Finite Group Databasebeta

← #11792282

Subgroups — #11792282

Order 1152.

833 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 833 conjugacy classes of subgroups — too many to draw. Only its 126 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×#5510C211yesmaximal, characteristic
2C2×#63831C212yesmaximal, complemented
3#10592672C211yesmaximal, characteristic, complemented
4C2×#63568C212yesmaximal, complemented
5C3×#4530C211yesmaximal, characteristic, complemented
6#71881—31nomaximal
7#69009—31nomaximal
8C22×#634C2211yescharacteristic
9C2×C3×#235C2212yes—
10C2×C32×C4⋊C4C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C3×#930—22no—
13C2×C3×#208C2212yes—
14C3×#897—22no—
15C3×#895—22no—
16C2×#3719—22no—
17#63831—24no—
18#63831—24no—
19C2×#3716—22no—
20#63658—22no—
21#63568—24no—
22C3×#537—31no—
23C2×#951—32no—
24C2×#909—32no—
25#5510D311yescharacteristic
26C2×#837—32no—
27C2×#825—32no—
28#4973—31no—
29#4973—31no—
30#4973—61no—
31C3×#343—31no—
32#4530D311yescharacteristic, complemented
33C22×C32×C4D412yes—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—21no—
36C22×C3⋊Dic3—21no—
37C2×#634—22no—
38C2×#634—22no—
39C2×#634—21no—
40C2×#634D412yescomplemented
41C2×C3×#67—22no—
42C3×#235—22no—
43C3×#235—22no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12—22no—
47C2×C3×D12D412yes—
48C2×C3×C4×D3—22no—
49C2×C3×Dic6D412yes—
50C32×C4⋊C4—22no—
51C4×C3⋊Dic3—22no—
52C3×(C2×D3)⋊C4—24no—
53C3×C4⋊Dic3—22no—
54C3×#208—22no—
55C3×#208D414yescomplemented
56C2×C3×C3⋊C8—22no—
57#3719—28no—
58#3716—28no—
59#2007—91noSylow
60C2×C3×#41—32no—
61C2×#235C2×D312yes—
62C22×Dic6—31no—
63C22×Dic6—31no—
64C22×Dic6—61no—
65C2×C3×M16—32no—
66C3×C22⋊Q8—62no—
67C3×#121—62no—
68C3×#121—62no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4C2×D311yescharacteristic
71C2×C3×C4⋊C4C2×D311yescharacteristic
72#951—64no—
73#951—64no—
74C2×#216—62no—
75C2×#214—62no—
76#930—22no—
77C2×C4×Dic3—31no—
78C2×C4×Dic3—31no—
79C2×C4×Dic3—61no—
80C2×#208C2×D312yes—
81#909—64no—
82#909—64no—
83C2×Dic12—62no—
84C2×#204—62no—
85#897—22no—
86#895—22no—
87#837—64no—
88C3⋊#95—64no—
89C3⋊#95—62no—
90C3⋊#95—62no—
91#825—64no—
92C23×C32C2×D411yescharacteristic
93C22×C3×D3—22no—
94C2×C32×C4—22no—
95C2×C32×C4—42no—
96C2×C32×C4C2×D412yes—
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×D412yes—
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—41no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106#634—24no—
107#634—42no—
108C3×#67—42no—
109C3×#67—42no—
110C2×C3×Dic3—22no—
111C3×D12—22no—
112C3×D12—22no—
113C3×D12—82no—
114C3×C4×D3—42no—
115C3×C4×D3—42no—
116C3×Dic6—22no—
117C3×Dic6—22no—
118C3×C3⋊C8—24no—
119C2×#137—92no—
120#537—31no—
121C2×#104—92no—
122#391—91no—
123#343—31no—
124C3×#41—62no—
125C3×#41—62no—
126C3×#41—62no—
127C3×#41—62no—
128C2×C3×Q8—32no—
129C2×C3×D4—32no—
130C2×C3×D4—62no—
131C2×C3×D4—62no—
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—62no—
135C22×C3×C4D1212yes—
136C22×C3×C4#6712yes—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C2×#67—22no—
140C22×Dic3—62no—
141C22×Dic3—62no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—61no—
145C22×Dic3—61no—
146#235—22no—
147#235—22no—
148#235—22no—
149#235—22no—
150C2×D12—22no—
151C2×D12#6712yes—
152C2×C4×D3—22no—
153C2×Dic6—32no—
154C2×Dic6—32no—
155C2×Dic6—62no—
156C2×Dic6—62no—
157C2×Dic6—62no—
158C2×Dic6—62no—
159C2×Dic6—62no—
160C2×Dic6—62no—
161C2×Dic6—61no—
162C2×Dic6—61no—
163C2×Dic6—122no—
164C2×Dic6—122no—
165C2×Dic6#6712yes—
166C3×M16—34no—
167C3×M16—62no—
168C2×C3×C8—62no—
169C3×C4⋊C4—22no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—42no—
172C3×C4⋊C4—62no—
173C3×C22⋊C4—64no—
174#216—68no—
175#214—68no—
176(C2×D3)⋊C4—24no—
177C4⋊Dic3—22no—
178C4×Dic3—62no—
179C4×Dic3—62no—
180C4×Dic3—122no—
181#208—22no—
182#208D1214yescomplemented
183C2×C3⋊C8—22no—
184Dic12—68no—
185#204—68no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32#12011yescharacteristic
189C22×C32#12111yescharacteristic
190C22×C32#12711yescharacteristic
191C2×C3×D3—42no—
192C2×C3×D3—42no—
193C2×C3×D3—42no—
194C32×C4—42no—
195C32×C4#12012yes—
196C32×C4#12112yes—
197C3⋊Dic3—42no—
198C3⋊Dic3—42no—
199C3×Dic3—42no—
200C2×#41—32no—
201C22×Q8—91no—
202#137—184no—
203#137—184no—
204C2×Q16—182no—
205C2×SD16—182no—
206C2×M16—32no—
207C22⋊Q8—62no—
208#121—62no—
209#121—62no—
210C2×C4⋊C4D3211yescharacteristic
211C2×C42—91no—
212#104—184no—
213#95—182no—
214C23×C3—21no—
215C23×C3—62no—
216C23×C3C2×D1211yescharacteristic
217C23×C3C2×#6711yescharacteristic
218C22×D3—22no—
219C3×Q8—62no—
220C3×Q8—62no—
221C3×D4—62no—
222C3×D4—62no—
223C3×D4—122no—
224C3×D4—122no—
225C3×D4—242no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—22no—
230C2×C3×C4—21no—
231C2×C3×C4—22no—
232C2×C3×C4—42no—
233C2×C3×C4—42no—
234C2×C3×C4—42no—
235C2×C3×C4—44no—
236C2×C3×C4—62no—
237C2×C3×C4—122no—
238C2×C3×C4—122no—
239C2×C3×C4C2×D1212yes—
240C2×C3×C4D3×D412yes—
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D412yes—
244C2×C3×C4#23711yescharacteristic
245C2×C3×C4#23911yescharacteristic
246C2×C3×C4C2×#6712yes—
247#67—42no—
248#67—42no—
249C2×Dic3—22no—
250C2×Dic3—64no—
251C2×Dic3—64no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254C2×Dic3—62no—
255C2×Dic3—62no—
256C2×Dic3—122no—
257C2×Dic3—122no—
258C2×Dic3—122no—
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—22no—
269D12—22no—
270D12—82no—
271C4×D3—42no—
272C4×D3—42no—
273Dic6—22no—
274Dic6—22no—
275Dic6—64no—
276Dic6—64no—
277Dic6—124no—
278Dic6—124no—
279Dic6—122no—
280Dic6—122no—
281C3×C8—64no—
282C3⋊C8—24no—
283C2×C32—21no—
284C2×C32—21no—
285C2×C32#39211yescharacteristic
286C2×C32#45511yescharacteristic
287C2×C32#45611yescharacteristic
288C3×D3—82no—
289#41—62no—
290#41—62no—
291#41—62no—
292#41—62no—
293C2×Q8—32no—
294C2×Q8—92no—
295C2×Q8—181no—
296C2×Q8—182no—
297C2×Q8—182no—
298C2×D4—32no—
299C2×D4—62no—
300C2×D4—62no—
301C22×C4—62no—
302C22×C4—181no—
303C22×C4—181no—
304C22×C4#62612yes—
305C22×C4C2×D3211yescharacteristic
306Q16—188no—
307SD16—188no—
308M16—34no—
309M16—62no—
310C2×C8—62no—
311C4⋊C4—22no—
312C4⋊C4—62no—
313C22⋊C4—64no—
314C42—182no—
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—122no—
325C22×C3—122no—
326C22×C3—122no—
327C22×C3#87411yescharacteristic
328C22×C3#88211yescharacteristic
329C22×C3#89511yescharacteristic
330C22×C3#93811yescharacteristic
331C22×C3#94011yescharacteristic
332C22×C3#95311yescharacteristic
333C2×D3—42no—
334C2×D3—42no—
335C2×D3—42no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—42no—
339C3×C4—42no—
340C3×C4—82no—
341C3×C4—122no—
342C3×C4#88212yes—
343C3×C4#89512yes—
344C3×C4#93712yes—
345C3×C4#93912yes—
346Dic3—42no—
347Dic3—124no—
348Dic3—124no—
349Dic3—122no—
350Dic3—122no—
351Dic3—122no—
352Dic3—122no—
353C32#200711yescharacteristic, complemented, Sylow
354C23—62no—
355C23C2×#62611yescharacteristic
356Q8—62no—
357Q8—62no—
358Q8—184no—
359Q8—362no—
360D4—62no—
361D4—62no—
362D4—122no—
363D4—122no—
364D4—242no—
365C2×C4—22no—
366C2×C4—42no—
367C2×C4—62no—
368C2×C4—122no—
369C2×C4—122no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—361no—
373C2×C4—361no—
374C2×C4—361no—
375C2×C4—361no—
376C2×C4#379611yescharacteristic
377C2×C4D3×D1212yes—
378C2×C4#380211yescharacteristic
379C2×C4D3×#6712yes—
380C8—64no—
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—242no—
391C2×C3#467111yescharacteristic
392C2×C3#474611yescharacteristic
393C2×C3#475211yescharacteristic
394C2×C3#522311yescharacteristic
395C2×C3#524211yescharacteristic
396C2×C3#524611yescharacteristic
397D3—82no—
398C22—21no—
399C22—21no—
400C22—122no—
401C22—122no—
402C22—122no—
403C22#6391111yescharacteristic
404C22#6391611yescharacteristic
405C22#6397711yescharacteristic
406C4—42no—
407C4—122no—
408C4—362no—
409C4—362no—
410C4#6388612yes—
411C4#6392212yes—
412C3—21no—
413C3#6900911yescharacteristic, complemented
414C3#7188111yescharacteristic, complemented
415C2—21no—
416C2—21no—
417C2—242no—
418C2#1059139111yescharacteristic
419C2#1059151311yescharacteristic
420C2#1059164911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC3×#5510C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2007
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63831C2semidirect
3. #10592672C2semidirect
4. C2×#63568C2semidirect
5. C3×#4530C2semidirect
32. #4530D3semidirect
40. C2×#634D4semidirect
55. C3×#208D4semidirect
182. #208D12semidirect
353. C32#2007semidirect
413. C3#69009semidirect
414. C3#71881semidirect

Maximal subgroups

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

subgroupindex
C3×#55102
C2×#638312
#105926722
C2×#635682
C3×#45302
#718813
#690093