Finite Group Databasebeta

← #11899779

Subgroups — #11899779

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5771C211yesmaximal, characteristic, complemented
2#10594692C211yesmaximal, characteristic, complemented
3#10592894C211yesmaximal, characteristic, complemented
4C3×#5194C211yesmaximal, characteristic, complemented
5#10591045C212yesmaximal, complemented
6D3×#829C212yesmaximal, complemented
7#10591032C212yesmaximal, complemented
8#10591028C212yesmaximal, complemented
9C2×#63551C211yesmaximal, characteristic, complemented
10#10590636C211yesmaximal, characteristic, complemented
11#10590621C211yesmaximal, characteristic, complemented
12#84017—31nomaximal
13#82033—31nomaximal
14C3×#1010—21no—
15#64298—21no—
16C32×#135C2211yescharacteristic
17C2×#3746C2211yescharacteristic
18C3×#951—21no—
19C3×D3×Q16C2212yes—
20C3×#915—22no—
21C3×#912C2212yes—
22C2×C3×Dic12C2211yescharacteristic
23C3×#904C2211yescharacteristic
24C3×#901C2211yescharacteristic
25#63831—21no—
26#63807C2212yes—
27#63800—22no—
28D3×Dic12C2212yes—
29#63656C2212yes—
30#63654C2212yes—
31#63639C2211yescharacteristic
32C3×#829C2211yescharacteristic
33C3×#828C2211yescharacteristic
34C3×#827C2211yescharacteristic
35C3×#826C2211yescharacteristic
36C2×C3×C3⋊C16C2211yescharacteristic
37#63551C2212yes—
38#63551C2212yes—
39#63550C2212yes—
40#63547C2212yes—
41#63543C2212yes—
42D3×C3⋊C16C2212yes—
43C3×#578—31no—
44#5771—31no—
45#5771D311yescharacteristic, complemented
46#5753—31no—
47C3×#508—31no—
48#5195—31no—
49#5195—31no—
50#5195—31no—
51#5195—32no—
52#5195—61no—
53#5194—32no—
54#5194D311yescharacteristic, complemented
55C2×#829—32no—
56C2×#829—31no—
57#5179—31no—
58#5179—32no—
59#5140—31no—
60D3×Q32—32no—
61#4915—32no—
62#4915—32no—
63#4912—32no—
64C2×Dic24—31no—
65#4901—31no—
66C32×#41—21no—
67C2×#634—21no—
68C3×D3×Q8—22no—
69C3×#237—22no—
70C3×#237—42no—
71C3×#235—21no—
72C3×#235—41no—
73C3×#235D411yescharacteristic
74C2×C3×Dic6—21no—
75C2×C3×Dic6—41no—
76#3805—42no—
77#3795—22no—
78#3795—41no—
79D3×Dic6—22no—
80D3×Dic6—41no—
81C32×Q16C2311yescharacteristic
82C32×SD16—21no—
83C32×D8C2311yescharacteristic
84C2×C32×C8C2311yescharacteristic
85#3746—21no—
86#3746C2312yes—
87C3×#216—22no—
88C3×#214—22no—
89C3×#208D411yescharacteristic
90C3×Dic12—21no—
91C3×Dic12C2311yescharacteristic
92C3×Dic12C2312yes—
93C3×D24C2311yescharacteristic
94C3×#204—21no—
95C3×ΓL(1,𝔽25)D412yes—
96C3×D3×C8C2312yes—
97#3719—22no—
98#3716—22no—
99C3⋊(C3⋊C16)C2312yes—
100C3×C3⋊C16C2311yescharacteristic
101C3×C3⋊C16C2311yescharacteristic
102#3417—91noSylow
103C3×2−1+4—61no—
104#1010—21no—
105#1010—61no—
106#1010—61no—
107C3×#137—62no—
108C3×#137—61no—
109C3×#135—21no—
110C3×#135—32no—
111C3×#135—31no—
112C3×#135C2×D311yescharacteristic
113C3×#135C2×D311yescharacteristic
114C2×C3×Q16—32no—
115C2×C3×Q16—31no—
116C3×#131—31no—
117#951—21no—
118#951—61no—
119D3×Q16—32no—
120D3×Q16C2×D312yes—
121#915—22no—
122#915—62no—
123#912—32no—
124#912C2×D312yes—
125#909—62no—
126#909—61no—
127C2×Dic12—31no—
128C2×Dic12—31no—
129C2×Dic12—32no—
130C2×Dic12—61no—
131C2×Dic12C2×D311yescharacteristic
132#904—32no—
133#904C2×D311yescharacteristic
134#901C2×D311yescharacteristic
135C3×Q32—31no—
136C3×SD32—31no—
137C3×SD32—31no—
138C3×D16—31no—
139C2×C3×C16—31no—
140#829—32no—
141#829—32no—
142#829—32no—
143#829—32no—
144#829—32no—
145#829—32no—
146#829—62no—
147#829C2×D311yescharacteristic
148#828—32no—
149#828C2×D311yescharacteristic
150#827—32no—
151#827—32no—
152#827—32no—
153#827—62no—
154#827C2×D311yescharacteristic
155#826C2×D311yescharacteristic
156#812—31no—
157#812—31no—
158#812—32no—
159#812—61no—
160C2×C3⋊C16—32no—
161C2×C3⋊C16C2×D311yescharacteristic
162Dic24—32no—
163Dic24—32no—
164#798—32no—
165D3×C16—32no—
166C32×Q8—21no—
167C32×D4—21no—
168C32×D4—41no—
169C2×C32×C4—41no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C3⋊Dic3—41no—
172#634—22no—
173#634—41no—
174C3×#67—41no—
175C3×#67—42no—
176C3×#67D812yes—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—42no—
179C3×D12—21no—
180C3×D12D811yescharacteristic
181C3×C4×D3—42no—
182C3×C4×D3—41no—
183C3×C4×D3C2×D412yes—
184C3×Dic6—21no—
185C3×Dic6—22no—
186C3×Dic6—41no—
187C3×Dic6—42no—
188C3×Dic6D811yescharacteristic
189#627—42no—
190#625—42no—
191D3×Dic3—42no—
192D3×Dic3—42no—
193C32×C8C2×D411yescharacteristic
194C32×C8C2411yescharacteristic
195C3×C3⋊C8C2×D412yes—
196#578—31no—
197#578—91no—
198#510—92no—
199#510—92no—
200#510—91no—
201#510—91no—
202#508—31no—
203#508—92no—
204C2×Q32—91no—
205C2×Q32—92no—
206#504—91no—
207C3×#41—21no—
208C3×#41—21no—
209C3×#41—31no—
210C3×#41—41no—
211C3×#41—62no—
212C3×#41—61no—
213C3×#41—121no—
214C3×#41—122no—
215C2×C3×Q8—62no—
216C2×C3×Q8—61no—
217C2×C3×Q8—121no—
218D3×Q8—22no—
219D3×Q8—62no—
220D3×Q8—121no—
221#237—22no—
222#237—42no—
223#237—62no—
224#237—121no—
225#237—122no—
226#237—122no—
227#235—21no—
228#235—41no—
229#235—62no—
230#235—121no—
231#235#6711yescharacteristic
232C2×Dic6—21no—
233C2×Dic6—41no—
234C2×Dic6—62no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6—121no—
239C3×Q16—21no—
240C3×Q16—32no—
241C3×Q16—31no—
242C3×Q16—62no—
243C3×Q16—61no—
244C3×Q16C22×D311yescharacteristic
245C3×Q16C22×D311yescharacteristic
246C3×SD16—21no—
247C3×SD16—21no—
248C3×SD16—41no—
249C3×SD16—62no—
250C3×SD16—61no—
251C3×D8—21no—
252C3×D8—31no—
253C3×D8C22×D311yescharacteristic
254C3×D8C22×D311yescharacteristic
255C3×M16—31no—
256C3×M16—32no—
257C2×C3×C8—21no—
258C2×C3×C8—32no—
259C2×C3×C8C22×D311yescharacteristic
260C2×C3×C8C22×D311yescharacteristic
261#216—22no—
262#216—62no—
263#214—22no—
264#214—62no—
265#208#6711yescharacteristic
266Dic12—21no—
267Dic12—32no—
268Dic12—32no—
269Dic12—62no—
270Dic12—62no—
271Dic12—61no—
272Dic12—61no—
273Dic12—121no—
274Dic12C22×D312yes—
275Dic12C22×D311yescharacteristic
276D24C22×D311yescharacteristic
277#204—21no—
278#204—62no—
279ΓL(1,𝔽25)#6712yes—
280D3×C8C22×D312yes—
281C3×C16—31no—
282C3×C16—31no—
283C3⋊C16—32no—
284C3⋊C16—32no—
285C3⋊C16—62no—
286C3⋊C16C22×D311yescharacteristic
287C3⋊C16C22×D311yescharacteristic
288C22×C32—41no—
289C22×C32C2×D811yescharacteristic
290C2×C3×D3—41no—
291C2×C3×D3C2×D812yes—
292C32×C4—41no—
293C32×C4C2×D811yescharacteristic
294C32×C4C22×D411yescharacteristic
295C3⋊Dic3—42no—
296C3×Dic3—41no—
297C3×Dic3—42no—
298C3×Dic3C2×D812yes—
2992−1+4—61no—
3002−1+4—181no—
301#137—62no—
302#137—61no—
303#137—182no—
304#137—181no—
305#135—32no—
306#135—31no—
307#135—92no—
308#135D3211yescharacteristic
309C2×Q16—32no—
310C2×Q16—31no—
311C2×Q16—92no—
312C2×Q16—91no—
313#131—31no—
314Q32—31no—
315Q32—92no—
316Q32—92no—
317Q32—92no—
318Q32—92no—
319SD32—31no—
320SD32—31no—
321SD32—92no—
322SD32—92no—
323D16—31no—
324M32—92no—
325M32—91no—
326C2×C16—31no—
327C2×C16—92no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—31no—
331C3×Q8—41no—
332C3×Q8—62no—
333C3×Q8—61no—
334C3×Q8—122no—
335C3×Q8—121no—
336C3×D4—21no—
337C3×D4—21no—
338C3×D4—32no—
339C3×D4—31no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—61no—
344C3×D4—81no—
345C3×D4—122no—
346C3×D4—121no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—41no—
350C2×C3×C4—41no—
351C2×C3×C4—81no—
352C2×C3×C4—122no—
353C2×C3×C4—122no—
354C2×C3×C4—121no—
355C2×C3×C4—121no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358#67—41no—
359#67—42no—
360#67—122no—
361#67—122no—
362#67#21312yes—
363C2×Dic3—41no—
364C2×Dic3—42no—
365C2×Dic3—122no—
366C2×Dic3—121no—
367C2×Dic3—121no—
368C2×Dic3—122no—
369C2×Dic3—241no—
370D12—21no—
371D12#21311yescharacteristic
372C4×D3—42no—
373C4×D3—41no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3C2×#6712yes—
377Dic6—21no—
378Dic6—22no—
379Dic6—41no—
380Dic6—42no—
381Dic6—62no—
382Dic6—62no—
383Dic6—122no—
384Dic6—122no—
385Dic6—121no—
386Dic6—121no—
387Dic6—122no—
388Dic6—241no—
389Dic6#21311yescharacteristic
390C3×C8—21no—
391C3×C8—21no—
392C3×C8—32no—
393C3×C8D3×D411yescharacteristic
394C3×C8C2×#6711yescharacteristic
395C3×C8C23×D311yescharacteristic
396C3×C8C23×D311yescharacteristic
397C3⋊C8C2×#6712yes—
398C2×C32—21no—
399C2×C32—81no—
400C2×C32C22×D811yescharacteristic
401C3×D3—22no—
402C3×D3—81no—
403#41—21no—
404#41—31no—
405#41—62no—
406#41—61no—
407#41—121no—
408#41—122no—
409#41—182no—
410#41—361no—
411#41—362no—
412C2×Q8—62no—
413C2×Q8—61no—
414C2×Q8—121no—
415C2×Q8—182no—
416C2×Q8—181no—
417C2×Q8—361no—
418Q16—31no—
419Q16—32no—
420Q16—62no—
421Q16—61no—
422Q16—92no—
423Q16—182no—
424Q16—181no—
425Q16C2×D3211yescharacteristic
426SD16—21no—
427SD16—62no—
428SD16—61no—
429SD16—182no—
430D8—31no—
431D8C2×D3211yescharacteristic
432M16—31no—
433M16—32no—
434C2×C8—32no—
435C2×C8C2×D3211yescharacteristic
436C16—31no—
437C16—31no—
438C16—92no—
439C22×C3—21no—
440C22×C3—32no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—81no—
444C22×C3—121no—
445C22×C3D3×D811yescharacteristic
446C22×C3C2×#21311yescharacteristic
447C2×D3—41no—
448C2×D3C2×#21312yes—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—32no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—81no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4D3×D811yescharacteristic
458C3×C4C2×#21311yescharacteristic
459C3×C4C2×D3×D411yescharacteristic
460C3×C4C22×#6711yescharacteristic
461Dic3—41no—
462Dic3—42no—
463Dic3—122no—
464Dic3—122no—
465Dic3—242no—
466Dic3C2×#21312yes—
467C32#341711yescharacteristic, complemented, Sylow
468Q8—21no—
469Q8—31no—
470Q8—62no—
471Q8—61no—
472Q8—122no—
473Q8—121no—
474Q8—182no—
475Q8—362no—
476Q8—361no—
477D4—21no—
478D4—32no—
479D4—31no—
480D4—41no—
481D4—61no—
482D4—122no—
483D4—121no—
484D4—362no—
485C2×C4—32no—
486C2×C4—41no—
487C2×C4—122no—
488C2×C4—122no—
489C2×C4—121no—
490C2×C4—121no—
491C2×C4—362no—
492C2×C4—362no—
493C2×C4—361no—
494C2×C4D3×#6711yescharacteristic
495C8—32no—
496C8D3×#6711yescharacteristic
497C8C22×D3211yescharacteristic
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—41no—
502C2×C3—62no—
503C2×C3—81no—
504C2×C3—81no—
505C2×C3—161no—
506C2×C3—241no—
507C2×C3C2×D3×D811yescharacteristic
508C2×C3C22×#21311yescharacteristic
509D3—22no—
510D3—81no—
511C22—32no—
512C22—41no—
513C22—121no—
514C22D3×#21311yescharacteristic
515C4—32no—
516C4—41no—
517C4—122no—
518C4—121no—
519C4—362no—
520C4D3×#21311yescharacteristic
521C4C2×D3×#6711yescharacteristic
522C3—21no—
523C3#8203311yescharacteristic, complemented
524C3#8401711yescharacteristic, complemented
525C2—21no—
526C2—62no—
527C2—81no—
528C2—241no—
529C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×#135C22
socleC2×C32C22×D8
hypercenter#135D32
hypocenterC32#3417
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#5771C2semidirect
2. #10594692C2semidirect
3. #10592894C2semidirect
4. C3×#5194C2semidirect
5. #10591045C2semidirect
6. D3×#829C2semidirect
7. #10591032C2semidirect
8. #10591028C2semidirect
9. C2×#63551C2semidirect
10. #10590636C2semidirect
11. #10590621C2semidirect
45. #5771D3semidirect
54. #5194D3semidirect
467. C32#3417semidirect
523. C3#82033semidirect
524. C3#84017semidirect

Maximal subgroups

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

subgroupindex
C3×#57712
#105946922
#105928942
C3×#51942
#105910452
D3×#8292
#105910322
#105910282
C2×#635512
#105906362
#105906212
#840173
#820333