Finite Group Databasebeta

← #11788918

Subgroups — #11788918

Order 1152.

689 conjugacy classes of subgroups.

The subgroup lattice has 485 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic
2#10594856C211yesmaximal, characteristic
3C2×#63651C211yesmaximal, characteristic, complemented
4C2×#63561C211yesmaximal, characteristic, complemented
5#10591076C211yesmaximal, characteristic
6C3×#4559C211yesmaximal, characteristic, complemented
7#10589170C211yesmaximal, characteristic, complemented
8#72031—31nomaximal
9#69041—31nomaximal
10C22×#634C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20#63962C414yes—
21#63866—21no—
22#63860—21no—
23#63857—22no—
24#63651—22no—
25#63561—22no—
26#63560—21no—
27#63558—21no—
28C3×#568—31no—
29#5825—31no—
30#5745D311yescharacteristic
31#5526—31no—
32#5237—31no—
33C2×#824—31no—
34C2×#824—31no—
35C2×#824—31no—
36C2×#824—31no—
37C2×#824—61no—
38#5132—31no—
39C3×#344—31no—
40#4559—31no—
41#4559D311yescharacteristic, complemented
42#4533—31no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2×C412yes—
45C2×#634—21no—
46C2×#634—21no—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×C3×#67C2×C412yes—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3D412yes—
58C2×C3×Dic6D411yescharacteristic
59C32×M16—21no—
60C32×M16D412yes—
61C2×C32×C8—21no—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217C2×C412yes—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C3×ΓL(1,𝔽25)—24no—
75C3×D3×C8—24no—
76Dic3⋊Dic3—24no—
77(C2×D3)⋊Dic3—24no—
78#1915—91noSylow
79C2×C3×#41—31no—
80C2×#235C2×D311yescharacteristic
81C22×Dic6—31no—
82C22×Dic6—31no—
83C22×Dic6—61no—
84C3×#131—62no—
85C3×#131—62no—
86C2×C3×M16—21no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C2×C3×M16—62no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C3×#117—31no—
93#944—61no—
94#936—61no—
95#935—34no—
96#926C2×D311yescharacteristic
97#924—62no—
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103#907—22no—
104D3×M16—22no—
105#901—22no—
106#897—62no—
107#886—34no—
108#875—61no—
109#869—61no—
110#836—61no—
111#833—61no—
112#824—62no—
113#824—64no—
114#824—61no—
115#824—62no—
116#824—62no—
117#824—62no—
118#823—61no—
119C23×C32C22×C411yescharacteristic
120C22×C3×D3C22⋊C412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C2×C3⋊Dic3—22no—
130#634—41no—
131#634—41no—
132#634—41no—
133#634—41no—
134C3×#67—22no—
135C3×#67—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3C22⋊C412yes—
138C3×D12—21no—
139C3×D12—21no—
140C3×C4×D3—22no—
141C3×C4×D3—22no—
142C3×Dic6—21no—
143C3×Dic6—21no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—41no—
146C3×C3⋊C8—22no—
147C3×C3⋊C8—41no—
148#568—31no—
149#536—91no—
150#413—91no—
151C2×#101—91no—
152C2×#101—91no—
153#344—31no—
154#344—91no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—32no—
161C2×C3×D4—31no—
162C22×C3×C4—21no—
163C22×C3×C4—32no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67C4×D312yes—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—62no—
170#235—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174C2×D12D1211yescharacteristic
175C2×C4×D3#6712yes—
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—61no—
189C2×Dic6—61no—
190C2×Dic6—121no—
191C2×Dic6—121no—
192C2×Dic6—121no—
193C2×Dic6—121no—
194C2×Dic6D1211yescharacteristic
195C3×M16—21no—
196C3×M16—21no—
197C3×M16—22no—
198C3×M16—32no—
199C3×M16—41no—
200C3×M16—64no—
201C3×M16—61no—
202C3×M16—61no—
203C3×M16—61no—
204C3×M16D1212yes—
205C3×M16#6712yes—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—41no—
209C2×C3×C8—64no—
210C2×C3×C8—61no—
211C2×C3×C8—61no—
212C3×C4⋊C4—61no—
213C3×C22⋊C4—32no—
214C3×C42—61no—
215#217—64no—
216#217C4×D312yes—
217(C2×D3)⋊C4—64no—
218C4⋊Dic3—21no—
219C4⋊Dic3—64no—
220Dic3⋊C4—64no—
221C4×Dic3—21no—
222#208—21no—
223#208—21no—
224#208—21no—
225#208—62no—
226#208—61no—
227#208—61no—
228#208—61no—
229#208—61no—
230#208—121no—
231#208#6712yes—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—121no—
237ΓL(1,𝔽25)—24no—
238D3×C8—24no—
239C22×C32—41no—
240C22×C32C2×C22⋊C411yescharacteristic
241C22×C32C4×D411yescharacteristic
242C22×C32C4×D411yescharacteristic
243C2×C3×D3—22no—
244C2×C3×D3—42no—
245C32×C4#12011yescharacteristic
246C32×C4#12111yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4#12311yescharacteristic
249C3⋊Dic3—42no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C2×#41—31no—
253C22×Q8—91no—
254#131—62no—
255#131—62no—
256C2×M16—31no—
257C2×M16—31no—
258C2×M16—62no—
259C2×M16—91no—
260C2×M16D3211yescharacteristic
261C4⋊Q8—181no—
262#124—181no—
263#123—94no—
264C22⋊Q8—182no—
265#117—31no—
266#101—182no—
267#101—181no—
268#101—182no—
269#100—181no—
270C23×C3—21no—
271C23×C3—32no—
272C23×C3C2×C4×D311yescharacteristic
273C23×C3C2×C4×D311yescharacteristic
274C22×D3(C2×D3)⋊C412yes—
275C3×Q8—61no—
276C3×Q8—61no—
277C3×D4—62no—
278C3×D4—62no—
279C3×D4—61no—
280C3×D4—61no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—32no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4C2×D1211yescharacteristic
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23911yescharacteristic
300C2×C3×C4C2×#6711yescharacteristic
301C2×C3×C4C2×#6711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303#67—22no—
304#67—22no—
305C2×Dic3—22no—
306C2×Dic3—64no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—122no—
315C2×Dic3(C2×D3)⋊C412yes—
316D12—21no—
317D12—21no—
318C4×D3—22no—
319C4×D3—22no—
320Dic6—21no—
321Dic6—21no—
322Dic6—122no—
323Dic6—122no—
324Dic6—122no—
325Dic6—122no—
326Dic6—121no—
327Dic6—121no—
328Dic6—121no—
329Dic6—121no—
330Dic6—121no—
331Dic6—121no—
332Dic6—121no—
333Dic6—121no—
334C3×C8—22no—
335C3×C8—22no—
336C3×C8—42no—
337C3×C8—62no—
338C3×C8—121no—
339C3⋊C8—22no—
340C3⋊C8—41no—
341C3⋊C8—122no—
342C3⋊C8—121no—
343C3⋊C8—121no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32#38611yescharacteristic
348C3×D3—42no—
349#41—61no—
350#41—61no—
351#41—61no—
352#41—61no—
353C2×Q8—31no—
354C2×Q8—181no—
355C2×Q8—181no—
356C2×Q8—181no—
357C2×Q8—181no—
358C2×Q8—181no—
359C2×Q8—181no—
360C2×D4—32no—
361C2×D4—31no—
362C22×C4—32no—
363C22×C4—92no—
364C22×C4C2×D3211yescharacteristic
365M16—21no—
366M16—32no—
367M16—64no—
368M16—61no—
369M16—61no—
370M16—61no—
371M16—181no—
372M16—181no—
373M16#62612yes—
374C2×C8—21no—
375C2×C8—64no—
376C2×C8—61no—
377C2×C8—61no—
378C2×C8—181no—
379C4⋊C4—61no—
380C4⋊C4—184no—
381C22⋊C4—32no—
382C22⋊C4—184no—
383C42—61no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—41no—
388C22×C3—41no—
389C22×C3—42no—
390C22×C3—62no—
391C22×C3—122no—
392C22×C3C4×D1211yescharacteristic
393C22×C3D3×C22⋊C411yescharacteristic
394C22×C3#89311yescharacteristic
395C22×C3C2×(C2×D3)⋊C411yescharacteristic
396C22×C3C4×#6711yescharacteristic
397C22×C3C4×#6711yescharacteristic
398C2×D3—22no—
399C2×D3—42no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—62no—
405C3×C4—122no—
406C3×C4#88211yescharacteristic
407C3×C4#88411yescharacteristic
408C3×C4#89411yescharacteristic
409C3×C4#89511yescharacteristic
410C3×C4#92911yescharacteristic
411C3×C4#93011yescharacteristic
412C3×C4#93011yescharacteristic
413C3×C4#95311yescharacteristic
414Dic3—22no—
415Dic3—42no—
416Dic3—124no—
417Dic3—122no—
418Dic3—122no—
419C32#191511yescharacteristic, complemented, Sylow
420C23—32no—
421C23C4×D3211yescharacteristic
422Q8—61no—
423Q8—61no—
424Q8—361no—
425Q8—361no—
426Q8—361no—
427Q8—361no—
428D4—62no—
429D4—62no—
430D4—61no—
431D4—61no—
432C2×C4—32no—
433C2×C4—62no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—182no—
437C2×C4—182no—
438C2×C4—182no—
439C2×C4#379811yescharacteristic
440C2×C4#379911yescharacteristic
441C2×C4D3×D1211yescharacteristic
442C2×C4C2×#62611yescharacteristic
443C2×C4D3×#6711yescharacteristic
444C2×C4D3×#6711yescharacteristic
445C8—22no—
446C8—62no—
447C8—121no—
448C8—361no—
449C2×C3—22no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—41no—
458C2×C3—41no—
459C2×C3—122no—
460C2×C3#466511yescharacteristic
461C2×C3#521311yescharacteristic
462D3—42no—
463C22—41no—
464C22—62no—
465C22—122no—
466C22C4×#62611yescharacteristic
467C22#6390411yescharacteristic
468C22D3×(C2×D3)⋊C411yescharacteristic
469C4—62no—
470C4—122no—
471C4—362no—
472C4#6385011yescharacteristic
473C4#6390611yescharacteristic
474C4#6390911yescharacteristic
475C4#6397711yescharacteristic
476C3—21no—
477C3#6904111yescharacteristic, complemented
478C3#7203111yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—21no—
482C2—122no—
483C2#1059138211yescharacteristic
subgroupG/H
centerC2#10591382
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1915
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×#63651C2semidirect
4. C2×#63561C2semidirect
6. C3×#4559C2semidirect
7. #10589170C2semidirect
41. #4559D3semidirect
419. C32#1915semidirect
477. C3#69041semidirect
478. C3#72031semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105948562
C2×#636512
C2×#635612
#105910762
C3×#45592
#105891702
#720313
#690413