Finite Group Databasebeta

← C2×#10594855 #11901108

Subgroups — C2×#10594855 #11901108

Order 1152.

3189 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C23×C3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64135C211yesmaximal, characteristic, complemented
4C2×#63961C214yesmaximal, complemented
5C2×#63873C212yesmaximal, complemented
6#10594855C2116yesmaximal, direct product factor
7C2×#63863C212yesmaximal, complemented
8C2×#63856C214yesmaximal, complemented
9C2×#5825—31nomaximal
10C2×#5816—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67C2212yes—
13C23×C3×Dic3C2212yes—
14C2×C3×#235—28no—
15C2×C3×#235C2218yes—
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×C3×Dic6—28no—
19C22×C3×Dic6C2212yes—
20C22×C3×Dic6C2212yes—
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2218yescomplemented
23C2×#3757C2212yes—
24#64135C2218yescomplemented
25C2×C4⋊(C3⋊Dic3)C2212yes—
26C2×C4×C3⋊Dic3C2212yes—
27C2×#3724C2218yes—
28#63961C22132yescomplemented
29C2×(C2×D3)⋊Dic3C2218yes—
30#63873C22116yescomplemented
31#63863C22116yescomplemented
32#63856C22132yescomplemented
33C22×C3×#41—31no—
34C23×C3×Q8—31no—
35C22×#235D311yescharacteristic
36C23×Dic6D311yescharacteristic, complemented
37#5825—316no—
38#5816—316no—
39C2×#947—32no—
40C2×#946—34no—
41C2×#944—32no—
42C2×#944—32no—
43C2×#936—32no—
44C2×#935—34no—
45C2×#929—34no—
46C2×#926—31no—
47C2×#926—31no—
48C2×#926—61no—
49C2×#924—34no—
50C24×C32C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×C32×C4D418yes—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2314yes—
56C22×C3⋊Dic3C2314yes—
57C2×C3×#67—28no—
58C2×C3×#67C2318yes—
59C22×C3×Dic3—28no—
60C22×C3×Dic3C2314yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2318yes—
63C3×#235—232no—
64C2×C3×D12—24no—
65C2×C3×D12C2314yes—
66C2×C3×C4×D3—28no—
67C2×C3×C4×D3C2318yes—
68C2×C3×Dic6—28no—
69C2×C3×Dic6—28no—
70C2×C3×Dic6—232no—
71C2×C3×Dic6—24no—
72C2×C3×Dic6C2318yes—
73C2×C3×Dic6C2318yes—
74C2×C3×Dic6C2314yes—
75#3757C2318yes—
76C4⋊(C3⋊Dic3)C2318yes—
77C4×C3⋊Dic3C2318yes—
78#3724C23132yes—
79(C2×D3)⋊Dic3C23132yes—
80C2×#536—91noSylow
81C2×C3×#41—38no—
82C2×C3×#41—68no—
83C22×C3×Q8—32no—
84C22×C3×Q8—32no—
85C22×C3×Q8—31no—
86C22×C3×Q8—38no—
87C22×C3×Q8—68no—
88C22×C3×D4—32no—
89C22×C3×D4—31no—
90C23×C3×C4—21no—
91C23×C3×C4—32no—
92C23×C3×C4—32no—
93C23×C3×C4C2×D311yescharacteristic
94C23×C3×C4C2×D311yescharacteristic
95C22×#67C2×D312yes—
96C23×Dic3C2×D312yes—
97C2×#235—28no—
98C2×#235C2×D318yes—
99C22×D12C2×D311yescharacteristic
100C22×C4×D3C2×D312yes—
101C22×Dic6—28no—
102C22×Dic6C2×D312yes—
103C22×Dic6C2×D312yes—
104C22×Dic6C2×D311yescharacteristic
105C22×Dic6C2×D318yescomplemented
106C2×#217—32no—
107C2×#217—32no—
108C2×#217—38no—
109C2×#217—62no—
110#947—316no—
111#946—332no—
112#944—316no—
113#944—316no—
114#936—316no—
115#935—332no—
116#929—332no—
117C2×(C2×D3)⋊C4—38no—
118#926—38no—
119#926—38no—
120#926—68no—
121C2×C4⋊Dic3—32no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—62no—
124#924—332no—
125C2×Dic3⋊C4—38no—
126C2×Dic3⋊C4—38no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—62no—
130C23×C32—24no—
131C23×C32C2×D414yes—
132C23×C32C2412yes—
133C23×C32C2411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—28no—
136C22×C3×D3C2414yes—
137C2×C32×C4C2×D414yes—
138C2×C32×C4C2×D414yes—
139C2×C32×C4C2×D4116yes—
140C2×C32×C4C2412yes—
141C2×C32×C4C2412yes—
142C2×C3⋊Dic3—28no—
143C2×C3⋊Dic3C2418yes—
144C3×#67—216no—
145C2×C3×Dic3—216no—
146C2×C3×Dic3—28no—
147C2×C3×Dic3—24no—
148C2×C3×Dic3C2418yes—
149C2×C3×Dic3C2414yes—
150C3×D12—28no—
151C3×C4×D3—216no—
152C3×Dic6—216no—
153C3×Dic6—216no—
154C3×Dic6—28no—
155C22×#41—31no—
156C23×Q8—31no—
157#536—916no—
158C2×C4⋊Q8—92no—
159C2×#124—92no—
160C2×#123—94no—
161C2×C22⋊Q8—94no—
162C2×#117—91no—
163C24×C3—21no—
164C24×C3—32no—
165C24×C3C22×D311yescharacteristic
166C24×C3C22×D311yescharacteristic
167C23×D3C22×D312yes—
168C3×#41—632no—
169C2×C3×Q8—34no—
170C2×C3×Q8—38no—
171C2×C3×Q8—38no—
172C2×C3×Q8—68no—
173C2×C3×Q8—68no—
174C2×C3×Q8—632no—
175C2×C3×Q8—64no—
176C2×C3×D4—38no—
177C2×C3×D4—34no—
178C2×C3×D4—68no—
179C2×C3×D4—64no—
180C22×C3×C4—28no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—24no—
184C22×C3×C4—32no—
185C22×C3×C4—34no—
186C22×C3×C4—38no—
187C22×C3×C4—38no—
188C22×C3×C4—68no—
189C22×C3×C4—68no—
190C22×C3×C4#6718yes—
191C22×C3×C4#6718yes—
192C22×C3×C4C22×D311yescharacteristic
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D314yes—
197C22×C3×C4C22×D314yes—
198C2×#67—28no—
199C2×#67C22×D318yes—
200C22×Dic3—28no—
201C22×Dic3—34no—
202C22×Dic3—34no—
203C22×Dic3—64no—
204C22×Dic3C22×D312yes—
205C22×Dic3C22×D314yes—
206C22×Dic3C22×D318yes—
207#235—232no—
208C2×D12—24no—
209C2×D12C22×D314yes—
210C2×C4×D3—28no—
211C2×C4×D3C22×D318yes—
212C2×Dic6—28no—
213C2×Dic6—28no—
214C2×Dic6—232no—
215C2×Dic6—24no—
216C2×Dic6C22×D318yes—
217C2×Dic6C22×D318yes—
218C2×Dic6C22×D314yes—
219#217—38no—
220#217—38no—
221#217—332no—
222#217—68no—
223(C2×D3)⋊C4—332no—
224C4⋊Dic3—38no—
225C4⋊Dic3—38no—
226C4⋊Dic3—68no—
227Dic3⋊C4—332no—
228Dic3⋊C4—332no—
229C4×Dic3—38no—
230C4×Dic3—38no—
231C4×Dic3—68no—
232C22×C32—28no—
233C22×C32—24no—
234C22×C32C22×D414yes—
235C22×C32C22×D412yes—
236C22×C322−1+414yes—
237C22×C32C2511yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—28no—
240C2×C3×D3—48no—
241C32×C4C22×D414yes—
242C32×C4C22×D414yes—
243C3⋊Dic3—28no—
244C3×Dic3—28no—
245C3×Dic3—24no—
246C2×#41—38no—
247C2×#41—68no—
248C22×Q8—32no—
249C22×Q8—32no—
250C22×Q8—31no—
251C22×Q8—38no—
252C22×Q8—68no—
253C22×D4—32no—
254C22×D4—31no—
255C23×C4—32no—
256C23×C4—32no—
257C23×C4D3211yescharacteristic
258C4⋊Q8—916no—
259#124—916no—
260#123—932no—
261C22⋊Q8—932no—
262#117—98no—
263C2×C4⋊C4—98no—
264C2×C4⋊C4—92no—
265C2×C22⋊C4—98no—
266C2×C22⋊C4—92no—
267C2×C42—92no—
268C23×C3—24no—
269C23×C3—24no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—24no—
273C23×C3—34no—
274C23×C3—44no—
275C23×C3—68no—
276C23×C3—64no—
277C23×C3C2×#6714yes—
278C23×C3C2×#6714yes—
279C23×C3C23×D312yes—
280C23×C3C23×D312yes—
281C23×C3C23×D311yescharacteristic
282C23×C3C23×D311yescharacteristic
283C22×D3—28no—
284C22×D3—24no—
285C22×D3C23×D314yes—
286C3×Q8—616no—
287C3×Q8—616no—
288C3×Q8—68no—
289C3×D4—616no—
290C3×D4—68no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—24no—
294C2×C3×C4—24no—
295C2×C3×C4—216no—
296C2×C3×C4—34no—
297C2×C3×C4—38no—
298C2×C3×C4—64no—
299C2×C3×C4—616no—
300C2×C3×C4—68no—
301C2×C3×C4—616no—
302C2×C3×C4C2×#6714yes—
303C2×C3×C4C2×#6714yes—
304C2×C3×C4C2×#67116yes—
305C2×C3×C4C2×#6714yes—
306C2×C3×C4C2×#6714yes—
307C2×C3×C4C2×#67116yes—
308C2×C3×C4C23×D312yes—
309C2×C3×C4C23×D312yes—
310C2×C3×C4C23×D312yes—
311C2×C3×C4C23×D312yes—
312#67—216no—
313C2×Dic3—216no—
314C2×Dic3—28no—
315C2×Dic3—24no—
316C2×Dic3—38no—
317C2×Dic3—38no—
318C2×Dic3—68no—
319C2×Dic3—68no—
320C2×Dic3—68no—
321C2×Dic3—128no—
322C2×Dic3C23×D314yes—
323C2×Dic3C23×D318yes—
324D12—28no—
325C4×D3—216no—
326Dic6—216no—
327Dic6—216no—
328Dic6—28no—
329C2×C32—24no—
330C2×C32#53614yescomplemented
331C2×C32C23×D411yescharacteristic
332C2×C32C2×2−1+412yes—
333C3×D3—44no—
334C24—32no—
335C24C2×D3211yescharacteristic
336#41—632no—
337C2×Q8—38no—
338C2×Q8—38no—
339C2×Q8—34no—
340C2×Q8—68no—
341C2×Q8—68no—
342C2×Q8—632no—
343C2×Q8—64no—
344C2×D4—38no—
345C2×D4—34no—
346C2×D4—68no—
347C2×D4—64no—
348C22×C4—38no—
349C22×C4—34no—
350C22×C4—32no—
351C22×C4—38no—
352C22×C4—68no—
353C22×C4—68no—
354C22×C4—94no—
355C22×C4#62518yes—
356C22×C4C2×D3214yes—
357C22×C4C2×D3211yescharacteristic
358C22×C4C2×D3211yescharacteristic
359C4⋊C4—932no—
360C4⋊C4—98no—
361C22⋊C4—932no—
362C22⋊C4—98no—
363C42—98no—
364C22×C3—24no—
365C22×C3—24no—
366C22×C3—28no—
367C22×C3—28no—
368C22×C3—24no—
369C22×C3—22no—
370C22×C3—24no—
371C22×C3—21no—
372C22×C3—48no—
373C22×C3—44no—
374C22×C3—68no—
375C22×C3—64no—
376C22×C3—128no—
377C22×C3#100714yes—
378C22×C3#101014yes—
379C22×C3C22×#6714yes—
380C22×C3C22×#6714yes—
381C22×C3C22×#6712yes—
382C22×C3C22×#6712yes—
383C22×C3C24×D311yescharacteristic
384C22×C3C24×D311yescharacteristic
385C2×D3—28no—
386C2×D3—24no—
387C2×D3—48no—
388C3×C4—24no—
389C3×C4—24no—
390C3×C4—64no—
391C3×C4—68no—
392C3×C4C22×#6714yes—
393C3×C4C22×#6714yes—
394C3×C4C22×#6714yes—
395C3×C4C22×#6714yes—
396Dic3—28no—
397Dic3—24no—
398Dic3—68no—
399Dic3—68no—
400Dic3—128no—
401C32C2×#53611yescharacteristic, complemented, Sylow
402C23—24no—
403C23—34no—
404C23—68no—
405C23—64no—
406C23C2×#62514yes—
407C23C22×D3212yes—
408C23C22×D3211yescharacteristic
409Q8—616no—
410Q8—616no—
411Q8—68no—
412D4—616no—
413D4—68no—
414C2×C4—38no—
415C2×C4—34no—
416C2×C4—64no—
417C2×C4—616no—
418C2×C4—68no—
419C2×C4—616no—
420C2×C4—98no—
421C2×C4—188no—
422C2×C4C2×#62514yes—
423C2×C4C2×#62514yes—
424C2×C4C2×#625116yes—
425C2×C4C22×D3212yes—
426C2×C4C22×D3212yes—
427C2×C3—24no—
428C2×C3—24no—
429C2×C3—24no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—44no—
433C2×C3—124no—
434C2×C3#581614yescomplemented
435C2×C3#582514yescomplemented
436C2×C3C2×#100712yes—
437C2×C3C2×#101012yes—
438C2×C3C23×#6711yescharacteristic
439C2×C3C23×#6711yescharacteristic
440D3—44no—
441C22—28no—
442C22—24no—
443C22—68no—
444C22—64no—
445C22—128no—
446C22#6429714yes—
447C22C22×#62514yes—
448C22C22×#62512yes—
449C22C23×D3211yescharacteristic
450C4—64no—
451C4—68no—
452C4—188no—
453C4C22×#62514yes—
454C4C22×#62514yes—
455C3—21no—
456C3C2×#581611yescharacteristic, complemented
457C3C2×#582511yescharacteristic, complemented
458C2—24no—
459C2—124no—
460C2#1059485514yesdirect product factor
461C2C2×#6429712yes—
462C2C23×#62511yescharacteristic
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
2. C23×C3×Dic6C2semidirect
3. C2×#64135C2semidirect
4. C2×#63961C2semidirect
5. C2×#63873C2semidirect
6. #10594855C2direct (N × H)
7. C2×#63863C2semidirect
8. C2×#63856C2semidirect
22. C22×C3×Dic6C22semidirect
24. #64135C22semidirect
28. #63961C22semidirect
30. #63873C22semidirect
31. #63863C22semidirect
32. #63856C22semidirect
36. C23×Dic6D3semidirect
105. C22×Dic6C2×D3semidirect
330. C2×C32#536semidirect
401. C32C2×#536semidirect
434. C2×C3#5816semidirect
435. C2×C3#5825semidirect
456. C3C2×#5816semidirect
457. C3C2×#5825semidirect
460. C2#10594855direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C23×C3×Dic62
C2×#641352
C2×#639612
C2×#638732
#105948552
C2×#638632
C2×#638562
C2×#58253
C2×#58163