Finite Group Databasebeta

← C2×#10591501 #11857647

Subgroups — C2×#10591501 #11857647

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C2×D3×#208C212yesmaximal, complemented
3C2×#63660C211yesmaximal, characteristic, complemented
4C2×C3×#833C211yesmaximal, characteristic, complemented
5#10591501C218yesmaximal, direct product factor
6C2×#63560C212yesmaximal, complemented
7C2×#5237—31nomaximal
8C2×#4745—31nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C3×#67C412yes—
11C23×C3×Dic3C412yes—
12C2×C3×#237—22no—
13C2×C3×#237—24no—
14C2×C3×#237—22no—
15C2×C3×#237C414yes—
16C2×C3×#237C2214yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×C3×Dic6C2211yescharacteristic
19C2×#3748C2212yes—
20C2×C3×#208C2212yes—
21C2×#3711—22no—
22D3×#208—24no—
23D3×#208C2218yescomplemented
24C2×D3×C3⋊C8—22no—
25#63660C2214yescomplemented
26C3×#833C2214yescomplemented
27#63560C2218yescomplemented
28C22×C3×#41—31no—
29C22×#237D311yescharacteristic
30C22×#208—32no—
31C2×D3×M16—32no—
32C2×C3×#100—31no—
33#5237—38no—
34C2×#836—32no—
35C2×#833—31no—
36C2×#833—31no—
37C2×#833—61no—
38C2×#833D311yescharacteristic, complemented
39C2×#824—32no—
40#4745—38no—
41C24×C32C2×C412yes—
42C23×C3×D3C2×C411yescharacteristic
43C2×C32×D4—22no—
44C2×C32×D4—22no—
45C2×C32×D4C2×C412yes—
46C2×C32×D4C2312yes—
47C22×C32×C4C2311yescharacteristic
48C2×C3×#67—24no—
49C2×C3×#67—24no—
50C2×C3×#67C2×C418yes—
51C22×C3×Dic3—24no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—22no—
54C22×C3×Dic3C2×C412yes—
55C22×C3×Dic3C2×C418yes—
56C22×C3×Dic3C2×C411yescharacteristic
57C3×#237—28no—
58C3×#237—28no—
59C3×#237—28no—
60C3×#237—28no—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3D412yes—
63C2×C3×C4×D3D414yes—
64C2×C3×C4×D3D412yes—
65C2×C3×C4×D3C2312yes—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2×C412yes—
69C2×C3×Dic6C2312yes—
70#3748—22no—
71#3748C2314yes—
72C2×C3⋊(C3⋊C8)—22no—
73C3×#208—22no—
74C3×#208C2314yes—
75C2×C3×C3⋊C8—22no—
76#3711—28no—
77D3×C3⋊C8—28no—
78C2×#413—91noSylow
79C2×C3×#41—34no—
80C2×C3×#41—34no—
81C2×C3×#41—62no—
82C2×C3×#41—64no—
83C2×C3×#41—62no—
84C22×C3×Q8—31no—
85C22×C3×D4—21no—
86C22×C3×D4—32no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C23×C3×C4—31no—
90C23×C3×C4—32no—
91C22×#67Dic312yes—
92C23×Dic3Dic312yes—
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—24no—
96C2×#237Dic314yes—
97C2×#237C2×D314yes—
98C22×C4×D3C2×D311yescharacteristic
99C22×Dic6C2×D311yescharacteristic
100C2×C3×M16—32no—
101C2×#208—32no—
102C2×#208—32no—
103C2×#208—38no—
104C2×#208—62no—
105C2×#208—62no—
106C2×#208—64no—
107C2×#208C2×D312yes—
108C22×C3⋊C8—62no—
109D3×M16—38no—
110D3×M16—64no—
111C2×ΓL(1,𝔽25)—62no—
112C2×D3×C8—62no—
113C3×#100—34no—
114#836—38no—
115#833—34no—
116#833—34no—
117#833—64no—
118#833C2×D314yescomplemented
119#824—38no—
120C23×C32—22no—
121C23×C32—22no—
122C23×C32—44no—
123C23×C32C22×C411yescharacteristic
124C23×C32C22×C414yes—
125C22×C3×D3—42no—
126C22×C3×D3C22⋊C412yes—
127C22×C3×D3C22⋊C412yes—
128C22×C3×D3C22×C412yes—
129C32×D4—24no—
130C32×D4—24no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2411yescharacteristic
135C3×#67—216no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—28no—
139C2×C3×Dic3—28no—
140C2×C3×Dic3C22⋊C412yes—
141C2×C3×Dic3C22⋊C411yescharacteristic
142C2×C3×Dic3C22⋊C411yescharacteristic
143C2×C3×Dic3C22×C414yes—
144C2×C3×Dic3C22×C412yes—
145C3×C4×D3C22⋊C414yes—
146C3×C4×D3C22⋊C414yes—
147C3×C4×D3C2×D414yes—
148C3×C4×D3C2×D414yes—
149C3×Dic6—24no—
150C3×Dic6—24no—
151C3⋊(C3⋊C8)—24no—
152C3×C3⋊C8—24no—
153C22×#41—31no—
154C22×M16—92no—
155#413—98no—
156C2×#101—92no—
157C2×#100—31no—
158C2×#100—91no—
159C24×C3—22no—
160C24×C3—31no—
161C24×C3C4×D312yes—
162C24×C3C2×Dic312yes—
163C23×D3C2×Dic311yescharacteristic
164C3×#41—68no—
165C3×#41—68no—
166C3×#41—68no—
167C3×#41—68no—
168C2×C3×Q8—32no—
169C2×C3×Q8—32no—
170C2×C3×Q8—62no—
171C2×C3×Q8—62no—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—38no—
179C2×C3×D4—42no—
180C2×C3×D4—42no—
181C2×C3×D4—64no—
182C2×C3×D4—64no—
183C2×C3×D4C4×D312yes—
184C2×C3×D4C2×Dic312yes—
185C2×C3×D4C22×D312yes—
186C2×C3×D4C22×D312yes—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—34no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—38no—
196C22×C3×C4—64no—
197C22×C3×C4—62no—
198C22×C3×C4—62no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—24no—
202C2×#67—24no—
203C2×#67C2×Dic318yes—
204C22×Dic3—24no—
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3C2×Dic312yes—
208C22×Dic3C2×Dic318yes—
209C22×Dic3C2×Dic311yescharacteristic
210#237—28no—
211#237—28no—
212#237—28no—
213#237—28no—
214C2×C4×D3C2×Dic312yes—
215C2×C4×D3#6712yes—
216C2×C4×D3#6712yes—
217C2×C4×D3#6714yes—
218C2×C4×D3C22×D312yes—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6C2×Dic312yes—
222C2×Dic6C22×D312yes—
223C3×M16—34no—
224C3×M16—62no—
225C2×C3×C8—62no—
226#208—22no—
227#208—34no—
228#208—34no—
229#208—64no—
230#208—68no—
231#208—62no—
232#208—62no—
233#208—122no—
234#208C22×D314yes—
235C2×C3⋊C8—22no—
236C2×C3⋊C8—68no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—62no—
239C2×C3⋊C8—122no—
240ΓL(1,𝔽25)—68no—
241D3×C8—68no—
242C22×C32—22no—
243C22×C32—24no—
244C22×C32—44no—
245C22×C32—44no—
246C22×C32—44no—
247C22×C32C2×C22⋊C411yescharacteristic
248C22×C32C2×C22⋊C411yescharacteristic
249C22×C32C23×C411yescharacteristic
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3C2×C22⋊C414yes—
254C32×C4C2×C22⋊C412yes—
255C32×C4C22×D412yes—
256C3×Dic3—24no—
257C3×Dic3C2×C22⋊C412yes—
258C3×Dic3C2×C22⋊C412yes—
259C2×#41—34no—
260C2×#41—34no—
261C2×#41—62no—
262C2×#41—64no—
263C2×#41—62no—
264C22×Q8—31no—
265C22×D4—32no—
266C22×D4D3211yescharacteristic
267C23×C4—31no—
268C23×C4—32no—
269C2×M16—32no—
270C2×M16—98no—
271C2×M16—92no—
272C2×M16—182no—
273C2×M16—184no—
274C22×C8—182no—
275#101—98no—
276#100—34no—
277#100—94no—
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—21no—
283C23×C3—24no—
284C23×C3—32no—
285C23×C3—32no—
286C23×C3—32no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—44no—
290C23×C3—44no—
291C23×C3—84no—
292C23×C3—122no—
293C23×C3C2×C4×D311yescharacteristic
294C23×C3C2×C4×D314yes—
295C23×C3C22×Dic311yescharacteristic
296C23×C3C22×Dic314yes—
297C22×D3—42no—
298C22×D3#21712yes—
299C22×D3#21712yes—
300C22×D3C22×Dic312yes—
301C3×Q8—64no—
302C3×Q8—64no—
303C3×D4—24no—
304C3×D4—24no—
305C3×D4—24no—
306C3×D4—24no—
307C3×D4—44no—
308C3×D4—44no—
309C3×D4—616no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—32no—
315C2×C3×C4—31no—
316C2×C3×C4—31no—
317C2×C3×C4—32no—
318C2×C3×C4—34no—
319C2×C3×C4—34no—
320C2×C3×C4—34no—
321C2×C3×C4—34no—
322C2×C3×C4—34no—
323C2×C3×C4—68no—
324C2×C3×C4—68no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4D3×D412yes—
329C2×C3×C4D3×D412yes—
330C2×C3×C4C22×Dic311yescharacteristic
331C2×C3×C4C2×#6712yes—
332C2×C3×C4C2×#6712yes—
333C2×C3×C4C23×D311yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335#67—216no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—28no—
339C2×Dic3—28no—
340C2×Dic3#21712yes—
341C2×Dic3#21711yescharacteristic
342C2×Dic3#21711yescharacteristic
343C2×Dic3C22×Dic314yes—
344C2×Dic3C22×Dic312yes—
345C4×D3#21714yes—
346C4×D3#21714yes—
347C4×D3C2×#6714yes—
348C4×D3C2×#6714yes—
349Dic6—24no—
350Dic6—24no—
351C3×C8—64no—
352C3⋊C8—24no—
353C3⋊C8—64no—
354C3⋊C8—64no—
355C3⋊C8—124no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32—44no—
359C2×C32#41312yescomplemented
360C2×C32C22×C22⋊C411yescharacteristic
361C3×D3—24no—
362C24—31no—
363C24D3×Dic312yes—
364#41—68no—
365#41—68no—
366#41—68no—
367#41—68no—
368C2×Q8—32no—
369C2×Q8—32no—
370C2×Q8—62no—
371C2×Q8—62no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—38no—
375C2×D4—64no—
376C2×D4—64no—
377C2×D4D3×Dic312yes—
378C2×D4C2×D3212yes—
379C22×C4—31no—
380C22×C4—32no—
381C22×C4—32no—
382C22×C4—32no—
383C22×C4—34no—
384C22×C4—32no—
385C22×C4—32no—
386C22×C4—38no—
387C22×C4—64no—
388C22×C4—62no—
389C22×C4—62no—
390C22×C4C2×D3211yescharacteristic
391M16—34no—
392M16—62no—
393M16—94no—
394M16—188no—
395M16—182no—
396C2×C8—62no—
397C2×C8—188no—
398C2×C8—182no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—24no—
402C22×C3—24no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—34no—
407C22×C3—42no—
408C22×C3—44no—
409C22×C3—44no—
410C22×C3—44no—
411C22×C3—44no—
412C22×C3—44no—
413C22×C3—44no—
414C22×C3—44no—
415C22×C3—64no—
416C22×C3—84no—
417C22×C3—84no—
418C22×C3—84no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3D3×C22⋊C411yescharacteristic
422C22×C3D3×C22⋊C411yescharacteristic
423C22×C3C2×#21711yescharacteristic
424C22×C3C2×#21711yescharacteristic
425C22×C3C22×C4×D311yescharacteristic
426C22×C3C23×Dic311yescharacteristic
427C2×D3—24no—
428C2×D3—42no—
429C2×D3—42no—
430C2×D3C2×#21714yes—
431C3×C4—22no—
432C3×C4—22no—
433C3×C4—32no—
434C3×C4—32no—
435C3×C4—64no—
436C3×C4D3×C22⋊C412yes—
437C3×C4C2×#21712yes—
438C3×C4C2×D3×D412yes—
439C3×C4C22×#6712yes—
440Dic3—24no—
441Dic3C2×#21712yes—
442Dic3C2×#21712yes—
443C32C2×#41311yescharacteristic, complemented, Sylow
444C23—22no—
445C23—22no—
446C23—32no—
447C23—32no—
448C23—32no—
449C23—44no—
450C23—122no—
451C23C2×D3×Dic311yescharacteristic
452C23C2×D3×Dic314yes—
453Q8—64no—
454Q8—64no—
455D4—24no—
456D4—24no—
457D4—616no—
458C2×C4—32no—
459C2×C4—32no—
460C2×C4—31no—
461C2×C4—31no—
462C2×C4—34no—
463C2×C4—34no—
464C2×C4—34no—
465C2×C4—34no—
466C2×C4—34no—
467C2×C4—68no—
468C2×C4—68no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4C2×D3×Dic311yescharacteristic
472C2×C4D3×#6712yes—
473C2×C4D3×#6712yes—
474C2×C4C22×D3211yescharacteristic
475C8—64no—
476C8—184no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—22no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—44no—
486C2×C3—44no—
487C2×C3—64no—
488C2×C3—84no—
489C2×C3#474512yescomplemented
490C2×C3#523712yescomplemented
491C2×C3C2×D3×C22⋊C411yescharacteristic
492C2×C3C22×#21711yescharacteristic
493D3—24no—
494C22—22no—
495C22—24no—
496C22—34no—
497C22—44no—
498C22—44no—
499C22—44no—
500C22—64no—
501C22—122no—
502C22—122no—
503C22D3×#21711yescharacteristic
504C22D3×#21711yescharacteristic
505C22C22×D3×Dic311yescharacteristic
506C4—32no—
507C4—32no—
508C4—64no—
509C4D3×#21712yes—
510C4C2×D3×#6712yes—
511C3—21no—
512C3C2×#474511yescharacteristic, complemented
513C3C2×#523711yescharacteristic, complemented
514C2—21no—
515C2—21no—
516C2—44no—
517C2—64no—
518C2#1059150112yesdirect product factor
519C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×#237C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#208C2semidirect
3. C2×#63660C2semidirect
4. C2×C3×#833C2semidirect
5. #10591501C2direct (N × H)
6. C2×#63560C2semidirect
23. D3×#208C22semidirect
25. #63660C22semidirect
26. C3×#833C22semidirect
27. #63560C22semidirect
38. C2×#833D3semidirect
118. #833C2×D3semidirect
359. C2×C32#413semidirect
443. C32C2×#413semidirect
489. C2×C3#4745semidirect
490. C2×C3#5237semidirect
512. C3C2×#4745semidirect
513. C3C2×#5237semidirect
518. C2#10591501direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×D3×#2082
C2×#636602
C2×C3×#8332
#105915012
C2×#635602
C2×#52373
C2×#47453