4—32no—
370C2×C3×C4—42no—
371C2×C3×C4—44no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—62no—
375C2×C3×C4—64no—
376C2×C3×C4—62no—
377C2×C3×C4—64no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—122no—
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4D3×D412yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4D3×D412yes—
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6712yes—
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390#67—616no—
391C2×Dic3—24no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—42no—
396C2×Dic3C2×#6712yes—
397D12—34no—
398D12—34no—
399D12—64no—
400D12—616no—
401D12—64no—
402D12—64no—
403D12—62no—
404D12—62no—
405D12—122no—
406D12—124no—
407C4×D3—24no—
408C4×D3—22no—
409C4×D3—22no—
410C4×D3—616no—
411C4×D3—616no—
412Dic6—24no—
413Dic6—22no—
414Dic6C2×#6714yes—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—64no—
418C3⋊C8—62no—
419C3⋊C8—62no—
420C2×C32#45214yescomplemented
421C2×C32C2×#12011yescharacteristic
422C2×C32C2×#13511yescharacteristic
423C2×C32C2×#13711yescharacteristic
424C3⋊D3—44no—
425C3×D3—42no—
426C24—31no—
427C24—181no—
428#41—188no—
429#41—188no—
430#41—1816no—
431C2×Q8—21no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—32no—
435C2×Q8—34no—
436C2×Q8—61no—
437C2×Q8—62no—
438C2×Q8C2×D3212yes—
439C2×D4—92no—
440C2×D4—94no—
441C2×D4—184no—
442C2×D4—188no—
443C2×D4—182no—
444C2×D4—181no—
445C22×C4—21no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—32no—
449C22×C4—61no—
450C22×C4—62no—
451C22×C4—62no—
452C22×C4—61no—
453C22×C4—184no—
454C22×C4—188no—
455C22×C4C2×D3211yescharacteristic
456Q16—68no—
457SD16—188no—
458C2×C8—32no—
459C2×C8—62no—
460C2×C8—92no—
461C2×C8—182no—
462C4⋊C4—32no—
463C4⋊C4—64no—
464C4⋊C4—61no—
465C22⋊C4—64no—
466C22×C3—21no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—124no—
474C22×C3#91812yes—
475C22×C3#91912yes—
476C22×C3#93712yes—
477C22×C3#93712yes—
478C22×C3#94212yes—
479C22×C3#95012yes—
480C22×C3C2×D3×D411yescharacteristic
481C22×C3C22×#6711yescharacteristic
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—44no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—124no—
489C2×D3—128no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—128no—
494C2×D3—122no—
495C2×D3—242no—
496C2×D3—242no—
497C2×D3—248no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—22no—
501C3×C4—44no—
502C3×C4—42no—
503C3×C4—42no—
504C3×C4—62no—
505C3×C4—64no—
506C3×C4—122no—
507C3×C4#93712yes—
508C3×C4#93712yes—
509C3×C4C2×D3×D411yescharacteristic
510C3×C4C2×D3×D411yescharacteristic
511C3×C4C2×D3×D411yescharacteristic
512C3×C4C22×#6711yescharacteristic
513Dic3—24no—
514Dic3—22no—
515Dic3—42no—
516C32C2×#45211yescharacteristic, complemented, Sylow
517C23—32no—
518C23—62no—
519C23—62no—
520C23—62no—
521C23—182no—
522C23—184no—
523C23—362no—
524C23—362no—
525C23D3×#6711yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—34no—
529Q8—42no—
530Q8—62no—
531Q8—64no—
532D4—94no—
533D4—1816no—
534D4—182no—
535D4—184no—
536C2×C4—22no—
537C2×C4—32no—
538C2×C4—42no—
539C2×C4—62no—
540C2×C4—62no—
541C2×C4—64no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—64no—
545C2×C4—62no—
546C2×C4—122no—
547C2×C4—1816no—
548C2×C4D3×#6712yes—
549C2×C4D3×#6711yescharacteristic
550C2×C4#381112yes—
551C2×C4C22×D3211yescharacteristic
552C8—62no—
553C8—182no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—24no—
557C2×C3—21no—
558C2×C3—122no—
559C2×C3#504714yescomplemented
560C2×C3#518714yescomplemented
561C2×C3C2×#91811yescharacteristic
562C2×C3C2×#91911yescharacteristic
563C2×C3C2×#93711yescharacteristic
564C2×C3C2×#93711yescharacteristic
565C2×C3C2×#94211yescharacteristic
566C2×C3C2×#95011yescharacteristic
567D3—42no—
568D3—124no—
569D3—124no—
570D3—244no—
571C22—62no—
572C22—62no—
573C22—62no—
574C22—124no—
575C22—184no—
576C22—362no—
577C22—362no—
578C22—368no—
579C22#6394812yes—
580C22#6394912yes—
581C22#6398312yes—
582C22C2×D3×#6711yescharacteristic
583C4—42no—
584C4—62no—
585C4—64no—
586C4—122no—
587C4#6398312yes—
588C4C2×D3×#6711yescharacteristic
589C4C2×#381111yescharacteristic
590C3—21no—
591C3C2×#504711yescharacteristic, complemented
592C3C2×#518711yescharacteristic, complemented
593C2—122no—
594C2—364no—
595C2#1059165714yesdirect product factor
596C2C2×#6394811yescharacteristic
597C2C2×#6394911yescharacteristic
598C2C2×#6398311yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3799C2
hypercenterC22×Q8D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#3755C2semidirect
3. C2×C3×#946C2semidirect
4. C22×C3×#216C2semidirect
5. #10591657C2direct (N × H)
6. C2×#63565C2semidirect
7. C2×#63564C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
22. C2×#3755C22semidirect
25. C3×#946C22semidirect
27. C2×C3×#216C22semidirect
32. #63565C22semidirect
33. #63564C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C2×#946D3semidirect
40. C22×#216D3semidirect
124. #946C2×D3semidirect
126. C2×#216C2×D3semidirect
420. C2×C32#452semidirect
516. C32C2×#452semidirect
559. C2×C3#5047semidirect
560. C2×C3#5187semidirect
591. C3C2×#5047semidirect
592. C3C2×#5187semidirect
595. C2#10591657direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×#37552
C2×C3×#9462
C22×C3×#2162
#105916572
C2×#635652
C2×#635642
C2×(C2×D3)⋊(C3⋊C8)2
C2×#51873
C2×#50473