Finite Group Databasebeta

← C3×#68694 #11787025

Subgroups — C3×#68694 #11787025

Order 1152.

599 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2C3×#5113C211yesmaximal, characteristic
3C2×C3×#819C211yesmaximal, characteristic, complemented
4C3×#5102C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic
6C32×#336C211yesmaximal, characteristic, complemented
7C3×#4523C211yesmaximal, characteristic, complemented
8C3×#1866—31nomaximal
9#68694C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#901—22no—
18C3×#901—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C3×#821C411yescharacteristic, complemented
22C3×#821C411yescharacteristic, complemented
23C3×#819—22no—
24C3×#816C411yescharacteristic, complemented
25C3×#816C411yescharacteristic, complemented
26C3×Dic3⋊C8—21no—
27C3×Dic3⋊C8—21no—
28C3×#805—22no—
29C2×C3×#131—31no—
30C2×#901C2×C311yescharacteristic
31C2×C3×#108—31no—
32C3×#424—31no—
33C2×C3×#104—31no—
34C3×#416—31no—
35#5113C2×C311yescharacteristic
36C2×#819C2×C311yescharacteristic, complemented
37#5102C2×C311yescharacteristic, complemented
38C2×#805C2×C311yescharacteristic
39C3×#339—31no—
40C3×#336—21no—
41C3×#336D311yescharacteristic, complemented
42C3×#336C2×C311yescharacteristic, complemented
43#4523C2×C311yescharacteristic, complemented
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×C3×#67—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235D412yes—
50C3×#235Q812yes—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8C2×C411yescharacteristic
59C2×C32×C8C2×C411yescharacteristic
60C2×C32×C8D411yescharacteristic
61C2×C32×C8D411yescharacteristic
62C32×C42—21no—
63C32×C42—21no—
64C3×#217—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×C4⋊Dic3C2×C411yescharacteristic
67C3×C4×Dic3—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C3×ΓL(1,𝔽25)—24no—
75C3×D3×C8—24no—
76#1866—31noSylow
77C2×C3×#41—31no—
78C2×#235C22×C311yescharacteristic
79C3×#131—62no—
80C3×#131—62no—
81C2×C3×M16—31no—
82C2×C3×M16—31no—
83C2×C3×M16—61no—
84C22×C3×C8—21no—
85C22×C3×C8—21no—
86C22×C3×C8—61no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C22×C311yescharacteristic
90C22×C3×C8C22×C311yescharacteristic
91C3×#117—31no—
92C2×C3×C42—21no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C22×C311yescharacteristic
95#926C22×C311yescharacteristic
96C2×#208C22×C311yescharacteristic
97C2×#208C22×C311yescharacteristic
98#901—22no—
99#901—22no—
100C2×ΓL(1,𝔽25)—21no—
101C2×D3×C8—21no—
102C3×#108—62no—
103C3×C4⋊C8—61no—
104C3×C4⋊C8—61no—
105C3×#104—62no—
106C3×#103—31no—
107C3×#103—31no—
108C3×#102—31no—
109C3×#102—31no—
110#821C3×C411yescharacteristic, complemented
111#821C3×C411yescharacteristic, complemented
112#819—22no—
113#816C3×C411yescharacteristic, complemented
114#816C3×C411yescharacteristic, complemented
115Dic3⋊C8—21no—
116Dic3⋊C8—21no—
117#805—22no—
118C23×C32#4111yescharacteristic
119C22×C3×D3—21no—
120C2×C32×C4—22no—
121C2×C32×C4—41no—
122C2×C32×C4—41no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C3×D12—21no—
135C3×D12C4⋊C412yes—
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×Dic6—21no—
139C3×Dic6C4⋊C412yes—
140C32×C8—21no—
141C32×C8—21no—
142C32×C8—21no—
143C32×C8—21no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C2×#131—31no—
147C2×#108—31no—
148#424—31no—
149C2×#104—31no—
150#416—31no—
151#339—31no—
152#336C3×D311yescharacteristic, complemented
153C3×#41—32no—
154C3×#41—32no—
155C3×#41—61no—
156C3×#41—61no—
157C2×C3×Q8—31no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—61no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C23×C311yescharacteristic
167C2×#67—21no—
168#235—21no—
169#235—21no—
170#235C3×D412yes—
171#235C3×Q812yes—
172C2×D12C2×C3×C411yescharacteristic
173C2×C4×D3—21no—
174C2×Dic6C2×C3×C411yescharacteristic
175C3×M16—32no—
176C3×M16—64no—
177C3×M16—61no—
178C3×M16—61no—
179C3×M16—61no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—41no—
193C2×C3×C8—41no—
194C2×C3×C8—41no—
195C2×C3×C8—41no—
196C2×C3×C8—64no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C2×C3×C8C4×D311yescharacteristic
200C2×C3×C8C4×D311yescharacteristic
201C2×C3×C8D1211yescharacteristic
202C2×C3×C8D1211yescharacteristic
203C2×C3×C8C2×C3×C411yescharacteristic
204C2×C3×C8C2×C3×C411yescharacteristic
205C2×C3×C8C3×D411yescharacteristic
206C2×C3×C8C3×D411yescharacteristic
207C3×C4⋊C4—31no—
208C3×C4⋊C4—31no—
209C3×C22⋊C4—61no—
210C3×C42—21no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—41no—
215C3×C42—41no—
216C3×C42—61no—
217#217—21no—
218C4⋊Dic3C2×C3×C411yescharacteristic
219C4⋊Dic3C2×C3×C411yescharacteristic
220C4×Dic3—21no—
221#208—21no—
222#208—21no—
223#208—21no—
224#208C3×D412yes—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227ΓL(1,𝔽25)—24no—
228D3×C8—24no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32C4×D411yescharacteristic
232C22×C32C22⋊Q811yescharacteristic
233C22×C32#12311yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4—42no—
238C32×C4C2×C4⋊C411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4#12011yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C3×Dic3—22no—
243C3×Dic3—41no—
244C3×Dic3—41no—
245C2×#41—31no—
246#131—62no—
247#131—62no—
248C2×M16—31no—
249C2×M16—31no—
250C2×M16—61no—
251C22×C8—61no—
252C22×C8C2×C3×D311yescharacteristic
253C22×C8C2×C3×D311yescharacteristic
254#117—31no—
255C2×C42C2×C3×D311yescharacteristic
256#108—62no—
257C4⋊C8—61no—
258C4⋊C8—61no—
259#104—62no—
260#103—31no—
261#103—31no—
262#102—31no—
263#102—31no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3#23511yescharacteristic
267C23×C3C3×#4111yescharacteristic
268C22×D3—21no—
269C3×Q8—32no—
270C3×Q8—61no—
271C3×D4—32no—
272C3×D4—62no—
273C3×D4—62no—
274C3×D4—61no—
275C2×C3×C4—24no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×D1211yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4D3×Q811yescharacteristic
301C2×C3×C4C22×C3×C411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C2×C3×Q811yescharacteristic
306C2×C3×C4C3×#4111yescharacteristic
307#67—22no—
308#67—22no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312D12—21no—
313D12C3×C4⋊C412yes—
314C4×D3—22no—
315C4×D3—22no—
316Dic6—21no—
317Dic6C3×C4⋊C412yes—
318C3×C8—21no—
319C3×C8—21no—
320C3×C8—21no—
321C3×C8—21no—
322C3×C8—21no—
323C3×C8—21no—
324C3×C8—21no—
325C3×C8—21no—
326C3×C8—41no—
327C3×C8—41no—
328C3×C8—41no—
329C3×C8—41no—
330C3×C8—62no—
331C3×C8—121no—
332C3⋊C8—22no—
333C3⋊C8—41no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38511yescharacteristic
337C2×C32#44311yescharacteristic
338C2×C32#44411yescharacteristic
339C3×D3—42no—
340#41—32no—
341#41—32no—
342#41—61no—
343#41—61no—
344C2×Q8—31no—
345C2×D4—31no—
346C2×D4—61no—
347C22×C4—21no—
348C22×C4—61no—
349C22×C4C22×C3×D311yescharacteristic
350M16—32no—
351M16—64no—
352M16—61no—
353M16—61no—
354M16—61no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—64no—
360C2×C8—61no—
361C2×C8—61no—
362C2×C8C3×C4×D311yescharacteristic
363C2×C8C3×C4×D311yescharacteristic
364C2×C8C3×D1211yescharacteristic
365C2×C8C3×D1211yescharacteristic
366C4⋊C4—31no—
367C4⋊C4—31no—
368C22⋊C4—61no—
369C42—21no—
370C42—21no—
371C42—61no—
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3C4×D1211yescharacteristic
385C22×C3#88311yescharacteristic
386C22×C3#89611yescharacteristic
387C22×C3C3×C4×D411yescharacteristic
388C22×C3C3×C22⋊Q811yescharacteristic
389C22×C3C3×#12311yescharacteristic
390C2×D3—22no—
391C2×D3—41no—
392C2×D3—41no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—44no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—62no—
401C3×C4—121no—
402C3×C4—121no—
403C3×C4#67⋊C411yescharacteristic
404C3×C4#88211yescharacteristic
405C3×C4D3×C4⋊C411yescharacteristic
406C3×C4#89711yescharacteristic
407C3×C4C2×C3×C4⋊C411yescharacteristic
408C3×C4C3×C4×D411yescharacteristic
409C3×C4C3×#12011yescharacteristic
410C3×C4C3×C22⋊Q811yescharacteristic
411Dic3—22no—
412Dic3—41no—
413Dic3—41no—
414C32#186611yescharacteristic, complemented, Sylow
415C23—61no—
416C23C3×#23511yescharacteristic
417Q8—32no—
418Q8—61no—
419D4—32no—
420D4—62no—
421D4—62no—
422D4—61no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—61no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—61no—
430C2×C4—61no—
431C2×C4C2×C3×C4×D311yescharacteristic
432C2×C4C2×C3×D1211yescharacteristic
433C2×C4C3×D3×D411yescharacteristic
434C2×C4C3×D3×D411yescharacteristic
435C2×C4C3×#23711yescharacteristic
436C2×C4C3×D3×Q811yescharacteristic
437C8—21no—
438C8—21no—
439C8—21no—
440C8—21no—
441C8—62no—
442C8—121no—
443C2×C3—22no—
444C2×C3—22no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—122no—
453C2×C3#466811yescharacteristic
454C2×C3#470011yescharacteristic
455C2×C3#471711yescharacteristic
456C2×C3C3×#38511yescharacteristic
457C2×C3C3×#44311yescharacteristic
458C2×C3C3×#44411yescharacteristic
459D3—42no—
460C22—21no—
461C22—21no—
462C22—62no—
463C22—121no—
464C22—121no—
465C22C3×C4×D1211yescharacteristic
466C22C3×#88311yescharacteristic
467C22C3×#89611yescharacteristic
468C4—42no—
469C4—62no—
470C4—121no—
471C4—121no—
472C4C3×#67⋊C411yescharacteristic
473C4C3×#88211yescharacteristic
474C4C3×D3×C4⋊C411yescharacteristic
475C4C3×#89711yescharacteristic
476C3—21no—
477C3#6869411yescharacteristic, direct product factor
478C3C3×#186611yescharacteristic, complemented
479C2—21no—
480C2—21no—
481C2—122no—
482C2C3×#466811yescharacteristic
483C2C3×#470011yescharacteristic
484C2C3×#471711yescharacteristic
subgroupG/H
centerC2×C3×C4C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#336C2
socleC22×C32C4×D4
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#336D3
hypocenterC3C3×#1866
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×C8 ◁ C3×#336

Complements

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

NH ≅ G/Ntype
3. C2×C3×#819C2semidirect
4. C3×#5102C2semidirect
6. C32×#336C2semidirect
7. C3×#4523C2semidirect
9. #68694C3direct (N × H)
21. C3×#821C4semidirect
22. C3×#821C4semidirect
24. C3×#816C4semidirect
25. C3×#816C4semidirect
36. C2×#819C2×C3semidirect
37. #5102C2×C3semidirect
41. C3×#336D3semidirect
42. C3×#336C2×C3semidirect
43. #4523C2×C3semidirect
110. #821C3×C4semidirect
111. #821C3×C4semidirect
113. #816C3×C4semidirect
114. #816C3×C4semidirect
152. #336C3×D3semidirect
414. C32#1866semidirect
477. C3#68694direct (N × H)
478. C3C3×#1866semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
C3×#51132
C2×C3×#8192
C3×#51022
C2×C3×#8052
C32×#3362
C3×#45232
C3×#18663
#686943