Finite Group Databasebeta

← #11789910

Subgroups — #11789910

Order 1152.

697 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#10592920C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591357C211yesmaximal, characteristic, complemented
5C2×#63555C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70188—31nomaximal
9#70187—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×#3757—21no—
12C2×#3757—21no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C3×#832—22no—
21C3×#832C414yescomplemented
22#63579—21no—
23#63555—22no—
24C2×C3×#102—31no—
25C2×C3×#102—31no—
26#5221—31no—
27#5221—31no—
28#5221—61no—
29C2×#832D311yescharacteristic
30C2×#832D311yescharacteristic
31C2×#815—31no—
32C2×#815—31no—
33#4984—31no—
34#4972—31no—
35#4551—31no—
36#4551—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⋊Dic3D411yescharacteristic
49C22×C3⋊Dic3D411yescharacteristic
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52#3757—42no—
53#3757—42no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3C2×C412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8D412yes—
68Dic3⋊Dic3—42no—
69#1936—91noSylow
70C22×C3×D4—21no—
71C22×C3×D4C2×D311yescharacteristic
72C22×C3×D4C2×D311yescharacteristic
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4—31no—
77C2×#217—61no—
78C2×#217—61no—
79C2×#217—61no—
80C2×#217—61no—
81C2×#217—62no—
82C2×#217—62no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—61no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×Dic3⋊C4—61no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊C8C2×D311yescharacteristic
95C3×#102—34no—
96C3×#102—62no—
97#832—22no—
98#832Dic314yescomplemented
99C3⋊#95—61no—
100C3⋊#95—61no—
101#815—62no—
102#815—62no—
103C23×C32—22no—
104C23×C32—41no—
105C23×C32—41no—
106C23×C32—41no—
107C23×C32—41no—
108C23×C32—41no—
109C23×C32—41no—
110C23×C32C2×D411yescharacteristic
111C32×D4—22no—
112C32×D4—22no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×C3⋊C8—22no—
137C3×C3⋊C8—22no—
138C2×#102—31no—
139C2×#102—31no—
140C2×#97—91no—
141#390—91no—
142#389—91no—
143#340—91no—
144#340—91no—
145C24×C3—22no—
146C24×C3—21no—
147C24×C3—21no—
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×D4—41no—
164C2×C3×D4C4×D312yes—
165C2×C3×D4C2×Dic312yes—
166C22×C3×C4—21no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—61no—
178C22×Dic3—61no—
179C22×Dic3—62no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C2×C3×C8—32no—
183C2×C3×C8—32no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C3×C4⋊C4—32no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—61no—
192#217—124no—
193#217—124no—
194#217—122no—
195#217—122no—
196#217—122no—
197#217—122no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—121no—
206C4⋊Dic3—121no—
207C4⋊Dic3—122no—
208C4⋊Dic3C2×Dic312yes—
209Dic3⋊C4—122no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—121no—
215C4×Dic3—121no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8C2×Dic312yes—
221C2×C3⋊C8#6712yes—
222C22×C32—42no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32—81no—
226C22×C32—81no—
227C22×C32—81no—
228C22×C32—81no—
229C22×C32C4×D411yescharacteristic
230C22×C32#12111yescharacteristic
231C22×C32#12411yescharacteristic
232C22×C32AGL(1,ℤ/8)11yescharacteristic
233C22×C32AGL(1,ℤ/8)11yescharacteristic
234C22×C32AGL(1,ℤ/8)11yescharacteristic
235C22×C32#13711yescharacteristic
236C32×C4#11711yescharacteristic
237C32×C4C4×D411yescharacteristic
238C32×C4#12311yescharacteristic
239C32×C4#12611yescharacteristic
240C3⋊Dic3—41no—
241C3⋊Dic3—41no—
242C3⋊Dic3—81no—
243C3×Dic3—42no—
244C3×Dic3—81no—
245C22×D4D3211yescharacteristic
246C22×C8—31no—
247C22×C8—31no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4—181no—
252C2×C22⋊C4—181no—
253C2×C22⋊C4—181no—
254C2×C42—91no—
255#102—34no—
256#102—62no—
257#97—182no—
258#95—181no—
259C23×C3—24no—
260C23×C3—22no—
261C23×C3—22no—
262C23×C3—21no—
263C23×C3—42no—
264C23×C3—42no—
265C23×C3—42no—
266C23×C3—42no—
267C23×C3—42no—
268C23×C3—42no—
269C23×C3—41no—
270C23×C3—41no—
271C23×C3—41no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3—41no—
275C23×C3—41no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—41no—
280C23×C3—41no—
281C23×C3D3×D411yescharacteristic
282C23×C3D3×D411yescharacteristic
283C3×D4—22no—
284C3×D4—22no—
285C3×D4—22no—
286C3×D4—22no—
287C3×D4—42no—
288C3×D4—42no—
289C3×D4—42no—
290C3×D4—42no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C3×D4—41no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—62no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4—121no—
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4#23711yescharacteristic
317C2×C3×C4C22×Dic311yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×Dic3—22no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—121no—
340C2×Dic3—121no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—122no—
344C2×Dic3—122no—
345C2×Dic3—122no—
346C2×Dic3—121no—
347C2×Dic3—121no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C3×C8—62no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—22no—
356C2×C32—82no—
357C2×C32#38811yescharacteristic
358C2×C32#44011yescharacteristic
359C2×C32#44211yescharacteristic
360C2×C32#46811yescharacteristic
361C2×C32#46911yescharacteristic
362C2×C32#48911yescharacteristic
363C2×C32#49011yescharacteristic
364C24—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4D3×Dic312yes—
371C22×C4—61no—
372C22×C4—61no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—181no—
376C22×C4C2×D3211yescharacteristic
377C2×C8—32no—
378C2×C8—32no—
379C2×C8—61no—
380C2×C8—61no—
381C2×C8—61no—
382C2×C8—61no—
383C4⋊C4—32no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4—61no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—362no—
390C22⋊C4—362no—
391C22⋊C4—362no—
392C42—181no—
393C42—181no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—44no—
402C22×C3—44no—
403C22×C3—44no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—42no—
407C22×C3—42no—
408C22×C3—42no—
409C22×C3—42no—
410C22×C3—82no—
411C22×C3—82no—
412C22×C3—82no—
413C22×C3—82no—
414C22×C3—81no—
415C22×C3—81no—
416C22×C3—81no—
417C22×C3—81no—
418C22×C3—81no—
419C22×C3—81no—
420C22×C3—81no—
421C22×C3—81no—
422C22×C3#67⋊C411yescharacteristic
423C22×C3#88411yescharacteristic
424C22×C3#88511yescharacteristic
425C22×C3#88511yescharacteristic
426C22×C3#91111yescharacteristic
427C22×C3#91111yescharacteristic
428C22×C3#91111yescharacteristic
429C22×C3#91111yescharacteristic
430C22×C3#91411yescharacteristic
431C22×C3#91411yescharacteristic
432C22×C3#91511yescharacteristic
433C22×C3#91511yescharacteristic
434C22×C3D4×Dic311yescharacteristic
435C22×C3#93811yescharacteristic
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—122no—
441C3×C4—241no—
442C3×C4#87711yescharacteristic
443C3×C4#87911yescharacteristic
444C3×C4#87911yescharacteristic
445C3×C4#88311yescharacteristic
446C3×C4#92611yescharacteristic
447C3×C4C4×#6711yescharacteristic
448C3×C4D4×Dic311yescharacteristic
449C3×C4#93511yescharacteristic
450Dic3—42no—
451Dic3—81no—
452Dic3—122no—
453Dic3—122no—
454Dic3—121no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458Dic3—242no—
459Dic3—241no—
460Dic3—241no—
461C32#193611yescharacteristic, complemented, Sylow
462C23—22no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23#381111yescharacteristic
470D4—22no—
471D4—22no—
472D4—41no—
473D4—41no—
474C2×C4—62no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—181no—
481C2×C4—181no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—361no—
487C2×C4—361no—
488C2×C4—361no—
489C2×C4C2×D3×Dic311yescharacteristic
490C2×C4#380411yescharacteristic
491C2×C4#380411yescharacteristic
492C2×C4#380411yescharacteristic
493C2×C4#380511yescharacteristic
494C2×C4D3×#6711yescharacteristic
495C8—62no—
496C8—62no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—84no—
505C2×C3—82no—
506C2×C3—82no—
507C2×C3#475711yescharacteristic
508C2×C3#476411yescharacteristic
509C2×C3#476411yescharacteristic
510C2×C3#476511yescharacteristic
511C2×C3#476511yescharacteristic
512C2×C3#478011yescharacteristic
513C2×C3#478211yescharacteristic
514C2×C3#478511yescharacteristic
515C2×C3#494411yescharacteristic
516C2×C3#495111yescharacteristic
517C2×C3#515211yescharacteristic
518C2×C3#515911yescharacteristic
519C2×C3#516411yescharacteristic
520C2×C3#517411yescharacteristic
521C22—42no—
522C22—42no—
523C22—42no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22#6392711yescharacteristic
529C22#6393111yescharacteristic
530C22#6393711yescharacteristic
531C22#6393711yescharacteristic
532C22#6395311yescharacteristic
533C22#6395811yescharacteristic
534C22#67⋊Dic311yescharacteristic
535C4—122no—
536C4—241no—
537C4—361no—
538C4—361no—
539C4—721no—
540C4#6395511yescharacteristic
541C4#6395611yescharacteristic
542C4#6396911yescharacteristic
543C4Dic3×#6711yescharacteristic
544C3—21no—
545C3#7018711yescharacteristic, complemented
546C3#7018811yescharacteristic, complemented
547C2—82no—
548C2#1059143611yescharacteristic
549C2#1059144611yescharacteristic
550C2#1059145411yescharacteristic
551C2#1059146411yescharacteristic
552C2#1059148011yescharacteristic
553C2#1059149611yescharacteristic
554C2#1059170111yescharacteristic
subgroupG/H
centerC23#3811
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. #10591357C2semidirect
5. C2×#63555C2semidirect
6. #10589164C2semidirect
7. #10589164C2semidirect
21. C3×#832C4semidirect
98. #832Dic3semidirect
461. C32#1936semidirect
545. C3#70187semidirect
546. C3#70188semidirect

Maximal subgroups

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

subgroupindex
#105929202
C2×C3×#8322
#105913572
C2×#635552
#105891642
#701883
#701873