Finite Group Databasebeta

← #11796374

Subgroups — #11796374

Order 1152.

595 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic
2#10592939C211yesmaximal, characteristic, complemented
3C3×#5240C211yesmaximal, characteristic, complemented
4#10589180C212yesmaximal, complemented
5#10589178C212yesmaximal, complemented
6#71819—31nomaximal
7#70060—31nomaximal
8C2×C32×#41C2211yescharacteristic
9C2×C3×#235C411yescharacteristic, complemented
10#64135—21no—
11C3×#947C411yescharacteristic, complemented
12C3×#944C411yescharacteristic, complemented
13C3×#940C2211yescharacteristic
14C3×#939—21no—
15C3×#939—21no—
16C3×#936C2211yescharacteristic
17C3×C4×#67—21no—
18C3×C4×#67—21no—
19C3×#926—21no—
20C2×C3×C4×Dic3C411yescharacteristic, complemented
21#63661—21no—
22#63661C2212yes—
23C3×#834—21no—
24C3×#834C2212yes—
25C3×#532—31no—
26#5832D311yescharacteristic
27C3×#410—31no—
28#5240—31no—
29#5240—31no—
30#5240—61no—
31#5240D311yescharacteristic, complemented
32#4545—32no—
33#4541—32no—
34#4474—32no—
35#4473—32no—
36C32×#41—41no—
37C32×#41—41no—
38C2×C32×Q8C2×C411yescharacteristic
39C2×C32×D4D411yescharacteristic
40C2×C32×D4D411yescharacteristic
41C2×C32×D4C2311yescharacteristic
42C22×C32×C4C2×C411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C3×#235—41no—
50C3×#235—41no—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54#3757—22no—
55C4⋊(C3⋊Dic3)—41no—
56C4×C3⋊Dic3—41no—
57C3×#217—21no—
58C3×#217—21no—
59C3×#217—22no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—41no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3—41no—
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3C2×C411yescharacteristic
69#2126—91noSylow
70C2×C3×#41—21no—
71C2×C3×#41—31no—
72C2×C3×#41C2×D311yescharacteristic
73C2×C3×#41C2×D311yescharacteristic
74C2×#235Dic311yescharacteristic, complemented
75C3×C4⋊Q8—31no—
76C3×#127—31no—
77C3×#124—31no—
78C3×#124—31no—
79C3×#121—61no—
80C3×#121—61no—
81C3×C4×D4—61no—
82C3×C4×D4—61no—
83C3×#117—61no—
84C2×C3×C42—31no—
85#947Dic311yescharacteristic, complemented
86#944Dic311yescharacteristic, complemented
87#940C2×D311yescharacteristic
88#939—21no—
89#939—21no—
90#936C2×D311yescharacteristic
91C4×#67—21no—
92C4×#67—21no—
93#926—21no—
94#926—62no—
95#926—61no—
96#926—61no—
97C2×C4×Dic3Dic311yescharacteristic, complemented
98C3×#99—32no—
99C3×#99—61no—
100#834—21no—
101#834—32no—
102#834—32no—
103#834—62no—
104#834—62no—
105#834—61no—
106#834—61no—
107#834C2×D312yes—
108C23×C32C22⋊C411yescharacteristic
109C23×C32C2×D411yescharacteristic
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—21no—
112C32×Q8—41no—
113C32×D4—41no—
114C32×D4—41no—
115C32×D4—41no—
116C2×C32×C4—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4C22⋊C411yescharacteristic
123C2×C32×C4C22⋊C411yescharacteristic
124C2×C32×C4C22⋊C411yescharacteristic
125C2×C32×C4C22×C411yescharacteristic
126C2×C3⋊Dic3—42no—
127C3×#67—42no—
128C3×#67—42no—
129C3×#67—42no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C3×D12—41no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3×Dic6—41no—
139#532—31no—
140#410—31no—
141#410—91no—
142#354—92no—
143#353—92no—
144C3×#41—41no—
145C3×#41—41no—
146C3×#41—41no—
147C3×#41—41no—
148C3×#41—42no—
149C3×#41—42no—
150C3×#41—121no—
151C3×#41—121no—
152C2×C3×Q8—21no—
153C2×C3×Q8—31no—
154C2×C3×Q8C4×D311yescharacteristic
155C2×C3×Q8C2×Dic311yescharacteristic
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—31no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4D1211yescharacteristic
164C2×C3×D4#6711yescharacteristic
165C2×C3×D4#6711yescharacteristic
166C2×C3×D4#6711yescharacteristic
167C2×C3×D4C22×D311yescharacteristic
168C2×C3×D4C22×D311yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—61no—
173C22×C3×C4—61no—
174C22×C3×C4C4×D311yescharacteristic
175C22×C3×C4D1211yescharacteristic
176C22×C3×C4C2×Dic311yescharacteristic
177C22×C3×C4#6711yescharacteristic
178C22×C3×C4#6711yescharacteristic
179C22×C3×C4#6711yescharacteristic
180C2×#67—21no—
181C2×#67—21no—
182C2×#67—21no—
183C22×Dic3—21no—
184#235—41no—
185#235—41no—
186C2×D12C2×Dic311yescharacteristic
187C2×C4×D3—21no—
188C2×Dic6C2×Dic311yescharacteristic
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4—121no—
192C3×C22⋊C4—61no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—62no—
197C3×C42—31no—
198C3×C42—31no—
199C3×C42—61no—
200C3×C42—121no—
201#217—21no—
202#217—21no—
203#217—22no—
204#217—64no—
205#217—62no—
206#217—62no—
207(C2×D3)⋊C4—21no—
208(C2×D3)⋊C4—21no—
209C4⋊Dic3—41no—
210C4⋊Dic3—122no—
211C4⋊Dic3—121no—
212C4⋊Dic3—121no—
213Dic3⋊C4—21no—
214Dic3⋊C4—21no—
215C4×Dic3—21no—
216C4×Dic3—41no—
217C4×Dic3—122no—
218C4×Dic3—121no—
219C4×Dic3—121no—
220C4×Dic3C2×Dic311yescharacteristic
221C4×Dic3C2×Dic311yescharacteristic
222C22×C32—21no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32—41no—
226C22×C32—41no—
227C22×C32—41no—
228C22×C32C2×C22⋊C411yescharacteristic
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C32×C4—21no—
233C32×C4—21no—
234C32×C4—21no—
235C32×C4#9911yescharacteristic
236C32×C4#9911yescharacteristic
237C3⋊Dic3—82no—
238C3×Dic3—22no—
239C3×Dic3—41no—
240C3×Dic3—41no—
241C3×Dic3—82no—
242C2×#41—31no—
243C2×#41D3211yescharacteristic
244C4⋊Q8—31no—
245#127—31no—
246#124—31no—
247#124—31no—
248#121—61no—
249#121—61no—
250C4×D4—61no—
251C4×D4—61no—
252#117—61no—
253#117—181no—
254C2×C42—31no—
255#99—32no—
256#99—61no—
257#99—92no—
258#99—181no—
259C23×C3—21no—
260C23×C3—21no—
261C23×C3—21no—
262C23×C3—61no—
263C23×C3(C2×D3)⋊C411yescharacteristic
264C23×C3#21711yescharacteristic
265C23×C3C2×D1211yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—21no—
270C3×Q8—41no—
271C3×Q8—41no—
272C3×Q8—42no—
273C3×Q8—121no—
274C3×D4—41no—
275C3×D4—41no—
276C3×D4—41no—
277C3×D4—41no—
278C3×D4—41no—
279C3×D4—41no—
280C3×D4—42no—
281C3×D4—42no—
282C3×D4—42no—
283C3×D4—121no—
284C3×D4—122no—
285C3×D4—122no—
286C3×D4—122no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
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—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—61no—
312C2×C3×C4—122no—
313C2×C3×C4—121no—
314C2×C3×C4—121no—
315C2×C3×C4—122no—
316C2×C3×C4(C2×D3)⋊C411yescharacteristic
317C2×C3×C4(C2×D3)⋊C411yescharacteristic
318C2×C3×C4(C2×D3)⋊C411yescharacteristic
319C2×C3×C4#21711yescharacteristic
320C2×C3×C4#21711yescharacteristic
321C2×C3×C4#21711yescharacteristic
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4C22×Dic311yescharacteristic
324#67—42no—
325#67—42no—
326#67—42no—
327C2×Dic3—21no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—42no—
331C2×Dic3—42no—
332C2×Dic3—124no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335D12—41no—
336C4×D3—41no—
337C4×D3—41no—
338Dic6—41no—
339C2×C32—21no—
340C2×C32—41no—
341C2×C32—41no—
342C2×C32—41no—
343C2×C32C2×#9911yescharacteristic
344C3×D3—81no—
345#41—41no—
346#41—41no—
347#41—121no—
348#41—121no—
349C2×Q8—31no—
350C2×Q8D3×Dic311yescharacteristic
351C2×D4—31no—
352C2×D4—61no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4#62511yescharacteristic
356C2×D4#62611yescharacteristic
357C2×D4C2×D3211yescharacteristic
358C22×C4—61no—
359C22×C4—61no—
360C22×C4D3×Dic311yescharacteristic
361C22×C4#62511yescharacteristic
362C22×C4#62611yescharacteristic
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—121no—
366C4⋊C4—361no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C22⋊C4—61no—
370C22⋊C4—61no—
371C22⋊C4—62no—
372C22⋊C4—182no—
373C42—31no—
374C42—31no—
375C42—61no—
376C42—121no—
377C42—361no—
378C22×C3—22no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—81no—
395C22×C3—81no—
396C22×C3—81no—
397C22×C3—121no—
398C22×C3—121no—
399C22×C3—121no—
400C22×C3C2×(C2×D3)⋊C411yescharacteristic
401C22×C3C2×#21711yescharacteristic
402C2×D3—41no—
403C2×D3—41no—
404C2×D3—41no—
405C3×C4—22no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—41no—
415C3×C4—41no—
416C3×C4—62no—
417C3×C4—121no—
418C3×C4—121no—
419C3×C4—242no—
420C3×C4#80611yescharacteristic
421C3×C4#80611yescharacteristic
422C3×C4#83411yescharacteristic
423C3×C4#83411yescharacteristic
424Dic3—22no—
425Dic3—41no—
426Dic3—41no—
427Dic3—82no—
428Dic3—244no—
429Dic3—242no—
430Dic3—242no—
431C32#212611yescharacteristic, complemented, Sylow
432C23—61no—
433C23(C2×D3)⋊Dic311yescharacteristic
434C23C2×#62511yescharacteristic
435C23C2×#62611yescharacteristic
436Q8—41no—
437Q8—121no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—121no—
442D4—122no—
443D4—122no—
444D4—122no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—122no—
455C2×C4—121no—
456C2×C4—121no—
457C2×C4—122no—
458C2×C4—362no—
459C2×C4(C2×D3)⋊Dic311yescharacteristic
460C2×C4(C2×D3)⋊Dic311yescharacteristic
461C2×C4(C2×D3)⋊Dic311yescharacteristic
462C2×C4C2×D3×Dic311yescharacteristic
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—42no—
468C2×C3—41no—
469C2×C3—41no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3—41no—
473C2×C3—41no—
474C2×C3—81no—
475C2×C3—81no—
476C2×C3—241no—
477C2×C3C2×#80611yescharacteristic
478C2×C3C2×#83411yescharacteristic
479D3—81no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—121no—
487C22—121no—
488C22—121no—
489C22C2×(C2×D3)⋊Dic311yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—62no—
494C4—121no—
495C4—121no—
496C4—242no—
497C4—722no—
498C4#6358011yescharacteristic
499C4#6358011yescharacteristic
500C3—21no—
501C3#7006011yescharacteristic, complemented
502C3#7181911yescharacteristic, complemented
503C2—21no—
504C2—41no—
505C2—41no—
506C2—41no—
507C2—241no—
508C2C2×#6358011yescharacteristic
subgroupG/H
centerC4#63580
commutatorC2×C32×C4C22×C4
FrattiniC2×D4C2×D32
FittingC2×C32×#41C22
socleC2×C32C2×#99
prime radicalC3×#5832C2
cosocleC2×C32×D4C23
hypercenterC2×#41D32
hypocenterC32#2126
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10592939C2semidirect
3. C3×#5240C2semidirect
4. #10589180C2semidirect
5. #10589178C2semidirect
9. C2×C3×#235C4semidirect
11. C3×#947C4semidirect
12. C3×#944C4semidirect
20. C2×C3×C4×Dic3C4semidirect
31. #5240D3semidirect
74. C2×#235Dic3semidirect
85. #947Dic3semidirect
86. #944Dic3semidirect
97. C2×C4×Dic3Dic3semidirect
431. C32#2126semidirect
501. C3#70060semidirect
502. C3#71819semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
#105929392
C3×#52402
#105891802
#105891782
#718193
#700603