Finite Group Databasebeta

← C2×#10590899 #11874400

Subgroups — C2×#10590899 #11874400

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C22×C3×Dic12C211yesmaximal, characteristic, complemented
3C2×#63866C211yesmaximal, characteristic, complemented
4C2×#63864C211yesmaximal, characteristic
5C22×#3719C211yesmaximal, characteristic, complemented
6C22×#3717C211yesmaximal, characteristic
7C2×C3×#815C211yesmaximal, characteristic, complemented
8#10590899C218yesmaximal, direct product factor
9C2×#5190—31nomaximal
10C2×#4715—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×#3744—24no—
17C2×#3744C2214yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×C3×Dic12—24no—
21C2×C3×Dic12C2214yescomplemented
22C2×Dic3⋊Dic3—22no—
23C2×#3722—22no—
24#63866—22no—
25#63866C2214yescomplemented
26#63864—22no—
27#63864C2214yes—
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yes—
32C3×#815C2214yescomplemented
33C22×C3×Q16—31no—
34C2×#947—31no—
35C2×#944—31no—
36C22×#216—31no—
37C22×#215—31no—
38C22×Dic12—31no—
39C22×Dic12D311yescharacteristic, complemented
40C22×#204—31no—
41C22×#204—31no—
42C22×#204—31no—
43C22×#204—61no—
44C2×#875—31no—
45C2×#869—31no—
46C2×C3×#97—31no—
47#5190—38no—
48C2×#815D311yescharacteristic, complemented
49#4715—38no—
50C23×C3⋊D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—21no—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D412yes—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C2×C3×Dic6C2312yes—
72C2×C32×C8D414yes—
73C2×C32×C8C2312yes—
74#3744—28no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8D414yes—
78C2×C3×C3⋊C8C2312yes—
79C3×Dic12—28no—
80Dic3⋊Dic3—28no—
81#3722—28no—
82#3719—28no—
83#3717—28no—
84C2×#497—91noSylow
85C22×C3×Q8—31no—
86C22×C3×Q8—31no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×Dic6—31no—
91C22×Dic6—31no—
92C22×Dic6—61no—
93C22×Dic6C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C2×C3×Q16—34no—
96C2×C3×Q16—64no—
97C22×C3×C8—21no—
98C22×C3×C8—31no—
99C22×C3×C8C2×D311yescharacteristic
100C22×C3×C8C2×D311yescharacteristic
101C2×C3×C42—31no—
102#947—34no—
103#947—62no—
104#944—34no—
105#944—62no—
106C2×#216—34no—
107C2×#216—64no—
108C2×#215—34no—
109C2×#215—64no—
110C2×(C2×D3)⋊C4—62no—
111C2×(C2×D3)⋊C4—62no—
112C2×C4⋊Dic3—62no—
113C2×Dic3⋊C4—62no—
114C2×C4×Dic3C2×D311yescharacteristic
115C22×C3⋊C8C2×D311yescharacteristic
116C2×Dic12—24no—
117C2×Dic12—34no—
118C2×Dic12—64no—
119C2×Dic12C2×D314yescomplemented
120C2×#204—34no—
121C2×#204—34no—
122C2×#204—34no—
123C2×#204—64no—
124C2×#204—68no—
125C2×#204—64no—
126C2×#204—64no—
127C2×#204—64no—
128#875—34no—
129#875—62no—
130#869—34no—
131#869—62no—
132C3×#97—34no—
133#815C2×D314yescomplemented
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—44no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—42no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—42no—
147#634—22no—
148#634—22no—
149#634—42no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—42no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3C2×D414yes—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—42no—
161C3×Dic6—42no—
162C32×C8C2×D414yes—
163C3×C3⋊C8C2×D414yes—
164C22×Q16—31no—
165C22×Q16—91no—
166C22×SD16—91no—
167C22×SD16—91no—
168C2×C4⋊Q8—91no—
169C2×#124—91no—
170#497—98no—
171C2×#97—31no—
172C23×D3—61no—
173C23×D3—61no—
174C23×D3—121no—
175C2×C3×Q8—32no—
176C2×C3×Q8—32no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×Q8—62no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C22×C3×C4—21no—
184C22×C3×C4—32no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—61no—
192C22×Dic3—61no—
193C22×Dic3—121no—
194C22×Dic3D1212yes—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×D12—64no—
199C2×D12—62no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—122no—
206C2×D12—121no—
207C2×Dic6—22no—
208C2×Dic6—22no—
209C2×Dic6—22no—
210C2×Dic6—22no—
211C2×Dic6—21no—
212C2×Dic6—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6—64no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—62no—
220C2×Dic6—62no—
221C2×Dic6—61no—
222C2×Dic6—61no—
223C2×Dic6—121no—
224C2×Dic6—122no—
225C2×Dic6C22×D312yes—
226C2×Dic6C22×D312yes—
227C3×Q16—68no—
228C2×C3×C8—24no—
229C2×C3×C8—22no—
230C2×C3×C8—34no—
231C2×C3×C8—32no—
232C2×C3×C8D1214yes—
233C2×C3×C8#6714yes—
234C2×C3×C8C22×D312yes—
235C2×C3×C8C22×D312yes—
236C3×C42—32no—
237C3×C42—32no—
238#216—68no—
239#215—68no—
240(C2×D3)⋊C4—68no—
241(C2×D3)⋊C4—68no—
242C4⋊Dic3—68no—
243Dic3⋊C4—68no—
244C4×Dic3D1212yes—
245C4×Dic3C22×D312yes—
246C2×C3⋊C8D1214yes—
247C2×C3⋊C8C22×D312yes—
248Dic12—28no—
249Dic12—68no—
250#204—616no—
251#204—68no—
252#204—68no—
253#204—68no—
254C22×C32#12712yes—
255C22×C32#13714yes—
256C22×C32C22×D411yescharacteristic
257C2×C3⋊D3—42no—
258C2×C3⋊D3—44no—
259C2×C3⋊D3—84no—
260C32×C4#12712yes—
261C32×C4C22×D411yescharacteristic
262C32×C4C22×D411yescharacteristic
263C3⋊Dic3—42no—
264C3×Dic3—24no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C22×Q8—31no—
269C22×Q8—91no—
270C22×D4—91no—
271C2×Q16—34no—
272C2×Q16—64no—
273C2×Q16—94no—
274C2×Q16—184no—
275C2×SD16—94no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×SD16—184no—
279C22×C8—31no—
280C22×C8D3211yescharacteristic
281C4⋊Q8—94no—
282C4⋊Q8—182no—
283#124—94no—
284#124—182no—
285C2×C4⋊C4—182no—
286C2×C22⋊C4—182no—
287C2×C42—31no—
288#97—34no—
289C23×C3—21no—
290C23×C3C2×D1211yescharacteristic
291C23×C3D3×D411yescharacteristic
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—122no—
295C22×D3—124no—
296C22×D3—122no—
297C22×D3—124no—
298C22×D3—124no—
299C22×D3—122no—
300C22×D3—244no—
301C3×Q8—62no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—62no—
305C3×Q8—122no—
306C3×Q8—122no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—34no—
312C2×C3×C4—64no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317C2×C3×C4C2×D1211yescharacteristic
318C2×C3×C4C2×D1212yes—
319C2×C3×C4C2×D1212yes—
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D412yes—
322C2×C3×C4C2×#6712yes—
323C2×C3×C4C23×D311yescharacteristic
324C2×C3×C4C23×D311yescharacteristic
325C2×Dic3—24no—
326C2×Dic3—22no—
327C2×Dic3—22no—
328C2×Dic3—42no—
329C2×Dic3—42no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—122no—
333C2×Dic3—124no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3C2×D1214yes—
337D12—64no—
338D12—62no—
339D12—62no—
340D12—62no—
341D12—62no—
342D12—122no—
343D12—124no—
344D12—122no—
345D12—122no—
346Dic6—22no—
347Dic6—22no—
348Dic6—22no—
349Dic6—22no—
350Dic6—42no—
351Dic6—42no—
352Dic6—64no—
353Dic6—62no—
354Dic6—62no—
355Dic6—62no—
356Dic6—62no—
357Dic6—122no—
358Dic6—124no—
359Dic6—122no—
360Dic6—122no—
361C3×C8—24no—
362C3×C8—34no—
363C3×C8C2×D1214yes—
364C3×C8C2×#6714yes—
365C3⋊C8C2×D1214yes—
366C2×C32#49714yescomplemented
367C2×C32C2×#12711yescharacteristic
368C2×C32C2×#13712yes—
369C3⋊D3—82no—
370C24—181no—
371C2×Q8—32no—
372C2×Q8—32no—
373C2×Q8—61no—
374C2×Q8—61no—
375C2×Q8—62no—
376C2×Q8—62no—
377C2×Q8—62no—
378C2×Q8—62no—
379C2×Q8—92no—
380C2×Q8—181no—
381C2×Q8—182no—
382C2×Q8—182no—
383C2×D4—92no—
384C2×D4—182no—
385C2×D4—181no—
386C2×D4—182no—
387C22×C4—32no—
388C22×C4—61no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—68no—
393Q16—188no—
394SD16—188no—
395SD16—188no—
396C2×C8—32no—
397C2×C8—34no—
398C2×C8#62614yes—
399C2×C8C2×D3212yes—
400C4⋊C4—188no—
401C22⋊C4—188no—
402C42—32no—
403C42—32no—
404C22×C3—21no—
405C22×C3—24no—
406C22×C3—22no—
407C22×C3#87412yes—
408C22×C3#90914yes—
409C22×C3#91814yes—
410C22×C3#94012yes—
411C22×C3C22×D1211yescharacteristic
412C22×C3C2×D3×D411yescharacteristic
413C2×D3—124no—
414C2×D3—122no—
415C2×D3—124no—
416C2×D3—124no—
417C2×D3—122no—
418C2×D3—244no—
419C2×D3—248no—
420C2×D3—244no—
421C2×D3—244no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—22no—
425C3×C4—64no—
426C3×C4—122no—
427C3×C4—122no—
428C3×C4#87412yes—
429C3×C4#94012yes—
430C3×C4C22×D1211yescharacteristic
431C3×C4C22×D1211yescharacteristic
432C3×C4C2×D3×D411yescharacteristic
433C3×C4C22×#6711yescharacteristic
434Dic3—24no—
435Dic3—42no—
436Dic3—42no—
437Dic3—124no—
438Dic3—122no—
439Dic3—122no—
440C32C2×#49711yescharacteristic, complemented, Sylow
441C23—182no—
442C23—364no—
443C23—362no—
444C23D3×D1211yescharacteristic
445Q8—62no—
446Q8—62no—
447Q8—62no—
448Q8—62no—
449Q8—122no—
450Q8—122no—
451Q8—182no—
452Q8—182no—
453Q8—362no—
454D4—182no—
455D4—182no—
456D4—362no—
457C2×C4—34no—
458C2×C4—64no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—122no—
462C2×C4—122no—
463C2×C4—182no—
464C2×C4—362no—
465C2×C4D3×D1212yes—
466C2×C4D3×D1211yescharacteristic
467C2×C4C2×#62612yes—
468C2×C4C22×D3211yescharacteristic
469C8—34no—
470C8C2×#62614yes—
471C2×C3—22no—
472C2×C3—24no—
473C2×C3—21no—
474C2×C3#471514yescomplemented
475C2×C3#519014yescomplemented
476C2×C3C2×#87411yescharacteristic
477C2×C3C2×#90912yes—
478C2×C3C2×#91812yes—
479C2×C3C2×#94011yescharacteristic
480D3—244no—
481D3—242no—
482D3—242no—
483C22—364no—
484C22—362no—
485C22—724no—
486C22#6380114yes—
487C22#6391112yes—
488C22C2×D3×D1211yescharacteristic
489C4—64no—
490C4—122no—
491C4—122no—
492C4—362no—
493C4#6391112yes—
494C4C2×D3×D1211yescharacteristic
495C4C22×#62611yescharacteristic
496C3—21no—
497C3C2×#471511yescharacteristic, complemented
498C3C2×#519011yescharacteristic, complemented
499C2—722no—
500C2#1059089914yesdirect product factor
501C2C2×#6380112yes—
502C2C2×#6391111yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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
2. C22×C3×Dic12C2semidirect
3. C2×#63866C2semidirect
5. C22×#3719C2semidirect
7. C2×C3×#815C2semidirect
8. #10590899C2direct (N × H)
21. C2×C3×Dic12C22semidirect
25. #63866C22semidirect
29. C2×#3719C22semidirect
32. C3×#815C22semidirect
39. C22×Dic12D3semidirect
48. C2×#815D3semidirect
119. C2×Dic12C2×D3semidirect
133. #815C2×D3semidirect
366. C2×C32#497semidirect
440. C32C2×#497semidirect
474. C2×C3#4715semidirect
475. C2×C3#5190semidirect
497. C3C2×#4715semidirect
498. C3C2×#5190semidirect
500. C2#10590899direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C22×C3×Dic122
C2×#638662
C2×#638642
C22×#37192
C22×#37172
C2×C3×#8152
#105908992
C2×#51903
C2×#47153