Finite Group Databasebeta

← C2×#10590870 #11874401

Subgroups — C2×#10590870 #11874401

Order 1152.

1201 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×Dic12C211yesmaximal, characteristic, complemented
2C22×C3×#204C211yesmaximal, characteristic
3C2×#63873C211yesmaximal, characteristic, complemented
4C2×#63863C211yesmaximal, characteristic
5C22×#3718C211yesmaximal, characteristic, complemented
6C22×#3715C211yesmaximal, characteristic
7C2×#63642C211yesmaximal, characteristic, complemented
8#10590870C218yesmaximal, direct product factor
9C2×#5190—31nomaximal
10C2×#5167—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×Dic12—24no—
19C2×C3×Dic12C2214yescomplemented
20C2×C3×#204—24no—
21C2×C3×#204C2214yes—
22C2×#3724—22no—
23C2×(C2×D3)⋊Dic3—22no—
24#63873—22no—
25#63873C2214yescomplemented
26#63863—22no—
27#63863C2214yes—
28C2×#3718—24no—
29C2×#3718C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yes—
32#63642C2214yescomplemented
33C22×C3×Q16—31no—
34C22×C3×SD16—31no—
35C2×#947—31no—
36C2×#944—31no—
37C2×#944—31no—
38C22×#216—31no—
39C22×#216—31no—
40C22×#215—31no—
41C2×#936—31no—
42C22×#214—31no—
43C22×Dic12D311yescharacteristic, complemented
44C22×#204D311yescharacteristic
45#5190—38no—
46#5167—38no—
47C2×#815—31no—
48C2×#815—31no—
49C2×#815—61no—
50C23×C3×D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3D412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×D12—22no—
57C2×C3×D12—22no—
58C2×C3×D12—21no—
59C2×C3×D12C2312yes—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6C2312yes—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2312yes—
72C2×C32×C8D414yes—
73C2×C32×C8C2312yes—
74C4×C3⋊Dic3D412yes—
75C4×C3⋊Dic3C2312yes—
76C2×C3⋊(C3⋊C8)D414yes—
77C2×C3⋊(C3⋊C8)C2312yes—
78C3×Dic12—28no—
79C3×#204—28no—
80#3724—28no—
81(C2×D3)⋊Dic3—28no—
82#3718—28no—
83#3715—28no—
84C2×#497—91noSylow
85C22×C3×Q8—31no—
86C22×C3×Q8—31no—
87C22×C3×Q8—31no—
88C22×C3×D4—31no—
89C22×D12C2×D311yescharacteristic
90C22×Dic6C2×D311yescharacteristic
91C22×Dic6C2×D311yescharacteristic
92C22×Dic6C2×D311yescharacteristic
93C2×C3×Q16—34no—
94C2×C3×Q16—64no—
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—21no—
98C22×C3×C8C2×D311yescharacteristic
99C22×C3×C8C2×D311yescharacteristic
100C2×#217—62no—
101#947—34no—
102#947—62no—
103#944—34no—
104#944—34no—
105#944—62no—
106#944—62no—
107C2×#216—34no—
108C2×#216—34no—
109C2×#216—64no—
110C2×#216—64no—
111C2×#215—34no—
112C2×#215—64no—
113#936—34no—
114#936—62no—
115C2×#214—34no—
116C2×#214—64no—
117C2×(C2×D3)⋊C4—62no—
118C2×Dic3⋊C4—62no—
119C2×Dic3⋊C4—62no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—61no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—61no—
126C2×Dic12—24no—
127C2×Dic12C2×D314yescomplemented
128C2×#204—24no—
129C2×#204C2×D314yes—
130#815—34no—
131#815—34no—
132#815—64no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—42no—
136C22×C3×D3—44no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D412yes—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—24no—
142C2×C3⋊Dic3C2×D414yes—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—42no—
149C3×D12—22no—
150C3×D12—22no—
151C3×D12—42no—
152C3×Dic6—22no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6—42no—
160C3×Dic6—42no—
161C32×C8C2×D414yes—
162C3⋊(C3⋊C8)C2×D414yes—
163C22×Q16—31no—
164C22×Q16—91no—
165C22×SD16—31no—
166C22×SD16—91no—
167C2×C4⋊Q8—91no—
168C2×#124—91no—
169#497—98no—
170C2×#97—91no—
171C24×C3—61no—
172C23×D3—21no—
173C2×C3×Q8—32no—
174C2×C3×Q8—32no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×Q8—62no—
184C2×C3×Q8—62no—
185C2×C3×D4—32no—
186C2×C3×D4—62no—
187C2×C3×D4—61no—
188C2×C3×D4—62no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—62no—
201C2×D12—22no—
202C2×D12—22no—
203C2×D12—21no—
204C2×D12C22×D312yes—
205C2×Dic6—22no—
206C2×Dic6—22no—
207C2×Dic6—22no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—21no—
214C2×Dic6C22×D312yes—
215C2×Dic6C22×D312yes—
216C2×Dic6C22×D312yes—
217C3×Q16—68no—
218C3×SD16—68no—
219C2×C3×C8—24no—
220C2×C3×C8—22no—
221C2×C3×C8#6714yes—
222C2×C3×C8#6714yes—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C22×D312yes—
225#217—68no—
226#216—68no—
227#216—68no—
228#215—68no—
229#214—68no—
230(C2×D3)⋊C4—68no—
231Dic3⋊C4—68no—
232Dic3⋊C4—68no—
233C4×Dic3—32no—
234C4×Dic3—32no—
235C4×Dic3—32no—
236C4×Dic3—32no—
237C4×Dic3—62no—
238C4×Dic3—62no—
239C2×C3⋊C8—34no—
240C2×C3⋊C8—34no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—64no—
245Dic12—28no—
246#204—28no—
247C22×C32#12712yes—
248C22×C32#13714yes—
249C22×C32C22×D411yescharacteristic
250C2×C3×D3—42no—
251C2×C3×D3—44no—
252C2×C3×D3—84no—
253C32×C4#12712yes—
254C32×C4C22×D411yescharacteristic
255C32×C4C22×D411yescharacteristic
256C3⋊Dic3—24no—
257C3×Dic3—42no—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C22×Q8—31no—
261C22×Q8—31no—
262C22×Q8—31no—
263C22×D4—31no—
264C2×Q16—34no—
265C2×Q16—64no—
266C2×Q16—94no—
267C2×Q16—184no—
268C2×SD16—34no—
269C2×SD16—64no—
270C2×SD16—94no—
271C2×SD16—184no—
272C22×C8—91no—
273C22×C8D3211yescharacteristic
274C4⋊Q8—94no—
275C4⋊Q8—182no—
276#124—94no—
277#124—182no—
278C2×C4⋊C4—182no—
279C2×C22⋊C4—182no—
280C2×C42—91no—
281#97—94no—
282C23×C3—21no—
283C23×C3—62no—
284C23×C3—124no—
285C23×C3—122no—
286C23×C3D3×D411yescharacteristic
287C23×C3D3×D411yescharacteristic
288C22×D3—22no—
289C22×D3—44no—
290C22×D3—42no—
291C3×Q8—62no—
292C3×Q8—62no—
293C3×Q8—62no—
294C3×Q8—62no—
295C3×Q8—62no—
296C3×Q8—62no—
297C3×Q8—122no—
298C3×Q8—122no—
299C3×Q8—122no—
300C3×D4—62no—
301C3×D4—62no—
302C3×D4—122no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—22no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—122no—
311C2×C3×C4—122no—
312C2×C3×C4—122no—
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D412yes—
316C2×C3×C4D3×D412yes—
317C2×C3×C4C2×#6712yes—
318C2×C3×C4C2×#6712yes—
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×Dic3—22no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—42no—
327C2×Dic3—42no—
328C2×Dic3—42no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331C2×Dic3—64no—
332C2×Dic3—124no—
333D12—22no—
334D12—22no—
335D12—42no—
336Dic6—22no—
337Dic6—22no—
338Dic6—22no—
339Dic6—22no—
340Dic6—22no—
341Dic6—22no—
342Dic6—42no—
343Dic6—42no—
344Dic6—42no—
345C3×C8—24no—
346C3×C8C2×#6714yes—
347C3×C8C2×#6714yes—
348C3⋊C8—34no—
349C3⋊C8—34no—
350C3⋊C8—64no—
351C2×C32#49714yescomplemented
352C2×C32C2×#12711yescharacteristic
353C2×C32C2×#13712yes—
354C3×D3—82no—
355C24—61no—
356C2×Q8—32no—
357C2×Q8—32no—
358C2×Q8—32no—
359C2×Q8—61no—
360C2×Q8—61no—
361C2×Q8—61no—
362C2×Q8—62no—
363C2×Q8—62no—
364C2×Q8—62no—
365C2×Q8—62no—
366C2×Q8—62no—
367C2×Q8—62no—
368C2×D4—32no—
369C2×D4—62no—
370C2×D4—61no—
371C2×D4—62no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—92no—
376C22×C4C2×D3211yescharacteristic
377Q16—68no—
378Q16—188no—
379SD16—68no—
380SD16—188no—
381C2×C8—92no—
382C2×C8—94no—
383C2×C8#62514yes—
384C2×C8C2×D3212yes—
385C4⋊C4—188no—
386C22⋊C4—188no—
387C42—92no—
388C42—92no—
389C22×C3—21no—
390C22×C3—24no—
391C22×C3—22no—
392C22×C3—124no—
393C22×C3—122no—
394C22×C3—244no—
395C22×C3#91514yes—
396C22×C3#91814yes—
397C22×C3#94012yes—
398C22×C3#94012yes—
399C22×C3C2×D3×D411yescharacteristic
400C22×C3C2×D3×D411yescharacteristic
401C2×D3—44no—
402C2×D3—42no—
403C2×D3—84no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—22no—
407C3×C4—122no—
408C3×C4—122no—
409C3×C4—122no—
410C3×C4#94012yes—
411C3×C4#94012yes—
412C3×C4C2×D3×D411yescharacteristic
413C3×C4C2×D3×D411yescharacteristic
414C3×C4C22×#6711yescharacteristic
415C3×C4C22×#6711yescharacteristic
416Dic3—42no—
417Dic3—42no—
418Dic3—42no—
419Dic3—64no—
420Dic3—64no—
421Dic3—124no—
422C32C2×#49711yescharacteristic, complemented, Sylow
423C23—62no—
424C23—124no—
425C23—122no—
426C23#380211yescharacteristic
427Q8—62no—
428Q8—62no—
429Q8—62no—
430Q8—62no—
431Q8—62no—
432Q8—62no—
433Q8—122no—
434Q8—122no—
435Q8—122no—
436D4—62no—
437D4—62no—
438D4—122no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—94no—
443C2×C4—122no—
444C2×C4—122no—
445C2×C4—122no—
446C2×C4—184no—
447C2×C4#380212yes—
448C2×C4#380211yescharacteristic
449C2×C4C2×#62512yes—
450C2×C4C22×D3211yescharacteristic
451C8—94no—
452C8C2×#62514yes—
453C2×C3—22no—
454C2×C3—24no—
455C2×C3—21no—
456C2×C3—242no—
457C2×C3#516714yescomplemented
458C2×C3#519014yescomplemented
459C2×C3C2×#91512yes—
460C2×C3C2×#91812yes—
461C2×C3C2×#94011yescharacteristic
462C2×C3C2×#94011yescharacteristic
463D3—82no—
464C22—124no—
465C22—122no—
466C22—244no—
467C22#6381114yes—
468C22#6391412yes—
469C22C2×#380211yescharacteristic
470C4—122no—
471C4—122no—
472C4—122no—
473C4—184no—
474C4#6391412yes—
475C4C2×#380211yescharacteristic
476C4C22×#62511yescharacteristic
477C3—21no—
478C3C2×#516711yescharacteristic, complemented
479C3C2×#519011yescharacteristic, complemented
480C2—242no—
481C2#1059087014yesdirect product factor
482C2C2×#6381112yes—
483C2C2×#6391411yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#497
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic12C2semidirect
3. C2×#63873C2semidirect
5. C22×#3718C2semidirect
7. C2×#63642C2semidirect
8. #10590870C2direct (N × H)
19. C2×C3×Dic12C22semidirect
25. #63873C22semidirect
29. C2×#3718C22semidirect
32. #63642C22semidirect
43. C22×Dic12D3semidirect
127. C2×Dic12C2×D3semidirect
351. C2×C32#497semidirect
422. C32C2×#497semidirect
457. C2×C3#5167semidirect
458. C2×C3#5190semidirect
478. C3C2×#5167semidirect
479. C3C2×#5190semidirect
481. C2#10590870direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×Dic122
C22×C3×#2042
C2×#638732
C2×#638632
C22×#37182
C22×#37152
C2×#636422
#105908702
C2×#51903
C2×#51673