Finite Group Databasebeta

← #11786651

Subgroups — #11786651

Order 1152.

633 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic
2C3×#5124C211yesmaximal, characteristic, complemented
3#10591141C211yesmaximal, characteristic, complemented
4#10591078C211yesmaximal, characteristic
5#10591073C211yesmaximal, characteristic
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70734—31nomaximal
9#68945—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13#64116—22no—
14M16×C3⋊D3—22no—
15#64110—22no—
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#822—22no—
21#63577—22no—
22#63561C412yes—
23#63559C412yes—
24#63557—22no—
25#5745—31no—
26#5745—31no—
27#5745—61no—
28C3×#430—31no—
29#5132—31no—
30#5132—31no—
31#5129—31no—
32#5125—31no—
33#5124—31no—
34#5124D311yescharacteristic, complemented
35#5110—31no—
36C3×#341—31no—
37#4558—31no—
38#4558D311yescharacteristic, complemented
39#4552—31no—
40C22×C32×C4C2311yescharacteristic
41C2×#638Q812yes—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45#3828—21no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
47C2×C4×C3⋊D3D412yes—
48C2×#634C2×C411yescharacteristic
49C32×M16—21no—
50C32×M16D412yes—
51C2×C32×C8—21no—
52#3748—21no—
53#3748D412yes—
54C2×C3⋊(C3⋊C8)—21no—
55#3743—24no—
56C8×C3⋊D3—24no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208C2×C412yes—
62C3×#208C2×C412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69#1858—91noSylow
70C2×#235—31no—
71C2×#235—31no—
72C2×#235—61no—
73C2×C3×M16—21no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16—31no—
77C2×C3×M16C2×D311yescharacteristic
78C2×C3×M16C2×D311yescharacteristic
79C22×C3×C8—31no—
80C2×#208—31no—
81C2×#208—31no—
82C2×#208—61no—
83C2×#208C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87#907—64no—
88#907—62no—
89#907—62no—
90D3×M16—62no—
91D3×M16—62no—
92D3×M16—64no—
93#901—62no—
94#901—62no—
95#901—64no—
96C3×#108—62no—
97#824—32no—
98#824—32no—
99#823—32no—
100#823—32no—
101#822—22no—
102#822—62no—
103(C2×D3)⋊C8—62no—
104(C2×D3)⋊C8—62no—
105#819—62no—
106C23×C32C2×Q811yescharacteristic
107C22×C3⋊D3C4⋊C412yes—
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114#638—22no—
115#638—22no—
116C2×C3⋊Dic3C4⋊C412yes—
117C4⋊(C3⋊D3)—21no—
118C4⋊(C3⋊D3)—21no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121#634—21no—
122#634—21no—
123C32×C8—22no—
124C3⋊(C3⋊C8)—22no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—22no—
127C3×C3⋊C8—41no—
128C3×C3⋊C8—41no—
129#568—91no—
130#430—31no—
131#430—91no—
132#413—91no—
133#408—91no—
134#341—31no—
135#341—91no—
136C22×C3×C4—21no—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C2×#67—32no—
140C2×#67—32no—
141C2×#67—62no—
142#235—62no—
143#235—62no—
144#235—62no—
145#235—62no—
146#235—61no—
147#235—61no—
148#235—61no—
149#235—61no—
150#235—61no—
151#235—61no—
152#235—61no—
153#235—61no—
154C2×D12—31no—
155C2×D12—31no—
156C2×D12—61no—
157C2×C4×D3—32no—
158C2×C4×D3—32no—
159C2×C4×D3—62no—
160C2×Dic6—31no—
161C2×Dic6—31no—
162C2×Dic6—61no—
163C3×M16—22no—
164C3×M16—21no—
165C3×M16—21no—
166C3×M16—22no—
167C3×M16—32no—
168C3×M16—32no—
169C3×M16—61no—
170C3×M16—61no—
171C3×M16—61no—
172C3×M16—61no—
173C3×M16D1212yes—
174C3×M16#6712yes—
175C2×C3×C8—22no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184#208—21no—
185#208—21no—
186#208—21no—
187#208—21no—
188#208—32no—
189#208—32no—
190#208—62no—
191#208—62no—
192#208—61no—
193#208—61no—
194#208C4×D312yes—
195#208C4×D312yes—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—62no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205ΓL(1,𝔽25)—68no—
206ΓL(1,𝔽25)—64no—
207ΓL(1,𝔽25)—64no—
208D3×C8—68no—
209D3×C8—64no—
210D3×C8—64no—
211C22×C32—41no—
212C22×C32C2×C4⋊C411yescharacteristic
213C22×C32C22⋊Q811yescharacteristic
214C22×C32C22⋊Q811yescharacteristic
215C2×C3⋊D3—22no—
216C2×C3⋊D3—42no—
217C32×C4C4×D411yescharacteristic
218C32×C4C4×D411yescharacteristic
219C32×C4#12011yescharacteristic
220C32×C4#12311yescharacteristic
221C3⋊Dic3—22no—
222C2×#41—91no—
223#131—182no—
224#131—182no—
225C2×M16—31no—
226C2×M16—31no—
227C2×M16—31no—
228C2×M16—91no—
229C2×M16—182no—
230C2×M16D3211yescharacteristic
231C22×C8—31no—
232#108—62no—
233#108—182no—
234#101—92no—
235#100—92no—
236C22⋊C8—182no—
237C23×C3—21no—
238C23×C3D3×Q811yescharacteristic
239C23×C3D3×Q811yescharacteristic
240C22×D3—32no—
241C22×D3—32no—
242C22×D3—62no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4C2×C4×D311yescharacteristic
250C2×C3×C4C2×C4×D311yescharacteristic
251C2×C3×C4C2×D1211yescharacteristic
252C2×C3×C4#23511yescharacteristic
253C2×C3×C4#23511yescharacteristic
254C2×C3×C4D3×D411yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4#23711yescharacteristic
259C2×C3×C4#23911yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261#67—64no—
262#67—64no—
263#67—62no—
264#67—62no—
265#67—62no—
266#67—62no—
267C2×Dic3—32no—
268C2×Dic3—32no—
269C2×Dic3—62no—
270D12—62no—
271D12—62no—
272D12—61no—
273D12—61no—
274D12—61no—
275D12—61no—
276C4×D3—64no—
277C4×D3—64no—
278C4×D3—62no—
279C4×D3—62no—
280C4×D3—62no—
281C4×D3—62no—
282Dic6—62no—
283Dic6—62no—
284Dic6—61no—
285Dic6—61no—
286Dic6—61no—
287Dic6—61no—
288C3×C8—24no—
289C3×C8—22no—
290C3×C8—22no—
291C3×C8—62no—
292C3×C8—62no—
293C3×C8—121no—
294C3×C8—121no—
295C3⋊C8—22no—
296C3⋊C8—22no—
297C3⋊C8—41no—
298C3⋊C8—41no—
299C3⋊C8—64no—
300C3⋊C8—62no—
301C3⋊C8—62no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32#38511yescharacteristic
306C3⋊D3—42no—
307#41—181no—
308#41—181no—
309#41—181no—
310#41—181no—
311C2×Q8—91no—
312C2×D4—92no—
313C2×D4—91no—
314C22×C4—92no—
315C22×C4C2×D3211yescharacteristic
316M16—21no—
317M16—32no—
318M16—32no—
319M16—61no—
320M16—61no—
321M16—61no—
322M16—61no—
323M16—92no—
324M16—184no—
325M16—181no—
326M16#62612yes—
327C2×C8—21no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—61no—
333C2×C8—61no—
334C2×C8—184no—
335C2×C8—181no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—81no—
342C22×C3D3×C4⋊C411yescharacteristic
343C22×C3D3×C4⋊C411yescharacteristic
344C22×C3#89611yescharacteristic
345C22×C3#89611yescharacteristic
346C22×C3#89711yescharacteristic
347C22×C3#94611yescharacteristic
348C2×D3—64no—
349C2×D3—62no—
350C2×D3—62no—
351C2×D3—122no—
352C2×D3—122no—
353C2×D3—242no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4C4×D1211yescharacteristic
359C3×C4#67⋊C411yescharacteristic
360C3×C4#88211yescharacteristic
361C3×C4#88311yescharacteristic
362C3×C4#89311yescharacteristic
363C3×C4#89411yescharacteristic
364C3×C4C4×#6711yescharacteristic
365C3×C4#93711yescharacteristic
366Dic3—64no—
367Dic3—62no—
368Dic3—62no—
369C32#185811yescharacteristic, complemented, Sylow
370C23—92no—
371C23#379711yescharacteristic
372Q8—181no—
373Q8—181no—
374D4—182no—
375D4—182no—
376D4—181no—
377D4—181no—
378C2×C4—92no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4#379611yescharacteristic
382C2×C4#379811yescharacteristic
383C2×C4C4×D3211yescharacteristic
384C2×C4C2×#62611yescharacteristic
385C2×C4#381111yescharacteristic
386C2×C4#381111yescharacteristic
387C8—22no—
388C8—62no—
389C8—62no—
390C8—121no—
391C8—121no—
392C8—182no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—41no—
401C2×C3—41no—
402C2×C3—41no—
403C2×C3#466811yescharacteristic
404C2×C3#498911yescharacteristic
405D3—124no—
406D3—122no—
407D3—122no—
408C22—41no—
409C22—182no—
410C22—362no—
411C22#6386511yescharacteristic
412C22#6387111yescharacteristic
413C22#6388311yescharacteristic
414C4—182no—
415C4#6385311yescharacteristic
416C4#6388111yescharacteristic
417C4C4×#62611yescharacteristic
418C4#6398111yescharacteristic
419C3—21no—
420C3#6894511yescharacteristic, complemented
421C3#7073411yescharacteristic, complemented
422C2—21no—
423C2—21no—
424C2—21no—
425C2—362no—
426C2#1059129011yescharacteristic
subgroupG/H
centerC4#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#385
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1858
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#5124C2semidirect
3. #10591141C2semidirect
6. C3×#4558C2semidirect
7. #10589166C2semidirect
34. #5124D3semidirect
38. #4558D3semidirect
369. C32#1858semidirect
420. C3#68945semidirect
421. C3#70734semidirect

Maximal subgroups

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

subgroupindex
#105962162
C3×#51242
#105911412
#105910782
#105910732
C3×#45582
#105891662
#707343
#689453