Finite Group Databasebeta

← #11784735

Subgroups — #11784735

Order 1152.

1301 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×#3797C211yesmaximal, characteristic
2#10592686C211yesmaximal, characteristic
3C2×C3×#810C212yesmaximal, complemented
4C2×#63566C212yesmaximal, complemented
5C2×#63557C211yesmaximal, characteristic
6#70266—32nomaximal
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C3×Dic6C2212yes—
9C22×#627—21no—
10C22×#624—21no—
11C2×#3797—22no—
12C2×#3797—24no—
13C2×#3797—24no—
14C2×#3797C414yescomplemented
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3×C3⋊C8C2212yes—
19#63658—21no—
20C3×#810—24no—
21#63566—24no—
22#63557—22no—
23C22×D3×Q8—32no—
24C2×C3×#103—32no—
25C2×#835—32no—
26C2×(C2×D3)⋊C8—32no—
27C2×#816—32no—
28#4987—32no—
29#4987—61no—
30C2×#810D312yescomplemented
31C23×C3⋊D3D411yescharacteristic
32C22×C32×C4—21no—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3—21no—
35C22×C3⋊Dic3D411yescharacteristic
36C2×C4×C3⋊D3—22no—
37C2×C4×C3⋊D3—22no—
38C2×C4×C3⋊D3C2×C412yes—
39C2×C4×C3⋊D3D412yes—
40C22×C3×Dic3—22no—
41C2×C3×Dic6—22no—
42C2×C3×Dic6—22no—
43C2×C3×Dic6—22no—
44C2×C3×Dic6C2×C414yes—
45C2×C3×Dic6D414yes—
46C2×C3×Dic6D414yes—
47C2×#627—24no—
48C2×#627—24no—
49C2×#627—24no—
50C2×#624—24no—
51C2×#624—24no—
52C2×#624—24no—
53#3797—216no—
54#3797—216no—
55C32×C4⋊C4—22no—
56#3752—42no—
57C4⋊(C3⋊Dic3)—22no—
58C2×C3×C3⋊C8—22no—
59C2×C3×C3⋊C8—22no—
60C2×C3×C3⋊C8—22no—
61#1787—91noSylow
62C22×C3×Q8—32no—
63C2×D3×Q8—38no—
64C2×D3×Q8—64no—
65C2×D3×Q8—64no—
66C2×D3×Q8—64no—
67C2×D3×Q8—64no—
68C2×D3×Q8—64no—
69C22×C4×D3—32no—
70C22×C4×D3—61no—
71C22×C4×D3—62no—
72C22×Dic6—62no—
73C22×Dic6C2×D312yes—
74C22×C3×C8—32no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4C2×D312yes—
77C2×(C2×D3)⋊C4—62no—
78C2×(C2×D3)⋊C4—62no—
79C2×C4⋊Dic3—32no—
80C2×C4⋊Dic3—61no—
81C22×C3⋊C8C2×D312yes—
82C3×#103—64no—
83#835—64no—
84C3⋊#95—62no—
85C3⋊#95—62no—
86(C2×D3)⋊C8—64no—
87#816—64no—
88#810—24no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3—21no—
91C22×C3⋊D3—21no—
92C22×C3⋊D3—21no—
93C22×C3⋊D3—21no—
94C22×C3⋊D3C22⋊C412yes—
95C22×C3⋊D3SD1612yes—
96C22×C3⋊D3Q1612yes—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C2×D412yes—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D412yes—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3C22⋊C412yes—
110C4×C3⋊D3—24no—
111C4×C3⋊D3—24no—
112C2×C3×Dic3—24no—
113C2×C3×Dic3—24no—
114C2×C3×Dic3—24no—
115C3×Dic6—24no—
116C3×Dic6—24no—
117C3×Dic6—24no—
118C3×Dic6C22⋊C418yescomplemented
119#627—216no—
120#624—216no—
121C3×C3⋊C8—42no—
122C23×Q8—91no—
123C2×#103—32no—
124C2×#103—92no—
125C2×C22⋊C8—91no—
126#380—91no—
127C23×D3—32no—
128C23×D3—61no—
129C2×C3×Q8—34no—
130C2×C3×Q8—34no—
131C2×C3×Q8—34no—
132C2×C3×Q8—62no—
133C2×C3×Q8—62no—
134C2×C3×Q8—62no—
135C22×C3×C4—22no—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—62no—
139C22×C3×C4C22×D312yes—
140C22×Dic3—22no—
141C22×Dic3—32no—
142C22×Dic3—61no—
143C22×Dic3—62no—
144C22×Dic3—62no—
145D3×Q8—616no—
146D3×Q8—616no—
147D3×Q8—616no—
148D3×Q8—616no—
149C2×C4×D3—34no—
150C2×C4×D3—34no—
151C2×C4×D3—62no—
152C2×C4×D3—62no—
153C2×C4×D3—68no—
154C2×C4×D3—68no—
155C2×C4×D3—68no—
156C2×C4×D3—62no—
157C2×C4×D3—62no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×C4×D3—122no—
161C2×C4×D3—122no—
162C2×Dic6—22no—
163C2×Dic6—22no—
164C2×Dic6—22no—
165C2×Dic6—68no—
166C2×Dic6—68no—
167C2×Dic6—68no—
168C2×Dic6C4×D314yes—
169C2×Dic6D1214yes—
170C2×Dic6#6714yes—
171C2×C3×C8—62no—
172C2×C3×C8—62no—
173C2×C3×C8—62no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—42no—
177(C2×D3)⋊C4—124no—
178(C2×D3)⋊C4—124no—
179C4⋊Dic3—62no—
180C4⋊Dic3—62no—
181C4⋊Dic3—122no—
182C2×C3⋊C8—22no—
183C2×C3⋊C8—22no—
184C2×C3⋊C8—22no—
185C22×C32C2×C22⋊C411yescharacteristic
186C22×C32#12011yescharacteristic
187C22×C32#12011yescharacteristic
188C22×C32C2×SD1611yescharacteristic
189C22×C32C2×Q1611yescharacteristic
190C22×C32#13711yescharacteristic
191C22×C32#13711yescharacteristic
192C2×C3⋊D3—22no—
193C2×C3⋊D3—22no—
194C2×C3⋊D3—22no—
195C2×C3⋊D3—22no—
196C2×C3⋊D3—22no—
197C2×C3⋊D3—22no—
198C2×C3⋊D3#10314yescomplemented
199C32×C4—81no—
200C32×C4C2×C22⋊C412yes—
201C32×C4#12012yes—
202C3⋊Dic3—22no—
203C3⋊Dic3—81no—
204C3×Dic3—28no—
205C22×Q8—32no—
206C22×Q8—94no—
207C22×Q8—181no—
208C22×Q8—182no—
209C22×Q8—184no—
210C22×Q8—184no—
211C23×C4—91no—
212C23×C4—181no—
213C22×C8—32no—
214C2×C4⋊C4—91no—
215C2×C4⋊C4D3211yescharacteristic
216C2×C22⋊C4—181no—
217#103—64no—
218#103—184no—
219C22⋊C8—182no—
220#95—181no—
221C23×C3—21no—
222C23×C3D3×D412yes—
223C22×D3—34no—
224C22×D3—34no—
225C22×D3—34no—
226C22×D3—62no—
227C22×D3—62no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—62no—
231C22×D3—62no—
232C22×D3—62no—
233C22×D3—121no—
234C22×D3—121no—
235C22×D3—121no—
236C22×D3—121no—
237C3×Q8—38no—
238C3×Q8—64no—
239C3×Q8—64no—
240C3×Q8—64no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—22no—
245C2×C3×C4—42no—
246C2×C3×C4—42no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—64no—
252C2×C3×C4—64no—
253C2×C3×C4—64no—
254C2×C3×C4C2×C4×D312yes—
255C2×C3×C4C2×D1212yes—
256C2×C3×C4D3×D412yes—
257C2×C3×C4D3×D412yes—
258C2×C3×C4D3×D412yes—
259C2×C3×C4C2×#6712yes—
260C2×Dic3—24no—
261C2×Dic3—24no—
262C2×Dic3—24no—
263C2×Dic3—34no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—121no—
268C2×Dic3—121no—
269C2×Dic3—122no—
270C2×Dic3—122no—
271C2×Dic3—122no—
272C2×Dic3—122no—
273C2×Dic3—122no—
274C2×Dic3—122no—
275C4×D3—632no—
276C4×D3—64no—
277C4×D3—64no—
278C4×D3—64no—
279C4×D3—64no—
280C4×D3—124no—
281C4×D3—124no—
282Dic6—24no—
283Dic6—24no—
284Dic6—24no—
285Dic6—632no—
286Dic6(C2×D3)⋊C418yescomplemented
287C3×C8—122no—
288C3⋊C8—42no—
289C2×C32#37911yescharacteristic
290C2×C32C2×#10311yescharacteristic
291C2×C32#41911yescharacteristic
292C2×C32#44811yescharacteristic
293C2×C32#44811yescharacteristic
294C2×C32#45111yescharacteristic
295C2×C32#45111yescharacteristic
296C3⋊D3—24no—
297C24—91no—
298C2×Q8—34no—
299C2×Q8—34no—
300C2×Q8—34no—
301C2×Q8—62no—
302C2×Q8—62no—
303C2×Q8—62no—
304C2×Q8—184no—
305C2×Q8—184no—
306C2×Q8—184no—
307C2×Q8—1816no—
308C2×Q8—1816no—
309C22×C4—21no—
310C22×C4—62no—
311C22×C4—91no—
312C22×C4—92no—
313C22×C4—92no—
314C22×C4—184no—
315C22×C4—184no—
316C22×C4—184no—
317C22×C4—182no—
318C22×C4—182no—
319C22×C4—181no—
320C22×C4C2×D3211yescharacteristic
321C2×C8—62no—
322C2×C8—62no—
323C2×C8—62no—
324C4⋊C4—22no—
325C4⋊C4—182no—
326C22⋊C4—362no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3D3×C22⋊C412yes—
335C22×C3#88212yes—
336C22×C3D3×SD1612yes—
337C22×C3#91512yes—
338C22×C3D3×Q1612yes—
339C22×C3#91812yes—
340C22×C3#93712yes—
341C2×D3—38no—
342C2×D3—64no—
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—64no—
346C2×D3—64no—
347C2×D3—64no—
348C2×D3—64no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—122no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—122no—
355C3×C4—22no—
356C3×C4—22no—
357C3×C4—68no—
358C3×C4—82no—
359C3×C4—82no—
360C3×C4D3×C22⋊C412yes—
361C3×C4#88212yes—
362C3×C4C2×(C2×D3)⋊C412yes—
363C3×C4#93712yes—
364Dic3—28no—
365Dic3—64no—
366Dic3—122no—
367Dic3—242no—
368Dic3—242no—
369C32#178711yescharacteristic, complemented, Sylow
370C23—92no—
371C23—92no—
372C23—92no—
373C23—181no—
374C23—181no—
375C23—181no—
376C23—181no—
377C23#381111yescharacteristic
378Q8—38no—
379Q8—64no—
380Q8—64no—
381Q8—64no—
382Q8—1816no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—64no—
387C2×C4—64no—
388C2×C4—64no—
389C2×C4—92no—
390C2×C4—1816no—
391C2×C4—181no—
392C2×C4—181no—
393C2×C4—184no—
394C2×C4—184no—
395C2×C4—361no—
396C2×C4—361no—
397C2×C4—361no—
398C2×C4C4×D3211yescharacteristic
399C2×C4D3×D1212yes—
400C2×C4#380211yescharacteristic
401C2×C4D3×#6712yes—
402C8—122no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3D3×#10312yes—
411C2×C3#480212yes—
412C2×C3#480612yes—
413C2×C3#480912yes—
414C2×C3#495512yes—
415C2×C3#517012yes—
416C2×C3#518612yes—
417D3—68no—
418D3—124no—
419C22—94no—
420C22—182no—
421C22—182no—
422C22—182no—
423C22—182no—
424C22—182no—
425C22—182no—
426C22#6392111yescharacteristic
427C22#6392311yescharacteristic
428C22#6393011yescharacteristic
429C22#6393111yescharacteristic
430C22#6394411yescharacteristic
431C22#6394511yescharacteristic
432C22#6398311yescharacteristic
433C4—68no—
434C4—81no—
435C4—182no—
436C4—721no—
437C4D3×(C2×D3)⋊C412yes—
438C4#6392212yes—
439C3—21no—
440C3#7026612yescomplemented
441C2—184no—
442C2#1059060111yescharacteristic
443C2#1059060211yescharacteristic
444C2#1059060511yescharacteristic
445C2#1059060611yescharacteristic
446C2#1059139911yescharacteristic
447C2#1059151811yescharacteristic
448C2#1059165411yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1787
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#810C2semidirect
4. C2×#63566C2semidirect
14. C2×#3797C4semidirect
30. C2×#810D3semidirect
118. C3×Dic6C22⋊C4semidirect
198. C2×C3⋊D3#103semidirect
286. Dic6(C2×D3)⋊C4semidirect
369. C32#1787semidirect
440. C3#70266semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
#105926862
C2×C3×#8102
C2×#635662
C2×#635572
#702663