Finite Group Databasebeta

← #11920441

Subgroups — #11920441

Order 1152.

515 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 515 conjugacy classes of subgroups — too many to draw. Only its 53 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#10593120C211yesmaximal, characteristic
2C2×#63690C211yesmaximal, characteristic, complemented
3#10589532C212yesmaximal, complemented
4#10589530C212yesmaximal, complemented
5#10589525C211yesmaximal, characteristic, complemented
6#84123—31nomaximal
72−1+4⋊C9—21no—
82−1+4⋊C9C2211yescharacteristic
9#63700C2211yescharacteristic
10C2×#41⋊C9—21no—
11C2×#41⋊C9C2211yescharacteristic
12#63690—21no—
13#63690C2212yescomplemented
14C2×#3688—21no—
15#63511—41nomaximal
16#63422C2212yescomplemented
17C3×#585D311yescharacteristic
18#5825—31no—
19C2×#951—31no—
20C2×#951—31no—
21#5246—32no—
22#5246—32no—
23#5242—32no—
24#5242—32no—
25#5237—31no—
26#5236—31no—
27#5236—31no—
28C9×#41—41no—
29C2×Dic18—41no—
30#41⋊C9—21no—
31#41⋊C9D411yescharacteristic
32#41⋊C9C2311yescharacteristic
33C2×Q8⋊C9—21no—
34C2×Q8⋊C9D411yescharacteristic
35#3688—22no—
36#3674—42no—
37#3672—42no—
38#3667—41no—
39#3022—91noSylow
40C3×2−1+4—21no—
41C3×2−1+4—31no—
42C3×2−1+4C2×D311yescharacteristic
43C3×H(5,𝔽2)—31no—
44C3×H(5,𝔽2)—61no—
45C3×H(5,𝔽2)C2×D311yescharacteristic
46C2×C3×#41—21no—
47C2×C3×#41—31no—
48C2×C3×#41—31no—
49C2×C3×#41—61no—
50C2×C3×#41C2×D311yescharacteristic
51C22×Dic6—31no—
52#951—32no—
53#951—32no—
54#951—32no—
55#951—32no—
56#951—61no—
57#951—61no—
58#951—61no—
59#951—61no—
60#944—32no—
61C2×#216—61no—
62C2×#216—61no—
63#936—32no—
64#935—62no—
65C2×#214—61no—
66C2×#214—61no—
67#926—31no—
68#924—62no—
69C2×#208—31no—
70C2×#208—31no—
71#837—32no—
72#837—32no—
73#837—32no—
74#837—32no—
75#836—32no—
76#833—32no—
77Q8×C9—41no—
78D4×C9—41no—
79D4×C9—81no—
80C2×C4×C9—41no—
81C2×C4×C9—81no—
82C2×Dic9—81no—
83Dic18—42no—
84Dic18—81no—
85Q8⋊C9C2×D411yescharacteristic
86C9⋊C8—42no—
87#585D911yescharacteristic
88C2×#137—91no—
89C2×#137—91no—
90#536—91no—
91#456—92no—
92#456—92no—
93#455—92no—
94#455—92no—
95#421—91no—
96#421—91no—
97#413—91no—
98C3×#41—21no—
99C3×#41—31no—
100C3×#41—31no—
101C3×#41—31no—
102C3×#41—31no—
103C3×#41—31no—
104C3×#41—61no—
105C3×#41—61no—
106C3×#41—61no—
107C3×#41—61no—
108C3×#41—62no—
109C3×#41—61no—
110C3×#41—61no—
111C3×#41—61no—
112C3×#41—61no—
113C3×#41#6711yescharacteristic
114C3×#41S411yescharacteristic
115C3×#41C22×D311yescharacteristic
116C2×C3×Q8—21no—
117C2×C3×Q8—31no—
118C2×C3×Q8—31no—
119C2×C3×Q8—61no—
120C2×C3×Q8#6711yescharacteristic
121C2×C3×D4—31no—
122C2×C3×D4—31no—
123C2×C3×D4—31no—
124C2×C3×D4—32no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—62no—
129C22×C3×C4—31no—
130C22×C3×C4—32no—
131C22×C3×C4—61no—
132C22×Dic3—61no—
133C2×Dic6—32no—
134C2×Dic6—61no—
135C2×Dic6—61no—
136C2×Dic6—61no—
137C2×Dic6—61no—
138C2×Dic6—61no—
139#217—64no—
140#217—61no—
141#216—62no—
142#216—62no—
143#216—62no—
144#216—62no—
145#214—62no—
146#214—62no—
147#214—62no—
148#214—62no—
149C4⋊Dic3—61no—
150Dic3⋊C4—64no—
151C4×Dic3—32no—
152#208—32no—
153#208—32no—
154#208—61no—
155#208—61no—
156C2×C3⋊C8—61no—
157C2×C3⋊C8—61no—
158C22×C9—41no—
159C22×C9—81no—
160C4×C9—41no—
161C4×C9—41no—
162C4×C9—81no—
163Dic9—82no—
1642−1+4—21no—
1652−1+4—31no—
1662−1+4C2×D911yescharacteristic
167H(5,𝔽2)—31no—
168H(5,𝔽2)—61no—
169H(5,𝔽2)C2×D911yescharacteristic
170C2×#41—21no—
171C2×#41—31no—
172C2×#41—31no—
173C2×#41—61no—
174C2×#41C2×D911yescharacteristic
175C22×Q8—91no—
176#137—92no—
177#137—92no—
178#137—92no—
179#137—92no—
180#137—181no—
181#137—181no—
182#137—181no—
183#137—181no—
184C2×Q16—181no—
185C2×Q16—181no—
186C2×SD16—181no—
187C2×SD16—181no—
188C2×M16—91no—
189C2×M16—91no—
190C4⋊Q8—92no—
191#124—92no—
192#123—182no—
193C22⋊Q8—182no—
194#117—91no—
195#104—92no—
196#104—92no—
197#104—92no—
198#104—92no—
199#101—92no—
200#100—92no—
201C23×C3—31no—
202C23×C3—32no—
203C23×C3—61no—
204C3×Q8—31no—
205C3×Q8—31no—
206C3×Q8—61no—
207C3×Q8—61no—
208C3×Q8C2×#6711yescharacteristic
209C3×Q8C2×S411yescharacteristic
210C3×D4—21no—
211C3×D4—31no—
212C3×D4—31no—
213C3×D4—31no—
214C3×D4—61no—
215C3×D4—61no—
216C3×D4—61no—
217C3×D4—61no—
218C3×D4—61no—
219C3×D4—62no—
220C3×D4—61no—
221C3×D4C2×S411yescharacteristic
222C2×C3×C4—21no—
223C2×C3×C4—31no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—32no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—61no—
232C2×C3×C4—62no—
233C2×C3×C4—61no—
234C2×C3×C4C2×S411yescharacteristic
235C2×Dic3—62no—
236C2×Dic3—62no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239Dic6—62no—
240Dic6—62no—
241Dic6—121no—
242Dic6—121no—
243C3⋊C8—62no—
244C3⋊C8—62no—
245C2×C9—41no—
246C2×C9—81no—
247C2×C9—161no—
248#41—21no—
249#41—31no—
250#41—31no—
251#41—31no—
252#41—31no—
253#41—31no—
254#41—61no—
255#41—61no—
256#41—61no—
257#41—61no—
258#41—62no—
259#41—61no—
260#41—61no—
261#41—61no—
262#41—61no—
263#41#61111yescharacteristic
264#41(C22⋊C9)⋊C211yescharacteristic
265#41C22×D911yescharacteristic
266C2×Q8—21no—
267C2×Q8—31no—
268C2×Q8—31no—
269C2×Q8—61no—
270C2×Q8—92no—
271C2×Q8—181no—
272C2×Q8—181no—
273C2×Q8—181no—
274C2×Q8—181no—
275C2×Q8—181no—
276C2×Q8#61111yescharacteristic
277C2×D4—31no—
278C2×D4—31no—
279C2×D4—31no—
280C2×D4—32no—
281C2×D4—61no—
282C2×D4—61no—
283C2×D4—61no—
284C2×D4—62no—
285C22×C4—31no—
286C22×C4—32no—
287C22×C4—61no—
288C22×C4—181no—
289Q16—182no—
290Q16—182no—
291Q16—182no—
292Q16—182no—
293SD16—182no—
294SD16—182no—
295SD16—182no—
296SD16—182no—
297M16—92no—
298M16—92no—
299M16—181no—
300M16—181no—
301C2×C8—181no—
302C2×C8—181no—
303C4⋊C4—181no—
304C4⋊C4—184no—
305C22⋊C4—181no—
306C22⋊C4—184no—
307C42—92no—
308C22×C3—21no—
309C22×C3—31no—
310C22×C3—31no—
311C22×C3—61no—
312C22×C3—121no—
313C22×C3—122no—
314C22×C3—241no—
315C22×C3GL(2,ℤ/4)11yescharacteristic
316C3×C4—21no—
317C3×C4—31no—
318C3×C4—31no—
319C3×C4—61no—
320C3×C4GL(2,ℤ/4)11yescharacteristic
321C3×C4C22×S411yescharacteristic
322Dic3—122no—
323Dic3—122no—
324C9—41noSylow
325C23—31no—
326C23—32no—
327C23—61no—
328Q8—31no—
329Q8—31no—
330Q8—61no—
331Q8—61no—
332Q8—182no—
333Q8—182no—
334Q8—361no—
335Q8—361no—
336Q8C2×#61111yescharacteristic
337Q8C2×(C22⋊C9)⋊C211yescharacteristic
338D4—21no—
339D4—31no—
340D4—31no—
341D4—31no—
342D4—61no—
343D4—61no—
344D4—61no—
345D4—61no—
346D4—61no—
347D4—62no—
348D4—61no—
349D4C2×(C22⋊C9)⋊C211yescharacteristic
350C2×C4—21no—
351C2×C4—31no—
352C2×C4—31no—
353C2×C4—31no—
354C2×C4—31no—
355C2×C4—31no—
356C2×C4—32no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—62no—
361C2×C4—61no—
362C2×C4—182no—
363C2×C4—182no—
364C2×C4—361no—
365C2×C4—361no—
366C2×C4C2×(C22⋊C9)⋊C211yescharacteristic
367C8—182no—
368C8—182no—
369C2×C3—21no—
370C2×C3—41no—
371C2×C3—61no—
372C2×C3—61no—
373C2×C3—121no—
374C2×C3C2×GL(2,ℤ/4)11yescharacteristic
375C22—21no—
376C22—31no—
377C22—31no—
378C22—61no—
379C22—121no—
380C22—122no—
381C22—241no—
382C22#6369411yescharacteristic
383C4—21no—
384C4—31no—
385C4—31no—
386C4—61no—
387C4—362no—
388C4—362no—
389C4#6369411yescharacteristic
390C4C22×(C22⋊C9)⋊C211yescharacteristic
391C3#8554211yescharacteristic
392C2—21no—
393C2—41no—
394C2—61no—
395C2—61no—
396C2—121no—
397C2C2×#6369411yescharacteristic
subgroupG/H
centerC2C2×#63694
commutator, cosocle#41⋊C9C23
FrattiniC3×C4C22×S4
Fitting, prime radicalC3×#585D3
socleC2×C3C2×GL(2,ℤ/4)
hypercenter#41(C22⋊C9)⋊C2
hypocenterQ8⋊C9C2×D4
LCSG ▷ #41⋊C9 ▷ Q8⋊C9
UCSC1 ◁ C2 ◁ C2×C4 ◁ #41

Complements

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

NH ≅ G/Ntype
2. C2×#63690C2semidirect
3. #10589532C2semidirect
4. #10589530C2semidirect
5. #10589525C2semidirect
13. #63690C22semidirect
16. #63422C22semidirect

Maximal subgroups

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

subgroupindex
#105931202
C2×#636902
#105895322
#105895302
#105895252
#841233
#635114