Finite Group Databasebeta

← #11795443

Subgroups — #11795443

Order 1152.

673 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592674C211yesmaximal, characteristic, complemented
2C2×C3×#809C211yesmaximal, characteristic
3C2×C3×#807C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589156C211yesmaximal, characteristic, complemented
8#70641—31nomaximal
9#70183—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3750—22no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—22no—
19C3×#809—22no—
20C3×#807—22no—
21#63575—22no—
22#63563—22no—
23C2×C3×#107—31no—
24C2×C3×#102—31no—
25#5221—31no—
26C2×#832—31no—
27C2×#821—31no—
28C2×#818—31no—
29#4988—31no—
30#4975—31no—
31#4975—31no—
32#4975—61no—
33C2×#809D311yescharacteristic
34C2×#807—31no—
35C2×#807D311yescharacteristic, complemented
36#4550—31no—
37#4550—31no—
38C23×C3×D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3D412yes—
43C22×C3×Dic3—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12Q812yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54#3750—44no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64C2×C3×C3⋊C8D412yes—
65(C2×D3)⋊Dic3—44no—
66#2093—91noSylow
67C22×C3×D4—31no—
68C22×D12C2×D311yescharacteristic
69C22×C3×C8—31no—
70C22×C3×C8—31no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4C2×D311yescharacteristic
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×#217—62no—
76C2×(C2×D3)⋊C4—62no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—61no—
80C2×C4⋊Dic3C2×D311yescharacteristic
81C2×Dic3⋊C4—62no—
82C2×Dic3⋊C4—62no—
83C2×Dic3⋊C4—64no—
84C2×C4×Dic3—31no—
85C2×C4×Dic3—31no—
86C2×C4×Dic3—61no—
87C22×C3⋊C8C2×D311yescharacteristic
88C22×C3⋊C8C2×D311yescharacteristic
89C3×#107—62no—
90C3×#102—62no—
91#832—62no—
92#821—62no—
93#818—62no—
94#809—22no—
95#807—22no—
96#807—62no—
97C23×C32C2×D411yescharacteristic
98C22×C3×D3—22no—
99C22×C3×D3—41no—
100C22×C3×D3—41no—
101C22×C3×D3—42no—
102C22×C3×D3—42no—
103C2×C32×C4—41no—
104C2×C32×C4—42no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×Q811yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3D814yes—
116C2×C3×Dic3—41no—
117C2×C3×Dic3—42no—
118C3×D12—22no—
119C3×D12—22no—
120C3×D12—41no—
121C3×D12—41no—
122C3×C3⋊C8—22no—
123C3×C3⋊C8—22no—
124C2×#107—31no—
125C2×#107—91no—
126C2×#102—31no—
127C2×#102—91no—
128#390—91no—
129#384—91no—
130#336—91no—
131C24×C3—61no—
132C23×D3—21no—
133C2×C3×D4—32no—
134C2×C3×D4—61no—
135C2×C3×D4—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C22×C3×C4—22no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×Dic3—21no—
147C22×Dic3—32no—
148C22×Dic3—32no—
149C22×Dic3—62no—
150C22×Dic3—62no—
151C22×Dic3—61no—
152C22×Dic3—61no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12—21no—
158C2×D12Dic612yes—
159C2×C3×C8—32no—
160C2×C3×C8—32no—
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C2×C3×C8—61no—
164C2×C3×C8—61no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—41no—
170C3×C4⋊C4—41no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173#217—124no—
174(C2×D3)⋊C4—124no—
175C4⋊Dic3—21no—
176C4⋊Dic3—21no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—61no—
181C4⋊Dic3—121no—
182C4⋊Dic3—121no—
183Dic3⋊C4—124no—
184Dic3⋊C4—124no—
185Dic3⋊C4—128no—
186C4×Dic3—62no—
187C4×Dic3—62no—
188C4×Dic3—61no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C2×C3⋊C8—21no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8#6712yes—
197C2×C3⋊C8#6712yes—
198C22×C32C22⋊Q811yescharacteristic
199C22×C32#12311yescharacteristic
200C22×C32#12711yescharacteristic
201C22×C32C2×D812yes—
202C22×C32#13712yes—
203C2×C3×D3—42no—
204C2×C3×D3—44no—
205C2×C3×D3—82no—
206C2×C3×D3—81no—
207C2×C3×D3—81no—
208C32×C4—81no—
209C32×C4C22⋊Q811yescharacteristic
210C32×C4C22⋊Q811yescharacteristic
211C32×C4#12311yescharacteristic
212C32×C4#12311yescharacteristic
213C3⋊Dic3—24no—
214C3⋊Dic3—81no—
215C3×Dic3—81no—
216C22×D4—31no—
217C22×C8—31no—
218C22×C8—31no—
219C2×C4⋊C4—31no—
220C2×C4⋊C4—91no—
221C2×C4⋊C4—182no—
222C2×C4⋊C4D3211yescharacteristic
223C2×C22⋊C4—182no—
224C2×C42—91no—
225#107—62no—
226#107—182no—
227#102—62no—
228#102—182no—
229C23×C3—21no—
230C23×C3—62no—
231C23×C3—121no—
232C23×C3—122no—
233C23×C3—122no—
234C23×C3—121no—
235C23×C3D3×D411yescharacteristic
236C23×C3D3×D411yescharacteristic
237C22×D3—22no—
238C22×D3—41no—
239C22×D3—42no—
240C22×D3—42no—
241C22×D3—41no—
242C3×D4—62no—
243C3×D4—62no—
244C3×D4—121no—
245C3×D4—121no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—44no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—42no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—122no—
259C2×C3×C4—121no—
260C2×C3×C4C2×Dic611yescharacteristic
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4#23711yescharacteristic
267C2×C3×C4#23711yescharacteristic
268C2×C3×C4D3×Q811yescharacteristic
269C2×C3×C4#23911yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—34no—
273C2×Dic3—34no—
274C2×Dic3—42no—
275C2×Dic3—41no—
276C2×Dic3—64no—
277C2×Dic3—64no—
278C2×Dic3—64no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—124no—
284C2×Dic3—122no—
285C2×Dic3—122no—
286C2×Dic3—122no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289D12—22no—
290D12—22no—
291D12—41no—
292D12—41no—
293C3×C8—62no—
294C3×C8—62no—
295C3⋊C8—22no—
296C3⋊C8—22no—
297C2×C32#39911yescharacteristic
298C2×C32#47412yes—
299C2×C32#48012yes—
300C2×C32#49311yescharacteristic
301C2×C32#49711yescharacteristic
302C3×D3—82no—
303C24—61no—
304C2×D4—32no—
305C2×D4—61no—
306C2×D4—61no—
307C2×D4—61no—
308C2×D4—61no—
309C2×D4—61no—
310C22×C4—21no—
311C22×C4—61no—
312C22×C4—92no—
313C22×C4—181no—
314C22×C4C2×D3211yescharacteristic
315C2×C8—32no—
316C2×C8—32no—
317C2×C8—61no—
318C2×C8—61no—
319C2×C8—61no—
320C2×C8—61no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—181no—
326C4⋊C4—181no—
327C4⋊C4—364no—
328C22⋊C4—364no—
329C42—181no—
330C42—181no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—124no—
337C22×C3—122no—
338C22×C3—242no—
339C22×C3—241no—
340C22×C3—241no—
341C22×C3#87811yescharacteristic
342C22×C3#88311yescharacteristic
343C22×C3#89411yescharacteristic
344C22×C3#89611yescharacteristic
345C22×C3D3×D812yes—
346C22×C3D3×D812yes—
347C22×C3#91512yes—
348C22×C3#91812yes—
349C22×C3#94011yescharacteristic
350C22×C3#94011yescharacteristic
351C2×D3—42no—
352C2×D3—44no—
353C2×D3—81no—
354C2×D3—81no—
355C2×D3—82no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—82no—
361C3×C4—81no—
362C3×C4—81no—
363C3×C4—241no—
364C3×C4#87811yescharacteristic
365C3×C4#88311yescharacteristic
366C3×C4#89411yescharacteristic
367C3×C4#89611yescharacteristic
368C3×C4#92411yescharacteristic
369C3×C4#92911yescharacteristic
370C3×C4#93511yescharacteristic
371C3×C4#94611yescharacteristic
372Dic3—68no—
373Dic3—64no—
374Dic3—64no—
375Dic3—81no—
376Dic3—242no—
377Dic3—241no—
378Dic3—241no—
379C32#209311yescharacteristic, complemented, Sylow
380C23—62no—
381C23—121no—
382C23—122no—
383C23—122no—
384C23—121no—
385C23#381111yescharacteristic
386D4—62no—
387D4—62no—
388D4—121no—
389D4—121no—
390C2×C4—42no—
391C2×C4—41no—
392C2×C4—94no—
393C2×C4—122no—
394C2×C4—121no—
395C2×C4—182no—
396C2×C4—182no—
397C2×C4—362no—
398C2×C4—361no—
399C2×C4D3×Dic611yescharacteristic
400C2×C4#379511yescharacteristic
401C2×C4#379611yescharacteristic
402C2×C4#379811yescharacteristic
403C2×C4D3×#6711yescharacteristic
404C2×C4D3×#6711yescharacteristic
405C8—62no—
406C8—62no—
407C2×C3—22no—
408C2×C3—22no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—242no—
413C2×C3#475912yes—
414C2×C3#477412yes—
415C2×C3#488212yes—
416C2×C3#489012yes—
417C2×C3#494911yescharacteristic
418C2×C3#499311yescharacteristic
419C2×C3#515111yescharacteristic
420C2×C3#515111yescharacteristic
421C2×C3#516711yescharacteristic
422C2×C3#519011yescharacteristic
423D3—82no—
424C22—124no—
425C22—122no—
426C22—242no—
427C22—241no—
428C22—241no—
429C22#6385311yescharacteristic
430C22#6389611yescharacteristic
431C22#6392612yes—
432C22#6395112yes—
433C22#6397911yescharacteristic
434C4—81no—
435C4—184no—
436C4—241no—
437C4—721no—
438C4#6385111yescharacteristic
439C4#6388411yescharacteristic
440C4#6388711yescharacteristic
441C4#6390511yescharacteristic
442C3—21no—
443C3#7018311yescharacteristic, complemented
444C3#7064111yescharacteristic, complemented
445C2—242no—
446C2#1059047112yes—
447C2#1059051012yes—
448C2#1059130311yescharacteristic
449C2#1059148411yescharacteristic
450C2#1059161111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2093
LCSG ▷ C22×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
1. #10592674C2semidirect
3. C2×C3×#807C2semidirect
5. C2×#63575C2semidirect
7. #10589156C2semidirect
35. C2×#807D3semidirect
379. C32#2093semidirect
443. C3#70183semidirect
444. C3#70641semidirect

Maximal subgroups

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

subgroupindex
#105926742
C2×C3×#8092
C2×C3×#8072
#105913232
C2×#635752
C2×#635632
#105891562
#706413
#701833