Finite Group Databasebeta

← #11787693

Subgroups — #11787693

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594986C211yesmaximal, characteristic
2C2×#63827C211yesmaximal, characteristic
3C3×#4929C211yesmaximal, characteristic, complemented
4C2×C3×#805C211yesmaximal, characteristic
5#10591100C211yesmaximal, characteristic, complemented
6#10589389C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70365—31nomaximal
9#69693—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17Dic3×#67—22no—
18#63898—21no—
19D3×C4⋊Dic3—21no—
20#63843—21no—
21#63841—21no—
22C2×#3718—21no—
23#63827—22no—
24#63827C414yescomplemented
25C2×#3715—21no—
26C3×C3⋊#95—22no—
27C3×#805—22no—
28#63566—21no—
29#63566—21no—
30#5827—31no—
31C2×#951—31no—
32C2×#942—31no—
33#5504—31no—
34C2×C3×#104—31no—
35C3×#391—31no—
36#5225—31no—
37#5120—31no—
38#4929D311yescharacteristic, complemented
39C2×#805D311yescharacteristic
40#4554—31no—
41#4530—31no—
42#4523—31no—
43#4523—31no—
44#4523—61no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D412yes—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235C2×C412yes—
53C3×#235D412yes—
54C2×C3×D12D411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yescomplemented
62C2×C3×Dic6D411yescharacteristic
63C2×D3×Dic3—22no—
64C32×C42—21no—
65C32×C42—21no—
66#3757—21no—
67C4⋊(C3⋊Dic3)D411yescharacteristic
68C4⋊(C3⋊Dic3)D411yescharacteristic
69C4×C3⋊Dic3—21no—
70#3748—21no—
71#3748C2×C412yescomplemented
72C2×C3⋊(C3⋊C8)—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78Dic3⋊Dic3—22no—
79(C2×D3)⋊Dic3—22no—
80Dic32—22no—
81#3718—24no—
82#3715—24no—
83#1882—91noSylow
84C2×C3×#41—31no—
85C22×C3×Q8—31no—
86C2×#235C2×D311yescharacteristic
87C22×Dic6C2×D311yescharacteristic
88C2×C3×M16—31no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C42—21no—
91C2×C3×C42C2×D311yescharacteristic
92C2×C3×C42C2×D311yescharacteristic
93#951—34no—
94#951—62no—
95Q8×Dic3—61no—
96C2×#216—61no—
97C2×#216—61no—
98#942—34no—
99#942—62no—
100C2×#215—61no—
101D4×Dic3—61no—
102D4×Dic3—62no—
103C2×#214—61no—
104C4×#67—62no—
105#926—31no—
106#926—31no—
107#926—61no—
108#926—61no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×#208—31no—
112C2×#208—31no—
113C2×#208—61no—
114C2×#208C2×D311yescharacteristic
115#893—61no—
116#892—61no—
117D3×C4⋊C4—61no—
118#887—61no—
119C3×#104—62no—
120C3×#95—62no—
121#835—61no—
122#835—61no—
123C3⋊#95—22no—
124#816—61no—
125#816—61no—
126#805—22no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—21no—
129C2×C32×C4—22no—
130C2×C32×C4—41no—
131C2×C32×C4—41no—
132C2×C32×C4C22×C411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4111yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C3⋊Dic3—21no—
139C2×C3⋊Dic3—21no—
140C3×#67—22no—
141C3×#67—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—42no—
148C3×D12—21no—
149C3×D12C22⋊C412yes—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×Dic6—21no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157C3×Dic6C22⋊C412yes—
158D3×Dic3—82no—
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—41no—
161C2×#137—91no—
162#520—91no—
163C2×#104—31no—
164#419—91no—
165#391—31no—
166#343—91no—
167#339—91no—
168C3×#41—32no—
169C3×#41—32no—
170C3×#41—61no—
171C3×#41—61no—
172C2×C3×Q8—32no—
173C2×C3×Q8—31no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—32no—
185C22×C3×C4—41no—
186C22×C3×C4—61no—
187C22×C3×C4—61no—
188C22×C3×C4C22×D311yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C2×#67—21no—
191C22×Dic3—21no—
192C22×Dic3—62no—
193C22×Dic3#6712yes—
194#235—21no—
195#235—21no—
196#235C4×D312yes—
197#235#6712yes—
198C2×D12D1211yescharacteristic
199C2×C4×D3—21no—
200C2×C4×D3—62no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6C4×D312yescomplemented
207C2×Dic6D1211yescharacteristic
208C3×M16—61no—
209C3×M16—61no—
210C2×C3×C8—61no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4—61no—
213C3×C42—22no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—41no—
219#217—62no—
220#217—61no—
221#217—61no—
222#217—121no—
223#216—64no—
224#216—64no—
225#215—64no—
226#214—64no—
227(C2×D3)⋊C4—62no—
228C4⋊Dic3—21no—
229C4⋊Dic3—21no—
230C4⋊Dic3—31no—
231C4⋊Dic3—31no—
232C4⋊Dic3—31no—
233C4⋊Dic3—31no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—62no—
237Dic3⋊C4—62no—
238C4×Dic3—62no—
239C4×Dic3—62no—
240C4×Dic3—61no—
241C4×Dic3—61no—
242C4×Dic3—121no—
243#208—21no—
244#208—21no—
245#208—32no—
246#208—32no—
247#208—62no—
248#208—61no—
249#208—61no—
250#208—121no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8—61no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—121no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32C4×D411yescharacteristic
258C22×C32#12011yescharacteristic
259C22×C32#12111yescharacteristic
260C2×C3×D3—22no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C32×C4—42no—
264C32×C4C2×C22⋊C411yescharacteristic
265C32×C4C4×D411yescharacteristic
266C32×C4#12111yescharacteristic
267C32×C4#12311yescharacteristic
268C3⋊Dic3—41no—
269C3⋊Dic3—41no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C2×#41—31no—
274C22×Q8—31no—
275#137—94no—
276#137—182no—
277C2×Q16—181no—
278C2×SD16—181no—
279C2×M16—31no—
280C2×M16—91no—
281C4×Q8—181no—
282C4×D4—181no—
283C4×D4—182no—
284#117—91no—
285#117—181no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—181no—
288C2×C42D3211yescharacteristic
289#104—62no—
290#103—181no—
291#103—181no—
292#95—62no—
293C23×C3—21no—
294C23×C3—61no—
295C23×C3D3×D411yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C22×D3—21no—
298C3×Q8—32no—
299C3×Q8—61no—
300C3×Q8—62no—
301C3×Q8—62no—
302C3×Q8—121no—
303C3×Q8—121no—
304C3×D4—32no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—61no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—42no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—61no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—121no—
329C2×C3×C4—121no—
330C2×C3×C4—122no—
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4#23511yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4#23711yescharacteristic
340C2×C3×C4#23711yescharacteristic
341C2×C3×C4#23711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343#67—22no—
344#67—22no—
345C2×Dic3—21no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—41no—
349C2×Dic3—41no—
350C2×Dic3—42no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—61no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—242no—
358D12—21no—
359D12(C2×D3)⋊C412yes—
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—242no—
363Dic6—21no—
364Dic6—22no—
365Dic6—22no—
366Dic6—41no—
367Dic6—41no—
368Dic6(C2×D3)⋊C412yes—
369C3×C8—121no—
370C3⋊C8—41no—
371C3⋊C8—62no—
372C3⋊C8—62no—
373C3⋊C8—122no—
374C2×C32—21no—
375C2×C32—21no—
376C2×C32#38611yescharacteristic
377C2×C32#45511yescharacteristic
378C2×C32#45611yescharacteristic
379C3×D3—42no—
380#41—32no—
381#41—32no—
382#41—61no—
383#41—61no—
384C2×Q8—32no—
385C2×Q8—31no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×D4—31no—
392C2×D4—61no—
393C22×C4—21no—
394C22×C4—32no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—182no—
398C22×C4C2×D3211yescharacteristic
399Q16—184no—
400SD16—184no—
401M16—61no—
402M16—61no—
403M16—92no—
404M16—181no—
405C2×C8—61no—
406C2×C8—181no—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4—91no—
410C4⋊C4—91no—
411C4⋊C4—182no—
412C22⋊C4—182no—
413C22⋊C4—181no—
414C42—21no—
415C42—21no—
416C42—182no—
417C42—181no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—62no—
428C22×C3—121no—
429C22×C3—121no—
430C22×C3#67⋊C411yescharacteristic
431C22×C3#88211yescharacteristic
432C22×C3C4×#6711yescharacteristic
433C22×C3#93711yescharacteristic
434C22×C3#93811yescharacteristic
435C22×C3#93911yescharacteristic
436C2×D3—22no—
437C2×D3—41no—
438C2×D3—41no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—42no—
444C3×C4—42no—
445C3×C4—44no—
446C3×C4—62no—
447C3×C4—122no—
448C3×C4—122no—
449C3×C4D3×C22⋊C411yescharacteristic
450C3×C4#67⋊C411yescharacteristic
451C3×C4#67⋊C411yescharacteristic
452C3×C4#88311yescharacteristic
453C3×C4#88411yescharacteristic
454C3×C4#88611yescharacteristic
455C3×C4C2×(C2×D3)⋊C411yescharacteristic
456C3×C4#93911yescharacteristic
457Dic3—22no—
458Dic3—42no—
459Dic3—42no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463Dic3—121no—
464Dic3—241no—
465Dic3—241no—
466C32#188211yescharacteristic, complemented, Sylow
467C23—61no—
468C23D3×#6711yescharacteristic
469Q8—32no—
470Q8—61no—
471Q8—62no—
472Q8—62no—
473Q8—121no—
474Q8—121no—
475D4—32no—
476D4—62no—
477D4—62no—
478D4—61no—
479C2×C4—22no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—122no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—722no—
493C2×C4#379511yescharacteristic
494C2×C4C4×D3211yescharacteristic
495C2×C4D3×D1211yescharacteristic
496C2×C4#380211yescharacteristic
497C2×C4#380511yescharacteristic
498C2×C4D3×#6711yescharacteristic
499C8—121no—
500C8—182no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—41no—
509C2×C3—41no—
510C2×C3—122no—
511C2×C3#482511yescharacteristic
512C2×C3#482611yescharacteristic
513C2×C3#495611yescharacteristic
514C2×C3#495811yescharacteristic
515C2×C3#506111yescharacteristic
516C2×C3#509511yescharacteristic
517D3—42no—
518C22—21no—
519C22—21no—
520C22—62no—
521C22—121no—
522C22—121no—
523C22#6387911yescharacteristic
524C22#6392211yescharacteristic
525C22#6397011yescharacteristic
526C4—42no—
527C4—62no—
528C4—122no—
529C4—122no—
530C4—361no—
531C4—361no—
532C4#6388511yescharacteristic
533C4#6389111yescharacteristic
534C4#6390211yescharacteristic
535C4D3×(C2×D3)⋊C411yescharacteristic
536C3—21no—
537C3#6969311yescharacteristic, complemented
538C3#7036511yescharacteristic, complemented
539C2—21no—
540C2—21no—
541C2—122no—
542C2#1059039611yescharacteristic
543C2#1059039911yescharacteristic
544C2#1059136311yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1882
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4929C2semidirect
5. #10591100C2semidirect
6. #10589389C2semidirect
7. #10589167C2semidirect
24. #63827C4semidirect
38. #4929D3semidirect
61. C2×C3×Dic6C2×C4semidirect
71. #3748C2×C4semidirect
206. C2×Dic6C4×D3semidirect
466. C32#1882semidirect
537. C3#69693semidirect
538. C3#70365semidirect

Maximal subgroups

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

subgroupindex
#105949862
C2×#638272
C3×#49292
C2×C3×#8052
#105911002
#105893892
#105891672
#703653
#696933