Finite Group Databasebeta

← #11788717

Subgroups — #11788717

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
1#10594856C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic
3#10592703C211yesmaximal, characteristic, complemented
4C3×#5006C211yesmaximal, characteristic
5#10591107C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#70046—31nomaximal
9#68712—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63962—22no—
18#63866C412yescomplemented
19#63860C412yescomplemented
20#63857—22no—
21#63815—22no—
22#63814—22no—
23D3×#208—22no—
24#63637—22no—
25C3×#806—22no—
26#63567—22no—
27#5825—31no—
28#5819—31no—
29#5745—31no—
30#5526—31no—
31C3×#410—31no—
32#5120—31no—
33#5006D311yescharacteristic
34#5004—31no—
35#5004—31no—
36#5004—31no—
37#5004—61no—
38C3×H(3,ℤ/4)—31no—
39#4531—31no—
40#4531—31no—
41#4531D311yescharacteristic, complemented
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×C4⋊C4—21no—
59C32×C22⋊C4—21no—
60C32×C42—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)D412yes—
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—
73Dic3⋊Dic3—24no—
74(C2×D3)⋊Dic3—24no—
75#3711—24no—
76D3×C3⋊C8—24no—
77#1909—91noSylow
78C2×C3×#41—31no—
79C2×#235C2×D311yescharacteristic
80C22×Dic6—31no—
81C22×Dic6—31no—
82C22×Dic6—61no—
83C2×C3×M16—31no—
84C3×#117—21no—
85C3×#117—31no—
86C3×#117—31no—
87C3×#117C2×D311yescharacteristic
88C3×#117C2×D311yescharacteristic
89#948—62no—
90#948—62no—
91#944—32no—
92#936—32no—
93#935—62no—
94#926C2×D311yescharacteristic
95#926C2×D311yescharacteristic
96#924—62no—
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208—62no—
101C2×#208C2×D311yescharacteristic
102#907—62no—
103D3×M16—62no—
104#901—62no—
105#897—62no—
106#886—62no—
107#875—32no—
108#869—32no—
109C3×#99—62no—
110#816—62no—
111#810—62no—
112#810—62no—
113#810—64no—
114#810—62no—
115#806—22no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3C22⋊C412yes—
118C2×C32×C4—41no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—22no—
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—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145#568—91no—
146#536—91no—
147#419—91no—
148#419—91no—
149#410—31no—
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×#67#6712yes—
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×D3D1212yes—
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—61no—
193C3×M16—61no—
194C2×C3×C8—32no—
195C3×C4⋊C4—22no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—21no—
202C3×C22⋊C4—41no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C42—21no—
206C3×C42—21no—
207C3×C42—32no—
208C3×C42—41no—
209C3×C42—61no—
210#217—21no—
211#217—21no—
212#217—64no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—64no—
217Dic3⋊C4—64no—
218C4×Dic3—21no—
219C4×Dic3C4×D312yes—
220#208—21no—
221#208—21no—
222#208—64no—
223#208—61no—
224#208—61no—
225#208—61no—
226#208—61no—
227#208—121no—
228#208—121no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—64no—
233C2×C3⋊C8D1212yes—
234ΓL(1,𝔽25)—64no—
235D3×C8—64no—
236C22×C32—41no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C2×C3×D3—22no—
241C2×C3×D3—42no—
242C32×C4—81no—
243C32×C4C4×D411yescharacteristic
244C32×C4C4×D411yescharacteristic
245C32×C4#12011yescharacteristic
246C32×C4#12311yescharacteristic
247C3⋊Dic3—42no—
248C3×Dic3—22no—
249C3×Dic3—42no—
250C3×Dic3—81no—
251C2×#41—31no—
252C22×Q8—91no—
253#131—182no—
254#131—182no—
255C2×M16—31no—
256C2×M16—91no—
257C2×M16—182no—
258C4⋊Q8—92no—
259#124—92no—
260#123—182no—
261C22⋊Q8—182no—
262#117—31no—
263#117—31no—
264#117D3211yescharacteristic
265#103—182no—
266#103—182no—
267#99—62no—
268C23×C3—21no—
269C23×C3—32no—
270C23×C3D3×D411yescharacteristic
271C23×C3C2×#6711yescharacteristic
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—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—121no—
293C2×C3×C4C2×C4×D311yescharacteristic
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4#23911yescharacteristic
305#67—22no—
306#67—22no—
307C2×Dic3—22no—
308C2×Dic3—41no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
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—62no—
338C3⋊C8—22no—
339C3⋊C8—62no—
340C3⋊C8—62no—
341C3⋊C8—122no—
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—61no—
364M16—61no—
365M16—184no—
366M16—181no—
367M16—181no—
368C2×C8—32no—
369C2×C8—92no—
370C2×C8—184no—
371C4⋊C4—21no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—184no—
375C22⋊C4—21no—
376C22⋊C4—61no—
377C22⋊C4—61no—
378C22⋊C4—184no—
379C42—21no—
380C42—32no—
381C42—61no—
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#93911yescharacteristic
395C22×C3#93911yescharacteristic
396C2×D3—22no—
397C2×D3—42no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—62no—
403C3×C4—82no—
404C3×C4—81no—
405C3×C4—81no—
406C3×C4—122no—
407C3×C4—241no—
408C3×C4C4×D1211yescharacteristic
409C3×C4#67⋊C411yescharacteristic
410C3×C4#67⋊C411yescharacteristic
411C3×C4#88211yescharacteristic
412C3×C4#88211yescharacteristic
413C3×C4#88611yescharacteristic
414C3×C4#89311yescharacteristic
415C3×C4#89411yescharacteristic
416Dic3—22no—
417Dic3—42no—
418Dic3—81no—
419Dic3—124no—
420Dic3—122no—
421Dic3—122no—
422C32#190911yescharacteristic, complemented, Sylow
423C23—32no—
424C23D3×#6711yescharacteristic
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—41no—
437C2×C4—62no—
438C2×C4—62no—
439C2×C4—62no—
440C2×C4—121no—
441C2×C4—182no—
442C2×C4—361no—
443C2×C4—361no—
444C2×C4#379611yescharacteristic
445C2×C4C4×D3211yescharacteristic
446C2×C4D3×D1211yescharacteristic
447C2×C4D3×D1211yescharacteristic
448C2×C4#380411yescharacteristic
449C2×C4#381111yescharacteristic
450C8—62no—
451C8—182no—
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#495811yescharacteristic
465D3—42no—
466C22—41no—
467C22—62no—
468C22—122no—
469C22#6388611yescharacteristic
470C22D3×(C2×D3)⋊C411yescharacteristic
471C22#6397111yescharacteristic
472C4—62no—
473C4—81no—
474C4—122no—
475C4—241no—
476C4—362no—
477C4#6388011yescharacteristic
478C4#6388111yescharacteristic
479C4#6389011yescharacteristic
480C4#6392311yescharacteristic
481C3—21no—
482C3#6871211yescharacteristic, complemented
483C3#7004611yescharacteristic, complemented
484C2—21no—
485C2—21no—
486C2—21no—
487C2—122no—
488C2#1059136411yescharacteristic
subgroupG/H
centerC2#10591364
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1909
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #10592703C2semidirect
5. #10591107C2semidirect
6. C3×#4531C2semidirect
7. #10589157C2semidirect
18. #63866C4semidirect
19. #63860C4semidirect
41. #4531D3semidirect
422. C32#1909semidirect
482. C3#68712semidirect
483. C3#70046semidirect

Maximal subgroups

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

subgroupindex
#105948562
#105947762
#105927032
C3×#50062
#105911072
C3×#45312
#105891572
#700463
#687123