Finite Group Databasebeta

← #11899773

Subgroups — #11899773

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5766C211yesmaximal, characteristic, complemented
2#10594692C211yesmaximal, characteristic, complemented
3C2×#63656C211yesmaximal, characteristic, complemented
4C3×#5179C211yesmaximal, characteristic, complemented
5#10591046C212yesmaximal, complemented
6#10591045C212yesmaximal, complemented
7#10591042C212yesmaximal, complemented
8D3×#829C212yesmaximal, complemented
9#10590638C211yesmaximal, characteristic, complemented
10#10590629C211yesmaximal, characteristic, complemented
11#10590622C211yesmaximal, characteristic, complemented
12#84017—31nomaximal
13#82041—31nomaximal
14C3×#1007—21no—
15#64298—21no—
16C2×C32×Q16C2211yescharacteristic
17C2×#3746C2211yescharacteristic
18C3×#942—21no—
19C3×#919C2212yes—
20C3×#918—22no—
21C3×D3×Q16C2212yes—
22C3×#904C2211yescharacteristic
23C3×#904C2211yescharacteristic
24C3×#901C2211yescharacteristic
25#63831—21no—
26#63807C2212yes—
27#63800—22no—
28D3×Dic12C2212yes—
29#63656C2212yes—
30#63656C2212yes—
31C2×C3⋊(C3⋊C16)C2211yescharacteristic
32C3×#829C2212yes—
33C3×#828C2212yes—
34C3×#812C2211yescharacteristic
35#63551C2212yes—
36#63550C2211yescharacteristic
37#63548C2212yes—
38#63547C2211yescharacteristic
39#63547C2211yescharacteristic
40#63545C2211yescharacteristic
41#63543C2212yes—
42D3×C3⋊C16C2212yes—
43C3×#578—31no—
44#5771—31no—
45#5766D311yescharacteristic, complemented
46#5753—31no—
47C3×#510—31no—
48#5195—32no—
49#5195—31no—
50#5194—31no—
51#5194—31no—
52#5194—32no—
53C2×#829—31no—
54C2×#829—31no—
55C2×#829—32no—
56C2×#829—61no—
57#5179—32no—
58#5179D311yescharacteristic, complemented
59#5140—31no—
60#4918—32no—
61D3×Q32—32no—
62#4916—32no—
63#4915—32no—
64#4909—31no—
65#4907—31no—
66C2×C32×Q8—21no—
67C2×#634—21no—
68C3×#239—22no—
69C3×#239—41no—
70C3×D3×Q8—22no—
71C3×D3×Q8—41no—
72C3×#235—21no—
73C3×#235—21no—
74C3×#235—42no—
75C3×#235D411yescharacteristic
76#3805—42no—
77#3795—22no—
78#3795—41no—
79D3×Dic6—22no—
80D3×Dic6—41no—
81C32×Q16—21no—
82C32×Q16C2312yes—
83C2×C32×C8C2311yescharacteristic
84#3746—21no—
85#3746C2312yes—
86C3×#216—22no—
87C3×#215—22no—
88C3×#208D411yescharacteristic
89C3×Dic12C2311yescharacteristic
90C3×Dic12C2311yescharacteristic
91C3×D24C2311yescharacteristic
92C3×D24C2311yescharacteristic
93C3×#204—21no—
94C3×#204—21no—
95C3×ΓL(1,𝔽25)D412yes—
96C3×D3×C8C2312yes—
97#3719—22no—
98#3716—22no—
99C3⋊(C3⋊C16)C2311yescharacteristic
100C3⋊(C3⋊C16)C2311yescharacteristic
101C3×C3⋊C16C2312yes—
102#3417—91noSylow
103C3×2−1+4—61no—
104#1010—61no—
105#1010—61no—
106#1007—21no—
107C3×#137—62no—
108C3×#137—61no—
109C3×#135—32no—
110C3×#135—31no—
111C3×#135—31no—
112C2×C3×Q16—21no—
113C2×C3×Q16—32no—
114C2×C3×Q16C2×D311yescharacteristic
115C2×C3×Q16C2×D311yescharacteristic
116C3×#131—31no—
117#951—61no—
118#942—21no—
119#919C2×D312yes—
120#918—22no—
121D3×Q16—32no—
122D3×Q16C2×D312yes—
123#915—62no—
124#912—32no—
125#909—62no—
126#909—61no—
127C2×Dic12—31no—
128C2×Dic12—31no—
129C2×Dic12—32no—
130C2×Dic12—61no—
131#904—32no—
132#904C2×D311yescharacteristic
133#904C2×D311yescharacteristic
134#901C2×D311yescharacteristic
135C3×Q32—32no—
136C3×SD32—32no—
137C3×M32—31no—
138#829—32no—
139#829—32no—
140#829—32no—
141#829—32no—
142#829—31no—
143#829—31no—
144#829—32no—
145#829—62no—
146#829—62no—
147#829C2×D312yes—
148#828—31no—
149#828—31no—
150#828C2×D312yes—
151#827—31no—
152#827—31no—
153#827—32no—
154#826—31no—
155#826—31no—
156#812—32no—
157#812C2×D311yescharacteristic
158C2×C3⋊C16—31no—
159C2×C3⋊C16—31no—
160C2×C3⋊C16—32no—
161C2×C3⋊C16—61no—
162Dic24—32no—
163#800—32no—
164#798—32no—
165D3×C16—32no—
166C32×Q8—22no—
167C32×Q8—41no—
168C2×C32×C4—41no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C3⋊Dic3—41no—
171#634—22no—
172#634—41no—
173C3×#67—41no—
174C3×#67—41no—
175C3×#67D812yes—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12—42no—
179C3×D12D811yescharacteristic
180C3×C4×D3—42no—
181C3×C4×D3—41no—
182C3×C4×D3—41no—
183C3×C4×D3—42no—
184C3×C4×D3C2×D412yes—
185C3×Dic6—21no—
186C3×Dic6—21no—
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—31no—
199#510—91no—
200#510—92no—
201#510—92no—
202#508—92no—
203#508—91no—
204C2×Q32—92no—
205C2×Q32—91no—
206#504—91no—
207C3×#41—31no—
208C3×#41—62no—
209C3×#41—61no—
210C3×#41—61no—
211C3×#41—122no—
212C3×#41—121no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—41no—
216C2×C3×Q8—62no—
217C2×C3×Q8—121no—
218#239—22no—
219#239—41no—
220D3×Q8—22no—
221D3×Q8—41no—
222D3×Q8—62no—
223D3×Q8—121no—
224#237—62no—
225#237—121no—
226#237—122no—
227#237—122no—
228#235—21no—
229#235—21no—
230#235—42no—
231#235—62no—
232#235—121no—
233#235#6711yescharacteristic
234C2×Dic6—62no—
235C2×Dic6—61no—
236C2×Dic6—61no—
237C2×Dic6—121no—
238C2×Dic6—121no—
239C3×Q16—21no—
240C3×Q16—21no—
241C3×Q16—22no—
242C3×Q16—31no—
243C3×Q16—31no—
244C3×Q16—41no—
245C3×Q16—62no—
246C3×Q16C22×D312yes—
247C3×Q16C22×D312yes—
248C3×SD16—62no—
249C3×SD16—61no—
250C3×SD16—61no—
251C3×D8—31no—
252C3×D8—31no—
253C3×M16—31no—
254C3×M16—32no—
255C2×C3×C8—21no—
256C2×C3×C8—32no—
257C2×C3×C8C22×D311yescharacteristic
258C2×C3×C8C22×D311yescharacteristic
259#216—22no—
260#216—62no—
261#215—22no—
262#214—62no—
263#208#6711yescharacteristic
264Dic12—32no—
265Dic12—32no—
266Dic12—62no—
267Dic12—62no—
268Dic12—61no—
269Dic12—61no—
270Dic12—121no—
271Dic12C22×D311yescharacteristic
272Dic12C22×D311yescharacteristic
273D24C22×D311yescharacteristic
274D24C22×D311yescharacteristic
275#204—21no—
276#204—21no—
277#204—62no—
278ΓL(1,𝔽25)#6712yes—
279D3×C8C22×D312yes—
280C3×C16—32no—
281C3⋊C16—31no—
282C3⋊C16—31no—
283C3⋊C16—31no—
284C3⋊C16—31no—
285C3⋊C16—61no—
286C3⋊C16—61no—
287C3⋊C16C22×D312yes—
288C22×C32C2×D811yescharacteristic
289C2×C3×D3—41no—
290C2×C3×D3—41no—
291C2×C3×D3C2×D812yes—
292C32×C4—42no—
293C32×C4C2×D811yescharacteristic
294C32×C4C22×D411yescharacteristic
295C3⋊Dic3—42no—
296C3×Dic3—41no—
297C3×Dic3—41no—
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—31no—
308#135—92no—
309C2×Q16—32no—
310C2×Q16—92no—
311C2×Q16—91no—
312C2×Q16D3211yescharacteristic
313#131—31no—
314Q32—32no—
315Q32—92no—
316Q32—91no—
317Q32—92no—
318Q32—92no—
319SD32—32no—
320SD32—92no—
321SD32—91no—
322SD32—91no—
323D16—91no—
324M32—31no—
325M32—92no—
326C2×C16—92no—
327C2×C16—91no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—31no—
331C3×Q8—42no—
332C3×Q8—41no—
333C3×Q8—41no—
334C3×Q8—61no—
335C3×Q8—61no—
336C3×Q8—81no—
337C3×Q8—122no—
338C3×D4—32no—
339C3×D4—31no—
340C3×D4—61no—
341C3×D4—61no—
342C3×D4—122no—
343C3×D4—121no—
344C3×D4—121no—
345C2×C3×C4—21no—
346C2×C3×C4—32no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—81no—
350C2×C3×C4—122no—
351C2×C3×C4—122no—
352C2×C3×C4—121no—
353C2×C3×C4—121no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356#67—41no—
357#67—41no—
358#67—122no—
359#67—122no—
360#67#21312yes—
361C2×Dic3—122no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—122no—
365C2×Dic3—241no—
366D12—21no—
367D12—21no—
368D12—42no—
369D12#21311yescharacteristic
370C4×D3—42no—
371C4×D3—41no—
372C4×D3—41no—
373C4×D3—42no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3C2×#6712yes—
377Dic6—21no—
378Dic6—21no—
379Dic6—42no—
380Dic6—62no—
381Dic6—62no—
382Dic6—122no—
383Dic6—122no—
384Dic6—121no—
385Dic6—121no—
386Dic6—122no—
387Dic6—241no—
388Dic6#21311yescharacteristic
389C3×C8—21no—
390C3×C8—21no—
391C3×C8—32no—
392C3×C8D3×D411yescharacteristic
393C3×C8C2×#6711yescharacteristic
394C3×C8C23×D311yescharacteristic
395C3×C8C23×D311yescharacteristic
396C3⋊C8C2×#6712yes—
397C2×C32—21no—
398C2×C32C22×D811yescharacteristic
399C3×D3—22no—
400C3×D3—81no—
401C3×D3—81no—
402#41—31no—
403#41—62no—
404#41—61no—
405#41—61no—
406#41—122no—
407#41—121no—
408#41—182no—
409#41—361no—
410#41—362no—
411C2×Q8—21no—
412C2×Q8—62no—
413C2×Q8—121no—
414C2×Q8—182no—
415C2×Q8—181no—
416C2×Q8—361no—
417Q16—21no—
418Q16—31no—
419Q16—31no—
420Q16—62no—
421Q16—92no—
422Q16—182no—
423Q16—181no—
424Q16C2×D3212yes—
425SD16—62no—
426SD16—61no—
427SD16—61no—
428SD16—182no—
429D8—31no—
430D8—31no—
431M16—31no—
432M16—32no—
433C2×C8—32no—
434C2×C8C2×D3211yescharacteristic
435C16—32no—
436C16—91no—
437C16—91no—
438C22×C3—21no—
439C22×C3—32no—
440C22×C3—121no—
441C22×C3—121no—
442C22×C3D3×D811yescharacteristic
443C22×C3C2×#21311yescharacteristic
444C2×D3—41no—
445C2×D3—41no—
446C2×D3C2×#21312yes—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—32no—
450C3×C4—42no—
451C3×C4—42no—
452C3×C4—82no—
453C3×C4—121no—
454C3×C4—121no—
455C3×C4D3×D811yescharacteristic
456C3×C4C2×#21311yescharacteristic
457C3×C4C2×D3×D411yescharacteristic
458C3×C4C22×#6711yescharacteristic
459Dic3—41no—
460Dic3—41no—
461Dic3—122no—
462Dic3—122no—
463Dic3—242no—
464Dic3C2×#21312yes—
465C32#341711yescharacteristic, complemented, Sylow
466Q8—22no—
467Q8—31no—
468Q8—41no—
469Q8—61no—
470Q8—61no—
471Q8—122no—
472Q8—182no—
473Q8—362no—
474Q8—361no—
475D4—32no—
476D4—31no—
477D4—61no—
478D4—61no—
479D4—122no—
480D4—121no—
481D4—121no—
482D4—362no—
483C2×C4—32no—
484C2×C4—41no—
485C2×C4—122no—
486C2×C4—122no—
487C2×C4—121no—
488C2×C4—121no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4—361no—
492C2×C4D3×#6711yescharacteristic
493C8—32no—
494C8D3×#6711yescharacteristic
495C8C22×D3211yescharacteristic
496C2×C3—22no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—62no—
501C2×C3—241no—
502C2×C3—241no—
503C2×C3C2×D3×D811yescharacteristic
504C2×C3C22×#21311yescharacteristic
505D3—22no—
506D3—81no—
507D3—81no—
508C22—32no—
509C22—121no—
510C22—121no—
511C22D3×#21311yescharacteristic
512C4—32no—
513C4—42no—
514C4—121no—
515C4—121no—
516C4—362no—
517C4D3×#21311yescharacteristic
518C4C2×D3×#6711yescharacteristic
519C3—21no—
520C3#8204111yescharacteristic, complemented
521C3#8401711yescharacteristic, complemented
522C2—21no—
523C2—62no—
524C2—241no—
525C2—241no—
526C2C2×D3×#21311yescharacteristic
subgroupG/H
centerC2C2×D3×#213
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×Q16C22
socleC2×C32C22×D8
hypercenterC2×Q16D32
hypocenterC32#3417
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C3×#5766C2semidirect
2. #10594692C2semidirect
3. C2×#63656C2semidirect
4. C3×#5179C2semidirect
5. #10591046C2semidirect
6. #10591045C2semidirect
7. #10591042C2semidirect
8. D3×#829C2semidirect
9. #10590638C2semidirect
10. #10590629C2semidirect
11. #10590622C2semidirect
45. #5766D3semidirect
58. #5179D3semidirect
465. C32#3417semidirect
520. C3#82041semidirect
521. C3#84017semidirect

Maximal subgroups

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

subgroupindex
C3×#57662
#105946922
C2×#636562
C3×#51792
#105910462
#105910452
#105910422
D3×#8292
#105906382
#105906292
#105906222
#840173
#820413