Finite Group Databasebeta

← C2×#10594973 #11901441

Subgroups — C2×#10594973 #11901441

Order 1152.

2449 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic
3C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×Dic3×#67C212yesmaximal, complemented
5C2×#63961C212yesmaximal, complemented
6#10594973C2116yesmaximal, direct product factor
7C2×#63896C212yesmaximal, complemented
8C2×#63884C212yesmaximal, complemented
9C2×#63861C212yesmaximal, complemented
10C2×#63847C212yesmaximal, complemented
11C2×#5602—31nomaximal
12C2×#5515—31nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C22×C3×#67C2212yes—
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×D3×Dic3C2212yes—
20C2×#3757C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22#64133C2218yescomplemented
23C2×#3750C2212yes—
24C3×#930C2218yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×Dic3⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2218yescomplemented
30Dic3×#67C22116yescomplemented
31C2×#3724C2212yes—
32C2×#3724C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34#63961C22116yescomplemented
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×Dic32C2212yes—
39#63896C22116yescomplemented
40#63884C22116yescomplemented
41#63861C22116yescomplemented
42#63847C22116yescomplemented
43C2×C3×#121—31no—
44C22×C3×C4⋊C4—31no—
45C2×#935—32no—
46C2×#935—32no—
47C2×D4×Dic3—32no—
48C2×#930D311yescharacteristic
49C2×#929—32no—
50C2×C4×#67—32no—
51C2×#924—31no—
52C2×#924—31no—
53C2×#924—61no—
54C22×Dic3⋊C4D311yescharacteristic, complemented
55#5602—316no—
56#5515—316no—
57C2×#898—32no—
58C2×#896—32no—
59C2×#894—32no—
60C2×#889—32no—
61C2×#889—32no—
62C2×#879—32no—
63C2×#878—32no—
64C24×C32C2311yescharacteristic
65C23×C3×D3C2312yes—
66C22×C32×C4—42no—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2314yes—
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×#634—42no—
73C2×#634C2314yes—
74C2×C3×#67—28no—
75C2×C3×#67C2318yes—
76C22×C3×Dic3—24no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2314yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2314yes—
83C2×C3×D12—42no—
84C2×C3×D12C2314yes—
85C2×D3×Dic3—44no—
86C2×D3×Dic3C2318yes—
87#3757C2318yes—
88C4⋊(C3⋊Dic3)C2314yes—
89#3750C2318yes—
90C3×(C2×D3)⋊C4C2318yes—
91C3×C4⋊Dic3C2314yes—
92C3×Dic3⋊C4C2318yes—
93C3×Dic3⋊C4C2318yes—
94#3724C2318yes—
95#3724C2318yes—
96Dic3⋊Dic3C2318yes—
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yes—
99(C2×D3)⋊Dic3C2318yes—
100Dic32C2318yes—
101C2×#539—91noSylow
102C22×C3×D4—32no—
103C22×C3×D4—31no—
104C23×C3×C4—21no—
105C23×C3×C4—31no—
106C23×C3×C4—31no—
107C23×C3×C4C2×D311yescharacteristic
108C23×C3×C4C2×D311yescharacteristic
109C22×#67C2×D312yes—
110C23×Dic3—32no—
111C23×Dic3C2×D311yescharacteristic
112C23×Dic3C2×D311yescharacteristic
113C22×D12C2×D311yescharacteristic
114C22×C4×D3—32no—
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C3×#121—38no—
119C2×C3×C4⋊C4—32no—
120C2×C3×C4⋊C4—32no—
121C2×C3×C4⋊C4—38no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—32no—
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—32no—
127C2×#217—32no—
128C2×#217—32no—
129C2×#217—62no—
130#935—316no—
131#935—316no—
132D4×Dic3—316no—
133#930C2×D318yes—
134#929—316no—
135C4×#67—316no—
136C2×(C2×D3)⋊C4—32no—
137C2×(C2×D3)⋊C4—32no—
138C2×(C2×D3)⋊C4—32no—
139C2×(C2×D3)⋊C4C2×D312yes—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—32no—
143C2×C4⋊Dic3—61no—
144C2×C4⋊Dic3C2×D311yescharacteristic
145#924—38no—
146#924—38no—
147#924—68no—
148C2×Dic3⋊C4—32no—
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—62no—
156C2×Dic3⋊C4C2×D312yes—
157C2×Dic3⋊C4C2×D312yes—
158C2×Dic3⋊C4C2×D318yescomplemented
159C2×C4×Dic3—32no—
160C2×C4×Dic3—32no—
161#898—316no—
162#896—316no—
163#894—316no—
164#889—316no—
165#889—316no—
166#879—316no—
167#878—316no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32#4114yes—
171C23×C32C2412yes—
172C23×C32C2411yescharacteristic
173C22×C3×D3—24no—
174C22×C3×D3—24no—
175C22×C3×D3—24no—
176C22×C3×D3C2414yes—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—44no—
180C2×C32×C4C2412yes—
181C2×C32×C4C2412yes—
182C2×C3⋊Dic3—24no—
183C2×C3⋊Dic3—24no—
184C2×C3⋊Dic3C2414yes—
185C2×C3⋊Dic3C2414yes—
186#634—44no—
187C3×#67—216no—
188C2×C3×Dic3—28no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—24no—
192C2×C3×Dic3—44no—
193C2×C3×Dic3C2414yes—
194C2×C3×Dic3C2414yes—
195C2×C3×Dic3C2414yes—
196C3×D12—44no—
197D3×Dic3—48no—
198#539—916no—
199C2×#126—92no—
200C2×#125—92no—
201C2×#123—92no—
202C2×#123—92no—
203C2×C22⋊Q8—92no—
204C2×C22⋊Q8—91no—
205C2×#121—31no—
206C2×C4×D4—92no—
207C22×C4⋊C4—31no—
208C24×C3—21no—
209C24×C3—32no—
210C24×C3C22×D311yescharacteristic
211C24×C3C22×D311yescharacteristic
212C23×D3C22×D312yes—
213C2×C3×D4—38no—
214C2×C3×D4—34no—
215C2×C3×D4—68no—
216C2×C3×D4—122no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—24no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—34no—
224C22×C3×C4—34no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—44no—
228C22×C3×C4—64no—
229C22×C3×C4—122no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D314yes—
235C22×C3×C4C22×D314yes—
236C2×#67—28no—
237C2×#67C22×D318yes—
238C22×Dic3—24no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—32no—
242C22×Dic3—32no—
243C22×Dic3—38no—
244C22×Dic3—42no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—124no—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D314yes—
252C22×Dic3C22×D314yes—
253C2×D12—42no—
254C2×D12C22×D314yes—
255C2×C4×D3—38no—
256C2×C4×D3—124no—
257C2×Dic6—34no—
258C2×Dic6—34no—
259C2×Dic6—64no—
260C2×Dic6—122no—
261C2×Dic6—122no—
262C2×Dic6—124no—
263C3×C4⋊C4—34no—
264C3×C4⋊C4—38no—
265C3×C4⋊C4—38no—
266C3×C22⋊C4—38no—
267#217—38no—
268#217—38no—
269#217—38no—
270#217—38no—
271#217—38no—
272#217—68no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—38no—
276(C2×D3)⋊C4C22×D318yes—
277C4⋊Dic3—34no—
278C4⋊Dic3—34no—
279C4⋊Dic3—38no—
280C4⋊Dic3—64no—
281C4⋊Dic3C22×D314yes—
282Dic3⋊C4—38no—
283Dic3⋊C4—38no—
284Dic3⋊C4—38no—
285Dic3⋊C4—38no—
286Dic3⋊C4—38no—
287Dic3⋊C4—38no—
288Dic3⋊C4—38no—
289Dic3⋊C4—68no—
290Dic3⋊C4C22×D318yes—
291Dic3⋊C4C22×D318yes—
292C4×Dic3—38no—
293C4×Dic3—38no—
294C22×C32—28no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32C2×#4114yes—
298C22×C32C2×#4112yes—
299C22×C32H(5,𝔽2)12yes—
300C22×C322−1+412yes—
301C22×C32C2511yescharacteristic
302C2×C3×D3—24no—
303C2×C3×D3—24no—
304C2×C3×D3—24no—
305C2×C3×D3—48no—
306C32×C4—22no—
307C32×C4—22no—
308C3⋊Dic3—24no—
309C3⋊Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3—24no—
313C22×Q8—91no—
314C22×D4—32no—
315C22×D4—31no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—92no—
319C23×C4D3211yescharacteristic
320#126—916no—
321#125—916no—
322#123—916no—
323#123—916no—
324C22⋊Q8—916no—
325C22⋊Q8—98no—
326#121—38no—
327C4×D4—916no—
328C2×C4⋊C4—32no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—38no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—92no—
333C2×C4⋊C4—92no—
334C2×C4⋊C4—92no—
335C2×C4⋊C4—92no—
336C2×C4⋊C4—91no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—92no—
341C2×C22⋊C4—92no—
342C2×C42—92no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—21no—
349C23×C3—24no—
350C23×C3—34no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—64no—
354C23×C3—64no—
355C23×C3—64no—
356C23×C3#23514yes—
357C23×C3#23714yes—
358C23×C3C23×D312yes—
359C23×C3C23×D312yes—
360C23×C3C23×D311yescharacteristic
361C23×C3C23×D311yescharacteristic
362C22×D3—24no—
363C22×D3—24no—
364C22×D3—24no—
365C22×D3C23×D314yes—
366C3×D4—616no—
367C3×D4—124no—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—34no—
376C2×C3×C4—34no—
377C2×C3×C4—34no—
378C2×C3×C4—42no—
379C2×C3×C4—44no—
380C2×C3×C4—44no—
381C2×C3×C4—48no—
382C2×C3×C4—64no—
383C2×C3×C4—68no—
384C2×C3×C4—64no—
385C2×C3×C4—64no—
386C2×C3×C4—124no—
387C2×C3×C4C23×D312yes—
388C2×C3×C4C23×D312yes—
389C2×C3×C4C23×D312yes—
390C2×C3×C4C23×D312yes—
391#67—216no—
392C2×Dic3—28no—
393C2×Dic3—24no—
394C2×Dic3—24no—
395C2×Dic3—24no—
396C2×Dic3—34no—
397C2×Dic3—34no—
398C2×Dic3—34no—
399C2×Dic3—34no—
400C2×Dic3—44no—
401C2×Dic3—64no—
402C2×Dic3—64no—
403C2×Dic3—64no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—64no—
407C2×Dic3—124no—
408C2×Dic3—124no—
409C2×Dic3—128no—
410C2×Dic3C23×D314yes—
411C2×Dic3C23×D314yes—
412C2×Dic3C23×D314yes—
413D12—44no—
414C4×D3—128no—
415Dic6—124no—
416Dic6—124no—
417Dic6—128no—
418C2×C32—24no—
419C2×C32#53914yescomplemented
420C2×C32C22×#4111yescharacteristic
421C2×C32C2×H(5,𝔽2)11yescharacteristic
422C2×C32C2×2−1+411yescharacteristic
423C3×D3—44no—
424C24—32no—
425C24C2×D3211yescharacteristic
426C2×Q8—94no—
427C2×Q8—362no—
428C2×D4—38no—
429C2×D4—34no—
430C2×D4—68no—
431C2×D4—122no—
432C22×C4—34no—
433C22×C4—32no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—34no—
437C22×C4—42no—
438C22×C4—64no—
439C22×C4—98no—
440C22×C4—92no—
441C22×C4—92no—
442C22×C4—122no—
443C22×C4—364no—
444C22×C4C2×D3211yescharacteristic
445C22×C4C2×D3211yescharacteristic
446C22×C4C2×D3214yes—
447C4⋊C4—38no—
448C4⋊C4—38no—
449C4⋊C4—34no—
450C4⋊C4—98no—
451C4⋊C4—98no—
452C4⋊C4—98no—
453C4⋊C4—98no—
454C4⋊C4—94no—
455C22⋊C4—38no—
456C22⋊C4—98no—
457C22⋊C4—98no—
458C22⋊C4—98no—
459C22⋊C4—98no—
460C42—98no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—28no—
466C22×C3—28no—
467C22×C3—22no—
468C22×C3—24no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—21no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—48no—
475C22×C3—64no—
476C22×C3—64no—
477C22×C3—64no—
478C22×C3—128no—
479C22×C3C2×#23514yes—
480C22×C3C2×#23512yes—
481C22×C3C2×#23714yes—
482C22×C3C2×#23712yes—
483C22×C3#100412yes—
484C22×C3#100412yes—
485C22×C3#100712yes—
486C22×C3#101012yes—
487C22×C3C24×D311yescharacteristic
488C22×C3C24×D311yescharacteristic
489C2×D3—24no—
490C2×D3—24no—
491C2×D3—24no—
492C2×D3—48no—
493C3×C4—24no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—22no—
498C3×C4—42no—
499C3×C4—64no—
500C3×C4—64no—
501C3×C4—64no—
502Dic3—24no—
503Dic3—24no—
504Dic3—24no—
505Dic3—64no—
506Dic3—64no—
507Dic3—64no—
508Dic3—64no—
509Dic3—124no—
510Dic3—124no—
511C32C2×#53911yescharacteristic, complemented, Sylow
512C23—22no—
513C23—22no—
514C23—34no—
515C23—64no—
516C23—64no—
517C23—64no—
518C23#379514yes—
519C23C22×D3212yes—
520C23C22×D3211yescharacteristic
521Q8—364no—
522D4—616no—
523D4—124no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—34no—
527C2×C4—34no—
528C2×C4—34no—
529C2×C4—44no—
530C2×C4—68no—
531C2×C4—64no—
532C2×C4—64no—
533C2×C4—64no—
534C2×C4—94no—
535C2×C4—94no—
536C2×C4—124no—
537C2×C4—184no—
538C2×C4—184no—
539C2×C4—368no—
540C2×C4C22×D3212yes—
541C2×C4C22×D3212yes—
542C2×C3—24no—
543C2×C3—24no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—24no—
548C2×C3—44no—
549C2×C3—124no—
550C2×C3#551514yescomplemented
551C2×C3#560214yescomplemented
552C2×C3C22×#23511yescharacteristic
553C2×C3C22×#23711yescharacteristic
554C2×C3C2×#100411yescharacteristic
555C2×C3C2×#100411yescharacteristic
556C2×C3C2×#100711yescharacteristic
557C2×C3C2×#101011yescharacteristic
558D3—44no—
559C22—22no—
560C22—22no—
561C22—28no—
562C22—64no—
563C22—64no—
564C22—64no—
565C22—128no—
566C22C2×#379514yes—
567C22C2×#379512yes—
568C22#6429712yes—
569C22#6433012yes—
570C22C23×D3211yescharacteristic
571C4—22no—
572C4—22no—
573C4—64no—
574C4—64no—
575C4—64no—
576C4—184no—
577C4—184no—
578C3—21no—
579C3C2×#551511yescharacteristic, complemented
580C3C2×#560211yescharacteristic, complemented
581C2—24no—
582C2—124no—
583C2#1059497314yesdirect product factor
584C2C22×#379511yescharacteristic
585C2C2×#6429711yescharacteristic
586C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32C2×#539
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64133C2semidirect
3. C22×C3×Dic3⋊C4C2semidirect
4. C2×Dic3×#67C2semidirect
5. C2×#63961C2semidirect
6. #10594973C2direct (N × H)
7. C2×#63896C2semidirect
8. C2×#63884C2semidirect
9. C2×#63861C2semidirect
10. C2×#63847C2semidirect
22. #64133C22semidirect
29. C2×C3×Dic3⋊C4C22semidirect
30. Dic3×#67C22semidirect
34. #63961C22semidirect
39. #63896C22semidirect
40. #63884C22semidirect
41. #63861C22semidirect
42. #63847C22semidirect
54. C22×Dic3⋊C4D3semidirect
158. C2×Dic3⋊C4C2×D3semidirect
419. C2×C32#539semidirect
511. C32C2×#539semidirect
550. C2×C3#5515semidirect
551. C2×C3#5602semidirect
579. C3C2×#5515semidirect
580. C3C2×#5602semidirect
583. C2#10594973direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641332
C2×C3×#9302
C22×C3×Dic3⋊C42
C2×Dic3×#672
C2×#639612
#105949732
C2×#638962
C2×#638842
C2×#638612
C2×#638472
C2×#56023
C2×#55153