Finite Group Databasebeta

← C2×#10590717 #11859173

Subgroups — C2×#10590717 #11859173

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic, complemented
2C2×C4×#625C211yesmaximal, characteristic
3C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
4C2×#63641C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×#63553C211yesmaximal, characteristic, complemented
8#10590717C218yesmaximal, direct product factor
9C2×C8×#67—31nomaximal
10C2×#67⋊C8—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×#625C411yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×D3×C8—24no—
20C2×C3×D3×C8C2214yescomplemented
21C2×#3724C411yescharacteristic
22C2×(C2×D3)⋊Dic3C411yescharacteristic
23C2×(C2×D3)⋊Dic3C411yescharacteristic
24C4×#625C414yes—
25C4×#625C2214yes—
26C2×D3×C3⋊C8—24no—
27C2×D3×C3⋊C8C2214yescomplemented
28#63641C2214yescomplemented
29C3×(C2×D3)⋊C8C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yescomplemented
31#63553C2214yescomplemented
32C23×C3×C8—31no—
33C2×C4×#67—31no—
34C2×C4×#67—31no—
35C23×C3⋊C8—31no—
36C22×D3×C8—31no—
37C22×D3×C8D311yescharacteristic, complemented
38C2×C3×C22⋊C8—31no—
39C2×#830—31no—
40C8×#67—38no—
41C2×(C2×D3)⋊C8—31no—
42C2×(C2×D3)⋊C8D311yescharacteristic, complemented
43C2×Dic3⋊C8—31no—
44C2×Dic3⋊C8—31no—
45C2×Dic3⋊C8—61no—
46C2×C8×Dic3—31no—
47C2×C8×Dic3—31no—
48#67⋊C8—38no—
49C23×C3×D3C2×C411yescharacteristic
50C23×C3×D3C2×C411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2×C411yescharacteristic
53C22×C3⋊Dic3C2×C411yescharacteristic
54C22×C3×Dic3C2×C411yescharacteristic
55C22×C3×Dic3C2×C411yescharacteristic
56C2×C3×C4×D3—22no—
57C2×C3×C4×D3—22no—
58C2×C3×C4×D3—22no—
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3C2×C412yes—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3C2312yes—
63C2×C3×C4×D3C2312yes—
64C2×#625C818yescomplemented
65C2×#625C2×C414yes—
66C2×C32×C8—22no—
67C2×C32×C8C2312yes—
68C4×C3⋊Dic3C2×C412yes—
69C4×C3⋊Dic3C2312yes—
70C2×C3⋊(C3⋊C8)—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8D414yescomplemented
74C2×C3×C3⋊C8C2312yes—
75C2×C3×C3⋊C8C2312yes—
76C3×D3×C8—28no—
77#3724C2×C414yes—
78(C2×D3)⋊Dic3C2×C414yes—
79(C2×D3)⋊Dic3C2×C414yes—
80D3×C3⋊C8—28no—
81C2×C8×D4—91noSylow
82C23×C3×C4—31no—
83C23×C3×C4—31no—
84C22×#67—31no—
85C22×#67—31no—
86C22×C4×D3C2×D311yescharacteristic
87C22×C4×D3C2×D311yescharacteristic
88C22×C3×C8—21no—
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C22×C3×C8—34no—
92C22×C3×C8—64no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C2×#217—31no—
96C2×#217—31no—
97C4×#67—34no—
98C4×#67—34no—
99C4×#67—34no—
100C4×#67—34no—
101C2×(C2×D3)⋊C4—31no—
102C2×(C2×D3)⋊C4—31no—
103C2×Dic3⋊C4—31no—
104C2×Dic3⋊C4—31no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—34no—
111C22×C3⋊C8—61no—
112C22×C3⋊C8—64no—
113C22×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊C8C2×D311yescharacteristic
115C2×D3×C8—24no—
116C2×D3×C8—34no—
117C2×D3×C8—64no—
118C2×D3×C8C2×D314yescomplemented
119C3×C22⋊C8—34no—
120#830—34no—
121(C2×D3)⋊C8—34no—
122(C2×D3)⋊C8C2×D314yescomplemented
123Dic3⋊C8—34no—
124Dic3⋊C8—34no—
125Dic3⋊C8—64no—
126C8×Dic3—34no—
127C8×Dic3—34no—
128C23×C32C22×C411yescharacteristic
129C22×C3×D3—22no—
130C22×C3×D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3C2×C814yescomplemented
134C22×C3×D3C2×C814yescomplemented
135C22×C3×D3C22×C412yes—
136C22×C3×D3C22×C412yes—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D412yes—
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3C2×C814yescomplemented
143C2×C3⋊Dic3C22×C412yes—
144C2×C3⋊Dic3C22×C412yes—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3C22×C412yes—
148C2×C3×Dic3C22×C412yes—
149C3×C4×D3—24no—
150C3×C4×D3—24no—
151C3×C4×D3—22no—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×C4×D3—22no—
155#625C2×C8116yescomplemented
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8C2×D414yescomplemented
160C23×C8—31no—
161C23×C8—91no—
162C2×C4×D4—91no—
163C8×D4—98no—
164C2×C4⋊C8—91no—
165C2×C22⋊C8—31no—
166C2×C22⋊C8—91no—
167C2×C4×C8—91no—
168C24×C3—31no—
169C24×C3—31no—
170C23×D3C4×D311yescharacteristic
171C23×D3C4×D311yescharacteristic
172C22×C3×C4—21no—
173C22×C3×C4—31no—
174C22×C3×C4—31no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4—32no—
179C22×C3×C4—62no—
180C22×C3×C4—62no—
181C22×C3×C4—62no—
182C22×C3×C4—62no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C2×#67—38no—
186C2×#67—38no—
187C2×#67—34no—
188C2×#67—34no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3C4×D311yescharacteristic
196C22×Dic3C4×D311yescharacteristic
197C2×C4×D3—22no—
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3—22no—
201C2×C4×D3C4×D312yes—
202C2×C4×D3C4×D312yes—
203C2×C4×D3C22×D312yes—
204C2×C4×D3C22×D312yes—
205C2×C3×C8—22no—
206C2×C3×C8—22no—
207C2×C3×C8—22no—
208C2×C3×C8—34no—
209C2×C3×C8—32no—
210C2×C3×C8—32no—
211C2×C3×C8—42no—
212C2×C3×C8—68no—
213C2×C3×C8—62no—
214C2×C3×C8C22×D312yes—
215C2×C3×C8C22×D312yes—
216#217—34no—
217#217—34no—
218(C2×D3)⋊C4—34no—
219(C2×D3)⋊C4—34no—
220Dic3⋊C4—34no—
221Dic3⋊C4—34no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—32no—
226C4×Dic3—62no—
227C4×Dic3—62no—
228C2×C3⋊C8—22no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—62no—
234C2×C3⋊C8—68no—
235C2×C3⋊C8—122no—
236C2×C3⋊C8#6714yescomplemented
237C2×C3⋊C8C22×D312yes—
238C2×C3⋊C8C22×D312yes—
239D3×C8—28no—
240D3×C8—68no—
241C22×C32C4×D412yes—
242C22×C32C22×C812yes—
243C22×C32#13112yes—
244C22×C32C23×C411yescharacteristic
245C2×C3×D3—22no—
246C2×C3×D3—22no—
247C2×C3×D3—22no—
248C2×C3×D3—22no—
249C2×C3×D3—28no—
250C2×C3×D3—28no—
251C2×C3×D3C22×C814yescomplemented
252C2×C3×D3C22×C814yescomplemented
253C32×C4C4×D412yes—
254C32×C4C22×D411yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3⋊Dic3—22no—
257C3⋊Dic3C22×C814yescomplemented
258C3×Dic3—22no—
259C3×Dic3—22no—
260C22×D4—91no—
261C23×C4—31no—
262C23×C4—31no—
263C22×C8—31no—
264C22×C8—31no—
265C22×C8—34no—
266C22×C8—64no—
267C22×C8—94no—
268C22×C8—91no—
269C22×C8—184no—
270C22×C8D3211yescharacteristic
271C4×D4—94no—
272C4×D4—94no—
273C2×C4⋊C4—91no—
274C2×C22⋊C4—91no—
275C2×C22⋊C4—91no—
276C2×C42—91no—
277C4⋊C8—94no—
278C22⋊C8—34no—
279C22⋊C8—94no—
280C4×C8—94no—
281C23×C3—21no—
282C23×C3—34no—
283C23×C3—34no—
284C23×C3—32no—
285C23×C3—32no—
286C23×C3—62no—
287C23×C3—62no—
288C23×C3—62no—
289C23×C3—62no—
290C23×C3C2×C4×D311yescharacteristic
291C23×C3C2×C4×D311yescharacteristic
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3D3×C814yescomplemented
297C22×D3D3×C814yescomplemented
298C22×D3C2×C4×D312yes—
299C22×D3C2×C4×D312yes—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—32no—
305C2×C3×C4—32no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—64no—
309C2×C3×C4—64no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4#23512yes—
317C2×C3×C4D3×D412yes—
318C2×C3×C4#23712yes—
319C2×C3×C4C2×#6712yes—
320C2×C3×C4C23×D311yescharacteristic
321C2×C3×C4C23×D311yescharacteristic
322#67—316no—
323#67—316no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—34no—
327C2×Dic3—34no—
328C2×Dic3—32no—
329C2×Dic3—32no—
330C2×Dic3—32no—
331C2×Dic3—32no—
332C2×Dic3—64no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—122no—
338C2×Dic3C2×C4×D312yes—
339C2×Dic3C2×C4×D312yes—
340C4×D3—24no—
341C4×D3—24no—
342C4×D3—22no—
343C4×D3—22no—
344C4×D3—22no—
345C4×D3—22no—
346C3×C8—22no—
347C3×C8—22no—
348C3×C8—34no—
349C3×C8—42no—
350C3×C8—62no—
351C3⋊C8—22no—
352C3⋊C8—62no—
353C3⋊C8—62no—
354C3⋊C8—122no—
355C3⋊C8C2×#6714yescomplemented
356C2×C32C8×D414yescomplemented
357C2×C32C2×C4×D411yescharacteristic
358C2×C32C23×C811yescharacteristic
359C2×C32C2×#13111yescharacteristic
360C3×D3—24no—
361C3×D3—24no—
362C24—31no—
363C24—31no—
364C2×D4—94no—
365C2×D4—98no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—32no—
369C22×C4—32no—
370C22×C4—32no—
371C22×C4—32no—
372C22×C4—62no—
373C22×C4—62no—
374C22×C4—62no—
375C22×C4—62no—
376C22×C4—91no—
377C22×C4—91no—
378C22×C4C2×D3211yescharacteristic
379C2×C8—22no—
380C2×C8—32no—
381C2×C8—34no—
382C2×C8—32no—
383C2×C8—68no—
384C2×C8—62no—
385C2×C8—92no—
386C2×C8—188no—
387C2×C8—182no—
388C2×C8C2×D3212yes—
389C4⋊C4—94no—
390C22⋊C4—94no—
391C22⋊C4—94no—
392C42—92no—
393C42—92no—
394C22×C3—22no—
395C22×C3—21no—
396C22×C3—22no—
397C22×C3—22no—
398C22×C3—34no—
399C22×C3—34no—
400C22×C3—62no—
401C22×C3—62no—
402C22×C3—62no—
403C22×C3—68no—
404C22×C3—62no—
405C22×C3—68no—
406C22×C3#67⋊C412yes—
407C22×C3C2×D3×C812yes—
408C22×C3C2×D3×C812yes—
409C22×C3#90112yes—
410C22×C3#90712yes—
411C22×C3C4×#6712yes—
412C22×C3C22×C4×D311yescharacteristic
413C22×C3C22×C4×D311yescharacteristic
414C2×D3—22no—
415C2×D3—22no—
416C2×D3—22no—
417C2×D3—28no—
418C2×D3—22no—
419C2×D3—28no—
420C2×D3C2×D3×C814yescomplemented
421C2×D3C2×D3×C814yescomplemented
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—62no—
426C3×C4—62no—
427C3×C4#67⋊C412yes—
428C3×C4C4×#6712yes—
429C3×C4C2×#23511yescharacteristic
430C3×C4C2×D3×D411yescharacteristic
431C3×C4C2×#23711yescharacteristic
432C3×C4C22×#6711yescharacteristic
433Dic3—22no—
434Dic3—22no—
435Dic3—34no—
436Dic3—34no—
437Dic3—64no—
438Dic3—62no—
439Dic3—62no—
440Dic3—122no—
441C32C2×C8×D411yescharacteristic, complemented, Sylow
442C23—34no—
443C23—34no—
444C23—32no—
445C23—32no—
446C23—62no—
447C23—62no—
448C23—62no—
449C23—62no—
450C23C4×D3211yescharacteristic
451D4—916no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—64no—
461C2×C4—64no—
462C2×C4—94no—
463C2×C4—92no—
464C2×C4—92no—
465C2×C4—182no—
466C2×C4#379512yes—
467C2×C4C4×D3211yescharacteristic
468C2×C4D3×#6712yes—
469C2×C4C22×D3211yescharacteristic
470C8—22no—
471C8—34no—
472C8—62no—
473C8—182no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—24no—
478C2×C3—64no—
479C2×C3—64no—
480C2×C3#67⋊C814yescomplemented
481C2×C3C8×#6714yescomplemented
482C2×C3C2×#67⋊C411yescharacteristic
483C2×C3C22×D3×C811yescharacteristic
484C2×C3C22×D3×C811yescharacteristic
485C2×C3C2×#90111yescharacteristic
486C2×C3C2×#90711yescharacteristic
487C2×C3C2×C4×#6711yescharacteristic
488D3—24no—
489D3—24no—
490C22—34no—
491C22—34no—
492C22—62no—
493C22—62no—
494C22—62no—
495C22—62no—
496C22—68no—
497C22—68no—
498C22D32×C812yes—
499C22#6380412yes—
500C22#6387912yes—
501C22C2×C4×D3211yescharacteristic
502C4—62no—
503C4—62no—
504C4—94no—
505C4—182no—
506C4#6387912yes—
507C4C2×#379511yescharacteristic
508C4C2×D3×#6711yescharacteristic
509C3—21no—
510C3C2×#67⋊C811yescharacteristic, complemented
511C3C2×C8×#6711yescharacteristic, complemented
512C2—64no—
513C2—64no—
514C2#1059071714yesdirect product factor
515C2C2×D32×C811yescharacteristic
516C2C2×#6380411yescharacteristic
517C2C2×#6387911yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC22×#625C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×C8×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C8C2semidirect
3. C22×D3×C3⋊C8C2semidirect
4. C2×#63641C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
7. C2×#63553C2semidirect
8. #10590717C2direct (N × H)
20. C2×C3×D3×C8C22semidirect
27. C2×D3×C3⋊C8C22semidirect
28. #63641C22semidirect
29. C3×(C2×D3)⋊C8C22semidirect
30. (C2×D3)⋊(C3⋊C8)C22semidirect
31. #63553C22semidirect
37. C22×D3×C8D3semidirect
42. C2×(C2×D3)⋊C8D3semidirect
64. C2×#625C8semidirect
73. C2×C3×C3⋊C8D4semidirect
118. C2×D3×C8C2×D3semidirect
122. (C2×D3)⋊C8C2×D3semidirect
133. C22×C3×D3C2×C8semidirect
134. C22×C3×D3C2×C8semidirect
142. C2×C3⋊Dic3C2×C8semidirect
155. #625C2×C8semidirect
159. C3×C3⋊C8C2×D4semidirect
236. C2×C3⋊C8#67semidirect
251. C2×C3×D3C22×C8semidirect
252. C2×C3×D3C22×C8semidirect
257. C3⋊Dic3C22×C8semidirect
296. C22×D3D3×C8semidirect
297. C22×D3D3×C8semidirect
355. C3⋊C8C2×#67semidirect
356. C2×C32C8×D4semidirect
420. C2×D3C2×D3×C8semidirect
421. C2×D3C2×D3×C8semidirect
441. C32C2×C8×D4semidirect
480. C2×C3#67⋊C8semidirect
481. C2×C3C8×#67semidirect
510. C3C2×#67⋊C8semidirect
511. C3C2×C8×#67semidirect
514. C2#10590717direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×C4×#6252
C22×D3×C3⋊C82
C2×#636412
C2×C3×(C2×D3)⋊C82
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635532
#105907172
C2×C8×#673
C2×#67⋊C83