Finite Group Databasebeta

← #11791411

Subgroups — #11791411

Order 1152.

827 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 827 conjugacy classes of subgroups — too many to draw. Only its 134 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
1#10596303C211yesmaximal, characteristic
2C2×C3×#837C212yesmaximal, complemented
3C4×#3724C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5#10591060C211yesmaximal, characteristic, complemented
6#70358—32nomaximal
7C2×C32×#41C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9#64156C411yescharacteristic, complemented
10#64153C411yescharacteristic, complemented
11#64149C411yescharacteristic, complemented
12#64148—21no—
13#64148—21no—
14#64145C411yescharacteristic, complemented
15C4×#638—21no—
16C4×#638—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2212yes—
19C2×C3×#208C2212yes—
20C2×#3724—21no—
21C3×#837—24no—
22#63579—21no—
23#63570—24no—
24#63555—21no—
25#63553—21no—
26#5832—32no—
27#5832—61no—
28C2×C3×#104—32no—
29C2×#837D312yescomplemented
30C2×#825—32no—
31Dic3×M16—32no—
32C4×Dic3⋊C4—32no—
33C2×#805—32no—
34C32×#41—22no—
35C32×#41—22no—
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4—21no—
38C2×C32×D4C2×C411yescharacteristic
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C2×#638—21no—
42C2×#638—21no—
43C2×#638—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46#3828—22no—
47#3828—22no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634C2×C411yescharacteristic
51C22×C3×Dic3—22no—
52#3757—21no—
53#3757—21no—
54#3752—21no—
55#3752—21no—
56#3750—21no—
57#3750—21no—
58C4×C3⋊Dic3C2×C411yescharacteristic
59C4×C3⋊Dic3C2×C411yescharacteristic
60C4×C3⋊Dic3D411yescharacteristic
61C4×C3⋊Dic3D411yescharacteristic
62C3×C4×Dic3—22no—
63C3×C4×Dic3—22no—
64C3×#208—22no—
65C3×#208D414yescomplemented
66C2×C3×C3⋊C8—22no—
67#3724—24no—
68#1980—91noSylow
69C2×C3×#41—21no—
70C2×C3×#41C2×D312yes—
71C2×#235—32no—
72C2×#235—61no—
73C2×C3×M16—32no—
74C2×C3×C42—32no—
75#947—32no—
76#947—61no—
77#944—32no—
78#944—61no—
79#940—32no—
80#940—61no—
81#939—62no—
82#939—62no—
83#939—62no—
84#939—62no—
85#936—32no—
86#936—61no—
87C4×#67—62no—
88C4×#67—62no—
89C4×#67—62no—
90C4×#67—62no—
91C2×Dic3⋊C4—62no—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3C2×D312yes—
95C2×#208C2×D312yes—
96C3×#104—64no—
97#837—24no—
98C3⋊#95—62no—
99#825—64no—
100#815—62no—
101C8×Dic3—62no—
102#805—64no—
103C23×C32—21no—
104C23×C32C2×D411yescharacteristic
105C22×C3⋊D3—21no—
106C32×Q8—22no—
107C32×D4—22no—
108C32×D4—41no—
109C32×D4—41no—
110C2×C32×C4—21no—
111C2×C32×C4—42no—
112C2×C32×C4C22×C411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D412yes—
115C2×C32×C4#4112yes—
116#638—42no—
117#638—41no—
118#638—41no—
119#638—42no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3C22⋊C411yescharacteristic
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C22⋊C411yescharacteristic
126C2×C3⋊Dic3C22⋊C411yescharacteristic
127C4⋊(C3⋊D3)—22no—
128C4×C3⋊D3—42no—
129#634—22no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—42no—
133C3×C3⋊C8—24no—
134#532—91no—
135C2×#104—32no—
136C2×#104—92no—
137C4×M16—91no—
138C4×C4⋊C4—91no—
139C3×#41—22no—
140C3×#41—22no—
141C3×#41—22no—
142C3×#41—22no—
143C3×#41—42no—
144C3×#41—42no—
145C2×C3×Q8—21no—
146C2×C3×Q8C4×D312yes—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—21no—
150C2×C3×D4C4×D312yes—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—21no—
154C22×C3×C4—62no—
155C22×C3×C4C22×D312yes—
156C2×#67—62no—
157C2×#67—62no—
158C2×#67—62no—
159C2×#67—62no—
160C2×#67—62no—
161C2×#67—62no—
162C22×Dic3—22no—
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167#235—62no—
168#235—62no—
169#235—62no—
170#235—62no—
171#235—122no—
172#235—122no—
173C2×D12—32no—
174C2×D12—61no—
175C2×C4×D3—62no—
176C2×C4×D3—62no—
177C2×Dic6—32no—
178C2×Dic6—61no—
179C3×M16—34no—
180C3×M16—62no—
181C2×C3×C8—62no—
182C3×C42—62no—
183C3×C42—62no—
184#217—62no—
185#217—62no—
186#217—62no—
187#217—62no—
188(C2×D3)⋊C4—62no—
189(C2×D3)⋊C4—62no—
190(C2×D3)⋊C4—62no—
191(C2×D3)⋊C4—62no—
192Dic3⋊C4—68no—
193Dic3⋊C4—62no—
194Dic3⋊C4—62no—
195Dic3⋊C4—62no—
196Dic3⋊C4—62no—
197C4×Dic3—22no—
198C4×Dic3—22no—
199C4×Dic3—32no—
200C4×Dic3—32no—
201C4×Dic3—32no—
202C4×Dic3—32no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C4×Dic3—61no—
207#208—22no—
208#208#6714yescomplemented
209C2×C3⋊C8—22no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32—41no—
215C22×C32C2×C22⋊C411yescharacteristic
216C22×C32#12411yescharacteristic
217C22×C32#12711yescharacteristic
218C2×C3⋊D3—41no—
219C2×C3⋊D3—41no—
220C2×C3⋊D3—41no—
221C32×C4—41no—
222C32×C4C4×D412yes—
223C32×C4#12112yes—
224C3⋊Dic3—21no—
225C3⋊Dic3—21no—
226C3⋊Dic3—21no—
227C3⋊Dic3—41no—
228C3⋊Dic3#10412yescomplemented
229C3×Dic3—44no—
230C2×#41—91no—
231C2×#41D3211yescharacteristic
232C2×M16—32no—
233C4⋊Q8—91no—
234#127—91no—
235#124—91no—
236#124—91no—
237#121—181no—
238#121—181no—
239C4×D4—181no—
240C4×D4—181no—
241C2×C4⋊C4—181no—
242C2×C42—32no—
243C2×C42—91no—
244#104—64no—
245#104—184no—
246#97—181no—
247C4×C8—181no—
248#95—181no—
249C23×C3—22no—
250C23×C3—22no—
251C23×C3—21no—
252C23×C3D3×D412yes—
253C22×D3—62no—
254C22×D3—62no—
255C3×Q8—22no—
256C3×Q8—22no—
257C3×Q8—42no—
258C3×D4—22no—
259C3×D4—22no—
260C3×D4—42no—
261C3×D4—42no—
262C3×D4—42no—
263C3×D4—42no—
264C3×D4—42no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—22no—
270C2×C3×C4—21no—
271C2×C3×C4—44no—
272C2×C3×C4—42no—
273C2×C3×C4—42no—
274C2×C3×C4—64no—
275C2×C3×C4—122no—
276C2×C3×C4—122no—
277C2×C3×C4C2×C4×D312yes—
278C2×C3×C4#23512yes—
279C2×C3×C4D3×D412yes—
280C2×C3×C4D3×D412yes—
281C2×C3×C4#23712yes—
282C2×C3×C4C2×#6712yes—
283#67—124no—
284#67—124no—
285#67—124no—
286#67—124no—
287#67—122no—
288#67—122no—
289#67—122no—
290#67—122no—
291C2×Dic3—24no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—32no—
296C2×Dic3—42no—
297C2×Dic3—42no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307C2×Dic3—122no—
308D12—62no—
309D12—62no—
310D12—122no—
311C4×D3—124no—
312C4×D3—122no—
313C4×D3—122no—
314Dic6—62no—
315Dic6—62no—
316Dic6—122no—
317C3×C8—64no—
318C3⋊C8—24no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32—81no—
322C2×C32#39011yescharacteristic
323C2×C32C2×#10411yescharacteristic
324C2×C32#42111yescharacteristic
325C3⋊D3—81no—
326#41—22no—
327#41—22no—
328#41—182no—
329#41—182no—
330C2×Q8—91no—
331C2×Q8#62411yescharacteristic
332C2×D4—21no—
333C2×D4—91no—
334C2×D4—181no—
335C2×D4—181no—
336C2×D4—181no—
337C2×D4#62411yescharacteristic
338C22×C4—21no—
339C22×C4—62no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—181no—
343C22×C4C2×D3211yescharacteristic
344M16—34no—
345M16—62no—
346C2×C8—62no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—184no—
350C22⋊C4—181no—
351C22⋊C4—181no—
352C22⋊C4—181no—
353C22⋊C4—181no—
354C42—62no—
355C42—62no—
356C42—91no—
357C42—91no—
358C42—91no—
359C42—91no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—42no—
371C22×C3—42no—
372C22×C3—42no—
373C22×C3D3×C22⋊C412yes—
374C22×C3#88512yes—
375C22×C3#94012yes—
376C2×D3—122no—
377C2×D3—122no—
378C2×D3—122no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—122no—
382C3×C4—22no—
383C3×C4—22no—
384C3×C4—42no—
385C3×C4—42no—
386C3×C4—124no—
387C3×C4#67⋊C412yes—
388C3×C4#88412yes—
389C3×C4C4×#6712yes—
390C3×C4#93912yes—
391Dic3—34no—
392Dic3—44no—
393Dic3—62no—
394Dic3—62no—
395Dic3—62no—
396Dic3—62no—
397Dic3—62no—
398Dic3—121no—
399Dic3—121no—
400Dic3—122no—
401Dic3—122no—
402C32#198011yescharacteristic, complemented, Sylow
403C23—21no—
404C23—181no—
405C23#381111yescharacteristic
406Q8—22no—
407Q8—182no—
408D4—22no—
409D4—41no—
410D4—41no—
411D4—182no—
412D4—362no—
413D4—362no—
414D4—361no—
415D4—361no—
416C2×C4—21no—
417C2×C4—42no—
418C2×C4—64no—
419C2×C4—91no—
420C2×C4—91no—
421C2×C4—91no—
422C2×C4—91no—
423C2×C4—122no—
424C2×C4—122no—
425C2×C4—182no—
426C2×C4—181no—
427C2×C4—361no—
428C2×C4—362no—
429C2×C4#380412yes—
430C2×C4C2×#62411yescharacteristic
431C2×C4D3×#6712yes—
432C2×C4#381111yescharacteristic
433C8—64no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—82no—
442C2×C3—82no—
443C2×C3D3×#10412yes—
444C2×C3#482112yes—
445C2×C3#495712yes—
446D3—242no—
447D3—242no—
448C22—21no—
449C22—21no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—361no—
454C22—361no—
455C22—361no—
456C22#6395311yescharacteristic
457C22#6397411yescharacteristic
458C22#6397911yescharacteristic
459C4—41no—
460C4—92no—
461C4—124no—
462C4—181no—
463C4—181no—
464C4—181no—
465C4—361no—
466C4#6395212yes—
467C4#6397112yes—
468C3—21no—
469C3#7035812yescomplemented
470C2—21no—
471C2—21no—
472C2—81no—
473C2—721no—
474C2#1059167111yescharacteristic
475C2#1059167211yescharacteristic
476C2#1059170411yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32C2×C22⋊C4
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×C3×#837C2semidirect
3. C4×#3724C2semidirect
4. C2×#63570C2semidirect
5. #10591060C2semidirect
9. #64156C4semidirect
10. #64153C4semidirect
11. #64149C4semidirect
14. #64145C4semidirect
29. C2×#837D3semidirect
65. C3×#208D4semidirect
208. #208#67semidirect
228. C3⋊Dic3#104semidirect
402. C32#1980semidirect
469. C3#70358semidirect

Maximal subgroups

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

subgroupindex
#105963032
C2×C3×#8372
C4×#37242
C2×#635702
#105910602
#703583