Finite Group Databasebeta

← #11795442

Subgroups — #11795442

Order 1152.

681 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63636C211yesmaximal, characteristic
2C3×#4975C211yesmaximal, characteristic, complemented
3C2×C3×#807C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7#10589155C211yesmaximal, characteristic, complemented
8#70641—31nomaximal
9#69586—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×Dic3⋊C4—22no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3722—22no—
19#63636—22no—
20C3×#807—22no—
21#63576—22no—
22#63564—22no—
23C2×C3×#107—31no—
24C3×#384—31no—
25C2×#821—31no—
26#4988—31no—
27#4975D311yescharacteristic, complemented
28C2×#809—31no—
29C2×#809—31no—
30C2×#809—31no—
31C2×#809—61no—
32C2×#807—31no—
33C2×#807—31no—
34C2×#807D311yescharacteristic, complemented
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×Dic3⋊C4—44no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8D412yes—
65#3722—44no—
66#2093—91noSylow
67C22×D12—31no—
68C22×D12—31no—
69C22×D12—61no—
70C22×C3×C8—31no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—62no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C42—31no—
78C2×(C2×D3)⋊C4—62no—
79C2×(C2×D3)⋊C4—62no—
80C2×C4⋊Dic3C2×D311yescharacteristic
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×Dic3⋊C4—22no—
83C2×C4×Dic3C2×D311yescharacteristic
84C22×C3⋊C8—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—61no—
87C22×C3⋊C8C2×D311yescharacteristic
88C3×#107—62no—
89#821—62no—
90#809—62no—
91#809—62no—
92#809—64no—
93#809—62no—
94#807—22no—
95#807—62no—
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
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3D814yes—
122C3⋊(C3⋊C8)—22no—
123C3×C3⋊C8—22no—
124C2×#107—31no—
125C2×#107—91no—
126C2×#102—91no—
127C2×#102—91no—
128#390—91no—
129#384—31no—
130#336—91no—
131C23×D3—61no—
132C23×D3—61no—
133C23×D3—121no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—21no—
137C22×C3×C4—32no—
138C22×C3×C4—41no—
139C22×C3×C4—61no—
140C22×C3×C4—61no—
141C22×C3×C4C22×D311yescharacteristic
142C22×C3×C4C22×D311yescharacteristic
143C22×Dic3—21no—
144C22×Dic3—21no—
145C22×Dic3#6712yes—
146C2×D12—32no—
147C2×D12—32no—
148C2×D12—62no—
149C2×D12—62no—
150C2×D12—62no—
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—61no—
161C2×D12—121no—
162C2×D12—121no—
163C2×D12—121no—
164C2×C3×C8—32no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—22no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—41no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—124no—
178C3×C42—61no—
179C3×C42—61no—
180(C2×D3)⋊C4—124no—
181(C2×D3)⋊C4—124no—
182C4⋊Dic3—21no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186Dic3⋊C4—44no—
187C4×Dic3—21no—
188C4×Dic3—21no—
189C2×C3⋊C8—21no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—32no—
192C2×C3⋊C8—32no—
193C2×C3⋊C8—62no—
194C2×C3⋊C8—61no—
195C2×C3⋊C8—61no—
196C2×C3⋊C8—61no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—121no—
199C2×C3⋊C8—121no—
200C2×C3⋊C8#6712yes—
201C22×C32C22⋊Q811yescharacteristic
202C22×C32#12311yescharacteristic
203C22×C32#12711yescharacteristic
204C22×C32C2×D812yes—
205C22×C32#13712yes—
206C2×C3⋊D3—42no—
207C2×C3⋊D3—44no—
208C2×C3⋊D3—82no—
209C2×C3⋊D3—81no—
210C2×C3⋊D3—81no—
211C32×C4—81no—
212C32×C4C22⋊Q811yescharacteristic
213C32×C4C22⋊Q811yescharacteristic
214C32×C4#12311yescharacteristic
215C32×C4#12311yescharacteristic
216C3×Dic3—24no—
217C3×Dic3—81no—
218C3×Dic3—81no—
219C22×D4—91no—
220C22×C8—31no—
221C22×C8—91no—
222C2×C4⋊C4—31no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4—62no—
225C2×C4⋊C4D3211yescharacteristic
226C2×C22⋊C4—182no—
227C2×C42—31no—
228#107—62no—
229#107—182no—
230#102—182no—
231#102—182no—
232C23×C3—21no—
233C23×C3D3×D411yescharacteristic
234C23×C3C2×#6711yescharacteristic
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—122no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—121no—
241C22×D3—122no—
242C22×D3—122no—
243C22×D3—121no—
244C22×D3—122no—
245C22×D3—121no—
246C22×D3—121no—
247C22×D3—122no—
248C22×D3—242no—
249C22×D3—242no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—34no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—41no—
261C2×C3×C4—41no—
262C2×C3×C4—62no—
263C2×C3×C4—62no—
264C2×C3×C4—82no—
265C2×C3×C4—122no—
266C2×C3×C4—122no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4#23511yescharacteristic
271C2×C3×C4#23511yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4D3×D411yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×Q811yescharacteristic
277C2×C3×C4D3×Q811yescharacteristic
278C2×C3×C4#23911yescharacteristic
279C2×C3×C4#23911yescharacteristic
280C2×C3×C4C2×#6711yescharacteristic
281C2×Dic3—22no—
282C2×Dic3—22no—
283C2×Dic3—42no—
284C2×Dic3—42no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3#21314yes—
288D12—64no—
289D12—62no—
290D12—62no—
291D12—62no—
292D12—62no—
293D12—122no—
294D12—122no—
295D12—122no—
296D12—121no—
297D12—121no—
298D12—121no—
299D12—121no—
300C3×C8—62no—
301C3⋊C8—22no—
302C3⋊C8—62no—
303C3⋊C8—62no—
304C3⋊C8—122no—
305C2×C32#39911yescharacteristic
306C2×C32#47412yes—
307C2×C32#48012yes—
308C2×C32#49311yescharacteristic
309C2×C32#49711yescharacteristic
310C3⋊D3—82no—
311C24—181no—
312C2×D4—92no—
313C2×D4—181no—
314C2×D4—181no—
315C2×D4—181no—
316C2×D4—181no—
317C2×D4—181no—
318C22×C4—21no—
319C22×C4—32no—
320C22×C4—61no—
321C22×C4—61no—
322C22×C4C2×D3211yescharacteristic
323C2×C8—32no—
324C2×C8—61no—
325C2×C8—61no—
326C2×C8—92no—
327C2×C8—181no—
328C2×C8—181no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—124no—
336C22⋊C4—364no—
337C42—61no—
338C42—61no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—21no—
344C22×C3#89411yescharacteristic
345C22×C3#89611yescharacteristic
346C22×C3D3×D812yes—
347C22×C3#91812yes—
348C22×C3#92911yescharacteristic
349C22×C3C2×#21312yes—
350C22×C3#94011yescharacteristic
351C22×C3#94011yescharacteristic
352C22×C3#94212yes—
353C22×C3#94611yescharacteristic
354C2×D3—124no—
355C2×D3—124no—
356C2×D3—122no—
357C2×D3—122no—
358C2×D3—124no—
359C2×D3—244no—
360C2×D3—242no—
361C2×D3—244no—
362C2×D3—242no—
363C2×D3—242no—
364C2×D3—241no—
365C2×D3—241no—
366C2×D3—242no—
367C2×D3—241no—
368C2×D3—241no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—64no—
374C3×C4—82no—
375C3×C4—81no—
376C3×C4—81no—
377C3×C4—241no—
378C3×C4—241no—
379C3×C4#89411yescharacteristic
380C3×C4#89411yescharacteristic
381C3×C4#89411yescharacteristic
382C3×C4#89611yescharacteristic
383C3×C4#89611yescharacteristic
384C3×C4#89611yescharacteristic
385C3×C4#92911yescharacteristic
386C3×C4#94611yescharacteristic
387Dic3—24no—
388Dic3—81no—
389Dic3—81no—
390C32#209311yescharacteristic, complemented, Sylow
391C23—182no—
392C23—361no—
393C23—362no—
394C23—362no—
395C23—361no—
396C23D3×#6711yescharacteristic
397D4—182no—
398D4—182no—
399D4—361no—
400D4—361no—
401C2×C4—34no—
402C2×C4—42no—
403C2×C4—41no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—122no—
407C2×C4—122no—
408C2×C4—121no—
409C2×C4—121no—
410C2×C4#379711yescharacteristic
411C2×C4#379811yescharacteristic
412C2×C4#379911yescharacteristic
413C2×C4#379911yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C2×C4#381111yescharacteristic
416C8—62no—
417C8—182no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—22no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3#488212yes—
424C2×C3#489012yes—
425C2×C3#496712yes—
426C2×C3#499311yescharacteristic
427C2×C3#499311yescharacteristic
428C2×C3#507311yescharacteristic
429C2×C3#508611yescharacteristic
430C2×C3#508712yes—
431C2×C3#515111yescharacteristic
432C2×C3#519011yescharacteristic
433D3—244no—
434D3—242no—
435D3—242no—
436C22—364no—
437C22—362no—
438C22—721no—
439C22—722no—
440C22—721no—
441C22#6385011yescharacteristic
442C22#6388811yescharacteristic
443C22D3×#21312yes—
444C22#6394812yes—
445C22#6397911yescharacteristic
446C4—64no—
447C4—81no—
448C4—241no—
449C4—241no—
450C4#6385011yescharacteristic
451C4#6386511yescharacteristic
452C4#6388811yescharacteristic
453C4#6389711yescharacteristic
454C3—21no—
455C3#6958611yescharacteristic, complemented
456C3#7064111yescharacteristic, complemented
457C2—722no—
458C2#1059042212yes—
459C2#1059046412yes—
460C2#1059120311yescharacteristic
461C2#1059148211yescharacteristic
462C2#1059160811yescharacteristic
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#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
2. C3×#4975C2semidirect
3. C2×C3×#807C2semidirect
5. C2×#63576C2semidirect
7. #10589155C2semidirect
27. #4975D3semidirect
34. C2×#807D3semidirect
390. C32#2093semidirect
455. C3#69586semidirect
456. C3#70641semidirect

Maximal subgroups

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

subgroupindex
C2×#636362
C3×#49752
C2×C3×#8072
#105913202
C2×#635762
C2×#635642
#105891552
#706413
#695863