Finite Group Databasebeta

← #11789909

Subgroups — #11789909

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×#63659C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591212C211yesmaximal, characteristic, complemented
5C2×#63554C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70188—31nomaximal
9#69645—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×#217—21no—
14C2×C3×#217—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3724—21no—
20#63659C414yescomplemented
21C3×#832—22no—
22#63579—21no—
23#63554—22no—
24C2×C3×#102—31no—
25C3×#390—31no—
26#5221D311yescharacteristic
27C2×#832—31no—
28C2×#832—31no—
29C2×#832—61no—
30C2×#832D311yescharacteristic
31C2×#815—31no—
32#4972—31no—
33#4928—31no—
34C2×#803—31no—
35#4551—31no—
36#4529—31no—
37#4529—31no—
38#4529—31no—
39C24×C32—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C412yes—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)C2×C412yes—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)C2×C412yes—
57C3×#217—42no—
58C3×#217—42no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D412yes—
68#3724—42no—
69#1936—91noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C2×D311yescharacteristic
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C22⋊C4—61no—
77C2×C3×C22⋊C4—61no—
78C2×C3×C42—31no—
79C2×#217—21no—
80C2×#217—21no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—61no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4—61no—
88C2×C4×Dic3C2×D311yescharacteristic
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93C3×#102—62no—
94#832—22no—
95#832—34no—
96#832—34no—
97#832—64no—
98C3⋊#95—61no—
99C3⋊#95—61no—
100#815—62no—
101#803—62no—
102C23×C32—22no—
103C23×C32—41no—
104C23×C32—41no—
105C23×C32—41no—
106C23×C32—41no—
107C23×C32—41no—
108C23×C32—41no—
109C23×C32C2×D411yescharacteristic
110C32×D4—22no—
111C32×D4—22no—
112C32×D4—41no—
113C32×D4—41no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
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—31no—
138C2×#102—91no—
139C2×#97—91no—
140#390—31no—
141#389—91no—
142#340—91no—
143#340—91no—
144C24×C3—21no—
145C24×C3—21no—
146C24×C3—41no—
147C2×C3×D4—22no—
148C2×C3×D4—22no—
149C2×C3×D4—21no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—21no—
154C2×C3×D4—21no—
155C2×C3×D4—21no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—22no—
160C2×C3×D4—41no—
161C2×C3×D4—41no—
162C2×C3×D4—41no—
163C2×C3×D4C4×D312yes—
164C2×C3×D4C4×D312yes—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—121no—
177C22×Dic3#6711yescharacteristic
178C22×Dic3#6711yescharacteristic
179C2×C3×C8—32no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C22⋊C4—122no—
187C3×C22⋊C4—122no—
188C3×C42—61no—
189C3×C42—61no—
190#217—42no—
191#217—42no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—32no—
197C4⋊Dic3—32no—
198C4⋊Dic3—62no—
199C4⋊Dic3—61no—
200C4⋊Dic3—61no—
201C4⋊Dic3—121no—
202Dic3⋊C4—122no—
203Dic3⋊C4—122no—
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⋊C8#6712yes—
218C22×C32—42no—
219C22×C32—42no—
220C22×C32—42no—
221C22×C32—81no—
222C22×C32—81no—
223C22×C32—81no—
224C22×C32—81no—
225C22×C32C4×D411yescharacteristic
226C22×C32#12111yescharacteristic
227C22×C32#12411yescharacteristic
228C22×C32AGL(1,ℤ/8)11yescharacteristic
229C22×C32AGL(1,ℤ/8)11yescharacteristic
230C22×C32AGL(1,ℤ/8)11yescharacteristic
231C22×C32#13711yescharacteristic
232C32×C4#11711yescharacteristic
233C32×C4C4×D411yescharacteristic
234C32×C4#12311yescharacteristic
235C32×C4#12611yescharacteristic
236C3⋊Dic3—42no—
237C3×Dic3—41no—
238C3×Dic3—41no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×D4D3211yescharacteristic
242C22×C8—31no—
243C22×C8—91no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—181no—
248C2×C22⋊C4—61no—
249C2×C22⋊C4—61no—
250C2×C42—31no—
251#102—62no—
252#102—94no—
253#97—182no—
254#95—181no—
255C23×C3—22no—
256C23×C3—22no—
257C23×C3—21no—
258C23×C3—42no—
259C23×C3—42no—
260C23×C3—42no—
261C23×C3—41no—
262C23×C3—41no—
263C23×C3—41no—
264C23×C3—41no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3—41no—
268C23×C3—41no—
269C23×C3—41no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—81no—
274C23×C3—81no—
275C23×C3—81no—
276C23×C3—81no—
277C23×C3D3×D411yescharacteristic
278C23×C3C2×#6711yescharacteristic
279C3×D4—24no—
280C3×D4—22no—
281C3×D4—22no—
282C3×D4—22no—
283C3×D4—22no—
284C3×D4—42no—
285C3×D4—42no—
286C3×D4—42no—
287C3×D4—41no—
288C3×D4—41no—
289C3×D4—41no—
290C3×D4—41no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—61no—
302C2×C3×C4—61no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4C2×C4×D311yescharacteristic
310C2×C3×C4C2×C4×D311yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4#23711yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4#23711yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—122no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340C2×Dic3—241no—
341C2×Dic3—241no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8—62no—
345C3⋊C8—62no—
346C3⋊C8—122no—
347C2×C32—82no—
348C2×C32#38811yescharacteristic
349C2×C32#44011yescharacteristic
350C2×C32#44211yescharacteristic
351C2×C32#46811yescharacteristic
352C2×C32#46911yescharacteristic
353C2×C32#48911yescharacteristic
354C2×C32#49011yescharacteristic
355C24—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4#62412yes—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—61no—
365C22×C4—61no—
366C22×C4—181no—
367C22×C4C2×D3211yescharacteristic
368C2×C8—32no—
369C2×C8—61no—
370C2×C8—61no—
371C2×C8—92no—
372C2×C8—181no—
373C2×C8—181no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4—92no—
379C4⋊C4—181no—
380C4⋊C4—362no—
381C22⋊C4—122no—
382C22⋊C4—122no—
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—44no—
393C22×C3—42no—
394C22×C3—42no—
395C22×C3—42no—
396C22×C3—42no—
397C22×C3—42no—
398C22×C3—42no—
399C22×C3—82no—
400C22×C3—82no—
401C22×C3—82no—
402C22×C3—82no—
403C22×C3—82no—
404C22×C3—82no—
405C22×C3—81no—
406C22×C3—81no—
407C22×C3—81no—
408C22×C3—81no—
409C22×C3—81no—
410C22×C3—81no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3#67⋊C411yescharacteristic
414C22×C3#88511yescharacteristic
415C22×C3#91111yescharacteristic
416C22×C3#91111yescharacteristic
417C22×C3#91411yescharacteristic
418C22×C3#91511yescharacteristic
419C22×C3C4×#6711yescharacteristic
420C22×C3#93211yescharacteristic
421C22×C3#93211yescharacteristic
422C22×C3#93611yescharacteristic
423C22×C3#93811yescharacteristic
424C22×C3#93911yescharacteristic
425C22×C3#94911yescharacteristic
426C22×C3#95111yescharacteristic
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—121no—
432C3×C4—121no—
433C3×C4—241no—
434C3×C4—241no—
435C3×C4#87711yescharacteristic
436C3×C4#87711yescharacteristic
437C3×C4#87911yescharacteristic
438C3×C4#87911yescharacteristic
439C3×C4#67⋊C411yescharacteristic
440C3×C4#88311yescharacteristic
441C3×C4C4×#6711yescharacteristic
442C3×C4#93511yescharacteristic
443Dic3—41no—
444Dic3—41no—
445Dic3—81no—
446Dic3—81no—
447Dic3—122no—
448Dic3—122no—
449Dic3—242no—
450C32#193611yescharacteristic, complemented, Sylow
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23D3×#6711yescharacteristic
459D4—22no—
460D4—22no—
461D4—41no—
462D4—41no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—182no—
476C2×C4—361no—
477C2×C4—361no—
478C2×C4#380411yescharacteristic
479C2×C4#380411yescharacteristic
480C2×C4#380511yescharacteristic
481C2×C4#380511yescharacteristic
482C2×C4C2×#62411yescharacteristic
483C2×C4D3×#6711yescharacteristic
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—84no—
494C2×C3—82no—
495C2×C3—82no—
496C2×C3#475711yescharacteristic
497C2×C3#476411yescharacteristic
498C2×C3#476511yescharacteristic
499C2×C3#478511yescharacteristic
500C2×C3#494411yescharacteristic
501C2×C3#494511yescharacteristic
502C2×C3#501411yescharacteristic
503C2×C3#501811yescharacteristic
504C2×C3#503911yescharacteristic
505C2×C3#504211yescharacteristic
506C2×C3#505511yescharacteristic
507C2×C3#507111yescharacteristic
508C2×C3#515911yescharacteristic
509C2×C3#517411yescharacteristic
510C22—42no—
511C22—42no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22#6392511yescharacteristic
518C22#6392911yescharacteristic
519C22#6393211yescharacteristic
520C22#6393411yescharacteristic
521C22#6395211yescharacteristic
522C22#6395911yescharacteristic
523C22#6397011yescharacteristic
524C4—121no—
525C4—121no—
526C4—241no—
527C4—241no—
528C4—362no—
529C4#6395211yescharacteristic
530C4#6395611yescharacteristic
531C4#6395711yescharacteristic
532C4#6396911yescharacteristic
533C3—21no—
534C3#6964511yescharacteristic, complemented
535C3#7018811yescharacteristic, complemented
536C2—82no—
537C2#1059140411yescharacteristic
538C2#1059140511yescharacteristic
539C2#1059145111yescharacteristic
540C2#1059147711yescharacteristic
541C2#1059148811yescharacteristic
542C2#1059150211yescharacteristic
543C2#1059170311yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1936
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591212C2semidirect
5. C2×#63554C2semidirect
6. #10589164C2semidirect
7. #10589163C2semidirect
20. #63659C4semidirect
450. C32#1936semidirect
534. C3#69645semidirect
535. C3#70188semidirect

Maximal subgroups

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

subgroupindex
C2×#636592
C3×#52212
C2×C3×#8322
#105912122
C2×#635542
#105891642
#105891632
#701883
#696453