Finite Group Databasebeta

← #11783844

Subgroups — #11783844

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63815C211yesmaximal, characteristic
2#10592696C211yesmaximal, characteristic, complemented
3C3×#5006C211yesmaximal, characteristic
4#10591076C211yesmaximal, characteristic
5#10591057C211yesmaximal, characteristic, complemented
6C3×#4533C211yesmaximal, characteristic, complemented
7#10589169C211yesmaximal, characteristic, complemented
8#70040—31nomaximal
9#69014—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711C412yescomplemented
18#63815—21no—
19#63815—21no—
20#63815—21no—
21#63815—21no—
22C2×D3×C3⋊C8C412yescomplemented
23#63630—21no—
24C4×C3⋊(C3⋊C8)—21no—
25C3×#806C414yes—
26#63560C412yescomplemented
27#63558C412yescomplemented
28#63554—21no—
29Dic3×C3⋊C8—21no—
30C2×#948—31no—
31C2×#907—31no—
32C3×#410—31no—
33#5237—31no—
34#5132—31no—
35#5122—31no—
36#5006D311yescharacteristic
37#4997—31no—
38#4997—31no—
39#4997—31no—
40#4997—61no—
41C3×#344—31no—
42#4556—31no—
43#4533—31no—
44#4533D311yescharacteristic, complemented
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67C2×C412yes—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235—21no—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3C2×C412yes—
53C2×C3×Dic6C2×C411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C22⋊C4C2×C412yes—
56C32×C42—21no—
57#3748—21no—
58#3748C2×C412yes—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
61C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
62C2×C3⋊(C3⋊C8)D411yescharacteristic
63C2×C3⋊(C3⋊C8)D411yescharacteristic
64C2×C3⋊(C3⋊C8)D411yescharacteristic
65C2×C3⋊(C3⋊C8)D411yescharacteristic
66C3×#217C2×C412yes—
67C3×C4⋊Dic3—21no—
68C3×C4×Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208C2×C412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8C2×C412yes—
75#3711—22no—
76#3711—22no—
77D3×C3⋊C8—22no—
78D3×C3⋊C8—22no—
79#1757—91noSylow
80C2×C3×#41—31no—
81C2×#235C2×D311yescharacteristic
82C2×C3×M16—31no—
83C2×C3×M16—31no—
84C3×#117—21no—
85C3×#117—31no—
86C3×#117C2×D311yescharacteristic
87C3×#117C2×D311yescharacteristic
88#948—61no—
89#948—61no—
90#948—61no—
91#948—61no—
92#926C2×D311yescharacteristic
93C2×#208—32no—
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—61no—
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99C22×C3⋊C8—31no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—32no—
102C22×C3⋊C8—61no—
103#907—61no—
104#907—61no—
105#907—61no—
106#907—61no—
107C2×ΓL(1,𝔽25)—32no—
108C2×D3×C8—32no—
109C3×#99—34no—
110#836—32no—
111#833—32no—
112#824—32no—
113#823—32no—
114#815—61no—
115C8×Dic3—61no—
116#806Dic314yes—
117#803—61no—
118#803—61no—
119#803—61no—
120#803—62no—
121C4×C3⋊C8—61no—
122C4×C3⋊C8—61no—
123C4×C3⋊C8—61no—
124C4×C3⋊C8—62no—
125C23×C32C22×C411yescharacteristic
126C22×C3×D3C4212yes—
127C2×C32×C4—22no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C3×#67—22no—
135C3×#67—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3C4212yes—
138C3×D12—21no—
139C3×D12—21no—
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142C3×Dic6—21no—
143C3×Dic6—21no—
144C3⋊(C3⋊C8)—22no—
145C3⋊(C3⋊C8)C22⋊C411yescharacteristic
146C3⋊(C3⋊C8)C22⋊C411yescharacteristic
147C3⋊(C3⋊C8)C22⋊C411yescharacteristic
148C3⋊(C3⋊C8)C22⋊C411yescharacteristic
149C3×C3⋊C8—22no—
150C3×C3⋊C8—22no—
151C2×#131—91no—
152#413—91no—
153#410—31no—
154#405—91no—
155#405—91no—
156#344—31no—
157#344—91no—
158C3×#41—61no—
159C3×#41—61no—
160C3×#41—61no—
161C3×#41—61no—
162C2×C3×Q8—31no—
163C2×C3×D4—32no—
164C2×C3×D4—31no—
165C22×C3×C4—21no—
166C22×C3×C4—32no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67C2×Dic312yes—
170#235—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174C2×D12C4×D311yescharacteristic
175C2×C4×D3C4×D312yes—
176C2×Dic6C4×D311yescharacteristic
177C3×M16—32no—
178C3×M16—61no—
179C3×M16—61no—
180C3×M16—61no—
181C2×C3×C8—32no—
182C2×C3×C8—61no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—61no—
187C3×C22⋊C4—22no—
188C3×C22⋊C4—32no—
189C3×C22⋊C4C4×D312yes—
190C3×C22⋊C4C2×Dic312yes—
191C3×C42—22no—
192C3×C42—21no—
193C3×C42—21no—
194C3×C42—61no—
195#217C2×Dic312yes—
196C4⋊Dic3—21no—
197C4×Dic3—21no—
198#208—21no—
199#208—21no—
200#208—21no—
201#208—32no—
202#208—32no—
203#208—62no—
204#208—62no—
205#208—62no—
206#208—62no—
207#208—61no—
208#208—61no—
209#208C4×D312yes—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—31no—
212C2×C3⋊C8—31no—
213C2×C3⋊C8—31no—
214C2×C3⋊C8—31no—
215C2×C3⋊C8—31no—
216C2×C3⋊C8—31no—
217C2×C3⋊C8—31no—
218C2×C3⋊C8—31no—
219C2×C3⋊C8—31no—
220C2×C3⋊C8—31no—
221C2×C3⋊C8—31no—
222C2×C3⋊C8—31no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8C4×D312yes—
235ΓL(1,𝔽25)—62no—
236ΓL(1,𝔽25)—62no—
237D3×C8—62no—
238D3×C8—62no—
239C22×C32—41no—
240C22×C32C2×C4211yescharacteristic
241C22×C32C4×D411yescharacteristic
242C22×C32C4×D411yescharacteristic
243C2×C3×D3—22no—
244C2×C3×D3—42no—
245C32×C4—42no—
246C32×C4C2×C22⋊C411yescharacteristic
247C32×C4#11711yescharacteristic
248C32×C4C4×D411yescharacteristic
249C32×C4C4×D411yescharacteristic
250C3×Dic3—22no—
251C3×Dic3—42no—
252C2×#41—31no—
253#131—181no—
254#131—181no—
255#131—181no—
256#131—181no—
257C2×M16—31no—
258C2×M16—31no—
259C2×M16—92no—
260C2×M16—91no—
261C22×C8—92no—
262C22×C8—91no—
263#117—31no—
264#117D3211yescharacteristic
265#101—92no—
266#100—92no—
267#99—34no—
268#97—181no—
269#97—181no—
270C4×C8—181no—
271C4×C8—181no—
272C23×C3—21no—
273C23×C3—32no—
274C23×C3C2×C4×D311yescharacteristic
275C23×C3C22×Dic311yescharacteristic
276C22×D3C4×Dic312yes—
277C3×Q8—61no—
278C3×Q8—61no—
279C3×D4—62no—
280C3×D4—62no—
281C3×D4—61no—
282C3×D4—61no—
283C2×C3×C4—24no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—32no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4C2×C4×D311yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4#23711yescharacteristic
306C2×C3×C4#23711yescharacteristic
307C2×C3×C4#23911yescharacteristic
308#67—22no—
309#67—22no—
310C2×Dic3—22no—
311C2×Dic3C4×Dic312yes—
312D12—21no—
313D12—21no—
314C4×D3—22no—
315C4×D3—22no—
316Dic6—21no—
317Dic6—21no—
318C3×C8—62no—
319C3×C8—62no—
320C3⋊C8—22no—
321C3⋊C8—22no—
322C3⋊C8—31no—
323C3⋊C8—31no—
324C3⋊C8—31no—
325C3⋊C8—31no—
326C3⋊C8—31no—
327C3⋊C8—31no—
328C3⋊C8—31no—
329C3⋊C8—31no—
330C3⋊C8—61no—
331C3⋊C8—61no—
332C3⋊C8—61no—
333C3⋊C8—61no—
334C3⋊C8—64no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C2×C32—21no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32C4×C22⋊C411yescharacteristic
341C3×D3—42no—
342#41—61no—
343#41—61no—
344#41—61no—
345#41—61no—
346C2×Q8—31no—
347C2×D4—32no—
348C2×D4—31no—
349C22×C4—32no—
350C22×C4C2×D3211yescharacteristic
351M16—32no—
352M16—61no—
353M16—61no—
354M16—61no—
355M16—92no—
356M16—182no—
357M16—182no—
358M16—181no—
359C2×C8—32no—
360C2×C8—61no—
361C2×C8—91no—
362C2×C8—91no—
363C2×C8—91no—
364C2×C8—91no—
365C2×C8—91no—
366C2×C8—91no—
367C2×C8—182no—
368C2×C8—182no—
369C2×C8—181no—
370C4⋊C4—21no—
371C4⋊C4—61no—
372C22⋊C4—32no—
373C22⋊C4D3×Dic312yes—
374C42—21no—
375C42—61no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—42no—
382C22×C3—62no—
383C22×C3—122no—
384C22×C3C42×D311yescharacteristic
385C22×C3#67⋊C411yescharacteristic
386C22×C3#89311yescharacteristic
387C22×C3C2×C4×Dic311yescharacteristic
388C22×C3D4×Dic311yescharacteristic
389C22×C3D4×Dic311yescharacteristic
390C2×D3—22no—
391C2×D3—42no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—44no—
397C3×C4—42no—
398C3×C4—42no—
399C3×C4—62no—
400C3×C4—122no—
401C3×C4#87711yescharacteristic
402C3×C4D3×C22⋊C411yescharacteristic
403C3×C4D3×C22⋊C411yescharacteristic
404C3×C4#67⋊C411yescharacteristic
405C3×C4#67⋊C411yescharacteristic
406C3×C4#67⋊C411yescharacteristic
407C3×C4#89211yescharacteristic
408C3×C4#89311yescharacteristic
409Dic3—22no—
410Dic3—42no—
411C32#175711yescharacteristic, complemented, Sylow
412C23—32no—
413C23C2×D3×Dic311yescharacteristic
414Q8—61no—
415Q8—61no—
416D4—62no—
417D4—62no—
418D4—61no—
419D4—61no—
420C2×C4—22no—
421C2×C4—32no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4#379611yescharacteristic
426C2×C4C4×D3211yescharacteristic
427C2×C4C4×D3211yescharacteristic
428C2×C4#380211yescharacteristic
429C2×C4#380511yescharacteristic
430C2×C4#381111yescharacteristic
431C8—62no—
432C8—62no—
433C8—91no—
434C8—91no—
435C8—91no—
436C8—91no—
437C8—182no—
438C2×C3—22no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—122no—
449C2×C3#466611yescharacteristic
450C2×C3Dic3×C22⋊C411yescharacteristic
451D3—42no—
452C22—41no—
453C22—62no—
454C22—122no—
455C22C4×D3×Dic311yescharacteristic
456C22#6389811yescharacteristic
457C22#67⋊Dic311yescharacteristic
458C4—42no—
459C4—62no—
460C4—122no—
461C4#6387811yescharacteristic
462C4#6388111yescharacteristic
463C4#6390211yescharacteristic
464C4#6392111yescharacteristic
465C3—21no—
466C3#6901411yescharacteristic, complemented
467C3#7004011yescharacteristic, complemented
468C2—21no—
469C2—21no—
470C2—21no—
471C2—122no—
472C2#1059136811yescharacteristic
subgroupG/H
centerC4#63921
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32C4×C22⋊C4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1757
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592696C2semidirect
5. #10591057C2semidirect
6. C3×#4533C2semidirect
7. #10589169C2semidirect
17. C2×#3711C4semidirect
22. C2×D3×C3⋊C8C4semidirect
26. #63560C4semidirect
27. #63558C4semidirect
44. #4533D3semidirect
411. C32#1757semidirect
466. C3#69014semidirect
467. C3#70040semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
#105926962
C3×#50062
#105910762
#105910572
C3×#45332
#105891692
#700403
#690143