Finite Group Databasebeta

← C2×#10591640 #11857652

Subgroups — C2×#10591640 #11857652

Order 1152.

1957 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3832C211yesmaximal, characteristic
2C2×#63818C212yesmaximal, complemented
3C2×C3×#836C212yesmaximal, complemented
4#10591640C218yesmaximal, direct product factor
5C2×#63559C212yesmaximal, complemented
6C2×#4751—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×#3832—22no—
9C2×#3832—24no—
10C2×#3832—22no—
11C2×#3832C414yes—
12C2×#3832C2214yes—
13C22×C4⋊(C3⋊D3)C412yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C412yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#208C2214yes—
18C2×#3712—22no—
19#63818—24no—
20#63818C2218yescomplemented
21C2×#3710—22no—
22C3×#836C2218yescomplemented
23#63559C2218yescomplemented
24C22×#239—32no—
25C22×#239—61no—
26C2×D3×M16—34no—
27C2×C3×#101—32no—
28C2×#836D312yescomplemented
29C2×#823—34no—
30#4751—316no—
31C23×C3⋊D3C2×C412yes—
32C23×C3⋊D3C2×C411yescharacteristic
33C2×C32×Q8—22no—
34C2×C32×Q8—22no—
35C2×C32×Q8C2×C412yes—
36C2×C32×Q8C2312yes—
37C22×C32×C4C2×C412yes—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3C2×C411yescharacteristic
40#3832—28no—
41#3832—28no—
42#3832—28no—
43#3832—28no—
44C2×C4⋊(C3⋊D3)—24no—
45C2×C4⋊(C3⋊D3)—24no—
46C2×C4⋊(C3⋊D3)—22no—
47C2×C4⋊(C3⋊D3)—22no—
48C2×C4⋊(C3⋊D3)C2×C418yes—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C4⋊(C3⋊D3)C2312yes—
51C2×C4×C3⋊D3—24no—
52C2×C4×C3⋊D3—22no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3C2×C418yes—
55C2×C4×C3⋊D3C2×C412yes—
56C2×C4×C3⋊D3D412yes—
57C2×C4×C3⋊D3D414yes—
58C2×C4×C3⋊D3D412yes—
59C2×C4×C3⋊D3C2312yes—
60C3×#208—24no—
61C3×#208C2318yes—
62C2×C3×C3⋊C8—24no—
63#3712—28no—
64#3710—28no—
65C2×#413—91noSylow
66C22×C3×Q8—21no—
67C22×C3×Q8C2×D312yes—
68C2×#239—38no—
69C2×#239—38no—
70C2×#239—64no—
71C2×#239—64no—
72C2×#239—64no—
73C2×#239—64no—
74C2×#239—68no—
75C2×#239—64no—
76C2×#239—68no—
77C2×#239—64no—
78C22×D12—34no—
79C22×D12—32no—
80C22×D12—62no—
81C22×D12—61no—
82C22×C4×D3—32no—
83C22×C4×D3—34no—
84C22×C4×D3—62no—
85C22×C4×D3—61no—
86C2×C3×M16—34no—
87C2×#208C2×D314yes—
88D3×M16—316no—
89D3×M16—68no—
90C2×ΓL(1,𝔽25)—64no—
91C2×D3×C8—64no—
92C3×#101—38no—
93#836C2×D318yescomplemented
94#823—316no—
95C23×C32C22×C411yescharacteristic
96C22×C3⋊D3—22no—
97C22×C3⋊D3—22no—
98C22×C3⋊D3—42no—
99C22×C3⋊D3—44no—
100C22×C3⋊D3C22⋊C412yes—
101C22×C3⋊D3C22⋊C412yes—
102C22×C3⋊D3C22×C414yes—
103C22×C3⋊D3C22×C412yes—
104C32×Q8—24no—
105C32×Q8—24no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4C22×C414yes—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2×D412yes—
112C2×C32×C4C2411yescharacteristic
113C2×C3⋊Dic3C22⋊C412yes—
114C2×C3⋊Dic3C22⋊C411yescharacteristic
115C2×C3⋊Dic3C22⋊C411yescharacteristic
116C2×C3⋊Dic3C22×C412yes—
117C4⋊(C3⋊D3)—216no—
118C4⋊(C3⋊D3)—24no—
119C4⋊(C3⋊D3)—24no—
120C4×C3⋊D3—28no—
121C4×C3⋊D3—28no—
122C4×C3⋊D3C22⋊C414yes—
123C4×C3⋊D3C22⋊C414yes—
124C4×C3⋊D3C2×D414yes—
125C4×C3⋊D3C2×D414yes—
126C3×C3⋊C8—28no—
127C22×#41—91no—
128C22×M16—92no—
129#413—98no—
130C2×#101—32no—
131C2×#100—92no—
132C23×D3—32no—
133C23×D3—34no—
134C23×D3—61no—
135C23×D3—62no—
136C2×C3×Q8—24no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8—24no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8C4×D314yes—
143C2×C3×Q8C22×D314yes—
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4C4×D314yes—
147C22×C3×C4C22×D312yes—
148C22×Dic3—32no—
149C22×Dic3—61no—
150#239—616no—
151#239—616no—
152#239—616no—
153#239—616no—
154#239—616no—
155#239—616no—
156#239—616no—
157#239—616no—
158C2×D12—316no—
159C2×D12—34no—
160C2×D12—34no—
161C2×D12—68no—
162C2×D12—62no—
163C2×D12—62no—
164C2×D12—68no—
165C2×D12—68no—
166C2×D12—68no—
167C2×D12—68no—
168C2×D12—64no—
169C2×D12—64no—
170C2×D12—64no—
171C2×D12—64no—
172C2×C4×D3—34no—
173C2×C4×D3—34no—
174C2×C4×D3—34no—
175C2×C4×D3—38no—
176C2×C4×D3—34no—
177C2×C4×D3—316no—
178C2×C4×D3—62no—
179C2×C4×D3—68no—
180C2×C4×D3—62no—
181C2×C4×D3—64no—
182C2×C4×D3—62no—
183C2×C4×D3—62no—
184C2×C4×D3—68no—
185C2×C4×D3—64no—
186C2×C4×D3—64no—
187C2×C4×D3—68no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C3×M16—38no—
191C3×M16—64no—
192C2×C3×C8—64no—
193#208—24no—
194#208C22×D318yes—
195C2×C3⋊C8—24no—
196ΓL(1,𝔽25)—616no—
197D3×C8—616no—
198C22×C32—22no—
199C22×C32C2×C22⋊C411yescharacteristic
200C22×C32C2×C22⋊C411yescharacteristic
201C22×C32C23×C411yescharacteristic
202C2×C3⋊D3—24no—
203C2×C3⋊D3—24no—
204C2×C3⋊D3—42no—
205C2×C3⋊D3—42no—
206C2×C3⋊D3—44no—
207C2×C3⋊D3—44no—
208C2×C3⋊D3—44no—
209C2×C3⋊D3C2×C22⋊C414yes—
210C32×C4—24no—
211C32×C4C2×C22⋊C412yes—
212C32×C4C22×D412yes—
213C3⋊Dic3C2×C22⋊C412yes—
214C3⋊Dic3C2×C22⋊C412yes—
215C2×#41—94no—
216C2×#41—94no—
217C2×#41—182no—
218C2×#41—184no—
219C2×#41—182no—
220C22×Q8D3211yescharacteristic
221C22×D4—92no—
222C22×D4—91no—
223C23×C4—91no—
224C23×C4—92no—
225C2×M16—34no—
226C2×M16—98no—
227C2×M16—182no—
228C2×M16—184no—
229C22×C8—182no—
230#101—38no—
231#100—98no—
232C23×C3—21no—
233C23×C3C2×C4×D312yes—
234C22×D3—34no—
235C22×D3—34no—
236C22×D3—34no—
237C22×D3—38no—
238C22×D3—62no—
239C22×D3—62no—
240C22×D3—62no—
241C22×D3—64no—
242C22×D3—64no—
243C22×D3—64no—
244C22×D3—64no—
245C22×D3—64no—
246C22×D3—124no—
247C22×D3—124no—
248C22×D3—128no—
249C22×D3—128no—
250C3×Q8—28no—
251C3×Q8—28no—
252C3×Q8—28no—
253C3×Q8—28no—
254C2×C3×C4—24no—
255C2×C3×C4—24no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—21no—
259C2×C3×C4—24no—
260C2×C3×C4—21no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4C2×C4×D318yes—
264C2×C3×C4C2×C4×D312yes—
265C2×C3×C4D3×D414yes—
266C2×C3×C4D3×D414yes—
267C2×C3×C4C23×D312yes—
268C2×Dic3—34no—
269C2×Dic3—32no—
270C2×Dic3—32no—
271C2×Dic3—34no—
272C2×Dic3—62no—
273C2×Dic3—61no—
274C2×Dic3—61no—
275C2×Dic3—62no—
276D12—632no—
277D12—632no—
278D12—68no—
279D12—68no—
280D12—68no—
281D12—68no—
282C4×D3—38no—
283C4×D3—38no—
284C4×D3—38no—
285C4×D3—38no—
286C4×D3—64no—
287C4×D3—64no—
288C4×D3—64no—
289C4×D3—64no—
290C4×D3—616no—
291C4×D3—616no—
292C4×D3—616no—
293C4×D3—616no—
294C3×C8—68no—
295C3⋊C8—28no—
296C2×C32—21no—
297C2×C32—21no—
298C2×C32#41312yescomplemented
299C2×C32C22×C22⋊C411yescharacteristic
300C3⋊D3—24no—
301C3⋊D3—44no—
302C24—91no—
303C24—92no—
304#41—188no—
305#41—188no—
306#41—188no—
307#41—188no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8#62412yes—
311C2×Q8C2×D3212yes—
312C2×D4—92no—
313C2×D4—98no—
314C2×D4—92no—
315C2×D4—184no—
316C2×D4—184no—
317C2×D4—182no—
318C2×D4—182no—
319C22×C4—91no—
320C22×C4—92no—
321C22×C4—92no—
322C22×C4—92no—
323C22×C4—94no—
324C22×C4—92no—
325C22×C4—98no—
326C22×C4—184no—
327C22×C4—182no—
328C22×C4—182no—
329C22×C4#62412yes—
330C22×C4C2×D3211yescharacteristic
331M16—38no—
332M16—64no—
333M16—188no—
334C2×C8—64no—
335C2×C8—188no—
336C22×C3—24no—
337C22×C3—24no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3D3×C22⋊C412yes—
342C22×C3D3×C22⋊C412yes—
343C22×C3C22×C4×D312yes—
344C2×D3—38no—
345C2×D3—64no—
346C2×D3—68no—
347C2×D3—68no—
348C2×D3—68no—
349C2×D3—124no—
350C2×D3—124no—
351C2×D3—124no—
352C2×D3—124no—
353C2×D3—124no—
354C2×D3—128no—
355C2×D3—128no—
356C2×D3—128no—
357C2×D3—128no—
358C2×D3—128no—
359C2×D3—128no—
360C3×C4—28no—
361C3×C4—28no—
362C3×C4—22no—
363C3×C4—22no—
364C3×C4D3×C22⋊C414yes—
365C3×C4C2×D3×D414yes—
366Dic3—34no—
367Dic3—34no—
368Dic3—62no—
369Dic3—62no—
370C32C2×#41311yescharacteristic, complemented, Sylow
371C23—92no—
372C23—92no—
373C23—92no—
374C23—94no—
375C23—182no—
376C23—182no—
377C23—362no—
378C23—364no—
379C23C2×#62411yescharacteristic
380Q8—24no—
381Q8—24no—
382D4—1816no—
383D4—184no—
384D4—184no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—92no—
388C2×C4—92no—
389C2×C4—91no—
390C2×C4—91no—
391C2×C4—94no—
392C2×C4—94no—
393C2×C4—94no—
394C2×C4—94no—
395C2×C4—188no—
396C2×C4—188no—
397C2×C4C2×#62414yes—
398C2×C4C2×#62411yescharacteristic
399C2×C4#381112yes—
400C2×C4#381112yes—
401C2×C4C22×D3211yescharacteristic
402C8—68no—
403C2×C3—22no—
404C2×C3—22no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3#475114yescomplemented
410C2×C3C2×D3×C22⋊C412yes—
411D3—68no—
412D3—124no—
413D3—128no—
414D3—128no—
415C22—22no—
416C22—94no—
417C22—184no—
418C22—184no—
419C22—362no—
420C22—362no—
421C22—364no—
422C22—364no—
423C22—364no—
424C22#6397411yescharacteristic
425C22#6397411yescharacteristic
426C22C22×#62411yescharacteristic
427C4—24no—
428C4—92no—
429C4—92no—
430C4#6397412yes—
431C4C2×#381112yes—
432C3—21no—
433C3C2×#475112yescomplemented
434C2—21no—
435C2—21no—
436C2—184no—
437C2—364no—
438C2#1059164012yesdirect product factor
439C2C2×#6397411yescharacteristic
subgroupG/H
centerC22#63974
commutatorC22×C32C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3832C2
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32C2×#413
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×#63818C2semidirect
3. C2×C3×#836C2semidirect
4. #10591640C2direct (N × H)
5. C2×#63559C2semidirect
20. #63818C22semidirect
22. C3×#836C22semidirect
23. #63559C22semidirect
28. C2×#836D3semidirect
93. #836C2×D3semidirect
298. C2×C32#413semidirect
370. C32C2×#413semidirect
409. C2×C3#4751semidirect
433. C3C2×#4751semidirect
438. C2#10591640direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C2×#638182
C2×C3×#8362
#105916402
C2×#635592
C2×#47513