Finite Group Databasebeta

← C2×#10592689 #11801404

Subgroups — C2×#10592689 #11801404

Order 1152.

2784 conjugacy classes of subgroups.

The subgroup lattice has 450 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⋊Dic3C211yesmaximal, characteristic, complemented
6C2×#63658C211yesmaximal, characteristic, complemented
7C2×#63658C211yesmaximal, characteristic, complemented
8#10592689C218yesmaximal, direct product factor
9C2×#4990—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×#3752C418yescomplemented
22C2×#3752C2214yes—
23C2×#3752C2214yes—
24C2×#3752C2214yes—
25C2×C4×C3⋊Dic3—24no—
26C2×C4×C3⋊Dic3C2214yescomplemented
27#63658C2214yescomplemented
28#63658C2214yescomplemented
29C22×C3×C4⋊C4D314yescomplemented
30C22×(C2×D3)⋊C4—34no—
31C22×(C2×D3)⋊C4—34no—
32C22×(C2×D3)⋊C4—34no—
33C22×C4×Dic3—34no—
34C2×C3⋊#95—34no—
35C2×C3⋊#95—34no—
36#4990—332no—
37C24×C32C2311yescharacteristic
38C23×C3⋊D3—22no—
39C23×C3⋊D3—22no—
40C23×C3⋊D3—22no—
41C23×C3⋊D3—22no—
42C23×C3⋊D3—22no—
43C23×C3⋊D3—22no—
44C23×C3⋊D3C2×C414yes—
45C23×C3⋊D3C2312yes—
46C22×C32×C4—22no—
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×C4C2×C414yes—
54C22×C32×C4D414yes—
55C22×C32×C4C2312yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2312yes—
58C22×C3⋊Dic3—22no—
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⋊Dic3C2×C414yes—
66C22×C3⋊Dic3D414yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C32×C4⋊C4—28no—
71#3752—28no—
72#3752—28no—
73#3752C2×C4116yescomplemented
74C4×C3⋊Dic3—28no—
75C2×#388—91noSylow
76C24×D3—34no—
77C23×C3×C4C2×D314yes—
78C23×C3×C4C2×D314yes—
79C23×C3×C4C2×D314yes—
80C23×Dic3—34no—
81C23×Dic3—34no—
82C23×Dic3—34no—
83C2×C3×C4⋊C4—216no—
84C2×C3×C4⋊C4C2×D3116yescomplemented
85C2×(C2×D3)⋊C4—332no—
86C2×(C2×D3)⋊C4—316no—
87C2×(C2×D3)⋊C4—316no—
88C2×(C2×D3)⋊C4—316no—
89C2×(C2×D3)⋊C4—616no—
90C2×(C2×D3)⋊C4—616no—
91C2×C4×Dic3—316no—
92C2×C4×Dic3—616no—
93C3⋊#95—316no—
94C3⋊#95—316no—
95C23×C32C22×C412yes—
96C23×C32C2×D412yes—
97C23×C32C2×D412yes—
98C23×C32#4112yes—
99C23×C32#4112yes—
100C23×C32#4112yes—
101C23×C32#4112yes—
102C23×C32C2411yescharacteristic
103C22×C3⋊D3—28no—
104C22×C3⋊D3—28no—
105C22×C3⋊D3—28no—
106C22×C3⋊D3—22no—
107C22×C3⋊D3—22no—
108C22×C3⋊D3—22no—
109C22×C3⋊D3—22no—
110C22×C3⋊D3—22no—
111C22×C3⋊D3—22no—
112C22×C3⋊D3—44no—
113C22×C3⋊D3—44no—
114C22×C3⋊D3—44no—
115C22×C3⋊D3—44no—
116C22×C3⋊D3C22×C414yes—
117C2×C32×C4—28no—
118C2×C32×C4—28no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—44no—
127C2×C32×C4C22×C414yes—
128C2×C32×C4C2×D414yes—
129C2×C3⋊Dic3—28no—
130C2×C3⋊Dic3—28no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—44no—
139C2×C3⋊Dic3C22×C414yes—
140C2×C3⋊Dic3C2×D414yes—
141C22×C4⋊C4C3⋊D311yescharacteristic, complemented
142C22×C22⋊C4—91no—
143C22×C22⋊C4—91no—
144C22×C22⋊C4—91no—
145C22×C42—91no—
146#388—98no—
147C2×#95—91no—
148C2×#95—91no—
149C24×C3C22×D314yes—
150C23×D3—316no—
151C23×D3—38no—
152C23×D3—68no—
153C23×D3—68no—
154C23×D3—68no—
155C23×D3—68no—
156C23×D3—68no—
157C23×D3—68no—
158C22×C3×C4—28no—
159C22×C3×C4—28no—
160C22×C3×C4—28no—
161C22×C3×C4—28no—
162C22×C3×C4—28no—
163C22×C3×C4—28no—
164C22×C3×C4—28no—
165C22×C3×C4C4×D3116yes—
166C22×C3×C4#67116yes—
167C22×C3×C4C22×D318yes—
168C22×C3×C4C22×D318yes—
169C22×C3×C4C22×D318yes—
170C22×Dic3—316no—
171C22×Dic3—316no—
172C22×Dic3—38no—
173C22×Dic3—38no—
174C22×Dic3—38no—
175C22×Dic3—68no—
176C22×Dic3—68no—
177C22×Dic3—68no—
178C22×Dic3—68no—
179C22×Dic3—68no—
180C22×Dic3—68no—
181C22×Dic3—68no—
182C3×C4⋊C4—232no—
183(C2×D3)⋊C4—364no—
184(C2×D3)⋊C4—632no—
185(C2×D3)⋊C4—632no—
186C4×Dic3—632no—
187C22×C32#11714yes—
188C22×C32C4×D414yes—
189C22×C32C4×D414yes—
190C22×C32#12114yes—
191C22×C32#12314yes—
192C22×C32#12414yes—
193C22×C32#12614yes—
194C22×C32C23×C411yescharacteristic
195C22×C32C22×D411yescharacteristic
196C22×C32C22×D411yescharacteristic
197C22×C32C2×#4111yescharacteristic
198C22×C32C2×#4111yescharacteristic
199C22×C32C2×#4111yescharacteristic
200C22×C32C2×#4111yescharacteristic
201C2×C3⋊D3—24no—
202C2×C3⋊D3—24no—
203C2×C3⋊D3—24no—
204C2×C3⋊D3—42no—
205C2×C3⋊D3—42no—
206C2×C3⋊D3—42no—
207C2×C3⋊D3—42no—
208C2×C3⋊D3—416no—
209C32×C4—24no—
210C32×C4—24no—
211C32×C4—42no—
212C3⋊Dic3—24no—
213C3⋊Dic3—24no—
214C3⋊Dic3—42no—
215C25—91no—
216C23×C4—91no—
217C23×C4—91no—
218C23×C4—91no—
219C23×C4C2×C3⋊D311yescharacteristic
220C23×C4C2×C3⋊D311yescharacteristic
221C23×C4C2×C3⋊D311yescharacteristic
222C2×C4⋊C4—24no—
223C2×C4⋊C4C2×C3⋊D314yescomplemented
224C2×C22⋊C4—98no—
225C2×C22⋊C4—94no—
226C2×C22⋊C4—94no—
227C2×C22⋊C4—94no—
228C2×C22⋊C4—184no—
229C2×C22⋊C4—184no—
230C2×C42—94no—
231C2×C42—184no—
232#95—94no—
233#95—94no—
234C23×C3C2×C4×D318yes—
235C23×C3#23518yes—
236C23×C3D3×D418yes—
237C23×C3#23718yes—
238C23×C3#23918yes—
239C23×C3#23918yes—
240C23×C3C2×#6718yes—
241C23×C3C23×D314yes—
242C22×D3—316no—
243C22×D3—632no—
244C22×D3—632no—
245C22×D3—632no—
246C22×D3—68no—
247C22×D3—68no—
248C22×D3—68no—
249C22×D3—68no—
250C22×D3—68no—
251C22×D3—68no—
252C22×D3—1216no—
253C22×D3—1216no—
254C22×D3—1216no—
255C22×D3—1216no—
256C2×C3×C4—232no—
257C2×C3×C4—232no—
258C2×C3×C4—28no—
259C2×C3×C4—28no—
260C2×C3×C4—28no—
261C2×C3×C4—28no—
262C2×C3×C4—28no—
263C2×C3×C4—28no—
264C2×C3×C4—28no—
265C2×C3×C4—416no—
266C2×C3×C4C2×C4×D3116yes—
267C2×C3×C4C2×#67116yes—
268C2×Dic3—316no—
269C2×Dic3—316no—
270C2×Dic3—632no—
271C2×Dic3—632no—
272C2×Dic3—68no—
273C2×Dic3—68no—
274C2×Dic3—68no—
275C2×Dic3—68no—
276C2×Dic3—68no—
277C2×Dic3—68no—
278C2×Dic3—68no—
279C2×Dic3—1216no—
280C2×C32#38818yescomplemented
281C2×C32C2×#11711yescharacteristic
282C2×C32C2×C4×D411yescharacteristic
283C2×C32C2×C4×D411yescharacteristic
284C2×C32C2×#12111yescharacteristic
285C2×C32C2×#12311yescharacteristic
286C2×C32C2×#12411yescharacteristic
287C2×C32C2×#12611yescharacteristic
288C3⋊D3—44no—
289C24—92no—
290C24—94no—
291C24—182no—
292C24—182no—
293C24—182no—
294C24—182no—
295C24—182no—
296C24—182no—
297C24C22×C3⋊D311yescharacteristic
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—92no—
306C22×C4—92no—
307C22×C4—94no—
308C22×C4—94no—
309C22×C4—92no—
310C22×C4—182no—
311C22×C4—182no—
312C22×C4—182no—
313C22×C4—182no—
314C22×C4—182no—
315C22×C4—182no—
316C22×C4—182no—
317C22×C4C4×C3⋊D314yes—
318C22×C4#63814yes—
319C22×C4C22×C3⋊D312yes—
320C22×C4C22×C3⋊D312yes—
321C22×C4C22×C3⋊D312yes—
322C4⋊C4—28no—
323C22⋊C4—916no—
324C22⋊C4—188no—
325C22⋊C4—188no—
326C42—188no—
327C22×C3#892116yes—
328C22×C3#893116yes—
329C22×C3#894116yes—
330C22×C3#898116yes—
331C22×C3C4×#67116yes—
332C22×C3#939116yes—
333C22×C3#947116yes—
334C22×C3C22×C4×D314yes—
335C22×C3C2×#23514yes—
336C22×C3C2×D3×D414yes—
337C22×C3C2×#23714yes—
338C22×C3C2×#23914yes—
339C22×C3C2×#23914yes—
340C22×C3C22×#6714yes—
341C2×D3—616no—
342C2×D3—616no—
343C2×D3—616no—
344C2×D3—1264no—
345C2×D3—128no—
346C2×D3—128no—
347C2×D3—128no—
348C2×D3—128no—
349C3×C4—216no—
350C3×C4—216no—
351C3×C4—48no—
352Dic3—616no—
353Dic3—616no—
354Dic3—128no—
355C32C2×#38811yescharacteristic, complemented, Sylow
356C23—94no—
357C23—188no—
358C23—188no—
359C23—182no—
360C23—182no—
361C23—182no—
362C23—182no—
363C23—182no—
364C23—182no—
365C23—188no—
366C23—364no—
367C23—364no—
368C23—364no—
369C23—364no—
370C23C2×C4×C3⋊D312yes—
371C23#382812yes—
372C23D4×C3⋊D312yes—
373C23#383012yes—
374C23#383212yes—
375C23#383212yes—
376C23C2×#63812yes—
377C23C23×C3⋊D311yescharacteristic
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—28no—
383C2×C4—28no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—44no—
388C2×C4—94no—
389C2×C4—94no—
390C2×C4—188no—
391C2×C4—182no—
392C2×C4—188no—
393C2×C4—182no—
394C2×C4—182no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—182no—
398C2×C4—182no—
399C2×C4—364no—
400C2×C4C2×C4×C3⋊D314yes—
401C2×C4C2×#63814yes—
402C2×C3#4990132yescomplemented
403C2×C3C2×#89214yes—
404C2×C3C2×#89314yes—
405C2×C3C2×#89414yes—
406C2×C3C2×#89814yes—
407C2×C3C2×C4×#6714yes—
408C2×C3C2×#93914yes—
409C2×C3C2×#94714yes—
410D3—1216no—
411C22—184no—
412C22—184no—
413C22—184no—
414C22—362no—
415C22—362no—
416C22—3616no—
417C22—362no—
418C22—362no—
419C22#6410114yes—
420C22#6410214yes—
421C22#6410314yes—
422C22#6410714yes—
423C22C4×#63814yes—
424C22#6414814yes—
425C22#6415614yes—
426C22C22×C4×C3⋊D311yescharacteristic
427C22C2×#382811yescharacteristic
428C22C2×D4×C3⋊D311yescharacteristic
429C22C2×#383011yescharacteristic
430C22C2×#383211yescharacteristic
431C22C2×#383211yescharacteristic
432C22C22×#63811yescharacteristic
433C4—24no—
434C4—24no—
435C4—42no—
436C4—184no—
437C4—184no—
438C4—362no—
439C3C2×#499014yescomplemented
440C2—364no—
441C2#1059268918yesdirect product factor
442C2C2×#6410111yescharacteristic
443C2C2×#6410211yescharacteristic
444C2C2×#6410311yescharacteristic
445C2C2×#6410711yescharacteristic
446C2C2×C4×#63811yescharacteristic
447C2C2×#6414811yescharacteristic
448C2C2×#6415611yescharacteristic
subgroupG/H
centerC24C22×C3⋊D3
commutatorC22×C32C23×C4
FrattiniC23C23×C3⋊D3
FittingC22×C32×C4⋊C4C2
socleC24×C32C23
prime radicalC24×C3⋊D3C22
cosocleC23×C32C24
hypercenterC22×C4⋊C4C3⋊D3
hypocenterC32C2×#388
LCSG ▷ C22×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⋊Dic3C2semidirect
6. C2×#63658C2semidirect
7. C2×#63658C2semidirect
8. #10592689C2direct (N × H)
18. C2×C32×C4⋊C4C22semidirect
21. C2×#3752C4semidirect
26. C2×C4×C3⋊Dic3C22semidirect
27. #63658C22semidirect
28. #63658C22semidirect
29. C22×C3×C4⋊C4D3semidirect
73. #3752C2×C4semidirect
84. C2×C3×C4⋊C4C2×D3semidirect
141. C22×C4⋊C4C3⋊D3semidirect
223. C2×C4⋊C4C2×C3⋊D3semidirect
280. C2×C32#388semidirect
355. C32C2×#388semidirect
402. C2×C3#4990semidirect
439. C3C2×#4990semidirect
441. C2#10592689direct (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⋊Dic32
C2×#636582
#105926892
C2×#49903