Finite Group Databasebeta

← C2×#10594856 #11901107

Subgroups — C2×#10594856 #11901107

Order 1152.

3449 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#634C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic
3C2×C3×#926C211yesmaximal, characteristic, complemented
4C2×#63962C214yesmaximal, complemented
5C2×#63866C212yesmaximal, complemented
6#10594856C2116yesmaximal, direct product factor
7C2×#63860C212yesmaximal, complemented
8C2×#63857C214yesmaximal, complemented
9C2×#5825—31nomaximal
10C2×#5526—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C23×C3⋊Dic3C2212yes—
13C22×#634—28no—
14C22×#634C2212yes—
15C22×#634C2212yes—
16C22×#634C2218yescomplemented
17C22×C3×#67C2212yes—
18C2×C3×#235—28no—
19C2×C3×#235C2218yes—
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2212yes—
22C22×C3×Dic6C2211yescharacteristic
23C2×C3×#217C2212yes—
24C3×#926C2218yescomplemented
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×C4×Dic3C2212yes—
27C2×Dic3⋊Dic3C2218yes—
28#63962C22132yescomplemented
29C2×(C2×D3)⋊Dic3C2218yes—
30#63866C22116yescomplemented
31#63860C22116yescomplemented
32#63857C22132yescomplemented
33C22×C3×#41—31no—
34C22×#235D311yescharacteristic
35C23×Dic6—31no—
36C23×Dic6—31no—
37C23×Dic6—61no—
38C2×C3×#117—31no—
39#5825—316no—
40C2×#944—32no—
41C2×#936—32no—
42C2×#935—34no—
43C2×#926D311yescharacteristic, complemented
44C2×#924—34no—
45#5526—316no—
46C2×#897—34no—
47C2×#886—34no—
48C2×#875—32no—
49C2×#869—32no—
50C24×C32C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×C32×C4D418yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2314yes—
56C22×C3⋊Dic3—28no—
57C22×C3⋊Dic3C2314yes—
58C22×C3⋊Dic3C2318yes—
59C2×#634—28no—
60C2×#634—28no—
61C2×#634—232no—
62C2×#634C2318yes—
63C2×#634C2318yes—
64C2×C3×#67—28no—
65C2×C3×#67C2318yes—
66C22×C3×Dic3C2314yes—
67C22×C3×Dic3C2312yes—
68C3×#235—232no—
69C2×C3×D12—24no—
70C2×C3×D12C2314yes—
71C2×C3×C4×D3—28no—
72C2×C3×C4×D3C2318yes—
73C2×C3×Dic6—24no—
74C2×C3×Dic6C2314yes—
75C3×#217C2318yes—
76C3×C4⋊Dic3C2318yes—
77C3×C4×Dic3C2318yes—
78Dic3⋊Dic3C23132yes—
79(C2×D3)⋊Dic3C23132yes—
80C2×#536—91noSylow
81C2×C3×#41—38no—
82C2×C3×#41—68no—
83C22×C3×Q8—31no—
84C22×C3×D4—32no—
85C22×C3×D4—31no—
86C23×C3×C4—21no—
87C23×C3×C4—32no—
88C23×C3×C4C2×D311yescharacteristic
89C23×C3×C4C2×D311yescharacteristic
90C22×#67C2×D312yes—
91C23×Dic3—32no—
92C23×Dic3—32no—
93C23×Dic3—62no—
94C2×#235—28no—
95C2×#235C2×D318yes—
96C22×D12C2×D311yescharacteristic
97C22×C4×D3C2×D312yes—
98C22×Dic6—32no—
99C22×Dic6—32no—
100C22×Dic6—32no—
101C22×Dic6—32no—
102C22×Dic6—38no—
103C22×Dic6—38no—
104C22×Dic6—62no—
105C22×Dic6—62no—
106C22×Dic6—68no—
107C22×Dic6—616no—
108C22×Dic6—68no—
109C22×Dic6—68no—
110C22×Dic6C2×D311yescharacteristic
111C3×#117—38no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C22⋊C4—32no—
114C2×C3×C42—32no—
115C2×#217—38no—
116C2×#217C2×D312yes—
117#944—316no—
118#936—316no—
119#935—332no—
120C2×(C2×D3)⋊C4—38no—
121#926C2×D318yescomplemented
122C2×C4⋊Dic3—38no—
123C2×C4⋊Dic3C2×D312yes—
124#924—332no—
125C2×Dic3⋊C4—38no—
126C2×C4×Dic3C2×D312yes—
127#897—332no—
128#886—332no—
129#875—316no—
130#869—316no—
131C23×C32—24no—
132C23×C32C2×D414yes—
133C23×C32C2412yes—
134C23×C32C2411yescharacteristic
135C22×C3×D3—24no—
136C22×C3×D3—28no—
137C22×C3×D3C2414yes—
138C2×C32×C4C2×D414yes—
139C2×C32×C4C2×D414yes—
140C2×C32×C4C2×D4116yes—
141C2×C32×C4C2412yes—
142C2×C32×C4C2412yes—
143C2×C3⋊Dic3—216no—
144C2×C3⋊Dic3—28no—
145C2×C3⋊Dic3C2418yes—
146#634—216no—
147#634—216no—
148C3×#67—216no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—28no—
151C2×C3×Dic3C2418yes—
152C2×C3×Dic3C2414yes—
153C3×D12—28no—
154C3×C4×D3—216no—
155C3×Dic6—28no—
156C22×#41—31no—
157C23×Q8—91no—
158#536—916no—
159C2×C4⋊Q8—92no—
160C2×#124—92no—
161C2×#123—94no—
162C2×C22⋊Q8—94no—
163C2×#117—31no—
164C24×C3—21no—
165C24×C3—32no—
166C24×C3C22×D311yescharacteristic
167C24×C3C22×D311yescharacteristic
168C23×D3C22×D312yes—
169C3×#41—632no—
170C2×C3×Q8—34no—
171C2×C3×Q8—64no—
172C2×C3×D4—38no—
173C2×C3×D4—34no—
174C2×C3×D4—68no—
175C2×C3×D4—64no—
176C22×C3×C4—28no—
177C22×C3×C4—24no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—32no—
181C22×C3×C4—34no—
182C22×C3×C4—38no—
183C22×C3×C4—68no—
184C22×C3×C4D1218yes—
185C22×C3×C4#6718yes—
186C22×C3×C4C22×D311yescharacteristic
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D314yes—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×C3×C4C22×D314yes—
192C2×#67—28no—
193C2×#67C22×D318yes—
194C22×Dic3—38no—
195C22×Dic3—34no—
196C22×Dic3—34no—
197C22×Dic3—38no—
198C22×Dic3—68no—
199C22×Dic3—64no—
200C22×Dic3—616no—
201C22×Dic3—68no—
202C22×Dic3—68no—
203C22×Dic3C22×D314yes—
204C22×Dic3C22×D312yes—
205#235—232no—
206C2×D12—24no—
207C2×D12C22×D314yes—
208C2×C4×D3—28no—
209C2×C4×D3C22×D318yes—
210C2×Dic6—24no—
211C2×Dic6—38no—
212C2×Dic6—38no—
213C2×Dic6—38no—
214C2×Dic6—38no—
215C2×Dic6—68no—
216C2×Dic6—68no—
217C2×Dic6—616no—
218C2×Dic6—616no—
219C2×Dic6—664no—
220C2×Dic6—68no—
221C2×Dic6—68no—
222C2×Dic6—632no—
223C2×Dic6—68no—
224C2×Dic6—68no—
225C2×Dic6—632no—
226C2×Dic6C22×D314yes—
227C3×C4⋊C4—38no—
228C3×C22⋊C4—38no—
229C3×C42—38no—
230#217—332no—
231#217C22×D318yes—
232(C2×D3)⋊C4—332no—
233C4⋊Dic3—332no—
234C4⋊Dic3C22×D318yes—
235Dic3⋊C4—332no—
236C4×Dic3C22×D318yes—
237C22×C32—28no—
238C22×C32—24no—
239C22×C32C22×D414yes—
240C22×C32C22×D412yes—
241C22×C322−1+414yes—
242C22×C32C2511yescharacteristic
243C2×C3×D3—24no—
244C2×C3×D3—28no—
245C2×C3×D3—48no—
246C32×C4C22×D414yes—
247C32×C4C22×D414yes—
248C3⋊Dic3—28no—
249C3×Dic3—24no—
250C3×Dic3—28no—
251C2×#41—38no—
252C2×#41—68no—
253C22×Q8—31no—
254C22×Q8—92no—
255C22×Q8—92no—
256C22×Q8—98no—
257C22×Q8—188no—
258C22×D4—32no—
259C22×D4—31no—
260C23×C4—32no—
261C23×C4—92no—
262C23×C4D3211yescharacteristic
263C4⋊Q8—916no—
264#124—916no—
265#123—932no—
266C22⋊Q8—932no—
267#117—38no—
268C2×C4⋊C4—32no—
269C2×C4⋊C4—98no—
270C2×C22⋊C4—32no—
271C2×C22⋊C4—98no—
272C2×C42—32no—
273C23×C3—28no—
274C23×C3—24no—
275C23×C3—24no—
276C23×C3—22no—
277C23×C3—21no—
278C23×C3—24no—
279C23×C3—34no—
280C23×C3—64no—
281C23×C3—68no—
282C23×C3C2×D1214yes—
283C23×C3C2×#6714yes—
284C23×C3C23×D312yes—
285C23×C3C23×D312yes—
286C23×C3C23×D311yescharacteristic
287C23×C3C23×D311yescharacteristic
288C22×D3—28no—
289C22×D3—24no—
290C22×D3C23×D314yes—
291C3×Q8—68no—
292C3×D4—616no—
293C3×D4—68no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—24no—
297C2×C3×C4—24no—
298C2×C3×C4—216no—
299C2×C3×C4—34no—
300C2×C3×C4—38no—
301C2×C3×C4—64no—
302C2×C3×C4—68no—
303C2×C3×C4—616no—
304C2×C3×C4C2×D1214yes—
305C2×C3×C4C2×D1214yes—
306C2×C3×C4C2×D12116yes—
307C2×C3×C4C2×#6714yes—
308C2×C3×C4C2×#6714yes—
309C2×C3×C4C2×#67116yes—
310C2×C3×C4C23×D312yes—
311C2×C3×C4C23×D312yes—
312C2×C3×C4C23×D312yes—
313C2×C3×C4C23×D312yes—
314#67—216no—
315C2×Dic3—28no—
316C2×Dic3—24no—
317C2×Dic3—38no—
318C2×Dic3—38no—
319C2×Dic3—68no—
320C2×Dic3—632no—
321C2×Dic3—616no—
322C2×Dic3—616no—
323C2×Dic3—68no—
324C2×Dic3—616no—
325C2×Dic3—68no—
326C2×Dic3C23×D318yes—
327C2×Dic3C23×D314yes—
328D12—28no—
329C4×D3—216no—
330Dic6—28no—
331Dic6—632no—
332Dic6—632no—
333Dic6—616no—
334Dic6—616no—
335Dic6—616no—
336Dic6—616no—
337C2×C32—24no—
338C2×C32#53614yescomplemented
339C2×C32C23×D411yescharacteristic
340C2×C32C2×2−1+412yes—
341C3×D3—44no—
342C24—32no—
343C24C2×D3211yescharacteristic
344#41—632no—
345C2×Q8—34no—
346C2×Q8—64no—
347C2×Q8—98no—
348C2×Q8—98no—
349C2×Q8—188no—
350C2×Q8—188no—
351C2×Q8—1832no—
352C2×D4—38no—
353C2×D4—34no—
354C2×D4—68no—
355C2×D4—64no—
356C22×C4—34no—
357C22×C4—32no—
358C22×C4—38no—
359C22×C4—68no—
360C22×C4—98no—
361C22×C4—94no—
362C22×C4—188no—
363C22×C4#62618yes—
364C22×C4C2×D3214yes—
365C22×C4C2×D3211yescharacteristic
366C22×C4C2×D3211yescharacteristic
367C4⋊C4—38no—
368C4⋊C4—932no—
369C22⋊C4—38no—
370C22⋊C4—932no—
371C42—38no—
372C22×C3—216no—
373C22×C3—28no—
374C22×C3—24no—
375C22×C3—24no—
376C22×C3—28no—
377C22×C3—28no—
378C22×C3—24no—
379C22×C3—24no—
380C22×C3—22no—
381C22×C3—21no—
382C22×C3—64no—
383C22×C3—68no—
384C22×C3—128no—
385C22×C3C22×D1214yes—
386C22×C3C22×D1212yes—
387C22×C3#101014yes—
388C22×C3#101014yes—
389C22×C3C22×#6714yes—
390C22×C3C22×#6712yes—
391C22×C3C24×D311yescharacteristic
392C22×C3C24×D311yescharacteristic
393C2×D3—28no—
394C2×D3—24no—
395C2×D3—48no—
396C3×C4—24no—
397C3×C4—24no—
398C3×C4—64no—
399C3×C4—68no—
400C3×C4C22×D1214yes—
401C3×C4C22×D1214yes—
402C3×C4C22×#6714yes—
403C3×C4C22×#6714yes—
404Dic3—28no—
405Dic3—24no—
406Dic3—616no—
407Dic3—68no—
408Dic3—68no—
409C32C2×#53611yescharacteristic, complemented, Sylow
410C23—24no—
411C23—34no—
412C23—68no—
413C23—64no—
414C23C2×#62614yes—
415C23C22×D3212yes—
416C23C22×D3211yescharacteristic
417Q8—68no—
418Q8—1816no—
419Q8—1816no—
420D4—616no—
421D4—68no—
422C2×C4—38no—
423C2×C4—34no—
424C2×C4—68no—
425C2×C4—64no—
426C2×C4—616no—
427C2×C4—98no—
428C2×C4—1816no—
429C2×C4—188no—
430C2×C4C2×#62614yes—
431C2×C4C2×#62614yes—
432C2×C4C2×#626116yes—
433C2×C4C22×D3212yes—
434C2×C4C22×D3212yes—
435C2×C3—28no—
436C2×C3—24no—
437C2×C3—24no—
438C2×C3—24no—
439C2×C3—22no—
440C2×C3—21no—
441C2×C3—124no—
442C2×C3#552614yescomplemented
443C2×C3#582514yescomplemented
444C2×C3C23×D1211yescharacteristic
445C2×C3C2×#101012yes—
446C2×C3C2×#101012yes—
447C2×C3C23×#6711yescharacteristic
448D3—44no—
449C22—28no—
450C22—24no—
451C22—68no—
452C22—64no—
453C22—128no—
454C22#6429814yes—
455C22C22×#62614yes—
456C22C22×#62612yes—
457C22C23×D3211yescharacteristic
458C4—68no—
459C4—64no—
460C4—188no—
461C4C22×#62614yes—
462C4C22×#62614yes—
463C3—21no—
464C3C2×#552611yescharacteristic, complemented
465C3C2×#582511yescharacteristic, complemented
466C2—24no—
467C2—124no—
468C2#1059485614yesdirect product factor
469C2C2×#6429812yes—
470C2C23×#62611yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
prime radicalC22×C3×#235C2
hypercenterC23×C4D32
hypocenterC32C2×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×#634C2semidirect
3. C2×C3×#926C2semidirect
4. C2×#63962C2semidirect
5. C2×#63866C2semidirect
6. #10594856C2direct (N × H)
7. C2×#63860C2semidirect
8. C2×#63857C2semidirect
16. C22×#634C22semidirect
24. C3×#926C22semidirect
28. #63962C22semidirect
30. #63866C22semidirect
31. #63860C22semidirect
32. #63857C22semidirect
43. C2×#926D3semidirect
121. #926C2×D3semidirect
338. C2×C32#536semidirect
409. C32C2×#536semidirect
442. C2×C3#5526semidirect
443. C2×C3#5825semidirect
464. C3C2×#5526semidirect
465. C3C2×#5825semidirect
468. C2#10594856direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6342
C22×C3×#2352
C2×C3×#9262
C2×#639622
C2×#638662
#105948562
C2×#638602
C2×#638572
C2×#58253
C2×#55263