Finite Group Databasebeta

← #11778749

Subgroups — #11778749

Order 1152.

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

normal subgroups only

This group has 473 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#10594980C211yesmaximal, characteristic
2#10592434C211yesmaximal, characteristic
3#10591226C211yesmaximal, characteristic, complemented
4#10591103C211yesmaximal, characteristic, complemented
5C3×#4469C211yesmaximal, characteristic, complemented
6C3×#4467C211yesmaximal, characteristic, complemented
7#10589151C211yesmaximal, characteristic
8#68330—31nomaximal
9#68136—31nomaximal
10#64139C2211yescharacteristic
11C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14#63966—21no—
15#63952—21no—
16#63897—21no—
17#63888—21no—
18#63848—21no—
19#63845—21no—
20C32×C22⋊C8C2211yescharacteristic
21#63648—21no—
22#63644—21no—
23C3×C3⋊#95C2211yescharacteristic
24C3×#830C2211yescharacteristic
25#63579—21no—
26#63579—21no—
27#63575—21no—
28#63566—21no—
29#5645—31no—
30#5515—31no—
31#5044—31no—
32#4986—31no—
33#4735—31no—
34#4735—31no—
35#4735—61no—
36#4722—31no—
37#4659—31no—
38C3×#328—31no—
39C3×#324—31no—
40#4470—31no—
41#4469D311yescharacteristic, complemented
42#4467D311yescharacteristic, complemented
43#4451—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#624—21no—
53C2×C32×C8—21no—
54#3752—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)D411yescharacteristic
58C3×#217—21no—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67#3722—21no—
68#3722—21no—
69#3722—21no—
70Dic32—21no—
71#1615—91noSylow
72C3×C22⋊Q8—31no—
73C2×C3×C4⋊C4—31no—
74#946—61no—
75#930—31no—
76#930—31no—
77#930—61no—
78#929—61no—
79C4×#67—61no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—31no—
82C2×C4⋊Dic3—61no—
83#924C2×D311yescharacteristic
84C2×Dic3⋊C4C2×D311yescharacteristic
85#898—61no—
86#898—61no—
87#896—61no—
88#894—61no—
89#894—61no—
90#890—61no—
91#889—61no—
92#886—61no—
93#67⋊C4—61no—
94C3×C22⋊C8—21no—
95C3×C22⋊C8—31no—
96C3×C22⋊C8C2×D311yescharacteristic
97C3×C22⋊C8C2×D311yescharacteristic
98C3×#95—31no—
99#835—61no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95C2×D311yescharacteristic
105#830C2×D311yescharacteristic
106#821—61no—
107#821—61no—
108#821—62no—
109#818—61no—
110#817—61no—
111#817—61no—
112#817—62no—
113#816—61no—
114#807—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3⋊D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120#638—41no—
121#638—41no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—42no—
125C4⋊(C3⋊D3)—41no—
126C2×C3×Dic3—21no—
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×Dic6—41no—
137#624—81no—
138C32×C8—41no—
139C3×C3⋊C8—41no—
140#539—91no—
141#484—91no—
142#481—91no—
143#400—91no—
144#328—31no—
145#327—91no—
146#324—31no—
147C2×C3×Q8—31no—
148C22×C3×C4—21no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—61no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—61no—
155C2×#67—61no—
156C2×#67—121no—
157C22×Dic3—21no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—121no—
161C22×Dic3D1211yescharacteristic
162C22×Dic3D1211yescharacteristic
163C2×D12—31no—
164C2×D12—31no—
165C2×D12—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×Dic6D1211yescharacteristic
169C2×C3×C8—22no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—61no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C22⋊C4—61no—
178#217—21no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—121no—
188C4⋊Dic3—31no—
189C4⋊Dic3—31no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—62no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—121no—
199C4⋊Dic3D1211yescharacteristic
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202Dic3⋊C4—21no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
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—81no—
222C3×Dic3—41no—
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—31no—
232C22⋊Q8—181no—
233#121—91no—
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×C3C2×D1211yescharacteristic
248C23×C3D3×D411yescharacteristic
249C22×D3—61no—
250C22×D3—61no—
251C22×D3—121no—
252C3×Q8—121no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—61no—
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—121no—
273#67—121no—
274#67—121no—
275#67—121no—
276#67—241no—
277#67—241no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—61no—
289C2×Dic3—61no—
290C2×Dic3—121no—
291C2×Dic3—122no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—242no—
297D12—121no—
298D12—121no—
299D12—122no—
300C4×D3—241no—
301C4×D3—241no—
302Dic6—41no—
303C3×C8—42no—
304C3×C8—41no—
305C3×C8—41no—
306C3×C8—121no—
307C3⋊C8—41no—
308C2×C32—21no—
309C2×C32—21no—
310C2×C32#45211yescharacteristic
311C2×C32#45411yescharacteristic
312C2×C32#45811yescharacteristic
313C3⋊D3—81no—
314C2×Q8—31no—
315C2×D4—91no—
316C2×D4—181no—
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—61no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323C2×C8—21no—
324C2×C8—61no—
325C4⋊C4—31no—
326C4⋊C4—61no—
327C4⋊C4—61no—
328C4⋊C4—61no—
329C4⋊C4—91no—
330C4⋊C4—181no—
331C4⋊C4—181no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C22⋊C4—61no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C42—181no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3#88211yescharacteristic
351C22×C3#88211yescharacteristic
352C22×C3#90411yescharacteristic
353C22×C3#90911yescharacteristic
354C22×C3#91611yescharacteristic
355C22×C3#91811yescharacteristic
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—121no—
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—241no—
363C2×D3—241no—
364C2×D3—241no—
365C3×C4—22no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—121no—
372C3×C4—121no—
373C3×C4—121no—
374C3×C4—121no—
375C3×C4—241no—
376Dic3—41no—
377Dic3—41no—
378Dic3—41no—
379Dic3—41no—
380Dic3—81no—
381Dic3—121no—
382Dic3—121no—
383Dic3—241no—
384Dic3—242no—
385Dic3—241no—
386Dic3—241no—
387C32#161511yescharacteristic, complemented, Sylow
388C23—181no—
389C23D3×D1211yescharacteristic
390Q8—121no—
391D4—361no—
392D4—361no—
393D4—361no—
394C2×C4—41no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—181no—
406C2×C4—362no—
407C2×C4—361no—
408C2×C4—721no—
409C2×C4D3×D1211yescharacteristic
410C2×C4#381111yescharacteristic
411C8—41no—
412C8—121no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—41no—
421C2×C3—41no—
422C2×C3#473311yescharacteristic
423C2×C3#474211yescharacteristic
424C2×C3#474211yescharacteristic
425C2×C3#475311yescharacteristic
426C2×C3#480811yescharacteristic
427C2×C3#482711yescharacteristic
428D3—241no—
429D3—241no—
430D3—481no—
431C22—21no—
432C22—21no—
433C22—361no—
434C22—361no—
435C22—361no—
436C22#6380111yescharacteristic
437C22#6380611yescharacteristic
438C22#6392311yescharacteristic
439C4—21no—
440C4—21no—
441C4—121no—
442C4—121no—
443C4—121no—
444C4—121no—
445C4—241no—
446C4—361no—
447C4—721no—
448C3—21no—
449C3#6813611yescharacteristic, complemented
450C3#6833011yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—721no—
454C2#1059040911yescharacteristic
455C2#1059097011yescharacteristic
456C2#1059102211yescharacteristic
subgroupG/H
centerC22#63923
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32#120
prime radical#64139C22
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. #10591226C2semidirect
4. #10591103C2semidirect
5. C3×#4469C2semidirect
6. C3×#4467C2semidirect
41. #4469D3semidirect
42. #4467D3semidirect
387. C32#1615semidirect
449. C3#68136semidirect
450. C3#68330semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105924342
#105912262
#105911032
C3×#44692
C3×#44672
#105891512
#683303
#681363