Finite Group Databasebeta

← C2×#10593867 #11901590

Subgroups — C2×#10593867 #11901590

Order 1152.

2173 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×C3×#870C211yesmaximal, characteristic, complemented
3C2×C3×#869C211yesmaximal, characteristic, complemented
4C2×#63871C212yesmaximal
5C2×#63848C214yesmaximal
6C2×#63846C214yesmaximal, complemented
7C2×#63843C212yesmaximal, complemented
8#10593867C2116yesmaximal, direct product factor
9C2×#5731—31nomaximal
10C2×#5698—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×#3752C2212yes—
15C2×#3750C2212yes—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17#64081C2218yes—
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×C4⋊Dic3C2214yes—
20C2×C3×Dic3⋊C4C2214yes—
21C3×#870C2218yescomplemented
22C3×#869C2218yescomplemented
23C2×Dic3⋊Dic3C2214yes—
24C2×Dic3⋊Dic3C2214yes—
25C2×#3722C2214yes—
26C2×Dic32C2214yes—
27#63871C22116yes—
28#63848C22132yes—
29#63846C22132yescomplemented
30#63843C22116yescomplemented
31C2×C3×C4⋊Q8—31no—
32C2×C3×#125—31no—
33C2×#946—32no—
34C2×Q8×Dic3—32no—
35#5731—316no—
36#5698—316no—
37C2×#898—34no—
38C2×#898—34no—
39C2×#897—32no—
40C2×#890—34no—
41C2×#889—34no—
42C2×#887—32no—
43C2×#872—31no—
44C2×#872—31no—
45C2×#872—61no—
46C2×#870D311yescharacteristic, complemented
47C2×#869D311yescharacteristic, complemented
48C23×C3⋊D3C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C2×C4×C3⋊D3—24no—
54C2×C4×C3⋊D3C2314yes—
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2314yes—
57C2×C3×Dic6—28no—
58C2×C3×Dic6C2318yes—
59C32×C42C2314yes—
60#3752C2318yes—
61#3750C2318yes—
62C4×C3⋊Dic3C2314yes—
63C3×C4⋊Dic3C2318yes—
64C3×C4⋊Dic3C23116yes—
65C3×Dic3⋊C4C23116yes—
66Dic3⋊Dic3C23116yes—
67Dic3⋊Dic3C23116yes—
68#3722C23116yes—
69Dic32C23116yes—
70C2×#541—91noSylow
71C22×C3×Q8—32no—
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3—61no—
75C22×Dic6C2×D312yes—
76C3×C4⋊Q8—38no—
77C3×#125—38no—
78C2×C3×C4⋊C4—34no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4—34no—
81C2×C3×C42—21no—
82C2×C3×C42C2×D311yescharacteristic
83C2×C3×C42C2×D311yescharacteristic
84#946—316no—
85Q8×Dic3—316no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—32no—
88C2×(C2×D3)⋊C4—34no—
89C2×(C2×D3)⋊C4—34no—
90C2×(C2×D3)⋊C4—62no—
91C2×C4⋊Dic3—34no—
92C2×C4⋊Dic3—34no—
93C2×C4⋊Dic3C2×D314yes—
94C2×C4⋊Dic3C2×D312yes—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—62no—
100C2×Dic3⋊C4C2×D314yes—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—34no—
104C2×C4×Dic3—34no—
105C2×C4×Dic3—61no—
106#898—332no—
107#898—332no—
108#897—316no—
109#890—332no—
110#889—332no—
111#887—316no—
112#872—38no—
113#872—38no—
114#872—68no—
115#870C2×D318yescomplemented
116#869C2×D318yescomplemented
117C23×C32C2411yescharacteristic
118C22×C3⋊D3—22no—
119C22×C3⋊D3—24no—
120C22×C3⋊D3C2412yes—
121C2×C32×C4—24no—
122C2×C32×C4#4114yes—
123C2×C32×C4C2414yes—
124C2×C32×C4C2412yes—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—24no—
127C2×C3⋊Dic3C2414yes—
128C2×C3⋊Dic3C2412yes—
129C4×C3⋊D3—28no—
130C2×C3×Dic3—28no—
131C2×C3×Dic3—28no—
132C2×C3×Dic3C2418yes—
133C2×C3×Dic3C2418yes—
134C3×Dic6—216no—
135#541—916no—
136C2×C4⋊Q8—31no—
137C2×#126—94no—
138C2×#125—31no—
139C2×#125—94no—
140C2×C22⋊Q8—92no—
141C2×C4×Q8—92no—
142C2×#117—91no—
143C23×D3—31no—
144C23×D3—31no—
145C23×D3—61no—
146C2×C3×Q8—38no—
147C2×C3×Q8—68no—
148C22×C3×C4—21no—
149C22×C3×C4—22no—
150C22×C3×C4—34no—
151C22×C3×C4—34no—
152C22×C3×C4C22×D312yes—
153C22×C3×C4C22×D312yes—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—61no—
161C22×Dic3—62no—
162C22×Dic3C22×D314yes—
163C22×Dic3C22×D314yes—
164C2×C4×D3—34no—
165C2×C4×D3—34no—
166C2×C4×D3—64no—
167C2×C4×D3—68no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×Dic6—28no—
171C2×Dic6C22×D318yes—
172C3×C4⋊C4—38no—
173C3×C4⋊C4—316no—
174C3×C4⋊C4—316no—
175C3×C42—24no—
176C3×C42C22×D314yes—
177C3×C42C22×D314yes—
178(C2×D3)⋊C4—38no—
179(C2×D3)⋊C4—38no—
180(C2×D3)⋊C4—316no—
181(C2×D3)⋊C4—316no—
182(C2×D3)⋊C4—68no—
183C4⋊Dic3—316no—
184C4⋊Dic3—316no—
185C4⋊Dic3C22×D3116yes—
186C4⋊Dic3C22×D318yes—
187Dic3⋊C4—38no—
188Dic3⋊C4—38no—
189Dic3⋊C4—316no—
190Dic3⋊C4—316no—
191Dic3⋊C4—68no—
192Dic3⋊C4C22×D3116yes—
193C4×Dic3—34no—
194C4×Dic3—34no—
195C4×Dic3—316no—
196C4×Dic3—316no—
197C4×Dic3—64no—
198C22×C32C2×#4112yes—
199C22×C322−1+414yes—
200C22×C32C2511yescharacteristic
201C2×C3⋊D3—22no—
202C2×C3⋊D3—24no—
203C2×C3⋊D3—44no—
204C32×C4—24no—
205C32×C4C2×#4114yes—
206C3⋊Dic3—22no—
207C3⋊Dic3—24no—
208C3×Dic3—28no—
209C3×Dic3—28no—
210C22×Q8—32no—
211C23×C4—91no—
212C4⋊Q8—38no—
213#126—932no—
214#125—38no—
215#125—932no—
216C22⋊Q8—916no—
217C4×Q8—916no—
218#117—98no—
219C2×C4⋊C4—32no—
220C2×C4⋊C4—34no—
221C2×C4⋊C4—34no—
222C2×C4⋊C4—94no—
223C2×C4⋊C4—94no—
224C2×C4⋊C4—92no—
225C2×C22⋊C4—94no—
226C2×C22⋊C4—92no—
227C2×C42—94no—
228C2×C42—91no—
229C2×C42D3211yescharacteristic
230C23×C3—21no—
231C23×C3C23×D311yescharacteristic
232C23×C3C23×D311yescharacteristic
233C22×D3—32no—
234C22×D3—32no—
235C22×D3—62no—
236C22×D3—64no—
237C22×D3—62no—
238C22×D3—62no—
239C22×D3—64no—
240C22×D3—64no—
241C22×D3—124no—
242C3×Q8—616no—
243C2×C3×C4—24no—
244C2×C3×C4—24no—
245C2×C3×C4—22no—
246C2×C3×C4—24no—
247C2×C3×C4—24no—
248C2×C3×C4—38no—
249C2×C3×C4—38no—
250C2×C3×C4—44no—
251C2×C3×C4—68no—
252C2×C3×C4—68no—
253C2×C3×C4#23714yes—
254C2×C3×C4#23914yes—
255C2×C3×C4C23×D314yes—
256C2×C3×C4C23×D314yes—
257C2×C3×C4C23×D312yes—
258C2×C3×C4C23×D312yes—
259C2×Dic3—28no—
260C2×Dic3—28no—
261C2×Dic3—34no—
262C2×Dic3—34no—
263C2×Dic3—32no—
264C2×Dic3—32no—
265C2×Dic3—62no—
266C2×Dic3—64no—
267C2×Dic3—64no—
268C2×Dic3—62no—
269C2×Dic3—62no—
270C2×Dic3—64no—
271C2×Dic3—64no—
272C2×Dic3—124no—
273C2×Dic3C23×D318yes—
274C2×Dic3C23×D318yes—
275C4×D3—616no—
276C4×D3—68no—
277C4×D3—68no—
278Dic6—216no—
279C2×C32#54114yescomplemented
280C2×C32C22×#4111yescharacteristic
281C2×C32C2×2−1+412yes—
282C3⋊D3—42no—
283C24—91no—
284C2×Q8—38no—
285C2×Q8—68no—
286C22×C4—34no—
287C22×C4—34no—
288C22×C4—92no—
289C22×C4—91no—
290C22×C4—94no—
291C22×C4—184no—
292C22×C4C2×D3212yes—
293C22×C4C2×D3211yescharacteristic
294C4⋊C4—38no—
295C4⋊C4—316no—
296C4⋊C4—316no—
297C4⋊C4—916no—
298C4⋊C4—916no—
299C4⋊C4—98no—
300C22⋊C4—916no—
301C22⋊C4—98no—
302C42—916no—
303C42—94no—
304C42C2×D3214yes—
305C22×C3—22no—
306C22×C3—24no—
307C22×C3—21no—
308C22×C3C2×#23712yes—
309C22×C3C2×#23912yes—
310C22×C3#100714yes—
311C22×C3#101014yes—
312C22×C3C24×D311yescharacteristic
313C22×C3C24×D311yescharacteristic
314C2×D3—64no—
315C2×D3—62no—
316C2×D3—62no—
317C2×D3—64no—
318C2×D3—64no—
319C2×D3—124no—
320C2×D3—128no—
321C2×D3—124no—
322C2×D3—124no—
323C3×C4—24no—
324C3×C4—24no—
325C3×C4—24no—
326C3×C4—44no—
327C3×C4—68no—
328C3×C4—68no—
329C3×C4C2×#23714yes—
330C3×C4C2×#23914yes—
331Dic3—28no—
332Dic3—28no—
333Dic3—64no—
334Dic3—62no—
335Dic3—62no—
336Dic3—64no—
337Dic3—64no—
338Dic3—124no—
339C32C2×#54111yescharacteristic, complemented, Sylow
340C23—92no—
341C23—182no—
342C23—184no—
343C23C22×D3211yescharacteristic
344Q8—616no—
345C2×C4—24no—
346C2×C4—38no—
347C2×C4—38no—
348C2×C4—68no—
349C2×C4—68no—
350C2×C4—94no—
351C2×C4—92no—
352C2×C4—182no—
353C2×C4—184no—
354C2×C4—188no—
355C2×C4#379614yes—
356C2×C4C22×D3214yes—
357C2×C4C22×D3212yes—
358C2×C3—21no—
359C2×C3—22no—
360C2×C3—24no—
361C2×C3#569814yescomplemented
362C2×C3#573114yescomplemented
363C2×C3C22×#23711yescharacteristic
364C2×C3C22×#23911yescharacteristic
365C2×C3C2×#100712yes—
366C2×C3C2×#101012yes—
367D3—124no—
368D3—122no—
369D3—122no—
370C22—182no—
371C22—184no—
372C22—364no—
373C22C2×#379612yes—
374C22#6429714yes—
375C22C23×D3211yescharacteristic
376C4—24no—
377C4—68no—
378C4—68no—
379C4—182no—
380C4—184no—
381C4C2×#379614yes—
382C3—21no—
383C3C2×#569811yescharacteristic, complemented
384C3C2×#573111yescharacteristic, complemented
385C2—362no—
386C2#1059386714yesdirect product factor
387C2C22×#379611yescharacteristic
388C2C2×#6429712yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32C2×#541
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#870C2semidirect
3. C2×C3×#869C2semidirect
6. C2×#63846C2semidirect
7. C2×#63843C2semidirect
8. #10593867C2direct (N × H)
21. C3×#870C22semidirect
22. C3×#869C22semidirect
29. #63846C22semidirect
30. #63843C22semidirect
46. C2×#870D3semidirect
47. C2×#869D3semidirect
115. #870C2×D3semidirect
116. #869C2×D3semidirect
279. C2×C32#541semidirect
339. C32C2×#541semidirect
361. C2×C3#5698semidirect
362. C2×C3#5731semidirect
383. C3C2×#5698semidirect
384. C3C2×#5731semidirect
386. C2#10593867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640812
C2×C3×#8702
C2×C3×#8692
C2×#638712
C2×#638482
C2×#638462
C2×#638432
#105938672
C2×#57313
C2×#56983