Finite Group Databasebeta

← #11784625

Subgroups — #11784625

Order 1152.

1669 conjugacy classes of subgroups; only the 164 normal subgroups are shown.

normal subgroups only

This group has 1669 conjugacy classes of subgroups — too many to draw. Only its 164 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic
2C2×C3×#834C212yesmaximal, complemented
3C2×#63581C212yesmaximal, complemented
4#10591697C212yesmaximal, complemented
5#70027—32nomaximal
6C22×C32×D4C2211yescharacteristic
7C22×#638C411yescharacteristic, complemented
8C22×#638C2211yescharacteristic
9C23×C3⋊Dic3C411yescharacteristic, complemented
10C23×C3⋊Dic3C2211yescharacteristic
11C2×#3830—24no—
12C2×#3830—24no—
13C2×#3830—24no—
14C22×C4×C3⋊D3C411yescharacteristic, complemented
15C22×#634C411yescharacteristic, complemented
16C2×C3×#217C2214yes—
17C3×#834—24no—
18#63581—24no—
19#63579—24no—
20C22×#237—32no—
21C22×#237—61no—
22C2×C3×#99—32no—
23C2×#834D312yescomplemented
24C2×#806—34no—
25#4943—34no—
26C24×C32C2×C411yescharacteristic
27C24×C32C2311yescharacteristic
28C23×C3⋊D3C2×C411yescharacteristic
29C2×C32×D4—22no—
30C2×C32×D4—22no—
31C2×C32×D4D414yes—
32C22×C32×C4C2×C411yescharacteristic
33C2×#638—22no—
34C2×#638—22no—
35C2×#638—22no—
36C2×#638—22no—
37C2×#638—22no—
38C2×#638D414yes—
39C22×C3⋊Dic3—22no—
40C22×C3⋊Dic3—22no—
41C22×C3⋊Dic3—22no—
42C22×C3⋊Dic3—22no—
43C22×C3⋊Dic3—22no—
44C22×C3⋊Dic3C2×C411yescharacteristic
45C22×C3⋊Dic3C2×C411yescharacteristic
46C22×C3⋊Dic3C2×C411yescharacteristic
47C22×C3⋊Dic3D414yes—
48#3830—232no—
49C2×C4×C3⋊D3—22no—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3—22no—
52C2×#634—22no—
53C2×#634—22no—
54C2×#634—22no—
55C22×C3×Dic3—24no—
56C3×#217—24no—
57C3×#217—24no—
58#1782—91noSylow
59C22×C3×D4—21no—
60C22×C3×D4C2×D312yes—
61C22×#67—32no—
62C22×#67—32no—
63C22×#67—61no—
64C22×#67—61no—
65C23×Dic3—32no—
66C23×Dic3—32no—
67C23×Dic3—61no—
68C23×Dic3—61no—
69C2×#237—68no—
70C2×#237—68no—
71C2×#237—68no—
72C2×#237—68no—
73C2×#237—68no—
74C2×#237—64no—
75C2×#237—64no—
76C22×C4×D3—32no—
77C22×C4×D3—61no—
78C22×Dic6—32no—
79C22×Dic6—61no—
80C2×C3×C22⋊C4—34no—
81C2×#217C2×D314yes—
82C3×#99—64no—
83#834—24no—
84C3⋊#95—68no—
85#806—68no—
86C23×C32—21no—
87C23×C32—21no—
88C23×C32—42no—
89C23×C32—42no—
90C23×C32C22⋊C412yes—
91C23×C32C22×C411yescharacteristic
92C23×C32C2×D412yes—
93C23×C32C2×D412yes—
94C23×C32C2×D412yes—
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—42no—
98C22×C3⋊D3C22⋊C412yes—
99C32×D4—28no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4C22⋊C412yes—
103#638—28no—
104#638—28no—
105C2×C3⋊Dic3—28no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—28no—
113C2×C3⋊Dic3C22⋊C412yes—
114C2×C3⋊Dic3C22⋊C412yes—
115C2×C3⋊Dic3C22⋊C412yes—
116C4×C3⋊D3—28no—
117#634—28no—
118C2×C3×Dic3—48no—
119C2×C3×Dic3—44no—
120C22×#41—91no—
121C2×#99—32no—
122C2×#99—92no—
123#381—92no—
124C24×C3—21no—
125C24×C3—21no—
126C24×C3C4×D312yes—
127C24×C3C22×D312yes—
128C23×D3—32no—
129C23×D3—61no—
130C2×C3×D4—24no—
131C2×C3×D4—24no—
132C2×C3×D4—24no—
133C2×C3×D4—24no—
134C2×C3×D4—24no—
135C2×C3×D4D1214yes—
136C2×C3×D4#6714yes—
137C22×C3×C4—21no—
138C22×C3×C4—64no—
139C22×C3×C4C4×D312yes—
140C2×#67—38no—
141C2×#67—64no—
142C2×#67—64no—
143C2×#67—64no—
144C2×#67—64no—
145C2×#67—64no—
146C2×#67—64no—
147C2×#67—64no—
148C2×#67—64no—
149C2×#67—64no—
150C2×#67—62no—
151C2×#67—64no—
152C2×#67—62no—
153C22×Dic3—24no—
154C22×Dic3—32no—
155C22×Dic3—32no—
156C22×Dic3—32no—
157C22×Dic3—38no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—64no—
162C22×Dic3—64no—
163C22×Dic3—64no—
164C22×Dic3—64no—
165C22×Dic3—64no—
166C22×Dic3—64no—
167C22×Dic3—64no—
168C22×Dic3—64no—
169C22×Dic3—64no—
170C22×Dic3—62no—
171C22×Dic3—64no—
172C22×Dic3—62no—
173#237—664no—
174#237—632no—
175#237—632no—
176C2×C4×D3—64no—
177C2×C4×D3—64no—
178C2×C4×D3—64no—
179C2×C4×D3—64no—
180C2×C4×D3—64no—
181C2×C4×D3—64no—
182C2×Dic6—64no—
183C2×Dic6—64no—
184C2×Dic6—64no—
185C2×Dic6—64no—
186C2×Dic6—64no—
187C2×Dic6—64no—
188C3×C22⋊C4—64no—
189C3×C22⋊C4—64no—
190#217—24no—
191#217—24no—
192C22×C32—22no—
193C22×C32—22no—
194C22×C32—24no—
195C22×C32—42no—
196C22×C32—42no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32—42no—
200C22×C32C2×C22⋊C411yescharacteristic
201C22×C32C2×C22⋊C411yescharacteristic
202C22×C32C2×C22⋊C411yescharacteristic
203C22×C32#12014yes—
204C2×C3⋊D3—22no—
205C2×C3⋊D3—42no—
206C2×C3⋊D3—42no—
207C2×C3⋊D3—42no—
208C32×C4—22no—
209C3⋊Dic3—22no—
210C3⋊Dic3—22no—
211C3⋊Dic3—22no—
212C3×Dic3—84no—
213C2×#41—184no—
214C2×#41—184no—
215C2×#41—184no—
216C22×Q8—91no—
217C22×D4—91no—
218C22×D4—91no—
219C22×D4D3211yescharacteristic
220C23×C4—91no—
221C23×C4—91no—
222C23×C4—91no—
223C2×C22⋊C4—34no—
224#99—64no—
225#99—184no—
226#95—184no—
227C23×C3—22no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—22no—
231C23×C3—22no—
232C23×C3—21no—
233C23×C3—22no—
234C23×C3—22no—
235C23×C3—22no—
236C23×C3—44no—
237C23×C3—44no—
238C23×C3—44no—
239C23×C3—44no—
240C23×C3(C2×D3)⋊C414yes—
241C23×C3C2×C4×D312yes—
242C23×C3C2×D1212yes—
243C23×C3D3×D414yes—
244C23×C3D3×D414yes—
245C23×C3C2×#6712yes—
246C22×D3—34no—
247C22×D3—62no—
248C22×D3—62no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—62no—
252C22×D3—124no—
253C22×D3—124no—
254C3×D4—216no—
255C3×D4—28no—
256C3×D4—28no—
257C2×C3×C4—22no—
258C2×C3×C4—22no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—22no—
262C2×C3×C4—128no—
263C2×C3×C4—124no—
264C2×C3×C4(C2×D3)⋊C414yes—
265#67—616no—
266#67—616no—
267#67—616no—
268#67—68no—
269#67—68no—
270C2×Dic3—34no—
271C2×Dic3—34no—
272C2×Dic3—34no—
273C2×Dic3—48no—
274C2×Dic3—44no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—62no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—616no—
285C2×Dic3—616no—
286C2×Dic3—616no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—68no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—68no—
295C4×D3—616no—
296C4×D3—616no—
297Dic6—616no—
298Dic6—616no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—24no—
302C2×C32—42no—
303C2×C32#37911yescharacteristic
304C2×C32#41012yes—
305C3⋊D3—42no—
306C24—91no—
307C24#62411yescharacteristic
308C24C2×D3211yescharacteristic
309#41—1832no—
310C2×Q8—182no—
311C2×Q8—182no—
312C2×Q8—182no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—94no—
316C2×D4—182no—
317C2×D4—182no—
318C2×D4—182no—
319C2×D4—182no—
320C2×D4—182no—
321C2×D4#62614yes—
322C22×C4—64no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—91no—
326C22×C4—94no—
327C22×C4—182no—
328C22×C4—182no—
329C22×C4—182no—
330C22×C4—182no—
331C22×C4—182no—
332C22×C4—182no—
333C22×C4—182no—
334C22×C4—182no—
335C22×C4#62411yescharacteristic
336C22⋊C4—64no—
337C22⋊C4—64no—
338C22×C3—24no—
339C22×C3—28no—
340C22×C3—24no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—24no—
347C22×C3—44no—
348C22×C3—42no—
349C22×C3—44no—
350C22×C3—42no—
351C22×C3—44no—
352C22×C3—44no—
353C22×C3—44no—
354C22×C3—44no—
355C22×C3—44no—
356C22×C3—44no—
357C22×C3—44no—
358C22×C3—44no—
359C22×C3D3×C22⋊C412yes—
360C22×C3D3×C22⋊C412yes—
361C22×C3#88214yes—
362C22×C3C2×(C2×D3)⋊C412yes—
363C22×C3#93714yes—
364C2×D3—64no—
365C2×D3—64no—
366C2×D3—124no—
367C2×D3—124no—
368C2×D3—124no—
369C2×D3—124no—
370C2×D3—124no—
371C2×D3—124no—
372C3×C4—24no—
373C3×C4—24no—
374C3×C4—244no—
375Dic3—64no—
376Dic3—64no—
377Dic3—64no—
378Dic3—64no—
379Dic3—64no—
380Dic3—64no—
381Dic3—84no—
382C32#178211yescharacteristic, complemented, Sylow
383C23—21no—
384C23—21no—
385C23—42no—
386C23—42no—
387C23—92no—
388C23—181no—
389C23—181no—
390C23—362no—
391C23#372212yes—
392C23C2×#62411yescharacteristic
393C23C2×#62612yes—
394C23#381112yes—
395C23#381112yes—
396Q8—188no—
397D4—28no—
398D4—188no—
399D4—188no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—92no—
403C2×C4—92no—
404C2×C4—92no—
405C2×C4—128no—
406C2×C4—124no—
407C2×C4—188no—
408C2×C4—188no—
409C2×C4—181no—
410C2×C4—181no—
411C2×C4—181no—
412C2×C4—181no—
413C2×C4—181no—
414C2×C4—181no—
415C2×C4—188no—
416C2×C4#372212yes—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—24no—
420C2×C3—24no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—44no—
426C2×C3—44no—
427C2×C3—44no—
428C2×C3#474014yes—
429C2×C3#495512yes—
430D3—124no—
431D3—124no—
432C22—24no—
433C22—22no—
434C22—22no—
435C22—42no—
436C22—42no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—182no—
441C22—362no—
442C22—362no—
443C22—362no—
444C22C2×#372211yescharacteristic
445C22#6397411yescharacteristic
446C22#6397411yescharacteristic
447C22#6398114yes—
448C4—22no—
449C4—182no—
450C4—182no—
451C4—182no—
452C4—244no—
453C3—21no—
454C3#7002712yescomplemented
455C2—24no—
456C2—21no—
457C2—21no—
458C2—42no—
459C2—362no—
460C2#1059152912yes—
461C2#1059171411yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3830C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1782
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#834C2semidirect
3. C2×#63581C2semidirect
4. #10591697C2semidirect
7. C22×#638C4semidirect
9. C23×C3⋊Dic3C4semidirect
14. C22×C4×C3⋊D3C4semidirect
15. C22×#634C4semidirect
23. C2×#834D3semidirect
382. C32#1782semidirect
454. C3#70027semidirect

Maximal subgroups

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

subgroupindex
C22×#38302
C2×C3×#8342
C2×#635812
#105916972
#700273