Finite Group Databasebeta

← C3×#69858 #11775709

Subgroups — C3×#69858 #11775709

Order 1152.

539 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5479C211yesmaximal, characteristic
2C32×C4×M16C211yesmaximal, characteristic, complemented
3C2×C3×#803C211yesmaximal, characteristic, complemented
4C3×#4465C212yesmaximal, complemented
5C3×#4464C212yesmaximal, complemented
6C3×#1524—31nomaximal
7#69858C311yesmaximal, characteristic, direct product factor
8C2×C32×M16—21no—
9C2×C32×C42C2211yescharacteristic
10C3×#930C411yescharacteristic
11C3×#929—21no—
12C3×C4×#67—21no—
13C3×#924C411yescharacteristic
14C22×C3×C3⋊C8—21no—
15C3×#876—21no—
16C3×#875C2211yescharacteristic
17C3×C4×D12C411yescharacteristic
18C3×#872—21no—
19C3×#870C2211yescharacteristic
20C3×C4×Dic6C411yescharacteristic
21C32×#97C2212yes—
22C32×C4×C8—21no—
23C3×#803—21no—
24C3×#803C2212yes—
25C3×#529—31no—
26#5479C2×C311yescharacteristic
27C3×C4×M16—21no—
28C3×C4×M16D311yescharacteristic, complemented
29C3×C4×M16C2×C311yescharacteristic, complemented
30C2×C3×#97—31no—
31C2×#803C2×C311yescharacteristic, complemented
32C3×#330—32no—
33C3×#329—32no—
34#4465C2×C312yescomplemented
35#4464C2×C312yescomplemented
36C22×C32×C4C2×C411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C2×C3×#67—21no—
40C2×C3×D12C2×C411yescharacteristic
41C2×C3×C4×D3—21no—
42C2×C3×Dic6C2×C411yescharacteristic
43C32×M16—24no—
44C2×C32×C8—22no—
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48C32×C42C2311yescharacteristic
49C3×#217—21no—
50C3×(C2×D3)⋊C4—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×(C2×D3)⋊C4—21no—
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3C2×C411yescharacteristic
55C3×C4⋊Dic3C2×C411yescharacteristic
56C3×Dic3⋊C4—21no—
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—24no—
62C2×C3×C3⋊C8—22no—
63#1524—31noSylow
64C2×C3×M16—22no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C22×C3×C8—61no—
68C3×#126—61no—
69C3×#125—31no—
70C3×#124—31no—
71C3×#123—61no—
72C3×C22⋊Q8—31no—
73C3×#121—31no—
74C3×C4×Q8—31no—
75C3×C4×D4—31no—
76C3×C4×D4—61no—
77C3×#117—61no—
78C2×C3×C42—21no—
79C2×C3×C42C2×D311yescharacteristic
80C2×C3×C42C22×C311yescharacteristic
81#930C3×C411yescharacteristic
82#929—21no—
83C4×#67—21no—
84#924C3×C411yescharacteristic
85C22×C3⋊C8—21no—
86#876—21no—
87#875C22×C311yescharacteristic
88C4×D12C3×C411yescharacteristic
89#872—21no—
90#870C22×C311yescharacteristic
91C4×Dic6C3×C411yescharacteristic
92C3×#97—22no—
93C3×#97—32no—
94C3×#97—61no—
95C3×#97C2×D312yes—
96C3×#97C22×C312yes—
97C3×C4×C8—22no—
98C3×C4×C8—21no—
99C3×C4×C8—21no—
100#803—21no—
101#803C22×C312yes—
102C23×C32C22⋊C411yescharacteristic
103C22×C3×D3—21no—
104C2×C32×C4—22no—
105C2×C32×C4—22no—
106C2×C32×C4—41no—
107C2×C32×C4C22⋊C411yescharacteristic
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C3×#67—42no—
114C2×C3×Dic3—21no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—21no—
117C3×D12—41no—
118C3×C4×D3—42no—
119C3×Dic6—41no—
120C32×C8—24no—
121C3×C3⋊C8—24no—
122#529—31no—
123C4×M16C3×D311yescharacteristic, complemented
124C2×#97—31no—
125#330—32no—
126#329—32no—
127C2×C3×Q8—31no—
128C2×C3×D4—31no—
129C2×C3×D4—61no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—61no—
134C22×C3×C4C4×D311yescharacteristic
135C22×C3×C4D1211yescharacteristic
136C22×C3×C4#6711yescharacteristic
137C22×C3×C4C2×C3×C411yescharacteristic
138C22×C3×C4C3×D411yescharacteristic
139C22×C3×C4C3×D411yescharacteristic
140C2×#67—21no—
141C2×D12C2×C3×C411yescharacteristic
142C2×C4×D3—21no—
143C2×Dic6C2×C3×C411yescharacteristic
144C3×M16—28no—
145C3×M16—24no—
146C3×M16—24no—
147C2×C3×C8—24no—
148C2×C3×C8—22no—
149C2×C3×C8—22no—
150C2×C3×C8—64no—
151C2×C3×C8—62no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C22⋊C4—61no—
159C3×C22⋊C4—61no—
160C3×C22⋊C4—61no—
161C3×C22⋊C4—61no—
162C3×C22⋊C4—61no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42—21no—
167C3×C42—61no—
168C3×C42C4×D311yescharacteristic
169C3×C42D1211yescharacteristic
170C3×C42#6711yescharacteristic
171C3×C42C2×C3×C411yescharacteristic
172C3×C42C3×D411yescharacteristic
173C3×C42C3×D411yescharacteristic
174C3×C42C22×D311yescharacteristic
175C3×C42C23×C311yescharacteristic
176#217—21no—
177(C2×D3)⋊C4—21no—
178(C2×D3)⋊C4—21no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—21no—
181C4⋊Dic3C2×C3×C411yescharacteristic
182C4⋊Dic3C2×C3×C411yescharacteristic
183Dic3⋊C4—21no—
184Dic3⋊C4—21no—
185Dic3⋊C4—21no—
186Dic3⋊C4—21no—
187C4×Dic3—21no—
188C2×C3⋊C8—24no—
189C2×C3⋊C8—22no—
190C22×C32—21no—
191C22×C32—21no—
192C22×C32#10412yes—
193C22×C32C2×C22⋊C411yescharacteristic
194C2×C3×D3—41no—
195C2×C3×D3—41no—
196C2×C3×D3—41no—
197C32×C4—21no—
198C32×C4—21no—
199C32×C4—21no—
200C32×C4—21no—
201C32×C4—21no—
202C32×C4#10412yes—
203C3×Dic3—41no—
204C3×Dic3—41no—
205C3×Dic3—41no—
206C2×M16—21no—
207C22×C8—61no—
208#126—61no—
209#125—31no—
210#124—31no—
211#123—61no—
212C22⋊Q8—31no—
213#121—31no—
214C4×Q8—31no—
215C4×D4—31no—
216C4×D4—61no—
217#117—61no—
218C2×C42C2×C3×D311yescharacteristic
219#97—32no—
220#97—61no—
221#97C2×C3×D312yes—
222C4×C8—21no—
223C23×C3—21no—
224C23×C3—61no—
225C23×C3(C2×D3)⋊C411yescharacteristic
226C23×C3C3×C22⋊C411yescharacteristic
227C22×D3—21no—
228C3×Q8—121no—
229C3×D4—121no—
230C3×D4—122no—
231C2×C3×C4—24no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—22no—
235C2×C3×C4—22no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—42no—
243C2×C3×C4—41no—
244C2×C3×C4—41no—
245C2×C3×C4—42no—
246C2×C3×C4—61no—
247C2×C3×C4—61no—
248C2×C3×C4—61no—
249C2×C3×C4—122no—
250C2×C3×C4(C2×D3)⋊C411yescharacteristic
251C2×C3×C4(C2×D3)⋊C411yescharacteristic
252C2×C3×C4(C2×D3)⋊C411yescharacteristic
253C2×C3×C4C3×C22⋊C411yescharacteristic
254C2×C3×C4C3×C22⋊C411yescharacteristic
255C2×C3×C4C3×C22⋊C411yescharacteristic
256C2×C3×C4C2×C4×D311yescharacteristic
257C2×C3×C4C2×D1211yescharacteristic
258C2×C3×C4C2×#6711yescharacteristic
259C2×C3×C4C22×C3×C411yescharacteristic
260C2×C3×C4C2×C3×D411yescharacteristic
261C2×C3×C4C2×C3×D411yescharacteristic
262#67—42no—
263C2×Dic3—21no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266D12—41no—
267C4×D3—42no—
268Dic6—41no—
269C3×C8—28no—
270C3×C8—24no—
271C3×C8—24no—
272C3×C8—64no—
273C3⋊C8—24no—
274C2×C32—22no—
275C2×C32#41311yescharacteristic
276C2×C32C2×#10411yescharacteristic
277C2×C32C2×#10411yescharacteristic
278C3×D3—81no—
279C2×Q8—31no—
280C2×D4—31no—
281C2×D4—61no—
282C22×C4—61no—
283C22×C4C3×C4×D311yescharacteristic
284C22×C4C3×D1211yescharacteristic
285C22×C4C3×#6711yescharacteristic
286M16—24no—
287C2×C8—22no—
288C2×C8—64no—
289C2×C8—62no—
290C4⋊C4—31no—
291C4⋊C4—31no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—61no—
295C4⋊C4—61no—
296C22⋊C4—61no—
297C22⋊C4—61no—
298C22⋊C4—61no—
299C22⋊C4—61no—
300C22⋊C4—61no—
301C42—61no—
302C42C3×C4×D311yescharacteristic
303C42C3×D1211yescharacteristic
304C42C3×#6711yescharacteristic
305C42C22×C3×D311yescharacteristic
306C22×C3—21no—
307C22×C3—21no—
308C22×C3—21no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—22no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—121no—
315C22×C3—121no—
316C22×C3—121no—
317C22×C3#80512yes—
318C22×C3C3×#10412yes—
319C22×C3C2×(C2×D3)⋊C411yescharacteristic
320C22×C3C2×C3×C22⋊C411yescharacteristic
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C3×C4—22no—
325C3×C4—22no—
326C3×C4—22no—
327C3×C4—21no—
328C3×C4—21no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—22no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—121no—
341C3×C4—121no—
342C3×C4—121no—
343C3×C4#82512yes—
344C3×C4C3×#10412yes—
345Dic3—41no—
346Dic3—41no—
347Dic3—41no—
348C32#152411yescharacteristic, complemented, Sylow
349C23—61no—
350C23C3×(C2×D3)⋊C411yescharacteristic
351Q8—121no—
352D4—121no—
353D4—122no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—61no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—122no—
361C2×C4C3×(C2×D3)⋊C411yescharacteristic
362C2×C4C3×(C2×D3)⋊C411yescharacteristic
363C2×C4C3×(C2×D3)⋊C411yescharacteristic
364C2×C4C2×C3×C4×D311yescharacteristic
365C2×C4C2×C3×D1211yescharacteristic
366C2×C4C2×C3×#6711yescharacteristic
367C8—24no—
368C8—64no—
369C2×C3—22no—
370C2×C3—22no—
371C2×C3—21no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3—42no—
375C2×C3—241no—
376C2×C3C2×#80511yescharacteristic
377C2×C3#513211yescharacteristic
378C2×C3C2×#82511yescharacteristic
379C2×C3C3×#41311yescharacteristic
380C2×C3C2×C3×#10411yescharacteristic
381C2×C3C2×C3×#10411yescharacteristic
382D3—81no—
383C22—21no—
384C22—21no—
385C22—121no—
386C22—121no—
387C22—121no—
388C22C3×#80512yes—
389C22C2×C3×(C2×D3)⋊C411yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—121no—
396C4—121no—
397C4—121no—
398C4C3×#82512yes—
399C3—21no—
400C3#6985811yescharacteristic, direct product factor
401C3C3×#152411yescharacteristic, complemented
402C2—22no—
403C2—241no—
404C2C2×C3×#80511yescharacteristic
405C2C3×#513211yescharacteristic
406C2C2×C3×#82511yescharacteristic
subgroupG/H
centerC2×C3×C4(C2×D3)⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×C4×M16C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C4
cosocleC3×C42C23×C3
hypercenterC3×C4×M16D3
hypocenterC3C3×#1524
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C42 ◁ C3×C4×M16

Complements

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

NH ≅ G/Ntype
2. C32×C4×M16C2semidirect
3. C2×C3×#803C2semidirect
4. C3×#4465C2semidirect
5. C3×#4464C2semidirect
7. #69858C3direct (N × H)
28. C3×C4×M16D3semidirect
29. C3×C4×M16C2×C3semidirect
31. C2×#803C2×C3semidirect
34. #4465C2×C3semidirect
35. #4464C2×C3semidirect
123. C4×M16C3×D3semidirect
348. C32#1524semidirect
400. C3#69858direct (N × H)
401. C3C3×#1524semidirect

Maximal subgroups

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

subgroupindex
C3×#54792
C32×C4×M162
C2×C3×#8032
C3×#44652
C3×#44642
C3×#15243
#698583