Finite Group Databasebeta

← C2×#10591070 #11857406

Subgroups — C2×#10591070 #11857406

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic
2C22×#3748C211yesmaximal, characteristic, complemented
3C23×C3×C3⋊C8C211yesmaximal, characteristic, complemented
4#10591070C218yesmaximal, direct product factor
5C2×(C2×D3)⋊(C3⋊C8)C214yesmaximal, complemented
6C2×#5234—31nomaximal
7C2×#5110—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C22×C3×#67C412yes—
10C2×C3×#235—24no—
11C2×C3×#235—24no—
12C2×C3×#235C414yes—
13C2×C3×#235C2214yes—
14C22×C3×D12C411yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×Dic6C411yescharacteristic
17C2×#3748—24no—
18C2×#3748C2214yescomplemented
19C22×C3⋊(C3⋊C8)C2212yes—
20C22×C3×C3⋊C8—24no—
21C22×C3×C3⋊C8C2212yes—
22C22×C3×C3⋊C8C2214yescomplemented
23(C2×D3)⋊(C3⋊C8)C22116yescomplemented
24C22×C3×#41—31no—
25C22×#235D311yescharacteristic
26C23×C3×C8—31no—
27C22×#208—31no—
28C22×#208—31no—
29C22×#208—61no—
30C23×C3⋊C8D311yescharacteristic, complemented
31#5234—38no—
32C2×#830—34no—
33#5110—38no—
34C2×(C2×D3)⋊C8—34no—
35C24×C32C2×C411yescharacteristic
36C23×C3×D3C2×C412yes—
37C22×C32×C4C2×C411yescharacteristic
38C22×C32×C4C2×C412yes—
39C22×C32×C4D414yes—
40C22×C32×C4D414yes—
41C22×C32×C4C2311yescharacteristic
42C22×C32×C4C2312yes—
43C2×C3×#67—28no—
44C2×C3×#67C2×C418yes—
45C22×C3×Dic3C2×C412yes—
46C3×#235—216no—
47C3×#235—28no—
48C3×#235—28no—
49C2×C3×D12—24no—
50C2×C3×D12C2×C414yes—
51C2×C3×C4×D3—24no—
52C2×C3×C4×D3—24no—
53C2×C3×C4×D3C2×C414yes—
54C2×C3×C4×D3C2314yes—
55C2×C3×Dic6—24no—
56C2×C3×Dic6C2×C414yes—
57#3748—28no—
58C2×C3⋊(C3⋊C8)—24no—
59C2×C3⋊(C3⋊C8)C2314yes—
60C2×C3×C3⋊C8—24no—
61C2×C3×C3⋊C8—28no—
62C2×C3×C3⋊C8C2314yes—
63C2×#408—91noSylow
64C2×C3×#41—34no—
65C2×C3×#41—34no—
66C2×C3×#41—64no—
67C2×C3×#41—64no—
68C22×C3×Q8—31no—
69C22×C3×D4—32no—
70C22×C3×D4—31no—
71C23×C3×C4—21no—
72C23×C3×C4—32no—
73C23×C3×C4C2×D311yescharacteristic
74C23×C3×C4C2×D311yescharacteristic
75C22×#67Dic312yes—
76C2×#235—24no—
77C2×#235—24no—
78C2×#235Dic314yes—
79C2×#235C2×D314yes—
80C22×D12Dic311yescharacteristic
81C22×C4×D3C2×D312yes—
82C22×Dic6Dic311yescharacteristic
83C22×C3×C8—32no—
84C22×C3×C8—34no—
85C22×C3×C8—64no—
86C2×#208—34no—
87C2×#208—34no—
88C2×#208—64no—
89C2×#208—68no—
90C2×#208—64no—
91C2×#208—64no—
92C22×C3⋊C8—24no—
93C22×C3⋊C8—32no—
94C22×C3⋊C8—32no—
95C22×C3⋊C8—62no—
96C22×C3⋊C8C2×D312yes—
97C22×C3⋊C8C2×D314yescomplemented
98#830—316no—
99(C2×D3)⋊C8—316no—
100C23×C32—24no—
101C23×C32C22⋊C414yes—
102C23×C32C22×C412yes—
103C23×C32C22×C411yescharacteristic
104C22×C3×D3—24no—
105C22×C3×D3—28no—
106C22×C3×D3C22×C414yes—
107C2×C32×C4C22⋊C414yes—
108C2×C32×C4C22⋊C418yes—
109C2×C32×C4C22×C412yes—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D412yes—
112C2×C32×C4C2×D414yes—
113C2×C32×C4C2×D412yes—
114C2×C32×C4C2×D414yes—
115C2×C32×C4C2411yescharacteristic
116C3×#67—216no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3C22×C414yes—
119C3×D12—28no—
120C3×C4×D3—28no—
121C3×C4×D3—24no—
122C3×C4×D3—24no—
123C3×Dic6—28no—
124C3⋊(C3⋊C8)—24no—
125C3×C3⋊C8—24no—
126C22×#41—31no—
127C22×M16—91no—
128C23×C8—31no—
129#408—98no—
130C2×C22⋊C8—94no—
131C24×C3—21no—
132C24×C3—32no—
133C24×C3C4×D311yescharacteristic
134C24×C3C2×Dic311yescharacteristic
135C23×D3C2×Dic312yes—
136C3×#41—616no—
137C3×#41—68no—
138C3×#41—68no—
139C2×C3×Q8—34no—
140C2×C3×Q8—64no—
141C2×C3×D4—38no—
142C2×C3×D4—34no—
143C2×C3×D4—68no—
144C2×C3×D4—64no—
145C22×C3×C4—21no—
146C22×C3×C4—22no—
147C22×C3×C4—24no—
148C22×C3×C4—24no—
149C22×C3×C4—22no—
150C22×C3×C4—21no—
151C22×C3×C4—32no—
152C22×C3×C4—34no—
153C22×C3×C4—34no—
154C22×C3×C4—64no—
155C22×C3×C4—64no—
156C22×C3×C4C4×D311yescharacteristic
157C22×C3×C4C4×D312yes—
158C22×C3×C4D1214yes—
159C22×C3×C4C2×Dic311yescharacteristic
160C22×C3×C4C2×Dic312yes—
161C22×C3×C4#6714yes—
162C22×C3×C4#6714yes—
163C22×C3×C4#6714yes—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D312yes—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—28no—
169C2×#67C2×Dic318yes—
170C22×Dic3C2×Dic312yes—
171#235—216no—
172#235—28no—
173#235—28no—
174C2×D12—24no—
175C2×D12C2×Dic314yes—
176C2×C4×D3—24no—
177C2×C4×D3—24no—
178C2×C4×D3C2×Dic314yes—
179C2×C4×D3C22×D314yes—
180C2×Dic6—24no—
181C2×Dic6C2×Dic314yes—
182C2×C3×C8—34no—
183C2×C3×C8—64no—
184C2×C3×C8—68no—
185#208—616no—
186#208—68no—
187#208—68no—
188C2×C3⋊C8—24no—
189C2×C3⋊C8—28no—
190C2×C3⋊C8—34no—
191C2×C3⋊C8—34no—
192C2×C3⋊C8—64no—
193C2×C3⋊C8—68no—
194C2×C3⋊C8—64no—
195C2×C3⋊C8—64no—
196C2×C3⋊C8C22×D314yes—
197C22×C32—24no—
198C22×C32—28no—
199C22×C32C2×C22⋊C414yes—
200C22×C32C2×C22⋊C412yes—
201C22×C32#13114yes—
202C22×C32C23×C411yescharacteristic
203C2×C3×D3—24no—
204C2×C3×D3—28no—
205C2×C3×D3—48no—
206C32×C4C2×C22⋊C414yes—
207C32×C4C2×C22⋊C412yes—
208C32×C4C22×D411yescharacteristic
209C32×C4C22×D411yescharacteristic
210C3×Dic3—24no—
211C2×#41—34no—
212C2×#41—34no—
213C2×#41—64no—
214C2×#41—64no—
215C22×Q8—31no—
216C22×D4—32no—
217C22×D4—31no—
218C23×C4—32no—
219C23×C4D3211yescharacteristic
220C2×M16—94no—
221C2×M16—184no—
222C22×C8—34no—
223C22×C8—32no—
224C22×C8—64no—
225C22×C8—92no—
226C22⋊C8—916no—
227C23×C3—24no—
228C23×C3—24no—
229C23×C3—24no—
230C23×C3—21no—
231C23×C3—22no—
232C23×C3—34no—
233C23×C3—44no—
234C23×C3—68no—
235C23×C3—64no—
236C23×C3(C2×D3)⋊C414yes—
237C23×C3#21714yes—
238C23×C3C2×C4×D312yes—
239C23×C3C2×C4×D311yescharacteristic
240C23×C3C22×Dic312yes—
241C23×C3C22×Dic311yescharacteristic
242C22×D3—28no—
243C22×D3—24no—
244C22×D3C22×Dic314yes—
245C3×Q8—68no—
246C3×D4—616no—
247C3×D4—68no—
248C2×C3×C4—21no—
249C2×C3×C4—24no—
250C2×C3×C4—28no—
251C2×C3×C4—21no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—24no—
255C2×C3×C4—22no—
256C2×C3×C4—24no—
257C2×C3×C4—34no—
258C2×C3×C4—64no—
259C2×C3×C4—68no—
260C2×C3×C4—64no—
261C2×C3×C4—64no—
262C2×C3×C4(C2×D3)⋊C414yes—
263C2×C3×C4(C2×D3)⋊C418yes—
264C2×C3×C4#21714yes—
265C2×C3×C4#21718yes—
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4C2×C4×D312yes—
268C2×C3×C4C2×D1212yes—
269C2×C3×C4C2×D1214yes—
270C2×C3×C4C22×Dic312yes—
271C2×C3×C4C22×Dic311yescharacteristic
272C2×C3×C4C2×#6712yes—
273C2×C3×C4C2×#6714yes—
274C2×C3×C4C2×#6712yes—
275C2×C3×C4C2×#6714yes—
276C2×C3×C4C2×#6712yes—
277C2×C3×C4C2×#6714yes—
278C2×C3×C4C23×D311yescharacteristic
279C2×C3×C4C23×D311yescharacteristic
280#67—216no—
281C2×Dic3—24no—
282C2×Dic3C22×Dic314yes—
283D12—28no—
284C4×D3—28no—
285C4×D3—24no—
286C4×D3—24no—
287Dic6—28no—
288C3×C8—64no—
289C3⋊C8—24no—
290C3⋊C8—68no—
291C3⋊C8—64no—
292C3⋊C8—64no—
293C2×C32—24no—
294C2×C32#40814yescomplemented
295C2×C32C22×C22⋊C411yescharacteristic
296C2×C32C2×#13112yes—
297C3×D3—44no—
298C24—32no—
299C24D3×Dic311yescharacteristic
300#41—616no—
301#41—68no—
302#41—68no—
303C2×Q8—34no—
304C2×Q8—64no—
305C2×D4—38no—
306C2×D4—34no—
307C2×D4—68no—
308C2×D4—64no—
309C22×C4—32no—
310C22×C4—34no—
311C22×C4—34no—
312C22×C4—64no—
313C22×C4—64no—
314C22×C4D3×Dic311yescharacteristic
315C22×C4D3×Dic312yes—
316C22×C4#62514yes—
317C22×C4#62614yes—
318C22×C4C2×D3212yes—
319C22×C4C2×D3211yescharacteristic
320M16—188no—
321C2×C8—34no—
322C2×C8—64no—
323C2×C8—68no—
324C2×C8—94no—
325C2×C8—184no—
326C22×C3—24no—
327C22×C3—28no—
328C22×C3—24no—
329C22×C3—28no—
330C22×C3—21no—
331C22×C3—24no—
332C22×C3—22no—
333C22×C3—24no—
334C22×C3—48no—
335C22×C3—44no—
336C22×C3—68no—
337C22×C3—64no—
338C22×C3—128no—
339C22×C3#90114yes—
340C22×C3C2×(C2×D3)⋊C414yes—
341C22×C3C2×(C2×D3)⋊C412yes—
342C22×C3#94814yes—
343C22×C3C2×#21714yes—
344C22×C3C2×#21712yes—
345C22×C3C22×C4×D311yescharacteristic
346C22×C3C23×Dic311yescharacteristic
347C2×D3—28no—
348C2×D3—24no—
349C2×D3—48no—
350C3×C4—21no—
351C3×C4—21no—
352C3×C4—22no—
353C3×C4—24no—
354C3×C4—64no—
355C3×C4C2×(C2×D3)⋊C412yes—
356C3×C4C2×(C2×D3)⋊C414yes—
357C3×C4C2×#21714yes—
358C3×C4C2×#21712yes—
359C3×C4C22×D1211yescharacteristic
360C3×C4C22×#6711yescharacteristic
361C3×C4C22×#6711yescharacteristic
362C3×C4C22×#6711yescharacteristic
363Dic3—24no—
364C32C2×#40811yescharacteristic, complemented, Sylow
365C23—24no—
366C23—34no—
367C23—68no—
368C23—64no—
369C23(C2×D3)⋊Dic314yes—
370C23C2×D3×Dic312yes—
371C23C2×D3×Dic311yescharacteristic
372Q8—68no—
373D4—616no—
374D4—68no—
375C2×C4—34no—
376C2×C4—64no—
377C2×C4—64no—
378C2×C4—64no—
379C2×C4—68no—
380C2×C4(C2×D3)⋊Dic314yes—
381C2×C4(C2×D3)⋊Dic318yes—
382C2×C4C2×D3×Dic311yescharacteristic
383C2×C4C2×D3×Dic312yes—
384C2×C4C2×#62512yes—
385C2×C4C2×#62514yes—
386C2×C4C2×#62612yes—
387C2×C4C2×#62614yes—
388C2×C4C22×D3211yescharacteristic
389C8—64no—
390C8—184no—
391C2×C3—24no—
392C2×C3—24no—
393C2×C3—24no—
394C2×C3—21no—
395C2×C3—22no—
396C2×C3—44no—
397C2×C3—124no—
398C2×C3#511014yescomplemented
399C2×C3#523414yescomplemented
400C2×C3C2×#90112yes—
401C2×C3C22×(C2×D3)⋊C411yescharacteristic
402C2×C3C2×#94812yes—
403C2×C3C22×#21711yescharacteristic
404D3—44no—
405C22—28no—
406C22—24no—
407C22—64no—
408C22—68no—
409C22—128no—
410C22#6381414yes—
411C22C2×(C2×D3)⋊Dic314yes—
412C22C2×(C2×D3)⋊Dic312yes—
413C22C22×D3×Dic311yescharacteristic
414C4—64no—
415C4C2×(C2×D3)⋊Dic312yes—
416C4C2×(C2×D3)⋊Dic314yes—
417C4C22×#62511yescharacteristic
418C4C22×#62611yescharacteristic
419C3—21no—
420C3C2×#511011yescharacteristic, complemented
421C3C2×#523411yescharacteristic, complemented
422C2—24no—
423C2—124no—
424C2#1059107014yesdirect product factor
425C2C2×#6381412yes—
426C2C22×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C22×C4
prime radicalC22×C3×#235C2
cosocleC2×C32×C4C24
hypercenterC23×C4D32
hypocenterC32C2×#408
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#3748C2semidirect
3. C23×C3×C3⋊C8C2semidirect
4. #10591070C2direct (N × H)
5. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
18. C2×#3748C22semidirect
22. C22×C3×C3⋊C8C22semidirect
23. (C2×D3)⋊(C3⋊C8)C22semidirect
30. C23×C3⋊C8D3semidirect
97. C22×C3⋊C8C2×D3semidirect
294. C2×C32#408semidirect
364. C32C2×#408semidirect
398. C2×C3#5110semidirect
399. C2×C3#5234semidirect
420. C3C2×#5110semidirect
421. C3C2×#5234semidirect
424. C2#10591070direct (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
C22×#37482
C23×C3×C3⋊C82
#105910702
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52343
C2×#51103