Finite Group Databasebeta

← C2×#10593861 #11903701

Subgroups — C2×#10593861 #11903701

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic
2C2×C3×#869C211yesmaximal, characteristic
3C2×C3×C4×Dic6C211yesmaximal, characteristic
4C2×#63872C212yesmaximal
5C2×#63866C212yesmaximal
6C2×#63846C214yesmaximal
7C2×#63843C212yesmaximal
8C2×Dic3×Dic6C212yesmaximal
9#10593861C2116yesmaximal, direct product factor
10C2×#5721—31nomaximal
11C2×#5570—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2212yes—
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750C2212yes—
18C2×C4×C3⋊Dic3C2212yes—
19C4×#634C2218yes—
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C3×#869C2218yes—
26C3×C4×Dic6C2218yes—
27C2×Dic3⋊Dic3C2214yes—
28C2×Dic3⋊Dic3C2214yes—
29C2×Dic3⋊Dic3C2214yes—
30C2×Dic32C2214yes—
31#63872C22116yes—
32#63866C22116yes—
33#63846C22132yes—
34#63843C22116yes—
35Dic3×Dic6C22116yes—
36C2×C3×C4⋊Q8—31no—
37C2×C3×C4×Q8—31no—
38C2×Q8×Dic3—32no—
39C2×Q8×Dic3—32no—
40C2×#944—32no—
41#5721—316no—
42#5570—316no—
43C2×#890—34no—
44C2×#890—32no—
45C2×#890—32no—
46C2×#889—34no—
47C2×#887—32no—
48C2×#869—32no—
49C2×#869D311yescharacteristic
50C2×C4×Dic6—32no—
51C2×C4×Dic6—31no—
52C2×C4×Dic6—31no—
53C2×C4×Dic6—61no—
54C2×C4×Dic6D311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2312yes—
59C22×C3⋊Dic3C2312yes—
60C2×#634—24no—
61C2×#634C2314yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2314yes—
64C22×C3×Dic3C2312yes—
65C2×C3×Dic6—28no—
66C2×C3×Dic6Q818yescomplemented
67C2×C3×Dic6C2318yes—
68C2×C3×Dic6C2314yes—
69C32×C42C2314yes—
70C4⋊(C3⋊Dic3)C2314yes—
71#3750C2318yes—
72C4×C3⋊Dic3C2318yes—
73C3×C4⋊Dic3C2318yes—
74C3×C4⋊Dic3C2318yes—
75C3×C4⋊Dic3C2314yes—
76C3×Dic3⋊C4C2318yes—
77C3×C4×Dic3C2318yes—
78Dic3⋊Dic3C23116yes—
79Dic3⋊Dic3C23116yes—
80Dic3⋊Dic3C23116yes—
81Dic32C23116yes—
82C2×#557—91noSylow
83C22×C3×Q8—31no—
84C22×C3×Q8—32no—
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—61no—
88C22×Dic6C2×D312yes—
89C22×Dic6C2×D311yescharacteristic
90C3×C4⋊Q8—38no—
91C3×C4×Q8—38no—
92C2×C3×C4⋊C4—32no—
93C2×C3×C4⋊C4—32no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C42—21no—
97C2×C3×C42—32no—
98C2×C3×C42C2×D311yescharacteristic
99C2×C3×C42C2×D311yescharacteristic
100Q8×Dic3—316no—
101Q8×Dic3—316no—
102#944—316no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—34no—
106C2×C4⋊Dic3—34no—
107C2×C4⋊Dic3—34no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4⋊Dic3C2×D312yes—
111C2×C4⋊Dic3C2×D312yes—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—34no—
115C2×Dic3⋊C4—34no—
116C2×Dic3⋊C4—34no—
117C2×Dic3⋊C4—62no—
118C2×Dic3⋊C4C2×D312yes—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—34no—
122C2×C4×Dic3—34no—
123C2×C4×Dic3—62no—
124C2×C4×Dic3C2×D312yes—
125#890—316no—
126#890—332no—
127#890—316no—
128#889—332no—
129#887—316no—
130#869—316no—
131#869C2×D318yes—
132C4×Dic6—316no—
133C4×Dic6—38no—
134C4×Dic6—38no—
135C4×Dic6—68no—
136C4×Dic6C2×D318yes—
137C23×C32C2411yescharacteristic
138C2×C32×C4—22no—
139C2×C32×C4C2×Q814yes—
140C2×C32×C4#4114yes—
141C2×C32×C4C2412yes—
142C2×C32×C4C2412yes—
143C2×C32×C4C2412yes—
144C2×C3⋊Dic3—24no—
145C2×C3⋊Dic3—24no—
146C2×C3⋊Dic3C2414yes—
147C2×C3⋊Dic3C2414yes—
148#634—28no—
149C2×C3×Dic3—28no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3C2×Q818yes—
152C2×C3×Dic3C2418yes—
153C2×C3×Dic3C2414yes—
154C2×C3×Dic3C2414yes—
155C3×Dic6—216no—
156C3×Dic6C2×Q8116yescomplemented
157#557—916no—
158C2×C4⋊Q8—31no—
159C2×C4⋊Q8—92no—
160C2×#125—94no—
161C2×#125—92no—
162C2×C4×Q8—31no—
163C2×C4×Q8—92no—
164C2×C4×Q8—92no—
165C2×C4×Q8—91no—
166C2×C3×Q8—38no—
167C2×C3×Q8—34no—
168C2×C3×Q8—38no—
169C2×C3×Q8—68no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—32no—
174C22×C3×C4—34no—
175C22×C3×C4—32no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×Dic3—32no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3C22×D314yes—
189C22×Dic3C22×D312yes—
190C22×Dic3C22×D312yes—
191C2×Dic6—28no—
192C2×Dic6—34no—
193C2×Dic6—34no—
194C2×Dic6—64no—
195C2×Dic6—68no—
196C2×Dic6—64no—
197C2×Dic6—64no—
198C2×Dic6Dic618yescomplemented
199C2×Dic6C22×D318yes—
200C2×Dic6C22×D314yes—
201C3×C4⋊C4—38no—
202C3×C4⋊C4—38no—
203C3×C4⋊C4—38no—
204C3×C4⋊C4—34no—
205C3×C42—24no—
206C3×C42—38no—
207C3×C42C22×D314yes—
208C3×C42C22×D314yes—
209C4⋊Dic3—34no—
210C4⋊Dic3—34no—
211C4⋊Dic3—316no—
212C4⋊Dic3—316no—
213C4⋊Dic3—316no—
214C4⋊Dic3—64no—
215C4⋊Dic3C22×D314yes—
216C4⋊Dic3C22×D318yes—
217C4⋊Dic3C22×D318yes—
218Dic3⋊C4—38no—
219Dic3⋊C4—38no—
220Dic3⋊C4—316no—
221Dic3⋊C4—316no—
222Dic3⋊C4—316no—
223Dic3⋊C4—68no—
224Dic3⋊C4C22×D318yes—
225C4×Dic3—38no—
226C4×Dic3—38no—
227C4×Dic3—316no—
228C4×Dic3—316no—
229C4×Dic3—68no—
230C4×Dic3C22×D318yes—
231C22×C32C22×Q812yes—
232C22×C32C2×#4112yes—
233C22×C322−1+412yes—
234C22×C32C2511yescharacteristic
235C32×C4—22no—
236C32×C4C22×Q814yes—
237C32×C4C2×#4114yes—
238C3⋊Dic3—24no—
239C3⋊Dic3—24no—
240C3×Dic3—28no—
241C3×Dic3—24no—
242C3×Dic3C22×Q818yes—
243C22×Q8—31no—
244C22×Q8—32no—
245C22×Q8—91no—
246C4⋊Q8—38no—
247C4⋊Q8—916no—
248#125—932no—
249#125—916no—
250C4×Q8—38no—
251C4×Q8—916no—
252C4×Q8—916no—
253C4×Q8—98no—
254C2×C4⋊C4—32no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—32no—
257C2×C4⋊C4—32no—
258C2×C4⋊C4—94no—
259C2×C4⋊C4—94no—
260C2×C4⋊C4—94no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—92no—
263C2×C42—32no—
264C2×C42—94no—
265C2×C42—92no—
266C2×C42D3211yescharacteristic
267C23×C3—21no—
268C23×C3C23×D311yescharacteristic
269C23×C3C23×D311yescharacteristic
270C3×Q8—316no—
271C3×Q8—616no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—24no—
278C2×C3×C4—24no—
279C2×C3×C4—38no—
280C2×C3×C4—34no—
281C2×C3×C4—38no—
282C2×C3×C4—34no—
283C2×C3×C4—42no—
284C2×C3×C4—68no—
285C2×C3×C4—64no—
286C2×C3×C4C2×Dic614yes—
287C2×C3×C4#23714yes—
288C2×C3×C4D3×Q814yes—
289C2×C3×C4#23914yes—
290C2×C3×C4C23×D312yes—
291C2×C3×C4C23×D312yes—
292C2×C3×C4C23×D312yes—
293C2×C3×C4C23×D312yes—
294C2×C3×C4C23×D312yes—
295C2×C3×C4C23×D312yes—
296C2×Dic3—28no—
297C2×Dic3—24no—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—34no—
301C2×Dic3—34no—
302C2×Dic3—64no—
303C2×Dic3—64no—
304C2×Dic3—68no—
305C2×Dic3—64no—
306C2×Dic3—64no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—124no—
310C2×Dic3C2×Dic618yes—
311C2×Dic3C23×D318yes—
312C2×Dic3C23×D314yes—
313C2×Dic3C23×D314yes—
314Dic6—216no—
315Dic6—616no—
316Dic6—68no—
317Dic6—68no—
318Dic6C2×Dic6116yescomplemented
319C2×C32#55714yescomplemented
320C2×C32C23×Q811yescharacteristic
321C2×C32C22×#4111yescharacteristic
322C2×C32C2×2−1+411yescharacteristic
323C2×Q8—34no—
324C2×Q8—38no—
325C2×Q8—38no—
326C2×Q8—68no—
327C2×Q8—94no—
328C2×Q8—184no—
329C22×C4—32no—
330C22×C4—32no—
331C22×C4—34no—
332C22×C4—92no—
333C22×C4—92no—
334C22×C4C2×D3211yescharacteristic
335C22×C4C2×D3211yescharacteristic
336C22×C4C2×D3211yescharacteristic
337C4⋊C4—38no—
338C4⋊C4—34no—
339C4⋊C4—38no—
340C4⋊C4—38no—
341C4⋊C4—916no—
342C4⋊C4—916no—
343C4⋊C4—916no—
344C4⋊C4—94no—
345C4⋊C4—98no—
346C42—38no—
347C42—916no—
348C42—98no—
349C42C2×D3214yes—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—21no—
354C22×C3C22×Dic612yes—
355C22×C3C2×#23712yes—
356C22×C3C2×D3×Q812yes—
357C22×C3C2×#23912yes—
358C22×C3#100712yes—
359C22×C3#101012yes—
360C22×C3C24×D311yescharacteristic
361C22×C3C24×D311yescharacteristic
362C3×C4—22no—
363C3×C4—22no—
364C3×C4—24no—
365C3×C4—24no—
366C3×C4—38no—
367C3×C4—42no—
368C3×C4—68no—
369C3×C4—64no—
370C3×C4C22×Dic614yes—
371C3×C4C2×#23714yes—
372C3×C4C2×D3×Q814yes—
373C3×C4C2×#23914yes—
374Dic3—28no—
375Dic3—24no—
376Dic3—68no—
377Dic3—64no—
378Dic3—64no—
379Dic3—64no—
380Dic3—64no—
381Dic3—124no—
382Dic3C22×Dic618yes—
383C32C2×#55711yescharacteristic, complemented, Sylow
384C23C22×D3211yescharacteristic
385Q8—316no—
386Q8—616no—
387Q8—188no—
388C2×C4—22no—
389C2×C4—38no—
390C2×C4—34no—
391C2×C4—34no—
392C2×C4—38no—
393C2×C4—68no—
394C2×C4—64no—
395C2×C4—94no—
396C2×C4—94no—
397C2×C4—184no—
398C2×C4—184no—
399C2×C4D3×Dic614yes—
400C2×C4#379614yes—
401C2×C4C22×D3212yes—
402C2×C4C22×D3212yes—
403C2×C4C22×D3212yes—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—24no—
408C2×C3#557014yescomplemented
409C2×C3#572114yescomplemented
410C2×C3C23×Dic611yescharacteristic
411C2×C3C22×#23711yescharacteristic
412C2×C3C22×D3×Q811yescharacteristic
413C2×C3C22×#23911yescharacteristic
414C2×C3C2×#100711yescharacteristic
415C2×C3C2×#101011yescharacteristic
416C22C2×D3×Dic612yes—
417C22C2×#379612yes—
418C22#6429712yes—
419C22C23×D3211yescharacteristic
420C4—22no—
421C4—38no—
422C4—68no—
423C4—64no—
424C4—184no—
425C4—184no—
426C4C2×D3×Dic614yes—
427C4C2×#379614yes—
428C3—21no—
429C3C2×#557011yescharacteristic, complemented
430C3C2×#572111yescharacteristic, complemented
431C2#1059386114yesdirect product factor
432C2C22×D3×Dic611yescharacteristic
433C2C22×#379611yescharacteristic
434C2C2×#6429711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#557
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
9. #10593861C2direct (N × H)
66. C2×C3×Dic6Q8semidirect
156. C3×Dic6C2×Q8semidirect
198. C2×Dic6Dic6semidirect
318. Dic6C2×Dic6semidirect
319. C2×C32#557semidirect
383. C32C2×#557semidirect
408. C2×C3#5570semidirect
409. C2×C3#5721semidirect
429. C3C2×#5570semidirect
430. C3C2×#5721semidirect
431. C2#10593861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×#6342
C2×C3×#8692
C2×C3×C4×Dic62
C2×#638722
C2×#638662
C2×#638462
C2×#638432
C2×Dic3×Dic62
#105938612
C2×#57213
C2×#55703