Finite Group Databasebeta

← #11784737

Subgroups — #11784737

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×C3×#835C212yesmaximal, complemented
3#10591325C211yesmaximal, characteristic
4C2×#63567C212yesmaximal, complemented
5C2×#63557C211yesmaximal, characteristic
6#70266—32nomaximal
7C22×C32×Q8C2211yescharacteristic
8C2×Q8×C3⋊D3—24no—
9C2×Q8×C3⋊D3—22no—
10C2×Q8×C3⋊D3—24no—
11C2×Q8×C3⋊D3C414yescomplemented
12C22×C4×C3⋊D3—21no—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#634—21no—
15C22×#634C2211yescharacteristic
16C2×C3×C4⋊Dic3C2212yes—
17C22×C3×C3⋊C8C2212yes—
18C2×#3722—21no—
19C3×#835—24no—
20#63579—21no—
21#63567—24no—
22#63557—22no—
23C22×D3×Q8—32no—
24C22×D3×Q8—61no—
25C2×C3×#103—32no—
26C2×#835D312yescomplemented
27C2×(C2×D3)⋊C8—32no—
28C2×#816—32no—
29#4987—32no—
30C2×#810—32no—
31C23×C3⋊D3D411yescharacteristic
32C2×C32×Q8—21no—
33C2×C32×Q8—22no—
34C2×C32×Q8C2×C412yes—
35C2×C32×Q8D414yes—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40Q8×C3⋊D3—216no—
41Q8×C3⋊D3—28no—
42Q8×C3⋊D3—28no—
43C2×C4×C3⋊D3—28no—
44C2×C4×C3⋊D3—24no—
45C2×C4×C3⋊D3—22no—
46C2×C4×C3⋊D3—22no—
47C2×C4×C3⋊D3C2×C412yes—
48C2×C4×C3⋊D3D412yes—
49C2×#634—28no—
50C2×#634—22no—
51C2×#634—21no—
52C2×#634—24no—
53C2×#634C2×C412yes—
54C2×#634D414yes—
55C22×C3×Dic3—22no—
56C3×C4⋊Dic3—22no—
57C3×C4⋊Dic3—22no—
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8—22no—
60C2×C3×C3⋊C8—22no—
61#3722—42no—
62#1787—91noSylow
63C22×C3×Q8—21no—
64C22×C3×Q8C2×D312yes—
65C2×D3×Q8—38no—
66C2×D3×Q8—64no—
67C2×D3×Q8—64no—
68C2×D3×Q8—64no—
69C2×D3×Q8—64no—
70C2×D3×Q8—64no—
71C2×D3×Q8—68no—
72C2×D3×Q8—68no—
73C2×D3×Q8—64no—
74C2×D3×Q8—64no—
75C22×C4×D3—32no—
76C22×C4×D3—61no—
77C22×C4×D3—62no—
78C22×C4×D3—62no—
79C22×Dic6—32no—
80C22×Dic6—61no—
81C22×Dic6—62no—
82C22×Dic6—62no—
83C22×C3×C8—32no—
84C2×C3×C4⋊C4—32no—
85C2×(C2×D3)⋊C4—62no—
86C2×C4⋊Dic3C2×D312yes—
87C22×C3⋊C8C2×D312yes—
88C3×#103—64no—
89#835—24no—
90C3⋊#95—62no—
91(C2×D3)⋊C8—64no—
92#816—64no—
93#810—64no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—22no—
96C22×C3⋊D3—22no—
97C22×C3⋊D3C22⋊C412yes—
98C22×C3⋊D3SD1612yes—
99C22×C3⋊D3Q1612yes—
100C32×Q8—22no—
101C32×Q8—24no—
102C32×Q8C22⋊C414yescomplemented
103C2×C32×C4—22no—
104C2×C32×C4—24no—
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D412yes—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3C22⋊C412yes—
113C4×C3⋊D3—216no—
114C4×C3⋊D3—22no—
115C4×C3⋊D3—22no—
116C4×C3⋊D3—24no—
117#634—216no—
118#634—22no—
119#634—24no—
120#634C22⋊C414yescomplemented
121C2×C3×Dic3—42no—
122C2×C3×Dic3—42no—
123C2×C3×Dic3—42no—
124C3×C3⋊C8—42no—
125C23×Q8—91no—
126C2×#103—32no—
127C2×#103—92no—
128C2×C22⋊C8—91no—
129#380—91no—
130C23×D3—32no—
131C23×D3—61no—
132C2×C3×Q8—22no—
133C2×C3×Q8—24no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8—22no—
138C2×C3×Q8—24no—
139C2×C3×Q8C4×D314yes—
140C2×C3×Q8D1214yes—
141C2×C3×Q8#6714yes—
142C22×C3×C4—22no—
143C22×C3×C4—22no—
144C22×C3×C4—21no—
145C22×C3×C4—62no—
146C22×C3×C4C22×D312yes—
147C22×Dic3—22no—
148C22×Dic3—32no—
149C22×Dic3—61no—
150C22×Dic3—62no—
151C22×Dic3—62no—
152D3×Q8—616no—
153D3×Q8—616no—
154D3×Q8—632no—
155D3×Q8—616no—
156D3×Q8—616no—
157D3×Q8—616no—
158D3×Q8—616no—
159C2×C4×D3—34no—
160C2×C4×D3—34no—
161C2×C4×D3—62no—
162C2×C4×D3—62no—
163C2×C4×D3—68no—
164C2×C4×D3—68no—
165C2×C4×D3—616no—
166C2×C4×D3—68no—
167C2×C4×D3—68no—
168C2×C4×D3—64no—
169C2×C4×D3—64no—
170C2×C4×D3—62no—
171C2×C4×D3—62no—
172C2×C4×D3—62no—
173C2×C4×D3—62no—
174C2×Dic6—34no—
175C2×Dic6—34no—
176C2×Dic6—34no—
177C2×Dic6—62no—
178C2×Dic6—64no—
179C2×Dic6—68no—
180C2×Dic6—68no—
181C2×Dic6—616no—
182C2×Dic6—68no—
183C2×Dic6—68no—
184C2×Dic6—64no—
185C2×Dic6—62no—
186C2×Dic6—62no—
187C2×Dic6—62no—
188C2×Dic6—62no—
189C2×C3×C8—62no—
190C2×C3×C8—62no—
191C2×C3×C8—62no—
192C3×C4⋊C4—62no—
193C3×C4⋊C4—62no—
194(C2×D3)⋊C4—124no—
195C4⋊Dic3—22no—
196C4⋊Dic3—22no—
197C2×C3⋊C8—22no—
198C2×C3⋊C8—22no—
199C2×C3⋊C8—22no—
200C22×C32C2×C22⋊C411yescharacteristic
201C22×C32#12012yes—
202C22×C32C2×SD1611yescharacteristic
203C22×C32C2×Q1611yescharacteristic
204C22×C32#13712yes—
205C2×C3⋊D3—22no—
206C2×C3⋊D3—22no—
207C2×C3⋊D3—24no—
208C2×C3⋊D3—24no—
209C2×C3⋊D3#10314yescomplemented
210C32×C4—24no—
211C32×C4C2×C22⋊C411yescharacteristic
212C32×C4C2×C22⋊C411yescharacteristic
213C32×C4#12012yes—
214C3⋊Dic3—22no—
215C3⋊Dic3—24no—
216C3×Dic3—82no—
217C22×Q8—94no—
218C22×Q8—91no—
219C22×Q8—181no—
220C22×Q8—182no—
221C22×Q8—184no—
222C22×Q8—184no—
223C22×Q8D3211yescharacteristic
224C23×C4—91no—
225C23×C4—181no—
226C22×C8—32no—
227C2×C4⋊C4—32no—
228C2×C22⋊C4—181no—
229#103—64no—
230#103—184no—
231C22⋊C8—182no—
232#95—181no—
233C23×C3—21no—
234C23×C3D3×D412yes—
235C22×D3—34no—
236C22×D3—34no—
237C22×D3—34no—
238C22×D3—62no—
239C22×D3—62no—
240C22×D3—62no—
241C22×D3—64no—
242C22×D3—64no—
243C22×D3—62no—
244C22×D3—62no—
245C22×D3—62no—
246C22×D3—62no—
247C3×Q8—24no—
248C3×Q8—28no—
249C3×Q8—24no—
250C3×Q8—24no—
251C3×Q8—24no—
252C3×Q8—24no—
253C3×Q8(C2×D3)⋊C418yescomplemented
254C2×C3×C4—24no—
255C2×C3×C4—28no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—24no—
259C2×C3×C4—21no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—21no—
263C2×C3×C4—122no—
264C2×C3×C4—122no—
265C2×C3×C4—122no—
266C2×C3×C4C2×C4×D312yes—
267C2×C3×C4C2×D1212yes—
268C2×C3×C4D3×D412yes—
269C2×C3×C4D3×D412yes—
270C2×C3×C4D3×D412yes—
271C2×C3×C4C2×#6712yes—
272C2×Dic3—34no—
273C2×Dic3—42no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276C2×Dic3—62no—
277C2×Dic3—64no—
278C2×Dic3—64no—
279C2×Dic3—68no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—62no—
283C2×Dic3—64no—
284C2×Dic3—62no—
285C4×D3—632no—
286C4×D3—632no—
287C4×D3—64no—
288C4×D3—64no—
289C4×D3—68no—
290C4×D3—64no—
291C4×D3—64no—
292C4×D3—64no—
293C4×D3—64no—
294Dic6—38no—
295Dic6—64no—
296Dic6—632no—
297Dic6—632no—
298Dic6—64no—
299Dic6—68no—
300Dic6—64no—
301Dic6—64no—
302Dic6—64no—
303C3×C8—122no—
304C3⋊C8—42no—
305C2×C32#37911yescharacteristic
306C2×C32C2×#10311yescharacteristic
307C2×C32#41911yescharacteristic
308C2×C32#44812yes—
309C2×C32#45112yes—
310C3⋊D3—24no—
311C24—91no—
312C2×Q8—21no—
313C2×Q8—22no—
314C2×Q8—92no—
315C2×Q8—94no—
316C2×Q8—184no—
317C2×Q8—188no—
318C2×Q8—188no—
319C2×Q8—1816no—
320C2×Q8—188no—
321C2×Q8—182no—
322C2×Q8—181no—
323C2×Q8#62412yes—
324C2×Q8#62614yes—
325C22×C4—21no—
326C22×C4—62no—
327C22×C4—91no—
328C22×C4—92no—
329C22×C4—92no—
330C22×C4—184no—
331C22×C4—188no—
332C22×C4—181no—
333C22×C4—182no—
334C22×C4—182no—
335C22×C4C2×D3211yescharacteristic
336C2×C8—62no—
337C2×C8—62no—
338C2×C8—62no—
339C4⋊C4—62no—
340C4⋊C4—62no—
341C22⋊C4—362no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—22no—
345C22×C3—21no—
346C22×C3—22no—
347C22×C3D3×C22⋊C412yes—
348C22×C3#88212yes—
349C22×C3D3×SD1612yes—
350C22×C3#91512yes—
351C22×C3D3×Q1612yes—
352C22×C3#91812yes—
353C22×C3#93712yes—
354C2×D3—38no—
355C2×D3—64no—
356C2×D3—64no—
357C2×D3—64no—
358C2×D3—68no—
359C2×D3—68no—
360C2×D3—64no—
361C2×D3—64no—
362C2×D3—64no—
363C2×D3—64no—
364C2×D3—64no—
365C2×D3—64no—
366C3×C4—28no—
367C3×C4—28no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—22no—
371C3×C4—242no—
372C3×C4D3×C22⋊C412yes—
373C3×C4#88212yes—
374C3×C4C2×(C2×D3)⋊C412yes—
375C3×C4#93712yes—
376Dic3—64no—
377Dic3—68no—
378Dic3—68no—
379Dic3—64no—
380Dic3—82no—
381C32#178711yescharacteristic, complemented, Sylow
382C23—92no—
383C23—92no—
384C23—92no—
385C23—182no—
386C23—182no—
387C23#381111yescharacteristic
388Q8—22no—
389Q8—24no—
390Q8—94no—
391Q8—1816no—
392Q8—182no—
393Q8—184no—
394Q8#372214yescomplemented
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—92no—
398C2×C4—122no—
399C2×C4—122no—
400C2×C4—122no—
401C2×C4—1816no—
402C2×C4—182no—
403C2×C4—182no—
404C2×C4—184no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—184no—
408C2×C4C2×#62411yescharacteristic
409C2×C4C2×#62612yes—
410C2×C4#381112yes—
411C2×C4#381111yescharacteristic
412C8—122no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3D3×#10312yes—
419C2×C3#480212yes—
420C2×C3#480612yes—
421C2×C3#480912yes—
422C2×C3#495512yes—
423C2×C3#517012yes—
424C2×C3#518612yes—
425D3—68no—
426D3—68no—
427C22—94no—
428C22—182no—
429C22—184no—
430C22—184no—
431C22—182no—
432C22#6394011yescharacteristic
433C22#6394411yescharacteristic
434C22#6395112yes—
435C22#6397411yescharacteristic
436C22#6398112yes—
437C4—24no—
438C4—182no—
439C4—184no—
440C4—242no—
441C4C2×#372211yescharacteristic
442C4#6397411yescharacteristic
443C4#6398112yes—
444C3—21no—
445C3#7026612yescomplemented
446C2—184no—
447C2#1059155211yescharacteristic
448C2#1059156211yescharacteristic
449C2#1059159212yes—
450C2#1059160312yes—
451C2#1059171411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1787
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#835C2semidirect
4. C2×#63567C2semidirect
11. C2×Q8×C3⋊D3C4semidirect
26. C2×#835D3semidirect
102. C32×Q8C22⋊C4semidirect
120. #634C22⋊C4semidirect
209. C2×C3⋊D3#103semidirect
253. C3×Q8(C2×D3)⋊C4semidirect
381. C32#1787semidirect
394. Q8#3722semidirect
445. C3#70266semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×C3×#8352
#105913252
C2×#635672
C2×#635572
#702663