Finite Group Databasebeta

← #11792283

Subgroups — #11792283

Order 1152.

887 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 887 conjugacy classes of subgroups — too many to draw. Only its 124 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#10595981C211yesmaximal, characteristic
2C2×#63833C212yesmaximal, complemented
3C3×#4973C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6#69694—31nomaximal
7#69009—31nomaximal
8C2×#3828C2212yes—
9C22×C3×Dic6C2211yescharacteristic
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139—22no—
12#64106—22no—
13#64104—22no—
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2212yes—
16C2×#3719—22no—
17#63833—24no—
18#63833—24no—
19C2×#3717—22no—
20C3×C3⋊#95—22no—
21#63570—24no—
22C2×#942—32no—
23C2×#909—32no—
24#5510—31no—
25#5510—31no—
26#5510—61no—
27C3×#391—31no—
28C2×#825—32no—
29#4973D311yescharacteristic, complemented
30C2×#805—32no—
31C3×#343—31no—
32#4530D311yescharacteristic, complemented
33C22×C32×C4D412yes—
34C22×C32×C4C2311yescharacteristic
35C2×#638—22no—
36#3828—22no—
37#3828—22no—
38#3828—22no—
39#3828—22no—
40C2×C4⋊(C3⋊D3)—22no—
41C2×C4⋊(C3⋊D3)D412yes—
42C2×C4×C3⋊D3—22no—
43C2×#634D412yes—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C2×C3×Dic6—22no—
47C2×C3×Dic6—22no—
48C2×C3×Dic6—21no—
49C2×C3×Dic6D412yescomplemented
50C32×C4⋊C4—22no—
51#3752—24no—
52C4⋊(C3⋊Dic3)—22no—
53C3×C4×Dic3—22no—
54C3×#208—22no—
55C3×#208D414yescomplemented
56C2×C3×C3⋊C8—22no—
57#3719—28no—
58#3717—28no—
59#2007—91noSylow
60C22×C3×Q8—31no—
61C2×#235—32no—
62C2×#235—32no—
63C2×#235—62no—
64C22×Dic6C2×D311yescharacteristic
65C2×C3×M16—32no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4C2×D311yescharacteristic
68C2×C3×C4⋊C4C2×D311yescharacteristic
69C2×C3×C42—31no—
70C2×#216—62no—
71#942—64no—
72#942—64no—
73C2×#215—62no—
74#930—64no—
75#930—62no—
76#930—62no—
77C2×C4×Dic3C2×D311yescharacteristic
78C2×#208C2×D312yes—
79#909—64no—
80#909—64no—
81C2×Dic12—62no—
82C2×#204—62no—
83#897—62no—
84#897—62no—
85#897—64no—
86#895—62no—
87#895—62no—
88#895—64no—
89C3×#95—62no—
90C3⋊#95—22no—
91#825—64no—
92#805—64no—
93C23×C32C2×D411yescharacteristic
94C22×C3⋊D3—22no—
95C2×C32×C4—22no—
96C2×C32×C4—42no—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C32×C4C2×D412yes—
100C2×C32×C4#4111yescharacteristic
101#638—42no—
102#638—42no—
103C2×C3⋊Dic3—22no—
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—22no—
106C4⋊(C3⋊D3)—82no—
107C4×C3⋊D3—42no—
108C4×C3⋊D3—42no—
109#634—22no—
110#634—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—41no—
114C2×C3×Dic3—41no—
115C2×C3×Dic3—41no—
116C2×C3×Dic3—41no—
117C3×Dic6—24no—
118C3×Dic6—42no—
119C3×C3⋊C8—24no—
120C2×#137—92no—
121#537—91no—
122C2×#104—92no—
123#391—31no—
124#343—31no—
125C2×C3×Q8—32no—
126C2×C3×Q8—61no—
127C2×C3×Q8—62no—
128C2×C3×Q8—62no—
129C22×C3×C4—22no—
130C22×C3×C4—21no—
131C22×C3×C4—61no—
132C22×C3×C4—61no—
133C22×C3×C4D1212yes—
134C22×C3×C4#6712yes—
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C2×#67—64no—
138C2×#67—62no—
139C2×#67—62no—
140C22×Dic3—21no—
141C22×Dic3—21no—
142#235—62no—
143#235—62no—
144#235—62no—
145#235—62no—
146#235—62no—
147#235—62no—
148#235—62no—
149#235—62no—
150#235—122no—
151#235—122no—
152#235—122no—
153#235—122no—
154C2×D12—32no—
155C2×D12—32no—
156C2×D12—62no—
157C2×D12—64no—
158C2×D12—62no—
159C2×D12—62no—
160C2×C4×D3—64no—
161C2×C4×D3—62no—
162C2×C4×D3—62no—
163C2×Dic6—22no—
164C2×Dic6—22no—
165C2×Dic6—21no—
166C2×Dic6—32no—
167C2×Dic6—32no—
168C2×Dic6—62no—
169C2×Dic6D1212yescomplemented
170C3×M16—34no—
171C3×M16—62no—
172C2×C3×C8—62no—
173C3×C4⋊C4—24no—
174C3×C4⋊C4—22no—
175C3×C4⋊C4—22no—
176C3×C42—62no—
177#216—68no—
178#215—68no—
179(C2×D3)⋊C4—68no—
180(C2×D3)⋊C4—64no—
181(C2×D3)⋊C4—64no—
182C4⋊Dic3—64no—
183C4⋊Dic3—62no—
184C4⋊Dic3—62no—
185C4×Dic3—22no—
186#208—22no—
187#208D1214yescomplemented
188C2×C3⋊C8—22no—
189Dic12—68no—
190#204—68no—
191C22×C32—21no—
192C22×C32—21no—
193C22×C32#12011yescharacteristic
194C22×C32#12111yescharacteristic
195C22×C32#12711yescharacteristic
196C2×C3⋊D3—42no—
197C2×C3⋊D3—42no—
198C2×C3⋊D3—42no—
199C32×C4—42no—
200C32×C4#12012yes—
201C32×C4#12112yes—
202C3⋊Dic3—42no—
203C3×Dic3—42no—
204C3×Dic3—42no—
205C2×#41—92no—
206C22×Q8—31no—
207#137—184no—
208#137—184no—
209C2×Q16—182no—
210C2×SD16—182no—
211C2×M16—32no—
212C22⋊Q8—182no—
213#121—182no—
214#121—182no—
215C2×C4⋊C4D3211yescharacteristic
216C2×C42—31no—
217#104—184no—
218#95—62no—
219C23×C3—21no—
220C23×C3C2×D1211yescharacteristic
221C23×C3C2×#6711yescharacteristic
222C22×D3—64no—
223C22×D3—62no—
224C22×D3—62no—
225C3×Q8—64no—
226C3×Q8—122no—
227C2×C3×C4—24no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—62no—
237C2×C3×C4—62no—
238C2×C3×C4—82no—
239C2×C3×C4—121no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4C2×D1211yescharacteristic
244C2×C3×C4C2×D1212yes—
245C2×C3×C4#23511yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D412yes—
248C2×C3×C4D3×D412yes—
249C2×C3×C4D3×D412yes—
250C2×C3×C4#23911yescharacteristic
251#67—124no—
252#67—124no—
253#67—122no—
254#67—122no—
255#67—122no—
256#67—122no—
257C2×Dic3—22no—
258C2×Dic3—22no—
259C2×Dic3—41no—
260C2×Dic3—41no—
261C2×Dic3—41no—
262C2×Dic3—41no—
263C2×Dic3—64no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266D12—62no—
267D12—62no—
268D12—62no—
269D12—62no—
270D12—122no—
271D12—122no—
272D12—244no—
273D12—242no—
274D12—242no—
275C4×D3—124no—
276C4×D3—124no—
277C4×D3—122no—
278C4×D3—122no—
279C4×D3—122no—
280C4×D3—122no—
281Dic6—24no—
282Dic6—42no—
283Dic6—62no—
284Dic6—62no—
285Dic6—62no—
286Dic6—62no—
287Dic6—122no—
288Dic6—122no—
289C3×C8—64no—
290C3⋊C8—24no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32#39211yescharacteristic
294C2×C32#45511yescharacteristic
295C2×C32#45611yescharacteristic
296C3⋊D3—82no—
297#41—182no—
298#41—182no—
299#41—182no—
300#41—182no—
301C2×Q8—32no—
302C2×Q8—61no—
303C2×Q8—62no—
304C2×Q8—62no—
305C2×Q8—92no—
306C2×D4—92no—
307C2×D4—182no—
308C2×D4—182no—
309C22×C4—61no—
310C22×C4—61no—
311C22×C4—182no—
312C22×C4#62612yes—
313C22×C4C2×D3211yescharacteristic
314Q16—188no—
315SD16—188no—
316M16—34no—
317M16—62no—
318C2×C8—62no—
319C4⋊C4—22no—
320C4⋊C4—182no—
321C22⋊C4—184no—
322C42—62no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3#87411yescharacteristic
333C22×C3#88211yescharacteristic
334C22×C3#89511yescharacteristic
335C22×C3#93011yescharacteristic
336C22×C3#93711yescharacteristic
337C22×C3#94011yescharacteristic
338C2×D3—124no—
339C2×D3—124no—
340C2×D3—124no—
341C2×D3—122no—
342C2×D3—122no—
343C2×D3—122no—
344C2×D3—122no—
345C2×D3—122no—
346C2×D3—122no—
347C3×C4—22no—
348C3×C4—22no—
349C3×C4—44no—
350C3×C4—42no—
351C3×C4—42no—
352C3×C4—122no—
353C3×C4—122no—
354C3×C4#88212yes—
355C3×C4#88212yes—
356C3×C4#88412yes—
357C3×C4#89512yes—
358Dic3—42no—
359Dic3—42no—
360Dic3—124no—
361Dic3—122no—
362Dic3—122no—
363C32#200711yescharacteristic, complemented, Sylow
364C23—182no—
365C23C2×#62611yescharacteristic
366Q8—64no—
367Q8—122no—
368Q8—182no—
369Q8—182no—
370D4—182no—
371D4—182no—
372D4—362no—
373D4—362no—
374D4—722no—
375C2×C4—22no—
376C2×C4—42no—
377C2×C4—62no—
378C2×C4—62no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4—121no—
382C2×C4—121no—
383C2×C4—182no—
384C2×C4—362no—
385C2×C4—362no—
386C2×C4#379911yescharacteristic
387C2×C4D3×D1212yes—
388C2×C4D3×D1211yescharacteristic
389C2×C4#381112yes—
390C8—64no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—21no—
398C2×C3—41no—
399C2×C3—41no—
400C2×C3#467111yescharacteristic
401C2×C3#474611yescharacteristic
402C2×C3#475211yescharacteristic
403C2×C3#496011yescharacteristic
404C2×C3#506111yescharacteristic
405C2×C3#509511yescharacteristic
406D3—244no—
407D3—242no—
408D3—242no—
409C22—21no—
410C22—21no—
411C22—362no—
412C22—362no—
413C22—362no—
414C22#6390911yescharacteristic
415C22#6391111yescharacteristic
416C22#6398111yescharacteristic
417C4—42no—
418C4—122no—
419C4—122no—
420C4—362no—
421C4#6391012yes—
422C4#6392312yes—
423C3—21no—
424C3#6900911yescharacteristic, complemented
425C3#6969411yescharacteristic, complemented
426C2—21no—
427C2—21no—
428C2—722no—
429C2#1059139511yescharacteristic
430C2#1059151411yescharacteristic
431C2#1059165011yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#10595981C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63833C2semidirect
3. C3×#4973C2semidirect
4. C2×#63570C2semidirect
5. C3×#4530C2semidirect
29. #4973D3semidirect
32. #4530D3semidirect
49. C2×C3×Dic6D4semidirect
55. C3×#208D4semidirect
169. C2×Dic6D12semidirect
187. #208D12semidirect
363. C32#2007semidirect
424. C3#69009semidirect
425. C3#69694semidirect

Maximal subgroups

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

subgroupindex
#105959812
C2×#638332
C3×#49732
C2×#635702
C3×#45302
#696943
#690093