Finite Group Databasebeta

← C3×#69041 #11788907

Subgroups — C3×#69041 #11788907

Order 1152.

661 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic
2C3×#5526C211yesmaximal, characteristic
3C2×C3×#824C211yesmaximal, characteristic, complemented
4C2×C3×#824C211yesmaximal, characteristic, complemented
5C3×#5132C211yesmaximal, characteristic
6C32×#344C211yesmaximal, characteristic, complemented
7C3×#4533C211yesmaximal, characteristic, complemented
8C3×#1915—31nomaximal
9#69041C311yesmaximal, characteristic, direct product factor
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C32×M16C2211yescharacteristic
14C32×#117C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#907—22no—
18C3×D3×M16—22no—
19C3×#901—22no—
20C3×#897—22no—
21C3×#886C414yes—
22C3×#875—21no—
23C3×#869—21no—
24C3×#824—21no—
25C3×#824—22no—
26C3×#824—22no—
27C3×#823—21no—
28C3×#568—31no—
29C3×#536—31no—
30#5745C2×C311yescharacteristic
31#5526C2×C311yescharacteristic
32C3×#413—31no—
33C2×C3×#101—31no—
34C2×C3×#101—31no—
35C2×#824C2×C311yescharacteristic, complemented
36C2×#824C2×C311yescharacteristic, complemented
37#5132C2×C311yescharacteristic
38C3×#344—21no—
39C3×#344—31no—
40C3×#344D311yescharacteristic, complemented
41C3×#344C2×C311yescharacteristic, complemented
42#4533C2×C311yescharacteristic, complemented
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67C2×C412yes—
45C22×C3×Dic3C2×C412yes—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3D412yes—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6D411yescharacteristic
59C32×M16—21no—
60C32×M16—21no—
61C32×M16—21no—
62C32×M16D412yes—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C32×C4⋊C4—21no—
66C32×C22⋊C4C2×C412yes—
67C32×C42—21no—
68C3×(C2×D3)⋊C4—24no—
69C3×C4⋊Dic3—24no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208D412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C3×ΓL(1,𝔽25)—24no—
77C3×D3×C8—24no—
78#1915—31noSylow
79C2×C3×#41—31no—
80C22×C3×Q8—31no—
81C2×#235C22×C311yescharacteristic
82C22×Dic6C22×C311yescharacteristic
83C3×#131—62no—
84C3×#131—62no—
85C2×C3×M16—21no—
86C2×C3×M16—21no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C2×C3×M16—62no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C2×C3×M16C22×C311yescharacteristic
93C2×C3×M16C22×C311yescharacteristic
94C3×C4⋊Q8—61no—
95C3×#124—61no—
96C3×#123—34no—
97C3×C22⋊Q8—62no—
98C3×#117—21no—
99C3×#117C2×D311yescharacteristic
100C3×#117C22×C311yescharacteristic
101C2×#208C22×C311yescharacteristic
102C2×#208C22×C311yescharacteristic
103#907—22no—
104D3×M16—22no—
105#901—22no—
106#897—22no—
107#886C3×C414yes—
108#875—21no—
109#869—21no—
110C3×#101—62no—
111C3×#101—61no—
112C3×#101—62no—
113C3×#100—61no—
114#824—21no—
115#824—22no—
116#824—22no—
117#823—21no—
118C23×C32C22×C411yescharacteristic
119C22×C3×D3C22⋊C412yes—
120C2×C32×C4—22no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C3×#67—22no—
128C3×#67—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3C22⋊C412yes—
133C3×D12—21no—
134C3×D12—21no—
135C3×C4×D3—22no—
136C3×C4×D3—22no—
137C3×Dic6—21no—
138C3×Dic6—21no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C32×C8—22no—
144C32×C8—41no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147#568—31no—
148#536—31no—
149#413—31no—
150C2×#101—31no—
151C2×#101—31no—
152#344—31no—
153#344C3×D311yescharacteristic, complemented
154C3×#41—61no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C2×C3×Q8—31no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×Q8—61no—
163C2×C3×Q8—61no—
164C2×C3×Q8—61no—
165C2×C3×D4—32no—
166C2×C3×D4—31no—
167C22×C3×C4—21no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C23×C311yescharacteristic
172C2×#67C2×C3×C412yes—
173C22×Dic3C2×C3×C412yes—
174#235—21no—
175#235—21no—
176#235—21no—
177#235—21no—
178C2×D12C3×D411yescharacteristic
179C2×C4×D3C3×D412yes—
180C2×Dic6—21no—
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6C3×D411yescharacteristic
187C3×M16—21no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—22no—
194C3×M16—32no—
195C3×M16—41no—
196C3×M16—41no—
197C3×M16—41no—
198C3×M16—64no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C3×M16D1212yes—
203C3×M16C3×D412yes—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—22no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—41no—
210C2×C3×C8—64no—
211C2×C3×C8—61no—
212C2×C3×C8—61no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—41no—
216C3×C4⋊C4—64no—
217C3×C22⋊C4—22no—
218C3×C22⋊C4—64no—
219C3×C22⋊C4C4×D312yes—
220C3×C22⋊C4C2×C3×C412yes—
221C3×C42—21no—
222C3×C42—21no—
223C3×C42—41no—
224(C2×D3)⋊C4—24no—
225C4⋊Dic3—24no—
226#208—21no—
227#208—21no—
228#208—21no—
229#208C3×D412yes—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232ΓL(1,𝔽25)—24no—
233D3×C8—24no—
234C22×C32—41no—
235C22×C32C2×C22⋊C411yescharacteristic
236C22×C32C4×D411yescharacteristic
237C22×C32C4×D411yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—42no—
240C32×C4—42no—
241C32×C4#12011yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12311yescharacteristic
245C3×Dic3—22no—
246C3×Dic3—42no—
247C2×#41—31no—
248C22×Q8—31no—
249#131—62no—
250#131—62no—
251C2×M16—31no—
252C2×M16—31no—
253C2×M16—62no—
254C2×M16C2×C3×D311yescharacteristic
255C2×M16C2×C3×D311yescharacteristic
256C4⋊Q8—61no—
257#124—61no—
258#123—34no—
259C22⋊Q8—62no—
260#117C2×C3×D311yescharacteristic
261#101—62no—
262#101—61no—
263#101—62no—
264#100—61no—
265C23×C3—21no—
266C23×C3—32no—
267C23×C3C2×C4×D311yescharacteristic
268C23×C3C22×C3×C411yescharacteristic
269C22×D3C3×C22⋊C412yes—
270C3×Q8—61no—
271C3×Q8—61no—
272C3×Q8—121no—
273C3×Q8—121no—
274C3×Q8—121no—
275C3×Q8—121no—
276C3×D4—62no—
277C3×D4—62no—
278C3×D4—61no—
279C3×D4—61no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—32no—
289C2×C3×C4—42no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23911yescharacteristic
301C2×C3×C4C2×C3×D411yescharacteristic
302C2×C3×C4C2×C3×D411yescharacteristic
303C2×C3×C4C2×C3×D411yescharacteristic
304C2×C3×C4C2×C3×D411yescharacteristic
305C2×C3×C4C3×#4111yescharacteristic
306C2×C3×C4C3×#4111yescharacteristic
307#67—22no—
308#67—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3C3×C22⋊C412yes—
313D12—21no—
314D12—21no—
315C4×D3—22no—
316C4×D3—22no—
317Dic6—21no—
318Dic6—21no—
319Dic6—41no—
320Dic6—41no—
321Dic6—41no—
322Dic6—41no—
323C3×C8—22no—
324C3×C8—22no—
325C3×C8—42no—
326C3×C8—42no—
327C3×C8—41no—
328C3×C8—41no—
329C3×C8—62no—
330C3×C8—121no—
331C3⋊C8—22no—
332C3⋊C8—41no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38611yescharacteristic
337C3×D3—42no—
338#41—61no—
339#41—61no—
340#41—61no—
341#41—61no—
342C2×Q8—31no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×Q8—61no—
347C2×Q8—61no—
348C2×Q8—61no—
349C2×D4—32no—
350C2×D4—31no—
351C22×C4—32no—
352C22×C4—32no—
353C22×C4C22×C3×D311yescharacteristic
354M16—21no—
355M16—21no—
356M16—21no—
357M16—32no—
358M16—64no—
359M16—61no—
360M16—61no—
361M16—61no—
362M16C3×D1212yes—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—64no—
366C2×C8—61no—
367C2×C8—61no—
368C4⋊C4—21no—
369C4⋊C4—64no—
370C22⋊C4—64no—
371C22⋊C4C3×C4×D312yes—
372C42—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—62no—
379C22×C3—81no—
380C22×C3—122no—
381C22×C3C4×D1211yescharacteristic
382C22×C3D3×C22⋊C411yescharacteristic
383C22×C3#89311yescharacteristic
384C22×C3C2×C3×C22⋊C411yescharacteristic
385C22×C3C3×C4×D411yescharacteristic
386C22×C3C3×C4×D411yescharacteristic
387C2×D3—22no—
388C2×D3—42no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—42no—
394C3×C4—42no—
395C3×C4—62no—
396C3×C4—82no—
397C3×C4—122no—
398C3×C4#88211yescharacteristic
399C3×C4#88411yescharacteristic
400C3×C4#89411yescharacteristic
401C3×C4#89511yescharacteristic
402C3×C4C3×#12011yescharacteristic
403C3×C4C3×#12111yescharacteristic
404C3×C4C3×#12111yescharacteristic
405C3×C4C3×#12311yescharacteristic
406Dic3—22no—
407Dic3—42no—
408C32#191511yescharacteristic, complemented, Sylow
409C23—32no—
410C23C2×C3×C4×D311yescharacteristic
411Q8—61no—
412Q8—61no—
413Q8—121no—
414Q8—121no—
415Q8—121no—
416Q8—121no—
417D4—62no—
418D4—62no—
419D4—61no—
420D4—61no—
421C2×C4—22no—
422C2×C4—32no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4C2×C3×D1211yescharacteristic
429C2×C4C3×#23511yescharacteristic
430C2×C4C3×D3×D411yescharacteristic
431C2×C4C3×D3×D411yescharacteristic
432C2×C4C3×D3×D411yescharacteristic
433C2×C4C3×#23911yescharacteristic
434C8—22no—
435C8—41no—
436C8—62no—
437C8—121no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—41no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—122no—
449C2×C3#466511yescharacteristic
450C2×C3C3×#38611yescharacteristic
451D3—42no—
452C22—41no—
453C22—62no—
454C22—122no—
455C22C3×C4×D1211yescharacteristic
456C22C3×D3×C22⋊C411yescharacteristic
457C22C3×#89311yescharacteristic
458C4—42no—
459C4—62no—
460C4—122no—
461C4C3×#88211yescharacteristic
462C4C3×#88411yescharacteristic
463C4C3×#89411yescharacteristic
464C4C3×#89511yescharacteristic
465C3—21no—
466C3#6904111yescharacteristic, direct product factor
467C3C3×#191511yescharacteristic, complemented
468C2—21no—
469C2—21no—
470C2—21no—
471C2—122no—
472C2C3×#466511yescharacteristic
subgroupG/H
centerC2×C3#4665
commutatorC23×C3C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC32×#344C2
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C3×C4C23×C3
hypercenterC3×#344D3
hypocenterC3C3×#1915
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#344

Complements

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

NH ≅ G/Ntype
3. C2×C3×#824C2semidirect
4. C2×C3×#824C2semidirect
6. C32×#344C2semidirect
7. C3×#4533C2semidirect
9. #69041C3direct (N × H)
35. C2×#824C2×C3semidirect
36. C2×#824C2×C3semidirect
40. C3×#344D3semidirect
41. C3×#344C2×C3semidirect
42. #4533C2×C3semidirect
153. #344C3×D3semidirect
408. C32#1915semidirect
466. C3#69041direct (N × H)
467. C3C3×#1915semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
C3×#55262
C2×C3×#8242
C3×#51322
C32×#3442
C3×#45332
C3×#19153
#690413