Finite Group Databasebeta

← #11786703

Subgroups — #11786703

Order 1152.

653 conjugacy classes of subgroups.

The subgroup lattice has 493 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5504C211yesmaximal, characteristic
2C3×#4975C211yesmaximal, characteristic, complemented
3#10591139C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic
5#10591087C211yesmaximal, characteristic
6#10589396C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71664—31nomaximal
9#69592—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×C4×#67—22no—
15C3×#926C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×Dic3⋊C4—22no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C3×#893—21no—
20C3×#892—21no—
21C3×D3×C4⋊C4—21no—
22C3×#887—21no—
23#63576—21no—
24#63574—21no—
25#63569C414yescomplemented
26#63565—21no—
27#63562—21no—
28C3×#520—31no—
29#5504D311yescharacteristic
30C3×#384—31no—
31C2×#837—31no—
32#5232—31no—
33#4995—31no—
34#4975D311yescharacteristic, complemented
35#4966—31no—
36#4964—31no—
37C2×#805—31no—
38#4532—31no—
39#4530—31no—
40#4530—31no—
41#4530—61no—
42#4523—31no—
43C22×C32×C4D412yes—
44C22×C32×C4C2311yescharacteristic
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58#3748—21no—
59#3748—21no—
60#3748—21no—
61#3748C2×C412yescomplemented
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—22no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3D411yescharacteristic
69C3×C4⋊Dic3D411yescharacteristic
70C3×Dic3⋊C4—22no—
71C3×Dic3⋊C4—44no—
72C3×C4×Dic3—22no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3C2×C412yescomplemented
76#1859—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C3×C4×Q8—61no—
80C3×C4×D4—61no—
81C3×C4×D4—62no—
82C3×#117—31no—
83C3×#117—61no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—61no—
87C2×C3×C4⋊C4—62no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×C3×C42—31no—
91C4×#67—22no—
92#926C2×D311yescharacteristic
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×Dic3⋊C4—22no—
95C2×C4×Dic3C2×D311yescharacteristic
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208—61no—
102#893—21no—
103#892—21no—
104D3×C4⋊C4—21no—
105#887—21no—
106#837—34no—
107#835—61no—
108#832—61no—
109#810—61no—
110#809—61no—
111#808—61no—
112#808—61no—
113#807—61no—
114#807—61no—
115#805—34no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—22no—
119C2×C32×C4—42no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C3×#67—22no—
127C3×#67—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—41no—
136C3×D12—21no—
137C3×D12C4⋊C412yescomplemented
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×C4×D3—82no—
141C3×Dic6—21no—
142C3×Dic6C4⋊C412yescomplemented
143C3⋊(C3⋊C8)—22no—
144C3⋊(C3⋊C8)—41no—
145#520—31no—
146#428—91no—
147C2×#104—91no—
148#417—91no—
149#384—31no—
150#343—91no—
151#339—91no—
152C3×#41—32no—
153C3×#41—32no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—22no—
160C22×C3×C4—21no—
161C22×C3×C4—62no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4#6712yes—
166C22×C3×C4#6712yes—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—21no—
170C22×Dic3—21no—
171C22×Dic3—21no—
172#235—21no—
173#235—21no—
174#235Dic612yes—
175#235C4×D312yes—
176C2×D12#6711yescharacteristic
177C2×C4×D3—21no—
178C2×C4×D3—22no—
179C2×Dic6#6711yescharacteristic
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—31no—
186C3×C4⋊C4—41no—
187C3×C4⋊C4—41no—
188C3×C4⋊C4—62no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—124no—
192C3×C22⋊C4—62no—
193C3×C22⋊C4—61no—
194C3×C42—32no—
195C3×C42—62no—
196C3×C42—61no—
197C3×C42—61no—
198#217—21no—
199(C2×D3)⋊C4—22no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3#6711yescharacteristic
203C4⋊Dic3#6711yescharacteristic
204Dic3⋊C4—22no—
205Dic3⋊C4—44no—
206C4×Dic3—22no—
207C4×Dic3—21no—
208C4×Dic3—21no—
209C4×Dic3C4×D312yescomplemented
210#208—32no—
211#208—32no—
212#208—62no—
213#208—61no—
214#208—61no—
215#208—62no—
216#208—61no—
217#208—61no—
218#208—61no—
219#208—61no—
220#208—121no—
221#208—121no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C2×C3⋊C8—121no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C4×D411yescharacteristic
231C22×C32#12011yescharacteristic
232C22×C32C22⋊Q811yescharacteristic
233C2×C3×D3—22no—
234C2×C3×D3—41no—
235C2×C3×D3—41no—
236C32×C4—42no—
237C32×C4C2×C4⋊C411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4C22⋊Q811yescharacteristic
240C32×C4#12311yescharacteristic
241C3×Dic3—24no—
242C3×Dic3—22no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C3×Dic3—81no—
246C2×#41—31no—
247C2×M16—91no—
248C2×M16—91no—
249C4×Q8—61no—
250C4×D4—61no—
251C4×D4—62no—
252#117—31no—
253#117—61no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—61no—
256C2×C4⋊C4—62no—
257C2×C4⋊C4D3211yescharacteristic
258C2×C42—31no—
259#107—181no—
260#106—181no—
261#104—94no—
262#103—181no—
263#102—181no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3C2×#6711yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C22×D3—21no—
269C3×Q8—32no—
270C3×Q8—61no—
271C3×D4—32no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—61no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—61no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—82no—
295C2×C3×C4—122no—
296C2×C3×C4—121no—
297C2×C3×C4—242no—
298C2×C3×C4C2×Dic611yescharacteristic
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×Q811yescharacteristic
307C2×C3×C4#23911yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310#67—22no—
311#67—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—42no—
319C2×Dic3—41no—
320D12—21no—
321D12Dic3⋊C412yescomplemented
322C4×D3—22no—
323C4×D3—22no—
324C4×D3—82no—
325Dic6—21no—
326Dic6Dic3⋊C412yescomplemented
327C3⋊C8—62no—
328C3⋊C8—62no—
329C3⋊C8—122no—
330C3⋊C8—122no—
331C3⋊C8—121no—
332C3⋊C8—121no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32#38511yescharacteristic
336C2×C32#45311yescharacteristic
337C2×C32#45611yescharacteristic
338C3×D3—42no—
339#41—32no—
340#41—32no—
341#41—61no—
342#41—61no—
343C2×Q8—31no—
344C2×D4—31no—
345C2×D4—61no—
346C22×C4—62no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4#62512yes—
351C22×C4C2×D3211yescharacteristic
352M16—92no—
353M16—181no—
354M16—181no—
355M16—181no—
356C2×C8—181no—
357C2×C8—181no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—31no—
361C4⋊C4—31no—
362C4⋊C4—62no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—124no—
366C22⋊C4—62no—
367C22⋊C4—61no—
368C42—32no—
369C42—62no—
370C42—61no—
371C42—61no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3#92411yescharacteristic
385C22×C3C4×#6711yescharacteristic
386C22×C3C4×#6711yescharacteristic
387C22×C3#93711yescharacteristic
388C22×C3#94611yescharacteristic
389C22×C3#95311yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—64no—
400C3×C4—62no—
401C3×C4—82no—
402C3×C4—121no—
403C3×C4—121no—
404C3×C4—241no—
405C3×C4D3×C4⋊C411yescharacteristic
406C3×C4#89311yescharacteristic
407C3×C4#89411yescharacteristic
408C3×C4#89611yescharacteristic
409C3×C4C2×Dic3⋊C411yescharacteristic
410C3×C4#92411yescharacteristic
411C3×C4C4×#6711yescharacteristic
412C3×C4#92911yescharacteristic
413Dic3—24no—
414Dic3—22no—
415Dic3—41no—
416Dic3—41no—
417Dic3—81no—
418C32#185911yescharacteristic, complemented, Sylow
419C23—61no—
420C23C2×#62511yescharacteristic
421Q8—32no—
422Q8—61no—
423D4—32no—
424D4—62no—
425D4—62no—
426D4—61no—
427C2×C4—22no—
428C2×C4—42no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—61no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—122no—
438C2×C4—121no—
439C2×C4—242no—
440C2×C4D3×Dic611yescharacteristic
441C2×C4#379811yescharacteristic
442C2×C4#379911yescharacteristic
443C2×C4C4×D3211yescharacteristic
444C2×C4D3×#6711yescharacteristic
445C2×C4D3×#6711yescharacteristic
446C8—182no—
447C8—361no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—41no—
456C2×C3—41no—
457C2×C3—122no—
458C2×C3#498911yescharacteristic
459C2×C3#507711yescharacteristic
460C2×C3#509511yescharacteristic
461C2×C3#521011yescharacteristic
462C2×C3#524111yescharacteristic
463C2×C3#524611yescharacteristic
464D3—42no—
465C22—21no—
466C22—21no—
467C22—62no—
468C22—121no—
469C22—121no—
470C22#6385611yescharacteristic
471C22C4×#62511yescharacteristic
472C22#6397611yescharacteristic
473C4—42no—
474C4—64no—
475C4—62no—
476C4—121no—
477C4—121no—
478C4—241no—
479C4#6385011yescharacteristic
480C4#6385111yescharacteristic
481C4D3×Dic3⋊C411yescharacteristic
482C4#6390411yescharacteristic
483C3—21no—
484C3#6959211yescharacteristic, complemented
485C3#7166411yescharacteristic, complemented
486C2—21no—
487C2—21no—
488C2—122no—
489C2#1059127711yescharacteristic
490C2#1059150911yescharacteristic
491C2#1059164811yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4975C2semidirect
3. #10591139C2semidirect
6. #10589396C2semidirect
7. #10589161C2semidirect
25. #63569C4semidirect
34. #4975D3semidirect
61. #3748C2×C4semidirect
75. C3×C4×Dic3C2×C4semidirect
137. C3×D12C4⋊C4semidirect
142. C3×Dic6C4⋊C4semidirect
209. C4×Dic3C4×D3semidirect
321. D12Dic3⋊C4semidirect
326. Dic6Dic3⋊C4semidirect
418. C32#1859semidirect
484. C3#69592semidirect
485. C3#71664semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
C3×#49752
#105911392
C2×#635692
#105910872
#105893962
#105891612
#716643
#695923