Finite Group Databasebeta

← #11788205

Subgroups — #11788205

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595023C211yesmaximal, characteristic
2C2×#63855C211yesmaximal, characteristic, complemented
3C2×#63652C211yesmaximal, characteristic, complemented
4C3×#5126C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#69966—31nomaximal
9#68757—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63977—21no—
18#63966—21no—
19C2×Dic3⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63909C412yescomplemented
22C4×#626—22no—
23#63857C412yescomplemented
24#63855—22no—
25#63855—22no—
26#63652—22no—
27C3×(C2×D3)⋊C8—22no—
28#63570—22no—
29#5791—31no—
30C2×#926—31no—
31#5524—31no—
32C2×#872—31no—
33C3×#407—31no—
34C2×#825—31no—
35C2×#825—31no—
36C2×#825—31no—
37C2×#825—61no—
38#5126D311yescharacteristic, complemented
39C2×#805—31no—
40C3×#339—31no—
41#4555—31no—
42#4555D311yescharacteristic, complemented
43#4532—31no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C22×C3⋊Dic3—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634C2×C411yescharacteristic
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3C2×C412yes—
62C2×C3×C4×D3D412yes—
63C2×#626—22no—
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3D412yescomplemented
69C3×#217—21no—
70C3×C4⋊Dic3C2×C412yes—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×C4×Dic3D412yescomplemented
74C3×#208—21no—
75C3×#208—21no—
76C2×C3×C3⋊C8—21no—
77Dic3⋊Dic3—24no—
78Dic3⋊Dic3—22no—
79#3722—22no—
80(C2×D3)⋊Dic3—24no—
81(C2×D3)⋊Dic3—22no—
82#1897—91noSylow
83C23×C3×C4—31no—
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—61no—
87C22×C4×D3C2×D311yescharacteristic
88C2×C3×M16—21no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C3×#117—31no—
93C2×C3×C42—31no—
94#953—61no—
95C2×#217—61no—
96#930—32no—
97#929—61no—
98C4×#67—62no—
99C2×(C2×D3)⋊C4—61no—
100#926—62no—
101#926—62no—
102#926C2×D311yescharacteristic
103C2×C4⋊Dic3—61no—
104#924—32no—
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208C2×D311yescharacteristic
111#897—32no—
112#895—32no—
113#886—61no—
114#882—61no—
115C4×D12—62no—
116#872—62no—
117#872—62no—
118C3×C22⋊C8—62no—
119#825—62no—
120#825—62no—
121#825—64no—
122#825—62no—
123(C2×D3)⋊C8—22no—
124#805—62no—
125C23×C32C2×D411yescharacteristic
126C22×C3⋊D3—21no—
127C22×C3×D3—21no—
128C22×C3×D3—21no—
129C22×C3×D3—42no—
130C22×C3×D3C22⋊C412yes—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C32×C4#4111yescharacteristic
137#638—41no—
138#638—41no—
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—42no—
142C4⋊(C3⋊D3)—21no—
143C4⋊(C3⋊D3)—21no—
144C4×C3⋊D3—41no—
145C4×C3⋊D3—41no—
146#634—21no—
147#634—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3C22⋊C412yes—
154C3×C4×D3—22no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×C4×D3—22no—
158#626—44no—
159C32×C8—41no—
160C3×C3⋊C8—41no—
161#525—91no—
162C2×#117—91no—
163C2×#104—91no—
164C2×#104—91no—
165#407—31no—
166#339—31no—
167#339—91no—
168C24×C3—31no—
169C23×D3D1211yescharacteristic
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—32no—
173C22×C3×C4—32no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—62no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—121no—
185C22×Dic3—21no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—121no—
189C22×Dic3D1211yescharacteristic
190#235—62no—
191#235—62no—
192#235—61no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—121no—
201#235—121no—
202C2×D12—31no—
203C2×D12—31no—
204C2×D12—61no—
205C2×D12—62no—
206C2×C4×D3—21no—
207C2×C4×D3—21no—
208C2×C4×D3—21no—
209C2×C4×D3—21no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—121no—
213C2×C4×D3C4×D312yes—
214C2×C4×D3#6712yes—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C3×M16—22no—
219C3×M16—21no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—21no—
223C3×M16—41no—
224C3×M16—61no—
225C3×M16—61no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—41no—
229C2×C3×C8—61no—
230C3×C4⋊C4—32no—
231C3×C22⋊C4—61no—
232C3×C42—32no—
233C3×C42—61no—
234C3×C42—61no—
235#217—21no—
236#217—62no—
237#217—64no—
238(C2×D3)⋊C4—62no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242C4⋊Dic3—64no—
243C4⋊Dic3—62no—
244C4⋊Dic3C4×D312yes—
245Dic3⋊C4—62no—
246Dic3⋊C4—64no—
247C4×Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—32no—
250C4×Dic3—32no—
251C4×Dic3—62no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C4×Dic3—121no—
255C4×Dic3D1212yescomplemented
256#208—21no—
257#208—21no—
258C2×C3⋊C8—21no—
259C22×C32—22no—
260C22×C32C2×C22⋊C411yescharacteristic
261C22×C32#12011yescharacteristic
262C22×C32#12311yescharacteristic
263C2×C3⋊D3—41no—
264C2×C3⋊D3—42no—
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—22no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C32×C4C4×D411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12111yescharacteristic
273C32×C4#12111yescharacteristic
274C3⋊Dic3—42no—
275C3⋊Dic3—41no—
276C3×Dic3—22no—
277C3×Dic3—42no—
278C3×Dic3—42no—
279C2×#41—91no—
280C23×C4—31no—
281C2×M16—31no—
282C2×M16D3211yescharacteristic
283#123—181no—
284C22⋊Q8—92no—
285#121—92no—
286#120—181no—
287C4×D4—182no—
288#117—31no—
289#117—182no—
290#117—182no—
291C2×C4⋊C4—181no—
292C2×C22⋊C4—181no—
293C2×C42—31no—
294C2×C42—91no—
295#104—182no—
296#104—182no—
297C22⋊C8—62no—
298C23×C3—21no—
299C23×C3—32no—
300C23×C3—61no—
301C23×C3—61no—
302C23×C3—122no—
303C23×C3C2×D1211yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—21no—
306C22×D3—21no—
307C22×D3—42no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—121no—
311C22×D3(C2×D3)⋊C412yes—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—32no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—122no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×C4×D311yescharacteristic
330C2×C3×C4C2×D1211yescharacteristic
331C2×C3×C4#23511yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
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—124no—
341#67—122no—
342#67—122no—
343#67—121no—
344#67—121no—
345#67—121no—
346#67—121no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—42no—
352C2×Dic3—61no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—61no—
356C2×Dic3—122no—
357C2×Dic3—121no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—124no—
361C2×Dic3(C2×D3)⋊C412yes—
362D12—62no—
363D12—61no—
364D12—61no—
365D12—61no—
366D12—61no—
367D12—121no—
368D12—124no—
369C4×D3—22no—
370C4×D3—22no—
371C4×D3—22no—
372C4×D3—22no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—121no—
376C4×D3—121no—
377C4×D3—121no—
378C4×D3—121no—
379Dic6—62no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—121no—
385C3×C8—42no—
386C3×C8—41no—
387C3×C8—41no—
388C3×C8—121no—
389C3⋊C8—41no—
390C2×C32—21no—
391C2×C32—21no—
392C2×C32#38611yescharacteristic
393C2×C32#42112yes—
394C3⋊D3—81no—
395C3×D3—42no—
396C24—31no—
397#41—181no—
398#41—181no—
399#41—181no—
400#41—181no—
401C2×Q8—91no—
402C2×D4—91no—
403C2×D4—182no—
404C2×D4—181no—
405C22×C4—31no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—61no—
409C22×C4—61no—
410C22×C4—61no—
411C22×C4—61no—
412C22×C4—61no—
413C22×C4—181no—
414C22×C4—181no—
415C22×C4C2×D3211yescharacteristic
416M16—21no—
417M16—21no—
418M16—61no—
419M16—61no—
420C2×C8—21no—
421C2×C8—61no—
422C4⋊C4—32no—
423C4⋊C4—182no—
424C4⋊C4—184no—
425C22⋊C4—61no—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C22⋊C4—184no—
429C42—32no—
430C42—61no—
431C42—61no—
432C42—92no—
433C42—181no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—42no—
440C22×C3—62no—
441C22×C3—62no—
442C22×C3—62no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3D3×C22⋊C411yescharacteristic
446C22×C3#88211yescharacteristic
447C22×C3#88211yescharacteristic
448C22×C3#88611yescharacteristic
449C22×C3#89411yescharacteristic
450C22×C3C2×(C2×D3)⋊C411yescharacteristic
451C2×D3—22no—
452C2×D3—22no—
453C2×D3—22no—
454C2×D3—42no—
455C2×D3—42no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—122no—
461C2×D3—242no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—62no—
467C3×C4—122no—
468C3×C4—122no—
469C3×C4C4×D1211yescharacteristic
470C3×C4#67⋊C411yescharacteristic
471C3×C4#67⋊C411yescharacteristic
472C3×C4#88411yescharacteristic
473C3×C4#89311yescharacteristic
474C3×C4#89511yescharacteristic
475C3×C4#93911yescharacteristic
476C3×C4#93911yescharacteristic
477Dic3—22no—
478Dic3—42no—
479Dic3—42no—
480Dic3—122no—
481Dic3—122no—
482Dic3—122no—
483Dic3—124no—
484Dic3—121no—
485Dic3—121no—
486C32#189711yescharacteristic, complemented, Sylow
487C23—32no—
488C23—61no—
489C23—61no—
490C23—122no—
491C23—181no—
492C23D3×D1211yescharacteristic
493Q8—181no—
494Q8—181no—
495D4—181no—
496D4—181no—
497D4—364no—
498D4—361no—
499D4—361no—
500C2×C4—32no—
501C2×C4—61no—
502C2×C4—61no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—122no—
510C2×C4—181no—
511C2×C4—182no—
512C2×C4—362no—
513C2×C4—361no—
514C2×C4—361no—
515C2×C4#379611yescharacteristic
516C2×C4C4×D3211yescharacteristic
517C2×C4D3×D1211yescharacteristic
518C2×C4#380411yescharacteristic
519C2×C4D3×#6711yescharacteristic
520C2×C4#381111yescharacteristic
521C8—41no—
522C8—121no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—22no—
528C2×C3—21no—
529C2×C3—41no—
530C2×C3—41no—
531C2×C3—122no—
532C2×C3#466511yescharacteristic
533C2×C3#482112yes—
534C2×C3#495811yescharacteristic
535C2×C3#513912yes—
536D3—42no—
537D3—242no—
538D3—241no—
539D3—241no—
540C22—22no—
541C22—62no—
542C22—62no—
543C22—62no—
544C22—122no—
545C22—122no—
546C22—362no—
547C22—361no—
548C22#6389011yescharacteristic
549C22D3×(C2×D3)⋊C411yescharacteristic
550C22#6392311yescharacteristic
551C4—62no—
552C4—122no—
553C4—122no—
554C4—362no—
555C4—361no—
556C4#6388011yescharacteristic
557C4#6388111yescharacteristic
558C4#6388611yescharacteristic
559C4#6397111yescharacteristic
560C3—21no—
561C3#6875711yescharacteristic, complemented
562C3#6996611yescharacteristic, complemented
563C2—21no—
564C2—21no—
565C2—122no—
566C2—721no—
567C2#1059100512yes—
568C2#1059136411yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595023C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63855C2semidirect
3. C2×#63652C2semidirect
4. C3×#5126C2semidirect
5. C2×#63570C2semidirect
6. C3×#4555C2semidirect
7. #10589160C2semidirect
21. #63909C4semidirect
23. #63857C4semidirect
38. #5126D3semidirect
42. #4555D3semidirect
68. C4×C3⋊Dic3D4semidirect
73. C3×C4×Dic3D4semidirect
255. C4×Dic3D12semidirect
486. C32#1897semidirect
561. C3#68757semidirect
562. C3#69966semidirect

Maximal subgroups

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

subgroupindex
#105950232
C2×#638552
C2×#636522
C3×#51262
C2×#635702
C3×#45552
#105891602
#699663
#687573