Finite Group Databasebeta

← #11861235

Subgroups — #11861235

Order 1152.

969 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic
2#10594776C212yesmaximal, complemented
3#10592800C211yesmaximal, characteristic, complemented
4C2×C3×#819C211yesmaximal, characteristic, complemented
5#10591110C212yesmaximal, complemented
6#10590920C214yesmaximal, complemented
7#10590919C214yesmaximal, complemented
8#83910—31nomaximal
9#79249—31nomaximal
10C2×C3×#235C2212yes—
11C22×C32×C8C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#208C2212yes—
15C2×C3×Dic12C411yescharacteristic, complemented
16C3×#904C412yescomplemented
17C3×#904C412yescomplemented
18C3×#904C2212yes—
19C3×#904C2212yes—
20C2×C3×D24C411yescharacteristic, complemented
21C2×C3×#204C412yescomplemented
22#63815C2218yescomplemented
23#63814—24no—
24D3×#208—24no—
25#63642C2212yescomplemented
26C8×C3⋊Dic3C2212yescomplemented
27C3×#819C2212yescomplemented
28C3×#819C2212yescomplemented
29#63568C2218yescomplemented
30C2×C3×#135—31no—
31#5819—32no—
32#5745—32no—
33C2×#904D311yescharacteristic
34C2×C3×#108—31no—
35#5236—32no—
36#5197—34no—
37#5196—34no—
38#5139—32no—
39C2×#819D311yescharacteristic, complemented
40#5101—31no—
41#5101—31no—
42#5101—61no—
43#4895—34no—
44#4894—34no—
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67—22no—
47C3×#235—22no—
48C3×#235—22no—
49C3×#235C2×C414yes—
50C3×#235C2314yes—
51C2×C3×D12C2×C412yes—
52C2×C3×C4×D3—22no—
53C2×C3×Dic6C2×C412yes—
54C2×C32×C8C2×C411yescharacteristic
55C2×C32×C8C2×C411yescharacteristic
56C2×C32×C8C2×C411yescharacteristic
57C2×C32×C8C2×C411yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60#3757—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4×C3⋊Dic3C2312yes—
63#3748D412yes—
64#3748D412yes—
65C2×C3⋊(C3⋊C8)C2312yes—
66C3×#208—22no—
67C3×#208C2314yes—
68C2×C3×C3⋊C8—22no—
69C3×Dic12C2×C412yes—
70C3×Dic12C2×C412yes—
71C3×D24C2×C412yes—
72C3×D24C2×C412yes—
73C3×#204C2×C414yes—
74C3×#204C2×C414yes—
75#3711—28no—
76D3×C3⋊C8—28no—
77#2957—91noSylow
78C2×C3×#41—32no—
79C2×#235C2×D312yes—
80C3×#135—32no—
81C3×#135—32no—
82C3×#135—32no—
83C3×#135—32no—
84C2×C3×Q16—31no—
85C2×C3×SD16—32no—
86C2×C3×D8—31no—
87C2×C3×M16—32no—
88C22×C3×C8—21no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C2×D311yescharacteristic
91#948—38no—
92#948—64no—
93#926—31no—
94#926—31no—
95#926—61no—
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—61no—
99C2×#208—64no—
100C2×#208C2×D312yes—
101#907—38no—
102D3×M16—64no—
103C2×Dic12Dic311yescharacteristic, complemented
104#904Dic312yescomplemented
105#904Dic312yescomplemented
106#904C2×D312yes—
107#904C2×D312yes—
108C2×D24Dic311yescharacteristic, complemented
109C2×#204Dic312yescomplemented
110#901—64no—
111C3×#108—32no—
112C3×#108—32no—
113#837—38no—
114#825—38no—
115#819C2×D312yescomplemented
116#819C2×D312yescomplemented
117#815—32no—
118#815—32no—
119#815—62no—
120C8×Dic3—32no—
121C8×Dic3—32no—
122C8×Dic3—62no—
123C23×C32#4111yescharacteristic
124C22×C3×D3—22no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C3×#67—24no—
133C3×#67—24no—
134C2×C3×Dic3—22no—
135C3×D12—22no—
136C3×D12C22×C414yes—
137C3×C4×D3—24no—
138C3×C4×D3—24no—
139C3×Dic6—22no—
140C3×Dic6C22×C414yes—
141C32×C8C22×C411yescharacteristic
142C32×C8C22×C411yescharacteristic
143C32×C8C22×C411yescharacteristic
144C32×C8C22×C411yescharacteristic
145C3⋊(C3⋊C8)C2×D414yes—
146C3×C3⋊C8—24no—
147C2×#135—31no—
148#568—92no—
149#444—94no—
150#443—94no—
151C2×#108—31no—
152#421—92no—
153#405—91no—
154C3×#41—34no—
155C3×#41—34no—
156C3×#41—62no—
157C3×#41—62no—
158C2×C3×Q8—32no—
159C2×C3×D4—32no—
160C2×C3×D4—62no—
161C22×C3×C4—21no—
162C22×C3×C4—62no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—22no—
166#235—22no—
167#235—22no—
168#235C2×Dic314yes—
169#235C22×D314yes—
170C2×D12C2×Dic312yes—
171C2×C4×D3—22no—
172C2×Dic6C2×Dic312yes—
173C3×Q16—32no—
174C3×Q16—32no—
175C3×SD16—34no—
176C3×SD16—34no—
177C3×D8—32no—
178C3×D8—32no—
179C3×M16—34no—
180C3×M16—62no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—62no—
188C2×C3×C8C4×D311yescharacteristic
189C2×C3×C8C4×D311yescharacteristic
190C2×C3×C8C4×D311yescharacteristic
191C2×C3×C8C4×D311yescharacteristic
192C2×C3×C8C2×Dic311yescharacteristic
193C2×C3×C8C2×Dic311yescharacteristic
194C2×C3×C8C2×Dic311yescharacteristic
195C2×C3×C8C2×Dic311yescharacteristic
196C2×C3×C8C22×D311yescharacteristic
197C2×C3×C8C22×D311yescharacteristic
198C2×C3×C8C22×D311yescharacteristic
199C2×C3×C8C22×D311yescharacteristic
200#217—62no—
201#217—61no—
202#217—61no—
203C4⋊Dic3—62no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4×Dic3—32no—
207C4×Dic3—32no—
208C4×Dic3—62no—
209#208—22no—
210#208—32no—
211#208—32no—
212#208—32no—
213#208—32no—
214#208—62no—
215#208—62no—
216#208—68no—
217#208C22×D314yes—
218C2×C3⋊C8—22no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—32no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—68no—
223Dic12C2×Dic312yes—
224Dic12C2×Dic312yes—
225D24C2×Dic312yes—
226D24C2×Dic312yes—
227#204C2×Dic314yes—
228#204C2×Dic314yes—
229ΓL(1,𝔽25)—68no—
230D3×C8—68no—
231C22×C32—41no—
232C22×C32C4×D411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C22×C32C2×#4111yescharacteristic
235C2×C3×D3—24no—
236C2×C3×D3—82no—
237C32×C4C4×D411yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4C23×C411yescharacteristic
240C32×C4C22×D411yescharacteristic
241C3⋊Dic3—42no—
242C3×Dic3—24no—
243C2×#41—32no—
244#135—32no—
245#135—32no—
246#135—32no—
247#135—32no—
248C2×Q16—31no—
249C2×SD16—32no—
250C2×D8—31no—
251#131—98no—
252#131—184no—
253C2×M16—32no—
254C2×M16—91no—
255C2×M16—184no—
256C22×C8D3211yescharacteristic
257#117—91no—
258#108—32no—
259#108—32no—
260#104—98no—
261#97—92no—
262C4×C8—92no—
263C23×C3—21no—
264C23×C3—62no—
265C23×C3#23711yescharacteristic
266C23×C3#23911yescharacteristic
267C22×D3—22no—
268C3×Q8—34no—
269C3×Q8—62no—
270C3×D4—34no—
271C3×D4—64no—
272C3×D4—64no—
273C3×D4—62no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—62no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4#23711yescharacteristic
290C2×C3×C4#23911yescharacteristic
291C2×C3×C4C22×Dic311yescharacteristic
292C2×C3×C4C22×Dic311yescharacteristic
293C2×C3×C4C23×D311yescharacteristic
294C2×C3×C4C23×D311yescharacteristic
295#67—24no—
296#67—24no—
297C2×Dic3—22no—
298C2×Dic3—64no—
299C2×Dic3—62no—
300C2×Dic3—62no—
301D12—22no—
302D12C22×Dic314yes—
303C4×D3—24no—
304C4×D3—24no—
305Dic6—22no—
306Dic6C22×Dic314yes—
307C3×C8—21no—
308C3×C8—21no—
309C3×C8—21no—
310C3×C8—21no—
311C3×C8—64no—
312C3×C8C2×C4×D311yescharacteristic
313C3×C8C2×C4×D311yescharacteristic
314C3×C8C2×C4×D311yescharacteristic
315C3×C8C2×C4×D311yescharacteristic
316C3×C8C22×Dic311yescharacteristic
317C3×C8C22×Dic311yescharacteristic
318C3×C8C22×Dic311yescharacteristic
319C3×C8C22×Dic311yescharacteristic
320C3⋊C8—24no—
321C3⋊C8—34no—
322C3⋊C8—34no—
323C3⋊C8—64no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32C2×C4×D411yescharacteristic
328C3×D3—44no—
329#41—34no—
330#41—34no—
331#41—62no—
332#41—62no—
333C2×Q8—32no—
334C2×D4—32no—
335C2×D4—62no—
336C22×C4—62no—
337C22×C4C2×D3211yescharacteristic
338Q16—32no—
339Q16—32no—
340SD16—34no—
341SD16—34no—
342D8—32no—
343D8—32no—
344M16—34no—
345M16—62no—
346M16—92no—
347M16—92no—
348M16—188no—
349C2×C8—62no—
350C2×C8—92no—
351C2×C8—188no—
352C2×C8D3×Dic311yescharacteristic
353C2×C8D3×Dic311yescharacteristic
354C2×C8D3×Dic311yescharacteristic
355C2×C8D3×Dic311yescharacteristic
356C2×C8C2×D3211yescharacteristic
357C2×C8C2×D3211yescharacteristic
358C4⋊C4—181no—
359C22⋊C4—181no—
360C42—92no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—42no—
367C22×C3—64no—
368C22×C3—242no—
369C22×C3#89311yescharacteristic
370C22×C3#89311yescharacteristic
371C22×C3D4×Dic311yescharacteristic
372C22×C3D4×Dic311yescharacteristic
373C22×C3C2×#23711yescharacteristic
374C22×C3C2×#23911yescharacteristic
375C2×D3—24no—
376C2×D3—82no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—64no—
382C3×C4#89311yescharacteristic
383C3×C4#89311yescharacteristic
384C3×C4D4×Dic311yescharacteristic
385C3×C4D4×Dic311yescharacteristic
386C3×C4C22×C4×D311yescharacteristic
387C3×C4C2×D3×D411yescharacteristic
388C3×C4C2×D3×D411yescharacteristic
389C3×C4C23×Dic311yescharacteristic
390Dic3—24no—
391Dic3—124no—
392Dic3—122no—
393Dic3—122no—
394C32#295711yescharacteristic, complemented, Sylow
395C23—62no—
396C23#379611yescharacteristic
397Q8—34no—
398Q8—62no—
399D4—34no—
400D4—64no—
401D4—64no—
402D4—62no—
403C2×C4—62no—
404C2×C4—64no—
405C2×C4—64no—
406C2×C4—182no—
407C2×C4#379611yescharacteristic
408C2×C4#380211yescharacteristic
409C2×C4#380211yescharacteristic
410C2×C4C2×D3×Dic311yescharacteristic
411C2×C4C2×D3×Dic311yescharacteristic
412C2×C4C22×D3211yescharacteristic
413C8—64no—
414C8—94no—
415C8C2×D3×Dic311yescharacteristic
416C8C2×D3×Dic311yescharacteristic
417C8C2×D3×Dic311yescharacteristic
418C8C2×D3×Dic311yescharacteristic
419C2×C3—22no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—41no—
428C2×C3—41no—
429C2×C3—124no—
430C2×C3C2×#89311yescharacteristic
431C2×C3C2×D4×Dic311yescharacteristic
432D3—44no—
433C22—41no—
434C22—64no—
435C22—242no—
436C22#6389811yescharacteristic
437C22#6389811yescharacteristic
438C22C2×#379611yescharacteristic
439C4—64no—
440C4—362no—
441C4#6389811yescharacteristic
442C4#6389811yescharacteristic
443C4C2×#380211yescharacteristic
444C4C22×D3×Dic311yescharacteristic
445C3—21no—
446C3#7924911yescharacteristic, complemented
447C3#8391011yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—21no—
451C2—124no—
452C2C2×#6389811yescharacteristic
subgroupG/H
centerC4C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC2×C32C2×C4×D4
prime radicalC2×C3×#904C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. #10592800C2semidirect
4. C2×C3×#819C2semidirect
5. #10591110C2semidirect
6. #10590920C2semidirect
7. #10590919C2semidirect
15. C2×C3×Dic12C4semidirect
16. C3×#904C4semidirect
17. C3×#904C4semidirect
20. C2×C3×D24C4semidirect
21. C2×C3×#204C4semidirect
22. #63815C22semidirect
25. #63642C22semidirect
26. C8×C3⋊Dic3C22semidirect
27. C3×#819C22semidirect
28. C3×#819C22semidirect
29. #63568C22semidirect
39. C2×#819D3semidirect
103. C2×Dic12Dic3semidirect
104. #904Dic3semidirect
105. #904Dic3semidirect
108. C2×D24Dic3semidirect
109. C2×#204Dic3semidirect
115. #819C2×D3semidirect
116. #819C2×D3semidirect
394. C32#2957semidirect
446. C3#79249semidirect
447. C3#83910semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
#105947762
#105928002
C2×C3×#8192
#105911102
#105909202
#105909192
#839103
#792493