Finite Group Databasebeta

← C3×#25657 #10644264

Subgroups — C3×#25657 #10644264

Order 768.

980 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#557C211yesmaximal, characteristic
2C2×C3×#491C211yesmaximal, characteristic
3C2×C3×#479C211yesmaximal, characteristic
4C3×#2584C211yesmaximal, characteristic
5C3×#2043C212yesmaximal
6C3×#2043C212yesmaximal
7C3×#1985C211yesmaximal, characteristic
8C3×#1981C211yesmaximal, characteristic
9C3×#1865C212yesmaximal
10C3×#1863C212yesmaximal
11C3×#1763C211yesmaximal, characteristic
12#25657C311yesmaximal, characteristic, direct product factor, Sylow
13C3×#557—24no—
14C3×#557—24no—
15C2×C3×C4⋊Q8C2212yes—
16C2×C3×C4⋊Q8C2211yescharacteristic
17C2×C3×#125—22no—
18C2×C3×#125—21no—
19C2×C3×#125C2211yescharacteristic
20C2×C3×C4×Q8—21no—
21C2×C3×C4×Q8C2212yes—
22C2×C3×C4×Q8C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C3×#491—24no—
25C3×#479—24no—
26C2×C3×#107C2211yescharacteristic
27C2×C3×#106C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×#103C2212yes—
30C2×C3×#103C2212yes—
31C2×C3×#103C2212yes—
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2212yes—
35C2×C3×#103C2212yes—
36C2×C3×#97C2211yescharacteristic
37C3×#398—21no—
38C3×#395—21no—
39C3×#389—22no—
40C3×#389C2212yes—
41C3×#389C2212yes—
42C3×C4×C4⋊C4C2211yescharacteristic
43C3×#340C2212yes—
44C3×#336C2212yes—
45C3×#336C2212yes—
46C2×#557C2×C311yescharacteristic
47C2×#491C2×C311yescharacteristic
48C2×#479C2×C311yescharacteristic
49#2584C2×C311yescharacteristic
50#2043C2×C312yes—
51#2043C2×C312yes—
52#1985C2×C311yescharacteristic
53#1981C2×C311yescharacteristic
54#1865C2×C312yes—
55#1863C2×C312yes—
56#1763C2×C311yescharacteristic
57C22×C3×Q8D411yescharacteristic
58C22×C3×Q8C2312yes—
59C22×C3×Q8C2311yescharacteristic
60C22×C3×C8C2312yes—
61C22×C3×C8C2311yescharacteristic
62C22×C3×C8C2311yescharacteristic
63C3×C4⋊Q8—24no—
64C3×C4⋊Q8—24no—
65C3×C4⋊Q8—22no—
66C3×C4⋊Q8D414yes—
67C3×#125—216no—
68C3×#125—28no—
69C3×#125—22no—
70C3×#125—22no—
71C3×C4×Q8—28no—
72C3×C4×Q8—24no—
73C3×C4×Q8—24no—
74C3×C4×Q8—22no—
75C3×C4×Q8—22no—
76C3×C4×Q8—22no—
77C3×C4×Q8D414yes—
78C2×C3×C4⋊C4—22no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—22no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—22no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—22no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—22no—
88C2×C3×C4⋊C4D412yes—
89C2×C3×C4⋊C4D411yescharacteristic
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2312yes—
94C2×C3×C42—22no—
95C2×C3×C42—21no—
96C2×C3×C42—21no—
97C2×C3×C42C2312yes—
98C2×C3×C42C2311yescharacteristic
99C3×#107—22no—
100C3×#106—22no—
101C3×C4⋊C8—22no—
102C3×#103—22no—
103C3×#103—22no—
104C3×#103—24no—
105C3×#103—24no—
106C3×#103—24no—
107C3×#103—24no—
108C3×#103—24no—
109C3×#97—22no—
110C3×#95—21no—
111C3×#95—22no—
112C3×#95—22no—
113#557—24no—
114#557—24no—
115C2×C4⋊Q8C22×C312yes—
116C2×C4⋊Q8C22×C311yescharacteristic
117C2×#125—22no—
118C2×#125—21no—
119C2×#125C22×C311yescharacteristic
120C2×C4×Q8—21no—
121C2×C4×Q8C22×C312yes—
122C2×C4×Q8C22×C311yescharacteristic
123C2×C4×Q8C22×C311yescharacteristic
124#491—24no—
125#479—24no—
126C2×#107C22×C311yescharacteristic
127C2×#106C22×C311yescharacteristic
128C2×C4⋊C8C22×C311yescharacteristic
129C2×#103C22×C311yescharacteristic
130C2×#103C22×C311yescharacteristic
131C2×#103C22×C312yes—
132C2×#103C22×C312yes—
133C2×#103C22×C312yes—
134C2×#103C22×C312yes—
135C2×#103C22×C312yes—
136C2×#97C22×C311yescharacteristic
137#398—21no—
138#395—21no—
139#389—22no—
140#389C22×C312yes—
141#389C22×C312yes—
142C4×C4⋊C4C22×C311yescharacteristic
143#340C22×C312yes—
144#336C22×C312yes—
145#336C22×C312yes—
146C2×C3×Q8—22no—
147C2×C3×Q8—24no—
148C2×C3×Q8—22no—
149C2×C3×Q8—21no—
150C2×C3×Q8—22no—
151C2×C3×Q8—22no—
152C2×C3×Q8—22no—
153C2×C3×Q8—22no—
154C2×C3×Q8—22no—
155C2×C3×Q8—22no—
156C2×C3×Q8C2×D414yes—
157C2×C3×Q8C2×D412yes—
158C22×C3×C4—22no—
159C22×C3×C4—21no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4C2×D412yes—
165C22×C3×C4C2×D411yescharacteristic
166C22×C3×C4C2×D411yescharacteristic
167C22×C3×C4C2×D412yes—
168C22×C3×C4C2411yescharacteristic
169C2×C3×C8—22no—
170C2×C3×C8—21no—
171C2×C3×C8—21no—
172C2×C3×C8—22no—
173C2×C3×C8—22no—
174C2×C3×C8—22no—
175C2×C3×C8—22no—
176C3×C4⋊C4—28no—
177C3×C4⋊C4—28no—
178C3×C4⋊C4—28no—
179C3×C4⋊C4—24no—
180C3×C4⋊C4—24no—
181C3×C4⋊C4—24no—
182C3×C4⋊C4—24no—
183C3×C4⋊C4—22no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—22no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—42no—
191C3×C4⋊C4—42no—
192C3×C4⋊C4—44no—
193C3×C4⋊C4—82no—
194C3×C4⋊C4C2×D412yes—
195C3×C4⋊C4#4114yes—
196C3×C42—28no—
197C3×C42—24no—
198C3×C42—22no—
199C3×C42—22no—
200C3×C42—81no—
201C3×C42C2×D412yes—
202C3×C42C2×D412yes—
203C22×Q8C3×D411yescharacteristic
204C22×Q8C23×C312yes—
205C22×Q8C23×C311yescharacteristic
206C22×C8C23×C312yes—
207C22×C8C23×C311yescharacteristic
208C22×C8C23×C311yescharacteristic
209C4⋊Q8—24no—
210C4⋊Q8—24no—
211C4⋊Q8—22no—
212C4⋊Q8C3×D414yes—
213#125—216no—
214#125—28no—
215#125—22no—
216#125—22no—
217C4×Q8—28no—
218C4×Q8—24no—
219C4×Q8—24no—
220C4×Q8—22no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8C3×D414yes—
224C2×C4⋊C4—22no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—22no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4C3×D412yes—
235C2×C4⋊C4C3×D411yescharacteristic
236C2×C4⋊C4C23×C311yescharacteristic
237C2×C4⋊C4C23×C311yescharacteristic
238C2×C4⋊C4C23×C311yescharacteristic
239C2×C4⋊C4C23×C312yes—
240C2×C42—22no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42C23×C312yes—
244C2×C42C23×C311yescharacteristic
245#107—22no—
246#106—22no—
247C4⋊C8—22no—
248#103—22no—
249#103—22no—
250#103—24no—
251#103—24no—
252#103—24no—
253#103—24no—
254#103—24no—
255#97—22no—
256#95—21no—
257#95—22no—
258#95—22no—
259C23×C3C22×D411yescharacteristic
260C3×Q8—28no—
261C3×Q8—22no—
262C3×Q8—22no—
263C3×Q8—24no—
264C3×Q8—24no—
265C3×Q8—42no—
266C3×Q8—42no—
267C3×Q8—42no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—24no—
276C2×C3×C4—22no—
277C2×C3×C4—24no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—42no—
281C2×C3×C4—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—42no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—42no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4#12012yes—
293C2×C3×C4#12012yes—
294C2×C3×C4#13714yes—
295C2×C3×C4C22×D411yescharacteristic
296C2×C3×C4C22×D411yescharacteristic
297C2×C3×C4C2×#4112yes—
298C2×C3×C42−1+412yes—
299C3×C8—41no—
300C3×C8—41no—
301C3×C8—42no—
302C2×Q8—22no—
303C2×Q8—24no—
304C2×Q8—22no—
305C2×Q8—21no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—22no—
311C2×Q8—22no—
312C2×Q8C2×C3×D414yes—
313C2×Q8C2×C3×D412yes—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4C2×C3×D412yes—
321C22×C4C2×C3×D411yescharacteristic
322C22×C4C2×C3×D411yescharacteristic
323C22×C4C2×C3×D412yes—
324C22×C4C24×C311yescharacteristic
325C2×C8—22no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—22no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C4⋊C4—28no—
333C4⋊C4—28no—
334C4⋊C4—28no—
335C4⋊C4—24no—
336C4⋊C4—24no—
337C4⋊C4—24no—
338C4⋊C4—24no—
339C4⋊C4—22no—
340C4⋊C4—21no—
341C4⋊C4—22no—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—42no—
348C4⋊C4—44no—
349C4⋊C4—82no—
350C4⋊C4C2×C3×D412yes—
351C4⋊C4C3×#4114yes—
352C42—28no—
353C42—24no—
354C42—22no—
355C42—22no—
356C42—81no—
357C42C2×C3×D412yes—
358C42C2×C3×D412yes—
359C22×C3C2×#12011yescharacteristic
360C22×C3#54812yes—
361C22×C3C2×#13712yes—
362C22×C3#57711yescharacteristic
363C22×C3#57811yescharacteristic
364C3×C4—22no—
365C3×C4—24no—
366C3×C4—22no—
367C3×C4—44no—
368C3×C4—42no—
369C3×C4—44no—
370C3×C4—42no—
371C3×C4—42no—
372C3×C4—81no—
373C3×C4—81no—
374C3×C4#53211yescharacteristic
375C3×C4#53611yescharacteristic
376C3×C4#54712yes—
377C23C22×C3×D411yescharacteristic
378Q8—28no—
379Q8—22no—
380Q8—22no—
381Q8—24no—
382Q8—24no—
383Q8—42no—
384Q8—42no—
385Q8—42no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—22no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4C3×#12012yes—
411C2×C4C3×#12012yes—
412C2×C4C3×#13714yes—
413C2×C4C22×C3×D411yescharacteristic
414C2×C4C22×C3×D411yescharacteristic
415C2×C4C2×C3×#4112yes—
416C2×C4C3×2−1+412yes—
417C8—41no—
418C8—41no—
419C8—42no—
420C2×C3#243211yescharacteristic
421C2×C3#300411yescharacteristic
422C2×C3#301311yescharacteristic
423C2×C3#337212yes—
424C2×C3#337412yes—
425C22C2×C3×#12011yescharacteristic
426C22C3×#54812yes—
427C22C2×C3×#13712yes—
428C22C3×#57711yescharacteristic
429C22C3×#57811yescharacteristic
430C4—22no—
431C4—24no—
432C4—22no—
433C4—42no—
434C4—44no—
435C4—42no—
436C4—42no—
437C4—44no—
438C4—81no—
439C4—81no—
440C4C3×#53211yescharacteristic
441C4C3×#53611yescharacteristic
442C4C3×#54712yes—
443C3#2565711yescharacteristic, direct product factor, Sylow
444C2C3×#243211yescharacteristic
445C2C3×#300411yescharacteristic
446C2C3×#301311yescharacteristic
447C2C3×#337212yes—
448C2C3×#337412yes—
subgroupG/H
center, socle, prime radicalC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
12. #25657C3direct (N × H)
443. C3#25657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5572
C2×C3×#4912
C2×C3×#4792
C3×#25842
C3×#20432
C3×#19852
C3×#19812
C3×#18652
C3×#18632
C3×#17632
#256573