Finite Group Databasebeta

← #11787695

Subgroups — #11787695

Order 1152.

761 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594992C211yesmaximal, characteristic
2C2×#63831C211yesmaximal, characteristic
3#10592628C211yesmaximal, characteristic, complemented
4C2×C3×#805C211yesmaximal, characteristic
5#10591107C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70365—31nomaximal
9#68775—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#67⋊Dic3—22no—
18Dic3×D12—21no—
19D3×C4⋊Dic3—21no—
20Dic3×Dic6—21no—
21#63841—21no—
22C2×#3719—21no—
23#63831—22no—
24#63831C414yescomplemented
25C2×#3716—21no—
26#63658—22no—
27C3×#805—22no—
28#63567—21no—
29#63567—21no—
30#5827—31no—
31C2×#951—31no—
32C2×#909—31no—
33#5523—31no—
34C2×C3×#104—31no—
35#5120—31no—
36#5004—31no—
37#4929—31no—
38#4929—31no—
39#4929—61no—
40C2×#805D311yescharacteristic
41C3×#339—31no—
42#4554—31no—
43#4554—31no—
44#4523D311yescharacteristic, complemented
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D412yes—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634C2×C412yescomplemented
55C2×C3×#67—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235C2×C412yes—
59C3×#235D412yes—
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6D411yescharacteristic
63C2×D3×Dic3—22no—
64C32×C42—21no—
65C32×C42—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C3×#217—21no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×C4⋊Dic3D411yescharacteristic
71C3×C4×Dic3—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208C2×C412yescomplemented
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78Dic3⋊Dic3—22no—
79(C2×D3)⋊Dic3—22no—
80Dic32—22no—
81#3719—24no—
82#3716—24no—
83#1882—91noSylow
84C2×C3×#41—31no—
85C2×#235C2×D311yescharacteristic
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C3×#117—31no—
92C2×C3×C42—21no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C2×D311yescharacteristic
95#951—34no—
96#951—62no—
97Q8×Dic3—61no—
98C2×#216—61no—
99D4×Dic3—61no—
100D4×Dic3—62no—
101C2×#214—61no—
102#926—61no—
103#926C2×D311yescharacteristic
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—61no—
107C2×C4⋊Dic3—61no—
108C2×#208C2×D311yescharacteristic
109C2×#208C2×D311yescharacteristic
110#909—34no—
111#909—62no—
112C2×Dic12—61no—
113C2×#204—61no—
114#892—61no—
115D3×C4⋊C4—61no—
116#67⋊C4—62no—
117C4×D12—61no—
118C4×Dic6—61no—
119C3×#104—62no—
120C3⋊#95—62no—
121C3⋊#95—62no—
122C3⋊#95—64no—
123#816—61no—
124#816—61no—
125#810—61no—
126#810—61no—
127#805—22no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—21no—
130C2×C32×C4—22no—
131C2×C32×C4—41no—
132C2×C32×C4—41no—
133C2×C32×C4C22×C411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4#4111yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—41no—
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—42no—
144#634—22no—
145#634—22no—
146#634—41no—
147#634—41no—
148C3×#67—22no—
149C3×#67—22no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C3×D12—21no—
154C3×D12C22⋊C412yes—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×Dic6—21no—
158C3×Dic6C22⋊C412yes—
159D3×Dic3—82no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—41no—
162C2×#137—91no—
163#520—91no—
164C2×#104—31no—
165#419—91no—
166#391—91no—
167#343—91no—
168#339—31no—
169C3×#41—32no—
170C3×#41—32no—
171C3×#41—61no—
172C3×#41—61no—
173C2×C3×Q8—31no—
174C2×C3×D4—31no—
175C2×C3×D4—61no—
176C22×C3×C4—22no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—21no—
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—62no—
187C22×Dic3—62no—
188C22×Dic3—62no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191#235—21no—
192#235—21no—
193#235C4×D312yes—
194#235#6712yes—
195C2×D12D1211yescharacteristic
196C2×C4×D3—21no—
197C2×C4×D3—62no—
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—62no—
201C2×Dic6—61no—
202C2×Dic6—61no—
203C2×Dic6—61no—
204C2×Dic6—61no—
205C2×Dic6—61no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—62no—
210C2×Dic6—61no—
211C2×Dic6—61no—
212C2×Dic6—121no—
213C2×Dic6—121no—
214C2×Dic6—121no—
215C2×Dic6—121no—
216C2×Dic6D1211yescharacteristic
217C3×M16—32no—
218C3×M16—61no—
219C3×M16—61no—
220C3×M16—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C3×C4⋊C4—31no—
224C3×C4⋊C4—31no—
225C3×C22⋊C4—61no—
226C3×C42—21no—
227C3×C42—21no—
228C3×C42—21no—
229C3×C42—21no—
230C3×C42—41no—
231C3×C42—41no—
232C3×C42—61no—
233#217—21no—
234#217—62no—
235#216—64no—
236#214—64no—
237(C2×D3)⋊C4—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3—61no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—121no—
244C4⋊Dic3—121no—
245C4⋊Dic3D1211yescharacteristic
246C4⋊Dic3D1211yescharacteristic
247Dic3⋊C4—62no—
248C4×Dic3—21no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251#208—21no—
252#208—21no—
253#208—21no—
254#208C4×D312yescomplemented
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257Dic12—64no—
258#204—64no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32C4×D411yescharacteristic
262C22×C32#12011yescharacteristic
263C22×C32#12111yescharacteristic
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—41no—
267C32×C4—42no—
268C32×C4C2×C22⋊C411yescharacteristic
269C32×C4C4×D411yescharacteristic
270C32×C4#12111yescharacteristic
271C32×C4#12311yescharacteristic
272C3⋊Dic3—42no—
273C3⋊Dic3—42no—
274C3×Dic3—22no—
275C3×Dic3—41no—
276C3×Dic3—41no—
277C2×#41—31no—
278C22×Q8—91no—
279#137—94no—
280#137—182no—
281C2×Q16—181no—
282C2×SD16—181no—
283C2×M16—31no—
284C2×M16—31no—
285C4×Q8—181no—
286C4×D4—181no—
287C4×D4—182no—
288#117—31no—
289#117—181no—
290C2×C4⋊C4—91no—
291C2×C4⋊C4—181no—
292C2×C42D3211yescharacteristic
293#104—62no—
294#103—181no—
295#103—181no—
296#95—182no—
297C23×C3—21no—
298C23×C3—61no—
299C23×C3D3×D411yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—21no—
302C3×Q8—32no—
303C3×Q8—61no—
304C3×D4—32no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—61no—
308C2×C3×C4—24no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—61no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—61no—
327C2×C3×C4—61no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4C2×D1211yescharacteristic
332C2×C3×C4#23511yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4#23711yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4#23911yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340#67—22no—
341#67—22no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—64no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—122no—
351C2×Dic3—122no—
352C2×Dic3—122no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—124no—
360C2×Dic3—242no—
361D12—21no—
362D12(C2×D3)⋊C412yes—
363C4×D3—22no—
364C4×D3—22no—
365C4×D3—242no—
366Dic6—21no—
367Dic6—62no—
368Dic6—62no—
369Dic6—62no—
370Dic6—62no—
371Dic6—122no—
372Dic6—122no—
373Dic6—122no—
374Dic6—122no—
375Dic6—121no—
376Dic6—121no—
377Dic6—121no—
378Dic6—121no—
379Dic6(C2×D3)⋊C412yes—
380C3×C8—62no—
381C3×C8—121no—
382C3⋊C8—22no—
383C3⋊C8—41no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#38611yescharacteristic
387C2×C32#45511yescharacteristic
388C2×C32#45611yescharacteristic
389C3×D3—42no—
390#41—32no—
391#41—32no—
392#41—61no—
393#41—61no—
394C2×Q8—31no—
395C2×Q8—92no—
396C2×Q8—181no—
397C2×Q8—181no—
398C2×Q8—181no—
399C2×Q8—181no—
400C2×Q8—181no—
401C2×D4—31no—
402C2×D4—61no—
403C22×C4—21no—
404C22×C4—61no—
405C22×C4—92no—
406C22×C4—182no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409Q16—184no—
410SD16—184no—
411M16—32no—
412M16—61no—
413M16—61no—
414M16—61no—
415C2×C8—61no—
416C2×C8—61no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—182no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C22⋊C4—61no—
423C22⋊C4—182no—
424C42—21no—
425C42—21no—
426C42—61no—
427C42—182no—
428C22×C3—22no—
429C22×C3—22no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—62no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3#67⋊C411yescharacteristic
441C22×C3#88211yescharacteristic
442C22×C3#88211yescharacteristic
443C22×C3#88411yescharacteristic
444C22×C3#89311yescharacteristic
445C22×C3#93911yescharacteristic
446C2×D3—22no—
447C2×D3—41no—
448C2×D3—41no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—44no—
454C3×C4—42no—
455C3×C4—42no—
456C3×C4—62no—
457C3×C4—121no—
458C3×C4—121no—
459C3×C4C4×D1211yescharacteristic
460C3×C4D3×C22⋊C411yescharacteristic
461C3×C4#67⋊C411yescharacteristic
462C3×C4#88611yescharacteristic
463C3×C4#89411yescharacteristic
464C3×C4#89511yescharacteristic
465C3×C4C2×(C2×D3)⋊C411yescharacteristic
466C3×C4#93911yescharacteristic
467Dic3—22no—
468Dic3—41no—
469Dic3—41no—
470Dic3—124no—
471Dic3—122no—
472Dic3—122no—
473Dic3—122no—
474Dic3—122no—
475Dic3—242no—
476C32#188211yescharacteristic, complemented, Sylow
477C23—61no—
478C23#381111yescharacteristic
479Q8—32no—
480Q8—61no—
481Q8—182no—
482Q8—182no—
483Q8—361no—
484Q8—361no—
485D4—32no—
486D4—62no—
487D4—62no—
488D4—61no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—61no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—361no—
500C2×C4—361no—
501C2×C4—362no—
502C2×C4—722no—
503C2×C4#379611yescharacteristic
504C2×C4C4×D3211yescharacteristic
505C2×C4D3×D1211yescharacteristic
506C2×C4D3×D1211yescharacteristic
507C2×C4#380411yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C8—62no—
510C8—121no—
511C2×C3—22no—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—122no—
521C2×C3#466511yescharacteristic
522C2×C3#482511yescharacteristic
523C2×C3#482511yescharacteristic
524C2×C3#482611yescharacteristic
525C2×C3#482611yescharacteristic
526C2×C3#495811yescharacteristic
527D3—42no—
528C22—21no—
529C22—21no—
530C22—62no—
531C22—121no—
532C22—121no—
533C22#6388111yescharacteristic
534C22#6392311yescharacteristic
535C22#6397111yescharacteristic
536C4—42no—
537C4—62no—
538C4—121no—
539C4—121no—
540C4—362no—
541C4—362no—
542C4#6388011yescharacteristic
543C4#6388611yescharacteristic
544C4#6389011yescharacteristic
545C4D3×(C2×D3)⋊C411yescharacteristic
546C3—21no—
547C3#6877511yescharacteristic, complemented
548C3#7036511yescharacteristic, complemented
549C2—21no—
550C2—21no—
551C2—122no—
552C2#1059039811yescharacteristic
553C2#1059040111yescharacteristic
554C2#1059136411yescharacteristic
subgroupG/H
centerC22#63923
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. #10592628C2semidirect
5. #10591107C2semidirect
6. C3×#4523C2semidirect
7. #10589168C2semidirect
24. #63831C4semidirect
44. #4523D3semidirect
54. C2×#634C2×C4semidirect
75. C3×#208C2×C4semidirect
254. #208C4×D3semidirect
476. C32#1882semidirect
547. C3#68775semidirect
548. C3#70365semidirect

Maximal subgroups

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

subgroupindex
#105949922
C2×#638312
#105926282
C2×C3×#8052
#105911072
C3×#45232
#105891682
#703653
#687753