Finite Group Databasebeta

← #11787812

Subgroups — #11787812

Order 1152.

889 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
1#10595992C211yesmaximal, characteristic
2C2×#63864C211yesmaximal, characteristic
3C3×#5004C211yesmaximal, characteristic, complemented
4#10591100C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic
6C3×#4532C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70343—31nomaximal
9#68759—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14#64102—22no—
15C22⋊C4×C3⋊D3—22no—
16C4×C4⋊(C3⋊D3)—22no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×#3722—22no—
21#63864—22no—
22#63864C414yescomplemented
23C3×#810—22no—
24#63566—22no—
25#63559—22no—
26C2×#947—31no—
27#5521—31no—
28#5521—31no—
29#5521—61no—
30C2×#875—31no—
31C3×#419—31no—
32#5225—31no—
33C2×#823—31no—
34C2×#823—31no—
35#5120—31no—
36#5004D311yescharacteristic, complemented
37C3×#339—31no—
38#4555—31no—
39#4532D311yescharacteristic, complemented
40#4523—31no—
41C23×C3⋊D3D412yes—
42C22×C32×C4C2311yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)C2×C412yes—
48C2×C4⋊(C3⋊D3)D412yes—
49C2×C4×C3⋊D3—24no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6C2×C412yescomplemented
58C32×C4⋊C4D412yes—
59C32×C22⋊C4—21no—
60C32×C42—21no—
61#3757—21no—
62#3752—24no—
63C4⋊(C3⋊Dic3)D412yes—
64C4×C3⋊Dic3—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C412yescomplemented
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#3722—28no—
74#1885—91noSylow
75C22×C3×Q8—31no—
76C22×D12—31no—
77C22×D12—31no—
78C22×D12—61no—
79C22×Dic6C2×D311yescharacteristic
80C2×C3×M16—31no—
81C2×C3×M16—31no—
82C3×#117—21no—
83C3×#117C2×D311yescharacteristic
84C3×#117C2×D311yescharacteristic
85C2×C3×C42—31no—
86#947—34no—
87#947—62no—
88C2×(C2×D3)⋊C4—62no—
89C2×(C2×D3)⋊C4—62no—
90#926—31no—
91#926—31no—
92#926—61no—
93C2×C4×Dic3C2×D311yescharacteristic
94C2×#208C2×D311yescharacteristic
95C2×#208C2×D311yescharacteristic
96#893—64no—
97#893—62no—
98#893—62no—
99D3×C22⋊C4—62no—
100D3×C22⋊C4—62no—
101D3×C22⋊C4—64no—
102#875—34no—
103#875—62no—
104C4×D12—62no—
105C4×D12—62no—
106C4×D12—64no—
107C3×#103—62no—
108#835—62no—
109#823—62no—
110#823—62no—
111#816—62no—
112#810—22no—
113C23×C32C2×D411yescharacteristic
114C22×C3⋊D3—22no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—44no—
117C22×C3⋊D3C22⋊C414yes—
118C2×C32×C4—22no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—22no—
126C4⋊(C3⋊D3)—22no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—22no—
130C4×C3⋊D3—84no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C3×C3⋊C8—41no—
141C3×C3⋊C8—41no—
142C2×#124—91no—
143#518—91no—
144#419—31no—
145#419—91no—
146C2×#100—91no—
147#339—31no—
148#339—91no—
149C23×D3—32no—
150C23×D3—32no—
151C23×D3—62no—
152C2×C3×Q8—32no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—61no—
158C22×C3×C4—21no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—21no—
165C2×D12—32no—
166C2×D12—32no—
167C2×D12—32no—
168C2×D12—32no—
169C2×D12—62no—
170C2×D12—62no—
171C2×D12—62no—
172C2×D12—62no—
173C2×D12—62no—
174C2×D12—62no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×C4×D3—68no—
184C2×C4×D3—64no—
185C2×C4×D3—64no—
186C2×Dic6—21no—
187C2×Dic6—21no—
188C2×Dic6—21no—
189C2×Dic6—21no—
190C2×Dic6—21no—
191C2×Dic6C4×D312yescomplemented
192C3×M16—61no—
193C3×M16—61no—
194C3×M16—61no—
195C3×M16—61no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4D1212yes—
200C3×C4⋊C4#6712yes—
201C3×C22⋊C4—22no—
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C42—22no—
205C3×C42—21no—
206C3×C42—21no—
207C3×C42—32no—
208C3×C42—61no—
209#217—62no—
210#217—61no—
211#217—61no—
212(C2×D3)⋊C4—68no—
213(C2×D3)⋊C4—68no—
214(C2×D3)⋊C4—68no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217C4⋊Dic3—32no—
218C4⋊Dic3—32no—
219C4⋊Dic3—62no—
220C4×Dic3—21no—
221C4×Dic3—62no—
222C4×Dic3—61no—
223C4×Dic3—61no—
224C4×Dic3C4×D312yescomplemented
225#208—21no—
226#208—21no—
227#208—21no—
228#208—21no—
229C2×C3⋊C8—21no—
230C2×C3⋊C8—21no—
231C22×C32—22no—
232C22×C32C2×C22⋊C411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32#12311yescharacteristic
235C2×C3⋊D3—24no—
236C2×C3⋊D3—44no—
237C2×C3⋊D3—44no—
238C2×C3⋊D3—82no—
239C32×C4—42no—
240C32×C4C4×D411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12111yescharacteristic
244C3⋊Dic3—42no—
245C3×Dic3—42no—
246C3×Dic3—42no—
247C22×Q8—31no—
248C22×D4—91no—
249C2×M16—31no—
250C2×M16—31no—
251#124—94no—
252#124—182no—
253C4×D4—182no—
254C4×D4—182no—
255#117—91no—
256#117D3211yescharacteristic
257C2×C22⋊C4—182no—
258C2×C22⋊C4—182no—
259C2×C42—31no—
260#103—62no—
261#103—182no—
262#100—182no—
263C23×C3—21no—
264C23×C3D3×D411yescharacteristic
265C23×C3D3×D411yescharacteristic
266C22×D3—34no—
267C22×D3—34no—
268C22×D3—64no—
269C22×D3—64no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—64no—
273C22×D3—62no—
274C22×D3—62no—
275C22×D3—124no—
276C22×D3—124no—
277C22×D3—244no—
278C3×Q8—62no—
279C3×Q8—62no—
280C3×Q8—121no—
281C3×Q8—121no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—122no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23911yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—42no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—64no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316D12—64no—
317D12—64no—
318D12—64no—
319D12—64no—
320D12—62no—
321D12—62no—
322D12—62no—
323D12—62no—
324D12—62no—
325D12—62no—
326D12—62no—
327D12—62no—
328C4×D3—248no—
329C4×D3—244no—
330C4×D3—244no—
331Dic6—22no—
332Dic6—22no—
333Dic6—41no—
334Dic6—41no—
335C3×C8—121no—
336C3×C8—121no—
337C3⋊C8—41no—
338C3⋊C8—41no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32#38611yescharacteristic
342C2×C32#45512yes—
343C3⋊D3—44no—
344C24—92no—
345C2×Q8—32no—
346C2×Q8—61no—
347C2×Q8—61no—
348C2×Q8—61no—
349C2×Q8—61no—
350C2×Q8—61no—
351C2×D4—92no—
352C2×D4—92no—
353C2×D4—181no—
354C2×D4—181no—
355C2×D4—181no—
356C2×D4—181no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—184no—
360C22×C4C2×D3211yescharacteristic
361M16—61no—
362M16—61no—
363M16—61no—
364M16—61no—
365C2×C8—61no—
366C2×C8—61no—
367C4⋊C4—92no—
368C4⋊C4#62612yes—
369C22⋊C4—21no—
370C22⋊C4—184no—
371C22⋊C4—188no—
372C22⋊C4—181no—
373C42—21no—
374C42—32no—
375C42—61no—
376C42—181no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—42no—
383C22×C3D3×C22⋊C411yescharacteristic
384C22×C3D3×C22⋊C411yescharacteristic
385C22×C3#88211yescharacteristic
386C22×C3#88311yescharacteristic
387C22×C3#89411yescharacteristic
388C22×C3#93711yescharacteristic
389C2×D3—68no—
390C2×D3—64no—
391C2×D3—64no—
392C2×D3—128no—
393C2×D3—124no—
394C2×D3—124no—
395C2×D3—124no—
396C2×D3—124no—
397C2×D3—244no—
398C2×D3—242no—
399C2×D3—242no—
400C2×D3—244no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—44no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—122no—
409C3×C4—122no—
410C3×C4C4×D1211yescharacteristic
411C3×C4#67⋊C411yescharacteristic
412C3×C4#88411yescharacteristic
413C3×C4#88411yescharacteristic
414C3×C4#89311yescharacteristic
415C3×C4#89511yescharacteristic
416C3×C4C4×#6711yescharacteristic
417C3×C4#93811yescharacteristic
418Dic3—42no—
419Dic3—42no—
420Dic3—124no—
421Dic3—122no—
422Dic3—122no—
423C32#188511yescharacteristic, complemented, Sylow
424C23—94no—
425C23—182no—
426C23—182no—
427C23—364no—
428C23#381111yescharacteristic
429Q8—62no—
430Q8—62no—
431Q8—121no—
432Q8—121no—
433D4—182no—
434D4—182no—
435D4—182no—
436D4—182no—
437C2×C4—22no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—122no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—182no—
444C2×C4—724no—
445C2×C4#379611yescharacteristic
446C2×C4#379811yescharacteristic
447C2×C4C4×D3211yescharacteristic
448C2×C4#380211yescharacteristic
449C2×C4C2×#62611yescharacteristic
450C2×C4#381111yescharacteristic
451C8—121no—
452C8—121no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—22no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3#466511yescharacteristic
462C2×C3#482512yes—
463C2×C3#495611yescharacteristic
464C2×C3#520212yes—
465D3—128no—
466D3—124no—
467D3—124no—
468C22—22no—
469C22—184no—
470C22—364no—
471C22—364no—
472C22—722no—
473C22#6385311yescharacteristic
474C22#6392111yescharacteristic
475C22#6398111yescharacteristic
476C4—42no—
477C4—122no—
478C4—122no—
479C4—362no—
480C4#6388111yescharacteristic
481C4C4×#62611yescharacteristic
482C4#6391211yescharacteristic
483C4#6391611yescharacteristic
484C3—21no—
485C3#6875911yescharacteristic, complemented
486C3#7034311yescharacteristic, complemented
487C2—21no—
488C2—21no—
489C2—364no—
490C2#1059138711yescharacteristic
491C2#1059169012yes—
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1885
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. C3×#5004C2semidirect
4. #10591100C2semidirect
6. C3×#4532C2semidirect
7. #10589162C2semidirect
22. #63864C4semidirect
36. #5004D3semidirect
39. #4532D3semidirect
57. C2×C3×Dic6C2×C4semidirect
66. C3×C4×Dic3C2×C4semidirect
191. C2×Dic6C4×D3semidirect
224. C4×Dic3C4×D3semidirect
423. C32#1885semidirect
485. C3#68759semidirect
486. C3#70343semidirect

Maximal subgroups

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

subgroupindex
#105959922
C2×#638642
C3×#50042
#105911002
C2×#635592
C3×#45322
#105891622
#703433
#687593