Finite Group Databasebeta

← #11795410

Subgroups — #11795410

Order 1152.

677 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
1#10592638C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic, complemented
3C2×#63575C211yesmaximal, characteristic, complemented
4C2×#63573C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6C2×#63564C211yesmaximal, characteristic
7C3×#4524C211yesmaximal, characteristic, complemented
8#69558—31nomaximal
9#68680—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3752—22no—
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C3×C3⋊#95—22no—
19#63575—22no—
20#63573—22no—
21#63564—22no—
22#63564—22no—
23C3×#382—31no—
24C2×#821—31no—
25C2×#821—31no—
26C2×#818—31no—
27C2×#817—31no—
28C2×#809—31no—
29C2×#809—31no—
30C2×#808—31no—
31C2×#807—31no—
32#4939—31no—
33#4939—31no—
34#4939—61no—
35#4936D311yescharacteristic, complemented
36C3×#336—31no—
37#4524D311yescharacteristic, complemented
38C23×C3⋊D3—21no—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—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)—21no—
47C2×C4⋊(C3⋊D3)Q812yes—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C32×C42—21no—
51C32×C42—21no—
52#3752—44no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊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#2092—91noSylow
66C22×D12—31no—
67C22×D12—31no—
68C22×D12—61no—
69C22×C3×C8—31no—
70C22×C3×C8—31no—
71C2×C3×C4⋊C4—31no—
72C2×C3×C4⋊C4—31no—
73C2×C3×C42—21no—
74C2×C3×C42C2×D311yescharacteristic
75C2×C3×C42C2×D311yescharacteristic
76C2×(C2×D3)⋊C4—64no—
77C2×(C2×D3)⋊C4—62no—
78C2×(C2×D3)⋊C4—62no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3C2×D311yescharacteristic
83C2×C4⋊Dic3C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C22×C3⋊C8C2×D311yescharacteristic
86C3×#95—62no—
87C3⋊#95—22no—
88#821—62no—
89#821—62no—
90#818—62no—
91#817—62no—
92#809—62no—
93#809—62no—
94#808—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—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
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—
113C4⋊(C3⋊D3)—22no—
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—41no—
116C4⋊(C3⋊D3)—41no—
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—91no—
125C2×#102—91no—
126C2×#102—91no—
127#390—91no—
128#382—31no—
129#336—31no—
130C23×D3—62no—
131C23×D3—61no—
132C23×D3—61no—
133C22×C3×C4—22no—
134C22×C3×C4—21no—
135C22×C3×C4—61no—
136C22×C3×C4—61no—
137C22×C3×C4D1212yes—
138C22×C3×C4#6712yes—
139C22×C3×C4C22×D311yescharacteristic
140C22×C3×C4C22×D311yescharacteristic
141C22×Dic3—21no—
142C22×Dic3—21no—
143C22×Dic3—62no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C2×D12—32no—
147C2×D12—32no—
148C2×D12—62no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—62no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—121no—
161C2×D12—121no—
162C2×D12—121no—
163C2×D12—121no—
164C2×C3×C8—32no—
165C2×C3×C8—32no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—61no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—21no—
177C3×C42—21no—
178C3×C42—41no—
179C3×C42—41no—
180(C2×D3)⋊C4—128no—
181(C2×D3)⋊C4—124no—
182(C2×D3)⋊C4—124no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—121no—
192C4⋊Dic3—121no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8D1212yes—
198C2×C3⋊C8D1212yes—
199C22×C32C22⋊Q811yescharacteristic
200C22×C32#12311yescharacteristic
201C22×C32#12711yescharacteristic
202C22×C32#13512yes—
203C22×C32AGL(1,ℤ/8)12yes—
204C2×C3⋊D3—42no—
205C2×C3⋊D3—44no—
206C2×C3⋊D3—82no—
207C2×C3⋊D3—81no—
208C2×C3⋊D3—81no—
209C32×C4—42no—
210C32×C4C22⋊Q811yescharacteristic
211C32×C4C22⋊Q811yescharacteristic
212C32×C4#12311yescharacteristic
213C32×C4#12311yescharacteristic
214C3⋊Dic3—81no—
215C3×Dic3—81no—
216C3×Dic3—81no—
217C22×D4—91no—
218C22×C8—31no—
219C22×C8—31no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4—31no—
222C2×C4⋊C4—91no—
223C2×C22⋊C4—182no—
224C2×C42D3211yescharacteristic
225#107—182no—
226#106—182no—
227#102—182no—
228#102—182no—
229#95—62no—
230C23×C3—21no—
231C23×C3C2×D1211yescharacteristic
232C23×C3C2×#6711yescharacteristic
233C22×D3—64no—
234C22×D3—62no—
235C22×D3—62no—
236C22×D3—124no—
237C22×D3—122no—
238C22×D3—122no—
239C22×D3—124no—
240C22×D3—121no—
241C22×D3—121no—
242C22×D3—122no—
243C22×D3—122no—
244C22×D3—121no—
245C22×D3—121no—
246C22×D3—122no—
247C22×D3—122no—
248C2×C3×C4—24no—
249C2×C3×C4—22no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4—122no—
266C2×C3×C4—122no—
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4#23511yescharacteristic
270C2×C3×C4#23511yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4#23711yescharacteristic
274C2×C3×C4#23711yescharacteristic
275C2×C3×C4#23711yescharacteristic
276C2×C3×C4D3×Q811yescharacteristic
277C2×C3×C4D3×Q811yescharacteristic
278C2×C3×C4#23911yescharacteristic
279C2×Dic3—41no—
280C2×Dic3—41no—
281C2×Dic3—42no—
282C2×Dic3—42no—
283C2×Dic3—122no—
284C2×Dic3—124no—
285C2×Dic3—121no—
286C2×Dic3—122no—
287C2×Dic3—121no—
288C2×Dic3—122no—
289D12—62no—
290D12—62no—
291D12—62no—
292D12—62no—
293D12—122no—
294D12—122no—
295D12—122no—
296D12—122no—
297D12—121no—
298D12—121no—
299D12—121no—
300D12—121no—
301C3×C8—62no—
302C3×C8—62no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C2×C32#39911yescharacteristic
306C2×C32#47812yes—
307C2×C32#48212yes—
308C2×C32#49511yescharacteristic
309C2×C32#49611yescharacteristic
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—61no—
319C22×C4—61no—
320C22×C4—181no—
321C22×C4#62612yes—
322C22×C4C2×D3211yescharacteristic
323C2×C8—32no—
324C2×C8—32no—
325C2×C8—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C22⋊C4—364no—
336C42—21no—
337C42—21no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3#87411yescharacteristic
344C22×C3#88611yescharacteristic
345C22×C3#89711yescharacteristic
346C22×C3#90412yes—
347C22×C3#90812yes—
348C22×C3#92911yescharacteristic
349C22×C3#94011yescharacteristic
350C22×C3#94611yescharacteristic
351C22×C3#94912yes—
352C22×C3#95012yes—
353C2×D3—124no—
354C2×D3—128no—
355C2×D3—122no—
356C2×D3—122no—
357C2×D3—124no—
358C2×D3—124no—
359C2×D3—242no—
360C2×D3—244no—
361C2×D3—242no—
362C2×D3—241no—
363C2×D3—241no—
364C2×D3—242no—
365C2×D3—242no—
366C2×D3—241no—
367C2×D3—241no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—44no—
373C3×C4—42no—
374C3×C4—42no—
375C3×C4—241no—
376C3×C4—241no—
377C3×C4#88611yescharacteristic
378C3×C4#88611yescharacteristic
379C3×C4#89411yescharacteristic
380C3×C4#89411yescharacteristic
381C3×C4#89611yescharacteristic
382C3×C4#89611yescharacteristic
383C3×C4#89711yescharacteristic
384C3×C4#89711yescharacteristic
385Dic3—81no—
386Dic3—81no—
387Dic3—242no—
388Dic3—241no—
389Dic3—241no—
390C32#209211yescharacteristic, complemented, Sylow
391C23—182no—
392C23—362no—
393C23—362no—
394C23—361no—
395C23—361no—
396C23C2×#62611yescharacteristic
397D4—182no—
398D4—182no—
399D4—361no—
400D4—361no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—122no—
405C2×C4—122no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—362no—
409C2×C4—361no—
410C2×C4#379611yescharacteristic
411C2×C4#379711yescharacteristic
412C2×C4D3×D1211yescharacteristic
413C2×C4D3×D1211yescharacteristic
414C2×C4#380411yescharacteristic
415C2×C4#380411yescharacteristic
416C8—62no—
417C8—62no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—22no—
422C2×C3—21no—
423C2×C3#467711yescharacteristic
424C2×C3#469611yescharacteristic
425C2×C3#471211yescharacteristic
426C2×C3#473712yes—
427C2×C3#484712yes—
428C2×C3#499311yescharacteristic
429C2×C3#500312yes—
430C2×C3#505811yescharacteristic
431C2×C3#505911yescharacteristic
432C2×C3#506612yes—
433D3—244no—
434D3—242no—
435D3—242no—
436C22—364no—
437C22—362no—
438C22—721no—
439C22—722no—
440C22—721no—
441C22#6382512yes—
442C22#6382912yes—
443C22#6387111yescharacteristic
444C22#6391111yescharacteristic
445C22#6396611yescharacteristic
446C4—42no—
447C4—241no—
448C4—241no—
449C4—721no—
450C4#6389011yescharacteristic
451C4#6389011yescharacteristic
452C4#6389511yescharacteristic
453C4#6389511yescharacteristic
454C3—21no—
455C3#6868011yescharacteristic, complemented
456C3#6955811yescharacteristic, complemented
457C2—722no—
458C2#1059030812yes—
459C2#1059035111yescharacteristic
460C2#1059037011yescharacteristic
461C2#1059113612yes—
462C2#1059135011yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2092
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4936C2semidirect
3. C2×#63575C2semidirect
4. C2×#63573C2semidirect
7. C3×#4524C2semidirect
35. #4936D3semidirect
37. #4524D3semidirect
390. C32#2092semidirect
455. C3#68680semidirect
456. C3#69558semidirect

Maximal subgroups

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

subgroupindex
#105926382
C3×#49362
C2×#635752
C2×#635732
C2×#635642
C3×#45242
#695583
#686803