Finite Group Databasebeta

← #11795395

Subgroups — #11795395

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×#63648C211yesmaximal, characteristic
2C2×C3×#818C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic
4#10591224C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic, complemented
8#70640—31nomaximal
9#68680—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3722—22no—
18#63648—22no—
19C3×#818—22no—
20#63579—22no—
21#63573—22no—
22#63564—22no—
23C2×C3×#107—31no—
24C2×#821—31no—
25C2×#821—31no—
26C2×#821—31no—
27C2×#821—61no—
28C2×#818D311yescharacteristic, complemented
29C2×#817—31no—
30#4988—31no—
31#4977—31no—
32C2×#809—31no—
33C2×#808—31no—
34#4939—31no—
35#4936—31no—
36C3×#336—31no—
37#4550D311yescharacteristic, complemented
38C23×C3⋊D3—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—21no—
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—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
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—21no—
70C22×C3×C8—31no—
71C22×C3×C8C2×D311yescharacteristic
72C22×C3×C8C2×D311yescharacteristic
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C42—31no—
76C2×(C2×D3)⋊C4—62no—
77C2×(C2×D3)⋊C4—62no—
78C2×C4⋊Dic3—31no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—61no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82C2×C4⋊Dic3C2×D311yescharacteristic
83C2×C4×Dic3C2×D311yescharacteristic
84C22×C3⋊C8C2×D311yescharacteristic
85C3×#107—62no—
86C3⋊#95—62no—
87C3⋊#95—62no—
88#821—62no—
89#821—64no—
90#821—62no—
91#821—62no—
92#818—22no—
93#817—62no—
94#809—62no—
95#808—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×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×Q811yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—42no—
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—
121C32×C8—22no—
122C3×C3⋊C8—22no—
123C2×#107—31no—
124C2×#106—91no—
125C2×#102—91no—
126C2×#102—91no—
127#390—91no—
128#382—91no—
129#336—31no—
130C23×D3—61no—
131C23×D3—61no—
132C23×D3—121no—
133C22×C3×C4—21no—
134C22×C3×C4—32no—
135C22×C3×C4—61no—
136C22×C3×C4—61no—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C22×Dic3—21no—
140C22×Dic3—21no—
141C22×Dic3—61no—
142C22×Dic3—61no—
143C22×Dic3—121no—
144C22×Dic3D1212yes—
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—21no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—22no—
168C2×C3×C8—32no—
169C2×C3×C8—41no—
170C2×C3×C8—41no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8D1212yes—
174C2×C3×C8#6712yes—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C42—61no—
180C3×C42—61no—
181(C2×D3)⋊C4—124no—
182(C2×D3)⋊C4—124no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—62no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—121no—
193C4×Dic3—21no—
194C4×Dic3—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8D1212yes—
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×C4C22⋊Q811yescharacteristic
209C32×C4C22⋊Q811yescharacteristic
210C32×C4#12311yescharacteristic
211C32×C4#12311yescharacteristic
212C3⋊Dic3—81no—
213C3×Dic3—42no—
214C3×Dic3—81no—
215C3×Dic3—81no—
216C22×D4—91no—
217C22×C8—31no—
218C22×C8D3211yescharacteristic
219C2×C4⋊C4—31no—
220C2×C4⋊C4—31no—
221C2×C4⋊C4—91no—
222C2×C22⋊C4—182no—
223C2×C42—31no—
224#107—62no—
225#106—182no—
226#102—182no—
227#102—182no—
228#95—182no—
229C23×C3—21no—
230C23×C3C2×D1211yescharacteristic
231C23×C3D3×D411yescharacteristic
232C22×D3—62no—
233C22×D3—62no—
234C22×D3—122no—
235C22×D3—122no—
236C22×D3—122no—
237C22×D3—121no—
238C22×D3—121no—
239C22×D3—121no—
240C22×D3—122no—
241C22×D3—122no—
242C22×D3—122no—
243C22×D3—122no—
244C22×D3—121no—
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—62no—
254C2×C3×C4—62no—
255C2×C3×C4—62no—
256C2×C3×C4—121no—
257C2×C3×C4—121no—
258C2×C3×C4—122no—
259C2×C3×C4—122no—
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4C2×D1211yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4#23511yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4#23711yescharacteristic
266C2×C3×C4#23711yescharacteristic
267C2×C3×C4#23711yescharacteristic
268C2×C3×C4D3×Q811yescharacteristic
269C2×C3×C4D3×Q811yescharacteristic
270C2×C3×C4#23911yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—22no—
275C2×Dic3—42no—
276C2×Dic3—42no—
277C2×Dic3—41no—
278C2×Dic3—41no—
279C2×Dic3—122no—
280C2×Dic3—121no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283C2×Dic3—121no—
284C2×Dic3—242no—
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—22no—
298C3×C8—22no—
299C3×C8—42no—
300C3×C8—62no—
301C3⋊C8—22no—
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—32no—
316C22×C4—61no—
317C22×C4—61no—
318C22×C4—181no—
319C22×C4C2×D3211yescharacteristic
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—32no—
323C2×C8—61no—
324C2×C8—61no—
325C2×C8#62612yes—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C22⋊C4—364no—
333C42—61no—
334C42—61no—
335C22×C3—22no—
336C22×C3—22no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3#87411yescharacteristic
341C22×C3#88611yescharacteristic
342C22×C3#89411yescharacteristic
343C22×C3#89611yescharacteristic
344C22×C3#89711yescharacteristic
345C22×C3#90412yes—
346C22×C3#90812yes—
347C22×C3#91112yes—
348C22×C3#91912yes—
349C22×C3#94011yescharacteristic
350C2×D3—124no—
351C2×D3—124no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—124no—
355C2×D3—244no—
356C2×D3—242no—
357C2×D3—242no—
358C2×D3—244no—
359C2×D3—242no—
360C2×D3—241no—
361C2×D3—241no—
362C2×D3—241no—
363C2×D3—241no—
364C2×D3—242no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—122no—
370C3×C4—241no—
371C3×C4—241no—
372C3×C4#88611yescharacteristic
373C3×C4#88611yescharacteristic
374C3×C4#89411yescharacteristic
375C3×C4#89611yescharacteristic
376C3×C4#89711yescharacteristic
377C3×C4#89711yescharacteristic
378C3×C4#92911yescharacteristic
379C3×C4#94611yescharacteristic
380Dic3—42no—
381Dic3—81no—
382Dic3—81no—
383Dic3—242no—
384Dic3—241no—
385Dic3—241no—
386C32#209211yescharacteristic, complemented, Sylow
387C23—182no—
388C23—362no—
389C23—362no—
390C23—361no—
391C23—361no—
392C23D3×D1211yescharacteristic
393D4—182no—
394D4—182no—
395D4—361no—
396D4—361no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—122no—
401C2×C4—122no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—362no—
405C2×C4—361no—
406C2×C4#379611yescharacteristic
407C2×C4#379711yescharacteristic
408C2×C4D3×D1211yescharacteristic
409C2×C4#380411yescharacteristic
410C2×C4#380411yescharacteristic
411C2×C4C2×#62611yescharacteristic
412C8—22no—
413C8—62no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—22no—
419C2×C3#467711yescharacteristic
420C2×C3#469611yescharacteristic
421C2×C3#471211yescharacteristic
422C2×C3#473712yes—
423C2×C3#484712yes—
424C2×C3#488512yes—
425C2×C3#489112yes—
426C2×C3#499311yescharacteristic
427C2×C3#515411yescharacteristic
428C2×C3#519111yescharacteristic
429D3—244no—
430D3—242no—
431D3—242no—
432C22—364no—
433C22—362no—
434C22—721no—
435C22—721no—
436C22—722no—
437C22#6379512yes—
438C22#6380812yes—
439C22#6389011yescharacteristic
440C22#6389511yescharacteristic
441C22#6391111yescharacteristic
442C4—122no—
443C4—241no—
444C4—241no—
445C4—721no—
446C4#6387111yescharacteristic
447C4#6389011yescharacteristic
448C4#6389511yescharacteristic
449C4#6396611yescharacteristic
450C3—21no—
451C3#6868011yescharacteristic, complemented
452C3#7064011yescharacteristic, complemented
453C2—722no—
454C2#1059070512yes—
455C2#1059077412yes—
456C2#1059086511yescharacteristic
457C2#1059088311yescharacteristic
458C2#1059135011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32#2092
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#818C2semidirect
4. #10591224C2semidirect
5. C2×#63573C2semidirect
7. C3×#4550C2semidirect
28. C2×#818D3semidirect
37. #4550D3semidirect
386. C32#2092semidirect
451. C3#68680semidirect
452. C3#70640semidirect

Maximal subgroups

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

subgroupindex
C2×#636482
C2×C3×#8182
#105913202
#105912242
C2×#635732
C2×#635642
C3×#45502
#706403
#686803