Finite Group Databasebeta

← #11772604

Subgroups — #11772604

Order 1152.

569 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63661C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic
3C2×C3×#834C211yesmaximal, characteristic
4#67695—31nomaximal
5#67641—31nomaximal
6C22×C32×D4C2211yescharacteristic
7C2×#3757—21no—
8C2×C3×#217—21no—
9C2×C3×#217—21no—
10C2×C3×#217—21no—
11C2×C3×C4⋊Dic3C411yescharacteristic, complemented
12C2×C3×C4×Dic3C411yescharacteristic, complemented
13#63661—21no—
14#63661C412yescomplemented
15C3×#834—21no—
16C3×#834C412yescomplemented
17C2×C3×#99—31no—
18C3×#390—31no—
19#5221D311yescharacteristic
20C2×#834—31no—
21C2×#834—31no—
22C2×#834—61no—
23C2×#834D311yescharacteristic
24C24×C32D411yescharacteristic
25C24×C32D411yescharacteristic
26C2×C32×D4—41no—
27C2×C32×D4—41no—
28C2×C32×D4C2×C411yescharacteristic
29C2×C32×D4C2×C411yescharacteristic
30C2×C32×D4D411yescharacteristic
31C2×C32×D4Q811yescharacteristic
32C22×C32×C4C2×C411yescharacteristic
33C22×C3⋊Dic3—41no—
34C22×C3×Dic3—21no—
35C22×C3×Dic3—21no—
36C22×C3×Dic3—41no—
37#3757—22no—
38#3757—41no—
39C3×#217—22no—
40C3×#217—42no—
41C3×#217—42no—
42C3×#217—41no—
43C3×C4⋊Dic3—41no—
44C3×C4×Dic3—41no—
45#1393—91noSylow
46C22×C3×D4—21no—
47C22×C3×D4C2×D311yescharacteristic
48C22×C3×D4C2×D311yescharacteristic
49C2×C3×C4⋊C4—31no—
50C2×C3×C22⋊C4—61no—
51C2×C3×C22⋊C4—61no—
52C2×C3×C22⋊C4—61no—
53C2×C3×C42—31no—
54C2×#217—21no—
55C2×#217—21no—
56C2×#217—21no—
57C2×#217—62no—
58C2×#217—61no—
59C2×#217—61no—
60C2×C4⋊Dic3Dic311yescharacteristic, complemented
61C2×C4×Dic3Dic311yescharacteristic, complemented
62C3×#99—32no—
63C3×#99—61no—
64#834—21no—
65#834—32no—
66#834—32no—
67#834—62no—
68#834—62no—
69#834—61no—
70#834—61no—
71#834Dic312yescomplemented
72C23×C32—21no—
73C23×C32—21no—
74C23×C32—21no—
75C23×C32—21no—
76C23×C32—41no—
77C23×C32—41no—
78C23×C32—41no—
79C23×C32—41no—
80C23×C32C22⋊C411yescharacteristic
81C23×C32C22⋊C411yescharacteristic
82C23×C32C22⋊C411yescharacteristic
83C23×C32C4⋊C411yescharacteristic
84C23×C32C4⋊C411yescharacteristic
85C32×D4—41no—
86C32×D4—41no—
87C32×D4—41no—
88C32×D4—41no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4C4211yescharacteristic
92C2×C32×C4C4⋊C411yescharacteristic
93C2×C3⋊Dic3—42no—
94C2×C3⋊Dic3—81no—
95C2×C3⋊Dic3—81no—
96C2×C3×Dic3—22no—
97C2×C3×Dic3—41no—
98C2×C3×Dic3—41no—
99C2×C3×Dic3—42no—
100C2×C3×Dic3—41no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—41no—
103C2×C3×Dic3—81no—
104C2×C3×Dic3—81no—
105C2×#99—31no—
106C2×#99—91no—
107#390—31no—
108C24×C3—21no—
109C24×C3—21no—
110C24×C3D1211yescharacteristic
111C24×C3#6711yescharacteristic
112C24×C3#6711yescharacteristic
113C24×C3#6711yescharacteristic
114C2×C3×D4—21no—
115C2×C3×D4—21no—
116C2×C3×D4—21no—
117C2×C3×D4—21no—
118C2×C3×D4—41no—
119C2×C3×D4—41no—
120C2×C3×D4—41no—
121C2×C3×D4—41no—
122C2×C3×D4—42no—
123C2×C3×D4—42no—
124C2×C3×D4Dic611yescharacteristic
125C2×C3×D4Dic611yescharacteristic
126C2×C3×D4C4×D311yescharacteristic
127C2×C3×D4C4×D311yescharacteristic
128C2×C3×D4C4×D311yescharacteristic
129C2×C3×D4D1211yescharacteristic
130C2×C3×D4C2×Dic311yescharacteristic
131C2×C3×D4#6711yescharacteristic
132C22×C3×C4—21no—
133C22×C3×C4—61no—
134C22×C3×C4—61no—
135C22×C3×C4—121no—
136C22×C3×C4C4×D311yescharacteristic
137C22×C3×C4C2×Dic311yescharacteristic
138C22×Dic3—21no—
139C22×Dic3—21no—
140C22×Dic3—41no—
141C22×Dic3—122no—
142C22×Dic3—121no—
143C22×Dic3—121no—
144C3×C4⋊C4—121no—
145C3×C22⋊C4—62no—
146C3×C22⋊C4—122no—
147C3×C22⋊C4—122no—
148C3×C22⋊C4—121no—
149C3×C42—121no—
150#217—22no—
151#217—42no—
152#217—42no—
153#217—41no—
154#217—64no—
155#217—62no—
156#217—62no—
157#217—122no—
158#217—121no—
159#217—121no—
160C4⋊Dic3—41no—
161C4×Dic3—41no—
162C22×C32—21no—
163C22×C32—21no—
164C22×C32—21no—
165C22×C32—21no—
166C22×C32—21no—
167C22×C32—21no—
168C22×C32—41no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32—41no—
175C22×C32—41no—
176C22×C32—81no—
177C22×C32—81no—
178C22×C32#9511yescharacteristic
179C22×C32#9911yescharacteristic
180C22×C32#9911yescharacteristic
181C32×C4—21no—
182C32×C4—21no—
183C3⋊Dic3—82no—
184C3×Dic3—42no—
185C3×Dic3—82no—
186C3×Dic3—81no—
187C22×D4D3211yescharacteristic
188C2×C4⋊C4—31no—
189C2×C22⋊C4—61no—
190C2×C22⋊C4—61no—
191C2×C22⋊C4—61no—
192C2×C22⋊C4—181no—
193C2×C42—31no—
194#99—32no—
195#99—61no—
196#99—92no—
197#99—181no—
198C23×C3—22no—
199C23×C3—22no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—21no—
207C23×C3—21no—
208C23×C3—21no—
209C23×C3—21no—
210C23×C3—21no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—41no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—41no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3—81no—
224C23×C3—81no—
225C23×C3—81no—
226C23×C3—81no—
227C23×C3Dic3⋊C411yescharacteristic
228C23×C3Dic3⋊C411yescharacteristic
229C23×C3Dic3⋊C411yescharacteristic
230C23×C3C4⋊Dic311yescharacteristic
231C23×C3(C2×D3)⋊C411yescharacteristic
232C23×C3(C2×D3)⋊C411yescharacteristic
233C23×C3(C2×D3)⋊C411yescharacteristic
234C23×C3(C2×D3)⋊C411yescharacteristic
235C23×C3#21711yescharacteristic
236C23×C3#21711yescharacteristic
237C3×D4—41no—
238C3×D4—41no—
239C3×D4—41no—
240C3×D4—41no—
241C3×D4—41no—
242C3×D4—41no—
243C3×D4—41no—
244C3×D4—41no—
245C3×D4—42no—
246C3×D4—42no—
247C3×D4—42no—
248C3×D4—42no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—62no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4—122no—
261C2×C3×C4—121no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4—241no—
265C2×C3×C4—241no—
266C2×C3×C4C4×Dic311yescharacteristic
267C2×C3×C4C4×Dic311yescharacteristic
268C2×C3×C4Dic3⋊C411yescharacteristic
269C2×C3×C4C4⋊Dic311yescharacteristic
270C2×Dic3—22no—
271C2×Dic3—41no—
272C2×Dic3—41no—
273C2×Dic3—42no—
274C2×Dic3—41no—
275C2×Dic3—41no—
276C2×Dic3—41no—
277C2×Dic3—81no—
278C2×Dic3—81no—
279C2×Dic3—124no—
280C2×Dic3—122no—
281C2×Dic3—122no—
282C2×Dic3—242no—
283C2×Dic3—242no—
284C2×Dic3—241no—
285C2×Dic3—241no—
286C2×Dic3—241no—
287C2×Dic3—241no—
288C2×C32—21no—
289C2×C32—21no—
290C2×C32—41no—
291C2×C32—41no—
292C2×C32—41no—
293C2×C32—41no—
294C2×C32#34211yescharacteristic
295C2×C32#35311yescharacteristic
296C2×C32#35411yescharacteristic
297C24#62511yescharacteristic
298C24#62611yescharacteristic
299C2×D4—41no—
300C2×D4—41no—
301C2×D4D3×Dic311yescharacteristic
302C2×D4#62411yescharacteristic
303C2×D4#62611yescharacteristic
304C2×D4#62711yescharacteristic
305C22×C4—61no—
306C22×C4—61no—
307C22×C4—121no—
308C22×C4—361no—
309C22×C4D3×Dic311yescharacteristic
310C4⋊C4—121no—
311C22⋊C4—62no—
312C22⋊C4—122no—
313C22⋊C4—122no—
314C22⋊C4—121no—
315C22⋊C4—182no—
316C22⋊C4—361no—
317C42—121no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—22no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—21no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—41no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—81no—
358C22×C3—81no—
359C22×C3—81no—
360C22×C3—81no—
361C22×C3—81no—
362C22×C3—81no—
363C22×C3—81no—
364C22×C3—81no—
365C22×C3—81no—
366C22×C3—81no—
367C22×C3—82no—
368C22×C3—82no—
369C22×C3#80611yescharacteristic
370C22×C3#80611yescharacteristic
371C22×C3C3⋊#9511yescharacteristic
372C22×C3C3⋊#9511yescharacteristic
373C22×C3#83411yescharacteristic
374C22×C3#83411yescharacteristic
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—122no—
382C3×C4—242no—
383C3×C4—241no—
384Dic3—42no—
385Dic3—82no—
386Dic3—81no—
387Dic3—244no—
388Dic3—242no—
389Dic3—242no—
390C32#139311yescharacteristic, complemented, Sylow
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23(C2×D3)⋊Dic311yescharacteristic
400C23(C2×D3)⋊Dic311yescharacteristic
401C23#372211yescharacteristic
402C23Dic3⋊Dic311yescharacteristic
403C23#372411yescharacteristic
404D4—41no—
405D4—41no—
406D4—41no—
407D4—41no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—62no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4—122no—
414C2×C4—121no—
415C2×C4—121no—
416C2×C4—121no—
417C2×C4—241no—
418C2×C4—241no—
419C2×C4—362no—
420C2×C4—721no—
421C2×C4—721no—
422C2×C4Dic3211yescharacteristic
423C2×C4Dic3⋊Dic311yescharacteristic
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3—42no—
434C2×C3—42no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—41no—
438C2×C3—41no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—41no—
442C2×C3—41no—
443C2×C3—81no—
444C2×C3—81no—
445C2×C3#447311yescharacteristic
446C2×C3#447411yescharacteristic
447C2×C3#452611yescharacteristic
448C2×C3#452711yescharacteristic
449C2×C3#454111yescharacteristic
450C2×C3#454511yescharacteristic
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—81no—
466C22—81no—
467C22#6357911yescharacteristic
468C22#6358011yescharacteristic
469C22#6358011yescharacteristic
470C4—21no—
471C4—21no—
472C4—122no—
473C4—242no—
474C4—241no—
475C4—722no—
476C3—21no—
477C3#6764111yescharacteristic, complemented
478C3#6769511yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—41no—
482C2—41no—
483C2—41no—
484C2—41no—
485C2#1058917811yescharacteristic
486C2#1058918011yescharacteristic
487C2#1058918611yescharacteristic
subgroupG/H
centerC22#63580
commutatorC2×C32×C4C42
Frattini, hypercenterC22×D4D32
Fitting, prime radical, cosocleC22×C32×D4C22
socleC22×C32#99
hypocenterC32#1393
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
11. C2×C3×C4⋊Dic3C4semidirect
12. C2×C3×C4×Dic3C4semidirect
14. #63661C4semidirect
16. C3×#834C4semidirect
60. C2×C4⋊Dic3Dic3semidirect
61. C2×C4×Dic3Dic3semidirect
71. #834Dic3semidirect
390. C32#1393semidirect
477. C3#67641semidirect
478. C3#67695semidirect

Maximal subgroups

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

subgroupindex
C2×#636612
C3×#52212
C2×C3×#8342
#676953
#676413