Finite Group Databasebeta

← C2×#10592693 #11808257

Subgroups — C2×#10592693 #11808257

Order 1152.

2724 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#3752C211yesmaximal, characteristic
3C22×#3752C211yesmaximal, characteristic
4C22×#3752C211yesmaximal, characteristic
5C22×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C22×#3750C211yesmaximal, characteristic, complemented
7C2×#63658C211yesmaximal, characteristic, complemented
8#10592693C218yesmaximal, direct product factor
9C2×#4994—34nomaximal
10C24×C3⋊D3C2211yescharacteristic
11C23×C32×C4C2211yescharacteristic
12C23×C32×C4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3⋊Dic3C2211yescharacteristic
17C2×C32×C4⋊C4—24no—
18C2×C32×C4⋊C4C2214yescomplemented
19C2×#3752—24no—
20C2×#3752—24no—
21C2×#3752—24no—
22C2×#3752C2214yes—
23C2×#3752C2214yes—
24C2×#3752C2214yes—
25C2×C4⋊(C3⋊Dic3)—24no—
26C2×C4⋊(C3⋊Dic3)C2214yescomplemented
27C2×#3750—24no—
28C2×#3750C2214yescomplemented
29#63658C2214yescomplemented
30C22×C3×C4⋊C4D314yescomplemented
31C22×(C2×D3)⋊C4—34no—
32C22×(C2×D3)⋊C4—34no—
33C22×(C2×D3)⋊C4—34no—
34C22×C4⋊Dic3—34no—
35C22×Dic3⋊C4—34no—
36C2×C3⋊#95—34no—
37#4994—332no—
38C24×C32C2311yescharacteristic
39C23×C3⋊D3—22no—
40C23×C3⋊D3—22no—
41C23×C3⋊D3—22no—
42C23×C3⋊D3—22no—
43C23×C3⋊D3—22no—
44C23×C3⋊D3—22no—
45C23×C3⋊D3Q814yes—
46C23×C3⋊D3C2312yes—
47C22×C32×C4—22no—
48C22×C32×C4—22no—
49C22×C32×C4—22no—
50C22×C32×C4—22no—
51C22×C32×C4—22no—
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4D414yes—
55C22×C32×C4D414yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2312yes—
58C22×C32×C4C2312yes—
59C22×C3⋊Dic3—22no—
60C22×C3⋊Dic3—22no—
61C22×C3⋊Dic3—22no—
62C22×C3⋊Dic3—22no—
63C22×C3⋊Dic3—22no—
64C22×C3⋊Dic3—22no—
65C22×C3⋊Dic3—22no—
66C22×C3⋊Dic3—22no—
67C22×C3⋊Dic3D414yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2312yes—
71C32×C4⋊C4—28no—
72#3752—28no—
73#3752—28no—
74#3752—28no—
75C4⋊(C3⋊Dic3)—28no—
76#3750—28no—
77C2×#396—91noSylow
78C24×D3—34no—
79C23×C3×C4C2×D314yes—
80C23×C3×C4C2×D314yes—
81C23×C3×C4C2×D314yes—
82C23×Dic3—34no—
83C23×Dic3—34no—
84C23×Dic3—34no—
85C2×C3×C4⋊C4—216no—
86C2×C3×C4⋊C4C2×D3116yescomplemented
87C2×(C2×D3)⋊C4—316no—
88C2×(C2×D3)⋊C4—316no—
89C2×(C2×D3)⋊C4—316no—
90C2×(C2×D3)⋊C4—616no—
91C2×(C2×D3)⋊C4—616no—
92C2×(C2×D3)⋊C4—616no—
93C2×C4⋊Dic3—316no—
94C2×C4⋊Dic3—616no—
95C2×Dic3⋊C4—316no—
96C2×Dic3⋊C4—616no—
97C3⋊#95—316no—
98C23×C32C2×D412yes—
99C23×C32C2×D412yes—
100C23×C32C2×D412yes—
101C23×C32C2×Q812yes—
102C23×C32#4112yes—
103C23×C32#4112yes—
104C23×C32#4112yes—
105C23×C32C2411yescharacteristic
106C22×C3⋊D3—28no—
107C22×C3⋊D3—28no—
108C22×C3⋊D3—28no—
109C22×C3⋊D3—22no—
110C22×C3⋊D3—22no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3—22no—
113C22×C3⋊D3—22no—
114C22×C3⋊D3—22no—
115C22×C3⋊D3—44no—
116C22×C3⋊D3—44no—
117C22×C3⋊D3—44no—
118C22×C3⋊D3—44no—
119C22×C3⋊D3C2×Q814yes—
120C2×C32×C4—28no—
121C2×C32×C4—28no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4—22no—
128C2×C32×C4—22no—
129C2×C32×C4—44no—
130C2×C32×C4C2×D414yes—
131C2×C32×C4C2×D414yes—
132C2×C3⋊Dic3—28no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—44no—
142C2×C3⋊Dic3—44no—
143C2×C3⋊Dic3C2×D414yes—
144C22×C4⋊C4—91no—
145C22×C4⋊C4—91no—
146C22×C4⋊C4C3⋊D311yescharacteristic, complemented
147C22×C22⋊C4—91no—
148C22×C22⋊C4—91no—
149C22×C22⋊C4—91no—
150#396—98no—
151C2×#95—91no—
152C24×C3C22×D314yes—
153C23×D3—316no—
154C23×D3—38no—
155C23×D3—68no—
156C23×D3—68no—
157C23×D3—68no—
158C23×D3—68no—
159C23×D3—68no—
160C23×D3—68no—
161C22×C3×C4—28no—
162C22×C3×C4—28no—
163C22×C3×C4—28no—
164C22×C3×C4—28no—
165C22×C3×C4—28no—
166C22×C3×C4—28no—
167C22×C3×C4—28no—
168C22×C3×C4D12116yes—
169C22×C3×C4#67116yes—
170C22×C3×C4C22×D318yes—
171C22×C3×C4C22×D318yes—
172C22×C3×C4C22×D318yes—
173C22×Dic3—316no—
174C22×Dic3—38no—
175C22×Dic3—38no—
176C22×Dic3—38no—
177C22×Dic3—68no—
178C22×Dic3—68no—
179C22×Dic3—68no—
180C22×Dic3—68no—
181C22×Dic3—68no—
182C22×Dic3—68no—
183C22×Dic3—68no—
184C22×Dic3—68no—
185C3×C4⋊C4—232no—
186(C2×D3)⋊C4—632no—
187(C2×D3)⋊C4—632no—
188(C2×D3)⋊C4—632no—
189C4⋊Dic3—632no—
190Dic3⋊C4—632no—
191C22×C32#12114yes—
192C22×C32#12114yes—
193C22×C32#12114yes—
194C22×C32C22⋊Q814yes—
195C22×C32C22⋊Q814yes—
196C22×C32C22⋊Q814yes—
197C22×C32#12614yes—
198C22×C32C22×D411yescharacteristic
199C22×C32C22×D411yescharacteristic
200C22×C32C22×D411yescharacteristic
201C22×C32C22×Q811yescharacteristic
202C22×C32C2×#4111yescharacteristic
203C22×C32C2×#4111yescharacteristic
204C22×C32C2×#4111yescharacteristic
205C2×C3⋊D3—24no—
206C2×C3⋊D3—24no—
207C2×C3⋊D3—24no—
208C2×C3⋊D3—42no—
209C2×C3⋊D3—42no—
210C2×C3⋊D3—42no—
211C2×C3⋊D3—42no—
212C2×C3⋊D3—416no—
213C32×C4—24no—
214C32×C4—24no—
215C32×C4—42no—
216C3⋊Dic3—24no—
217C3⋊Dic3—42no—
218C3⋊Dic3—42no—
219C25—91no—
220C23×C4—91no—
221C23×C4—91no—
222C23×C4—91no—
223C23×C4C2×C3⋊D311yescharacteristic
224C23×C4C2×C3⋊D311yescharacteristic
225C23×C4C2×C3⋊D311yescharacteristic
226C2×C4⋊C4—24no—
227C2×C4⋊C4—94no—
228C2×C4⋊C4—94no—
229C2×C4⋊C4—184no—
230C2×C4⋊C4—184no—
231C2×C4⋊C4C2×C3⋊D314yescomplemented
232C2×C22⋊C4—94no—
233C2×C22⋊C4—94no—
234C2×C22⋊C4—94no—
235C2×C22⋊C4—184no—
236C2×C22⋊C4—184no—
237C2×C22⋊C4—184no—
238#95—94no—
239C23×C3C2×D1218yes—
240C23×C3#23518yes—
241C23×C3D3×D418yes—
242C23×C3#23718yes—
243C23×C3D3×Q818yes—
244C23×C3#23918yes—
245C23×C3C2×#6718yes—
246C23×C3C23×D314yes—
247C22×D3—316no—
248C22×D3—632no—
249C22×D3—632no—
250C22×D3—632no—
251C22×D3—68no—
252C22×D3—68no—
253C22×D3—68no—
254C22×D3—68no—
255C22×D3—68no—
256C22×D3—68no—
257C22×D3—1216no—
258C22×D3—1216no—
259C22×D3—1216no—
260C22×D3—1216no—
261C2×C3×C4—232no—
262C2×C3×C4—232no—
263C2×C3×C4—28no—
264C2×C3×C4—28no—
265C2×C3×C4—28no—
266C2×C3×C4—28no—
267C2×C3×C4—28no—
268C2×C3×C4—28no—
269C2×C3×C4—28no—
270C2×C3×C4—416no—
271C2×C3×C4C2×D12116yes—
272C2×C3×C4C2×#67116yes—
273C2×Dic3—316no—
274C2×Dic3—632no—
275C2×Dic3—68no—
276C2×Dic3—68no—
277C2×Dic3—68no—
278C2×Dic3—68no—
279C2×Dic3—68no—
280C2×Dic3—68no—
281C2×Dic3—68no—
282C2×Dic3—68no—
283C2×Dic3—1216no—
284C2×Dic3—1216no—
285C2×C32#39618yescomplemented
286C2×C32C2×#12111yescharacteristic
287C2×C32C2×#12111yescharacteristic
288C2×C32C2×#12111yescharacteristic
289C2×C32C2×C22⋊Q811yescharacteristic
290C2×C32C2×C22⋊Q811yescharacteristic
291C2×C32C2×C22⋊Q811yescharacteristic
292C2×C32C2×#12611yescharacteristic
293C3⋊D3—44no—
294C24—92no—
295C24—94no—
296C24—182no—
297C24—182no—
298C24—182no—
299C24—182no—
300C24—182no—
301C24—182no—
302C24C22×C3⋊D311yescharacteristic
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—92no—
311C22×C4—94no—
312C22×C4—92no—
313C22×C4—92no—
314C22×C4—182no—
315C22×C4—182no—
316C22×C4—182no—
317C22×C4—182no—
318C22×C4—182no—
319C22×C4—182no—
320C22×C4—182no—
321C22×C4—182no—
322C22×C4C4⋊(C3⋊D3)14yes—
323C22×C4#63814yes—
324C22×C4C22×C3⋊D312yes—
325C22×C4C22×C3⋊D312yes—
326C22×C4C22×C3⋊D312yes—
327C4⋊C4—28no—
328C4⋊C4—188no—
329C4⋊C4—188no—
330C22⋊C4—188no—
331C22⋊C4—188no—
332C22⋊C4—188no—
333C22×C3#895116yes—
334C22×C3#896116yes—
335C22×C3#897116yes—
336C22×C3#898116yes—
337C22×C3#930116yes—
338C22×C3#939116yes—
339C22×C3#946116yes—
340C22×C3C22×D1214yes—
341C22×C3C2×#23514yes—
342C22×C3C2×D3×D414yes—
343C22×C3C2×#23714yes—
344C22×C3C2×D3×Q814yes—
345C22×C3C2×#23914yes—
346C22×C3C22×#6714yes—
347C2×D3—616no—
348C2×D3—616no—
349C2×D3—616no—
350C2×D3—1264no—
351C2×D3—128no—
352C2×D3—128no—
353C2×D3—128no—
354C2×D3—128no—
355C3×C4—216no—
356C3×C4—216no—
357C3×C4—48no—
358Dic3—616no—
359Dic3—128no—
360Dic3—128no—
361C32C2×#39611yescharacteristic, complemented, Sylow
362C23—94no—
363C23—182no—
364C23—182no—
365C23—182no—
366C23—182no—
367C23—188no—
368C23—188no—
369C23—182no—
370C23—182no—
371C23—188no—
372C23—364no—
373C23—364no—
374C23—364no—
375C23—364no—
376C23C2×C4⋊(C3⋊D3)12yes—
377C23#382812yes—
378C23D4×C3⋊D312yes—
379C23#383012yes—
380C23Q8×C3⋊D312yes—
381C23#383212yes—
382C23C2×#63812yes—
383C23C23×C3⋊D311yescharacteristic
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—28no—
389C2×C4—28no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—44no—
394C2×C4—94no—
395C2×C4—182no—
396C2×C4—188no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—182no—
400C2×C4—182no—
401C2×C4—182no—
402C2×C4—182no—
403C2×C4—182no—
404C2×C4—364no—
405C2×C4—364no—
406C2×C4C2×C4⋊(C3⋊D3)14yes—
407C2×C4C2×#63814yes—
408C2×C3#4994132yescomplemented
409C2×C3C2×#89514yes—
410C2×C3C2×#89614yes—
411C2×C3C2×#89714yes—
412C2×C3C2×#89814yes—
413C2×C3C2×#93014yes—
414C2×C3C2×#93914yes—
415C2×C3C2×#94614yes—
416D3—1216no—
417C22—184no—
418C22—184no—
419C22—184no—
420C22—362no—
421C22—362no—
422C22—362no—
423C22—362no—
424C22—3616no—
425C22#6410414yes—
426C22#6410514yes—
427C22#6410614yes—
428C22#6410714yes—
429C22#6413914yes—
430C22#6414814yes—
431C22#6415514yes—
432C22C22×C4⋊(C3⋊D3)11yescharacteristic
433C22C2×#382811yescharacteristic
434C22C2×D4×C3⋊D311yescharacteristic
435C22C2×#383011yescharacteristic
436C22C2×Q8×C3⋊D311yescharacteristic
437C22C2×#383211yescharacteristic
438C22C22×#63811yescharacteristic
439C4—24no—
440C4—24no—
441C4—42no—
442C4—184no—
443C4—362no—
444C4—362no—
445C3C2×#499414yescomplemented
446C2—364no—
447C2#1059269318yesdirect product factor
448C2C2×#6410411yescharacteristic
449C2C2×#6410511yescharacteristic
450C2C2×#6410611yescharacteristic
451C2C2×#6410711yescharacteristic
452C2C2×#6413911yescharacteristic
453C2C2×#6414811yescharacteristic
454C2C2×#6415511yescharacteristic
subgroupG/H
centerC24C22×C3⋊D3
commutator, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC22×C32×C4⋊C4C2
socleC24×C32C23
prime radicalC24×C3⋊D3C22
hypercenterC22×C4⋊C4C3⋊D3
hypocenterC32C2×#396
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4⋊C4C2semidirect
5. C22×C4⋊(C3⋊Dic3)C2semidirect
6. C22×#3750C2semidirect
7. C2×#63658C2semidirect
8. #10592693C2direct (N × H)
18. C2×C32×C4⋊C4C22semidirect
26. C2×C4⋊(C3⋊Dic3)C22semidirect
28. C2×#3750C22semidirect
29. #63658C22semidirect
30. C22×C3×C4⋊C4D3semidirect
86. C2×C3×C4⋊C4C2×D3semidirect
146. C22×C4⋊C4C3⋊D3semidirect
231. C2×C4⋊C4C2×C3⋊D3semidirect
285. C2×C32#396semidirect
361. C32C2×#396semidirect
408. C2×C3#4994semidirect
445. C3C2×#4994semidirect
447. C2#10592693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C22×#37522
C22×C4⋊(C3⋊Dic3)2
C22×#37502
C2×#636582
#105926932
C2×#49943