Finite Group Databasebeta

← #11784135

Subgroups — #11784135

Order 1152.

639 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63814C211yesmaximal, characteristic
2C2×C3×#805C211yesmaximal, characteristic
3C2×C3×#803C211yesmaximal, characteristic, complemented
4#10591084C211yesmaximal, characteristic
5#10591059C211yesmaximal, characteristic, complemented
6#10589389C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#70370—31nomaximal
9#69839—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3711—21no—
18#63814—22no—
19#63814C414yescomplemented
20C2×D3×C3⋊C8—21no—
21C3×#805C414yescomplemented
22C3×#803—22no—
23#63566C412yescomplemented
24#63563C412yescomplemented
25#63555—21no—
26#63553—21no—
27C2×#948—31no—
28C2×#901—31no—
29C2×C3×#104—31no—
30C2×C3×#97—31no—
31#5233—31no—
32#5122—31no—
33#5113—31no—
34#5101—31no—
35C2×#805D311yescharacteristic
36C2×#803D311yescharacteristic, complemented
37#4558—31no—
38#4552—31no—
39#4523—31no—
40#4523—31no—
41#4523—61no—
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—21no—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235C2×C412yes—
48C3×#235C2×C412yes—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6C2×C411yescharacteristic
52C32×C42—21no—
53C32×C42C2×C412yes—
54#3757—21no—
55C4⋊(C3⋊Dic3)C2×C412yes—
56C4×C3⋊Dic3—21no—
57#3748—21no—
58#3748C2×C412yes—
59C2×C3⋊(C3⋊C8)—21no—
60C3×#208—21no—
61C3×#208C2×C412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69C2×C3×C3⋊C8D412yes—
70#3711—24no—
71D3×C3⋊C8—24no—
72#1765—91noSylow
73C2×C3×#41—31no—
74C2×#235C2×D311yescharacteristic
75C2×C3×M16—31no—
76C22×C3×C8—31no—
77C22×C3×C8—31no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C2×D311yescharacteristic
81#948—34no—
82#948—62no—
83#926—31no—
84#926—31no—
85#926—61no—
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—61no—
89C2×#208—61no—
90C2×#208C2×D311yescharacteristic
91C22×C3⋊C8—61no—
92C22×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊C8C2×D311yescharacteristic
94#901—34no—
95#901—62no—
96C2×ΓL(1,𝔽25)—61no—
97C2×D3×C8—61no—
98C3×#104—34no—
99C3×#97—62no—
100#835—32no—
101#832—32no—
102#821—32no—
103#816—32no—
104#815—61no—
105#815—61no—
106C8×Dic3—61no—
107C8×Dic3—61no—
108#805Dic314yescomplemented
109#803—22no—
110C23×C32#4111yescharacteristic
111C22×C3×D3—21no—
112C2×C32×C4—22no—
113C2×C32×C4—42no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—22no—
121C3×#67—22no—
122C3×#67—22no—
123C2×C3×Dic3—21no—
124C3×D12—21no—
125C3×D12C4212yes—
126C3×C4×D3—22no—
127C3×C4×D3—22no—
128C3×Dic6—21no—
129C3×Dic6C4212yes—
130C3⋊(C3⋊C8)—22no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8C22⋊C412yes—
134C3×C3⋊C8C22⋊C412yes—
135C2×#131—91no—
136C2×#104—31no—
137#416—91no—
138#405—91no—
139C2×#97—31no—
140#341—91no—
141#339—91no—
142C3×#41—32no—
143C3×#41—32no—
144C3×#41—61no—
145C3×#41—61no—
146C2×C3×Q8—31no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—41no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C2×#67—21no—
157#235—21no—
158#235—21no—
159#235C4×D312yes—
160#235C2×Dic312yes—
161C2×D12C4×D311yescharacteristic
162C2×C4×D3—21no—
163C2×Dic6C4×D311yescharacteristic
164C3×M16—32no—
165C3×M16—61no—
166C2×C3×C8—32no—
167C2×C3×C8—31no—
168C2×C3×C8—31no—
169C2×C3×C8—32no—
170C2×C3×C8—32no—
171C2×C3×C8—61no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C3×C42—21no—
175C3×C42—21no—
176C3×C42—22no—
177C3×C42—41no—
178C3×C42C4×D312yes—
179C3×C42C2×Dic312yes—
180#217—61no—
181#217—61no—
182#217—121no—
183C4⋊Dic3—32no—
184C4⋊Dic3—32no—
185C4⋊Dic3—62no—
186C4×Dic3—61no—
187C4×Dic3—61no—
188C4×Dic3—121no—
189#208—21no—
190#208—32no—
191#208—32no—
192#208—62no—
193#208—61no—
194#208—61no—
195#208—64no—
196#208—121no—
197#208C2×Dic312yes—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—64no—
204C2×C3⋊C8—121no—
205C2×C3⋊C8C4×D312yes—
206C2×C3⋊C8C4×D312yes—
207C2×C3⋊C8D1211yescharacteristic
208C2×C3⋊C8D1211yescharacteristic
209C2×C3⋊C8#6712yes—
210ΓL(1,𝔽25)—64no—
211D3×C8—64no—
212C22×C32—22no—
213C22×C32#11711yescharacteristic
214C22×C32C4×D411yescharacteristic
215C22×C32C4×D411yescharacteristic
216C2×C3×D3—22no—
217C2×C3×D3—42no—
218C32×C4—42no—
219C32×C4C2×C4211yescharacteristic
220C32×C4C2×C22⋊C411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C32×C4C4×D411yescharacteristic
223C3⋊Dic3—42no—
224C3×Dic3—22no—
225C2×#41—31no—
226#131—94no—
227#131—182no—
228C2×M16—31no—
229C2×M16—91no—
230C2×M16—181no—
231C22×C8—31no—
232C22×C8—31no—
233C22×C8—181no—
234#117—91no—
235C2×C42D3211yescharacteristic
236#104—34no—
237#103—92no—
238#102—92no—
239#97—62no—
240#97—181no—
241C4×C8—181no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3#23511yescharacteristic
245C23×C3#23711yescharacteristic
246C22×D3—21no—
247C3×Q8—32no—
248C3×Q8—61no—
249C3×D4—32no—
250C3×D4—62no—
251C3×D4—62no—
252C3×D4—61no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—42no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—44no—
265C2×C3×C4—61no—
266C2×C3×C4—62no—
267C2×C3×C4—62no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4C2×D1211yescharacteristic
274C2×C3×C4#23511yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4C22×Dic311yescharacteristic
279C2×C3×C4C2×#6711yescharacteristic
280#67—22no—
281#67—22no—
282C2×Dic3—21no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—122no—
286D12—21no—
287D12C4×Dic312yes—
288C4×D3—22no—
289C4×D3—22no—
290Dic6—21no—
291Dic6C4×Dic312yes—
292C3×C8—32no—
293C3×C8—32no—
294C3×C8—62no—
295C3×C8—62no—
296C3⋊C8—22no—
297C3⋊C8—22no—
298C3⋊C8—62no—
299C3⋊C8—62no—
300C3⋊C8—122no—
301C3⋊C8(C2×D3)⋊C412yes—
302C3⋊C8(C2×D3)⋊C412yes—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32C4×C22⋊C411yescharacteristic
306C2×C32#44412yes—
307C3×D3—42no—
308#41—32no—
309#41—32no—
310#41—61no—
311#41—61no—
312C2×Q8—31no—
313C2×D4—31no—
314C2×D4—61no—
315C22×C4—21no—
316C22×C4—61no—
317C22×C4C2×D3211yescharacteristic
318M16—32no—
319M16—61no—
320M16—92no—
321M16—184no—
322M16—181no—
323C2×C8—32no—
324C2×C8—31no—
325C2×C8—31no—
326C2×C8—32no—
327C2×C8—32no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—61no—
331C2×C8—184no—
332C2×C8—181no—
333C4⋊C4—92no—
334C22⋊C4—181no—
335C42—21no—
336C42—181no—
337C42D3×Dic312yes—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—42no—
344C22×C3—62no—
345C22×C3—122no—
346C22×C3#87211yescharacteristic
347C22×C3C4×D1211yescharacteristic
348C22×C3#87711yescharacteristic
349C22×C3#67⋊C411yescharacteristic
350C22×C3C4×#6711yescharacteristic
351C22×C3D4×Dic311yescharacteristic
352C2×D3—22no—
353C2×D3—42no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—42no—
359C3×C4—42no—
360C3×C4—44no—
361C3×C4—62no—
362C3×C4C42×D311yescharacteristic
363C3×C4C4×D1211yescharacteristic
364C3×C4D3×C22⋊C411yescharacteristic
365C3×C4#67⋊C411yescharacteristic
366C3×C4C2×C4×Dic311yescharacteristic
367C3×C4C2×(C2×D3)⋊C411yescharacteristic
368C3×C4C4×#6711yescharacteristic
369C3×C4D4×Dic311yescharacteristic
370Dic3—22no—
371Dic3—122no—
372Dic3—122no—
373Dic3—242no—
374C32#176511yescharacteristic, complemented, Sylow
375C23—61no—
376C23#380411yescharacteristic
377Q8—32no—
378Q8—61no—
379D4—32no—
380D4—62no—
381D4—62no—
382D4—61no—
383C2×C4—22no—
384C2×C4—42no—
385C2×C4—61no—
386C2×C4—62no—
387C2×C4—62no—
388C2×C4—182no—
389C2×C4#379511yescharacteristic
390C2×C4C4×D3211yescharacteristic
391C2×C4C4×D3211yescharacteristic
392C2×C4D3×D1211yescharacteristic
393C2×C4C2×D3×Dic311yescharacteristic
394C2×C4D3×#6711yescharacteristic
395C8—32no—
396C8—32no—
397C8—62no—
398C8—62no—
399C8—182no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—22no—
406C2×C3—41no—
407C2×C3—41no—
408C2×C3—122no—
409C2×C3#471712yes—
410C2×C3#482312yes—
411C2×C3C4×(C2×D3)⋊C411yescharacteristic
412C2×C3Dic3×C22⋊C411yescharacteristic
413D3—42no—
414C22—22no—
415C22—62no—
416C22—122no—
417C22#6387711yescharacteristic
418C22#6388011yescharacteristic
419C22Dic3×#6711yescharacteristic
420C4—42no—
421C4—62no—
422C4—362no—
423C4C4×D3×Dic311yescharacteristic
424C4#6387911yescharacteristic
425C4Dic3×D1211yescharacteristic
426C4D3×(C2×D3)⋊C411yescharacteristic
427C3—21no—
428C3#6983911yescharacteristic, complemented
429C3#7037011yescharacteristic, complemented
430C2—21no—
431C2—21no—
432C2—122no—
433C2#1059034212yes—
434C2Dic3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1765
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C2×C3×#803C2semidirect
5. #10591059C2semidirect
6. #10589389C2semidirect
7. #10589166C2semidirect
19. #63814C4semidirect
21. C3×#805C4semidirect
23. #63566C4semidirect
24. #63563C4semidirect
36. C2×#803D3semidirect
108. #805Dic3semidirect
374. C32#1765semidirect
428. C3#69839semidirect
429. C3#70370semidirect

Maximal subgroups

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

subgroupindex
C2×#638142
C2×C3×#8052
C2×C3×#8032
#105910842
#105910592
#105893892
#105891662
#703703
#698393