Finite Group Databasebeta

← C3×#71490 #11798426

Subgroups — C3×#71490 #11798426

Order 1152.

477 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 477 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C3×#5757C211yesmaximal, characteristic
2C2×C32×SD32C211yesmaximal, characteristic, complemented
3C3×#5192C211yesmaximal, characteristic, complemented
4C3×#5179C211yesmaximal, characteristic, complemented
5C3×#4563C211yesmaximal, characteristic, complemented
6C3×#4510C211yesmaximal, characteristic, complemented
7C3×#4508C211yesmaximal, characteristic, complemented
8C3×#2194—31nomaximal
9#71490C311yesmaximal, characteristic, direct product factor
10C3×#1004—21no—
11C2×C32×Q16C2211yescharacteristic, complemented
12C2×C32×D8C2211yescharacteristic
13C3×#942—21no—
14C3×#932—21no—
15C3×#912—21no—
16C3×#911—22no—
17C3×D3×D8—21no—
18C3×#904C2211yescharacteristic
19C3×#901C2211yescharacteristic
20C32×SD32—22no—
21C2×C32×C16C2211yescharacteristic, complemented
22C3×#836—21no—
23C3×#829—21no—
24C3×#828—21no—
25C3×#819C2211yescharacteristic, complemented
26C3×#812C2211yescharacteristic, complemented
27C3×#576—31no—
28#5757C2×C311yescharacteristic
29C3×#510—31no—
30C2×C3×SD32—21no—
31C2×C3×SD32D311yescharacteristic, complemented
32C2×C3×SD32C2×C311yescharacteristic, complemented
33C3×#473—31no—
34#5192C2×C311yescharacteristic, complemented
35#5179C2×C311yescharacteristic, complemented
36C3×#361—31no—
37C3×#359—31no—
38C3×#350—31no—
39#4563C2×C311yescharacteristic, complemented
40#4510C2×C311yescharacteristic, complemented
41#4508C2×C311yescharacteristic, complemented
42C2×C32×Q8—21no—
43C2×C32×D4—21no—
44C2×C3×#67—42no—
45C3×#237—22no—
46C3×#237—41no—
47C3×D3×D4—22no—
48C3×D3×D4—41no—
49C3×#235—21no—
50C3×#235D411yescharacteristic
51C32×Q16—21no—
52C32×Q16—21no—
53C32×D8—21no—
54C32×D8D412yes—
55C2×C32×C8C2311yescharacteristic
56C3×#216—41no—
57C3×#215—41no—
58C3×#214—22no—
59C3×#213—22no—
60C3×#208—21no—
61C3×#208D411yescharacteristic
62C3×Dic12D411yescharacteristic
63C3×D24D411yescharacteristic
64C3×#204—21no—
65C3×ΓL(1,𝔽25)—21no—
66C3×D3×C8—21no—
67C32×C16—21no—
68C3×C3⋊C16—21no—
69#2194—31noSylow
70C3×H(5,𝔽2)—61no—
71#1004—21no—
72C3×#137—61no—
73C3×AGL(1,ℤ/8)—61no—
74C3×AGL(1,ℤ/8)—62no—
75C3×#135—31no—
76C3×#135—61no—
77C2×C3×Q16—21no—
78C2×C3×Q16C2×D311yescharacteristic, complemented
79C2×C3×Q16C22×C311yescharacteristic, complemented
80C2×C3×D8—21no—
81C2×C3×D8—61no—
82C2×C3×D8C2×D311yescharacteristic
83C2×C3×D8C22×C311yescharacteristic
84C3×#131—31no—
85#942—21no—
86#932—21no—
87#912—21no—
88#911—22no—
89D3×D8—21no—
90#904C22×C311yescharacteristic
91#901C22×C311yescharacteristic
92C3×Q32—61no—
93C3×SD32—24no—
94C3×SD32—22no—
95C3×SD32—22no—
96C3×SD32—61no—
97C3×M32—31no—
98C2×C3×C16—21no—
99C2×C3×C16C2×D311yescharacteristic, complemented
100C2×C3×C16C22×C311yescharacteristic, complemented
101C3×#108—31no—
102C3×#101—61no—
103#836—21no—
104#829—21no—
105#828—21no—
106#819C22×C311yescharacteristic, complemented
107#812C22×C311yescharacteristic, complemented
108C23×C32—41no—
109C22×C3×D3—42no—
110C32×Q8—41no—
111C32×Q8—41no—
112C32×D4—22no—
113C32×D4—41no—
114C2×C32×C4—41no—
115C2×C32×C4C2×D411yescharacteristic
116C3×#67—21no—
117C3×#67—42no—
118C3×#67—42no—
119C3×#67—41no—
120C2×C3×Dic3—42no—
121C3×D12—21no—
122C3×D12D811yescharacteristic
123C3×C4×D3—21no—
124C3×C4×D3—41no—
125C3×Dic6—21no—
126C3×Dic6D811yescharacteristic
127C32×C8C2×D411yescharacteristic
128C32×C8C2×D411yescharacteristic
129C3×C3⋊C8—21no—
130C3×C3⋊C8—41no—
131#576—31no—
132#510—31no—
133C2×SD32C3×D311yescharacteristic, complemented
134#473—31no—
135#361—31no—
136#359—31no—
137#350—31no—
138C3×#41—31no—
139C3×#41—62no—
140C3×#41—61no—
141C3×#41—121no—
142C2×C3×Q8—21no—
143C2×C3×Q8—21no—
144C2×C3×Q8—41no—
145C2×C3×D4—21no—
146C2×C3×D4—21no—
147C2×C3×D4—41no—
148C2×C3×D4—62no—
149C2×C3×D4—121no—
150C2×C3×D4—122no—
151C2×#67—42no—
152#237—22no—
153#237—41no—
154D3×D4—22no—
155D3×D4—41no—
156#235—21no—
157#235C3×D411yescharacteristic
158C3×Q16—22no—
159C3×Q16—21no—
160C3×Q16—21no—
161C3×Q16—21no—
162C3×Q16—21no—
163C3×Q16—31no—
164C3×Q16—41no—
165C3×Q16—121no—
166C3×SD16—62no—
167C3×SD16—61no—
168C3×SD16—121no—
169C3×D8—21no—
170C3×D8—21no—
171C3×D8—22no—
172C3×D8—31no—
173C3×D8—41no—
174C3×D8—62no—
175C3×D8#6712yes—
176C3×D8C3×D412yes—
177C3×M16—31no—
178C3×M16—61no—
179C3×M16—61no—
180C2×C3×C8—21no—
181C2×C3×C8—61no—
182C2×C3×C8C22×D311yescharacteristic
183C2×C3×C8C23×C311yescharacteristic
184#216—41no—
185#215—41no—
186#214—22no—
187#213—22no—
188#208—21no—
189#208C3×D411yescharacteristic
190Dic12C3×D411yescharacteristic
191D24C3×D411yescharacteristic
192#204—21no—
193ΓL(1,𝔽25)—21no—
194D3×C8—21no—
195C3×C16—22no—
196C3×C16—21no—
197C3×C16—21no—
198C3×C16—61no—
199C3⋊C16—21no—
200C22×C32—42no—
201C22×C32—161no—
202C22×C32AGL(1,ℤ/8)11yescharacteristic
203C2×C3×D3—21no—
204C2×C3×D3—41no—
205C2×C3×D3—162no—
206C32×C4—81no—
207C32×C4#12011yescharacteristic
208C32×C4C2×D811yescharacteristic
209C3×Dic3—21no—
210C3×Dic3—41no—
211H(5,𝔽2)—61no—
212#137—61no—
213AGL(1,ℤ/8)—61no—
214AGL(1,ℤ/8)—62no—
215#135—31no—
216#135—61no—
217C2×Q16C2×C3×D311yescharacteristic, complemented
218C2×D8—61no—
219C2×D8C2×C3×D311yescharacteristic
220#131—31no—
221Q32—61no—
222SD32—22no—
223SD32—61no—
224M32—31no—
225C2×C16C2×C3×D311yescharacteristic, complemented
226#108—31no—
227#101—61no—
228C23×C3—41no—
229C23×C3—41no—
230C23×C3—81no—
231C23×C3—122no—
232C22×D3—42no—
233C3×Q8—31no—
234C3×Q8—42no—
235C3×Q8—41no—
236C3×Q8—41no—
237C3×Q8—41no—
238C3×Q8—41no—
239C3×Q8—61no—
240C3×Q8—81no—
241C3×D4—22no—
242C3×D4—22no—
243C3×D4—31no—
244C3×D4—42no—
245C3×D4—41no—
246C3×D4—41no—
247C3×D4—61no—
248C3×D4—61no—
249C3×D4—81no—
250C3×D4—122no—
251C3×D4—122no—
252C3×D4—121no—
253C2×C3×C4—21no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—61no—
257C2×C3×C4—81no—
258C2×C3×C4—122no—
259C2×C3×C4—121no—
260C2×C3×C4D3×D411yescharacteristic
261C2×C3×C4C2×C3×D411yescharacteristic
262#67—21no—
263#67—42no—
264#67—42no—
265#67—41no—
266C2×Dic3—42no—
267D12—21no—
268D12C3×D811yescharacteristic
269C4×D3—21no—
270C4×D3—41no—
271Dic6—21no—
272Dic6C3×D811yescharacteristic
273C3×C8—21no—
274C3×C8—21no—
275C3×C8—61no—
276C3×C8—121no—
277C3×C8D3×D411yescharacteristic
278C3×C8C2×#6711yescharacteristic
279C3×C8C2×C3×D411yescharacteristic
280C3×C8C2×C3×D411yescharacteristic
281C3⋊C8—21no—
282C3⋊C8—41no—
283C2×C32—21no—
284C2×C32—82no—
285C2×C32#44711yescharacteristic
286C3×D3—41no—
287C3×D3—81no—
288#41—31no—
289#41—62no—
290#41—61no—
291#41—121no—
292C2×Q8—21no—
293C2×D4—21no—
294C2×D4—62no—
295C2×D4—121no—
296C2×D4—122no—
297Q16—21no—
298Q16—21no—
299Q16—31no—
300Q16—121no—
301SD16—62no—
302SD16—61no—
303SD16—121no—
304D8—21no—
305D8—31no—
306D8—62no—
307D8C3×#6712yes—
308M16—31no—
309M16—61no—
310M16—61no—
311C2×C8—61no—
312C2×C8C22×C3×D311yescharacteristic
313C16—21no—
314C16—61no—
315C22×C3—21no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3—61no—
319C22×C3—82no—
320C22×C3—121no—
321C22×C3—161no—
322C22×C3—161no—
323C22×C3—162no—
324C22×C3—482no—
325C22×C3#91111yescharacteristic
326C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
327C2×D3—21no—
328C2×D3—41no—
329C2×D3—162no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—61no—
333C3×C4—82no—
334C3×C4—81no—
335C3×C4—81no—
336C3×C4—121no—
337C3×C4D3×D811yescharacteristic
338C3×C4#93711yescharacteristic
339C3×C4C3×#12011yescharacteristic
340C3×C4C2×C3×D811yescharacteristic
341Dic3—21no—
342Dic3—41no—
343C32#219411yescharacteristic, complemented, Sylow
344C23—41no—
345C23—122no—
346Q8—31no—
347Q8—41no—
348Q8—41no—
349Q8—61no—
350D4—22no—
351D4—31no—
352D4—41no—
353D4—61no—
354D4—61no—
355D4—122no—
356D4—122no—
357D4—121no—
358C2×C4—41no—
359C2×C4—61no—
360C2×C4—122no—
361C2×C4—121no—
362C2×C4C3×D3×D411yescharacteristic
363C8—61no—
364C8—121no—
365C8C3×D3×D411yescharacteristic
366C8C2×C3×#6711yescharacteristic
367C2×C3—22no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—82no—
372C2×C3—82no—
373C2×C3—121no—
374C2×C3—162no—
375C2×C3—241no—
376C2×C3#515611yescharacteristic
377C2×C3C3×#44711yescharacteristic
378D3—41no—
379D3—81no—
380C22—42no—
381C22—61no—
382C22—121no—
383C22—161no—
384C22—482no—
385C22C3×#91111yescharacteristic
386C4—61no—
387C4—81no—
388C4—121no—
389C4C3×D3×D811yescharacteristic
390C4C3×#93711yescharacteristic
391C3—21no—
392C3#7149011yescharacteristic, direct product factor
393C3C3×#219411yescharacteristic, complemented
394C2—21no—
395C2—82no—
396C2—121no—
397C2—241no—
398C2C3×#515611yescharacteristic
subgroupG/H
centerC2×C3#5156
commutator, cosocleC2×C3×C8C23×C3
FrattiniC2×C8C22×C3×D3
FittingC2×C32×SD32C2
socleC2×C32#447
prime radicalC3×#5757C2
hypercenterC2×C3×SD32D3
hypocenterC3C3×#2194
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×C8 ◁ C2×C3×SD32

Complements

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

NH ≅ G/Ntype
2. C2×C32×SD32C2semidirect
3. C3×#5192C2semidirect
4. C3×#5179C2semidirect
5. C3×#4563C2semidirect
6. C3×#4510C2semidirect
7. C3×#4508C2semidirect
9. #71490C3direct (N × H)
11. C2×C32×Q16C22semidirect
21. C2×C32×C16C22semidirect
25. C3×#819C22semidirect
26. C3×#812C22semidirect
31. C2×C3×SD32D3semidirect
32. C2×C3×SD32C2×C3semidirect
34. #5192C2×C3semidirect
35. #5179C2×C3semidirect
39. #4563C2×C3semidirect
40. #4510C2×C3semidirect
41. #4508C2×C3semidirect
78. C2×C3×Q16C2×D3semidirect
79. C2×C3×Q16C22×C3semidirect
99. C2×C3×C16C2×D3semidirect
100. C2×C3×C16C22×C3semidirect
106. #819C22×C3semidirect
107. #812C22×C3semidirect
133. C2×SD32C3×D3semidirect
217. C2×Q16C2×C3×D3semidirect
225. C2×C16C2×C3×D3semidirect
343. C32#2194semidirect
392. C3#71490direct (N × H)
393. C3C3×#2194semidirect

Maximal subgroups

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

subgroupindex
C3×#57572
C2×C32×SD322
C3×#51922
C3×#51792
C3×#45632
C3×#45102
C3×#45082
C3×#21943
#714903