Finite Group Databasebeta

← #11780249

Subgroups — #11780249

Order 1152.

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

normal subgroups only

This group has 506 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#10596013C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic
3#10590311C211yesmaximal, characteristic, complemented
4#10590307C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic
6#10589094C211yesmaximal, characteristic, complemented
7#10589085C211yesmaximal, characteristic, complemented
8#71049—31nomaximal
9#68209—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64145—21no—
12#64135—21no—
13#64133—21no—
14#64096—21no—
15#64088—22no—
16#64078C2211yescharacteristic
17C4×#634C2211yescharacteristic
18C2×C3×#214—21no—
19C3×#869C2211yescharacteristic
20C3×#810—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4×C3⋊C8C2211yescharacteristic
24#63575—22no—
25#63573—21no—
26#63567—21no—
27#5542—31no—
28#5542—31no—
29#5542—61no—
30C3×#461—31no—
31#5094—31no—
32#5078—31no—
33#5019D311yescharacteristic
34#4851—31no—
35#4682—31no—
36C3×D4⋊C8—31no—
37D4⋊(C3⋊C8)D311yescharacteristic
38#4486—31no—
39#4484—31no—
40#4482—31no—
41#4456—31no—
42C2×C32×D4D411yescharacteristic
43C22×C32×C4—21no—
44C2×#634—21no—
45C2×#634D411yescharacteristic
46C2×C3×Dic6—21no—
47C32×C4⋊C4D411yescharacteristic
48C32×C22⋊C4—21no—
49C32×C42C2311yescharacteristic
50#3757—22no—
51#3757—22no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)D411yescharacteristic
54C4⋊(C3⋊Dic3)D412yes—
55#3750—22no—
56#3750—21no—
57C4×C3⋊Dic3—22no—
58C4×C3⋊Dic3—21no—
59C3×#214—42no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65#1650—91noSylow
66C2×C3×SD16—61no—
67C3×C4⋊Q8—31no—
68C3×C4×D4—21no—
69C3×C4×D4C2×D311yescharacteristic
70C3×C4×D4C2×D311yescharacteristic
71#936—62no—
72#936—61no—
73#936—61no—
74C2×#214—21no—
75#926—61no—
76#926—61no—
77#926—62no—
78#924—61no—
79#924—61no—
80#924—62no—
81#887—62no—
82#887—61no—
83#887—61no—
84#879—62no—
85#879—62no—
86#879—64no—
87#869—31no—
88#869—31no—
89#869—61no—
90#869C2×D311yescharacteristic
91C4×Dic6—31no—
92C4×Dic6—31no—
93C4×Dic6—61no—
94C3×C4⋊C8—31no—
95C3×C4⋊C8—31no—
96C3×#103—61no—
97C3×C4×C8—31no—
98#818—62no—
99#817—61no—
100#816—61no—
101#810—21no—
102#810—61no—
103#808—61no—
104#807—62no—
105C4⋊(C3⋊C8)C2×D311yescharacteristic
106C4⋊(C3⋊C8)C2×D311yescharacteristic
107C4×C3⋊C8C2×D311yescharacteristic
108C23×C32—21no—
109C32×D4—21no—
110C32×D4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—22no—
120#634—21no—
121#634—21no—
122#634—41no—
123#634—41no—
124C2×C3×Dic3—41no—
125C3×Dic6—41no—
126C3×Dic6—41no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129C3×C3⋊C8—41no—
130#556—91no—
131#500—91no—
132#475—91no—
133#461—31no—
134#332—91no—
135Q8⋊C8—91no—
136D4⋊C8—31no—
137C2×C3×Q8—61no—
138C2×C3×D4—21no—
139C2×C3×D4D1211yescharacteristic
140C2×C3×D4#6711yescharacteristic
141C22×C3×C4—22no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C2×Dic6—21no—
145C2×Dic6—31no—
146C2×Dic6—31no—
147C2×Dic6—61no—
148C2×Dic6—62no—
149C2×Dic6—61no—
150C2×Dic6—61no—
151C3×SD16—122no—
152C2×C3×C8—61no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4D1211yescharacteristic
159C3×C4⋊C4#6711yescharacteristic
160C3×C22⋊C4—22no—
161C3×C22⋊C4—21no—
162C3×C22⋊C4—21no—
163C3×C42—21no—
164C3×C42C22×D311yescharacteristic
165C3×C42C22×D311yescharacteristic
166#217—64no—
167#217—62no—
168#217—62no—
169#217—64no—
170#217—62no—
171#217—62no—
172#214—42no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3—32no—
176C4⋊Dic3—31no—
177C4⋊Dic3—31no—
178C4⋊Dic3—32no—
179C4⋊Dic3—61no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184Dic3⋊C4—62no—
185Dic3⋊C4—64no—
186Dic3⋊C4—62no—
187Dic3⋊C4—62no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190C4×Dic3—62no—
191C4×Dic3—64no—
192C4×Dic3—62no—
193C4×Dic3—62no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C2×C3⋊C8—21no—
197C2×C3⋊C8—21no—
198C2×C3⋊C8—21no—
199C22×C32—41no—
200C22×C32—41no—
201C22×C32—41no—
202C22×C32#12011yescharacteristic
203C32×C4—21no—
204C32×C4—41no—
205C32×C4#13511yescharacteristic
206C32×C4#13511yescharacteristic
207C32×C4AGL(1,ℤ/8)11yescharacteristic
208C32×C4#13711yescharacteristic
209C3⋊Dic3—42no—
210C3⋊Dic3—41no—
211C3⋊Dic3—41no—
212C3×Dic3—81no—
213C2×SD16—61no—
214C4⋊Q8—31no—
215C4⋊Q8—91no—
216#126—182no—
217#124—181no—
218C22⋊Q8—181no—
219C4×Q8—91no—
220C4×Q8—181no—
221C4×D4D3211yescharacteristic
222#117—181no—
223#107—182no—
224#106—181no—
225C4⋊C8—31no—
226C4⋊C8—31no—
227#103—61no—
228#103—181no—
229C4×C8—31no—
230C23×C3—22no—
231C23×C3—21no—
232C23×C3—21no—
233C3×Q8—121no—
234C3×Q8—121no—
235C3×D4—21no—
236C3×D4—21no—
237C3×D4—21no—
238C3×D4—21no—
239C3×D4—41no—
240C3×D4—41no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—121no—
254C2×C3×C4C2×D1211yescharacteristic
255C2×C3×C4D3×D411yescharacteristic
256C2×C3×C4D3×D411yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C2×#6711yescharacteristic
260C2×Dic3—41no—
261C2×Dic3—62no—
262C2×Dic3—62no—
263C2×Dic3—64no—
264C2×Dic3—61no—
265C2×Dic3—61no—
266C2×Dic3—62no—
267C2×Dic3—61no—
268C2×Dic3—61no—
269C2×Dic3—62no—
270Dic6—41no—
271Dic6—41no—
272Dic6—61no—
273Dic6—61no—
274Dic6—61no—
275Dic6—61no—
276Dic6—121no—
277Dic6—121no—
278Dic6—122no—
279Dic6—122no—
280Dic6—121no—
281Dic6—121no—
282Dic6—121no—
283Dic6—121no—
284C3×C8—62no—
285C3×C8—121no—
286C3×C8—121no—
287C3⋊C8—22no—
288C3⋊C8—41no—
289C3⋊C8—41no—
290C2×C32—81no—
291C2×C32#44911yescharacteristic
292C2×C32#45211yescharacteristic
293C2×C32#45611yescharacteristic
294C2×Q8—61no—
295C2×Q8—91no—
296C2×Q8—181no—
297C2×D4#62611yescharacteristic
298C22×C4—21no—
299SD16—122no—
300C2×C8—61no—
301C2×C8—61no—
302C2×C8—61no—
303C4⋊C4—61no—
304C4⋊C4—61no—
305C4⋊C4—91no—
306C4⋊C4—92no—
307C4⋊C4—182no—
308C4⋊C4—181no—
309C4⋊C4—181no—
310C4⋊C4#62611yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—182no—
313C22⋊C4—182no—
314C42—182no—
315C42—181no—
316C42C2×D3211yescharacteristic
317C22×C3—21no—
318C22×C3—42no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—41no—
322C22×C3—41no—
323C22×C3—41no—
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3#88211yescharacteristic
328C22×C3#93711yescharacteristic
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—41no—
336C3×C4—42no—
337C3×C4—41no—
338C3×C4—41no—
339C3×C4—241no—
340C3×C4#90411yescharacteristic
341C3×C4#90811yescharacteristic
342C3×C4#91211yescharacteristic
343C3×C4#91511yescharacteristic
344C3×C4#91511yescharacteristic
345C3×C4#91611yescharacteristic
346C3×C4#93211yescharacteristic
347C3×C4#95011yescharacteristic
348Dic3—81no—
349Dic3—124no—
350Dic3—122no—
351Dic3—122no—
352Dic3—121no—
353Dic3—121no—
354Dic3—122no—
355Dic3—122no—
356Dic3—121no—
357Dic3—121no—
358C32#165011yescharacteristic, complemented, Sylow
359C23—21no—
360Q8—121no—
361Q8—121no—
362Q8—181no—
363Q8—181no—
364Q8—361no—
365Q8—361no—
366D4—21no—
367D4—21no—
368C2×C4—21no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—121no—
372C2×C4—181no—
373C2×C4—182no—
374C2×C4—181no—
375C2×C4C2×#62611yescharacteristic
376C2×C4#381111yescharacteristic
377C2×C4#381111yescharacteristic
378C8—62no—
379C8—121no—
380C8—121no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—82no—
385C2×C3—81no—
386C2×C3—81no—
387C2×C3#473411yescharacteristic
388C2×C3#478311yescharacteristic
389C2×C3#482611yescharacteristic
390C2×C3#503711yescharacteristic
391C2×C3#517311yescharacteristic
392C2×C3#520511yescharacteristic
393C22—41no—
394C22—41no—
395C22—41no—
396C22#6398111yescharacteristic
397C4—21no—
398C4—41no—
399C4—241no—
400C4—361no—
401C4—362no—
402C4—361no—
403C4#6382911yescharacteristic
404C4#6383011yescharacteristic
405C4#6393111yescharacteristic
406C4#6393611yescharacteristic
407C3—21no—
408C3#6820911yescharacteristic, complemented
409C3#7104911yescharacteristic, complemented
410C2—81no—
411C2#1059118211yescharacteristic
412C2#1059146611yescharacteristic
413C2#1059166811yescharacteristic
subgroupG/H
centerC22#63981
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10590311C2semidirect
4. #10590307C2semidirect
6. #10589094C2semidirect
7. #10589085C2semidirect
358. C32#1650semidirect
408. C3#68209semidirect
409. C3#71049semidirect

Maximal subgroups

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

subgroupindex
#105960132
C3×#50192
#105903112
#105903072
C3×D4⋊(C3⋊C8)2
#105890942
#105890852
#710493
#682093