Finite Group Databasebeta

← #11780648

Subgroups — #11780648

Order 1152.

526 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 72 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
1#10596171C211yesmaximal, characteristic
2C3×#5064C211yesmaximal, characteristic, complemented
3#10590374C211yesmaximal, characteristic, complemented
4#10590294C211yesmaximal, characteristic, complemented
5C3×#4543C211yesmaximal, characteristic, complemented
6#10589087C211yesmaximal, characteristic, complemented
7#10589087C211yesmaximal, characteristic, complemented
8#71392—31nomaximal
9#68373—31nomaximal
10C32×#125C2211yescharacteristic
11#64105—21no—
12#64105—21no—
13#64104—21no—
14#64104—21no—
15#64103—21no—
16#64103—21no—
17#64084C2211yescharacteristic
18#64084C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C2×#3719—21no—
21C2×#3717—21no—
22C3×#808—21no—
23C3×#807—21no—
24C3×#803C2211yescharacteristic
25C3×#803C2211yescharacteristic
26C3×#803C2211yescharacteristic
27#63567—21no—
28#63564—21no—
29#5700—31no—
30#5700—31no—
31#5700—61no—
32C3×#501—31no—
33#5089—31no—
34#5086—31no—
35#5064D311yescharacteristic, complemented
36#4715—31no—
37#4714—31no—
38C3×#330—31no—
39#4543D311yescharacteristic, complemented
40#4464—31no—
41#4464—31no—
42#4464—31no—
43#4464—31no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)D411yescharacteristic
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C2×C4×C3⋊D3—21no—
49C2×C4×C3⋊D3—21no—
50C2×#634D411yescharacteristic
51C2×#634D411yescharacteristic
52C2×C3×Dic6—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C42C2311yescharacteristic
58#3752—21no—
59#3752—21no—
60#3752—21no—
61#3752—21no—
62#3752—21no—
63#3752—21no—
64#3750—21no—
65#3750—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#3719—42no—
72#3717—42no—
73#1661—91noSylow
74C3×C4⋊Q8—31no—
75C3×#125—21no—
76C3×#125C2×D311yescharacteristic
77C3×#125C2×D311yescharacteristic
78C2×#216—61no—
79C2×#215—61no—
80C2×Dic12—61no—
81C2×#204—61no—
82#896—61no—
83#896—61no—
84#896—61no—
85#896—61no—
86#896—62no—
87#896—62no—
88#895—61no—
89#895—61no—
90#895—61no—
91#895—61no—
92#895—62no—
93#895—62no—
94#894—62no—
95#894—62no—
96#894—61no—
97#894—61no—
98#894—61no—
99#894—61no—
100#875—31no—
101#875—31no—
102#875—31no—
103#875—31no—
104#875—61no—
105#875—61no—
106#869C2×D311yescharacteristic
107C3×#107—61no—
108C3×#106—61no—
109C3×#97—31no—
110C3×#97—31no—
111C3×#97—31no—
112#821—61no—
113#816—61no—
114#810—61no—
115#809—61no—
116#808—21no—
117#807—21no—
118#803C2×D311yescharacteristic
119#803C2×D311yescharacteristic
120#803C2×D311yescharacteristic
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C4⋊(C3⋊D3)—41no—
131C4⋊(C3⋊D3)—41no—
132C4⋊(C3⋊D3)—81no—
133C4⋊(C3⋊D3)—81no—
134C4×C3⋊D3—81no—
135C4×C3⋊D3—81no—
136#634—41no—
137#634—41no—
138C2×C3×Dic3—41no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—41no—
144#562—91no—
145#501—31no—
146#497—91no—
147#489—91no—
148#330—31no—
149#329—91no—
150#329—91no—
151C2×C3×Q8—61no—
152C2×D12—31no—
153C2×D12—31no—
154C2×D12—31no—
155C2×D12—31no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—62no—
159C2×D12—62no—
160C2×D12—61no—
161C2×D12—61no—
162C2×D12—61no—
163C2×D12—61no—
164C2×C4×D3—62no—
165C2×C4×D3—62no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×Dic6—21no—
171C2×Dic6—31no—
172C2×Dic6—31no—
173C2×Dic6—31no—
174C2×Dic6—31no—
175C2×Dic6—61no—
176C2×Dic6—61no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—22no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4D1211yescharacteristic
191C3×C4⋊C4D1211yescharacteristic
192C3×C4⋊C4#6711yescharacteristic
193C3×C4⋊C4#6711yescharacteristic
194C3×C42—21no—
195C3×C42C22×D311yescharacteristic
196C3×C42C22×D311yescharacteristic
197#216—122no—
198#215—122no—
199(C2×D3)⋊C4—62no—
200(C2×D3)⋊C4—62no—
201(C2×D3)⋊C4—62no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—61no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210(C2×D3)⋊C4—61no—
211(C2×D3)⋊C4—61no—
212(C2×D3)⋊C4—61no—
213(C2×D3)⋊C4—61no—
214(C2×D3)⋊C4—61no—
215(C2×D3)⋊C4—61no—
216(C2×D3)⋊C4—61no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219Dic3⋊C4—62no—
220Dic3⋊C4—62no—
221Dic3⋊C4—61no—
222Dic3⋊C4—61no—
223Dic3⋊C4—61no—
224Dic3⋊C4—61no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228Dic12—122no—
229#204—122no—
230C22×C32#12011yescharacteristic
231C2×C3⋊D3—41no—
232C2×C3⋊D3—41no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C2×C3⋊D3—41no—
236C2×C3⋊D3—41no—
237C32×C4—21no—
238C32×C4—21no—
239C32×C4—21no—
240C32×C4—41no—
241C32×C4—41no—
242C3⋊Dic3—41no—
243C3⋊Dic3—41no—
244C3×Dic3—81no—
245C2×Q16—181no—
246C2×SD16—181no—
247C4⋊Q8—31no—
248#125D3211yescharacteristic
249#124—91no—
250#124—91no—
251#123—181no—
252#123—181no—
253C22⋊Q8—181no—
254C22⋊Q8—181no—
255#121—181no—
256#121—181no—
257#107—61no—
258#106—61no—
259#103—181no—
260#102—181no—
261#97—31no—
262#97—31no—
263#97—31no—
264C22×D3—62no—
265C22×D3—62no—
266C22×D3—61no—
267C22×D3—61no—
268C22×D3—61no—
269C22×D3—61no—
270C3×Q8—121no—
271C3×Q8—121no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
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—21no—
281C2×C3×C4—121no—
282C2×C3×C4C2×D1211yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288C2×Dic3—41no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293C2×Dic3—61no—
294C2×Dic3—61no—
295D12—121no—
296D12—121no—
297D12—121no—
298D12—121no—
299D12—241no—
300D12—241no—
301D12—242no—
302D12—242no—
303D12—241no—
304D12—241no—
305D12—241no—
306D12—241no—
307C4×D3—242no—
308C4×D3—242no—
309C4×D3—241no—
310C4×D3—241no—
311C4×D3—241no—
312C4×D3—241no—
313Dic6—41no—
314Dic6—41no—
315Dic6—121no—
316Dic6—121no—
317Dic6—121no—
318Dic6—121no—
319Dic6—241no—
320Dic6—241no—
321C3×C8—62no—
322C3×C8—62no—
323C3×C8—121no—
324C3⋊C8—22no—
325C3⋊C8—22no—
326C3⋊C8—41no—
327C2×C32#45311yescharacteristic
328C2×C32#45511yescharacteristic
329C2×C32#45611yescharacteristic
330C3⋊D3—81no—
331C3⋊D3—81no—
332C2×Q8—61no—
333C2×Q8—91no—
334C2×Q8—91no—
335C2×D4—91no—
336C2×D4—91no—
337C2×D4—181no—
338C2×D4—181no—
339C22×C4—181no—
340C22×C4—181no—
341Q16—362no—
342SD16—362no—
343C2×C8—61no—
344C2×C8—61no—
345C2×C8—61no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C4⋊C4#62611yescharacteristic
353C4⋊C4#62611yescharacteristic
354C22⋊C4—181no—
355C22⋊C4—181no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C22⋊C4—181no—
359C22⋊C4—181no—
360C42C2×D3211yescharacteristic
361C22×C3—21no—
362C22×C3#88211yescharacteristic
363C22×C3#93711yescharacteristic
364C2×D3—122no—
365C2×D3—122no—
366C2×D3—122no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—121no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—121no—
374C2×D3—121no—
375C2×D3—121no—
376C2×D3—121no—
377C2×D3—121no—
378C2×D3—121no—
379C2×D3—121no—
380C2×D3—121no—
381C2×D3—121no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—41no—
394C3×C4—41no—
395C3×C4—41no—
396C3×C4—41no—
397C3×C4—241no—
398Dic3—81no—
399Dic3—122no—
400Dic3—122no—
401Dic3—121no—
402Dic3—121no—
403Dic3—121no—
404Dic3—121no—
405C32#166111yescharacteristic, complemented, Sylow
406C23—181no—
407C23—181no—
408Q8—121no—
409Q8—121no—
410Q8—361no—
411Q8—361no—
412D4—361no—
413D4—361no—
414D4—721no—
415D4—721no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—121no—
419C2×C4—181no—
420C2×C4—181no—
421C2×C4—721no—
422C2×C4—721no—
423C2×C4C2×#62611yescharacteristic
424C2×C4#381111yescharacteristic
425C2×C4#381111yescharacteristic
426C8—62no—
427C8—62no—
428C8—121no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3#475211yescharacteristic
433C2×C3#482211yescharacteristic
434C2×C3#482511yescharacteristic
435C2×C3#509511yescharacteristic
436C2×C3#519811yescharacteristic
437C2×C3#520211yescharacteristic
438D3—242no—
439D3—242no—
440D3—241no—
441D3—241no—
442D3—241no—
443D3—241no—
444C22—361no—
445C22—361no—
446C22—361no—
447C22—361no—
448C22—361no—
449C22—361no—
450C22#6398111yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—41no—
455C4—41no—
456C4—241no—
457C4—361no—
458C4—361no—
459C3—21no—
460C3#6837311yescharacteristic, complemented
461C3#7139211yescharacteristic, complemented
462C2—721no—
463C2—721no—
464C2#1059165011yescharacteristic
465C2#1059166711yescharacteristic
466C2#1059169011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32#120
prime radical#10596171C2
hypercenter#125D32
hypocenterC32#1661
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. C3×#5064C2semidirect
3. #10590374C2semidirect
4. #10590294C2semidirect
5. C3×#4543C2semidirect
6. #10589087C2semidirect
7. #10589087C2semidirect
35. #5064D3semidirect
39. #4543D3semidirect
405. C32#1661semidirect
460. C3#68373semidirect
461. C3#71392semidirect

Maximal subgroups

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

subgroupindex
#105961712
C3×#50642
#105903742
#105902942
C3×#45432
#105890872
#713923
#683733