Finite Group Databasebeta

← #11788720

Subgroups — #11788720

Order 1152.

699 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic
2#10594856C211yesmaximal, characteristic
3#10592819C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic
5#10591107C211yesmaximal, characteristic, complemented
6C3×#4557C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#72024—31nomaximal
9#68712—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63962—22no—
21#63866C412yescomplemented
22#63860C412yescomplemented
23#63857—22no—
24#63643—22no—
25#63580—22no—
26#63567—22no—
27C3×#568—31no—
28#5825—31no—
29#5745D311yescharacteristic
30#5526—31no—
31#5240—31no—
32#5120—31no—
33#5120—31no—
34#5120—31no—
35#5120—61no—
36#5006—31no—
37#5004—31no—
38C3×H(3,ℤ/4)—31no—
39#4557—31no—
40#4557D311yescharacteristic, complemented
41#4531—31no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634C2×C412yes—
50C2×C3×#67D412yes—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×C4×D3D412yes—
57C2×C3×Dic6C2×C411yescharacteristic
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8D412yes—
61#3757—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4×C3⋊Dic3—21no—
64C3×#217—21no—
65C3×#217—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×C4×Dic3C2×C412yes—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8D412yes—
73C3×ΓL(1,𝔽25)—24no—
74C3×D3×C8—24no—
75Dic3⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77#1909—91noSylow
78C2×C3×#41—31no—
79C2×#235C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C3×#131—62no—
84C3×#131—62no—
85C2×C3×M16—21no—
86C2×C3×M16—31no—
87C2×C3×M16—62no—
88C2×C3×M16C2×D311yescharacteristic
89C2×C3×M16C2×D311yescharacteristic
90C3×#117—31no—
91C3×#117—31no—
92#944—32no—
93#936—32no—
94#935—62no—
95#926—31no—
96#926—31no—
97#926—61no—
98#926C2×D311yescharacteristic
99#926C2×D311yescharacteristic
100#924—62no—
101C2×#208C2×D311yescharacteristic
102#907—22no—
103D3×M16—22no—
104#901—22no—
105#897—62no—
106#886—62no—
107#875—32no—
108#869—32no—
109#834—62no—
110#816—62no—
111#816—64no—
112#816—62no—
113#816—62no—
114#810—62no—
115#806—62no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3C22⋊C412yes—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128#634—22no—
129#634—22no—
130#634—41no—
131#634—41no—
132C3×#67—22no—
133C3×#67—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3C22⋊C412yes—
137C3×D12—21no—
138C3×D12—21no—
139C3×C4×D3—22no—
140C3×C4×D3—22no—
141C3×Dic6—21no—
142C3×Dic6—21no—
143C32×C8—22no—
144C3×C3⋊C8—22no—
145#568—31no—
146#536—91no—
147#419—91no—
148#419—91no—
149#410—91no—
150H(3,ℤ/4)—31no—
151H(3,ℤ/4)—91no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—31no—
157C2×C3×D4—32no—
158C2×C3×D4—31no—
159C22×C3×C4—21no—
160C22×C3×C4—32no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67D1212yes—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—121no—
167#235—21no—
168#235—21no—
169#235—21no—
170#235—21no—
171C2×D12C4×D311yescharacteristic
172C2×C4×D3#6712yes—
173C2×Dic6—32no—
174C2×Dic6—32no—
175C2×Dic6—62no—
176C2×Dic6—62no—
177C2×Dic6—62no—
178C2×Dic6—61no—
179C2×Dic6—61no—
180C2×Dic6—61no—
181C2×Dic6—61no—
182C2×Dic6—61no—
183C2×Dic6—61no—
184C2×Dic6—61no—
185C2×Dic6—61no—
186C2×Dic6—61no—
187C2×Dic6—61no—
188C2×Dic6—121no—
189C2×Dic6—121no—
190C2×Dic6—121no—
191C2×Dic6C4×D311yescharacteristic
192C3×M16—21no—
193C3×M16—21no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—41no—
197C3×M16—41no—
198C3×M16—64no—
199C3×M16—61no—
200C3×M16—61no—
201C2×C3×C8—22no—
202C2×C3×C8—32no—
203C2×C3×C8—64no—
204C2×C3×C8D1212yes—
205C2×C3×C8#6712yes—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C22⋊C4—61no—
210C3×C42—32no—
211C3×C42—61no—
212#217—21no—
213#217—21no—
214#217—64no—
215#217—61no—
216#217—61no—
217#217—121no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—64no—
222C4⋊Dic3—62no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225Dic3⋊C4—64no—
226C4×Dic3—21no—
227C4×Dic3—61no—
228C4×Dic3—61no—
229C4×Dic3—121no—
230C4×Dic3C4×D312yes—
231#208—21no—
232#208—21no—
233C2×C3⋊C8#6712yes—
234ΓL(1,𝔽25)—24no—
235D3×C8—24no—
236C22×C32—41no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—42no—
242C32×C4C4×D411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4#12011yescharacteristic
245C32×C4#12311yescharacteristic
246C3⋊Dic3—42no—
247C3⋊Dic3—81no—
248C3×Dic3—22no—
249C3×Dic3—42no—
250C3×Dic3—81no—
251C2×#41—31no—
252C22×Q8—91no—
253#131—62no—
254#131—62no—
255C2×M16—31no—
256C2×M16—62no—
257C2×M16D3211yescharacteristic
258C4⋊Q8—92no—
259#124—92no—
260#123—182no—
261C22⋊Q8—182no—
262#117—31no—
263#117—31no—
264#117—91no—
265#103—182no—
266#103—182no—
267#99—182no—
268C23×C3—21no—
269C23×C3—32no—
270C23×C3C2×D1211yescharacteristic
271C23×C3D3×D411yescharacteristic
272C22×D3(C2×D3)⋊C412yes—
273C3×Q8—61no—
274C3×Q8—61no—
275C3×D4—62no—
276C3×D4—62no—
277C3×D4—61no—
278C3×D4—61no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—32no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—121no—
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4#23911yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302#67—22no—
303#67—22no—
304C2×Dic3—22no—
305C2×Dic3—41no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—121no—
314C2×Dic3—121no—
315C2×Dic3—122no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3(C2×D3)⋊C412yes—
319D12—21no—
320D12—21no—
321C4×D3—22no—
322C4×D3—22no—
323Dic6—21no—
324Dic6—21no—
325Dic6—64no—
326Dic6—62no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330Dic6—122no—
331Dic6—122no—
332Dic6—122no—
333Dic6—121no—
334Dic6—121no—
335Dic6—121no—
336Dic6—121no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—42no—
340C3×C8—62no—
341C3⋊C8—22no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#38611yescharacteristic
346C3×D3—42no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—31no—
352C2×Q8—92no—
353C2×Q8—181no—
354C2×Q8—181no—
355C2×Q8—181no—
356C2×Q8—181no—
357C2×Q8—181no—
358C2×D4—32no—
359C2×D4—31no—
360C22×C4—32no—
361C22×C4—181no—
362C22×C4C2×D3211yescharacteristic
363M16—21no—
364M16—21no—
365M16—64no—
366M16—61no—
367M16—61no—
368C2×C8—32no—
369C2×C8—64no—
370C2×C8#62612yes—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—184no—
374C4⋊C4—181no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—184no—
378C22⋊C4—181no—
379C42—32no—
380C42—61no—
381C42—181no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—42no—
388C22×C3—62no—
389C22×C3—122no—
390C22×C3D3×C22⋊C411yescharacteristic
391C22×C3#88411yescharacteristic
392C22×C3#89511yescharacteristic
393C22×C3C2×(C2×D3)⋊C411yescharacteristic
394C22×C3#93011yescharacteristic
395C22×C3#93011yescharacteristic
396C2×D3—22no—
397C2×D3—42no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—62no—
403C3×C4—122no—
404C3×C4—241no—
405C3×C4C4×D1211yescharacteristic
406C3×C4#88211yescharacteristic
407C3×C4#89311yescharacteristic
408C3×C4#89411yescharacteristic
409C3×C4C4×#6711yescharacteristic
410C3×C4C4×#6711yescharacteristic
411C3×C4#92911yescharacteristic
412C3×C4#95311yescharacteristic
413Dic3—22no—
414Dic3—42no—
415Dic3—81no—
416Dic3—124no—
417Dic3—122no—
418Dic3—122no—
419Dic3—242no—
420Dic3—241no—
421Dic3—241no—
422C32#190911yescharacteristic, complemented, Sylow
423C23—32no—
424C23D3×D1211yescharacteristic
425Q8—61no—
426Q8—61no—
427Q8—182no—
428Q8—182no—
429Q8—361no—
430Q8—361no—
431D4—62no—
432D4—62no—
433D4—61no—
434D4—61no—
435C2×C4—32no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—121no—
440C2×C4—182no—
441C2×C4—361no—
442C2×C4—361no—
443C2×C4—361no—
444C2×C4#379811yescharacteristic
445C2×C4#379911yescharacteristic
446C2×C4C4×D3211yescharacteristic
447C2×C4C2×#62611yescharacteristic
448C2×C4D3×#6711yescharacteristic
449C2×C4D3×#6711yescharacteristic
450C8—22no—
451C8—62no—
452C2×C3—22no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3—122no—
463C2×C3#466511yescharacteristic
464C2×C3#521311yescharacteristic
465D3—42no—
466C22—41no—
467C22—62no—
468C22—122no—
469C22#6390611yescharacteristic
470C22#6390911yescharacteristic
471C22D3×(C2×D3)⋊C411yescharacteristic
472C4—62no—
473C4—122no—
474C4—241no—
475C4—362no—
476C4—721no—
477C4#6385011yescharacteristic
478C4C4×#62611yescharacteristic
479C4#6390411yescharacteristic
480C4#6397711yescharacteristic
481C3—21no—
482C3#6871211yescharacteristic, complemented
483C3#7202411yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—21no—
487C2—122no—
488C2#1059138211yescharacteristic
subgroupG/H
centerC2#10591382
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1909
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. #10592819C2semidirect
5. #10591107C2semidirect
6. C3×#4557C2semidirect
7. #10589158C2semidirect
21. #63866C4semidirect
22. #63860C4semidirect
40. #4557D3semidirect
422. C32#1909semidirect
482. C3#68712semidirect
483. C3#72024semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105948562
#105928192
#105912312
#105911072
C3×#45572
#105891582
#720243
#687123