Finite Group Databasebeta

← #11808859

Subgroups — #11808859

Order 1152.

1105 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
1C2×C4×#627C212yesmaximal
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4C3×#4932C211yesmaximal, characteristic
5#10591397C212yesmaximal
6#10591351C212yesmaximal
7#10591348C212yesmaximal
8#10591338C212yesmaximal
9C4×Dic3⋊Dic3C212yesmaximal
10#73669—31nomaximal
11#73397—31nomaximal
12C22×#627C2212yes—
13C2×C32×C42C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2212yes—
15C2×C4×C3⋊Dic3C2212yes—
16C2×C3×C4⋊Dic3C2212yes—
17C2×C3×C4×Dic3C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×#3724C2212yes—
21C2×Dic3⋊Dic3C2212yes—
22C2×Dic3⋊Dic3C2212yes—
23C2×Dic3⋊Dic3C2212yes—
24C2×Dic3⋊Dic3C2212yes—
25C4×#627—28no—
26#63658C2211yescharacteristic
27#63658C2211yescharacteristic
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32#63579C2212yes—
33#63579C2212yes—
34C2×C4×Dic6—32no—
35C2×C4×Dic6—32no—
36C3×C4×C4⋊C4—31no—
37C3×#376—31no—
38#4982—32no—
39#4979—32no—
40C4×C4⋊Dic3—31no—
41C4×C4⋊Dic3—31no—
42C4×C4⋊Dic3—32no—
43C4×C4⋊Dic3—61no—
44C4×C4⋊Dic3D311yescharacteristic
45#4932D311yescharacteristic
46C4×Dic3⋊C4—32no—
47#4661—32no—
48#4661—32no—
49#4657—32no—
50#4656—32no—
51#4656—32no—
52#4656—32no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C22×C3×Dic3C2312yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C2×#627—24no—
63C2×#627—24no—
64C2×#627—24no—
65C32×C42Q814yescomplemented
66C4⋊(C3⋊Dic3)—24no—
67C4×C3⋊Dic3—24no—
68C3×C4⋊Dic3—24no—
69C3×C4×Dic3—24no—
70C3×C4×Dic3D414yes—
71C3×C4×Dic3Q814yescomplemented
72#3724—24no—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3—24no—
75Dic3⋊Dic3—24no—
76Dic3⋊Dic3—24no—
77#2399—91noSylow
78C22×Dic6—32no—
79C22×Dic6—32no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C42—21no—
82C2×C3×C42—31no—
83C2×C3×C42—31no—
84C2×C3×C42—32no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3—32no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—32no—
92C2×C4⋊Dic3—32no—
93C2×C4⋊Dic3—62no—
94C2×C4⋊Dic3C2×D312yes—
95C2×Dic3⋊C4—32no—
96C2×Dic3⋊C4—32no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—32no—
100C2×Dic3⋊C4—32no—
101C2×C4×Dic3—32no—
102C2×C4×Dic3—32no—
103C2×C4×Dic3—62no—
104C2×C4×Dic3C2×D312yes—
105C2×C4×Dic3C2×D311yescharacteristic
106C2×C4×Dic3C2×D311yescharacteristic
107C4×Dic6—68no—
108C4×Dic6—68no—
109C3×#95—31no—
110C3×#95—32no—
111C3×#95—32no—
112C3×#95—31no—
113C3⋊#95—31no—
114C3⋊#95—31no—
115C3⋊#95—31no—
116C3⋊#95—31no—
117C3⋊#95—32no—
118C3⋊#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—61no—
122C3⋊#95—61no—
123C3⋊#95C2×D311yescharacteristic
124C3⋊#95C2×D312yes—
125C3⋊#95C2×D311yescharacteristic
126C3⋊#95C2×D312yes—
127C23×C32C2411yescharacteristic
128C2×C32×C4—22no—
129C2×C32×C4—22no—
130C2×C32×C4C2×D412yes—
131C2×C32×C4C2×Q812yes—
132C2×C32×C4C2×Q812yes—
133C2×C32×C4C2×Q812yes—
134C2×C32×C4C2×Q812yes—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3#4114yes—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3C2×D414yes—
151C2×C3×Dic3C2×Q814yes—
152C2×C3×Dic3#4114yes—
153#627—216no—
154C2×C4×Q8—92no—
155#398—92no—
156#398—92no—
157#395—92no—
158#395—92no—
159C4×C4⋊C4—31no—
160C4×C4⋊C4—92no—
161C4×C4⋊C4—91no—
162#376—31no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—32no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×Dic3—32no—
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—32no—
180C22×Dic3—62no—
181C22×Dic3—62no—
182C22×Dic3C22×D312yes—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D312yes—
185C22×Dic3C22×D312yes—
186C2×Dic6—64no—
187C2×Dic6—64no—
188C2×Dic6—64no—
189C2×Dic6—64no—
190C2×Dic6—64no—
191C2×Dic6—64no—
192C3×C4⋊C4—64no—
193C3×C42—24no—
194C3×C42—34no—
195C3×C42—34no—
196C3×C42—64no—
197C3×C42Dic614yescomplemented
198C3×C42Dic614yescomplemented
199C4⋊Dic3—24no—
200C4⋊Dic3—64no—
201C4⋊Dic3—64no—
202C4⋊Dic3—64no—
203C4⋊Dic3—64no—
204C4⋊Dic3—68no—
205C4⋊Dic3—64no—
206C4⋊Dic3—64no—
207Dic3⋊C4—64no—
208Dic3⋊C4—64no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212Dic3⋊C4—64no—
213C4×Dic3—24no—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C4×Dic3—124no—
217C4×Dic3Dic614yescomplemented
218C4×Dic3D1214yes—
219C22×C32C22×D411yescharacteristic
220C22×C32C22×Q811yescharacteristic
221C22×C32C22×Q811yescharacteristic
222C22×C32C2×#4112yes—
223C22×C32C2×#4112yes—
224C32×C4—22no—
225C32×C4—22no—
226C32×C4C4⋊Q814yes—
227C3⋊Dic3—24no—
228C3⋊Dic3—42no—
229C3×Dic3—24no—
230C3×Dic3—24no—
231C3×Dic3—24no—
232C3×Dic3—42no—
233C22×Q8—92no—
234C4×Q8—188no—
235C2×C4⋊C4—32no—
236C2×C4⋊C4—92no—
237C2×C4⋊C4—92no—
238C2×C4⋊C4—92no—
239C2×C4⋊C4—92no—
240C2×C4⋊C4—92no—
241C2×C4⋊C4—92no—
242C2×C42—31no—
243C2×C42—31no—
244C2×C42—32no—
245C2×C42—92no—
246C2×C42D3211yescharacteristic
247#95—32no—
248#95—32no—
249#95—31no—
250#95—31no—
251#95—92no—
252#95—92no—
253#95—91no—
254#95—91no—
255C23×C3—21no—
256C23×C3C23×D311yescharacteristic
257C23×C3C23×D311yescharacteristic
258C2×C3×C4—24no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—34no—
269C2×C3×C4—34no—
270C2×C3×C4—34no—
271C2×C3×C4—42no—
272C2×C3×C4—62no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4C2×Dic612yes—
282C2×C3×C4C2×Dic612yes—
283C2×C3×C4C2×Dic612yes—
284C2×C3×C4C2×Dic612yes—
285C2×C3×C4C2×Dic612yes—
286C2×C3×C4C2×Dic612yes—
287C2×C3×C4C2×Dic612yes—
288C2×C3×C4C2×D1212yes—
289C2×C3×C4D3×D412yes—
290C2×C3×C4D3×Q812yes—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—22no—
299C2×Dic3—22no—
300C2×Dic3—34no—
301C2×Dic3—34no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—64no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—122no—
315C2×Dic3—122no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318C2×Dic3C2×Dic614yes—
319C2×Dic3C2×D1214yes—
320C2×Dic3#23514yes—
321Dic6—616no—
322Dic6—616no—
323C2×C32#52512yes—
324C2×C32C2×C4⋊Q811yescharacteristic
325C2×C32#53311yescharacteristic
326C2×C32#53311yescharacteristic
327C2×C32#53312yes—
328C2×Q8—184no—
329C2×Q8—184no—
330C2×Q8—184no—
331C22×C4—32no—
332C22×C4—32no—
333C22×C4—32no—
334C22×C4—32no—
335C22×C4—92no—
336C22×C4—92no—
337C22×C4C2×D3211yescharacteristic
338C22×C4C2×D3211yescharacteristic
339C22×C4C2×D3211yescharacteristic
340C4⋊C4—64no—
341C4⋊C4—184no—
342C4⋊C4—184no—
343C4⋊C4—184no—
344C4⋊C4—184no—
345C4⋊C4—184no—
346C4⋊C4—184no—
347C42—34no—
348C42—34no—
349C42—64no—
350C42—184no—
351C42#62714yescomplemented
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—21no—
357C22×C3C22×Dic611yescharacteristic
358C22×C3C22×Dic611yescharacteristic
359C22×C3C22×Dic611yescharacteristic
360C22×C3C22×D1211yescharacteristic
361C22×C3C2×#23512yes—
362C22×C3C2×D3×D411yescharacteristic
363C22×C3C2×D3×Q811yescharacteristic
364C22×C3D3×#4112yes—
365C22×C3D3×#4112yes—
366C22×C3D3×#4112yes—
367C3×C4—24no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—24no—
373C3×C4—42no—
374C3×C4—64no—
375C3×C4—64no—
376C3×C4—64no—
377C3×C4—122no—
378C3×C4#86914yes—
379C3×C4#88814yes—
380Dic3—24no—
381Dic3—24no—
382Dic3—24no—
383Dic3—42no—
384Dic3—64no—
385Dic3—64no—
386Dic3—124no—
387Dic3—124no—
388Dic3—122no—
389Dic3—122no—
390C32#239911yescharacteristic, complemented, Sylow
391C23C22×D3211yescharacteristic
392Q8—1816no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—34no—
396C2×C4—34no—
397C2×C4—34no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—94no—
408C2×C4—182no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4D3×Dic612yes—
414C2×C4D3×D1212yes—
415C2×C4C2×#62712yes—
416C2×C4C2×#62712yes—
417C2×C4C2×#62712yes—
418C2×C3—22no—
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3C2×#86911yescharacteristic
424C2×C3#547011yescharacteristic
425C2×C3C2×#88811yescharacteristic
426C2×C3#551712yes—
427C2×C3#551711yescharacteristic
428C2×C3#551711yescharacteristic
429C2×C3#551711yescharacteristic
430C2×C3#552412yes—
431C2×C3#554712yes—
432C2×C3#557812yes—
433C22C2×D3×Dic611yescharacteristic
434C22C2×D3×D1211yescharacteristic
435C22D3×#23512yes—
436C22#6430612yes—
437C22C22×#62711yescharacteristic
438C4—22no—
439C4—22no—
440C4—64no—
441C4—64no—
442C4—64no—
443C4—122no—
444C4—184no—
445C4—362no—
446C4#6391814yes—
447C3—21no—
448C3#7339711yescharacteristic, complemented
449C3#7366911yescharacteristic, complemented
450C2#1059392612yes—
451C2#1059399712yes—
452C2C2×#6391811yescharacteristic
453C2#1059504911yescharacteristic
454C2#1059505011yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, prime radical, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
65. C32×C42Q8semidirect
71. C3×C4×Dic3Q8semidirect
197. C3×C42Dic6semidirect
198. C3×C42Dic6semidirect
217. C4×Dic3Dic6semidirect
351. C42#627semidirect
390. C32#2399semidirect
448. C3#73397semidirect
449. C3#73669semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C4×C4⋊(C3⋊Dic3)2
C3×C4×C4⋊Dic32
C3×#49322
#105913972
#105913512
#105913482
#105913382
C4×Dic3⋊Dic32
#736693
#733973