Finite Group Databasebeta

← #11791404

Subgroups — #11791404

Order 1152.

769 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 769 conjugacy classes of subgroups — too many to draw. Only its 132 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#10595032C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic, complemented
3C2×C3×#805C212yesmaximal, complemented
4C2×#63568C212yesmaximal, complemented
5#10591060C211yesmaximal, characteristic, complemented
6#70358—32nomaximal
7C2×C3×#235C2212yes—
8C2×C32×C42C2211yescharacteristic
9C2×#3750—21no—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×#208C2212yes—
13#63980—21no—
14#63980—21no—
15#63914C411yescharacteristic, complemented
16C4×#625—21no—
17C4×#625—21no—
18#63873C411yescharacteristic, complemented
19#63863C412yescomplemented
20#63658—21no—
21C3×#805—24no—
22#63568—24no—
23#63555—21no—
24#63553—21no—
25#5832—32no—
26C2×C3×#104—32no—
27C2×#837—32no—
28C2×#825—32no—
29Dic3×M16—32no—
30C4×Dic3⋊C4—32no—
31C4×Dic3⋊C4—61no—
32C2×#805D312yescomplemented
33C22×C32×C4—21no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3D411yescharacteristic
37C22×C3⋊Dic3D411yescharacteristic
38C2×C3×#67—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235—22no—
42C3×#235—22no—
43C2×C3×D12C2×C412yes—
44C2×C3×C4×D3—22no—
45C2×C3×Dic6C2×C412yes—
46C2×#625—21no—
47C2×#625—21no—
48C32×C42—22no—
49#3750—24no—
50C4×C3⋊Dic3—22no—
51C4×C3⋊Dic3C2×C411yescharacteristic
52C4×C3⋊Dic3C2×C411yescharacteristic
53C4×C3⋊Dic3D411yescharacteristic
54C4×C3⋊Dic3D411yescharacteristic
55C3×#208—22no—
56C3×#208D414yescomplemented
57C2×C3×C3⋊C8—22no—
58#3724—21no—
59#3724—21no—
60(C2×D3)⋊Dic3—22no—
61(C2×D3)⋊Dic3—22no—
62#1980—91noSylow
63C2×C3×#41—32no—
64C2×#235C2×D312yes—
65C2×C3×M16—32no—
66C2×C3×C42—21no—
67C2×C3×C42C2×D312yes—
68#947—32no—
69#944—32no—
70#940—32no—
71#939—62no—
72#939—62no—
73#936—32no—
74C4×#67—62no—
75C4×#67—62no—
76C2×Dic3⋊C4—62no—
77C2×Dic3⋊C4—62no—
78C2×C4×Dic3—32no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—61no—
81C2×C4×Dic3—61no—
82C2×#208C2×D312yes—
83C3×#104—64no—
84#837—64no—
85C3⋊#95—62no—
86C3⋊#95—62no—
87#825—64no—
88#815—62no—
89C8×Dic3—62no—
90#805—24no—
91C23×C32C2×D411yescharacteristic
92C22×C3×D3—22no—
93C2×C32×C4—22no—
94C2×C32×C4—41no—
95C2×C32×C4—41no—
96C2×C32×C4C22×C411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C32×C4#4112yes—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3C22⋊C411yescharacteristic
106C2×C3⋊Dic3C22⋊C411yescharacteristic
107C2×C3⋊Dic3C22⋊C411yescharacteristic
108C2×C3⋊Dic3C22⋊C411yescharacteristic
109C3×#67—42no—
110C3×#67—42no—
111C2×C3×Dic3—22no—
112C3×D12—22no—
113C3×D12—22no—
114C3×C4×D3—42no—
115C3×C4×D3—42no—
116C3×Dic6—22no—
117C3×Dic6—22no—
118#625—42no—
119#625—42no—
120C3×C3⋊C8—24no—
121#532—91no—
122C2×#104—32no—
123C2×#104—92no—
124C4×M16—91no—
125C4×C4⋊C4—91no—
126C3×#41—62no—
127C3×#41—62no—
128C3×#41—62no—
129C3×#41—62no—
130C2×C3×Q8—32no—
131C2×C3×D4—32no—
132C2×C3×D4—62no—
133C22×C3×C4—22no—
134C22×C3×C4—22no—
135C22×C3×C4—21no—
136C22×C3×C4—62no—
137C22×C3×C4C22×D312yes—
138C2×#67—22no—
139C2×#67—62no—
140C2×#67—62no—
141C22×Dic3—32no—
142C22×Dic3—32no—
143C22×Dic3—61no—
144C22×Dic3—61no—
145C22×Dic3—62no—
146C22×Dic3—62no—
147#235—22no—
148#235—22no—
149#235—22no—
150#235—22no—
151C2×D12C4×D312yes—
152C2×C4×D3—22no—
153C2×Dic6C4×D312yes—
154C3×M16—34no—
155C3×M16—62no—
156C2×C3×C8—62no—
157C3×C42—22no—
158C3×C42—22no—
159C3×C42—42no—
160#217—62no—
161#217—62no—
162(C2×D3)⋊C4—62no—
163(C2×D3)⋊C4—62no—
164Dic3⋊C4—62no—
165Dic3⋊C4—62no—
166Dic3⋊C4—68no—
167Dic3⋊C4—68no—
168C4×Dic3—32no—
169C4×Dic3—32no—
170C4×Dic3—32no—
171C4×Dic3—32no—
172C4×Dic3—61no—
173C4×Dic3—61no—
174C4×Dic3—61no—
175C4×Dic3—61no—
176C4×Dic3—62no—
177C4×Dic3—62no—
178C4×Dic3—122no—
179#208—22no—
180#208#6714yescomplemented
181C2×C3⋊C8—22no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32C2×C22⋊C411yescharacteristic
185C22×C32#12411yescharacteristic
186C22×C32#12711yescharacteristic
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C32×C4—42no—
191C32×C4C4×D412yes—
192C32×C4#12112yes—
193C3⋊Dic3—21no—
194C3⋊Dic3—21no—
195C3⋊Dic3—21no—
196C3⋊Dic3—42no—
197C3⋊Dic3#10412yescomplemented
198C3×Dic3—42no—
199C2×#41—32no—
200C2×M16—32no—
201C4⋊Q8—91no—
202#127—91no—
203#124—92no—
204#121—181no—
205#121—181no—
206C4×D4—181no—
207C4×D4—181no—
208C2×C4⋊C4—181no—
209C2×C42—91no—
210C2×C42—91no—
211C2×C42D3211yescharacteristic
212#104—64no—
213#104—184no—
214#97—181no—
215C4×C8—181no—
216#95—181no—
217C23×C3—21no—
218C23×C3—62no—
219C23×C3D3×D412yes—
220C22×D3—22no—
221C3×Q8—62no—
222C3×Q8—62no—
223C3×D4—62no—
224C3×D4—62no—
225C3×D4—122no—
226C3×D4—122no—
227C2×C3×C4—24no—
228C2×C3×C4—24no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—42no—
236C2×C3×C4—42no—
237C2×C3×C4—62no—
238C2×C3×C4—122no—
239C2×C3×C4—122no—
240C2×C3×C4C2×C4×D312yes—
241C2×C3×C4#23512yes—
242C2×C3×C4D3×D412yes—
243C2×C3×C4D3×D412yes—
244C2×C3×C4#23712yes—
245C2×C3×C4C2×#6712yes—
246#67—42no—
247#67—42no—
248#67—124no—
249#67—124no—
250C2×Dic3—22no—
251C2×Dic3—32no—
252C2×Dic3—32no—
253C2×Dic3—32no—
254C2×Dic3—32no—
255C2×Dic3—61no—
256C2×Dic3—61no—
257C2×Dic3—61no—
258C2×Dic3—61no—
259C2×Dic3—64no—
260C2×Dic3—64no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—122no—
264C2×Dic3—122no—
265C2×Dic3—122no—
266C2×Dic3—122no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269D12—22no—
270D12—22no—
271C4×D3—42no—
272C4×D3—42no—
273Dic6—22no—
274Dic6—22no—
275C3×C8—64no—
276C3⋊C8—24no—
277C2×C32—21no—
278C2×C32—21no—
279C2×C32#39011yescharacteristic
280C2×C32C2×#10411yescharacteristic
281C2×C32#42111yescharacteristic
282C3×D3—82no—
283#41—62no—
284#41—62no—
285#41—62no—
286#41—62no—
287C2×Q8—32no—
288C2×D4—32no—
289C2×D4—62no—
290C2×D4—181no—
291C2×D4—181no—
292C22×C4—21no—
293C22×C4—62no—
294C22×C4—91no—
295C22×C4—91no—
296C22×C4—181no—
297C22×C4C2×D3211yescharacteristic
298M16—34no—
299M16—62no—
300C2×C8—62no—
301C4⋊C4—184no—
302C4⋊C4—181no—
303C4⋊C4—181no—
304C22⋊C4—182no—
305C22⋊C4—182no—
306C42—22no—
307C42—91no—
308C42—91no—
309C42—91no—
310C42—91no—
311C42—182no—
312C22×C3—22no—
313C22×C3—22no—
314C22×C3—22no—
315C22×C3—22no—
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—122no—
320C22×C3—122no—
321C22×C3—122no—
322C22×C3D3×C22⋊C412yes—
323C22×C3#88512yes—
324C22×C3#94012yes—
325C2×D3—42no—
326C2×D3—42no—
327C2×D3—42no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—44no—
331C3×C4—44no—
332C3×C4—122no—
333C3×C4#67⋊C412yes—
334C3×C4#88412yes—
335C3×C4C4×#6712yes—
336C3×C4#93912yes—
337Dic3—34no—
338Dic3—42no—
339Dic3—62no—
340Dic3—62no—
341Dic3—62no—
342Dic3—62no—
343Dic3—62no—
344Dic3—121no—
345Dic3—121no—
346Dic3—124no—
347Dic3—124no—
348C32#198011yescharacteristic, complemented, Sylow
349C23—62no—
350C23#381111yescharacteristic
351Q8—62no—
352Q8—62no—
353D4—62no—
354D4—62no—
355D4—122no—
356D4—122no—
357D4—362no—
358D4—362no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—62no—
363C2×C4—91no—
364C2×C4—91no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—122no—
368C2×C4—122no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—361no—
372C2×C4—361no—
373C2×C4—361no—
374C2×C4#379512yes—
375C2×C4C4×D3211yescharacteristic
376C2×C4#380211yescharacteristic
377C2×C4D3×#6712yes—
378C8—64no—
379C2×C3—22no—
380C2×C3—22no—
381C2×C3—22no—
382C2×C3—22no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—242no—
387C2×C3D3×#10412yes—
388C2×C3#482112yes—
389C2×C3#495712yes—
390D3—82no—
391C22—21no—
392C22—21no—
393C22—122no—
394C22—122no—
395C22—122no—
396C22#6391311yescharacteristic
397C22#6392111yescharacteristic
398C22#6397911yescharacteristic
399C4—42no—
400C4—92no—
401C4—122no—
402C4—181no—
403C4—181no—
404C4—181no—
405C4—362no—
406C4#6387912yes—
407C4#6388512yes—
408C3—21no—
409C3#7035812yescomplemented
410C2—21no—
411C2—21no—
412C2—242no—
413C2#1059039311yescharacteristic
414C2#1059039411yescharacteristic
415C2#1059138611yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595032C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#3750C2semidirect
3. C2×C3×#805C2semidirect
4. C2×#63568C2semidirect
5. #10591060C2semidirect
15. #63914C4semidirect
18. #63873C4semidirect
19. #63863C4semidirect
32. C2×#805D3semidirect
56. C3×#208D4semidirect
180. #208#67semidirect
197. C3⋊Dic3#104semidirect
348. C32#1980semidirect
409. C3#70358semidirect

Maximal subgroups

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

subgroupindex
#105950322
C4×#37502
C2×C3×#8052
C2×#635682
#105910602
#703583