Finite Group Databasebeta

← #11923091

Subgroups — #11923091

Order 1152.

686 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C3×#5945C211yesmaximal, characteristic
2C2×#64265C211yesmaximal, characteristic, complemented
3#10593664C212yesmaximal, complemented
4#10593662C212yesmaximal, complemented
5#10593657C211yesmaximal, characteristic, complemented
6#85542—33nomaximal
7#84123—31nomaximal
8C3×2−1+4⋊C3—21no—
9C3×2−1+4⋊C3C2211yescharacteristic
10C3×#994C2211yescharacteristic
11C2×C3×#41⋊C3—21no—
12C2×C3×#41⋊C3C2211yescharacteristic
13#64265—21no—
14#64265C2212yescomplemented
15C2×C3⋊#226—21no—
16#64160—41nomaximal
17C3⋊GU(2,𝔽3)C2212yescomplemented
18C3×#585D311yescharacteristic
19#5945D313yes—
20C2×#984—33no—
21#5825—31no—
22C2×#951—31no—
23C2×#951—31no—
24#5430—36no—
25#5428—36no—
26#5423—33no—
27#5246—32no—
28#5246—32no—
29#5242—32no—
30#5242—32no—
31#5237—31no—
32#5236—31no—
33#5236—31no—
34C32×#41—41no—
35C2×#634—41no—
36C3×#41⋊C3—21no—
37C3×#41⋊C3D411yescharacteristic
38C3×#41⋊C3C2311yescharacteristic
39C2×C3×SL(2,𝔽3)—21no—
40C2×C3×SL(2,𝔽3)D411yescharacteristic
41C3⋊#226—22no—
42#3756—42no—
43#3754—42no—
44#3748—41no—
45#3022—91noSylow
46C3×2−1+4—21no—
47C3×2−1+4—31no—
48C3×2−1+4C2×D311yescharacteristic
49C3×H(5,𝔽2)—31no—
50C3×H(5,𝔽2)—61no—
51C3×H(5,𝔽2)C2×D311yescharacteristic
52C2×C3×#41—21no—
53C2×C3×#41—31no—
54C2×C3×#41—31no—
55C2×C3×#41—61no—
56C2×C3×#41C2×D311yescharacteristic
57C22×Dic6—31no—
582−1+4⋊C3—23no—
592−1+4⋊C3C2×D313yes—
60#994C2×D313yes—
61C2×#41⋊C3—23no—
62C2×#41⋊C3C2×D313yes—
63#984—36no—
64#984—63no—
65C2×#226—63no—
66#951—32no—
67#951—32no—
68#951—32no—
69#951—32no—
70#951—61no—
71#951—61no—
72#951—61no—
73#951—61no—
74#951—123no—
75#944—32no—
76C2×#216—61no—
77C2×#216—61no—
78#936—32no—
79#935—62no—
80C2×#214—61no—
81C2×#214—61no—
82#926—31no—
83#924—62no—
84C2×#208—31no—
85C2×#208—31no—
86GU(2,𝔽3)—36no—
87#837—32no—
88#837—32no—
89#837—32no—
90#837—32no—
91#836—32no—
92#833—32no—
93C32×Q8—41no—
94C32×D4—41no—
95C32×D4—81no—
96C2×C32×C4—41no—
97C2×C32×C4—81no—
98C2×C3⋊Dic3—81no—
99#634—42no—
100#634—81no—
101C3×SL(2,𝔽3)C2×D411yescharacteristic
102C3⋊(C3⋊C8)—42no—
103#585C3⋊D311yescharacteristic
104C2×#137—91no—
105C2×#137—91no—
106#536—91no—
107#456—92no—
108#456—92no—
109#455—92no—
110#455—92no—
111#421—91no—
112#421—91no—
113#413—91no—
114C3×#41—21no—
115C3×#41—31no—
116C3×#41—31no—
117C3×#41—31no—
118C3×#41—31no—
119C3×#41—31no—
120C3×#41—43no—
121C3×#41—61no—
122C3×#41—61no—
123C3×#41—61no—
124C3×#41—61no—
125C3×#41—62no—
126C3×#41—61no—
127C3×#41—61no—
128C3×#41—61no—
129C3×#41—61no—
130C3×#41#6711yescharacteristic
131C3×#41S411yescharacteristic
132C3×#41C22×D311yescharacteristic
133C2×C3×Q8—21no—
134C2×C3×Q8—31no—
135C2×C3×Q8—31no—
136C2×C3×Q8—61no—
137C2×C3×Q8#6711yescharacteristic
138C2×C3×D4—31no—
139C2×C3×D4—31no—
140C2×C3×D4—31no—
141C2×C3×D4—32no—
142C2×C3×D4—61no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—62no—
146C22×C3×C4—31no—
147C22×C3×C4—32no—
148C22×C3×C4—61no—
149C22×Dic3—61no—
150C2×Dic6—32no—
151C2×Dic6—61no—
152C2×Dic6—61no—
153C2×Dic6—61no—
154C2×Dic6—61no—
155C2×Dic6—61no—
156C2×Dic6—123no—
157#41⋊C3—23no—
158#41⋊C3#6713yes—
159#41⋊C3C22×D313yes—
160C2×SL(2,𝔽3)—23no—
161C2×SL(2,𝔽3)#6713yes—
162#226—66no—
163#217—64no—
164#217—61no—
165#216—62no—
166#216—62no—
167#216—62no—
168#216—62no—
169#216—126no—
170#214—62no—
171#214—62no—
172#214—62no—
173#214—62no—
174#214—126no—
175C4⋊Dic3—61no—
176Dic3⋊C4—64no—
177C4×Dic3—32no—
178#208—32no—
179#208—32no—
180#208—61no—
181#208—61no—
182#208—123no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C22×C32—41no—
186C22×C32—81no—
187C32×C4—41no—
188C32×C4—41no—
189C32×C4—81no—
190C3⋊Dic3—82no—
1912−1+4—21no—
1922−1+4—31no—
1932−1+4C2×C3⋊D311yescharacteristic
194H(5,𝔽2)—31no—
195H(5,𝔽2)—61no—
196H(5,𝔽2)C2×C3⋊D311yescharacteristic
197C2×#41—21no—
198C2×#41—31no—
199C2×#41—31no—
200C2×#41—61no—
201C2×#41C2×C3⋊D311yescharacteristic
202C22×Q8—91no—
203#137—92no—
204#137—92no—
205#137—92no—
206#137—92no—
207#137—181no—
208#137—181no—
209#137—181no—
210#137—181no—
211C2×Q16—181no—
212C2×Q16—181no—
213C2×SD16—181no—
214C2×SD16—181no—
215C2×M16—91no—
216C2×M16—91no—
217C4⋊Q8—92no—
218#124—92no—
219#123—182no—
220C22⋊Q8—182no—
221#117—91no—
222#104—92no—
223#104—92no—
224#104—92no—
225#104—92no—
226#101—92no—
227#100—92no—
228C23×C3—31no—
229C23×C3—32no—
230C23×C3—61no—
231C3×Q8—31no—
232C3×Q8—31no—
233C3×Q8—43no—
234C3×Q8—61no—
235C3×Q8—61no—
236C3×Q8C2×#6711yescharacteristic
237C3×Q8C2×S411yescharacteristic
238C3×D4—21no—
239C3×D4—31no—
240C3×D4—31no—
241C3×D4—31no—
242C3×D4—43no—
243C3×D4—61no—
244C3×D4—61no—
245C3×D4—61no—
246C3×D4—61no—
247C3×D4—61no—
248C3×D4—62no—
249C3×D4—61no—
250C3×D4—83no—
251C3×D4C2×S411yescharacteristic
252C2×C3×C4—21no—
253C2×C3×C4—31no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—31no—
258C2×C3×C4—32no—
259C2×C3×C4—43no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—62no—
264C2×C3×C4—61no—
265C2×C3×C4—83no—
266C2×C3×C4C2×S411yescharacteristic
267C2×Dic3—62no—
268C2×Dic3—62no—
269C2×Dic3—121no—
270C2×Dic3—121no—
271C2×Dic3—243no—
272Dic6—62no—
273Dic6—62no—
274Dic6—126no—
275Dic6—121no—
276Dic6—121no—
277Dic6—243no—
278SL(2,𝔽3)C2×#6713yes—
279C3⋊C8—62no—
280C3⋊C8—62no—
281C3⋊C8—126no—
282C2×C32—41no—
283C2×C32—81no—
284C2×C32—161no—
285#41—21no—
286#41—31no—
287#41—31no—
288#41—31no—
289#41—31no—
290#41—31no—
291#41—61no—
292#41—61no—
293#41—61no—
294#41—61no—
295#41—62no—
296#41—61no—
297#41—61no—
298#41—61no—
299#41—61no—
300#41#63811yescharacteristic
301#41C3⋊S411yescharacteristic
302#41C22×C3⋊D311yescharacteristic
303C2×Q8—21no—
304C2×Q8—31no—
305C2×Q8—31no—
306C2×Q8—61no—
307C2×Q8—92no—
308C2×Q8—181no—
309C2×Q8—181no—
310C2×Q8—181no—
311C2×Q8—181no—
312C2×Q8—181no—
313C2×Q8#63811yescharacteristic
314C2×D4—31no—
315C2×D4—31no—
316C2×D4—31no—
317C2×D4—32no—
318C2×D4—61no—
319C2×D4—61no—
320C2×D4—61no—
321C2×D4—62no—
322C22×C4—31no—
323C22×C4—32no—
324C22×C4—61no—
325C22×C4—181no—
326Q16—182no—
327Q16—182no—
328Q16—182no—
329Q16—182no—
330SD16—182no—
331SD16—182no—
332SD16—182no—
333SD16—182no—
334M16—92no—
335M16—92no—
336M16—181no—
337M16—181no—
338C2×C8—181no—
339C2×C8—181no—
340C4⋊C4—181no—
341C4⋊C4—184no—
342C22⋊C4—181no—
343C22⋊C4—184no—
344C42—92no—
345C22×C3—21no—
346C22×C3—31no—
347C22×C3—31no—
348C22×C3—43no—
349C22×C3—61no—
350C22×C3—83no—
351C22×C3—121no—
352C22×C3—122no—
353C22×C3—241no—
354C22×C3GL(2,ℤ/4)11yescharacteristic
355C3×C4—21no—
356C3×C4—31no—
357C3×C4—31no—
358C3×C4—43no—
359C3×C4—43no—
360C3×C4—61no—
361C3×C4—83no—
362C3×C4GL(2,ℤ/4)11yescharacteristic
363C3×C4C22×S411yescharacteristic
364Dic3—122no—
365Dic3—122no—
366Dic3—246no—
367C32—41noSylow
368C23—31no—
369C23—32no—
370C23—61no—
371Q8—31no—
372Q8—31no—
373Q8—61no—
374Q8—61no—
375Q8—182no—
376Q8—182no—
377Q8—361no—
378Q8—361no—
379Q8C2×#63811yescharacteristic
380Q8C2×C3⋊S411yescharacteristic
381D4—21no—
382D4—31no—
383D4—31no—
384D4—31no—
385D4—61no—
386D4—61no—
387D4—61no—
388D4—61no—
389D4—61no—
390D4—62no—
391D4—61no—
392D4C2×C3⋊S411yescharacteristic
393C2×C4—21no—
394C2×C4—31no—
395C2×C4—31no—
396C2×C4—31no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—32no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—62no—
404C2×C4—61no—
405C2×C4—182no—
406C2×C4—182no—
407C2×C4—361no—
408C2×C4—361no—
409C2×C4C2×C3⋊S411yescharacteristic
410C8—182no—
411C8—182no—
412C2×C3—21no—
413C2×C3—41no—
414C2×C3—43no—
415C2×C3—61no—
416C2×C3—61no—
417C2×C3—83no—
418C2×C3—121no—
419C2×C3—163no—
420C2×C3C2×GL(2,ℤ/4)11yescharacteristic
421C22—21no—
422C22—31no—
423C22—31no—
424C22—61no—
425C22—121no—
426C22—122no—
427C22—241no—
428C22#6426911yescharacteristic
429C4—21no—
430C4—31no—
431C4—31no—
432C4—61no—
433C4—362no—
434C4—362no—
435C4#6426911yescharacteristic
436C4C22×C3⋊S411yescharacteristic
437C3—43no—
438C3#8554211yescharacteristic, complemented
439C2—21no—
440C2—41no—
441C2—61no—
442C2—61no—
443C2—121no—
444C2C2×#6426911yescharacteristic
subgroupG/H
centerC2C2×#64269
commutator, cosocleC3×#41⋊C3C23
FrattiniC4C22×C3⋊S4
FittingC3×#585D3
socleC2×C3C2×GL(2,ℤ/4)
prime radicalC3×#5945C2
hypercenter#41C3⋊S4
hypocenterC3×SL(2,𝔽3)C2×D4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C2×#64265C2semidirect
3. #10593664C2semidirect
4. #10593662C2semidirect
5. #10593657C2semidirect
14. #64265C22semidirect
17. C3⋊GU(2,𝔽3)C22semidirect
438. C3#85542semidirect

Maximal subgroups

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

subgroupindex
C3×#59452
C2×#642652
#105936642
#105936622
#105936572
#855423
#841233
#641604