Finite Group Databasebeta

← C3×#68235 #11774514

Subgroups — C3×#68235 #11774514

Order 1152.

471 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5578C211yesmaximal, characteristic
2C3×#4833C211yesmaximal, characteristic
3C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic
4C32×Q8⋊C8C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7C3×#4456C211yesmaximal, characteristic, complemented
8C3×#1485—31nomaximal
9#68235C311yesmaximal, characteristic, direct product factor
10C32×C4×Q8C2211yescharacteristic
11C3×#946C411yescharacteristic
12C3×#944C411yescharacteristic
13C2×C3×ΓL(1,𝔽25)—21no—
14C3×#897C411yescharacteristic
15C3×#896—21no—
16C3×#889—21no—
17C3×#888C411yescharacteristic
18C3×#872—21no—
19C3×C42×D3C2211yescharacteristic
20C3×C4×Dic6—21no—
21C3×C4×Dic6C2211yescharacteristic
22C32×C4⋊C8C2211yescharacteristic
23C32×C4×C8C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×#815—21no—
26C3×C8×Dic3—21no—
27C3×C4⋊(C3⋊C8)C2211yescharacteristic
28C3×C4×C3⋊C8C2211yescharacteristic
29C3×#533—31no—
30#5578C2×C311yescharacteristic
31C3×#431—31no—
32C3×C4×M16—31no—
33#4833C2×C311yescharacteristic
34C4×ΓL(1,𝔽25)C2×C311yescharacteristic
35C3×Q8⋊C8—21no—
36C3×Q8⋊C8—31no—
37C3×Q8⋊C8—31no—
38C3×Q8⋊C8—31no—
39C3×Q8⋊C8D311yescharacteristic, complemented
40C3×Q8⋊C8C2×C311yescharacteristic, complemented
41#4535C2×C311yescharacteristic, complemented
42#4484C2×C311yescharacteristic, complemented
43#4456C2×C311yescharacteristic, complemented
44C2×C32×Q8C2×C411yescharacteristic
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6—21no—
49C2×C3×Dic6C2×C411yescharacteristic
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C42—21no—
55C32×C42C2311yescharacteristic
56C3×(C2×D3)⋊C4—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3C2×C411yescharacteristic
60C3×Dic3⋊C4—21no—
61C3×Dic3⋊C4—21no—
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C3×ΓL(1,𝔽25)—24no—
72#1485—31noSylow
73C2×C3×M16—61no—
74C3×C4⋊Q8—31no—
75C3×C4⋊Q8—31no—
76C3×#125—61no—
77C3×C22⋊Q8—31no—
78C3×C22⋊Q8—31no—
79C3×C22⋊Q8—61no—
80C3×C4×Q8—21no—
81C3×C4×Q8—31no—
82C3×C4×Q8—61no—
83C3×C4×Q8C2×D311yescharacteristic
84C3×C4×Q8C22×C311yescharacteristic
85C3×#117—61no—
86C2×C3×C42—31no—
87#946C3×C411yescharacteristic
88#944C3×C411yescharacteristic
89C2×ΓL(1,𝔽25)—21no—
90#897C3×C411yescharacteristic
91#896—21no—
92#889—21no—
93#888C3×C411yescharacteristic
94#872—21no—
95C42×D3C22×C311yescharacteristic
96C4×Dic6—21no—
97C4×Dic6C22×C311yescharacteristic
98C3×C4⋊C8—21no—
99C3×C4⋊C8—31no—
100C3×C4⋊C8C2×D311yescharacteristic
101C3×C4⋊C8C22×C311yescharacteristic
102C3×C22⋊C8—61no—
103C3×#97—61no—
104C3×C4×C8—21no—
105C3×C4×C8—31no—
106C3×C4×C8—61no—
107C3×C4×C8C2×D311yescharacteristic
108C3×C4×C8C22×C311yescharacteristic
109(C2×D3)⋊C8—21no—
110#815—21no—
111C8×Dic3—21no—
112C4⋊(C3⋊C8)C22×C311yescharacteristic
113C4×C3⋊C8C22×C311yescharacteristic
114C22×C3×D3C22⋊C411yescharacteristic
115C32×Q8—21no—
116C32×Q8—21no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C3×C4×D3—21no—
128C3×C4×D3—21no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—22no—
132C3×Dic6—21no—
133C3×Dic6—21no—
134C3×Dic6—42no—
135C32×C8—22no—
136C32×C8—41no—
137C3×C3⋊C8—22no—
138C3×C3⋊C8—41no—
139#533—31no—
140#431—31no—
141C4×M16—31no—
142Q8⋊C8—31no—
143Q8⋊C8—31no—
144Q8⋊C8—31no—
145Q8⋊C8C3×D311yescharacteristic, complemented
146C2×C3×Q8—21no—
147C2×C3×Q8—31no—
148C2×C3×Q8—61no—
149C2×C3×Q8C4×D311yescharacteristic
150C2×C3×Q8C2×C3×C411yescharacteristic
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—31no—
154C2×C4×D3C2×C3×C411yescharacteristic
155C2×C4×D3C3×D411yescharacteristic
156C2×C4×D3C3×D411yescharacteristic
157C2×Dic6—21no—
158C2×Dic6C2×C3×C411yescharacteristic
159C3×M16—64no—
160C2×C3×C8—21no—
161C2×C3×C8—21no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—41no—
165C2×C3×C8—41no—
166C2×C3×C8—61no—
167C2×C3×C8—61no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—21no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—41no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4C4×D311yescharacteristic
180C3×C4⋊C4C2×C3×C411yescharacteristic
181C3×C22⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C42—21no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—31no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—41no—
190C3×C42—61no—
191C3×C42C22×D311yescharacteristic
192C3×C42C23×C311yescharacteristic
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3C2×C3×C411yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—21no—
202C4×Dic3—21no—
203C4×Dic3C2×C3×C411yescharacteristic
204C4×Dic3C3×D411yescharacteristic
205C4×Dic3C3×D411yescharacteristic
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208ΓL(1,𝔽25)—24no—
209C22×C32C2×C22⋊C411yescharacteristic
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—21no—
213C32×C4—21no—
214C32×C4—41no—
215C32×C4—41no—
216C32×C4#13111yescharacteristic
217C32×C4#13111yescharacteristic
218C32×C4#13711yescharacteristic
219C32×C4#13711yescharacteristic
220C3×Dic3—21no—
221C3×Dic3—21no—
222C3×Dic3—41no—
223C3×Dic3—41no—
224C3×Dic3#10412yes—
225C2×M16—61no—
226C4⋊Q8—31no—
227C4⋊Q8—31no—
228#125—61no—
229C22⋊Q8—31no—
230C22⋊Q8—31no—
231C22⋊Q8—61no—
232C4×Q8—31no—
233C4×Q8—61no—
234C4×Q8C2×C3×D311yescharacteristic
235#117—61no—
236C2×C42—31no—
237C4⋊C8—31no—
238C4⋊C8C2×C3×D311yescharacteristic
239C22⋊C8—61no—
240#97—61no—
241C4×C8—31no—
242C4×C8—61no—
243C4×C8C2×C3×D311yescharacteristic
244C23×C3—31no—
245C22×D3C3×C22⋊C411yescharacteristic
246C3×Q8—22no—
247C3×Q8—21no—
248C3×Q8—21no—
249C3×Q8—21no—
250C3×Q8—21no—
251C3×Q8—41no—
252C3×Q8—61no—
253C3×Q8—61no—
254C3×Q8—122no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—31no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—62no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4—61no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4C2×C4×D311yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4C22×C3×C411yescharacteristic
278C2×C3×C4C2×C3×D411yescharacteristic
279C2×C3×C4C2×C3×D411yescharacteristic
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3C3×C22⋊C411yescharacteristic
283C2×Dic3C3×C22⋊C411yescharacteristic
284C2×Dic3C3×C22⋊C411yescharacteristic
285C4×D3—21no—
286C4×D3—21no—
287C4×D3—21no—
288C4×D3—21no—
289C4×D3—22no—
290Dic6—21no—
291Dic6—21no—
292Dic6—42no—
293C3×C8—22no—
294C3×C8—22no—
295C3×C8—42no—
296C3×C8—41no—
297C3×C8—41no—
298C3×C8—62no—
299C3×C8—81no—
300C3×C8—121no—
301C3⋊C8—22no—
302C3⋊C8—41no—
303C2×C32#40811yescharacteristic
304C2×C32#41911yescharacteristic
305C2×C32C2×#10411yescharacteristic
306C3×D3—41no—
307C2×Q8—31no—
308C2×Q8—61no—
309C2×Q8C3×C4×D311yescharacteristic
310C22×C4—31no—
311C22×C4—31no—
312C22×C4—31no—
313M16—64no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—61no—
317C2×C8—61no—
318C4⋊C4—21no—
319C4⋊C4—31no—
320C4⋊C4—61no—
321C4⋊C4—61no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4C3×C4×D311yescharacteristic
327C22⋊C4—61no—
328C22⋊C4—61no—
329C42—21no—
330C42—31no—
331C42—31no—
332C42—31no—
333C42—61no—
334C42C22×C3×D311yescharacteristic
335C22×C3—21no—
336C22×C3—61no—
337C22×C3—61no—
338C22×C3—61no—
339C22×C3D3×C22⋊C411yescharacteristic
340C22×C3C2×C3×C22⋊C411yescharacteristic
341C2×D3—21no—
342C2×D3—21no—
343C2×D3—21no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—32no—
351C3×C4—41no—
352C3×C4—42no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—61no—
358C3×C4—61no—
359C3×C4—81no—
360C3×C4—121no—
361C3×C4—121no—
362C3×C4#90111yescharacteristic
363C3×C4#90711yescharacteristic
364C3×C4#91511yescharacteristic
365C3×C4#91811yescharacteristic
366C3×C4C3×#13111yescharacteristic
367C3×C4C3×#13111yescharacteristic
368C3×C4C3×#13711yescharacteristic
369C3×C4C3×#13711yescharacteristic
370Dic3—21no—
371Dic3—21no—
372Dic3—41no—
373Dic3—41no—
374Dic3C3×#10412yes—
375C32#148511yescharacteristic, complemented, Sylow
376C23—31no—
377Q8—21no—
378Q8—21no—
379Q8—61no—
380Q8—61no—
381Q8—122no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—62no—
388C2×C4—61no—
389C2×C4—61no—
390C2×C4—61no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4C2×C3×C4×D311yescharacteristic
395C2×C4C3×D3×D411yescharacteristic
396C2×C4C3×D3×D411yescharacteristic
397C8—22no—
398C8—41no—
399C8—62no—
400C8—121no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—121no—
405C2×C3#472711yescharacteristic
406C2×C3#480211yescharacteristic
407C2×C3D3×#10411yescharacteristic
408C2×C3C3×#40811yescharacteristic
409C2×C3C3×#41911yescharacteristic
410C2×C3C2×C3×#10411yescharacteristic
411D3—41no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22C3×D3×C22⋊C411yescharacteristic
416C4—21no—
417C4—32no—
418C4—41no—
419C4—41no—
420C4—61no—
421C4—61no—
422C4—121no—
423C4—121no—
424C4C3×#90111yescharacteristic
425C4C3×#90711yescharacteristic
426C4C3×#91511yescharacteristic
427C4C3×#91811yescharacteristic
428C3—21no—
429C3#6823511yescharacteristic, direct product factor
430C3C3×#148511yescharacteristic, complemented
431C2—121no—
432C2C3×#472711yescharacteristic
433C2C3×#480211yescharacteristic
434C2C3×D3×#10411yescharacteristic
subgroupG/H
centerC2×C3×C4D3×D4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×Q8⋊C8C2
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC3×C42C23×C3
hypercenterC3×Q8⋊C8D3
hypocenterC3C3×#1485
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C32×Q8⋊C8C2semidirect
5. C3×#4535C2semidirect
6. C3×#4484C2semidirect
7. C3×#4456C2semidirect
9. #68235C3direct (N × H)
39. C3×Q8⋊C8D3semidirect
40. C3×Q8⋊C8C2×C3semidirect
41. #4535C2×C3semidirect
42. #4484C2×C3semidirect
43. #4456C2×C3semidirect
145. Q8⋊C8C3×D3semidirect
375. C32#1485semidirect
429. C3#68235direct (N × H)
430. C3C3×#1485semidirect

Maximal subgroups

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

subgroupindex
C3×#55782
C3×#48332
C3×C4×ΓL(1,𝔽25)2
C32×Q8⋊C82
C3×#45352
C3×#44842
C3×#44562
C3×#14853
#682353