Finite Group Databasebeta

← #11795407

Subgroups — #11795407

Order 1152.

649 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63636C211yesmaximal, characteristic
2C3×#4977C211yesmaximal, characteristic, complemented
3C2×C3×#808C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7#10589155C211yesmaximal, characteristic, complemented
8#70586—31nomaximal
9#69558—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3722—22no—
18#63636—22no—
19C3×C3⋊#95—22no—
20C3×#808—22no—
21#63576—22no—
22#63564—22no—
23C2×C3×#106—31no—
24C3×#382—31no—
25C2×#821—31no—
26#4988—31no—
27#4977D311yescharacteristic, complemented
28C2×#809—31no—
29C2×#809—31no—
30C2×#809—31no—
31C2×#809—61no—
32C2×#808D311yescharacteristic, complemented
33C2×#807—31no—
34C2×#807—31no—
35#4939—31no—
36#4550—31no—
37#4524—31no—
38C23×C3⋊D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)Q812yes—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)D412yes—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64#3722—44no—
65#2092—91noSylow
66C22×D12—31no—
67C22×D12—31no—
68C22×D12—61no—
69C22×C3×C8—31no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4C2×D311yescharacteristic
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C42—31no—
76C2×(C2×D3)⋊C4—62no—
77C2×(C2×D3)⋊C4—62no—
78C2×C4⋊Dic3C2×D311yescharacteristic
79C2×C4⋊Dic3C2×D311yescharacteristic
80C2×C4×Dic3C2×D311yescharacteristic
81C22×C3⋊C8—31no—
82C22×C3⋊C8—31no—
83C22×C3⋊C8—61no—
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#106—62no—
86C3×#95—62no—
87C3⋊#95—22no—
88#821—62no—
89#809—62no—
90#809—62no—
91#809—64no—
92#809—62no—
93#808—22no—
94#807—62no—
95#807—62no—
96C23×C32C2×D411yescharacteristic
97C22×C3⋊D3—22no—
98C22×C3⋊D3—41no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—42no—
101C22×C3⋊D3—42no—
102C2×C32×C4—41no—
103C2×C32×C4—42no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×Q811yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—41no—
113C4⋊(C3⋊D3)—41no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3⋊(C3⋊C8)—22no—
122C3×C3⋊C8—22no—
123C2×#107—91no—
124C2×#106—31no—
125C2×#102—91no—
126C2×#102—91no—
127#390—91no—
128#382—31no—
129#336—91no—
130C23×D3—61no—
131C23×D3—61no—
132C23×D3—121no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—32no—
137C22×C3×C4—41no—
138C22×C3×C4—61no—
139C22×C3×C4—61no—
140C22×C3×C4C22×D311yescharacteristic
141C22×C3×C4C22×D311yescharacteristic
142C22×Dic3—21no—
143C22×Dic3—21no—
144C22×Dic3#6712yes—
145C2×D12—32no—
146C2×D12—32no—
147C2×D12—62no—
148C2×D12—62no—
149C2×D12—62no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—121no—
161C2×D12—121no—
162C2×D12—121no—
163C2×C3×C8—32no—
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—22no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—41no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C42—61no—
177C3×C42—61no—
178(C2×D3)⋊C4—124no—
179(C2×D3)⋊C4—124no—
180C4⋊Dic3—21no—
181C4⋊Dic3—21no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4×Dic3—21no—
185C4×Dic3—21no—
186C2×C3⋊C8—21no—
187C2×C3⋊C8—21no—
188C2×C3⋊C8—32no—
189C2×C3⋊C8—32no—
190C2×C3⋊C8—62no—
191C2×C3⋊C8—61no—
192C2×C3⋊C8—61no—
193C2×C3⋊C8—61no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—121no—
196C2×C3⋊C8—121no—
197C2×C3⋊C8#6712yes—
198C22×C32C22⋊Q811yescharacteristic
199C22×C32#12311yescharacteristic
200C22×C32#12711yescharacteristic
201C22×C32#13512yes—
202C22×C32AGL(1,ℤ/8)12yes—
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—42no—
214C3×Dic3—81no—
215C3×Dic3—81no—
216C22×D4—91no—
217C22×C8—31no—
218C22×C8—91no—
219C2×C4⋊C4—31no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4D3211yescharacteristic
222C2×C22⋊C4—182no—
223C2×C42—31no—
224#107—182no—
225#106—62no—
226#102—182no—
227#102—182no—
228#95—62no—
229C23×C3—21no—
230C23×C3D3×D411yescharacteristic
231C23×C3C2×#6711yescharacteristic
232C22×D3—62no—
233C22×D3—62no—
234C22×D3—122no—
235C22×D3—122no—
236C22×D3—122no—
237C22×D3—121no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—121no—
241C22×D3—121no—
242C22×D3—121no—
243C22×D3—122no—
244C22×D3—122no—
245C22×D3—242no—
246C22×D3—242no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—42no—
254C2×C3×C4—42no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—62no—
259C2×C3×C4—62no—
260C2×C3×C4—62no—
261C2×C3×C4—82no—
262C2×C3×C4—122no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4—122no—
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4#23511yescharacteristic
268C2×C3×C4#23511yescharacteristic
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4D3×Q811yescharacteristic
274C2×C3×C4D3×Q811yescharacteristic
275C2×C3×C4#23911yescharacteristic
276C2×C3×C4#23911yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×Dic3—22no—
279C2×Dic3—22no—
280C2×Dic3—22no—
281C2×Dic3—42no—
282C2×Dic3—41no—
283C2×Dic3—41no—
284C2×Dic3—42no—
285D12—64no—
286D12—62no—
287D12—62no—
288D12—62no—
289D12—62no—
290D12—122no—
291D12—122no—
292D12—122no—
293D12—121no—
294D12—121no—
295D12—121no—
296D12—121no—
297C3×C8—62no—
298C3⋊C8—22no—
299C3⋊C8—62no—
300C3⋊C8—62no—
301C3⋊C8—122no—
302C2×C32#39911yescharacteristic
303C2×C32#47812yes—
304C2×C32#48212yes—
305C2×C32#49511yescharacteristic
306C2×C32#49611yescharacteristic
307C3⋊D3—82no—
308C24—181no—
309C2×D4—92no—
310C2×D4—181no—
311C2×D4—181no—
312C2×D4—181no—
313C2×D4—181no—
314C2×D4—181no—
315C22×C4—21no—
316C22×C4—32no—
317C22×C4—61no—
318C22×C4—61no—
319C22×C4C2×D3211yescharacteristic
320C2×C8—32no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—92no—
324C2×C8—181no—
325C2×C8—181no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C22⋊C4—364no—
333C42—61no—
334C42—61no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3#89411yescharacteristic
341C22×C3#89611yescharacteristic
342C22×C3#91412yes—
343C22×C3#91612yes—
344C22×C3#92911yescharacteristic
345C22×C3#94011yescharacteristic
346C22×C3#94011yescharacteristic
347C22×C3#94611yescharacteristic
348C22×C3#94912yes—
349C22×C3#95012yes—
350C2×D3—124no—
351C2×D3—124no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—124no—
355C2×D3—244no—
356C2×D3—242no—
357C2×D3—244no—
358C2×D3—242no—
359C2×D3—242no—
360C2×D3—241no—
361C2×D3—241no—
362C2×D3—242no—
363C2×D3—241no—
364C2×D3—241no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—82no—
370C3×C4—81no—
371C3×C4—81no—
372C3×C4—122no—
373C3×C4—241no—
374C3×C4—241no—
375C3×C4#89411yescharacteristic
376C3×C4#89411yescharacteristic
377C3×C4#89411yescharacteristic
378C3×C4#89611yescharacteristic
379C3×C4#89611yescharacteristic
380C3×C4#89611yescharacteristic
381C3×C4#92911yescharacteristic
382C3×C4#94611yescharacteristic
383Dic3—42no—
384Dic3—81no—
385Dic3—81no—
386C32#209211yescharacteristic, complemented, Sylow
387C23—182no—
388C23—361no—
389C23—362no—
390C23—362no—
391C23—361no—
392C23D3×#6711yescharacteristic
393D4—182no—
394D4—182no—
395D4—361no—
396D4—361no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—122no—
403C2×C4—122no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4#379711yescharacteristic
407C2×C4#379811yescharacteristic
408C2×C4#379911yescharacteristic
409C2×C4#379911yescharacteristic
410C2×C4D3×#6711yescharacteristic
411C2×C4#381111yescharacteristic
412C8—62no—
413C8—182no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—22no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3#486612yes—
420C2×C3#487112yes—
421C2×C3#499311yescharacteristic
422C2×C3#499311yescharacteristic
423C2×C3#500312yes—
424C2×C3#505811yescharacteristic
425C2×C3#505911yescharacteristic
426C2×C3#506612yes—
427C2×C3#516811yescharacteristic
428C2×C3#517611yescharacteristic
429D3—244no—
430D3—242no—
431D3—242no—
432C22—364no—
433C22—362no—
434C22—721no—
435C22—722no—
436C22—721no—
437C22#6385011yescharacteristic
438C22#6388811yescharacteristic
439C22#6393512yes—
440C22#6393912yes—
441C22#6397911yescharacteristic
442C4—81no—
443C4—122no—
444C4—241no—
445C4—241no—
446C4#6385011yescharacteristic
447C4#6386511yescharacteristic
448C4#6388811yescharacteristic
449C4#6389711yescharacteristic
450C3—21no—
451C3#6955811yescharacteristic, complemented
452C3#7058611yescharacteristic, complemented
453C2—722no—
454C2#1059042512yes—
455C2#1059047012yes—
456C2#1059120311yescharacteristic
457C2#1059147311yescharacteristic
458C2#1059161911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2092
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
2. C3×#4977C2semidirect
3. C2×C3×#808C2semidirect
5. C2×#63576C2semidirect
7. #10589155C2semidirect
27. #4977D3semidirect
32. C2×#808D3semidirect
386. C32#2092semidirect
451. C3#69558semidirect
452. C3#70586semidirect

Maximal subgroups

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

subgroupindex
C2×#636362
C3×#49772
C2×C3×#8082
#105913202
C2×#635762
C2×#635642
#105891552
#705863
#695583