Finite Group Databasebeta

← #11778751

Subgroups — #11778751

Order 1152.

456 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 78 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#10594973C211yesmaximal, characteristic
2C3×#4735C211yesmaximal, characteristic
3#10591225C211yesmaximal, characteristic, complemented
4#10591135C211yesmaximal, characteristic, complemented
5#10589333C211yesmaximal, characteristic, complemented
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589150C211yesmaximal, characteristic
8#71170—31nomaximal
9#68136—31nomaximal
10#64133C2211yescharacteristic
11C3×#930C2211yescharacteristic
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14Dic3×#67—21no—
15#63961—21no—
16#63896—21no—
17#63884—21no—
18#63861—21no—
19#63847—21no—
20C32×C22⋊C8C2211yescharacteristic
21#63658C2211yescharacteristic
22C3×#830C2211yescharacteristic
23C3×#821—21no—
24C3×#817—21no—
25#63579—21no—
26#63579—21no—
27#63575—21no—
28#63567—21no—
29#5602—31no—
30#5515—31no—
31C3×#481—31no—
32#4986—31no—
33#4985—31no—
34#4970—31no—
35#4735D311yescharacteristic
36#4722—31no—
37C3×#324—31no—
38#4537—31no—
39#4470—31no—
40#4469D311yescharacteristic, complemented
41#4467—31no—
42#4467—31no—
43#4467—61no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×#634D411yescharacteristic
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12D411yescharacteristic
52C2×D3×Dic3—21no—
53C2×C32×C8—21no—
54#3757—21no—
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3D411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65#3724—21no—
66Dic3⋊Dic3—21no—
67(C2×D3)⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70Dic32—21no—
71#1615—91noSylow
72C3×#121—31no—
73C2×C3×C4⋊C4—31no—
74C2×C3×C4⋊C4—31no—
75#935—61no—
76#935—61no—
77D4×Dic3—61no—
78#930C2×D311yescharacteristic
79#929—61no—
80C4×#67—61no—
81C2×C4⋊Dic3C2×D311yescharacteristic
82#924—31no—
83#924—31no—
84#924—61no—
85C2×Dic3⋊C4C2×D311yescharacteristic
86#898—61no—
87#896—61no—
88#894—61no—
89#889—61no—
90#889—61no—
91#879—61no—
92#878—61no—
93C3×#106—61no—
94C3×#102—61no—
95C3×C22⋊C8—21no—
96C3×C22⋊C8—31no—
97C3×C22⋊C8C2×D311yescharacteristic
98C3×C22⋊C8C2×D311yescharacteristic
99C3⋊#95—31no—
100C3⋊#95—31no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95—61no—
106#830C2×D311yescharacteristic
107#821—21no—
108#818—61no—
109#817—21no—
110#816—61no—
111#810—61no—
112#807—61no—
113C23×C32C2×D411yescharacteristic
114C22×C3×D3—21no—
115C2×C32×C4—41no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—41no—
123#634—41no—
124C3×#67—41no—
125C3×#67—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—41no—
134C3×D12—41no—
135D3×Dic3—81no—
136C32×C8—41no—
137C3×C3⋊C8—41no—
138#539—91no—
139#484—91no—
140#481—31no—
141#400—91no—
142#328—91no—
143#327—91no—
144#324—31no—
145C2×C3×D4—31no—
146C2×C3×D4—61no—
147C22×C3×C4—21no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—61no—
151C22×C3×C4C22×D311yescharacteristic
152C22×C3×C4C22×D311yescharacteristic
153C2×#67—21no—
154C22×Dic3—21no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C22×Dic3—121no—
159C22×Dic3D1211yescharacteristic
160C22×Dic3D1211yescharacteristic
161C2×D12#6711yescharacteristic
162C2×C4×D3—61no—
163C2×Dic6—31no—
164C2×Dic6—31no—
165C2×Dic6—61no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—41no—
169C2×C3×C8—61no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C22⋊C4—61no—
176#217—61no—
177#217—61no—
178#217—61no—
179#217—61no—
180#217—61no—
181#217—121no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3#6711yescharacteristic
193Dic3⋊C4—21no—
194Dic3⋊C4—21no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—121no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C2×C3⋊C8—21no—
206C22×C32—21no—
207C22×C32—21no—
208C22×C32#12011yescharacteristic
209C22×C32#13511yescharacteristic
210C22×C32#13711yescharacteristic
211C2×C3×D3—41no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C32×C4—21no—
215C32×C4—21no—
216C3⋊Dic3—41no—
217C3⋊Dic3—41no—
218C3⋊Dic3—81no—
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—81no—
223#126—181no—
224#125—181no—
225#123—181no—
226#123—181no—
227C22⋊Q8—91no—
228C22⋊Q8—181no—
229#121—31no—
230C4×D4—181no—
231C2×C4⋊C4—31no—
232C2×C4⋊C4—31no—
233#107—181no—
234#106—61no—
235#103—181no—
236#102—61no—
237C22⋊C8—31no—
238C22⋊C8D3211yescharacteristic
239#95—91no—
240#95—181no—
241#95—181no—
242C23×C3—21no—
243C23×C3—61no—
244C23×C3C2×D1211yescharacteristic
245C23×C3D3×D411yescharacteristic
246C22×D3—21no—
247C3×D4—121no—
248C3×D4—121no—
249C3×D4—121no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—61no—
255C2×C3×C4—61no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—81no—
260C2×C3×C4—121no—
261C2×C3×C4—122no—
262C2×C3×C4—121no—
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4C2×#6711yescharacteristic
267#67—41no—
268#67—41no—
269C2×Dic3—21no—
270C2×Dic3—21no—
271C2×Dic3—21no—
272C2×Dic3—21no—
273C2×Dic3—21no—
274C2×Dic3—41no—
275C2×Dic3—42no—
276C2×Dic3—41no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3—121no—
287C2×Dic3—122no—
288C2×Dic3—121no—
289C2×Dic3—121no—
290C2×Dic3—241no—
291C2×Dic3—241no—
292C2×Dic3—241no—
293D12—41no—
294C4×D3—241no—
295Dic6—121no—
296Dic6—121no—
297Dic6—241no—
298C3×C8—41no—
299C3×C8—41no—
300C3×C8—81no—
301C3×C8—121no—
302C3⋊C8—41no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32#45211yescharacteristic
306C2×C32#45411yescharacteristic
307C2×C32#45811yescharacteristic
308C3×D3—81no—
309C2×Q8—91no—
310C2×D4—31no—
311C2×D4—61no—
312C22×C4—31no—
313C22×C4—31no—
314C22×C4—61no—
315C22×C4—181no—
316C22×C4—181no—
317C22×C4C2×D3211yescharacteristic
318C2×C8—21no—
319C2×C8—61no—
320C4⋊C4—31no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—91no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C22⋊C4—61no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C22⋊C4—181no—
335C42—181no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—121no—
346C22×C3—121no—
347C22×C3—121no—
348C22×C3#88211yescharacteristic
349C22×C3#90411yescharacteristic
350C22×C3#90911yescharacteristic
351C22×C3#91511yescharacteristic
352C22×C3#91611yescharacteristic
353C22×C3#93711yescharacteristic
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—41no—
363C3×C4—121no—
364C3×C4—121no—
365C3×C4—121no—
366C3×C4—241no—
367Dic3—41no—
368Dic3—41no—
369Dic3—41no—
370Dic3—81no—
371Dic3—121no—
372Dic3—121no—
373Dic3—121no—
374Dic3—121no—
375Dic3—241no—
376Dic3—241no—
377Dic3—241no—
378Dic3—241no—
379Dic3—242no—
380C32#161511yescharacteristic, complemented, Sylow
381C23—61no—
382C23D3×D1211yescharacteristic
383Q8—361no—
384D4—121no—
385D4—121no—
386D4—121no—
387C2×C4—41no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—121no—
394C2×C4—122no—
395C2×C4—121no—
396C2×C4—181no—
397C2×C4—181no—
398C2×C4—361no—
399C2×C4—361no—
400C2×C4—361no—
401C2×C4—721no—
402C2×C4#380211yescharacteristic
403C2×C4D3×#6711yescharacteristic
404C8—41no—
405C8—121no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—241no—
416C2×C3#473311yescharacteristic
417C2×C3#474211yescharacteristic
418C2×C3#475311yescharacteristic
419C2×C3#505311yescharacteristic
420C2×C3#517311yescharacteristic
421C2×C3#520111yescharacteristic
422D3—81no—
423C22—21no—
424C22—21no—
425C22—121no—
426C22—121no—
427C22—121no—
428C22#6380011yescharacteristic
429C22#6380611yescharacteristic
430C22#6392211yescharacteristic
431C4—21no—
432C4—21no—
433C4—121no—
434C4—121no—
435C4—121no—
436C4—241no—
437C4—361no—
438C4—361no—
439C4—721no—
440C3—21no—
441C3#6813611yescharacteristic, complemented
442C3#7117011yescharacteristic, complemented
443C2—21no—
444C2—21no—
445C2—241no—
446C2#1059040811yescharacteristic
447C2#1059096011yescharacteristic
448C2#1059102011yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radicalC3×#930C22
hypercenterC22⋊C8D32
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #10591225C2semidirect
4. #10591135C2semidirect
5. #10589333C2semidirect
6. C3×#4469C2semidirect
40. #4469D3semidirect
380. C32#1615semidirect
441. C3#68136semidirect
442. C3#71170semidirect

Maximal subgroups

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

subgroupindex
#105949732
C3×#47352
#105912252
#105911352
#105893332
C3×#44692
#105891502
#711703
#681363