Finite Group Databasebeta

← C2×#10593897 #11900783

Subgroups — C2×#10593897 #11900783

Order 1152.

3601 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C212yesmaximal, complemented
2C2×#64078C211yesmaximal, characteristic, complemented
3C2×C3×#874C211yesmaximal, characteristic, complemented
4C2×C3×C42×D3C211yesmaximal, characteristic, complemented
5C2×#63908C214yesmaximal, complemented
6C2×Dic3×D12C214yesmaximal, complemented
7C2×#63860C212yesmaximal, complemented
8#10593897C2116yesmaximal, direct product factor
9C2×#5716—31nomaximal
10C2×#5477—31nomaximal
11C22×#634C2212yes—
12C22×C3×D12C2212yes—
13C22×C3×D12C2214yes—
14C22×C3×C4×D3C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C22×#625C2214yes—
17C22×D3×Dic3C2214yes—
18C2×#3795—216no—
19C2×#3795C22116yescomplemented
20C2×C32×C42C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2214yes—
22#64078C2218yescomplemented
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C3×#874C2218yescomplemented
26C3×C42×D3C2218yescomplemented
27C2×(C2×D3)⋊Dic3C2218yes—
28#63908C22132yescomplemented
29Dic3×D12C22132yescomplemented
30#63860C22116yescomplemented
31C22×#237—32no—
32C22×#235—32no—
33C2×C3×#127—31no—
34C22×C3×C42—31no—
35C2×#938—34no—
36C2×#936—32no—
37C2×D4×Dic3—34no—
38C2×#930—34no—
39#5716—316no—
40#5477—316no—
41C2×#875—32no—
42C2×#874D311yescharacteristic, complemented
43C2×C4×D12—34no—
44C2×C42×D3D311yescharacteristic, complemented
45C2×#869—31no—
46C2×#869—31no—
47C2×#869—61no—
48C23×C3×D3C2314yes—
49C23×C3×D3C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C3⋊Dic3C2314yes—
53C2×#634—28no—
54C2×#634C2318yes—
55C22×C3×Dic3C2312yes—
56C22×C3×Dic3C2311yescharacteristic
57C2×C3×D12—28no—
58C2×C3×D12—216no—
59C2×C3×D12C2318yes—
60C2×C3×D12C23116yes—
61C2×C3×C4×D3—28no—
62C2×C3×C4×D3D418yescomplemented
63C2×C3×C4×D3C2318yes—
64C2×C3×C4×D3C2314yes—
65C2×#625—216no—
66C2×#625C23116yes—
67C2×D3×Dic3—216no—
68C2×D3×Dic3C23116yes—
69#3795—264no—
70C32×C42C2314yes—
71C4⋊(C3⋊Dic3)C23116yes—
72C3×C4×Dic3C2314yes—
73C3×C4×Dic3C2318yes—
74(C2×D3)⋊Dic3C23132yes—
75C2×#532—91noSylow
76C22×C3×D4—32no—
77C22×C3×D4—34no—
78C23×C3×C4—31no—
79C23×C3×C4—32no—
80C22×#67—34no—
81C22×#67—34no—
82C23×Dic3—34no—
83C2×#237—316no—
84C2×#237—616no—
85C2×#235—316no—
86C2×#235—616no—
87C22×D12C2×D312yes—
88C22×D12C2×D314yes—
89C22×C4×D3—34no—
90C22×C4×D3C2×D312yes—
91C22×C4×D3C2×D311yescharacteristic
92C22×Dic6—32no—
93C22×Dic6—32no—
94C22×Dic6—62no—
95C3×#127—38no—
96C2×C3×C42—21no—
97C2×C3×C42—32no—
98C2×C3×C42—31no—
99C2×C3×C42—38no—
100C2×C3×C42C2×D311yescharacteristic
101C2×C3×C42C2×D311yescharacteristic
102C2×#217—38no—
103#938—332no—
104#936—316no—
105D4×Dic3—332no—
106#930—332no—
107C2×(C2×D3)⋊C4—38no—
108C2×C4⋊Dic3—34no—
109C2×C4⋊Dic3—34no—
110C2×C4⋊Dic3—64no—
111C2×C4×Dic3C2×D312yes—
112C2×C4×Dic3C2×D311yescharacteristic
113#875—316no—
114#874C2×D318yescomplemented
115C4×D12—332no—
116C42×D3C2×D318yescomplemented
117#869—38no—
118#869—38no—
119#869—68no—
120C23×C32C2411yescharacteristic
121C22×C3×D3—24no—
122C22×C3×D3—28no—
123C22×C3×D3—216no—
124C22×C3×D3C2×D414yes—
125C22×C3×D3C2418yes—
126C22×C3×D3C2412yes—
127C2×C32×C4C2×D414yes—
128C2×C32×C4#4118yescomplemented
129C2×C32×C4C2412yes—
130C2×C32×C4C2414yes—
131C2×C3⋊Dic3—28no—
132C2×C3⋊Dic3C2418yes—
133#634—216no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3C2×D414yes—
136C2×C3×Dic3C2414yes—
137C2×C3×Dic3C2412yes—
138C3×D12—216no—
139C3×D12—232no—
140C3×C4×D3—216no—
141C3×C4×D3C2×D4116yescomplemented
142#625—232no—
143D3×Dic3—232no—
144C22×#41—92no—
145#532—916no—
146C2×C4⋊Q8—91no—
147C2×#127—31no—
148C2×#124—92no—
149C2×#121—94no—
150C2×C4×D4—94no—
151C22×C42—31no—
152C24×C3—31no—
153C24×C3—34no—
154C23×D3C22×D314yes—
155C23×D3C22×D311yescharacteristic
156C2×C3×D4—316no—
157C2×C3×D4—38no—
158C2×C3×D4—68no—
159C2×C3×D4—616no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—31no—
163C22×C3×C4—38no—
164C22×C3×C4—34no—
165C22×C3×C4—32no—
166C22×C3×C4—38no—
167C22×C3×C4—68no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D312yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D312yes—
172C2×#67—316no—
173C2×#67—316no—
174C2×#67—616no—
175C2×#67—616no—
176C22×Dic3—34no—
177C22×Dic3—34no—
178C22×Dic3—316no—
179C22×Dic3—64no—
180C22×Dic3—616no—
181C22×Dic3C22×D312yes—
182C22×Dic3C22×D311yescharacteristic
183#237—664no—
184#235—664no—
185C2×D12—28no—
186C2×D12—216no—
187C2×D12C22×D3116yes—
188C2×D12C22×D318yes—
189C2×C4×D3—28no—
190C2×C4×D3—316no—
191C2×C4×D3—616no—
192C2×C4×D3D1218yescomplemented
193C2×C4×D3C22×D318yes—
194C2×C4×D3C22×D314yes—
195C2×Dic6—38no—
196C2×Dic6—38no—
197C2×Dic6—68no—
198C2×Dic6—68no—
199C2×Dic6—68no—
200C2×Dic6—128no—
201C3×C42—24no—
202C3×C42—38no—
203C3×C42—34no—
204C3×C42C22×D314yes—
205C3×C42C22×D314yes—
206#217—332no—
207(C2×D3)⋊C4—332no—
208C4⋊Dic3—316no—
209C4⋊Dic3—316no—
210C4⋊Dic3—616no—
211C4×Dic3C22×D318yes—
212C4×Dic3C22×D314yes—
213C22×C32C22×D412yes—
214C22×C32C2×#4114yes—
215C22×C32C2511yescharacteristic
216C2×C3×D3—28no—
217C2×C3×D3—24no—
218C2×C3×D3—28no—
219C2×C3×D3—216no—
220C2×C3×D3—416no—
221C2×C3×D3C22×D414yes—
222C32×C4C22×D414yes—
223C32×C4C2×#4118yescomplemented
224C3⋊Dic3—28no—
225C3×Dic3—24no—
226C3×Dic3C22×D414yes—
227C2×#41—916no—
228C2×#41—1816no—
229C22×Q8—92no—
230C22×D4—34no—
231C22×D4—32no—
232C22×D4—94no—
233C23×C4—31no—
234C23×C4—32no—
235C23×C4—94no—
236C4⋊Q8—98no—
237#127—38no—
238#124—916no—
239#121—932no—
240C4×D4—932no—
241C2×C4⋊C4—94no—
242C2×C22⋊C4—98no—
243C2×C42—32no—
244C2×C42—31no—
245C2×C42—38no—
246C2×C42D3211yescharacteristic
247C23×C3—21no—
248C23×C3—34no—
249C23×C3—32no—
250C23×C3—38no—
251C23×C3—64no—
252C23×C3—68no—
253C23×C3—616no—
254C23×C3C23×D311yescharacteristic
255C23×C3C23×D311yescharacteristic
256C22×D3—24no—
257C22×D3—28no—
258C22×D3—216no—
259C22×D3C2×D1214yes—
260C22×D3C23×D318yes—
261C22×D3C23×D312yes—
262C3×D4—616no—
263C3×D4—632no—
264C2×C3×C4—24no—
265C2×C3×C4—22no—
266C2×C3×C4—28no—
267C2×C3×C4—24no—
268C2×C3×C4—34no—
269C2×C3×C4—32no—
270C2×C3×C4—316no—
271C2×C3×C4—34no—
272C2×C3×C4—64no—
273C2×C3×C4—616no—
274C2×C3×C4C2×D1214yes—
275C2×C3×C4#23518yescomplemented
276C2×C3×C4D3×D414yes—
277C2×C3×C4#23718yescomplemented
278C2×C3×C4C23×D312yes—
279C2×C3×C4C23×D314yes—
280C2×C3×C4C23×D312yes—
281C2×C3×C4C23×D314yes—
282#67—632no—
283#67—632no—
284C2×Dic3—24no—
285C2×Dic3—38no—
286C2×Dic3—38no—
287C2×Dic3—68no—
288C2×Dic3—68no—
289C2×Dic3—68no—
290C2×Dic3—632no—
291C2×Dic3—128no—
292C2×Dic3C2×D1214yes—
293C2×Dic3C23×D314yes—
294C2×Dic3C23×D312yes—
295D12—216no—
296D12—232no—
297C4×D3—216no—
298C4×D3—632no—
299C4×D3C2×D12116yescomplemented
300Dic6—616no—
301Dic6—616no—
302Dic6—1216no—
303C2×C32#53214yescomplemented
304C2×C32C23×D411yescharacteristic
305C2×C32C22×#4112yes—
306C3×D3—24no—
307C3×D3—48no—
308C24—31no—
309C24—34no—
310#41—1864no—
311C2×Q8—98no—
312C2×Q8—188no—
313C2×D4—316no—
314C2×D4—38no—
315C2×D4—616no—
316C2×D4—68no—
317C2×D4—916no—
318C2×D4—1816no—
319C22×C4—31no—
320C22×C4—34no—
321C22×C4—38no—
322C22×C4—32no—
323C22×C4—38no—
324C22×C4—68no—
325C22×C4—916no—
326C22×C4—94no—
327C22×C4—1816no—
328C22×C4C2×D3212yes—
329C22×C4C2×D3211yescharacteristic
330C4⋊C4—916no—
331C22⋊C4—932no—
332C42—38no—
333C42—34no—
334C42C2×D3214yes—
335C22×C3—24no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—34no—
339C22×C3—64no—
340C22×C3—68no—
341C22×C3—68no—
342C22×C3—616no—
343C22×C3—1216no—
344C22×C3C22×D1212yes—
345C22×C3C2×#23514yes—
346C22×C3C2×D3×D412yes—
347C22×C3C2×#23714yes—
348C22×C3C24×D311yescharacteristic
349C22×C3C24×D311yescharacteristic
350C2×D3—24no—
351C2×D3—28no—
352C2×D3—28no—
353C2×D3—216no—
354C2×D3—416no—
355C2×D3C22×D1214yes—
356C3×C4—28no—
357C3×C4—24no—
358C3×C4—34no—
359C3×C4—64no—
360C3×C4C22×D1214yes—
361C3×C4C2×#23518yescomplemented
362C3×C4C2×D3×D414yes—
363C3×C4C2×#23718yescomplemented
364Dic3—24no—
365Dic3—68no—
366Dic3—68no—
367Dic3—128no—
368Dic3C22×D1214yes—
369C32C2×#53211yescharacteristic, complemented, Sylow
370C23—34no—
371C23—32no—
372C23—38no—
373C23—64no—
374C23—616no—
375C23—68no—
376C23C22×D3211yescharacteristic
377Q8—1816no—
378D4—632no—
379D4—616no—
380D4—1832no—
381C2×C4—34no—
382C2×C4—32no—
383C2×C4—316no—
384C2×C4—34no—
385C2×C4—64no—
386C2×C4—616no—
387C2×C4—98no—
388C2×C4—1832no—
389C2×C4—188no—
390C2×C4#379518yescomplemented
391C2×C4D3×D1214yes—
392C2×C4C22×D3214yes—
393C2×C4C22×D3212yes—
394C2×C3—22no—
395C2×C3—21no—
396C2×C3—24no—
397C2×C3—64no—
398C2×C3—128no—
399C2×C3#547714yescomplemented
400C2×C3#571614yescomplemented
401C2×C3C23×D1211yescharacteristic
402C2×C3C22×#23512yes—
403C2×C3C22×D3×D411yescharacteristic
404C2×C3C22×#23712yes—
405D3—24no—
406D3—48no—
407C22—34no—
408C22—64no—
409C22—68no—
410C22—616no—
411C22—68no—
412C22—1216no—
413C22C2×#379514yes—
414C22C2×D3×D1212yes—
415C22C23×D3211yescharacteristic
416C4—34no—
417C4—64no—
418C4—188no—
419C4C2×#379518yescomplemented
420C4C2×D3×D1214yes—
421C3—21no—
422C3C2×#547711yescharacteristic, complemented
423C3C2×#571611yescharacteristic, complemented
424C2—64no—
425C2—128no—
426C2#1059389714yesdirect product factor
427C2C22×#379512yes—
428C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3795C2semidirect
2. C2×#64078C2semidirect
3. C2×C3×#874C2semidirect
4. C2×C3×C42×D3C2semidirect
5. C2×#63908C2semidirect
6. C2×Dic3×D12C2semidirect
7. C2×#63860C2semidirect
8. #10593897C2direct (N × H)
19. C2×#3795C22semidirect
22. #64078C22semidirect
25. C3×#874C22semidirect
26. C3×C42×D3C22semidirect
28. #63908C22semidirect
29. Dic3×D12C22semidirect
30. #63860C22semidirect
42. C2×#874D3semidirect
44. C2×C42×D3D3semidirect
62. C2×C3×C4×D3D4semidirect
114. #874C2×D3semidirect
116. C42×D3C2×D3semidirect
128. C2×C32×C4#41semidirect
141. C3×C4×D3C2×D4semidirect
192. C2×C4×D3D12semidirect
223. C32×C4C2×#41semidirect
275. C2×C3×C4#235semidirect
277. C2×C3×C4#237semidirect
299. C4×D3C2×D12semidirect
303. C2×C32#532semidirect
361. C3×C4C2×#235semidirect
363. C3×C4C2×#237semidirect
369. C32C2×#532semidirect
390. C2×C4#3795semidirect
399. C2×C3#5477semidirect
400. C2×C3#5716semidirect
419. C4C2×#3795semidirect
422. C3C2×#5477semidirect
423. C3C2×#5716semidirect
426. C2#10593897direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C2×#640782
C2×C3×#8742
C2×C3×C42×D32
C2×#639082
C2×Dic3×D122
C2×#638602
#105938972
C2×#57163
C2×#54773