Finite Group Databasebeta

← C2×#10593950 #11901517

Subgroups — C2×#10593950 #11901517

Order 1152.

2685 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2C2×C3×#874C211yesmaximal, characteristic, complemented
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63916C212yesmaximal, complemented
5C2×#63898C212yesmaximal, complemented
6C2×#63886C214yesmaximal, complemented
7C2×#63884C214yesmaximal, complemented
8#10593950C2116yesmaximal, direct product factor
9C2×#5719—31nomaximal
10C2×#5697—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2212yes—
13C22×C3×D12C2214yes—
14C22×#626C2214yes—
15C22×D3×Dic3C2214yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3750C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64081C2218yescomplemented
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×Dic3⋊C4C2214yes—
23C3×#874C2218yescomplemented
24C3×#870C2218yescomplemented
25C2×(C2×D3)⋊Dic3C2214yes—
26C2×(C2×D3)⋊Dic3C2214yes—
27#63916C22116yescomplemented
28#63898C22116yescomplemented
29#63886C22132yescomplemented
30#63884C22132yescomplemented
31C2×C3×#127—31no—
32C2×C3×#125—31no—
33C2×#939—34no—
34C2×#938—32no—
35C2×#935—34no—
36C2×D4×Dic3—32no—
37#5719—316no—
38#5697—316no—
39C2×#895—34no—
40C2×#895—32no—
41C2×#894—34no—
42C2×#893—32no—
43C2×#874D311yescharacteristic, complemented
44C2×#872—31no—
45C2×#872—31no—
46C2×#872—61no—
47C2×#870D311yescharacteristic, complemented
48C23×C3⋊D3C2311yescharacteristic
49C23×C3×D3C2314yes—
50C22×C32×C4C2312yes—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C22×C3⋊Dic3C2311yescharacteristic
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3C2314yes—
56C22×C3×Dic3C2314yes—
57C2×C3×D12—28no—
58C2×C3×D12—48no—
59C2×C3×D12C2318yes—
60C2×C3×D12C23116yes—
61C2×#626—48no—
62C2×#626C23116yes—
63C2×D3×Dic3—48no—
64C2×D3×Dic3C23116yes—
65C32×C42C2314yes—
66#3752C2318yes—
67#3750C2318yes—
68C4×C3⋊Dic3C2314yes—
69C3×C4⋊Dic3C2318yes—
70C3×Dic3⋊C4C23116yes—
71(C2×D3)⋊Dic3C23116yes—
72(C2×D3)⋊Dic3C23116yes—
73C2×#540—91noSylow
74C22×C3×D4—32no—
75C22×C3×D4—34no—
76C22×#67—34no—
77C23×Dic3—34no—
78C22×D12—34no—
79C22×D12C2×D312yes—
80C22×D12C2×D314yes—
81C22×C4×D3—31no—
82C22×C4×D3—31no—
83C22×C4×D3—34no—
84C22×C4×D3—61no—
85C3×#127—38no—
86C3×#125—38no—
87C2×C3×C4⋊C4—34no—
88C2×C3×C4⋊C4—32no—
89C2×C3×C42—21no—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C2×D311yescharacteristic
92C2×#217—34no—
93C2×#217—34no—
94#939—332no—
95#938—316no—
96#935—332no—
97D4×Dic3—316no—
98C2×(C2×D3)⋊C4—34no—
99C2×(C2×D3)⋊C4—34no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—62no—
103C2×C4⋊Dic3C2×D312yes—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—62no—
107C2×Dic3⋊C4C2×D314yes—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—61no—
111#895—332no—
112#895—316no—
113#894—332no—
114#893—316no—
115#874C2×D318yescomplemented
116#872—38no—
117#872—38no—
118#872—68no—
119#870C2×D318yescomplemented
120C23×C32C2411yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—24no—
123C22×C3⋊D3C2412yes—
124C22×C3×D3—28no—
125C22×C3×D3—28no—
126C22×C3×D3—28no—
127C22×C3×D3C2418yes—
128C2×C32×C4—24no—
129C2×C32×C4#4114yes—
130C2×C32×C4C2414yes—
131C2×C32×C4C2412yes—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—24no—
134C2×C3⋊Dic3C2412yes—
135C2×C3⋊Dic3C2414yes—
136C4×C3⋊D3—28no—
137C2×C3×Dic3—28no—
138C2×C3×Dic3C2418yes—
139C3×D12—216no—
140C3×D12—416no—
141#626—416no—
142D3×Dic3—416no—
143#540—916no—
144C2×#127—31no—
145C2×#125—31no—
146C2×#123—94no—
147C2×#121—92no—
148C2×#121—94no—
149C2×C4×D4—92no—
150C2×#117—91no—
151C24×C3—34no—
152C23×D3—31no—
153C23×D3—31no—
154C23×D3—61no—
155C23×D3C22×D314yes—
156C2×C3×D4—38no—
157C2×C3×D4—316no—
158C2×C3×D4—68no—
159C2×C3×D4—128no—
160C22×C3×C4—21no—
161C22×C3×C4—22no—
162C22×C3×C4—34no—
163C22×C3×C4C22×D312yes—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—316no—
168C2×#67—128no—
169C22×Dic3—32no—
170C22×Dic3—32no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—316no—
174C22×Dic3—61no—
175C22×Dic3—62no—
176C22×Dic3—128no—
177C22×Dic3C22×D314yes—
178C2×D12—28no—
179C2×D12—316no—
180C2×D12—48no—
181C2×D12—128no—
182C2×D12C22×D318yes—
183C2×D12C22×D3116yes—
184C2×C4×D3—34no—
185C2×C4×D3—34no—
186C2×C4×D3—316no—
187C2×C4×D3—64no—
188C2×C4×D3—68no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—128no—
192C3×C4⋊C4—38no—
193C3×C4⋊C4—316no—
194C3×C42—24no—
195C3×C42C22×D314yes—
196C3×C42C22×D314yes—
197#217—316no—
198#217—316no—
199(C2×D3)⋊C4—316no—
200(C2×D3)⋊C4—316no—
201(C2×D3)⋊C4—38no—
202(C2×D3)⋊C4—38no—
203(C2×D3)⋊C4—68no—
204C4⋊Dic3C22×D318yes—
205Dic3⋊C4—38no—
206Dic3⋊C4—38no—
207Dic3⋊C4—68no—
208Dic3⋊C4C22×D3116yes—
209C4×Dic3—34no—
210C4×Dic3—34no—
211C4×Dic3—64no—
212C22×C32C2×#4112yes—
213C22×C32H(5,𝔽2)14yes—
214C22×C32C2511yescharacteristic
215C2×C3⋊D3—22no—
216C2×C3⋊D3—24no—
217C2×C3⋊D3—44no—
218C2×C3×D3—28no—
219C2×C3×D3—28no—
220C2×C3×D3—28no—
221C2×C3×D3—416no—
222C32×C4—24no—
223C32×C4C2×#4114yes—
224C3⋊Dic3—22no—
225C3⋊Dic3—24no—
226C3×Dic3—28no—
227C22×D4—32no—
228C22×D4—34no—
229C22×D4—94no—
230C23×C4—94no—
231C23×C4—91no—
232#127—38no—
233#125—38no—
234#123—932no—
235#121—916no—
236#121—932no—
237C4×D4—916no—
238#117—98no—
239C2×C4⋊C4—32no—
240C2×C4⋊C4—34no—
241C2×C4⋊C4—92no—
242C2×C22⋊C4—94no—
243C2×C22⋊C4—94no—
244C2×C22⋊C4—92no—
245C2×C42—91no—
246C2×C42D3211yescharacteristic
247C23×C3—21no—
248C23×C3—38no—
249C23×C3—68no—
250C23×C3—68no—
251C23×C3—68no—
252C23×C3C23×D311yescharacteristic
253C23×C3C23×D311yescharacteristic
254C22×D3—28no—
255C22×D3—28no—
256C22×D3—28no—
257C22×D3—32no—
258C22×D3—32no—
259C22×D3—62no—
260C22×D3—64no—
261C22×D3—62no—
262C22×D3—64no—
263C22×D3—62no—
264C22×D3—64no—
265C22×D3—124no—
266C22×D3C23×D318yes—
267C3×D4—616no—
268C3×D4—1216no—
269C2×C3×C4—24no—
270C2×C3×C4—24no—
271C2×C3×C4—22no—
272C2×C3×C4—24no—
273C2×C3×C4—24no—
274C2×C3×C4—38no—
275C2×C3×C4—44no—
276C2×C3×C4—68no—
277C2×C3×C4#23714yes—
278C2×C3×C4#23914yes—
279C2×C3×C4C23×D314yes—
280C2×C3×C4C23×D314yes—
281C2×C3×C4C23×D312yes—
282C2×C3×C4C23×D312yes—
283#67—1216no—
284C2×Dic3—28no—
285C2×Dic3—34no—
286C2×Dic3—34no—
287C2×Dic3—32no—
288C2×Dic3—32no—
289C2×Dic3—62no—
290C2×Dic3—64no—
291C2×Dic3—64no—
292C2×Dic3—62no—
293C2×Dic3—64no—
294C2×Dic3—62no—
295C2×Dic3—64no—
296C2×Dic3—124no—
297C2×Dic3—1216no—
298C2×Dic3C23×D318yes—
299D12—216no—
300D12—416no—
301D12—1216no—
302C4×D3—616no—
303C4×D3—68no—
304C4×D3—68no—
305C4×D3—1216no—
306C2×C32#54014yescomplemented
307C2×C32C22×#4111yescharacteristic
308C2×C32C2×H(5,𝔽2)12yes—
309C3⋊D3—42no—
310C3×D3—48no—
311C24—34no—
312C24—91no—
313C2×D4—38no—
314C2×D4—316no—
315C2×D4—68no—
316C2×D4—916no—
317C2×D4—128no—
318C2×D4—368no—
319C22×C4—34no—
320C22×C4—916no—
321C22×C4—92no—
322C22×C4—91no—
323C22×C4—94no—
324C22×C4—184no—
325C22×C4—368no—
326C22×C4C2×D3212yes—
327C22×C4C2×D3211yescharacteristic
328C4⋊C4—38no—
329C4⋊C4—316no—
330C4⋊C4—98no—
331C22⋊C4—916no—
332C22⋊C4—916no—
333C22⋊C4—98no—
334C42—94no—
335C42C2×D3214yes—
336C22×C3—22no—
337C22×C3—24no—
338C22×C3—21no—
339C22×C3—68no—
340C22×C3—68no—
341C22×C3—68no—
342C22×C3—1216no—
343C22×C3C2×#23712yes—
344C22×C3#100414yes—
345C22×C3C2×#23912yes—
346C22×C3#100914yes—
347C22×C3C24×D311yescharacteristic
348C22×C3C24×D311yescharacteristic
349C2×D3—28no—
350C2×D3—28no—
351C2×D3—28no—
352C2×D3—416no—
353C2×D3—64no—
354C2×D3—62no—
355C2×D3—64no—
356C2×D3—62no—
357C2×D3—64no—
358C2×D3—124no—
359C2×D3—128no—
360C2×D3—124no—
361C2×D3—124no—
362C3×C4—24no—
363C3×C4—24no—
364C3×C4—24no—
365C3×C4—44no—
366C3×C4—68no—
367C3×C4C2×#23714yes—
368C3×C4C2×#23914yes—
369Dic3—28no—
370Dic3—64no—
371Dic3—62no—
372Dic3—64no—
373Dic3—62no—
374Dic3—64no—
375Dic3—124no—
376C32C2×#54011yescharacteristic, complemented, Sylow
377C23—38no—
378C23—68no—
379C23—68no—
380C23—68no—
381C23—92no—
382C23—182no—
383C23—184no—
384C23C22×D3211yescharacteristic
385D4—616no—
386D4—1216no—
387D4—3616no—
388C2×C4—24no—
389C2×C4—38no—
390C2×C4—68no—
391C2×C4—94no—
392C2×C4—92no—
393C2×C4—182no—
394C2×C4—184no—
395C2×C4—188no—
396C2×C4—3616no—
397C2×C4#379614yes—
398C2×C4C22×D3214yes—
399C2×C4C22×D3212yes—
400C2×C3—21no—
401C2×C3—22no—
402C2×C3—24no—
403C2×C3—128no—
404C2×C3#569714yescomplemented
405C2×C3#571914yescomplemented
406C2×C3C22×#23711yescharacteristic
407C2×C3C2×#100412yes—
408C2×C3C22×#23911yescharacteristic
409C2×C3C2×#100912yes—
410D3—48no—
411D3—124no—
412D3—122no—
413D3—122no—
414C22—68no—
415C22—68no—
416C22—68no—
417C22—1216no—
418C22—182no—
419C22—184no—
420C22—364no—
421C22C2×#379612yes—
422C22#6430714yes—
423C22C23×D3211yescharacteristic
424C4—24no—
425C4—68no—
426C4—182no—
427C4—184no—
428C4C2×#379614yes—
429C3—21no—
430C3C2×#569711yescharacteristic, complemented
431C3C2×#571911yescharacteristic, complemented
432C2—128no—
433C2—362no—
434C2#1059395014yesdirect product factor
435C2C22×#379611yescharacteristic
436C2C2×#6430712yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#540
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64081C2semidirect
2. C2×C3×#874C2semidirect
3. C2×C3×#870C2semidirect
4. C2×#63916C2semidirect
5. C2×#63898C2semidirect
6. C2×#63886C2semidirect
7. C2×#63884C2semidirect
8. #10593950C2direct (N × H)
20. #64081C22semidirect
23. C3×#874C22semidirect
24. C3×#870C22semidirect
27. #63916C22semidirect
28. #63898C22semidirect
29. #63886C22semidirect
30. #63884C22semidirect
43. C2×#874D3semidirect
47. C2×#870D3semidirect
115. #874C2×D3semidirect
119. #870C2×D3semidirect
306. C2×C32#540semidirect
376. C32C2×#540semidirect
404. C2×C3#5697semidirect
405. C2×C3#5719semidirect
430. C3C2×#5697semidirect
431. C3C2×#5719semidirect
434. C2#10593950direct (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×#8742
C2×C3×#8702
C2×#639162
C2×#638982
C2×#638862
C2×#638842
#105939502
C2×#57193
C2×#56973