Finite Group Databasebeta

← #11922333

Subgroups — #11922333

Order 1152.

618 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊#994C211yesmaximal, characteristic, complemented
2C3×#5923C211yesmaximal, characteristic, complemented
3#10593657C211yesmaximal, characteristic, complemented
4#10593235C212yesmaximal, complemented
5#10593233C212yesmaximal, complemented
6#85526—31nomaximal
7#84005—31nomaximal
8C2×C3×#41⋊C3C2211yescharacteristic
9C3⋊#994—21no—
10C3⋊#994C2212yes—
11C2×C3⋊(#41⋊C3)—21no—
12C3×#986C2211yescharacteristic, complemented
13C3×#985—21no—
14C3×#984C2211yescharacteristic, complemented
15C3×#983—21no—
16#63827—41nomaximal
17C3⋊GU(2,𝔽3)C2212yescomplemented
18C2×#1009D311yescharacteristic, complemented
19C2×#994—31no—
20#5923D311yescharacteristic, complemented
21C3×#575—31no—
22#5830—31no—
23#5822—31no—
24#5429—32no—
25#5428—32no—
26#5423—31no—
27#5423—61no—
28#5236—31no—
29#5202—32no—
30#5202—32no—
31#5198—32no—
32#5198—32no—
33#5139—31no—
34C2×#823—31no—
35C3×#235—41no—
36C2×C3×Dic6—41no—
37C3×#41⋊C3D411yescharacteristic, complemented
38C3×#41⋊C3C2311yescharacteristic
39C2×C3×SL(2,𝔽3)D411yescharacteristic, complemented
40C3⋊(#41⋊C3)—22no—
41C3×GL(2,𝔽3)—21no—
42C3×#226—21no—
43#3748—41no—
44#3718—42no—
45#3715—42no—
46#3019—91noSylow
47C2×C3×#41—31no—
48C2×C3×#41C2×D311yescharacteristic
49#1009—21no—
50#1009—32no—
51#1009—61no—
52#1009C2×D312yes—
53C2×#239—21no—
54C2×D3×D4—61no—
55C2×#235—31no—
56C22×D12—31no—
57#994—32no—
58#994—61no—
59C2×#41⋊C3—21no—
60C2×#41⋊C3—61no—
61C2×#41⋊C3C2×D311yescharacteristic
62#986C2×D311yescharacteristic, complemented
63#985—21no—
64#984C2×D311yescharacteristic, complemented
65#983—21no—
66C3×#137—31no—
67C3×#137—31no—
68C3×#137—61no—
69C3×AGL(1,ℤ/8)—31no—
70C3×AGL(1,ℤ/8)—31no—
71C3×AGL(1,ℤ/8)—61no—
72C3×#135—61no—
73C3×#135—61no—
74C2×C3×M16—31no—
75#951—61no—
76#950—62no—
77#949—61no—
78#947—32no—
79#942—32no—
80#942—121no—
81#940—32no—
82#937—62no—
83#932—32no—
84#930—62no—
85#926—31no—
86C2×#208—31no—
87GU(2,𝔽3)—32no—
88GU(2,𝔽3)—62no—
89#837—32no—
90#837—32no—
91#825—32no—
92#825—32no—
93#823—32no—
94#823—32no—
95C2×C32×C4—41no—
96C3×#67—81no—
97C2×C3×Dic3—81no—
98C3×D12—41no—
99C3×C4×D3—81no—
100C3×Dic6—41no—
101C3×Dic6—42no—
102C3×Dic6—81no—
103C3×SL(2,𝔽3)C2×D411yescharacteristic
104C3⋊(C3⋊C8)—42no—
105C2×H(5,𝔽2)—31no—
106#575—31no—
107#575—91no—
108#535—91no—
109#455—92no—
110#455—92no—
111#453—92no—
112#453—92no—
113#421—91no—
114#421—91no—
115C2×#100—91no—
116C23×D3—32no—
117C3×#41—31no—
118C3×#41—31no—
119C3×#41—61no—
120C3×#41—61no—
121C3×#41—61no—
122C3×#41—61no—
123C3×#41#6711yescharacteristic
124C3×#41C22×D311yescharacteristic
125C2×C3×Q8—31no—
126C2×C3×Q8—121no—
127C2×C3×Q8#6711yescharacteristic
128C2×C3×D4—31no—
129C2×C3×D4—31no—
130C2×C3×D4—61no—
131C22×C3×C4—31no—
132C22×C3×C4—61no—
133C2×#67—61no—
134C2×#67—64no—
135#239—22no—
136#239—62no—
137D3×D4—64no—
138D3×D4—62no—
139D3×D4—62no—
140#235—32no—
141#235—32no—
142#235—41no—
143#235—61no—
144#235—61no—
145C2×D12—31no—
146C2×D12—32no—
147C2×D12—32no—
148C2×D12—61no—
149C2×D12—61no—
150C2×D12—61no—
151C2×C4×D3—61no—
152C2×Dic6S411yescharacteristic
153#41⋊C3—21no—
154#41⋊C3—21no—
155#41⋊C3—62no—
156#41⋊C3#6711yescharacteristic, complemented
157#41⋊C3C22×D311yescharacteristic
158C2×SL(2,𝔽3)—21no—
159C2×SL(2,𝔽3)#6711yescharacteristic, complemented
160GL(2,𝔽3)—21no—
161#226—21no—
162C3×Q16—61no—
163C3×Q16—61no—
164C3×SD16—61no—
165C3×SD16—61no—
166C3×SD16—61no—
167C3×SD16—61no—
168C3×D8—61no—
169C3×D8—61no—
170C3×M16—31no—
171C3×M16—31no—
172C3×M16—61no—
173C2×C3×C8—61no—
174#217—61no—
175#216—62no—
176#216—122no—
177#215—62no—
178#215—122no—
179#214—62no—
180#213—62no—
181(C2×D3)⋊C4—64no—
182C4⋊Dic3—61no—
183C4×Dic3—32no—
184#208—32no—
185#208—61no—
186#208—121no—
187#208—241no—
188C2×C3⋊C8—61no—
189C22×C32—41no—
190C2×C3×D3—81no—
191C32×C4—41no—
192C32×C4—41no—
193C3×Dic3—82no—
194C3×Dic3—81no—
195H(5,𝔽2)—32no—
196H(5,𝔽2)—61no—
197H(5,𝔽2)—92no—
198H(5,𝔽2)—181no—
199C2×#41—31no—
200C2×#41—61no—
201C2×#41—91no—
202C2×#41D3211yescharacteristic
203C22×D4—91no—
204C22×D4—181no—
205#137—31no—
206#137—31no—
207#137—61no—
208#137—92no—
209#137—181no—
210AGL(1,ℤ/8)—31no—
211AGL(1,ℤ/8)—31no—
212AGL(1,ℤ/8)—61no—
213AGL(1,ℤ/8)—92no—
214AGL(1,ℤ/8)—181no—
215#135—61no—
216#135—61no—
217#135—182no—
218C2×M16—31no—
219C2×M16—91no—
220#127—92no—
221#124—92no—
222#121—182no—
223#120—182no—
224#117—91no—
225#104—92no—
226#104—92no—
227#104—92no—
228#104—92no—
229#100—92no—
230#100—92no—
231C23×C3—31no—
232C23×C3—61no—
233C22×D3—34no—
234C22×D3—61no—
235C22×D3—62no—
236C22×D3—242no—
237C3×Q8—31no—
238C3×Q8—61no—
239C3×Q8—61no—
240C3×Q8—122no—
241C3×Q8—241no—
242C3×Q8C2×#6711yescharacteristic
243C3×D4—31no—
244C3×D4—31no—
245C3×D4—61no—
246C3×D4—61no—
247C3×D4—61no—
248C3×D4—121no—
249C3×D4—121no—
250C2×C3×C4—31no—
251C2×C3×C4—31no—
252C2×C3×C4—31no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—41no—
256C2×C3×C4—61no—
257C2×C3×C4—81no—
258C2×C3×C4—121no—
259C2×C3×C4—121no—
260C2×C3×C4—241no—
261C2×C3×C4C2×S411yescharacteristic
262#67—62no—
263#67—62no—
264#67—81no—
265#67—244no—
266C2×Dic3—21no—
267C2×Dic3—62no—
268D12—32no—
269D12—41no—
270D12—62no—
271D12—62no—
272D12—61no—
273C4×D3—62no—
274C4×D3—62no—
275C4×D3—81no—
276Dic6—21no—
277Dic6—41no—
278Dic6C2×S412yes—
279SL(2,𝔽3)—21no—
280SL(2,𝔽3)C2×#6711yescharacteristic
281C3×C8—61no—
282C3×C8—61no—
283C3⋊C8—62no—
284C3⋊C8—122no—
285C3⋊C8—242no—
286C2×C32—41no—
287C2×C32—81no—
288C3×D3—161no—
289C24—92no—
290#41—31no—
291#41—31no—
292#41—61no—
293#41—61no—
294#41—61no—
295#41—61no—
296#41—62no—
297#41—92no—
298#41—92no—
299#41—181no—
300#41—181no—
301#41—182no—
302#41#62511yescharacteristic
303#41C2×D3211yescharacteristic
304C2×Q8—31no—
305C2×Q8—31no—
306C2×Q8#62511yescharacteristic
307C2×D4—31no—
308C2×D4—31no—
309C2×D4—61no—
310C2×D4—92no—
311C2×D4—92no—
312C2×D4—91no—
313C2×D4—181no—
314C2×D4—181no—
315C2×D4—181no—
316C2×D4—181no—
317C2×D4—182no—
318C2×D4—182no—
319C2×D4—184no—
320C2×D4—184no—
321C22×C4—31no—
322C22×C4—61no—
323C22×C4—181no—
324Q16—61no—
325Q16—61no—
326Q16—182no—
327SD16—61no—
328SD16—61no—
329SD16—61no—
330SD16—61no—
331SD16—182no—
332SD16—182no—
333D8—61no—
334D8—61no—
335D8—182no—
336M16—31no—
337M16—31no—
338M16—61no—
339M16—92no—
340M16—181no—
341C2×C8—61no—
342C2×C8—181no—
343C4⋊C4—181no—
344C22⋊C4—184no—
345C22⋊C4—181no—
346C42—92no—
347C22×C3—31no—
348C22×C3—31no—
349C22×C3—41no—
350C22×C3—81no—
351C22×C3—121no—
352C22×C3—122no—
353C22×C3—121no—
354C22×C3GL(2,ℤ/4)11yescharacteristic
355C2×D3—62no—
356C2×D3—81no—
357C2×D3—122no—
358C2×D3—124no—
359C2×D3—242no—
360C3×C4—31no—
361C3×C4—31no—
362C3×C4—41no—
363C3×C4—41no—
364C3×C4—81no—
365C3×C4—81no—
366C3×C4—121no—
367C3×C4—242no—
368C3×C4GL(2,ℤ/4)11yescharacteristic
369C3×C4C22×S411yescharacteristic
370Dic3—22no—
371Dic3—81no—
372Dic3—122no—
373C32—41noSylow
374C23—31no—
375C23—61no—
376C23—94no—
377C23—182no—
378C23—181no—
379C23—722no—
380Q8—31no—
381Q8—32no—
382Q8—61no—
383Q8—61no—
384Q8—61no—
385Q8C2×#62511yescharacteristic
386D4—31no—
387D4—31no—
388D4—61no—
389D4—61no—
390D4—61no—
391D4—92no—
392D4—121no—
393D4—121no—
394D4—182no—
395D4—182no—
396D4—182no—
397D4—182no—
398D4—181no—
399D4—724no—
400C2×C4—31no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—31no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4—182no—
410C2×C4—182no—
411C2×C4—182no—
412C2×C4D3×S411yescharacteristic
413C8—61no—
414C8—61no—
415C8—182no—
416C2×C3—21no—
417C2×C3—41no—
418C2×C3—61no—
419C2×C3—61no—
420C2×C3—81no—
421C2×C3—81no—
422C2×C3—161no—
423C2×C3—241no—
424C2×C3C2×GL(2,ℤ/4)11yescharacteristic
425D3—122no—
426D3—161no—
427C22—31no—
428C22—31no—
429C22—121no—
430C22—122no—
431C22—121no—
432C22—182no—
433C22—362no—
434C22—364no—
435C22—722no—
436C22#6420911yescharacteristic
437C4—31no—
438C4—31no—
439C4—62no—
440C4—121no—
441C4—362no—
442C4#6420911yescharacteristic
443C4C2×D3×S411yescharacteristic
444C3—41no—
445C3—81no—
446C3#8552611yescharacteristic, complemented
447C2—21no—
448C2—61no—
449C2—61no—
450C2—241no—
451C2—362no—
452C2C2×#6420911yescharacteristic
subgroupG/H
centerC2C2×#64209
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C2×D3×S4
FittingC2×C3×#41C2×D3
socleC2×C3C2×GL(2,ℤ/4)
hypercenterC2×C4D3×S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊#994C2semidirect
2. C3×#5923C2semidirect
3. #10593657C2semidirect
4. #10593235C2semidirect
5. #10593233C2semidirect
12. C3×#986C22semidirect
14. C3×#984C22semidirect
17. C3⋊GU(2,𝔽3)C22semidirect
18. C2×#1009D3semidirect
20. #5923D3semidirect
37. C3×#41⋊C3D4semidirect
39. C2×C3×SL(2,𝔽3)D4semidirect
62. #986C2×D3semidirect
64. #984C2×D3semidirect
156. #41⋊C3#67semidirect
159. C2×SL(2,𝔽3)#67semidirect
446. C3#85526semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊#9942
C3×#59232
#105936572
#105932352
#105932332
#855263
#840053
#638274