Finite Group Databasebeta

← #11781709

Subgroups — #11781709

Order 1152.

466 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592771C211yesmaximal, characteristic, complemented
2C3×#5073C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic, complemented
4#10590338C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6#10589097C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71283—31nomaximal
9#68399—31nomaximal
10C32×#127C2211yescharacteristic
11C2×#3753—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C3×#213—21no—
14C2×C3×#213—21no—
15C3×#874C2211yescharacteristic
16C2×#3714—21no—
17C2×#3712—21no—
18#63659—21no—
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63563—21no—
24#63557—21no—
25C3×#493—31no—
26#5073D311yescharacteristic, complemented
27#5072—31no—
28#5072—31no—
29#5072—31no—
30#5072—61no—
31#4843—31no—
32#4838—31no—
33#4688—31no—
34C3×#331—31no—
35#4544—31no—
36#4544D311yescharacteristic, complemented
37#4485—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C32×C42C2311yescharacteristic
49#3753—42no—
50#3752—21no—
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C3×#213—42no—
54C3×#213—42no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#3714—42no—
60#3712—42no—
61#1687—91noSylow
62C2×C3×D8—61no—
63C2×C3×D8—61no—
64C3×#127—21no—
65C3×#127—31no—
66C3×#127C2×D311yescharacteristic
67C3×#127C2×D311yescharacteristic
68C2×#213—21no—
69C2×#213—21no—
70C2×#213—61no—
71C2×#213—61no—
72C2×#213—61no—
73C2×#213—62no—
74C2×D24—61no—
75C2×ΓL(1,𝔽25)—61no—
76C2×ΓL(1,𝔽25)—61no—
77#874C2×D311yescharacteristic
78C4×D12—31no—
79C4×D12—31no—
80C4×D12—61no—
81C3×C4⋊C8—31no—
82C3×C4⋊C8—31no—
83C3×C4×C8—31no—
84#832—61no—
85#832—61no—
86#832—61no—
87#832—62no—
88#821—61no—
89(C2×D3)⋊C8—61no—
90(C2×D3)⋊C8—61no—
91C4⋊(C3⋊C8)—31no—
92C4⋊(C3⋊C8)—31no—
93C4⋊(C3⋊C8)—61no—
94C4⋊(C3⋊C8)C2×D311yescharacteristic
95C4⋊(C3⋊C8)C2×D311yescharacteristic
96C4×C3⋊C8C2×D311yescharacteristic
97C23×C32—41no—
98C22×C3⋊D3—21no—
99C22×C3×D3—41no—
100C32×D4—41no—
101C32×D4—41no—
102C32×D4—41no—
103C32×D4—41no—
104C32×D4—81no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C3⋊Dic3—21no—
109C4⋊(C3⋊D3)—21no—
110C4⋊(C3⋊D3)—21no—
111C4×C3⋊D3—41no—
112C4×C3⋊D3—41no—
113C3×D12—41no—
114C3×D12—41no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—81no—
118C3⋊(C3⋊C8)—41no—
119C3×C3⋊C8—21no—
120C3×C3⋊C8—41no—
121C3×C3⋊C8—41no—
122C3×C3⋊C8D812yescomplemented
123#493—31no—
124#459—91no—
125#459—91no—
126#436—91no—
127#334—91no—
128#331—31no—
129#331—91no—
130C2×C3×D4—22no—
131C2×C3×D4—21no—
132C2×C3×D4—21no—
133C2×C3×D4—21no—
134C2×C3×D4—21no—
135C2×C3×D4—21no—
136C2×C3×D4—21no—
137C2×C3×D4—41no—
138C2×C3×D4—41no—
139C2×C3×D4—61no—
140C2×C3×D4—61no—
141C2×C3×D4—61no—
142C2×D12—21no—
143C2×D12—21no—
144C2×D12—21no—
145C2×D12—31no—
146C2×D12—31no—
147C2×D12—61no—
148C2×C4×D3—61no—
149C2×C4×D3—61no—
150C2×C4×D3—121no—
151C3×D8—122no—
152C3×D8—122no—
153C2×C3×C8—31no—
154C2×C3×C8—31no—
155C2×C3×C8—61no—
156C2×C3×C8—61no—
157C3×C42—21no—
158C3×C42C22×D311yescharacteristic
159C3×C42C22×D311yescharacteristic
160#213—42no—
161#213—42no—
162#213—122no—
163#213—124no—
164#213—122no—
165#213—122no—
166(C2×D3)⋊C4—61no—
167(C2×D3)⋊C4—61no—
168(C2×D3)⋊C4—121no—
169C4⋊Dic3—31no—
170C4⋊Dic3—31no—
171C4⋊Dic3—61no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8—21no—
174C2×C3⋊C8—62no—
175C2×C3⋊C8—61no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8#6711yescharacteristic
178C2×C3⋊C8#6711yescharacteristic
179D24—122no—
180ΓL(1,𝔽25)—122no—
181ΓL(1,𝔽25)—122no—
182C22×C32—81no—
183C22×C32—81no—
184C22×C32—81no—
185C22×C32#12111yescharacteristic
186C2×C3⋊D3—41no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3×D3—81no—
190C2×C3×D3—81no—
191C2×C3×D3—81no—
192C32×C4—21no—
193C32×C4C2×D811yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C32×C4AGL(1,ℤ/8)11yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C3⋊Dic3—41no—
198C2×D8—61no—
199C2×D8—61no—
200C2×D8—181no—
201C2×D8—181no—
202C2×M16—181no—
203#127—31no—
204#127D3211yescharacteristic
205C4×D4—91no—
206C4⋊C8—31no—
207C4⋊C8—31no—
208C4⋊C8—91no—
209#102—181no—
210#102—181no—
211C22⋊C8—181no—
212C4×C8—31no—
213C23×C3—42no—
214C23×C3—41no—
215C23×C3—41no—
216C23×C3—121no—
217C22×D3—41no—
218C22×D3—61no—
219C22×D3—61no—
220C22×D3—121no—
221C3×D4—42no—
222C3×D4—42no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—41no—
228C3×D4—41no—
229C3×D4—41no—
230C3×D4—41no—
231C3×D4—81no—
232C3×D4—81no—
233C3×D4—81no—
234C3×D4—81no—
235C3×D4—82no—
236C3×D4—121no—
237C3×D4—121no—
238C3×D4—121no—
239C3×D4—121no—
240C3×D4—241no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4#23511yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4#23711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—121no—
253D12—41no—
254D12—41no—
255D12—41no—
256D12—41no—
257D12—62no—
258D12—61no—
259D12—61no—
260D12—61no—
261D12—61no—
262D12—81no—
263D12—121no—
264C4×D3—121no—
265C4×D3—121no—
266C4×D3—121no—
267C4×D3—121no—
268C4×D3—241no—
269C4×D3—241no—
270C3×C8—32no—
271C3×C8—61no—
272C3×C8—121no—
273C3×C8—121no—
274C3⋊C8—21no—
275C3⋊C8—41no—
276C3⋊C8—41no—
277C3⋊C8—122no—
278C3⋊C8—121no—
279C3⋊C8—121no—
280C3⋊C8#21312yescomplemented
281C2×C32—161no—
282C2×C32#45911yescharacteristic
283C2×C32#46911yescharacteristic
284C2×C32#47211yescharacteristic
285C3⋊D3—81no—
286C3×D3—161no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—61no—
291C2×D4—61no—
292C2×D4—61no—
293C2×D4—91no—
294C22×C4—181no—
295D8—122no—
296D8—122no—
297D8—362no—
298D8—362no—
299M16—362no—
300C2×C8—31no—
301C2×C8—31no—
302C2×C8—61no—
303C2×C8—61no—
304C2×C8—181no—
305C4⋊C4—91no—
306C22⋊C4—181no—
307C42C2×D3211yescharacteristic
308C22×C3—21no—
309C22×C3—82no—
310C22×C3—82no—
311C22×C3—82no—
312C22×C3—81no—
313C22×C3—81no—
314C22×C3—81no—
315C22×C3—81no—
316C22×C3—81no—
317C22×C3—81no—
318C22×C3—241no—
319C22×C3—241no—
320C22×C3—241no—
321C22×C3#88411yescharacteristic
322C22×C3#93811yescharacteristic
323C2×D3—81no—
324C2×D3—81no—
325C2×D3—81no—
326C2×D3—122no—
327C2×D3—121no—
328C2×D3—121no—
329C2×D3—121no—
330C2×D3—121no—
331C2×D3—121no—
332C2×D3—121no—
333C2×D3—241no—
334C2×D3—241no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—41no—
342C3×C4D3×D811yescharacteristic
343C3×C4#91111yescharacteristic
344C3×C4#91111yescharacteristic
345C3×C4#91111yescharacteristic
346C3×C4#91411yescharacteristic
347C3×C4#91411yescharacteristic
348C3×C4C2×#21311yescharacteristic
349C3×C4#93211yescharacteristic
350Dic3—121no—
351Dic3—121no—
352Dic3—241no—
353C32#168711yescharacteristic, complemented, Sylow
354C23—41no—
355C23—121no—
356C23—181no—
357D4—41no—
358D4—41no—
359D4—41no—
360D4—41no—
361D4—81no—
362D4—121no—
363D4—121no—
364D4—121no—
365D4—121no—
366D4—181no—
367D4—181no—
368D4—241no—
369C2×C4—181no—
370C2×C4—361no—
371C2×C4—361no—
372C2×C4#380411yescharacteristic
373C2×C4D3×#6711yescharacteristic
374C2×C4#381111yescharacteristic
375C8—32no—
376C8—61no—
377C8—121no—
378C8—121no—
379C8—361no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—162no—
384C2×C3—161no—
385C2×C3—161no—
386C2×C3—481no—
387C2×C3#474911yescharacteristic
388C2×C3#478211yescharacteristic
389C2×C3#478611yescharacteristic
390C2×C3#507211yescharacteristic
391C2×C3#515911yescharacteristic
392C2×C3#516011yescharacteristic
393D3—161no—
394D3—242no—
395D3—241no—
396D3—241no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—241no—
401C22—241no—
402C22—241no—
403C22—361no—
404C22—361no—
405C22—361no—
406C22#6395811yescharacteristic
407C4—21no—
408C4—361no—
409C4D3×#21311yescharacteristic
410C4#6392711yescharacteristic
411C4#6393411yescharacteristic
412C4#6393711yescharacteristic
413C3—21no—
414C3#6839911yescharacteristic, complemented
415C3#7128311yescharacteristic, complemented
416C2—161no—
417C2—481no—
418C2—721no—
419C2#1059140611yescharacteristic
420C2#1059142911yescharacteristic
421C2#1059145411yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#121
hypercenter#127D32
hypocenterC32#1687
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10592771C2semidirect
2. C3×#5073C2semidirect
3. #10590355C2semidirect
4. #10590338C2semidirect
5. C3×#4544C2semidirect
6. #10589097C2semidirect
7. #10589090C2semidirect
26. #5073D3semidirect
36. #4544D3semidirect
122. C3×C3⋊C8D8semidirect
280. C3⋊C8#213semidirect
353. C32#1687semidirect
414. C3#68399semidirect
415. C3#71283semidirect

Maximal subgroups

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

subgroupindex
#105927712
C3×#50732
#105903552
#105903382
C3×#45442
#105890972
#105890902
#712833
#683993