Finite Group Databasebeta

← #11784623

Subgroups — #11784623

Order 1152.

1333 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 1333 conjugacy classes of subgroups — too many to draw. Only its 154 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×#3805C211yesmaximal, characteristic
2#10592642C211yesmaximal, characteristic, complemented
3C2×C3×#806C212yesmaximal, complemented
4C2×#63580C212yesmaximal, complemented
5#10591697C211yesmaximal, characteristic, complemented
6#70027—32nomaximal
7C23×C3⋊Dic3C2211yescharacteristic
8C22×C3×#67C2212yes—
9C22×#627C411yescharacteristic, complemented
10C22×#625C411yescharacteristic, complemented
11C2×#3805—22no—
12C2×#3805—22no—
13C2×#3805—24no—
14C2×#3805—24no—
15C22×D3×Dic3C412yescomplemented
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C2×C3×#217C2212yes—
19#63658—22no—
20C3×#806—24no—
21#63580—24no—
22#63579—22no—
23C22×#237—32no—
24C2×C3×#99—32no—
25C2×#834—32no—
26C2×#806—32no—
27C2×#806D312yescomplemented
28#4943—32no—
29#4943—32no—
30#4943—61no—
31C24×C32C2311yescharacteristic
32C23×C3×D3C2×C412yes—
33C22×C32×C4—21no—
34C22×C3⋊Dic3—22no—
35C22×C3⋊Dic3—22no—
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3C2×C411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C22×C3⋊Dic3D412yes—
40C22×C3⋊Dic3D412yes—
41C2×C3×#67—22no—
42C2×C3×#67—22no—
43C2×C3×#67—22no—
44C2×C3×#67—22no—
45C2×C3×#67D414yes—
46C2×C3×#67D414yes—
47C22×C3×Dic3—22no—
48C22×C3×Dic3C2×C412yes—
49C2×#627—22no—
50C2×#627—24no—
51C2×#625—24no—
52C2×#625—22no—
53#3805—28no—
54#3805—216no—
55#3805—28no—
56C2×D3×Dic3—24no—
57C2×D3×Dic3—24no—
58C2×D3×Dic3—24no—
59C32×C22⋊C4—22no—
60#3757—22no—
61C3×#217—22no—
62C3×#217—22no—
63#1782—91noSylow
64C22×C3×D4—32no—
65C22×#67—32no—
66C22×#67C2×D312yes—
67C23×Dic3—32no—
68C23×Dic3—32no—
69C23×Dic3—61no—
70C2×#237—64no—
71C2×#237—64no—
72C2×#237—64no—
73C2×#237—64no—
74C2×#237—64no—
75C2×#237—64no—
76C22×C4×D3—32no—
77C22×Dic6—32no—
78C2×C3×C22⋊C4—21no—
79C2×C3×C22⋊C4—32no—
80C2×C3×C22⋊C4C2×D312yes—
81C2×#217—32no—
82C2×#217—61no—
83C2×#217C2×D312yes—
84C3×#99—64no—
85#834—64no—
86C3⋊#95—64no—
87C3⋊#95—64no—
88C3⋊#95—64no—
89#806—24no—
90#806—64no—
91C23×C32—42no—
92C23×C32C22×C411yescharacteristic
93C23×C32C2×D412yes—
94C23×C32C2×D411yescharacteristic
95C23×C32C2×D411yescharacteristic
96C23×C32C2×D412yes—
97C22×C3×D3—22no—
98C22×C3×D3—22no—
99C22×C3×D3—44no—
100C22×C3×D3C22⋊C414yes—
101C2×C32×C4—42no—
102C2×C32×C4—41no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—22no—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3C22⋊C412yes—
111C2×C3⋊Dic3C22⋊C412yes—
112C3×#67—24no—
113C3×#67—24no—
114C3×#67—24no—
115C3×#67—24no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—22no—
118C2×C3×Dic3—44no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3C22⋊C414yes—
121#627—28no—
122#625—28no—
123D3×Dic3—216no—
124C22×#41—91no—
125C2×#99—32no—
126C2×#99—92no—
127#381—91no—
128#381—91no—
129C24×C3—21no—
130C24×C3—32no—
131C24×C3C22×D312yes—
132C23×D3C4×D312yes—
133C2×C3×D4—34no—
134C2×C3×D4—34no—
135C2×C3×D4—62no—
136C2×C3×D4—62no—
137C2×C3×D4—62no—
138C2×C3×D4—62no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—32no—
142C22×C3×C4—62no—
143C2×#67—22no—
144C2×#67—22no—
145C2×#67—22no—
146C2×#67—22no—
147C2×#67—64no—
148C2×#67—64no—
149C2×#67—64no—
150C2×#67D1214yes—
151C2×#67#6714yes—
152C22×Dic3—22no—
153C22×Dic3—32no—
154C22×Dic3—32no—
155C22×Dic3—34no—
156C22×Dic3—34no—
157C22×Dic3—62no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—62no—
161C22×Dic3—64no—
162C22×Dic3—64no—
163C22×Dic3—62no—
164C22×Dic3—62no—
165C22×Dic3—62no—
166C22×Dic3—62no—
167C22×Dic3—64no—
168C22×Dic3—62no—
169C22×Dic3—62no—
170C22×Dic3—122no—
171C22×Dic3—122no—
172C22×Dic3C4×D312yes—
173#237—616no—
174#237—616no—
175#237—616no—
176#237—616no—
177C2×C4×D3—64no—
178C2×C4×D3—64no—
179C2×C4×D3—64no—
180C2×Dic6—64no—
181C2×Dic6—64no—
182C2×Dic6—64no—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—22no—
185C3×C22⋊C4—42no—
186C3×C22⋊C4—62no—
187C3×C22⋊C4—62no—
188#217—22no—
189#217—22no—
190#217—62no—
191#217—62no—
192#217—122no—
193C22×C32—22no—
194C22×C32—22no—
195C22×C32—22no—
196C22×C32—42no—
197C22×C32—42no—
198C22×C32C2×C22⋊C411yescharacteristic
199C22×C32C2×C22⋊C412yes—
200C22×C32#12011yescharacteristic
201C22×C32#12012yes—
202C22×C32#12011yescharacteristic
203C2×C3×D3—24no—
204C2×C3×D3—44no—
205C2×C3×D3—44no—
206C2×C3×D3—44no—
207C32×C4—81no—
208C3⋊Dic3—22no—
209C3⋊Dic3—22no—
210C3⋊Dic3—81no—
211C3×Dic3—24no—
212C3×Dic3—82no—
213C2×#41—182no—
214C2×#41—182no—
215C2×#41—184no—
216C2×#41—184no—
217C22×Q8—91no—
218C22×D4—32no—
219C22×D4—91no—
220C23×C4—92no—
221C23×C4—91no—
222C2×C22⋊C4—32no—
223C2×C22⋊C4—91no—
224C2×C22⋊C4D3211yescharacteristic
225#99—64no—
226#99—184no—
227#95—182no—
228#95—182no—
229C23×C3—21no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—22no—
233C23×C3—21no—
234C23×C3—34no—
235C23×C3—44no—
236C23×C3—44no—
237C23×C3—62no—
238C23×C3—62no—
239C23×C3—124no—
240C23×C3C2×C4×D312yes—
241C23×C3C2×D1212yes—
242C23×C3D3×D412yes—
243C23×C3D3×D412yes—
244C23×C3D3×D412yes—
245C23×C3D3×D412yes—
246C23×C3C2×#6712yes—
247C22×D3—22no—
248C22×D3—22no—
249C22×D3—44no—
250C22×D3(C2×D3)⋊C414yes—
251C3×D4—64no—
252C3×D4—64no—
253C3×D4—64no—
254C3×D4—64no—
255C2×C3×C4—34no—
256C2×C3×C4—42no—
257C2×C3×C4—44no—
258C2×C3×C4—44no—
259C2×C3×C4—42no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—124no—
263C2×C3×C4—122no—
264#67—24no—
265#67—24no—
266#67—24no—
267#67—24no—
268#67—616no—
269C2×Dic3—22no—
270C2×Dic3—22no—
271C2×Dic3—34no—
272C2×Dic3—34no—
273C2×Dic3—44no—
274C2×Dic3—42no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—616no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—64no—
285C2×Dic3—64no—
286C2×Dic3—122no—
287C2×Dic3—122no—
288C2×Dic3—124no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291C2×Dic3—122no—
292C2×Dic3—124no—
293C2×Dic3—124no—
294C2×Dic3—122no—
295C2×Dic3(C2×D3)⋊C414yes—
296C4×D3—616no—
297Dic6—616no—
298C2×C32—21no—
299C2×C32—21no—
300C2×C32—22no—
301C2×C32—22no—
302C2×C32#37911yescharacteristic
303C2×C32#41012yes—
304C3×D3—44no—
305C24—32no—
306C24C2×D3211yescharacteristic
307#41—1816no—
308#41—188no—
309#41—188no—
310C2×Q8—184no—
311C2×Q8—182no—
312C2×D4—34no—
313C2×D4—34no—
314C2×D4—62no—
315C2×D4—62no—
316C2×D4—62no—
317C2×D4—62no—
318C2×D4—182no—
319C2×D4—184no—
320C22×C4—21no—
321C22×C4—32no—
322C22×C4—62no—
323C22×C4—91no—
324C22×C4—91no—
325C22×C4—92no—
326C22×C4—92no—
327C22×C4—184no—
328C22×C4—184no—
329C22×C4—184no—
330C22×C4—182no—
331C22×C4—182no—
332C22×C4—181no—
333C22⋊C4—22no—
334C22⋊C4—62no—
335C22⋊C4—62no—
336C22⋊C4—182no—
337C22×C3—24no—
338C22×C3—24no—
339C22×C3—24no—
340C22×C3—24no—
341C22×C3—22no—
342C22×C3—21no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—42no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—42no—
351C22×C3—42no—
352C22×C3—44no—
353C22×C3—44no—
354C22×C3—64no—
355C22×C3—124no—
356C22×C3—124no—
357C22×C3—124no—
358C22×C3D3×C22⋊C412yes—
359C22×C3D3×C22⋊C412yes—
360C22×C3#88212yes—
361C22×C3#88212yes—
362C22×C3C2×(C2×D3)⋊C412yes—
363C22×C3#93712yes—
364C22×C3#93712yes—
365C2×D3—24no—
366C2×D3—44no—
367C2×D3—44no—
368C2×D3—44no—
369C3×C4—64no—
370C3×C4—82no—
371C3×C4—82no—
372C3×C4—242no—
373Dic3—24no—
374Dic3—64no—
375Dic3—64no—
376Dic3—82no—
377Dic3—122no—
378Dic3—122no—
379Dic3—242no—
380Dic3—242no—
381C32#178211yescharacteristic, complemented, Sylow
382C23—34no—
383C23—42no—
384C23—62no—
385C23—62no—
386C23—124no—
387C23C4×D3211yescharacteristic
388C23D3×D1212yes—
389C23#380211yescharacteristic
390C23D3×#6712yes—
391C23#381111yescharacteristic
392Q8—188no—
393D4—64no—
394D4—64no—
395D4—64no—
396D4—64no—
397D4—188no—
398C2×C4—34no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—92no—
404C2×C4—92no—
405C2×C4—124no—
406C2×C4—122no—
407C2×C4—1816no—
408C2×C4—182no—
409C2×C4—182no—
410C2×C4—184no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4—362no—
414C2×C4—361no—
415C2×C3—22no—
416C2×C3—22no—
417C2×C3—22no—
418C2×C3—22no—
419C2×C3—22no—
420C2×C3—22no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—21no—
424C2×C3—22no—
425C2×C3—42no—
426C2×C3—42no—
427C2×C3—124no—
428C2×C3#474014yes—
429C2×C3#495512yes—
430D3—44no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—42no—
435C22—42no—
436C22—64no—
437C22—124no—
438C22—124no—
439C22—124no—
440C22D3×(C2×D3)⋊C412yes—
441C22#6392111yescharacteristic
442C22#6392212yes—
443C22#6392311yescharacteristic
444C22#6398311yescharacteristic
445C4—64no—
446C4—81no—
447C4—182no—
448C4—182no—
449C4—242no—
450C4—721no—
451C3—21no—
452C3#7002712yescomplemented
453C2—21no—
454C2—22no—
455C2—21no—
456C2—22no—
457C2—124no—
458C2#1059040612yes—
459C2#1059139911yescharacteristic
subgroupG/H
centerC22#63921
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#3805C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1782
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592642C2semidirect
3. C2×C3×#806C2semidirect
4. C2×#63580C2semidirect
5. #10591697C2semidirect
9. C22×#627C4semidirect
10. C22×#625C4semidirect
15. C22×D3×Dic3C4semidirect
27. C2×#806D3semidirect
381. C32#1782semidirect
452. C3#70027semidirect

Maximal subgroups

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

subgroupindex
C22×#38052
#105926422
C2×C3×#8062
C2×#635802
#105916972
#700273