Finite Group Databasebeta

← C2×#10591158 #11859231

Subgroups — C2×#10591158 #11859231

Order 1152.

1297 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C22×#3711C211yesmaximal, characteristic, complemented
4C2×C3×#830C211yesmaximal, characteristic, complemented
5#10591158C218yesmaximal, direct product factor
6C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63554C211yesmaximal, characteristic, complemented
9C2×#5011—31nomaximal
10C2×#4730—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67C411yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)—24no—
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2214yescomplemented
18C2×C3×#217C411yescharacteristic
19C3×C4×#67C414yes—
20C3×C4×#67C2214yes—
21C2×C3×(C2×D3)⋊C4C411yescharacteristic
22C2×C3×Dic3⋊C4C411yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3711—24no—
27C2×#3711C2214yescomplemented
28C3×#830C2214yescomplemented
29Dic3⋊(C3⋊C8)C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yescomplemented
31#63554C2214yescomplemented
32C2×C3×C4×D4—31no—
33C2×C4×#67D311yescharacteristic
34C22×#208—31no—
35C23×C3⋊C8—31no—
36C23×C3⋊C8—31no—
37C23×C3⋊C8—61no—
38C22×ΓL(1,𝔽25)—31no—
39C2×C3×C22⋊C8—31no—
40C2×#830—31no—
41C2×#830D311yescharacteristic, complemented
42C2×(C2×D3)⋊C8—31no—
43C2×#815—31no—
44C2×Dic3⋊C8—31no—
45#5011—38no—
46C2×C4⋊(C3⋊C8)—31no—
47C2×#803—31no—
48#4730—38no—
49C24×C32C2×C411yescharacteristic
50C23×C3×D3C2×C411yescharacteristic
51C22×C32×C4—22no—
52C22×C32×C4—22no—
53C22×C32×C4C2×C411yescharacteristic
54C22×C32×C4C2×C412yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C2×C3×#67—24no—
58C2×C3×#67C2×C414yes—
59C22×C3×Dic3C2×C411yescharacteristic
60C22×C3×Dic3C2×C411yescharacteristic
61C22×C3×Dic3C2×C411yescharacteristic
62C2×C3×C4×D3—22no—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3C2×C412yes—
65C2×C3×C4×D3C2312yes—
66C2×C3⋊(C3⋊C8)—22no—
67C2×C3⋊(C3⋊C8)—28no—
68C2×C3⋊(C3⋊C8)D414yescomplemented
69C2×C3⋊(C3⋊C8)C2312yes—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×#217C2×C414yes—
72C3×(C2×D3)⋊C4C2×C414yes—
73C3×Dic3⋊C4C2×C414yes—
74C3×C4×Dic3C2×C412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80#3711—28no—
81C2×#435—91noSylow
82C22×C3×D4—31no—
83C23×C3×C4—21no—
84C23×C3×C4—31no—
85C23×C3×C4C2×D311yescharacteristic
86C23×C3×C4C2×D311yescharacteristic
87C22×#67Dic311yescharacteristic
88C22×C4×D3C2×D311yescharacteristic
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C3×C4×D4—34no—
92C3×C4×D4—34no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C22⋊C4—31no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C42—31no—
97C2×#217Dic311yescharacteristic
98C4×#67Dic314yes—
99C4×#67C2×D314yes—
100C2×(C2×D3)⋊C4Dic311yescharacteristic
101C2×Dic3⋊C4Dic311yescharacteristic
102C2×C4×Dic3C2×D311yescharacteristic
103C2×#208—34no—
104C2×#208—64no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—34no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—34no—
111C22×C3⋊C8—61no—
112C22×C3⋊C8—61no—
113C22×C3⋊C8—64no—
114C22×C3⋊C8—64no—
115C22×C3⋊C8—64no—
116C22×C3⋊C8—68no—
117C22×C3⋊C8C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119C2×ΓL(1,𝔽25)—34no—
120C2×ΓL(1,𝔽25)—64no—
121C3×C22⋊C8—34no—
122#830—34no—
123#830C2×D314yescomplemented
124(C2×D3)⋊C8—34no—
125#815—34no—
126Dic3⋊C8—34no—
127C4⋊(C3⋊C8)—34no—
128#803—34no—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32M1614yescomplemented
132C23×C32C22×C412yes—
133C23×C32C22×C411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3C22×C412yes—
138C2×C32×C4—22no—
139C2×C32×C4—24no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C3×#67—28no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3C22×C412yes—
152C2×C3×Dic3C22×C412yes—
153C2×C3×Dic3C22×C412yes—
154C3×C4×D3—24no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3⋊(C3⋊C8)—22no—
158C3⋊(C3⋊C8)C2×D414yescomplemented
159C3×C3⋊C8—22no—
160C3×C3⋊C8—22no—
161C22×M16—91no—
162C23×C8—91no—
163C2×C4×D4—31no—
164#435—98no—
165C2×C4⋊C8—91no—
166C2×C22⋊C8—31no—
167C2×C22⋊C8—91no—
168C2×#97—91no—
169C24×C3—21no—
170C24×C3—31no—
171C24×C3C4×D311yescharacteristic
172C24×C3C2×Dic311yescharacteristic
173C23×D3C2×Dic311yescharacteristic
174C2×C3×D4—34no—
175C2×C3×D4—64no—
176C22×C3×C4—24no—
177C22×C3×C4—24no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—31no—
187C22×C3×C4—31no—
188C22×C3×C4—31no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193C22×C3×C4C4×D311yescharacteristic
194C22×C3×C4C4×D312yes—
195C22×C3×C4C2×Dic311yescharacteristic
196C22×C3×C4C2×Dic312yes—
197C22×C3×C4C22×D312yes—
198C22×C3×C4C22×D312yes—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—24no—
202C2×#67C2×Dic314yes—
203C22×Dic3C2×Dic311yescharacteristic
204C22×Dic3C2×Dic311yescharacteristic
205C22×Dic3C2×Dic311yescharacteristic
206C2×C4×D3—22no—
207C2×C4×D3—22no—
208C2×C4×D3C2×Dic312yes—
209C2×C4×D3C22×D312yes—
210C2×C3×C8—32no—
211C2×C3×C8—32no—
212C2×C3×C8—62no—
213C2×C3×C8—62no—
214C3×C4⋊C4—34no—
215C3×C22⋊C4—34no—
216C3×C22⋊C4—34no—
217C3×C42—32no—
218C3×C42—32no—
219#217C2×Dic314yes—
220(C2×D3)⋊C4C2×Dic314yes—
221Dic3⋊C4C2×Dic314yes—
222C4×Dic3C2×Dic312yes—
223C4×Dic3C22×D312yes—
224#208—68no—
225C2×C3⋊C8—22no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8—34no—
228C2×C3⋊C8—34no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—32no—
233C2×C3⋊C8—64no—
234C2×C3⋊C8—62no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—68no—
237C2×C3⋊C8—68no—
238C2×C3⋊C8—616no—
239C2×C3⋊C8—64no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—62no—
242C2×C3⋊C8C22×D312yes—
243C2×C3⋊C8C22×D312yes—
244ΓL(1,𝔽25)—68no—
245C22×C32—22no—
246C22×C32—22no—
247C22×C32—28no—
248C22×C32C4×D412yes—
249C22×C32C2×M1612yes—
250C22×C32C2×M1614yescomplemented
251C22×C32#13112yes—
252C22×C32C23×C411yescharacteristic
253C2×C3×D3—22no—
254C2×C3×D3—22no—
255C2×C3×D3—22no—
256C2×C3×D3—44no—
257C32×C4—22no—
258C32×C4C4×D412yes—
259C32×C4C22×D411yescharacteristic
260C32×C4C2×#4111yescharacteristic
261C3×Dic3—22no—
262C3×Dic3—22no—
263C3×Dic3—22no—
264C22×D4—31no—
265C23×C4—31no—
266C23×C4D3211yescharacteristic
267C2×M16—94no—
268C2×M16—184no—
269C22×C8—31no—
270C22×C8—31no—
271C22×C8—91no—
272C22×C8—94no—
273C22×C8—91no—
274C22×C8—184no—
275C4×D4—34no—
276C4×D4—34no—
277C2×C4⋊C4—31no—
278C2×C22⋊C4—31no—
279C2×C22⋊C4—31no—
280C2×C42—31no—
281C4⋊C8—94no—
282C22⋊C8—34no—
283C22⋊C8—94no—
284#97—94no—
285C23×C3—24no—
286C23×C3—24no—
287C23×C3—22no—
288C23×C3—22no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—24no—
292C23×C3—22no—
293C23×C3—21no—
294C23×C3—32no—
295C23×C3—62no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3ΓL(1,𝔽25)14yescomplemented
299C23×C3#20814yescomplemented
300C23×C3C2×C4×D312yes—
301C23×C3C2×C4×D311yescharacteristic
302C23×C3C22×Dic312yes—
303C23×C3C22×Dic311yescharacteristic
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—22no—
307C22×D3C22×Dic312yes—
308C3×D4—68no—
309C2×C3×C4—24no—
310C2×C3×C4—24no—
311C2×C3×C4—24no—
312C2×C3×C4—28no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—24no—
316C2×C3×C4—24no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—64no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4C2×C4×D312yes—
336C2×C3×C4C2×C4×D311yescharacteristic
337C2×C3×C4D3×D412yes—
338C2×C3×C4D3×D412yes—
339C2×C3×C4#23712yes—
340C2×C3×C4#23712yes—
341C2×C3×C4C22×Dic312yes—
342C2×C3×C4C22×Dic311yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—28no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3C22×Dic312yes—
350C2×Dic3C22×Dic312yes—
351C2×Dic3C22×Dic312yes—
352C4×D3—24no—
353C4×D3—22no—
354C4×D3—22no—
355C3×C8—62no—
356C3×C8—62no—
357C3⋊C8—22no—
358C3⋊C8—22no—
359C3⋊C8—34no—
360C3⋊C8—34no—
361C3⋊C8—64no—
362C3⋊C8—64no—
363C3⋊C8—62no—
364C3⋊C8—62no—
365C2×C32—24no—
366C2×C32#43514yescomplemented
367C2×C32C2×C4×D411yescharacteristic
368C2×C32C22×M1611yescharacteristic
369C2×C32C2×#13111yescharacteristic
370C3×D3—42no—
371C24—31no—
372C24D3×Dic311yescharacteristic
373C2×D4—34no—
374C2×D4—64no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—31no—
378C22×C4—31no—
379C22×C4—31no—
380C22×C4—32no—
381C22×C4—32no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4D3×Dic311yescharacteristic
385C22×C4D3×Dic312yes—
386C22×C4C2×D3212yes—
387C22×C4C2×D3211yescharacteristic
388M16—188no—
389C2×C8—32no—
390C2×C8—32no—
391C2×C8—62no—
392C2×C8—62no—
393C2×C8—92no—
394C2×C8—94no—
395C2×C8—92no—
396C2×C8—188no—
397C2×C8—182no—
398C4⋊C4—34no—
399C22⋊C4—34no—
400C22⋊C4—34no—
401C42—32no—
402C42—32no—
403C22×C3—24no—
404C22×C3—216no—
405C22×C3—24no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—28no—
409C22×C3—28no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—24no—
416C22×C3—22no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3—62no—
420C22×C3—124no—
421C22×C3#67⋊C412yes—
422C22×C3C2×ΓL(1,𝔽25)12yes—
423C22×C3C2×ΓL(1,𝔽25)14yescomplemented
424C22×C3#90712yes—
425C22×C3C2×#20812yes—
426C22×C3C2×#20814yescomplemented
427C22×C3D4×Dic312yes—
428C22×C3#94812yes—
429C22×C3C22×C4×D311yescharacteristic
430C22×C3C23×Dic311yescharacteristic
431C2×D3—22no—
432C2×D3—22no—
433C2×D3—22no—
434C2×D3—44no—
435C3×C4—24no—
436C3×C4—22no—
437C3×C4—22no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—22no—
441C3×C4—62no—
442C3×C4—62no—
443C3×C4—62no—
444C3×C4#67⋊C412yes—
445C3×C4D4×Dic312yes—
446C3×C4C2×D3×D411yescharacteristic
447C3×C4C2×D3×D411yescharacteristic
448C3×C4C2×#23711yescharacteristic
449C3×C4C2×#23711yescharacteristic
450Dic3—22no—
451Dic3—22no—
452Dic3—22no—
453C32C2×#43511yescharacteristic, complemented, Sylow
454C23—22no—
455C23—22no—
456C23—32no—
457C23—62no—
458C23—62no—
459C23—62no—
460C23#371114yescomplemented
461C23C2×D3×Dic312yes—
462C23C2×D3×Dic311yescharacteristic
463D4—68no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—62no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—64no—
477C2×C4C2×D3×Dic312yes—
478C2×C4C2×D3×Dic311yescharacteristic
479C2×C4#380512yes—
480C2×C4#381112yes—
481C2×C4C22×D3211yescharacteristic
482C8—62no—
483C8—62no—
484C8—94no—
485C8—182no—
486C2×C3—28no—
487C2×C3—24no—
488C2×C3—24no—
489C2×C3—21no—
490C2×C3—24no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—122no—
494C2×C3#473014yescomplemented
495C2×C3#501114yescomplemented
496C2×C3C2×#67⋊C411yescharacteristic
497C2×C3C22×ΓL(1,𝔽25)11yescharacteristic
498C2×C3C2×#90711yescharacteristic
499C2×C3C22×#20811yescharacteristic
500C2×C3C2×D4×Dic311yescharacteristic
501C2×C3C2×#94811yescharacteristic
502D3—42no—
503C22—22no—
504C22—28no—
505C22—22no—
506C22—62no—
507C22—62no—
508C22—62no—
509C22—124no—
510C22#6381512yes—
511C22C2×#371112yes—
512C22C2×#371114yescomplemented
513C22#67⋊Dic312yes—
514C22C22×D3×Dic311yescharacteristic
515C4—22no—
516C4—62no—
517C4—62no—
518C4—62no—
519C4#67⋊Dic312yes—
520C4C2×#380511yescharacteristic
521C4C2×#381111yescharacteristic
522C3—21no—
523C3C2×#473011yescharacteristic, complemented
524C3C2×#501111yescharacteristic, complemented
525C2—24no—
526C2—122no—
527C2#1059115814yesdirect product factor
528C2C2×#6381511yescharacteristic
529C2C22×#371111yescharacteristic
530C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×C3×#67C4
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#435
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C3⋊(C3⋊C8)C2semidirect
3. C22×#3711C2semidirect
4. C2×C3×#830C2semidirect
5. #10591158C2direct (N × H)
6. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. C2×#63554C2semidirect
17. C22×C3⋊(C3⋊C8)C22semidirect
27. C2×#3711C22semidirect
28. C3×#830C22semidirect
29. Dic3⋊(C3⋊C8)C22semidirect
30. (C2×D3)⋊(C3⋊C8)C22semidirect
31. #63554C22semidirect
41. C2×#830D3semidirect
68. C2×C3⋊(C3⋊C8)D4semidirect
123. #830C2×D3semidirect
131. C23×C32M16semidirect
158. C3⋊(C3⋊C8)C2×D4semidirect
250. C22×C32C2×M16semidirect
298. C23×C3ΓL(1,𝔽25)semidirect
299. C23×C3#208semidirect
366. C2×C32#435semidirect
423. C22×C3C2×ΓL(1,𝔽25)semidirect
426. C22×C3C2×#208semidirect
453. C32C2×#435semidirect
460. C23#3711semidirect
494. C2×C3#4730semidirect
495. C2×C3#5011semidirect
512. C22C2×#3711semidirect
523. C3C2×#4730semidirect
524. C3C2×#5011semidirect
527. C2#10591158direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3⋊(C3⋊C8)2
C2×C3×C4×#672
C22×#37112
C2×C3×#8302
#105911582
C2×Dic3⋊(C3⋊C8)2
C2×(C2×D3)⋊(C3⋊C8)2
C2×#635542
C2×#50113
C2×#47303