Finite Group Databasebeta

← #11778760

Subgroups — #11778760

Order 1152.

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

normal subgroups only

This group has 468 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
2#10592421C211yesmaximal, characteristic, complemented
3#10591226C211yesmaximal, characteristic, complemented
4#10591092C211yesmaximal, characteristic
5C3×#4470C211yesmaximal, characteristic
6C3×#4469C211yesmaximal, characteristic, complemented
7#10589154C211yesmaximal, characteristic, complemented
8#68298—31nomaximal
9#68136—31nomaximal
10C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
11#64133C2211yescharacteristic
12C3×#930C2211yescharacteristic
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#63645—21no—
22#63643—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63573—21no—
28#63563—21no—
29#5602—31no—
30#5515—31no—
31#5034—31no—
32#4986—31no—
33#4735—31no—
34#4722—31no—
35#4722—31no—
36#4722—61no—
37#4659—31no—
38C3×#327—31no—
39C3×#324—31no—
40#4470D311yescharacteristic
41#4469D311yescharacteristic, complemented
42#4467—31no—
43#4452—31no—
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)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58#3750—21no—
59C3×(C2×D3)⋊C4—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—
74#935—61no—
75#935—61no—
76D4×Dic3—61no—
77#930C2×D311yescharacteristic
78#929—61no—
79C4×#67—61no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—61no—
83#924—31no—
84#924—31no—
85#924—61no—
86C2×Dic3⋊C4C2×D311yescharacteristic
87#898—61no—
88#896—61no—
89#894—61no—
90#889—61no—
91#889—61no—
92#879—61no—
93#878—61no—
94C3×C22⋊C8—21no—
95C3×C22⋊C8—31no—
96C3×C22⋊C8C2×D311yescharacteristic
97C3×C22⋊C8C2×D311yescharacteristic
98C3×#95—31no—
99#832—61no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95C2×D311yescharacteristic
105#830C2×D311yescharacteristic
106#821—61no—
107#818—61no—
108#818—61no—
109#818—62no—
110#817—61no—
111#816—61no—
112#816—61no—
113#816—62no—
114#808—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—42no—
124#634—41no—
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×D12—41no—
137D3×Dic3—81no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#539—91no—
141#484—91no—
142#481—91no—
143#400—91no—
144#328—91no—
145#327—31no—
146#324—31no—
147C2×C3×D4—31no—
148C2×C3×D4—61no—
149C22×C3×C4—21no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—61no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C2×#67—21no—
156C22×Dic3—21no—
157C22×Dic3—61no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—121no—
161C22×Dic3D1211yescharacteristic
162C22×Dic3D1211yescharacteristic
163C2×D12D1211yescharacteristic
164C2×C4×D3—61no—
165C2×Dic6—31no—
166C2×Dic6—31no—
167C2×Dic6—61no—
168C2×C3×C8—22no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—61no—
172C3×C4⋊C4—31no—
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—31no—
187C4⋊Dic3—31no—
188C4⋊Dic3—61no—
189C4⋊Dic3—61no—
190C4⋊Dic3—62no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—121no—
196C4⋊Dic3D1211yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—121no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C2×C3⋊C8—21no—
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#12011yescharacteristic
213C22×C32#13511yescharacteristic
214C22×C32#13711yescharacteristic
215C2×C3×D3—41no—
216C2×C3×D3—41no—
217C2×C3×D3—41no—
218C32×C4—21no—
219C32×C4—21no—
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C3⋊Dic3—81no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—81no—
227#126—181no—
228#125—181no—
229#123—181no—
230#123—181no—
231C22⋊Q8—91no—
232C22⋊Q8—181no—
233#121—31no—
234C4×D4—181no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—91no—
237#107—181no—
238#106—181no—
239#103—181no—
240#102—181no—
241C22⋊C8—31no—
242C22⋊C8D3211yescharacteristic
243#95—31no—
244#95—181no—
245#95—181no—
246C23×C3—21no—
247C23×C3—61no—
248C23×C3C2×D1211yescharacteristic
249C23×C3D3×D411yescharacteristic
250C22×D3—21no—
251C3×D4—121no—
252C3×D4—121no—
253C3×D4—121no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—41no—
257C2×C3×C4—41no—
258C2×C3×C4—42no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—121no—
265C2×C3×C4—121no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4C2×D1211yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272#67—41no—
273#67—41no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—41no—
280C2×Dic3—41no—
281C2×Dic3—41no—
282C2×Dic3—41no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291C2×Dic3—122no—
292C2×Dic3—121no—
293C2×Dic3—121no—
294C2×Dic3—242no—
295C2×Dic3—241no—
296D12—41no—
297C4×D3—241no—
298Dic6—121no—
299Dic6—121no—
300Dic6—122no—
301C3×C8—42no—
302C3×C8—41no—
303C3×C8—41no—
304C3×C8—121no—
305C3⋊C8—41no—
306C2×C32—21no—
307C2×C32—21no—
308C2×C32#45211yescharacteristic
309C2×C32#45411yescharacteristic
310C2×C32#45811yescharacteristic
311C3×D3—81no—
312C2×Q8—91no—
313C2×D4—31no—
314C2×D4—61no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—61no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4C2×D3211yescharacteristic
321C2×C8—21no—
322C2×C8—61no—
323C4⋊C4—31no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—91no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C22⋊C4—61no—
334C22⋊C4—181no—
335C22⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C42—181no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3#88211yescharacteristic
352C22×C3#88211yescharacteristic
353C22×C3#90411yescharacteristic
354C22×C3#90911yescharacteristic
355C22×C3#91211yescharacteristic
356C22×C3#91511yescharacteristic
357C2×D3—41no—
358C2×D3—41no—
359C2×D3—41no—
360C3×C4—22no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—41no—
366C3×C4—121no—
367C3×C4—121no—
368C3×C4—121no—
369C3×C4—241no—
370Dic3—41no—
371Dic3—41no—
372Dic3—41no—
373Dic3—81no—
374Dic3—121no—
375Dic3—121no—
376Dic3—121no—
377Dic3—121no—
378Dic3—241no—
379Dic3—241no—
380Dic3—242no—
381Dic3—241no—
382Dic3—241no—
383C32#161511yescharacteristic, complemented, Sylow
384C23—61no—
385C23D3×D1211yescharacteristic
386Q8—361no—
387D4—121no—
388D4—121no—
389D4—121no—
390C2×C4—41no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—121no—
397C2×C4—121no—
398C2×C4—121no—
399C2×C4—121no—
400C2×C4—181no—
401C2×C4—181no—
402C2×C4—362no—
403C2×C4—361no—
404C2×C4—721no—
405C2×C4D3×D1211yescharacteristic
406C2×C4#381111yescharacteristic
407C8—41no—
408C8—121no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—241no—
419C2×C3#473311yescharacteristic
420C2×C3#474211yescharacteristic
421C2×C3#474211yescharacteristic
422C2×C3#475311yescharacteristic
423C2×C3#478311yescharacteristic
424C2×C3#482711yescharacteristic
425D3—81no—
426C22—21no—
427C22—21no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22#6380011yescharacteristic
432C22#6380711yescharacteristic
433C22#6392311yescharacteristic
434C4—21no—
435C4—21no—
436C4—121no—
437C4—121no—
438C4—121no—
439C4—241no—
440C4—361no—
441C4—361no—
442C4—721no—
443C3—21no—
444C3#6813611yescharacteristic, complemented
445C3#6829811yescharacteristic, complemented
446C2—21no—
447C2—21no—
448C2—241no—
449C2#1059040911yescharacteristic
450C2#1059096911yescharacteristic
451C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
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
2. #10592421C2semidirect
3. #10591226C2semidirect
6. C3×#4469C2semidirect
7. #10589154C2semidirect
41. #4469D3semidirect
383. C32#1615semidirect
444. C3#68136semidirect
445. C3#68298semidirect

Maximal subgroups

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

subgroupindex
#105949732
#105924212
#105912262
#105910922
C3×#44702
C3×#44692
#105891542
#682983
#681363