Finite Group Databasebeta

← #11778449

Subgroups — #11778449

Order 1152.

733 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 733 conjugacy classes of subgroups — too many to draw. Only its 88 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#10595964C211yesmaximal, characteristic
2C3×#4953C211yesmaximal, characteristic, complemented
3#10591133C212yesmaximal, complemented
4C3×#4525C211yesmaximal, characteristic, complemented
5#10589151C212yesmaximal, complemented
6#69708—31nomaximal
7#68110—31nomaximal
8C22×#638—21no—
9C2×C32×C22⋊C4C2211yescharacteristic
10#64139—21no—
11#64139C2212yes—
12#64095—22no—
13#64091—22no—
14C2×C3×#217—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
16C3×C3⋊#95—21no—
17C3×C3⋊#95C2211yescharacteristic, complemented
18C3×#830C2212yescomplemented
19#63575—22no—
20#63564—22no—
21#5493—31no—
22#5493—31no—
23#5493—61no—
24C3×#397—31no—
25#4967—32no—
26#4953D311yescharacteristic, complemented
27#4736—32no—
28C3×#323—31no—
29#4525D311yescharacteristic, complemented
30#4470—32no—
31#4451—32no—
32C24×C32D411yescharacteristic
33C23×C3⋊D3—21no—
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C2×#638—22no—
37C2×#638—22no—
38C2×#638—42no—
39C2×#638—42no—
40C22×C3⋊Dic3—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)D412yes—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C32×C22⋊C4—22no—
46#3752—22no—
47#3752—22no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D412yes—
50C3×#217—42no—
51C3×C4⋊Dic3—22no—
52C2×C3×C3⋊C8—22no—
53#1607—91noSylow
54C22×#67—62no—
55C22×#67—61no—
56C22×#67—61no—
57C2×C3×C4⋊C4—31no—
58C2×C3×C22⋊C4—21no—
59C2×C3×C22⋊C4—61no—
60C2×C3×C22⋊C4C2×D311yescharacteristic
61C2×C3×C22⋊C4C2×D311yescharacteristic
62C2×#217—21no—
63#930—32no—
64#930—32no—
65#930—62no—
66#930—62no—
67#930—61no—
68#930—61no—
69C2×C4⋊Dic3C2×D311yescharacteristic, complemented
70#886—62no—
71#886—62no—
72#886—64no—
73#882—62no—
74#882—62no—
75#882—64no—
76C3×C22⋊C8—32no—
77C3×#95—31no—
78C3×#95—61no—
79C3⋊#95—21no—
80C3⋊#95C2×D311yescharacteristic, complemented
81#830C2×D312yescomplemented
82#821—62no—
83#818—62no—
84#809—62no—
85#807—62no—
86C23×C32—21no—
87C23×C32—21no—
88C23×C32—41no—
89C23×C32—41no—
90C23×C32D812yes—
91C23×C32C2×D411yescharacteristic
92C22×C3⋊D3—22no—
93C22×C3⋊D3—42no—
94C22×C3⋊D3—81no—
95C22×C3⋊D3—81no—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D412yes—
100#638—44no—
101#638—42no—
102#638—42no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—42no—
105C4⋊(C3⋊D3)—42no—
106C4⋊(C3⋊D3)—81no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C2×C3×Dic3—41no—
110C2×C3×Dic3—41no—
111C2×C3×Dic3—41no—
112C2×C3×Dic3—41no—
113C3×C3⋊C8—42no—
114#534—91no—
115#480—92no—
116#397—31no—
117#327—92no—
118#323—31no—
119C24×C3—21no—
120C24×C3D1211yescharacteristic
121C24×C3#6711yescharacteristic
122C23×D3—62no—
123C23×D3—61no—
124C23×D3—61no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—61no—
128C22×C3×C4—61no—
129C22×C3×C4D1211yescharacteristic
130C22×C3×C4#6711yescharacteristic
131C22×C3×C4C22×D311yescharacteristic
132C22×C3×C4C22×D311yescharacteristic
133C2×#67—64no—
134C2×#67—62no—
135C2×#67—62no—
136C2×#67—64no—
137C2×#67—62no—
138C2×#67—62no—
139C2×#67—124no—
140C2×#67—122no—
141C2×#67—122no—
142C2×#67—124no—
143C2×#67—122no—
144C2×#67—122no—
145C22×Dic3—21no—
146C22×Dic3—21no—
147C22×Dic3—62no—
148C22×Dic3—61no—
149C22×Dic3—61no—
150C2×D12—32no—
151C2×D12—32no—
152C2×D12—62no—
153C2×D12—62no—
154C2×D12—61no—
155C2×D12—61no—
156C2×C3×C8—62no—
157C3×C4⋊C4—62no—
158C3×C22⋊C4—24no—
159C3×C22⋊C4—22no—
160C3×C22⋊C4—22no—
161C3×C22⋊C4—122no—
162#217—42no—
163(C2×D3)⋊C4—64no—
164(C2×D3)⋊C4—62no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—62no—
168(C2×D3)⋊C4—62no—
169C4⋊Dic3—22no—
170C4⋊Dic3—32no—
171C4⋊Dic3—32no—
172C4⋊Dic3—62no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C2×C3⋊C8—22no—
177C22×C32—22no—
178C22×C32—21no—
179C22×C32—21no—
180C22×C32—41no—
181C22×C32—41no—
182C22×C32—42no—
183C22×C32—81no—
184C22×C32#12011yescharacteristic
185C22×C32C2×D811yescharacteristic
186C22×C32AGL(1,ℤ/8)11yescharacteristic
187C2×C3⋊D3—42no—
188C2×C3⋊D3—42no—
189C2×C3⋊D3—42no—
190C2×C3⋊D3—84no—
191C32×C4—22no—
192C32×C4—41no—
193C3⋊Dic3—42no—
194C3×Dic3—81no—
195C3×Dic3—81no—
196C22×D4—181no—
197#123—182no—
198#121—92no—
199#121—181no—
200#120—182no—
201C2×C4⋊C4—31no—
202C2×C22⋊C4—61no—
203C2×C22⋊C4D3211yescharacteristic
204#107—182no—
205#102—182no—
206C22⋊C8—32no—
207#95—31no—
208#95—61no—
209C23×C3—22no—
210C23×C3—22no—
211C23×C3—21no—
212C23×C3—21no—
213C23×C3—21no—
214C23×C3—21no—
215C23×C3—22no—
216C23×C3—21no—
217C23×C3—41no—
218C23×C3—41no—
219C23×C3—41no—
220C23×C3—41no—
221C23×C3—81no—
222C23×C3—81no—
223C23×C3D2412yes—
224C23×C3#21312yes—
225C23×C3C2×D1211yescharacteristic
226C23×C3C2×#6711yescharacteristic
227C22×D3—64no—
228C22×D3—62no—
229C22×D3—62no—
230C22×D3—124no—
231C22×D3—122no—
232C22×D3—122no—
233C22×D3—242no—
234C22×D3—242no—
235C22×D3—241no—
236C22×D3—241no—
237C22×D3—241no—
238C22×D3—241no—
239C2×C3×C4—22no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—22no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—41no—
246C2×C3×C4—41no—
247C2×C3×C4—81no—
248C2×C3×C4—81no—
249C2×C3×C4—121no—
250C2×C3×C4—121no—
251C2×C3×C4—121no—
252C2×C3×C4—121no—
253C2×C3×C4—121no—
254C2×C3×C4—121no—
255C2×C3×C4D3×D412yes—
256C2×C3×C4D3×D412yes—
257#67—128no—
258#67—124no—
259#67—124no—
260#67—124no—
261#67—124no—
262#67—122no—
263#67—122no—
264#67—122no—
265#67—122no—
266C2×Dic3—41no—
267C2×Dic3—41no—
268C2×Dic3—41no—
269C2×Dic3—41no—
270C2×Dic3—41no—
271C2×Dic3—41no—
272C2×Dic3—64no—
273C2×Dic3—62no—
274C2×Dic3—62no—
275C2×Dic3—124no—
276C2×Dic3—122no—
277C2×Dic3—122no—
278D12—122no—
279D12—122no—
280D12—242no—
281D12—242no—
282D12—241no—
283D12—241no—
284C3×C8—122no—
285C3⋊C8—42no—
286C2×C32—21no—
287C2×C32—21no—
288C2×C32—42no—
289C2×C32#44711yescharacteristic
290C2×C32#45511yescharacteristic
291C2×C32#45811yescharacteristic
292C3⋊D3—82no—
293C24—181no—
294C24#62611yescharacteristic
295C2×D4—92no—
296C2×D4—181no—
297C2×D4—182no—
298C2×D4—182no—
299C2×D4—362no—
300C2×D4—362no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4—181no—
304C22×C4#62611yescharacteristic
305C22×C4C2×D3211yescharacteristic
306C2×C8—62no—
307C4⋊C4—62no—
308C4⋊C4—92no—
309C4⋊C4—181no—
310C22⋊C4—22no—
311C22⋊C4—122no—
312C22⋊C4—182no—
313C22⋊C4—182no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—24no—
319C22×C3—22no—
320C22×C3—22no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—42no—
327C22×C3—42no—
328C22×C3—42no—
329C22×C3—42no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—41no—
334C22×C3—82no—
335C22×C3—81no—
336C22×C3—81no—
337C22×C3—82no—
338C22×C3#88211yescharacteristic
339C22×C3C2×D2411yescharacteristic
340C22×C3#90811yescharacteristic
341C22×C3C2×#21311yescharacteristic
342C22×C3#93711yescharacteristic
343C22×C3#94911yescharacteristic
344C2×D3—124no—
345C2×D3—124no—
346C2×D3—124no—
347C2×D3—122no—
348C2×D3—122no—
349C2×D3—122no—
350C2×D3—122no—
351C2×D3—122no—
352C2×D3—122no—
353C2×D3—248no—
354C2×D3—244no—
355C2×D3—244no—
356C3×C4—22no—
357C3×C4—22no—
358C3×C4—42no—
359C3×C4—42no—
360C3×C4—41no—
361C3×C4—41no—
362C3×C4—241no—
363C3×C4—241no—
364Dic3—81no—
365Dic3—81no—
366Dic3—124no—
367Dic3—122no—
368Dic3—122no—
369C32#160711yescharacteristic, complemented, Sylow
370C23—21no—
371C23—21no—
372C23—41no—
373C23—41no—
374C23—182no—
375C23—362no—
376C23—721no—
377C23—721no—
378C23#371412yes—
379C23C2×#62611yescharacteristic
380D4—362no—
381D4—364no—
382D4—362no—
383D4—362no—
384D4—721no—
385C2×C4—21no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—121no—
389C2×C4—121no—
390C2×C4—121no—
391C2×C4—121no—
392C2×C4—121no—
393C2×C4—121no—
394C2×C4—182no—
395C2×C4—362no—
396C2×C4#381112yes—
397C8—122no—
398C2×C3—21no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—41no—
406C2×C3—41no—
407C2×C3—44no—
408C2×C3—42no—
409C2×C3—42no—
410C2×C3#473211yescharacteristic
411C2×C3#474211yescharacteristic
412C2×C3#474611yescharacteristic
413C2×C3#503611yescharacteristic
414C2×C3#505311yescharacteristic
415C2×C3#506111yescharacteristic
416D3—244no—
417D3—242no—
418D3—242no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—81no—
426C22—362no—
427C22—362no—
428C22—362no—
429C22—724no—
430C22C2×#371411yescharacteristic
431C22#6382511yescharacteristic
432C22#6398111yescharacteristic
433C4—22no—
434C4—41no—
435C4—241no—
436C4—241no—
437C4—362no—
438C3—21no—
439C3#6811011yescharacteristic, complemented
440C3#6970811yescharacteristic, complemented
441C2—21no—
442C2—21no—
443C2—42no—
444C2—722no—
445C2#1059116811yescharacteristic
446C2#1059151411yescharacteristic
447C2#1059153511yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radical#10595964C2
hypercenterC2×C22⋊C4D32
hypocenterC32#1607
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4953C2semidirect
3. #10591133C2semidirect
4. C3×#4525C2semidirect
5. #10589151C2semidirect
15. C2×C3×C4⋊Dic3C22semidirect
17. C3×C3⋊#95C22semidirect
18. C3×#830C22semidirect
26. #4953D3semidirect
29. #4525D3semidirect
69. C2×C4⋊Dic3C2×D3semidirect
80. C3⋊#95C2×D3semidirect
81. #830C2×D3semidirect
369. C32#1607semidirect
439. C3#68110semidirect
440. C3#69708semidirect

Maximal subgroups

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

subgroupindex
#105959642
C3×#49532
#105911332
C3×#45252
#105891512
#697083
#681103