Finite Group Databasebeta

← #11778448

Subgroups — #11778448

Order 1152.

645 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 645 conjugacy classes of subgroups — too many to draw. Only its 92 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×#5493C211yesmaximal, characteristic
2#10592652C211yesmaximal, characteristic, complemented
3#10591094C212yesmaximal, complemented
4C3×#4525C211yesmaximal, characteristic, complemented
5#10589150C212yesmaximal, complemented
6#71843—31nomaximal
7#68110—31nomaximal
8C22×C3×#67—21no—
9C2×C32×C22⋊C4C2211yescharacteristic
10C2×#3757—21no—
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
12C3×#930—21no—
13C3×#930C2212yes—
14C3×#886—22no—
15C3×#882—22no—
16#63658—21no—
17#63658C2211yescharacteristic, complemented
18C3×#830C2212yescomplemented
19#63575—22no—
20#63563—22no—
21C3×#534—31no—
22#5493D311yescharacteristic
23#5033—32no—
24#4953—31no—
25#4953—31no—
26#4953—61no—
27#4736—32no—
28C3×#323—31no—
29#4537—32no—
30#4525D311yescharacteristic, complemented
31#4470—32no—
32C24×C32D411yescharacteristic
33C23×C3×D3—21no—
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C2×C3×#67—22no—
39C2×C3×#67—22no—
40C2×C3×#67—42no—
41C2×C3×#67—42no—
42C22×C3×Dic3—21no—
43C2×C3×D12—21no—
44C2×C3×D12D412yes—
45C32×C22⋊C4—22no—
46#3757—42no—
47C4⋊(C3⋊Dic3)—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×(C2×D3)⋊C4—22no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3D412yes—
52C2×C3×C3⋊C8—22no—
53#1607—91noSylow
54C22×C3×D4—61no—
55C22×#67—21no—
56C3×#123—62no—
57C3×#121—32no—
58C3×#121—61no—
59C3×#120—62no—
60C2×C3×C22⋊C4—21no—
61C2×C3×C22⋊C4C2×D311yescharacteristic
62C2×C3×C22⋊C4C2×D311yescharacteristic
63C2×#217—62no—
64C2×#217—61no—
65C2×#217—61no—
66#930—21no—
67#930C2×D312yes—
68C2×C4⋊Dic3—31no—
69C2×C4⋊Dic3—31no—
70C2×C4⋊Dic3—61no—
71#886—22no—
72#882—22no—
73C3×C22⋊C8—32no—
74#832—62no—
75C3⋊#95—31no—
76C3⋊#95—31no—
77C3⋊#95—61no—
78C3⋊#95—62no—
79C3⋊#95—61no—
80C3⋊#95—61no—
81#830C2×D312yescomplemented
82#821—62no—
83#818—62no—
84#807—62no—
85C23×C32—21no—
86C23×C32—21no—
87C23×C32—41no—
88C23×C32—41no—
89C23×C32D812yes—
90C23×C32C2×D411yescharacteristic
91C22×C3×D3—22no—
92C22×C3×D3—42no—
93C22×C3×D3—81no—
94C22×C3×D3—81no—
95C2×C32×C4—21no—
96C2×C32×C4—41no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D412yes—
99C2×C3⋊Dic3—41no—
100C2×C3⋊Dic3—41no—
101C2×C3⋊Dic3—41no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C3×#67—44no—
106C3×#67—42no—
107C3×#67—42no—
108C2×C3×Dic3—22no—
109C2×C3×Dic3—42no—
110C3×D12—42no—
111C3×D12—81no—
112C3×C3⋊C8—42no—
113#534—31no—
114#480—92no—
115#397—91no—
116#327—92no—
117#323—31no—
118C24×C3—21no—
119C24×C3—61no—
120C24×C3D1211yescharacteristic
121C24×C3#6711yescharacteristic
122C23×D3—21no—
123C2×C3×D4—32no—
124C2×C3×D4—61no—
125C2×C3×D4—62no—
126C2×C3×D4—62no—
127C2×C3×D4—122no—
128C2×C3×D4—122no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—61no—
132C22×C3×C4D1211yescharacteristic
133C22×C3×C4#6711yescharacteristic
134C22×C3×C4C22×D311yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C2×#67—22no—
137C2×#67—22no—
138C2×#67—42no—
139C2×#67—42no—
140C22×Dic3—21no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143C22×Dic3—61no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146C22×Dic3—61no—
147C2×D12—21no—
148C2×D12#6712yes—
149C2×C3×C8—62no—
150C3×C4⋊C4—32no—
151C3×C4⋊C4—61no—
152C3×C22⋊C4—22no—
153C3×C22⋊C4—22no—
154C3×C22⋊C4—42no—
155C3×C22⋊C4—62no—
156C3×C22⋊C4—62no—
157#217—124no—
158#217—122no—
159#217—122no—
160(C2×D3)⋊C4—22no—
161(C2×D3)⋊C4—22no—
162C4⋊Dic3—21no—
163C4⋊Dic3—62no—
164C4⋊Dic3—62no—
165C4⋊Dic3—122no—
166C4⋊Dic3#6712yes—
167C2×C3⋊C8—22no—
168C22×C32—21no—
169C22×C32—21no—
170C22×C32—22no—
171C22×C32—42no—
172C22×C32—41no—
173C22×C32—41no—
174C22×C32—81no—
175C22×C32#12011yescharacteristic
176C22×C32C2×D811yescharacteristic
177C22×C32AGL(1,ℤ/8)11yescharacteristic
178C2×C3×D3—42no—
179C2×C3×D3—42no—
180C2×C3×D3—42no—
181C2×C3×D3—84no—
182C32×C4—22no—
183C32×C4—41no—
184C3⋊Dic3—81no—
185C3⋊Dic3—81no—
186C3×Dic3—42no—
187C22×D4—61no—
188#123—62no—
189#121—32no—
190#121—61no—
191#120—62no—
192C2×C4⋊C4—91no—
193C2×C22⋊C4—181no—
194C2×C22⋊C4D3211yescharacteristic
195#107—182no—
196#102—182no—
197C22⋊C8—32no—
198#95—91no—
199#95—181no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—22no—
205C23×C3—21no—
206C23×C3—41no—
207C23×C3—41no—
208C23×C3—41no—
209C23×C3—41no—
210C23×C3—41no—
211C23×C3—41no—
212C23×C3—42no—
213C23×C3—42no—
214C23×C3—62no—
215C23×C3—122no—
216C23×C3—241no—
217C23×C3—241no—
218C23×C3D2412yes—
219C23×C3#21312yes—
220C23×C3C2×D1211yescharacteristic
221C23×C3C2×#6711yescharacteristic
222C22×D3—22no—
223C22×D3—42no—
224C22×D3—81no—
225C22×D3—81no—
226C3×D4—122no—
227C3×D4—124no—
228C3×D4—122no—
229C3×D4—122no—
230C3×D4—241no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—22no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—42no—
238C2×C3×C4—41no—
239C2×C3×C4—41no—
240C2×C3×C4—42no—
241C2×C3×C4—62no—
242C2×C3×C4—122no—
243C2×C3×C4D3×D412yes—
244C2×C3×C4C2×#6712yes—
245#67—44no—
246#67—42no—
247#67—42no—
248C2×Dic3—22no—
249C2×Dic3—42no—
250C2×Dic3—122no—
251C2×Dic3—122no—
252C2×Dic3—122no—
253C2×Dic3—122no—
254C2×Dic3—122no—
255C2×Dic3—121no—
256C2×Dic3—121no—
257C2×Dic3—121no—
258C2×Dic3—121no—
259C2×Dic3—122no—
260C2×Dic3—121no—
261C2×Dic3—121no—
262C2×Dic3—121no—
263C2×Dic3—121no—
264C2×Dic3—121no—
265C2×Dic3—121no—
266C2×Dic3—121no—
267C2×Dic3—121no—
268D12—42no—
269D12—81no—
270C3×C8—122no—
271C3⋊C8—42no—
272C2×C32—21no—
273C2×C32—21no—
274C2×C32—42no—
275C2×C32#44711yescharacteristic
276C2×C32#45511yescharacteristic
277C2×C32#45811yescharacteristic
278C3×D3—82no—
279C24—61no—
280C24#62611yescharacteristic
281C2×D4—32no—
282C2×D4—61no—
283C2×D4—62no—
284C2×D4—62no—
285C2×D4—122no—
286C2×D4—122no—
287C22×C4—61no—
288C22×C4—181no—
289C22×C4—181no—
290C22×C4#62611yescharacteristic
291C22×C4C2×D3211yescharacteristic
292C2×C8—62no—
293C4⋊C4—32no—
294C4⋊C4—61no—
295C4⋊C4—182no—
296C22⋊C4—22no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—362no—
300C22×C3—22no—
301C22×C3—22no—
302C22×C3—21no—
303C22×C3—21no—
304C22×C3—21no—
305C22×C3—21no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3—44no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3—81no—
320C22×C3—81no—
321C22×C3—81no—
322C22×C3—81no—
323C22×C3—82no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3—122no—
327C22×C3—244no—
328C22×C3#88211yescharacteristic
329C22×C3C2×D2411yescharacteristic
330C22×C3#90811yescharacteristic
331C22×C3C2×#21311yescharacteristic
332C22×C3#93211yescharacteristic
333C22×C3#95311yescharacteristic
334C2×D3—42no—
335C2×D3—42no—
336C2×D3—42no—
337C2×D3—84no—
338C3×C4—22no—
339C3×C4—22no—
340C3×C4—42no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—81no—
344C3×C4—122no—
345Dic3—42no—
346Dic3—242no—
347Dic3—241no—
348Dic3—241no—
349Dic3—242no—
350Dic3—241no—
351Dic3—241no—
352C32#160711yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—41no—
356C23—41no—
357C23—62no—
358C23—122no—
359C23—241no—
360C23—241no—
361C23#371412yes—
362C23C2×#62611yescharacteristic
363D4—122no—
364D4—124no—
365D4—122no—
366D4—122no—
367D4—241no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—62no—
372C2×C4—122no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4—361no—
376C2×C4—361no—
377C2×C4—361no—
378C2×C4—361no—
379C2×C4D3×#6712yes—
380C8—122no—
381C2×C3—22no—
382C2×C3—22no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—42no—
391C2×C3—42no—
392C2×C3—82no—
393C2×C3—242no—
394C2×C3#473211yescharacteristic
395C2×C3#474211yescharacteristic
396C2×C3#474611yescharacteristic
397C2×C3#521711yescharacteristic
398C2×C3#524211yescharacteristic
399C2×C3#524311yescharacteristic
400D3—82no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—42no—
405C22—41no—
406C22—41no—
407C22—81no—
408C22—122no—
409C22—122no—
410C22—122no—
411C22—244no—
412C22C2×#371411yescharacteristic
413C22#6383011yescharacteristic
414C22#6397711yescharacteristic
415C4—22no—
416C4—41no—
417C4—122no—
418C4—721no—
419C4—721no—
420C3—21no—
421C3#6811011yescharacteristic, complemented
422C3#7184311yescharacteristic, complemented
423C2—21no—
424C2—21no—
425C2—42no—
426C2—242no—
427C2#1059116211yescharacteristic
428C2#1059151311yescharacteristic
429C2#1059153411yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC3×#5493C2
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. #10592652C2semidirect
3. #10591094C2semidirect
4. C3×#4525C2semidirect
5. #10589150C2semidirect
11. C2×C4⋊(C3⋊Dic3)C22semidirect
17. #63658C22semidirect
18. C3×#830C22semidirect
30. #4525D3semidirect
81. #830C2×D3semidirect
352. C32#1607semidirect
421. C3#68110semidirect
422. C3#71843semidirect

Maximal subgroups

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

subgroupindex
C3×#54932
#105926522
#105910942
C3×#45252
#105891502
#718433
#681103