Finite Group Databasebeta

← #11788818

Subgroups — #11788818

Order 1152.

675 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594855C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C3×#5139C211yesmaximal, characteristic
4C2×C3×#824C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic
6#10589423C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70411—31nomaximal
9#70105—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14#64135C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63961—22no—
18#63955—22no—
19#63873C412yescomplemented
20#63863C412yescomplemented
21#63856—22no—
22#63843—22no—
23Dic3×Dic6—22no—
24C3×#825—22no—
25C3×#824—22no—
26#63568—22no—
27#5825—31no—
28#5816—31no—
29#5812—31no—
30#5516—31no—
31C3×#421—31no—
32C2×C3×#101—31no—
33#5236—31no—
34#5139—31no—
35#5139D311yescharacteristic
36C2×#824D311yescharacteristic, complemented
37#4557—31no—
38#4557—31no—
39#4557—31no—
40#4557—61no—
41#4531—31no—
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67—21no—
44C22×C3×Dic3D412yes—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6C2×C411yescharacteristic
56C2×C3×Dic6C2×C412yes—
57C2×C3×Dic6D412yes—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61#3757—21no—
62#3757—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4×C3⋊Dic3C2×C412yes—
66C4×C3⋊Dic3D412yes—
67C3×#217—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3D412yes—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73#3724—24no—
74Dic3⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76Dic32—24no—
77#1912—91noSylow
78C2×C3×#41—31no—
79C22×C3×Q8—31no—
80C2×#235C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C2×C3×M16—21no—
83C2×C3×M16—31no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C3×#117—31no—
87#947—32no—
88#946—62no—
89Q8×Dic3—62no—
90Q8×Dic3—62no—
91#944—32no—
92#944—32no—
93#936—32no—
94#935—62no—
95#929—62no—
96#926—31no—
97#926—31no—
98#926—31no—
99#926—31no—
100#926—61no—
101#926—61no—
102#926—62no—
103#926C2×D311yescharacteristic
104#924—62no—
105C2×#208C2×D311yescharacteristic
106#887—62no—
107#877—62no—
108C4×Dic6—62no—
109C3×#104—62no—
110C3×#101—62no—
111#837—62no—
112#825—22no—
113#825—62no—
114#824—22no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C22⋊C414yes—
132C3×D12—21no—
133C3×D12—21no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—22no—
139C3×Dic6—22no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C32×C8—41no—
143C3×C3⋊C8—41no—
144#536—91no—
145#519—91no—
146#421—31no—
147#421—91no—
148C2×#101—31no—
149H(3,ℤ/4)—91no—
150H(3,ℤ/4)—91no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—32no—
156C2×C3×Q8—32no—
157C2×C3×Q8—31no—
158C2×C3×Q8—61no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×D4—31no—
163C2×C3×D4—61no—
164C22×C3×C4—21no—
165C22×C3×C4—32no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—21no—
170C22×Dic3D1212yes—
171#235—21no—
172#235—21no—
173#235—21no—
174#235—21no—
175C2×D12C4×D311yescharacteristic
176C2×C4×D3—21no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—21no—
181C2×Dic6C4×D311yescharacteristic
182C2×Dic6C4×D312yes—
183C2×Dic6#6712yes—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—21no—
187C3×M16—21no—
188C3×M16—41no—
189C3×M16—41no—
190C3×M16—61no—
191C3×M16—61no—
192C2×C3×C8—22no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—61no—
196C3×C4⋊C4—61no—
197C3×C22⋊C4—61no—
198C3×C42—32no—
199#217—21no—
200#217—61no—
201#217—61no—
202#217—61no—
203#217—61no—
204#217—64no—
205#217—121no—
206#217—121no—
207(C2×D3)⋊C4—64no—
208C4⋊Dic3—21no—
209C4⋊Dic3—64no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—121no—
215C4⋊Dic3—121no—
216Dic3⋊C4—64no—
217Dic3⋊C4—64no—
218Dic3⋊C4—64no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—62no—
224C4×Dic3—62no—
225C4×Dic3—64no—
226C4×Dic3—64no—
227C4×Dic3#6712yes—
228#208—21no—
229#208—21no—
230C2×C3⋊C8—21no—
231C22×C32—41no—
232C22×C32C2×C22⋊C411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32#12311yescharacteristic
235C2×C3×D3—42no—
236C2×C3×D3—41no—
237C32×C4C4×D411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4#12111yescharacteristic
240C32×C4#12111yescharacteristic
241C3⋊Dic3—42no—
242C3⋊Dic3—42no—
243C3×Dic3—24no—
244C3×Dic3—42no—
245C3×Dic3—41no—
246C2×#41—31no—
247C22×Q8—31no—
248C2×M16—31no—
249C2×M16D3211yescharacteristic
250C4⋊Q8—92no—
251#124—92no—
252#123—182no—
253C22⋊Q8—182no—
254C4×Q8—182no—
255C4×Q8—182no—
256#117—31no—
257#117—91no—
258#117—91no—
259#117—182no—
260#104—62no—
261#104—182no—
262#101—62no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3C2×D1211yescharacteristic
266C23×C3D3×D411yescharacteristic
267C22×D3—21no—
268C3×Q8—62no—
269C3×Q8—62no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—61no—
273C3×Q8—61no—
274C3×D4—61no—
275C3×D4—61no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—34no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—61no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4#23711yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—41no—
304#67—41no—
305C2×Dic3—22no—
306C2×Dic3—22no—
307C2×Dic3—21no—
308C2×Dic3—22no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3(C2×D3)⋊C414yes—
316D12—21no—
317D12—21no—
318C4×D3—41no—
319C4×D3—41no—
320Dic6—22no—
321Dic6—22no—
322Dic6—22no—
323Dic6—22no—
324Dic6—21no—
325Dic6—21no—
326C3×C8—42no—
327C3×C8—41no—
328C3×C8—41no—
329C3×C8—121no—
330C3⋊C8—41no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#38611yescharacteristic
335C3×D3—81no—
336#41—61no—
337#41—61no—
338#41—61no—
339#41—61no—
340C2×Q8—32no—
341C2×Q8—32no—
342C2×Q8—31no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×Q8—61no—
347C2×D4—31no—
348C2×D4—61no—
349C22×C4—32no—
350C22×C4—61no—
351C22×C4C2×D3211yescharacteristic
352M16—21no—
353M16—21no—
354M16—61no—
355M16—61no—
356C2×C8—21no—
357C2×C8—61no—
358C4⋊C4—61no—
359C4⋊C4—184no—
360C4⋊C4—184no—
361C4⋊C4—181no—
362C4⋊C4—181no—
363C22⋊C4—61no—
364C22⋊C4—184no—
365C22⋊C4—181no—
366C22⋊C4—181no—
367C42—32no—
368C42—92no—
369C42—92no—
370C42—184no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—81no—
377C22×C3—122no—
378C22×C3—121no—
379C22×C3D3×C22⋊C411yescharacteristic
380C22×C3#88211yescharacteristic
381C22×C3#88311yescharacteristic
382C22×C3#88611yescharacteristic
383C22×C3C2×(C2×D3)⋊C411yescharacteristic
384C22×C3#93711yescharacteristic
385C2×D3—42no—
386C2×D3—41no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—64no—
392C3×C4—122no—
393C3×C4—121no—
394C3×C4#67⋊C411yescharacteristic
395C3×C4#67⋊C411yescharacteristic
396C3×C4#67⋊C411yescharacteristic
397C3×C4#88411yescharacteristic
398C3×C4C4×#6711yescharacteristic
399C3×C4#93811yescharacteristic
400C3×C4#93911yescharacteristic
401C3×C4#93911yescharacteristic
402Dic3—24no—
403Dic3—42no—
404Dic3—41no—
405Dic3—122no—
406Dic3—122no—
407Dic3—122no—
408Dic3—122no—
409Dic3—242no—
410Dic3—242no—
411C32#191211yescharacteristic, complemented, Sylow
412C23—61no—
413C23D3×D1211yescharacteristic
414Q8—62no—
415Q8—62no—
416Q8—62no—
417Q8—62no—
418Q8—61no—
419Q8—61no—
420D4—61no—
421D4—61no—
422D4—121no—
423D4—121no—
424C2×C4—34no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—61no—
428C2×C4—62no—
429C2×C4—121no—
430C2×C4—121no—
431C2×C4—182no—
432C2×C4—182no—
433C2×C4#379511yescharacteristic
434C2×C4C4×D3211yescharacteristic
435C2×C4#380211yescharacteristic
436C2×C4#380511yescharacteristic
437C2×C4D3×#6711yescharacteristic
438C2×C4D3×#6711yescharacteristic
439C8—41no—
440C8—121no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—241no—
452C2×C3#495611yescharacteristic
453C2×C3#495811yescharacteristic
454D3—81no—
455C22—41no—
456C22—122no—
457C22—121no—
458C22#6389111yescharacteristic
459C22D3×(C2×D3)⋊C411yescharacteristic
460C22#6392211yescharacteristic
461C4—64no—
462C4—122no—
463C4—121no—
464C4—362no—
465C4—362no—
466C4#6387911yescharacteristic
467C4#6388511yescharacteristic
468C4#6390211yescharacteristic
469C4#6397011yescharacteristic
470C3—21no—
471C3#7010511yescharacteristic, complemented
472C3#7041111yescharacteristic, complemented
473C2—21no—
474C2—21no—
475C2—21no—
476C2—241no—
477C2#1059136311yescharacteristic
subgroupG/H
centerC2#10591363
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1912
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
2. #10594818C2semidirect
4. C2×C3×#824C2semidirect
6. #10589423C2semidirect
7. #10589158C2semidirect
19. #63873C4semidirect
20. #63863C4semidirect
36. C2×#824D3semidirect
411. C32#1912semidirect
471. C3#70105semidirect
472. C3#70411semidirect

Maximal subgroups

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

subgroupindex
#105948552
#105948182
C3×#51392
C2×C3×#8242
#105911102
#105894232
#105891582
#704113
#701053