Finite Group Databasebeta

← #11778740

Subgroups — #11778740

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#10592667C211yesmaximal, characteristic
3C3×#4985C211yesmaximal, characteristic, complemented
4C3×#4970C211yesmaximal, characteristic, complemented
5#10589153C211yesmaximal, characteristic, complemented
6#10589151C211yesmaximal, characteristic
7#10589147C211yesmaximal, characteristic, complemented
8#71178—31nomaximal
9#69717—31nomaximal
10C2×C32×C4⋊C4C2211yescharacteristic
11#64139C2211yescharacteristic
12C3×#924C2211yescharacteristic
13C2×C3×Dic3⋊C4C2211yescharacteristic
14#63966—21no—
15#63952—21no—
16#63897—21no—
17#63888—21no—
18#63848—21no—
19#63845—21no—
20#63657C2211yescharacteristic
21#63636—21no—
22#63635—21no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×#810—21no—
28C3×#807—21no—
29#5645—31no—
30#5515—31no—
31C3×#484—31no—
32C3×#400—31no—
33#4985D311yescharacteristic, complemented
34#4970D311yescharacteristic, complemented
35#4968—31no—
36#4968—31no—
37#4968—61no—
38#4538—31no—
39#4528—31no—
40#4470—31no—
41#4469—31no—
42#4452—31no—
43#4451—31no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—21no—
47C2×C4⋊(C3⋊D3)D411yescharacteristic
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×Dic6D411yescharacteristic
52C2×#624—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55#3752—21no—
56C4⋊(C3⋊Dic3)D411yescharacteristic
57C2×C3⋊(C3⋊C8)—21no—
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—21no—
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77#946—61no—
78#930—31no—
79#930—31no—
80#930—61no—
81#929—61no—
82C4×#67—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×#107—61no—
95C3×#103—61no—
96C3×C22⋊C8—31no—
97C3×#95—31no—
98C3×#95—61no—
99C3×#95—61no—
100C3⋊#95—21no—
101C3⋊#95—21no—
102C3⋊#95C2×D311yescharacteristic
103#830—31no—
104#830—31no—
105#830—61no—
106#830C2×D311yescharacteristic
107#810—21no—
108#809—61no—
109#809—61no—
110#809—62no—
111#808—61no—
112#808—61no—
113#808—62no—
114#807—21no—
115C23×C32C2×D411yescharacteristic
116C22×C3⋊D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4—41no—
119C2×C32×C4—42no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122#638—41no—
123#638—41no—
124C2×C3⋊Dic3—21no—
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—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140#539—91no—
141#484—31no—
142#481—91no—
143#400—31no—
144#328—91no—
145#327—91no—
146#324—91no—
147C2×C3×Q8—31no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—41no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—61no—
158C2×#67—61no—
159C2×#67—121no—
160C22×Dic3—21no—
161C22×Dic3#6711yescharacteristic
162C22×Dic3#6711yescharacteristic
163C2×D12—31no—
164C2×D12—31no—
165C2×D12—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×Dic6#6711yescharacteristic
169C2×C3×C8—61no—
170C3×C4⋊C4—22no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C22⋊C4—61no—
181#217—21no—
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—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—61no—
190(C2×D3)⋊C4—121no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3#6711yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
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—
220C32×C4—81no—
221C3⋊Dic3—41no—
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⋊C4D3211yescharacteristic
237#107—61no—
238#106—181no—
239#103—61no—
240#102—181no—
241C22⋊C8—31no—
242C22⋊C8—91no—
243#95—31no—
244#95—61no—
245#95—61no—
246C23×C3—21no—
247C23×C3D3×D411yescharacteristic
248C23×C3C2×#6711yescharacteristic
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—42no—
259C2×C3×C4—42no—
260C2×C3×C4—42no—
261C2×C3×C4—41no—
262C2×C3×C4—41no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—82no—
270C2×C3×C4—121no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4—121no—
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278#67—121no—
279#67—121no—
280#67—121no—
281#67—121no—
282#67—241no—
283#67—241no—
284C2×Dic3—21no—
285C2×Dic3—21no—
286C2×Dic3—21no—
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3—21no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—41no—
293C2×Dic3—41no—
294C2×Dic3—61no—
295C2×Dic3—61no—
296C2×Dic3—121no—
297D12—121no—
298D12—121no—
299D12—122no—
300C4×D3—241no—
301C4×D3—241no—
302Dic6—41no—
303C3×C8—121no—
304C3⋊C8—41no—
305C3⋊C8—122no—
306C3⋊C8—121no—
307C3⋊C8—121no—
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—21no—
318C22×C4—31no—
319C22×C4—31no—
320C22×C4—61no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323C2×C8—61no—
324C2×C8—181no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—31no—
328C4⋊C4—61no—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—91no—
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#91811yescharacteristic
351C22×C3#91911yescharacteristic
352C22×C3#93711yescharacteristic
353C22×C3#93711yescharacteristic
354C22×C3#94211yescharacteristic
355C22×C3#95011yescharacteristic
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—82no—
372C3×C4—81no—
373C3×C4—81no—
374C3×C4—121no—
375C3×C4—121no—
376C3×C4—121no—
377C3×C4—121no—
378C3×C4—241no—
379Dic3—41no—
380Dic3—41no—
381Dic3—41no—
382Dic3—41no—
383Dic3—81no—
384Dic3—121no—
385Dic3—121no—
386Dic3—241no—
387C32#161511yescharacteristic, complemented, Sylow
388C23—181no—
389C23D3×#6711yescharacteristic
390Q8—121no—
391D4—361no—
392D4—361no—
393D4—361no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—121no—
404C2×C4—121no—
405C2×C4—121no—
406C2×C4—121no—
407C2×C4—181no—
408C2×C4—721no—
409C2×C4D3×#6711yescharacteristic
410C2×C4#381111yescharacteristic
411C8—121no—
412C8—361no—
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#504711yescharacteristic
423C2×C3#505311yescharacteristic
424C2×C3#505311yescharacteristic
425C2×C3#506211yescharacteristic
426C2×C3#518711yescharacteristic
427C2×C3#520111yescharacteristic
428D3—241no—
429D3—241no—
430D3—481no—
431C22—21no—
432C22—21no—
433C22—361no—
434C22—361no—
435C22—361no—
436C22#6394811yescharacteristic
437C22#6394911yescharacteristic
438C22#6398311yescharacteristic
439C4—21no—
440C4—21no—
441C4—81no—
442C4—121no—
443C4—121no—
444C4—121no—
445C4—121no—
446C4—241no—
447C4—361no—
448C3—21no—
449C3#6971711yescharacteristic, complemented
450C3#7117811yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—721no—
454C2#1059139811yescharacteristic
455C2#1059152511yescharacteristic
456C2#1059165711yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radical#64139C22
hypercenterC2×C4⋊C4D32
hypocenterC32#1615
LCSG ▷ C22×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4985C2semidirect
4. C3×#4970C2semidirect
5. #10589153C2semidirect
7. #10589147C2semidirect
33. #4985D3semidirect
34. #4970D3semidirect
387. C32#1615semidirect
449. C3#69717semidirect
450. C3#71178semidirect

Maximal subgroups

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

subgroupindex
#105949802
#105926672
C3×#49852
C3×#49702
#105891532
#105891512
#105891472
#711783
#697173