Finite Group Databasebeta

← #11789899

Subgroups — #11789899

Order 1152.

669 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63636C211yesmaximal, characteristic
2C3×#4972C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic
4C2×#63564C211yesmaximal, characteristic
5C2×#63554C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#69617—31nomaximal
9#68856—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×Dic3⋊C4—21no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3722—21no—
19C2×#3722—21no—
20#63636—22no—
21C3×C3⋊#95—21no—
22#63564C414yescomplemented
23#63554—22no—
24C3×#389—31no—
25C2×#821—31no—
26C2×#815—31no—
27#4988—31no—
28#4972D311yescharacteristic, complemented
29C2×#809—31no—
30C2×#809—31no—
31C2×#809—31no—
32C2×#809—61no—
33#4939—31no—
34C2×#803—31no—
35C3×#340—31no—
36#4529—31no—
37#4529—31no—
38#4529D311yescharacteristic, complemented
39C23×C3⋊D3—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C2×C4⋊(C3⋊D3)—21no—
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—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)D412yes—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3C2×C412yes—
61C3×Dic3⋊C4—42no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8C2×C412yes—
67#3722—42no—
68#3722—42no—
69#1936—91noSylow
70C22×D12—31no—
71C22×D12—31no—
72C22×D12—61no—
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—61no—
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C4⋊C4C2×D311yescharacteristic
80C2×C3×C42—31no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×Dic3⋊C4—21no—
88C2×C4×Dic3C2×D311yescharacteristic
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93C3×#95—61no—
94C3⋊#95—21no—
95#821—34no—
96#815—62no—
97#809—34no—
98#809—62no—
99#809—62no—
100#809—64no—
101#803—62no—
102C23×C32C2×D411yescharacteristic
103C22×C3⋊D3—22no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—41no—
107C22×C3⋊D3—41no—
108C22×C3⋊D3—41no—
109C22×C3⋊D3—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—22no—
121C4⋊(C3⋊D3)—41no—
122C4⋊(C3⋊D3)—41no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C3⋊(C3⋊C8)—22no—
136C3×C3⋊C8—22no—
137C2×#102—91no—
138C2×#102—91no—
139C2×#97—91no—
140#390—91no—
141#389—31no—
142#340—31no—
143#340—91no—
144C23×D3—61no—
145C23×D3—61no—
146C23×D3—121no—
147C22×C3×C4—21no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—41no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3#6711yescharacteristic
160C22×Dic3#6711yescharacteristic
161C2×D12—32no—
162C2×D12—32no—
163C2×D12—62no—
164C2×D12—62no—
165C2×D12—62no—
166C2×D12—61no—
167C2×D12—61no—
168C2×D12—61no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—61no—
176C2×D12—121no—
177C2×D12—121no—
178C2×D12—121no—
179C2×C3×C8—32no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—32no—
188C3×C4⋊C4—41no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—122no—
193C3×C42—61no—
194C3×C42—61no—
195(C2×D3)⋊C4—122no—
196(C2×D3)⋊C4—122no—
197(C2×D3)⋊C4—122no—
198(C2×D3)⋊C4—122no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3C4×D312yes—
203Dic3⋊C4—42no—
204C4×Dic3—21no—
205C4×Dic3—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—32no—
209C2×C3⋊C8—32no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—121no—
216C2×C3⋊C8—121no—
217C2×C3⋊C8C4×D312yes—
218C22×C32C4×D411yescharacteristic
219C22×C32#12111yescharacteristic
220C22×C32#12411yescharacteristic
221C22×C32AGL(1,ℤ/8)11yescharacteristic
222C22×C32AGL(1,ℤ/8)11yescharacteristic
223C22×C32AGL(1,ℤ/8)11yescharacteristic
224C22×C32#13711yescharacteristic
225C2×C3⋊D3—42no—
226C2×C3⋊D3—42no—
227C2×C3⋊D3—42no—
228C2×C3⋊D3—81no—
229C2×C3⋊D3—81no—
230C2×C3⋊D3—81no—
231C2×C3⋊D3—81no—
232C32×C4—81no—
233C32×C4#11711yescharacteristic
234C32×C4C4×D411yescharacteristic
235C32×C4#12311yescharacteristic
236C32×C4#12611yescharacteristic
237C3×Dic3—42no—
238C3×Dic3—41no—
239C3×Dic3—41no—
240C3×Dic3—81no—
241C22×D4—91no—
242C22×C8—31no—
243C22×C8—91no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—61no—
247C2×C4⋊C4D3211yescharacteristic
248C2×C22⋊C4—181no—
249C2×C22⋊C4—181no—
250C2×C42—31no—
251#102—94no—
252#102—182no—
253#97—182no—
254#95—61no—
255C23×C3—21no—
256C23×C3D3×D411yescharacteristic
257C23×C3C2×#6711yescharacteristic
258C22×D3—62no—
259C22×D3—62no—
260C22×D3—122no—
261C22×D3—122no—
262C22×D3—122no—
263C22×D3—121no—
264C22×D3—121no—
265C22×D3—121no—
266C22×D3—121no—
267C22×D3—121no—
268C22×D3—121no—
269C22×D3—121no—
270C22×D3—121no—
271C22×D3—121no—
272C22×D3—121no—
273C22×D3—121no—
274C22×D3—121no—
275C22×D3—241no—
276C22×D3—241no—
277C22×D3—241no—
278C22×D3—241no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—61no—
293C2×C3×C4—61no—
294C2×C3×C4—62no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—81no—
300C2×C3×C4—81no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23911yescharacteristic
316C2×C3×C4#23911yescharacteristic
317C2×C3×C4#23911yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—21no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330D12—64no—
331D12—62no—
332D12—62no—
333D12—62no—
334D12—62no—
335D12—122no—
336D12—122no—
337D12—122no—
338D12—121no—
339D12—121no—
340D12—121no—
341D12—121no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—122no—
347C2×C32#38811yescharacteristic
348C2×C32#44011yescharacteristic
349C2×C32#44211yescharacteristic
350C2×C32#46811yescharacteristic
351C2×C32#46911yescharacteristic
352C2×C32#48911yescharacteristic
353C2×C32#49011yescharacteristic
354C3⋊D3—82no—
355C24—181no—
356C2×D4—92no—
357C2×D4—181no—
358C2×D4—181no—
359C2×D4—181no—
360C2×D4—181no—
361C2×D4—181no—
362C22×C4—21no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4C2×D3211yescharacteristic
368C2×C8—32no—
369C2×C8—61no—
370C2×C8—61no—
371C2×C8—92no—
372C2×C8—181no—
373C2×C8—181no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—32no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C4⋊C4—61no—
380C4⋊C4—122no—
381C22⋊C4—362no—
382C22⋊C4—362no—
383C42—61no—
384C42—61no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—21no—
392C22×C3#88411yescharacteristic
393C22×C3#88511yescharacteristic
394C22×C3#89311yescharacteristic
395C22×C3#91111yescharacteristic
396C22×C3#91411yescharacteristic
397C22×C3#91411yescharacteristic
398C22×C3#91811yescharacteristic
399C22×C3C4×#6711yescharacteristic
400C22×C3#93211yescharacteristic
401C22×C3#93911yescharacteristic
402C22×C3#94211yescharacteristic
403C22×C3#94711yescharacteristic
404C22×C3#94911yescharacteristic
405C22×C3#94911yescharacteristic
406C2×D3—124no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—122no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—242no—
414C2×D3—242no—
415C2×D3—242no—
416C2×D3—242no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—241no—
420C2×D3—241no—
421C2×D3—241no—
422C2×D3—241no—
423C2×D3—241no—
424C2×D3—241no—
425C2×D3—241no—
426C2×D3—241no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—82no—
432C3×C4—81no—
433C3×C4—81no—
434C3×C4—122no—
435C3×C4—121no—
436C3×C4—121no—
437C3×C4—241no—
438C3×C4#87211yescharacteristic
439C3×C4#67⋊C411yescharacteristic
440C3×C4#89211yescharacteristic
441C3×C4#89311yescharacteristic
442C3×C4#89411yescharacteristic
443C3×C4#89411yescharacteristic
444C3×C4#89811yescharacteristic
445C3×C4#89811yescharacteristic
446Dic3—42no—
447Dic3—41no—
448Dic3—41no—
449Dic3—81no—
450C32#193611yescharacteristic, complemented, Sylow
451C23—182no—
452C23—361no—
453C23—361no—
454C23—361no—
455C23—361no—
456C23—361no—
457C23—361no—
458C23D3×#6711yescharacteristic
459D4—182no—
460D4—182no—
461D4—361no—
462D4—361no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—62no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4#379611yescharacteristic
479C2×C4#379911yescharacteristic
480C2×C4#379911yescharacteristic
481C2×C4C4×D3211yescharacteristic
482C2×C4#380411yescharacteristic
483C2×C4#381111yescharacteristic
484C8—62no—
485C8—182no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3#466911yescharacteristic
494C2×C3#476411yescharacteristic
495C2×C3#478211yescharacteristic
496C2×C3#479411yescharacteristic
497C2×C3#481211yescharacteristic
498C2×C3#486911yescharacteristic
499C2×C3#488911yescharacteristic
500C2×C3#499011yescharacteristic
501C2×C3#501411yescharacteristic
502C2×C3#502611yescharacteristic
503C2×C3#503911yescharacteristic
504C2×C3#504911yescharacteristic
505C2×C3#506711yescharacteristic
506C2×C3#508911yescharacteristic
507D3—244no—
508D3—242no—
509D3—242no—
510C22—362no—
511C22—362no—
512C22—362no—
513C22—721no—
514C22—721no—
515C22—721no—
516C22—721no—
517C22#6390411yescharacteristic
518C22#6390711yescharacteristic
519C22#6392511yescharacteristic
520C22#6393411yescharacteristic
521C22#6393911yescharacteristic
522C22#6394811yescharacteristic
523C22#6397111yescharacteristic
524C4—81no—
525C4—121no—
526C4—122no—
527C4—121no—
528C4—241no—
529C4#6383611yescharacteristic
530C4#6384811yescharacteristic
531C4#6388111yescharacteristic
532C4#6389711yescharacteristic
533C3—21no—
534C3#6885611yescharacteristic, complemented
535C3#6961711yescharacteristic, complemented
536C2—722no—
537C2#1059045711yescharacteristic
538C2#1059053511yescharacteristic
539C2#1059055011yescharacteristic
540C2#1059058911yescharacteristic
541C2#1059125811yescharacteristic
542C2#1059145311yescharacteristic
543C2#1059158911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1936
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4972C2semidirect
5. C2×#63554C2semidirect
6. C3×#4529C2semidirect
7. #10589163C2semidirect
22. #63564C4semidirect
28. #4972D3semidirect
38. #4529D3semidirect
450. C32#1936semidirect
534. C3#68856semidirect
535. C3#69617semidirect

Maximal subgroups

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

subgroupindex
C2×#636362
C3×#49722
#105913202
C2×#635642
C2×#635542
C3×#45292
#105891632
#696173
#688563