Finite Group Databasebeta

← #11795437

Subgroups — #11795437

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63634C211yesmaximal, characteristic, complemented
2C3×#4988C211yesmaximal, characteristic
3C2×C3×#807C211yesmaximal, characteristic, complemented
4#10591349C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6C2×#63562C211yesmaximal, characteristic
7#10589155C211yesmaximal, characteristic, complemented
8#70641—31nomaximal
9#69655—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—22no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×Dic3⋊Dic3—22no—
19#63634—22no—
20C3×#807—22no—
21#63563—22no—
22#63562—22no—
23C2×C3×#107—31no—
24C3×#390—31no—
25C2×#832—31no—
26C2×#832—31no—
27C2×#821—31no—
28#4988D311yescharacteristic
29#4975—31no—
30C2×#809—31no—
31C2×#807—31no—
32C2×#807—31no—
33C2×#807—61no—
34C2×#807D311yescharacteristic, complemented
35#4935—31no—
36#4550—31no—
37#4524—31no—
38C23×C3×D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3×Dic3—21no—
43C22×C3×Dic3D412yes—
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—
54C2×C3⋊(C3⋊C8)—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C2×C3⋊(C3⋊C8)D412yes—
57C3×(C2×D3)⋊C4—44no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65Dic3⋊Dic3—44no—
66#2093—91noSylow
67C22×C3×D4—31no—
68C22×D12C2×D311yescharacteristic
69C22×C3×C8—31no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4C2×D311yescharacteristic
73C2×C3×C4⋊C4C2×D311yescharacteristic
74C2×C3×C22⋊C4—62no—
75C2×C3×C42—31no—
76C2×(C2×D3)⋊C4—22no—
77C2×C4⋊Dic3—31no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—61no—
80C2×C4⋊Dic3—62no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×Dic3⋊C4—62no—
83C2×C4×Dic3C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C22×C3⋊C8C2×D311yescharacteristic
88C3×#107—62no—
89#832—62no—
90#832—62no—
91#821—62no—
92#809—62no—
93#807—22no—
94#807—62no—
95#807—62no—
96#807—64no—
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—41no—
112C2×C3⋊Dic3—42no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—42no—
117C2×C3×Dic3D814yes—
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—91no—
127C2×#102—91no—
128#390—31no—
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—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—32no—
143C22×C3×C4—41no—
144C22×C3×C4—61no—
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×Dic3—21no—
148C22×Dic3—61no—
149C22×Dic3—61no—
150C22×Dic3—121no—
151C22×Dic3#6712yes—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12—21no—
157C2×D12Dic612yes—
158C2×C3×C8—32no—
159C2×C3×C8—61no—
160C2×C3×C8—61no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—41no—
167C3×C4⋊C4—61no—
168C3×C4⋊C4—61no—
169C3×C22⋊C4—124no—
170C3×C42—61no—
171C3×C42—61no—
172(C2×D3)⋊C4—44no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—62no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—121no—
181C4⋊Dic3—124no—
182Dic3⋊C4—124no—
183C4×Dic3—21no—
184C4×Dic3—21no—
185C2×C3⋊C8—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—32no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—62no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—62no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8#6712yes—
197C22×C32C22⋊Q811yescharacteristic
198C22×C32#12311yescharacteristic
199C22×C32#12711yescharacteristic
200C22×C32C2×D812yes—
201C22×C32#13712yes—
202C2×C3×D3—42no—
203C2×C3×D3—44no—
204C2×C3×D3—82no—
205C2×C3×D3—81no—
206C2×C3×D3—81no—
207C32×C4—81no—
208C32×C4C22⋊Q811yescharacteristic
209C32×C4C22⋊Q811yescharacteristic
210C32×C4#12311yescharacteristic
211C32×C4#12311yescharacteristic
212C3⋊Dic3—81no—
213C3×Dic3—24no—
214C3×Dic3—81no—
215C22×D4—31no—
216C22×C8—31no—
217C22×C8—91no—
218C2×C4⋊C4—31no—
219C2×C4⋊C4—91no—
220C2×C4⋊C4—182no—
221C2×C4⋊C4D3211yescharacteristic
222C2×C22⋊C4—62no—
223C2×C42—31no—
224#107—62no—
225#107—182no—
226#102—182no—
227#102—182no—
228C23×C3—21no—
229C23×C3—62no—
230C23×C3—121no—
231C23×C3—122no—
232C23×C3—122no—
233C23×C3—121no—
234C23×C3D3×D411yescharacteristic
235C23×C3C2×#6711yescharacteristic
236C22×D3—22no—
237C22×D3—42no—
238C22×D3—41no—
239C22×D3—41no—
240C22×D3—42no—
241C3×D4—62no—
242C3×D4—62no—
243C3×D4—121no—
244C3×D4—121no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—34no—
252C2×C3×C4—42no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—82no—
260C2×C3×C4—122no—
261C2×C3×C4—121no—
262C2×C3×C4C2×Dic611yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4#23511yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4D3×Q811yescharacteristic
272C2×C3×C4#23911yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×Dic3—22no—
275C2×Dic3—22no—
276C2×Dic3—42no—
277C2×Dic3—41no—
278C2×Dic3—122no—
279C2×Dic3—122no—
280C2×Dic3—122no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3—242no—
284C2×Dic3#21314yes—
285D12—22no—
286D12—22no—
287D12—41no—
288D12—41no—
289C3×C8—62no—
290C3⋊C8—22no—
291C3⋊C8—64no—
292C3⋊C8—62no—
293C3⋊C8—62no—
294C2×C32#39911yescharacteristic
295C2×C32#47412yes—
296C2×C32#48012yes—
297C2×C32#49311yescharacteristic
298C2×C32#49711yescharacteristic
299C3×D3—82no—
300C24—61no—
301C2×D4—32no—
302C2×D4—61no—
303C2×D4—61no—
304C2×D4—61no—
305C2×D4—61no—
306C2×D4—61no—
307C22×C4—21no—
308C22×C4—32no—
309C22×C4—61no—
310C22×C4—181no—
311C22×C4C2×D3211yescharacteristic
312C2×C8—32no—
313C2×C8—61no—
314C2×C8—61no—
315C2×C8—92no—
316C2×C8—181no—
317C2×C8—181no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4—364no—
325C22⋊C4—124no—
326C42—61no—
327C42—61no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—21no—
333C22×C3—124no—
334C22×C3—122no—
335C22×C3—242no—
336C22×C3—241no—
337C22×C3—241no—
338C22×C3#89411yescharacteristic
339C22×C3#89611yescharacteristic
340C22×C3D3×D812yes—
341C22×C3#91812yes—
342C22×C3#92411yescharacteristic
343C22×C3C2×#21312yes—
344C22×C3#93511yescharacteristic
345C22×C3#94011yescharacteristic
346C22×C3#94011yescharacteristic
347C22×C3#95112yes—
348C2×D3—42no—
349C2×D3—44no—
350C2×D3—82no—
351C2×D3—81no—
352C2×D3—81no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—64no—
358C3×C4—82no—
359C3×C4—81no—
360C3×C4—81no—
361C3×C4—241no—
362C3×C4#87811yescharacteristic
363C3×C4#87811yescharacteristic
364C3×C4#88311yescharacteristic
365C3×C4#88311yescharacteristic
366C3×C4#89411yescharacteristic
367C3×C4#89611yescharacteristic
368C3×C4#92911yescharacteristic
369C3×C4#94611yescharacteristic
370Dic3—24no—
371Dic3—81no—
372Dic3—242no—
373Dic3—241no—
374Dic3—241no—
375C32#209311yescharacteristic, complemented, Sylow
376C23—62no—
377C23—121no—
378C23—122no—
379C23—122no—
380C23—121no—
381C23D3×#6711yescharacteristic
382D4—62no—
383D4—62no—
384D4—121no—
385D4—121no—
386C2×C4—34no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—122no—
392C2×C4—121no—
393C2×C4—362no—
394C2×C4—361no—
395C2×C4D3×Dic611yescharacteristic
396C2×C4#379511yescharacteristic
397C2×C4#379611yescharacteristic
398C2×C4#379811yescharacteristic
399C2×C4D3×#6711yescharacteristic
400C2×C4#381111yescharacteristic
401C8—62no—
402C8—182no—
403C2×C3—21no—
404C2×C3—22no—
405C2×C3—21no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3—242no—
409C2×C3#488212yes—
410C2×C3#489012yes—
411C2×C3#494911yescharacteristic
412C2×C3#499311yescharacteristic
413C2×C3#500712yes—
414C2×C3#503312yes—
415C2×C3#506011yescharacteristic
416C2×C3#507311yescharacteristic
417C2×C3#515111yescharacteristic
418C2×C3#519011yescharacteristic
419D3—82no—
420C22—122no—
421C22—124no—
422C22—241no—
423C22—242no—
424C22—241no—
425C22#6385111yescharacteristic
426C22#6388411yescharacteristic
427C22D3×#21312yes—
428C22#6394312yes—
429C22#6397911yescharacteristic
430C4—64no—
431C4—81no—
432C4—241no—
433C4—721no—
434C4#6385311yescharacteristic
435C4#6388711yescharacteristic
436C4#6389611yescharacteristic
437C4#6390511yescharacteristic
438C3—21no—
439C3#6965511yescharacteristic, complemented
440C3#7064111yescharacteristic, complemented
441C2—242no—
442C2#1059043812yes—
443C2#1059055512yes—
444C2#1059130311yescharacteristic
445C2#1059148211yescharacteristic
446C2#1059162711yescharacteristic
subgroupG/H
centerC23D3×#67
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. C2×#63634C2semidirect
3. C2×C3×#807C2semidirect
4. #10591349C2semidirect
7. #10589155C2semidirect
34. C2×#807D3semidirect
375. C32#2093semidirect
439. C3#69655semidirect
440. C3#70641semidirect

Maximal subgroups

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

subgroupindex
C2×#636342
C3×#49882
C2×C3×#8072
#105913492
C2×#635632
C2×#635622
#105891552
#706413
#696553