Finite Group Databasebeta

← #11778707

Subgroups — #11778707

Order 1152.

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

normal subgroups only

This group has 565 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×#5483C211yesmaximal, characteristic
2#10592648C211yesmaximal, characteristic
3#10591103C212yesmaximal, complemented
4C3×#4525C211yesmaximal, characteristic
5#10589152C212yesmaximal, complemented
6#71891—31nomaximal
7#68117—31nomaximal
8C2×C32×C22⋊C4C2211yescharacteristic
9C2×#3757—21no—
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11C2×#3750—21no—
12C2×C3×#217—21no—
13C3×#924—21no—
14C3×#924C2212yes—
15C3×#878—22no—
16C3×#878—22no—
17#63658C2211yescharacteristic
18C3×#830C2212yes—
19#63575—22no—
20#63566—22no—
21C3×#543—31no—
22#5483D311yescharacteristic
23#5044—32no—
24#4949—31no—
25#4949—31no—
26#4949—61no—
27#4722—32no—
28C3×#323—31no—
29#4538—32no—
30#4525D311yescharacteristic
31#4467—32no—
32C24×C32D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C22×C3×Dic3—21no—
38C22×C3×Dic3—21no—
39C2×C3×Dic6—21no—
40C2×C3×Dic6D412yes—
41C32×C22⋊C4—22no—
42#3757—42no—
43C4⋊(C3⋊Dic3)—22no—
44#3750—42no—
45C3×#217—22no—
46C3×#217—22no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3D412yes—
49C3×Dic3⋊C4—22no—
50C3×Dic3⋊C4—22no—
51C2×C3×C3⋊C8—22no—
52#1614—91noSylow
53C3×C22⋊Q8—32no—
54C3×C22⋊Q8—62no—
55C3×C22⋊Q8—62no—
56C3×C22⋊Q8—61no—
57C2×C3×C22⋊C4—21no—
58C2×C3×C22⋊C4—61no—
59C2×C3×C22⋊C4C2×D311yescharacteristic
60C2×C3×C22⋊C4C2×D311yescharacteristic
61C2×#217—21no—
62C2×#217—62no—
63C2×#217—61no—
64C2×#217—61no—
65C2×C4⋊Dic3—31no—
66C2×C4⋊Dic3—31no—
67C2×C4⋊Dic3—61no—
68#924—21no—
69#924C2×D312yes—
70C2×Dic3⋊C4—62no—
71C2×Dic3⋊C4—61no—
72C2×Dic3⋊C4—61no—
73#878—22no—
74#878—22no—
75C3×C22⋊C8—32no—
76#835—62no—
77C3⋊#95—31no—
78C3⋊#95—31no—
79C3⋊#95—61no—
80#830C2×D312yes—
81#818—62no—
82#816—62no—
83#807—62no—
84C23×C32—21no—
85C23×C32—21no—
86C23×C32—41no—
87C23×C32—41no—
88C23×C32Q1612yes—
89C23×C32C2×D411yescharacteristic
90C2×C32×C4—21no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4C2×D412yes—
94C2×C3⋊Dic3—22no—
95C2×C3⋊Dic3—41no—
96C2×C3⋊Dic3—41no—
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—41no—
99C2×C3⋊Dic3—41no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—22no—
102C2×C3×Dic3—81no—
103C2×C3×Dic3—81no—
104C3×Dic6—42no—
105C3×Dic6—81no—
106C3×C3⋊C8—42no—
107#543—31no—
108#484—92no—
109#399—91no—
110#328—92no—
111#323—31no—
112C24×C3—21no—
113C24×C3D1211yescharacteristic
114C24×C3#6711yescharacteristic
115C2×C3×Q8—32no—
116C2×C3×Q8—61no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—61no—
120C22×C3×C4—61no—
121C22×C3×C4D1211yescharacteristic
122C22×C3×C4#6711yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C22×C3×C4C22×D311yescharacteristic
125C22×Dic3—21no—
126C22×Dic3—21no—
127C22×Dic3—62no—
128C22×Dic3—61no—
129C22×Dic3—61no—
130C22×Dic3—62no—
131C22×Dic3—61no—
132C22×Dic3—61no—
133C2×Dic6—21no—
134C2×Dic6#6712yes—
135C2×C3×C8—62no—
136C3×C4⋊C4—32no—
137C3×C4⋊C4—62no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4—62no—
140C3×C22⋊C4—22no—
141C3×C22⋊C4—22no—
142C3×C22⋊C4—42no—
143C3×C22⋊C4—62no—
144C3×C22⋊C4—62no—
145#217—22no—
146#217—22no—
147#217—122no—
148#217—122no—
149#217—124no—
150C4⋊Dic3—21no—
151C4⋊Dic3—62no—
152C4⋊Dic3—62no—
153C4⋊Dic3—122no—
154C4⋊Dic3#6712yes—
155Dic3⋊C4—22no—
156Dic3⋊C4—22no—
157Dic3⋊C4—122no—
158Dic3⋊C4—122no—
159Dic3⋊C4—124no—
160C2×C3⋊C8—22no—
161C22×C32—21no—
162C22×C32—21no—
163C22×C32—22no—
164C22×C32—42no—
165C22×C32—41no—
166C22×C32—41no—
167C22×C32—81no—
168C22×C32#12011yescharacteristic
169C22×C32C2×Q1611yescharacteristic
170C22×C32#13711yescharacteristic
171C32×C4—22no—
172C32×C4—41no—
173C3⋊Dic3—42no—
174C3⋊Dic3—81no—
175C3×Dic3—42no—
176C3×Dic3—42no—
177C22⋊Q8—32no—
178C22⋊Q8—62no—
179C22⋊Q8—62no—
180C22⋊Q8—61no—
181C2×C4⋊C4—91no—
182C2×C4⋊C4—181no—
183C2×C22⋊C4—61no—
184C2×C22⋊C4—181no—
185C2×C22⋊C4D3211yescharacteristic
186#107—182no—
187#103—182no—
188C22⋊C8—32no—
189#95—91no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—22no—
195C23×C3—21no—
196C23×C3—41no—
197C23×C3—41no—
198C23×C3—41no—
199C23×C3—41no—
200C23×C3—41no—
201C23×C3—41no—
202C23×C3—42no—
203C23×C3—42no—
204C23×C3Dic1212yes—
205C23×C3#21612yes—
206C23×C3C2×D1211yescharacteristic
207C23×C3C2×#6711yescharacteristic
208C3×Q8—122no—
209C3×Q8—241no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—22no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—42no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—42no—
220C2×C3×C4—62no—
221C2×C3×C4—62no—
222C2×C3×C4—241no—
223C2×C3×C4—241no—
224C2×C3×C4D3×D412yes—
225C2×C3×C4C2×#6712yes—
226C2×Dic3—22no—
227C2×Dic3—22no—
228C2×Dic3—64no—
229C2×Dic3—62no—
230C2×Dic3—62no—
231C2×Dic3—81no—
232C2×Dic3—81no—
233C2×Dic3—122no—
234C2×Dic3—121no—
235C2×Dic3—121no—
236C2×Dic3—122no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239C2×Dic3—122no—
240C2×Dic3—121no—
241C2×Dic3—121no—
242C2×Dic3—122no—
243C2×Dic3—122no—
244C2×Dic3—121no—
245C2×Dic3—121no—
246C2×Dic3—121no—
247C2×Dic3—121no—
248Dic6—42no—
249Dic6—81no—
250C3×C8—122no—
251C3⋊C8—42no—
252C2×C32—21no—
253C2×C32—21no—
254C2×C32—42no—
255C2×C32#45111yescharacteristic
256C2×C32#45311yescharacteristic
257C2×C32#45811yescharacteristic
258C24#62611yescharacteristic
259C2×Q8—32no—
260C2×Q8—61no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—181no—
264C22×C4—181no—
265C22×C4#62611yescharacteristic
266C22×C4C2×D3211yescharacteristic
267C2×C8—62no—
268C4⋊C4—32no—
269C4⋊C4—62no—
270C4⋊C4—61no—
271C4⋊C4—62no—
272C4⋊C4—182no—
273C4⋊C4—362no—
274C22⋊C4—22no—
275C22⋊C4—62no—
276C22⋊C4—62no—
277C22⋊C4—362no—
278C22×C3—22no—
279C22×C3—22no—
280C22×C3—21no—
281C22×C3—21no—
282C22×C3—21no—
283C22×C3—21no—
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—21no—
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—42no—
290C22×C3—42no—
291C22×C3—42no—
292C22×C3—44no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—81no—
298C22×C3—81no—
299C22×C3—81no—
300C22×C3—81no—
301C22×C3—82no—
302C22×C3#88211yescharacteristic
303C22×C3C2×Dic1211yescharacteristic
304C22×C3#90911yescharacteristic
305C22×C3#94211yescharacteristic
306C22×C3C2×#21611yescharacteristic
307C22×C3#95311yescharacteristic
308C3×C4—22no—
309C3×C4—22no—
310C3×C4—42no—
311C3×C4—41no—
312C3×C4—41no—
313C3×C4—81no—
314C3×C4—122no—
315C3×C4—122no—
316Dic3—42no—
317Dic3—42no—
318Dic3—124no—
319Dic3—122no—
320Dic3—122no—
321Dic3—242no—
322Dic3—241no—
323Dic3—241no—
324C32#161411yescharacteristic, complemented, Sylow
325C23—21no—
326C23—21no—
327C23—41no—
328C23—41no—
329C23#371912yes—
330C23C2×#62611yescharacteristic
331Q8—122no—
332Q8—241no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—62no—
337C2×C4—62no—
338C2×C4—182no—
339C2×C4—241no—
340C2×C4—241no—
341C2×C4—361no—
342C2×C4—361no—
343C2×C4—361no—
344C2×C4—361no—
345C2×C4—361no—
346C2×C4D3×#6712yes—
347C8—122no—
348C2×C3—22no—
349C2×C3—22no—
350C2×C3—21no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—42no—
358C2×C3—42no—
359C2×C3—82no—
360C2×C3#473911yescharacteristic
361C2×C3#474211yescharacteristic
362C2×C3#474711yescharacteristic
363C2×C3#522811yescharacteristic
364C2×C3#524111yescharacteristic
365C2×C3#524311yescharacteristic
366C22—21no—
367C22—21no—
368C22—22no—
369C22—42no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22#6383311yescharacteristic
374C22C2×#371911yescharacteristic
375C22#6397711yescharacteristic
376C4—22no—
377C4—41no—
378C4—122no—
379C4—122no—
380C4—362no—
381C4—721no—
382C3—21no—
383C3#6811711yescharacteristic, complemented
384C3#7189111yescharacteristic, complemented
385C2—21no—
386C2—21no—
387C2—42no—
388C2#1059118611yescharacteristic
389C2#1059151011yescharacteristic
390C2#1059153411yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32#120
prime radicalC24×C32D4
hypercenterC2×C22⋊C4D32
hypocenterC32#1614
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
3. #10591103C2semidirect
5. #10589152C2semidirect
324. C32#1614semidirect
383. C3#68117semidirect
384. C3#71891semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
#105926482
#105911032
C3×#45252
#105891522
#718913
#681173