Finite Group Databasebeta

← #11899654

Subgroups — #11899654

Order 1152.

770 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#904C212yesmaximal, complemented
2#10592603C211yesmaximal, characteristic, complemented
3C3×#4904C211yesmaximal, characteristic, complemented
4C2×C3×#798C211yesmaximal, characteristic, complemented
5#10590632C212yesmaximal, complemented
6#10590239C212yesmaximal, complemented
7#10590238C212yesmaximal, complemented
8#10590233C212yesmaximal, complemented
9#10590232C212yesmaximal, complemented
10#82030—31nomaximal
11#82009—31nomaximal
12D3×#235—22no—
13#64113C2212yescomplemented
14C3×#904C2212yescomplemented
15C2×C3×D3×C8C2211yescharacteristic
16#63829—22no—
17#63808C2212yes—
18#63807C2212yes—
19#63806—22no—
20D3×Dic12C2212yescomplemented
21D3×D24C2212yescomplemented
22D3×#204—22no—
23C2×C32×C16C2211yescharacteristic, complemented
24#63628C2211yescharacteristic, complemented
25#63627C2212yescomplemented
26#63626C2211yescharacteristic, complemented
27C2×C3×C3⋊C16C2211yescharacteristic, complemented
28C3×Dic24C2211yescharacteristic, complemented
29C3×#800C2212yescomplemented
30C3×D48C2211yescharacteristic, complemented
31C3×#798C2212yescomplemented
32C3×#798C2212yescomplemented
33#63551C2212yescomplemented
34#63549C2212yescomplemented
35#63548C2212yescomplemented
36#63546C2212yescomplemented
37D3×#135—32no—
38C2×#904—32no—
39C3×#508—31no—
40C2×C3×M32—31no—
41#5194—32no—
42#4918—32no—
43#4915—32no—
44#4914—32no—
45#4911—32no—
46#4909—32no—
47#4909—32no—
48#4908—32no—
49#4908—32no—
50#4904—32no—
51#4904—31no—
52#4904—31no—
53#4904—61no—
54#4904D311yescharacteristic, complemented
55C2×#798D311yescharacteristic, complemented
56#3828—22no—
57C3×#235—22no—
58C2×C3×C4×D3D411yescharacteristic
59D3×#67—42no—
60#3804—42no—
61D3×D12—22no—
62C4×D32—42no—
63#3799—22no—
64#3798—42no—
65#3795—22no—
66D3×Dic6—22no—
67C2×C32×C8C2311yescharacteristic
68#3746C2312yes—
69#3745C2312yes—
70#3744—22no—
71C2×C3×C3⋊C8D411yescharacteristic
72C3×Dic12C2312yes—
73C3×D24C2312yes—
74C3×#204—22no—
75C3×D3×C8D412yes—
76C3×D3×C8C2312yes—
77#3719—22no—
78#3717—22no—
79#3716—22no—
80#3714—22no—
81C32×C16C2311yescharacteristic
82C32×C16C2311yescharacteristic
83C3×C3⋊C16C2312yes—
84#3414—91noSylow
85D3×#41—62no—
86C2×#235—62no—
87C3×#135—32no—
88C22×C3×C8—31no—
89#950—62no—
90#919—32no—
91D3×Q16—32no—
92#916—62no—
93D3×SD16—62no—
94#912—32no—
95D3×D8—32no—
96C2×Dic12—32no—
97#904—32no—
98#904—32no—
99#904—32no—
100#904—32no—
101#904—62no—
102#904—62no—
103#904—62no—
104#904C2×D312yescomplemented
105C2×D24—32no—
106C2×#204—62no—
107C2×D3×C8C2×D311yescharacteristic
108C3×Q32—31no—
109C3×SD32—32no—
110C3×D16—31no—
111C3×M32—32no—
112C3×M32—32no—
113C2×C3×C16—21no—
114C2×C3×C16—31no—
115C2×C3×C16C2×D311yescharacteristic, complemented
116C2×C3×C16C2×D311yescharacteristic, complemented
117#829—32no—
118#828—32no—
119#827—32no—
120#826—32no—
121C2×C3⋊C16C2×D311yescharacteristic, complemented
122Dic24—32no—
123Dic24—31no—
124Dic24—31no—
125Dic24—61no—
126Dic24C2×D311yescharacteristic, complemented
127#800—32no—
128#800—32no—
129#800—32no—
130#800—32no—
131#800—62no—
132#800C2×D312yescomplemented
133D48—32no—
134D48—31no—
135D48—31no—
136D48—61no—
137D48C2×D311yescharacteristic, complemented
138#798C2×D312yescomplemented
139#798C2×D312yescomplemented
140C22×C3×D3D811yescharacteristic
141C2×D32—42no—
142C2×C32×C4C2×D411yescharacteristic
143#638—42no—
144C4⋊(C3⋊D3)—22no—
145C4×C3⋊D3—42no—
146#634—22no—
147C3×#67—42no—
148C2×C3×Dic3D811yescharacteristic
149C3×D12—22no—
150C3×C4×D3—42no—
151C3×C4×D3D812yes—
152C3×C4×D3C2×D412yes—
153C3×Dic6—22no—
154#627—42no—
155#626—42no—
156#626—42no—
157#625—42no—
158#624—42no—
159D3×Dic3—42no—
160D3×Dic3—42no—
161C32×C8C2×D411yescharacteristic
162C32×C8C2411yescharacteristic
163C3×C3⋊C8C2×D412yes—
164C2×#135—92no—
165#510—92no—
166#510—92no—
167#509—92no—
168#509—92no—
169#508—31no—
170#508—92no—
171#508—91no—
172C2×M32—31no—
173C3×#41—62no—
174C22×C3×C4—31no—
175C2×#67—122no—
176#239—62no—
177D3×Q8—62no—
178#237—62no—
179#237—122no—
180D3×D4—62no—
181D3×D4—122no—
182#235—22no—
183#235—62no—
184#235—62no—
185#235—62no—
186#235—62no—
187#235—122no—
188#235—122no—
189#235—122no—
190#235—122no—
191C2×D12—62no—
192C2×C4×D3—122no—
193C2×C4×D3—122no—
194C2×C4×D3D1211yescharacteristic
195C2×Dic6—62no—
196C3×Q16—32no—
197C3×SD16—62no—
198C3×D8—32no—
199C2×C3×C8—21no—
200C2×C3×C8—31no—
201C2×C3×C8—32no—
202C2×C3×C8—32no—
203C2×C3×C8C22×D311yescharacteristic
204C2×C3×C8C22×D311yescharacteristic
205#216—62no—
206#215—62no—
207#214—62no—
208#213—62no—
209C2×C3⋊C8D1211yescharacteristic
210Dic12—32no—
211Dic12—32no—
212Dic12—62no—
213Dic12—62no—
214Dic12C22×D312yes—
215D24—32no—
216D24—32no—
217D24—62no—
218D24—62no—
219D24C22×D312yes—
220#204—22no—
221#204—62no—
222#204—62no—
223#204—62no—
224#204—62no—
225#204—122no—
226D3×C8D1212yes—
227D3×C8C22×D312yes—
228C3×C16—21no—
229C3×C16—21no—
230C3×C16—32no—
231C3×C16C22×D311yescharacteristic
232C3×C16C22×D311yescharacteristic
233C3×C16C22×D311yescharacteristic
234C3×C16C22×D311yescharacteristic
235C3⋊C16C22×D312yes—
236C22×C32C2×D811yescharacteristic
237C2×C3⋊D3—42no—
238C2×C3×D3—41no—
239C2×C3×D3—42no—
240C2×C3×D3C2×D812yes—
241D32—84no—
242C32×C4C2×D811yescharacteristic
243C32×C4C22×D411yescharacteristic
244C3⋊Dic3—42no—
245C3×Dic3—42no—
246C3×Dic3C2×D812yes—
247C2×#41—182no—
248#135—32no—
249#135—92no—
250#135—92no—
251#135—92no—
252#135—182no—
253#135—182no—
254C2×Q16—92no—
255C2×SD16—182no—
256C2×D8—92no—
257C22×C8—31no—
258Q32—31no—
259Q32—92no—
260Q32—91no—
261SD32—32no—
262SD32—92no—
263SD32—92no—
264SD32—92no—
265D16—31no—
266D16—92no—
267D16—91no—
268M32—32no—
269M32—32no—
270C2×C16—31no—
271C2×C16D3211yescharacteristic, complemented
272C23×C3—31no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3D2411yescharacteristic
276C3×Q8—62no—
277C3×D4—62no—
278C3×D4—122no—
279C2×C3×C4—21no—
280C2×C3×C4—31no—
281C2×C3×C4—32no—
282C2×C3×C4—32no—
283C2×C3×C4—122no—
284C2×C3×C4C2×D1211yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286#67—42no—
287#67—122no—
288#67—122no—
289#67—122no—
290#67—122no—
291#67—122no—
292#67—122no—
293#67—242no—
294C2×Dic3—122no—
295C2×Dic3—122no—
296C2×Dic3D2411yescharacteristic
297D12—22no—
298D12—62no—
299D12—62no—
300D12—122no—
301D12—122no—
302D12—122no—
303C4×D3—42no—
304C4×D3—122no—
305C4×D3—122no—
306C4×D3—122no—
307C4×D3—122no—
308C4×D3—122no—
309C4×D3—122no—
310C4×D3—242no—
311C4×D3D2412yes—
312C4×D3C2×D1212yes—
313Dic6—22no—
314Dic6—62no—
315Dic6—62no—
316Dic6—122no—
317Dic6—122no—
318Dic6—122no—
319C3×C8—21no—
320C3×C8—21no—
321C3×C8—32no—
322C3×C8C2×D1211yescharacteristic
323C3×C8D3×D411yescharacteristic
324C3×C8C23×D311yescharacteristic
325C3×C8C23×D311yescharacteristic
326C3⋊C8C2×D1212yes—
327C2×C32—21no—
328C2×C32C22×D811yescharacteristic
329C3⋊D3—82no—
330C3×D3—22no—
331C3×D3—82no—
332#41—62no—
333#41—182no—
334#41—182no—
335#41—182no—
336#41—362no—
337#41—362no—
338C2×Q8—182no—
339C2×D4—182no—
340C2×D4—362no—
341C22×C4—31no—
342C22×C4—362no—
343Q16—32no—
344Q16—92no—
345Q16—182no—
346SD16—62no—
347SD16—182no—
348SD16—182no—
349SD16—182no—
350D8—32no—
351D8—92no—
352D8—182no—
353C2×C8—31no—
354C2×C8—32no—
355C2×C8—32no—
356C2×C8C2×D3211yescharacteristic
357C16—32no—
358C16C2×D3211yescharacteristic
359C16C2×D3211yescharacteristic
360C22×C3—21no—
361C22×C3—32no—
362C22×C3—121no—
363C22×C3—122no—
364C22×C3C2×D2411yescharacteristic
365C22×C3D3×D811yescharacteristic
366C2×D3—41no—
367C2×D3—42no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—242no—
371C2×D3—244no—
372C2×D3—244no—
373C2×D3C2×D2412yes—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—32no—
377C3×C4—122no—
378C3×C4C2×D2411yescharacteristic
379C3×C4D3×D811yescharacteristic
380C3×C4C22×D1211yescharacteristic
381C3×C4C2×D3×D411yescharacteristic
382Dic3—42no—
383Dic3—122no—
384Dic3—122no—
385Dic3—242no—
386Dic3C2×D2412yes—
387C32#341411yescharacteristic, complemented, Sylow
388C23—31no—
389C23—362no—
390Q8—62no—
391Q8—182no—
392Q8—362no—
393D4—62no—
394D4—122no—
395D4—182no—
396D4—362no—
397D4—362no—
398D4—362no—
399D4—362no—
400C2×C4—31no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—122no—
404C2×C4—362no—
405C2×C4—362no—
406C2×C4—362no—
407C2×C4—362no—
408C2×C4D3×D1211yescharacteristic
409C8—32no—
410C8D3×D1211yescharacteristic
411C8C22×D3211yescharacteristic
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—41no—
416C2×C3—62no—
417C2×C3—242no—
418C2×C3C22×D2411yescharacteristic
419C2×C3C2×D3×D811yescharacteristic
420D3—22no—
421D3—82no—
422D3—242no—
423D3—242no—
424D3—482no—
425C22—32no—
426C22—121no—
427C22—122no—
428C22—362no—
429C22—724no—
430C22D3×D2411yescharacteristic
431C4—32no—
432C4—122no—
433C4—362no—
434C4D3×D2411yescharacteristic
435C4C2×D3×D1211yescharacteristic
436C3—21no—
437C3#8200911yescharacteristic, complemented
438C3#8203011yescharacteristic, complemented
439C2—21no—
440C2—62no—
441C2—242no—
442C2—722no—
443C2C2×D3×D2411yescharacteristic
subgroupG/H
centerC4D3×D24
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×C16C22
socleC2×C32C22×D8
hypercenterC2×C16D32
hypocenterC32#3414
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. D3×#904C2semidirect
2. #10592603C2semidirect
3. C3×#4904C2semidirect
4. C2×C3×#798C2semidirect
5. #10590632C2semidirect
6. #10590239C2semidirect
7. #10590238C2semidirect
8. #10590233C2semidirect
9. #10590232C2semidirect
13. #64113C22semidirect
14. C3×#904C22semidirect
20. D3×Dic12C22semidirect
21. D3×D24C22semidirect
23. C2×C32×C16C22semidirect
24. #63628C22semidirect
25. #63627C22semidirect
26. #63626C22semidirect
27. C2×C3×C3⋊C16C22semidirect
28. C3×Dic24C22semidirect
29. C3×#800C22semidirect
30. C3×D48C22semidirect
31. C3×#798C22semidirect
32. C3×#798C22semidirect
33. #63551C22semidirect
34. #63549C22semidirect
35. #63548C22semidirect
36. #63546C22semidirect
54. #4904D3semidirect
55. C2×#798D3semidirect
104. #904C2×D3semidirect
115. C2×C3×C16C2×D3semidirect
116. C2×C3×C16C2×D3semidirect
121. C2×C3⋊C16C2×D3semidirect
126. Dic24C2×D3semidirect
132. #800C2×D3semidirect
137. D48C2×D3semidirect
138. #798C2×D3semidirect
139. #798C2×D3semidirect
271. C2×C16D32semidirect
387. C32#3414semidirect
437. C3#82009semidirect
438. C3#82030semidirect

Maximal subgroups

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

subgroupindex
D3×#9042
#105926032
C3×#49042
C2×C3×#7982
#105906322
#105902392
#105902382
#105902332
#105902322
#820303
#820093