Finite Group Databasebeta

← C3×#71902 #11778129

Subgroups — C3×#71902 #11778129

Order 1152.

635 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 635 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C32×#544C211yesmaximal, characteristic, complemented
2C3×#5046C212yesmaximal
3C3×#4991C211yesmaximal, characteristic
4C3×#4538C212yesmaximal, complemented
5C3×#4528C211yesmaximal, characteristic, complemented
6C3×#1599—31nomaximal
7#71902C311yesmaximal, characteristic, direct product factor
8C22×C3×D12C2211yescharacteristic
9C32×C4⋊Q8—22no—
10C32×#125—22no—
11C32×C22⋊Q8—21no—
12C32×C22⋊Q8C2212yes—
13C32×#117—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C3×#215—22no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×(C2×D3)⋊C4—21no—
18C3×C3⋊#95C2211yescharacteristic
19C3×#830C2212yes—
20C3×#809—22no—
21C3×#544—21no—
22C3×#544D311yescharacteristic, complemented
23C3×#544C2×C311yescharacteristic, complemented
24C3×#450—32no—
25C3×#394—31no—
26#5046C2×C312yes—
27#4991C2×C311yescharacteristic
28C3×#328—32no—
29C3×#324—31no—
30#4538C2×C312yescomplemented
31#4528C2×C311yescharacteristic, complemented
32C23×C3×D3—21no—
33C2×C32×Q8—21no—
34C2×C32×Q8D412yes—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3×Dic3—21no—
39C2×C3×D12—22no—
40C2×C3×D12—42no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—22no—
45C32×C4⋊C4—22no—
46C32×C4⋊C4—22no—
47C32×C4⋊C4D412yes—
48C32×C22⋊C4—22no—
49C32×C42—22no—
50C3×#215—44no—
51C3×(C2×D3)⋊C4—42no—
52C3×(C2×D3)⋊C4—42no—
53C2×C3×C3⋊C8—22no—
54#1599—31noSylow
55C22×C3×D4—31no—
56C22×D12C22×C311yescharacteristic
57C2×C3×SD16—62no—
58C3×C4⋊Q8—24no—
59C3×C4⋊Q8—22no—
60C3×C4⋊Q8—22no—
61C3×#125—24no—
62C3×#125—22no—
63C3×#125—22no—
64C3×C22⋊Q8—22no—
65C3×C22⋊Q8—21no—
66C3×C22⋊Q8—21no—
67C3×C22⋊Q8—22no—
68C3×C22⋊Q8C2×D312yes—
69C3×C22⋊Q8C22×C312yes—
70C3×#117—22no—
71C3×#117—21no—
72C3×#117—21no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4C2×D311yescharacteristic
75C2×C3×C4⋊C4C22×C311yescharacteristic
76C2×C3×C22⋊C4—61no—
77C2×C3×C22⋊C4—61no—
78C2×#215—22no—
79C2×(C2×D3)⋊C4—21no—
80C2×(C2×D3)⋊C4—21no—
81C3×#102—62no—
82C3×C22⋊C8—32no—
83C3×#95—31no—
84C3⋊#95C22×C311yescharacteristic
85#830C22×C312yes—
86#809—22no—
87C23×C32C2×D411yescharacteristic
88C22×C3×D3—22no—
89C22×C3×D3—41no—
90C22×C3×D3—41no—
91C22×C3×D3—41no—
92C22×C3×D3—41no—
93C22×C3×D3—41no—
94C22×C3×D3—41no—
95C32×Q8—42no—
96C32×Q8—81no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4—21no—
102C2×C32×C4—41no—
103C2×C32×C4—41no—
104C2×C32×C4SD1612yescomplemented
105C2×C32×C4C2×D412yes—
106C2×C3×Dic3—41no—
107C2×C3×Dic3—41no—
108C2×C3×Dic3—41no—
109C3×D12—24no—
110C3×D12—42no—
111C3×C3⋊C8—42no—
112#544C3×D311yescharacteristic, complemented
113#450—32no—
114#394—31no—
115#328—32no—
116#324—31no—
117C24×C3—61no—
118C23×D3—21no—
119C2×C3×Q8—22no—
120C2×C3×Q8—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—22no—
123C2×C3×Q8#6712yes—
124C2×C3×Q8C3×D412yes—
125C2×C3×D4—62no—
126C2×C3×D4—122no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—61no—
131C22×C3×C4#6711yescharacteristic
132C22×C3×C4#6711yescharacteristic
133C22×C3×C4C3×D411yescharacteristic
134C22×C3×C4C3×D411yescharacteristic
135C22×C3×C4C22×D311yescharacteristic
136C22×C3×C4C23×C311yescharacteristic
137C22×Dic3—21no—
138C2×D12—22no—
139C2×D12—42no—
140C3×SD16—124no—
141C2×C3×C8—62no—
142C3×C4⋊C4—24no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—22no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—24no—
153C3×C4⋊C4—22no—
154C3×C4⋊C4—22no—
155C3×C4⋊C4—24no—
156C3×C4⋊C4—22no—
157C3×C4⋊C4—22no—
158C3×C4⋊C4—22no—
159C3×C4⋊C4—22no—
160C3×C4⋊C4—22no—
161C3×C4⋊C4#6712yes—
162C3×C4⋊C4C3×D412yes—
163C3×C22⋊C4—24no—
164C3×C22⋊C4—22no—
165C3×C22⋊C4—22no—
166C3×C22⋊C4—122no—
167C3×C22⋊C4—122no—
168C3×C42—24no—
169C3×C42—22no—
170C3×C42—22no—
171#215—44no—
172(C2×D3)⋊C4—42no—
173(C2×D3)⋊C4—42no—
174C2×C3⋊C8—22no—
175C22×C32—21no—
176C22×C32—21no—
177C22×C32#12011yescharacteristic
178C22×C32C2×SD1611yescharacteristic
179C22×C32#13711yescharacteristic
180C2×C3×D3—42no—
181C2×C3×D3—42no—
182C2×C3×D3—42no—
183C2×C3×D3—81no—
184C2×C3×D3—81no—
185C2×C3×D3—81no—
186C2×C3×D3—81no—
187C32×C4—22no—
188C32×C4—22no—
189C32×C4—42no—
190C32×C4—41no—
191C32×C4—42no—
192C3×Dic3—81no—
193C22×D4—31no—
194C2×SD16—62no—
195C4⋊Q8—22no—
196#125—22no—
197C22⋊Q8—21no—
198C22⋊Q8C2×C3×D312yes—
199#117—21no—
200C2×C4⋊C4C2×C3×D311yescharacteristic
201C2×C22⋊C4—61no—
202C2×C22⋊C4—61no—
203#102—62no—
204C22⋊C8—32no—
205#95—31no—
206C23×C3—21no—
207C23×C3—62no—
208C23×C3—121no—
209C23×C3—121no—
210C23×C3—121no—
211C23×C3—121no—
212C23×C3—121no—
213C23×C3—121no—
214C23×C3C2×#6711yescharacteristic
215C23×C3C2×C3×D411yescharacteristic
216C22×D3—22no—
217C22×D3—41no—
218C22×D3—41no—
219C22×D3—41no—
220C22×D3—41no—
221C22×D3—41no—
222C22×D3—41no—
223C3×Q8—42no—
224C3×Q8—42no—
225C3×Q8—82no—
226C3×Q8—82no—
227C3×Q8—81no—
228C3×Q8—81no—
229C3×D4—64no—
230C3×D4—122no—
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—24no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—21no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—41no—
249C2×C3×C4—41no—
250C2×C3×C4—41no—
251C2×C3×C4—41no—
252C2×C3×C4—81no—
253C2×C3×C4—81no—
254C2×C3×C4—121no—
255C2×C3×C4—121no—
256C2×C3×C4—121no—
257C2×C3×C4#21512yescomplemented
258C2×C3×C4C3×SD1612yescomplemented
259C2×C3×C4C2×#6712yes—
260C2×C3×C4C2×C3×D412yes—
261C2×Dic3—41no—
262C2×Dic3—41no—
263C2×Dic3—41no—
264D12—24no—
265D12—42no—
266C3×C8—122no—
267C3⋊C8—42no—
268C2×C32—21no—
269C2×C32—21no—
270C2×C32#44811yescharacteristic
271C2×C32#45411yescharacteristic
272C2×C32B(4,𝔽2)11yescharacteristic
273C3×D3—82no—
274C24—61no—
275C2×Q8—21no—
276C2×Q8C3×#6712yes—
277C2×D4—62no—
278C2×D4—122no—
279C22×C4—61no—
280C22×C4C3×#6711yescharacteristic
281C22×C4C3×#6711yescharacteristic
282C22×C4C22×C3×D311yescharacteristic
283SD16—124no—
284C2×C8—62no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—22no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4C3×#6712yes—
292C22⋊C4—22no—
293C22⋊C4—122no—
294C22⋊C4—122no—
295C42—22no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—21no—
302C22×C3—21no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—122no—
306C22×C3—122no—
307C22×C3—122no—
308C22×C3—241no—
309C22×C3—241no—
310C22×C3—241no—
311C22×C3—241no—
312C22×C3C2×#21511yescharacteristic
313C22×C3#94211yescharacteristic
314C22×C3#95311yescharacteristic
315C22×C3C3×#12011yescharacteristic
316C22×C3C2×C3×SD1611yescharacteristic
317C22×C3C3×#13711yescharacteristic
318C2×D3—42no—
319C2×D3—42no—
320C2×D3—42no—
321C2×D3—81no—
322C2×D3—81no—
323C2×D3—81no—
324C2×D3—81no—
325C3×C4—24no—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—42no—
331C3×C4—42no—
332C3×C4—44no—
333C3×C4—44no—
334C3×C4—41no—
335C3×C4—42no—
336C3×C4—42no—
337C3×C4—42no—
338C3×C4—41no—
339C3×C4—42no—
340C3×C4—241no—
341Dic3—81no—
342C32#159911yescharacteristic, complemented, Sylow
343C23—62no—
344C23—121no—
345C23—121no—
346C23—121no—
347C23—121no—
348C23—121no—
349C23—121no—
350C23C2×C3×#6711yescharacteristic
351Q8—42no—
352Q8—81no—
353D4—64no—
354D4—122no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—121no—
363C2×C4—121no—
364C2×C4—121no—
365C2×C4C3×#21512yescomplemented
366C2×C4C2×C3×#6712yes—
367C8—122no—
368C2×C3—21no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—21no—
375C2×C3—41no—
376C2×C3—41no—
377C2×C3—242no—
378C2×C3#522711yescharacteristic
379C2×C3#524411yescharacteristic
380C2×C3#524511yescharacteristic
381C2×C3C3×#44811yescharacteristic
382C2×C3C3×#45411yescharacteristic
383C2×C3C3×B(4,𝔽2)11yescharacteristic
384D3—82no—
385C22—21no—
386C22—21no—
387C22—122no—
388C22—122no—
389C22—122no—
390C22—241no—
391C22—241no—
392C22—241no—
393C22—241no—
394C22C2×C3×#21511yescharacteristic
395C22C3×#94211yescharacteristic
396C22C3×#95311yescharacteristic
397C4—22no—
398C4—22no—
399C4—41no—
400C4—42no—
401C4—42no—
402C4—241no—
403C3—21no—
404C3#7190211yescharacteristic, direct product factor
405C3C3×#159911yescharacteristic, complemented
406C2—21no—
407C2—21no—
408C2—242no—
409C2C3×#522711yescharacteristic
410C2C3×#524411yescharacteristic
411C2C3×#524511yescharacteristic
subgroupG/H
centerC22×C3#953
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC32×#544C2
socleC22×C32#120
prime radicalC22×C3×D12C22
hypercenterC3×#544D3
hypocenterC3C3×#1599
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#544

Complements

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

NH ≅ G/Ntype
1. C32×#544C2semidirect
4. C3×#4538C2semidirect
5. C3×#4528C2semidirect
7. #71902C3direct (N × H)
22. C3×#544D3semidirect
23. C3×#544C2×C3semidirect
30. #4538C2×C3semidirect
31. #4528C2×C3semidirect
104. C2×C32×C4SD16semidirect
112. #544C3×D3semidirect
257. C2×C3×C4#215semidirect
258. C2×C3×C4C3×SD16semidirect
342. C32#1599semidirect
365. C2×C4C3×#215semidirect
404. C3#71902direct (N × H)
405. C3C3×#1599semidirect

Maximal subgroups

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

subgroupindex
C32×#5442
C3×#50462
C3×#49912
C3×#45382
C3×#45282
C3×#15993
#719023