Finite Group Databasebeta

← #11788816

Subgroups — #11788816

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 497 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594866C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3#10592838C211yesmaximal, characteristic
4C2×C3×#824C211yesmaximal, characteristic, complemented
5#10591113C211yesmaximal, characteristic
6C3×#4557C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70105—31nomaximal
9#68708—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63966—22no—
18#63955—22no—
19#63871—22no—
20#63866C412yescomplemented
21#63864C412yescomplemented
22#63843—22no—
23Dic3×Dic6—22no—
24#63652—22no—
25C3×#824—22no—
26#63570—22no—
27#5816—31no—
28#5812—31no—
29#5526—31no—
30#5516—31no—
31C2×C3×#101—31no—
32#5139—31no—
33#5139—31no—
34#5139—31no—
35#5139—61no—
36C2×#824D311yescharacteristic, complemented
37#5005—31no—
38C3×H(3,ℤ/4)—31no—
39#4557—31no—
40#4557D311yescharacteristic, complemented
41#4531—31no—
42C22×C32×C4C2311yescharacteristic
43C2×#638—21no—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×#634C2×C411yescharacteristic
51C22×C3×Dic3D412yes—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6C2×C412yes—
57C2×C3×Dic6D412yes—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61#3757—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4×C3⋊Dic3D412yes—
64C3×#217—21no—
65C3×#217—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3C2×C412yes—
69C3×C4×Dic3D412yes—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3—24no—
75#3722—24no—
76Dic32—24no—
77#1912—91noSylow
78C22×C3×Q8—31no—
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C22×Dic6C2×D311yescharacteristic
83C2×C3×M16—21no—
84C2×C3×M16—31no—
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×M16C2×D311yescharacteristic
87C3×#117—31no—
88C3×#117—31no—
89#947—32no—
90#946—62no—
91Q8×Dic3—62no—
92Q8×Dic3—62no—
93#944—32no—
94#929—62no—
95#926—31no—
96#926—31no—
97#926—61no—
98#926—62no—
99#926C2×D311yescharacteristic
100#926C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102#897—62no—
103#887—62no—
104#886—62no—
105#877—62no—
106#875—32no—
107#869—32no—
108C4×Dic6—62no—
109C3×#101—62no—
110#825—62no—
111#825—62no—
112#825—64no—
113#825—62no—
114#824—22no—
115#805—62no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124#638—41no—
125#638—41no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—22no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—21no—
130C4×C3⋊D3—41no—
131C4×C3⋊D3—41no—
132#634—21no—
133#634—21no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3C22⋊C414yes—
139C3×Dic6—22no—
140C3×Dic6—22no—
141C3×Dic6—22no—
142C3×Dic6—22no—
143C32×C8—41no—
144C3×C3⋊C8—41no—
145#536—91no—
146#519—91no—
147#421—91no—
148#421—91no—
149C2×#101—31no—
150H(3,ℤ/4)—31no—
151H(3,ℤ/4)—91no—
152C2×C3×Q8—32no—
153C2×C3×Q8—32no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×Q8—61no—
158C22×C3×C4—21no—
159C22×C3×C4—32no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—61no—
163C2×#67—61no—
164C2×#67—121no—
165C22×Dic3D1212yes—
166#235—62no—
167#235—62no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—121no—
177#235—121no—
178C2×D12—31no—
179C2×D12—31no—
180C2×D12—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—121no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6—21no—
187C2×Dic6—21no—
188C2×Dic6—31no—
189C2×Dic6—31no—
190C2×Dic6—61no—
191C2×Dic6C4×D312yes—
192C2×Dic6#6712yes—
193C3×M16—22no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—21no—
198C3×M16—41no—
199C3×M16—61no—
200C3×M16—61no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—41no—
204C2×C3×C8—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C22⋊C4—61no—
208C3×C22⋊C4—61no—
209C3×C42—32no—
210C3×C42—32no—
211#217—21no—
212#217—21no—
213#217—61no—
214#217—61no—
215#217—121no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—64no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—64no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—64no—
224C4⋊Dic3—121no—
225Dic3⋊C4—64no—
226Dic3⋊C4—64no—
227C4×Dic3—32no—
228C4×Dic3—32no—
229C4×Dic3—62no—
230C4×Dic3—64no—
231C4×Dic3—64no—
232C4×Dic3C4×D312yes—
233C4×Dic3D1212yes—
234#208—21no—
235#208—21no—
236C2×C3⋊C8—21no—
237C22×C32—41no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32#12011yescharacteristic
240C22×C32#12311yescharacteristic
241C2×C3⋊D3—41no—
242C2×C3⋊D3—42no—
243C32×C4C4×D411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4#12111yescharacteristic
246C32×C4#12111yescharacteristic
247C3⋊Dic3—41no—
248C3⋊Dic3—42no—
249C3×Dic3—24no—
250C3×Dic3—42no—
251C3×Dic3—42no—
252C2×#41—91no—
253C22×Q8—31no—
254C2×M16—31no—
255C2×M16D3211yescharacteristic
256C4⋊Q8—92no—
257#124—92no—
258#123—182no—
259C22⋊Q8—182no—
260C4×Q8—182no—
261C4×Q8—182no—
262#117—31no—
263#117—31no—
264#117—91no—
265#117—182no—
266#104—182no—
267#104—182no—
268#101—62no—
269C23×C3—21no—
270C23×C3C2×D1211yescharacteristic
271C23×C3D3×D411yescharacteristic
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—121no—
275C3×Q8—62no—
276C3×Q8—62no—
277C3×Q8—62no—
278C3×Q8—62no—
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—34no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4C2×C4×D311yescharacteristic
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
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#23911yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302#67—122no—
303#67—122no—
304#67—121no—
305#67—121no—
306#67—121no—
307#67—121no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—61no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—121no—
317C2×Dic3—122no—
318C2×Dic3(C2×D3)⋊C414yes—
319D12—62no—
320D12—61no—
321D12—61no—
322D12—61no—
323D12—61no—
324D12—121no—
325C4×D3—122no—
326C4×D3—122no—
327C4×D3—121no—
328C4×D3—121no—
329C4×D3—121no—
330C4×D3—121no—
331Dic6—22no—
332Dic6—22no—
333Dic6—22no—
334Dic6—22no—
335Dic6—62no—
336Dic6—61no—
337Dic6—61no—
338Dic6—61no—
339Dic6—61no—
340Dic6—121no—
341C3×C8—42no—
342C3×C8—41no—
343C3×C8—41no—
344C3×C8—121no—
345C3⋊C8—41no—
346C2×C32—21no—
347C2×C32—21no—
348C2×C32—21no—
349C2×C32#38611yescharacteristic
350C3⋊D3—81no—
351#41—181no—
352#41—181no—
353#41—181no—
354#41—181no—
355C2×Q8—32no—
356C2×Q8—32no—
357C2×Q8—61no—
358C2×Q8—61no—
359C2×Q8—61no—
360C2×Q8—61no—
361C2×Q8—91no—
362C2×D4—91no—
363C2×D4—181no—
364C22×C4—32no—
365C22×C4—181no—
366C22×C4C2×D3211yescharacteristic
367M16—21no—
368M16—21no—
369M16—61no—
370M16—61no—
371C2×C8—21no—
372C2×C8—61no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—184no—
376C4⋊C4—184no—
377C4⋊C4—181no—
378C22⋊C4—61no—
379C22⋊C4—61no—
380C22⋊C4—184no—
381C22⋊C4—181no—
382C42—32no—
383C42—32no—
384C42—92no—
385C42—184no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—81no—
392C22×C3D3×C22⋊C411yescharacteristic
393C22×C3#88211yescharacteristic
394C22×C3#88211yescharacteristic
395C22×C3#88611yescharacteristic
396C22×C3#89411yescharacteristic
397C22×C3C2×(C2×D3)⋊C411yescharacteristic
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—121no—
402C2×D3—121no—
403C2×D3—242no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—64no—
409C3×C4—122no—
410C3×C4—122no—
411C3×C4C4×D1211yescharacteristic
412C3×C4#67⋊C411yescharacteristic
413C3×C4#67⋊C411yescharacteristic
414C3×C4#88411yescharacteristic
415C3×C4#89311yescharacteristic
416C3×C4#89511yescharacteristic
417C3×C4#93911yescharacteristic
418C3×C4#93911yescharacteristic
419Dic3—24no—
420Dic3—42no—
421Dic3—42no—
422Dic3—122no—
423Dic3—122no—
424Dic3—122no—
425Dic3—121no—
426Dic3—121no—
427Dic3—242no—
428C32#191211yescharacteristic, complemented, Sylow
429C23—181no—
430C23D3×D1211yescharacteristic
431Q8—62no—
432Q8—62no—
433Q8—62no—
434Q8—62no—
435Q8—181no—
436Q8—181no—
437D4—181no—
438D4—181no—
439D4—361no—
440D4—361no—
441C2×C4—34no—
442C2×C4—62no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—181no—
447C2×C4—182no—
448C2×C4—361no—
449C2×C4—361no—
450C2×C4#379611yescharacteristic
451C2×C4C4×D3211yescharacteristic
452C2×C4D3×D1211yescharacteristic
453C2×C4#380411yescharacteristic
454C2×C4D3×#6711yescharacteristic
455C2×C4#381111yescharacteristic
456C8—41no—
457C8—121no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—41no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3#466511yescharacteristic
469C2×C3#495811yescharacteristic
470D3—242no—
471D3—241no—
472D3—241no—
473C22—41no—
474C22—362no—
475C22—361no—
476C22#6389011yescharacteristic
477C22D3×(C2×D3)⋊C411yescharacteristic
478C22#6392311yescharacteristic
479C4—64no—
480C4—122no—
481C4—122no—
482C4—362no—
483C4—361no—
484C4#6388011yescharacteristic
485C4#6388111yescharacteristic
486C4#6388611yescharacteristic
487C4#6397111yescharacteristic
488C3—21no—
489C3#6870811yescharacteristic, complemented
490C3#7010511yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—21no—
494C2—721no—
495C2#1059136411yescharacteristic
subgroupG/H
centerC2#10591364
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radicalC2×#3828C22
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. C3×#4557C2semidirect
7. #10589158C2semidirect
20. #63866C4semidirect
21. #63864C4semidirect
36. C2×#824D3semidirect
40. #4557D3semidirect
428. C32#1912semidirect
489. C3#68708semidirect
490. C3#70105semidirect

Maximal subgroups

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

subgroupindex
#105948662
#105948182
#105928382
C2×C3×#8242
#105911132
C3×#45572
#105891582
#701053
#687083