Finite Group Databasebeta

← #11788817

Subgroups — #11788817

Order 1152.

701 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594856C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3C2×#63651C211yesmaximal, characteristic, complemented
4C3×#5139C211yesmaximal, characteristic
5#10591111C211yesmaximal, characteristic
6C3×#4557C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#70411—31nomaximal
9#68708—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C3×#926C2211yescharacteristic
17#63962—22no—
18#63957—22no—
19#63866C412yescomplemented
20#63860C412yescomplemented
21#63857—22no—
22#63844—22no—
23#63844—22no—
24#63651—22no—
25C3×#825—22no—
26#63569—22no—
27#5825—31no—
28#5526—31no—
29#5516—31no—
30#5516—31no—
31C3×#421—31no—
32#5236—31no—
33#5139D311yescharacteristic
34C2×#824—31no—
35C2×#824—31no—
36C2×#824—61no—
37#5005—31no—
38C3×H(3,ℤ/4)—31no—
39#4557D311yescharacteristic, complemented
40#4531—31no—
41#4531—31no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D412yes—
44C2×#634—21no—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634C2×C412yes—
49C2×#634D412yes—
50C2×C3×#67—21no—
51C3×#235—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C2×C3×D12C2×C411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×Dic6C2×C411yescharacteristic
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×#217—21no—
66C3×#217—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3C2×C412yes—
71C3×C4×Dic3D412yes—
72C3×C4×Dic3D412yes—
73#3724—24no—
74Dic3⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76Dic32—24no—
77#1912—91noSylow
78C2×C3×#41—31no—
79C2×#235C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C2×C3×M16—21no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C3×#117—31no—
87C3×#117—31no—
88C3×#117—31no—
89#944—32no—
90#936—32no—
91#935—62no—
92#926C2×D311yescharacteristic
93#926C2×D311yescharacteristic
94#926C2×D311yescharacteristic
95#924—62no—
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—61no—
99#897—62no—
100#887—62no—
101#887—62no—
102#886—62no—
103#877—62no—
104#877—62no—
105#875—32no—
106#869—32no—
107C4×Dic6—62no—
108C4×Dic6—62no—
109C3×#104—62no—
110#837—62no—
111#825—22no—
112#824—62no—
113#824—62no—
114#824—64no—
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
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3C22⋊C414yes—
127#634—22no—
128#634—22no—
129#634—22no—
130#634—22no—
131C3×#67—41no—
132C3×#67—41no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C3×D12—21no—
138C3×D12—21no—
139C3×C4×D3—41no—
140C3×C4×D3—41no—
141C3×Dic6—21no—
142C3×Dic6—21no—
143C32×C8—41no—
144C3⋊(C3⋊C8)—41no—
145#536—91no—
146#519—91no—
147#421—31no—
148#421—91no—
149C2×#101—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—31no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—21no—
164C22×Dic3—32no—
165C22×Dic3—32no—
166C22×Dic3—62no—
167#235—21no—
168#235—21no—
169#235—21no—
170#235—21no—
171C2×D12C4×D311yescharacteristic
172C2×C4×D3—21no—
173C2×Dic6—32no—
174C2×Dic6—32no—
175C2×Dic6—32no—
176C2×Dic6—32no—
177C2×Dic6—62no—
178C2×Dic6—62no—
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—121no—
188C2×Dic6—121no—
189C2×Dic6—121no—
190C2×Dic6—121no—
191C2×Dic6C4×D311yescharacteristic
192C3×M16—22no—
193C3×M16—21no—
194C3×M16—21no—
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—41no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—41no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C42—32no—
208C3×C42—32no—
209C3×C42—32no—
210#217—21no—
211#217—21no—
212#217—21no—
213#217—64no—
214(C2×D3)⋊C4—64no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3—64no—
219Dic3⋊C4—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—64no—
222C4×Dic3—64no—
223C4×Dic3—64no—
224C4×Dic3C4×D312yes—
225C4×Dic3D1212yes—
226C4×Dic3#6712yes—
227#208—62no—
228#208—61no—
229#208—61no—
230#208—61no—
231#208—61no—
232#208—121no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—121no—
236C22×C32—41no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12011yescharacteristic
239C22×C32#12311yescharacteristic
240C2×C3×D3—42no—
241C2×C3×D3—41no—
242C32×C4C4×D411yescharacteristic
243C32×C4C4×D411yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4#12111yescharacteristic
246C3⋊Dic3—24no—
247C3×Dic3—42no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C3×Dic3—41no—
251C2×#41—31no—
252C22×Q8—91no—
253C2×M16—91no—
254C2×M16D3211yescharacteristic
255C4⋊Q8—92no—
256#124—92no—
257#123—182no—
258C22⋊Q8—182no—
259C4×Q8—182no—
260C4×Q8—182no—
261#117—31no—
262#117—31no—
263#117—31no—
264#117—182no—
265#104—62no—
266#104—182no—
267#101—182no—
268C23×C3—21no—
269C23×C3—61no—
270C23×C3D3×D411yescharacteristic
271C23×C3D3×D411yescharacteristic
272C22×D3—21no—
273C3×Q8—61no—
274C3×Q8—61no—
275C3×D4—61no—
276C3×D4—61no—
277C3×D4—121no—
278C3×D4—121no—
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—61no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4C2×C4×D311yescharacteristic
292C2×C3×C4C2×C4×D311yescharacteristic
293C2×C3×C4C2×D1211yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23911yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—41no—
304#67—41no—
305C2×Dic3—22no—
306C2×Dic3—21no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—34no—
310C2×Dic3—34no—
311C2×Dic3—64no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—122no—
317C2×Dic3—122no—
318D12—21no—
319D12—21no—
320C4×D3—41no—
321C4×D3—41no—
322Dic6—21no—
323Dic6—21no—
324Dic6—62no—
325Dic6—62no—
326Dic6—62no—
327Dic6—62no—
328Dic6—62no—
329Dic6—62no—
330Dic6—62no—
331Dic6—62no—
332Dic6—122no—
333Dic6—122no—
334Dic6—122no—
335Dic6—122no—
336C3×C8—42no—
337C3×C8—41no—
338C3×C8—41no—
339C3⋊C8—122no—
340C3⋊C8—121no—
341C3⋊C8—121no—
342C2×C32—21no—
343C2×C32—21no—
344C2×C32—21no—
345C2×C32#38611yescharacteristic
346C3×D3—81no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—31no—
352C2×Q8—92no—
353C2×Q8—92no—
354C2×Q8—181no—
355C2×Q8—181no—
356C2×Q8—181no—
357C2×Q8—181no—
358C2×D4—31no—
359C2×D4—61no—
360C22×C4—61no—
361C22×C4—92no—
362C22×C4C2×D3211yescharacteristic
363M16—21no—
364M16—21no—
365M16—181no—
366M16—181no—
367C2×C8—21no—
368C2×C8—181no—
369C4⋊C4—61no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—184no—
373C4⋊C4—184no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4—61no—
377C22⋊C4—184no—
378C42—32no—
379C42—32no—
380C42—32no—
381C42—184no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—41no—
386C22×C3—41no—
387C22×C3—42no—
388C22×C3—122no—
389C22×C3—121no—
390C22×C3D3×C22⋊C411yescharacteristic
391C22×C3D3×C22⋊C411yescharacteristic
392C22×C3#88211yescharacteristic
393C22×C3#88311yescharacteristic
394C22×C3#89411yescharacteristic
395C22×C3#93711yescharacteristic
396C2×D3—42no—
397C2×D3—41no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—122no—
403C3×C4—122no—
404C3×C4—122no—
405C3×C4—121no—
406C3×C4C4×D1211yescharacteristic
407C3×C4#67⋊C411yescharacteristic
408C3×C4#88411yescharacteristic
409C3×C4#88411yescharacteristic
410C3×C4#89311yescharacteristic
411C3×C4#89511yescharacteristic
412C3×C4C4×#6711yescharacteristic
413C3×C4#93811yescharacteristic
414Dic3—42no—
415Dic3—42no—
416Dic3—42no—
417Dic3—41no—
418Dic3—64no—
419Dic3—64no—
420Dic3—124no—
421C32#191211yescharacteristic, complemented, Sylow
422C23—61no—
423C23#380211yescharacteristic
424Q8—61no—
425Q8—61no—
426Q8—182no—
427Q8—182no—
428Q8—182no—
429Q8—182no—
430D4—61no—
431D4—61no—
432D4—121no—
433D4—121no—
434C2×C4—62no—
435C2×C4—61no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—94no—
439C2×C4—121no—
440C2×C4—121no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4#379911yescharacteristic
444C2×C4C4×D3211yescharacteristic
445C2×C4D3×D1211yescharacteristic
446C2×C4#380411yescharacteristic
447C2×C4D3×#6711yescharacteristic
448C2×C4#381111yescharacteristic
449C8—41no—
450C8—361no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—41no—
460C2×C3—41no—
461C2×C3—241no—
462C2×C3#466511yescharacteristic
463C2×C3#495611yescharacteristic
464D3—81no—
465C22—41no—
466C22—122no—
467C22—121no—
468C22#6385411yescharacteristic
469C22#6392111yescharacteristic
470C22#6392211yescharacteristic
471C4—122no—
472C4—122no—
473C4—122no—
474C4—121no—
475C4—184no—
476C4#6388011yescharacteristic
477C4#6390411yescharacteristic
478C4#6391011yescharacteristic
479C4#6395811yescharacteristic
480C3—21no—
481C3#6870811yescharacteristic, complemented
482C3#7041111yescharacteristic, complemented
483C2—21no—
484C2—21no—
485C2—21no—
486C2—241no—
487C2#1059127511yescharacteristic
subgroupG/H
centerC2#10591275
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. #10594828C2semidirect
3. C2×#63651C2semidirect
6. C3×#4557C2semidirect
7. #10589157C2semidirect
19. #63866C4semidirect
20. #63860C4semidirect
39. #4557D3semidirect
421. C32#1912semidirect
481. C3#68708semidirect
482. C3#70411semidirect

Maximal subgroups

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

subgroupindex
#105948562
#105948282
C2×#636512
C3×#51392
#105911112
C3×#45572
#105891572
#704113
#687083