Finite Group Databasebeta

← C3×#68345 #11775864

Subgroups — C3×#68345 #11775864

Order 1152.

547 conjugacy classes of subgroups.

The subgroup lattice has 473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5668C211yesmaximal, characteristic
2C3×#4705C211yesmaximal, characteristic, complemented
3C3×D3×#97C211yesmaximal, characteristic, complemented
4C32×#329C211yesmaximal, characteristic, complemented
5C3×#4540C211yesmaximal, characteristic, complemented
6C3×#4464C211yesmaximal, characteristic, complemented
7C3×#4464C211yesmaximal, characteristic, complemented
8C3×#1530—31nomaximal
9#68345C311yesmaximal, characteristic, direct product factor
10C2×C3×#239C411yescharacteristic
11C2×C3×#237C411yescharacteristic
12C32×#124C2211yescharacteristic
13C3×#944C411yescharacteristic
14C3×#940C411yescharacteristic
15C2×C3×D3×C8—21no—
16C3×#884—21no—
17C3×#884—21no—
18C3×#67⋊C4—21no—
19C3×#67⋊C4—21no—
20C3×#875C2211yescharacteristic
21C3×C42×D3C2211yescharacteristic
22C32×#97C2211yescharacteristic
23C32×#97C2211yescharacteristic
24C3×(C2×D3)⋊C8—21no—
25C3×#815—21no—
26C3×Dic3⋊C8—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29C3×#532—31no—
30#5668C2×C311yescharacteristic
31C3×#432—31no—
32C2×C3×#97—31no—
33#4705C2×C311yescharacteristic, complemented
34D3×#97C2×C311yescharacteristic, complemented
35C3×#329—21no—
36C3×#329—31no—
37C3×#329—31no—
38C3×#329—31no—
39C3×#329D311yescharacteristic, complemented
40C3×#329C2×C311yescharacteristic, complemented
41#4540C2×C311yescharacteristic, complemented
42#4464C2×C311yescharacteristic, complemented
43#4464C2×C311yescharacteristic, complemented
44C2×C32×Q8C2×C411yescharacteristic
45C2×C32×D4C2×C411yescharacteristic
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C3×#239—42no—
51C3×#237—42no—
52C2×C3×D12—21no—
53C2×C3×D12C2×C411yescharacteristic
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3C2×C411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×Dic6C2×C411yescharacteristic
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C32×C22⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C42C2311yescharacteristic
64C3×(C2×D3)⋊C4—21no—
65C3×(C2×D3)⋊C4—21no—
66C3×Dic3⋊C4—21no—
67C3×Dic3⋊C4—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C3×D3×C8—24no—
74#1530—31noSylow
75C2×C3×#41—31no—
76C2×C3×#41—31no—
77C2×#239C3×C411yescharacteristic
78C2×#237C3×C411yescharacteristic
79C22×C3×C8—61no—
80C3×C4⋊Q8—31no—
81C3×#127—31no—
82C3×#124—21no—
83C3×#124—31no—
84C3×#124C2×D311yescharacteristic
85C3×#124C22×C311yescharacteristic
86C3×#121—61no—
87C3×#121—61no—
88C3×C4×D4—61no—
89C3×C4×D4—61no—
90C2×C3×C42—31no—
91#944C3×C411yescharacteristic
92#940C3×C411yescharacteristic
93C2×D3×C8—21no—
94#884—21no—
95#884—21no—
96#67⋊C4—21no—
97#67⋊C4—21no—
98#875C22×C311yescharacteristic
99C42×D3C22×C311yescharacteristic
100C3×C4⋊C8—61no—
101C3×C22⋊C8—61no—
102C3×#97—21no—
103C3×#97—21no—
104C3×#97—31no—
105C3×#97—31no—
106C3×#97—61no—
107C3×#97C2×D311yescharacteristic
108C3×#97C2×D311yescharacteristic
109C3×#97C22×C311yescharacteristic
110C3×#97C22×C311yescharacteristic
111(C2×D3)⋊C8—21no—
112#815—21no—
113Dic3⋊C8—21no—
114#803C22×C311yescharacteristic
115#803C22×C311yescharacteristic
116C23×C32—21no—
117C22×C3×D3—21no—
118C22×C3×D3C22⋊C411yescharacteristic
119C32×Q8—41no—
120C32×D4—41no—
121C2×C32×C4—21no—
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C3×#67—42no—
126C3×#67—42no—
127C3×#67—42no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3C22⋊C411yescharacteristic
131C2×C3×Dic3C22⋊C411yescharacteristic
132C2×C3×Dic3C22⋊C411yescharacteristic
133C3×D12—41no—
134C3×D12—42no—
135C3×C4×D3—22no—
136C3×C4×D3—22no—
137C3×C4×D3—41no—
138C3×C4×D3—42no—
139C3×Dic6—41no—
140C32×C8—22no—
141C32×C8—41no—
142C3×C3⋊C8—22no—
143C3×C3⋊C8—41no—
144#532—31no—
145#432—31no—
146C2×#97—31no—
147#329—31no—
148#329—31no—
149#329—31no—
150#329C3×D311yescharacteristic, complemented
151C3×#41—122no—
152C3×#41—122no—
153C2×C3×Q8—21no—
154C2×C3×Q8—31no—
155C2×C3×Q8C4×D311yescharacteristic
156C2×C3×Q8C2×C3×C411yescharacteristic
157C2×C3×D4—21no—
158C2×C3×D4—31no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4C4×D311yescharacteristic
164C2×C3×D4C2×C3×C411yescharacteristic
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C2×#67—21no—
171C2×#67—21no—
172C2×#67—21no—
173C22×Dic3—21no—
174#239—42no—
175#237—42no—
176C2×D12—21no—
177C2×D12C2×C3×C411yescharacteristic
178C2×C4×D3—21no—
179C2×C4×D3C2×C3×C411yescharacteristic
180C2×C4×D3C3×D411yescharacteristic
181C2×C4×D3C3×D411yescharacteristic
182C2×Dic6C2×C3×C411yescharacteristic
183C2×C3×C8—21no—
184C2×C3×C8—21no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—41no—
188C2×C3×C8—41no—
189C2×C3×C8—64no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—41no—
199C3×C22⋊C4—41no—
200C3×C22⋊C4—61no—
201C3×C22⋊C4—61no—
202C3×C42—21no—
203C3×C42—31no—
204C3×C42—31no—
205C3×C42—31no—
206C3×C42C22×D311yescharacteristic
207C3×C42C23×C311yescharacteristic
208(C2×D3)⋊C4—21no—
209(C2×D3)⋊C4—21no—
210Dic3⋊C4—21no—
211Dic3⋊C4—21no—
212C4×Dic3C2×C3×C411yescharacteristic
213C4×Dic3C3×D411yescharacteristic
214C4×Dic3C3×D411yescharacteristic
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217D3×C8—24no—
218C22×C32—41no—
219C22×C32—41no—
220C22×C32—41no—
221C22×C32C2×C22⋊C411yescharacteristic
222C2×C3×D3—21no—
223C2×C3×D3—21no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C2×C3×D3#10012yes—
228C32×C4—21no—
229C32×C4—21no—
230C32×C4—21no—
231C32×C4—41no—
232C3×Dic3—21no—
233C3×Dic3—21no—
234C3×Dic3—41no—
235C3×Dic3#10412yes—
236C2×#41—31no—
237C2×#41—31no—
238C22×C8—61no—
239C4⋊Q8—31no—
240#127—31no—
241#124—31no—
242#124C2×C3×D311yescharacteristic
243#121—61no—
244#121—61no—
245C4×D4—61no—
246C4×D4—61no—
247C2×C42—31no—
248C4⋊C8—61no—
249C22⋊C8—61no—
250#97—31no—
251#97—31no—
252#97—61no—
253#97C2×C3×D311yescharacteristic
254#97C2×C3×D311yescharacteristic
255C23×C3—21no—
256C23×C3—21no—
257C23×C3—31no—
258C23×C3—41no—
259C23×C3—61no—
260C22×D3—21no—
261C22×D3C3×C22⋊C411yescharacteristic
262C3×Q8—41no—
263C3×Q8—41no—
264C3×Q8—81no—
265C3×Q8—121no—
266C3×D4—41no—
267C3×D4—41no—
268C3×D4—81no—
269C3×D4—121no—
270C3×D4—122no—
271C3×D4—122no—
272C3×D4—122no—
273C3×D4—122no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—31no—
280C2×C3×C4—31no—
281C2×C3×C4—31no—
282C2×C3×C4—41no—
283C2×C3×C4—62no—
284C2×C3×C4—62no—
285C2×C3×C4—61no—
286C2×C3×C4—121no—
287C2×C3×C4—122no—
288C2×C3×C4—122no—
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4C22×C3×C411yescharacteristic
293C2×C3×C4C2×C3×D411yescharacteristic
294C2×C3×C4C2×C3×D411yescharacteristic
295#67—42no—
296#67—42no—
297#67—42no—
298C2×Dic3—21no—
299C2×Dic3—42no—
300C2×Dic3C3×C22⋊C411yescharacteristic
301C2×Dic3C3×C22⋊C411yescharacteristic
302C2×Dic3C3×C22⋊C411yescharacteristic
303D12—41no—
304D12—42no—
305C4×D3—22no—
306C4×D3—22no—
307C4×D3—41no—
308C4×D3—42no—
309Dic6—41no—
310C3×C8—22no—
311C3×C8—22no—
312C3×C8—42no—
313C3×C8—41no—
314C3×C8—41no—
315C3×C8—42no—
316C3×C8—62no—
317C3×C8—121no—
318C3⋊C8—22no—
319C3⋊C8—41no—
320C2×C32—81no—
321C2×C32C2×#10011yescharacteristic
322C2×C32C2×#10411yescharacteristic
323C2×C32#42111yescharacteristic
324C3×D3—22no—
325C3×D3—81no—
326#41—122no—
327#41—122no—
328C2×Q8—31no—
329C2×Q8C3×C4×D311yescharacteristic
330C2×D4—31no—
331C2×D4—61no—
332C2×D4—61no—
333C2×D4—61no—
334C2×D4—61no—
335C2×D4C3×C4×D311yescharacteristic
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—31no—
339C22×C4—61no—
340C22×C4—61no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—64no—
344C2×C8—61no—
345C2×C8—61no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C22⋊C4—21no—
349C22⋊C4—21no—
350C22⋊C4—61no—
351C22⋊C4—61no—
352C42—31no—
353C42—31no—
354C42—31no—
355C42C22×C3×D311yescharacteristic
356C22×C3—21no—
357C22×C3—32no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—61no—
365C22×C3—61no—
366C22×C3—81no—
367C22×C3—81no—
368C22×C3—81no—
369C22×C3—121no—
370C22×C3—121no—
371C22×C3—121no—
372C22×C3D3×C22⋊C411yescharacteristic
373C22×C3C2×C3×C22⋊C411yescharacteristic
374C2×D3—21no—
375C2×D3—21no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—41no—
379C2×D3C3×#10012yes—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—21no—
386C3×C4—32no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—61no—
393C3×C4—61no—
394C3×C4—81no—
395C3×C4—121no—
396Dic3—21no—
397Dic3—21no—
398Dic3—41no—
399Dic3C3×#10412yes—
400C32#153011yescharacteristic, complemented, Sylow
401C23—21no—
402C23—31no—
403C23—61no—
404Q8—41no—
405Q8—121no—
406D4—41no—
407D4—121no—
408D4—122no—
409D4—122no—
410D4—122no—
411D4—122no—
412C2×C4—21no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—61no—
419C2×C4—121no—
420C2×C4—122no—
421C2×C4—122no—
422C2×C4C2×C3×C4×D311yescharacteristic
423C2×C4C3×D3×D411yescharacteristic
424C2×C4C3×D3×D411yescharacteristic
425C8—22no—
426C8—41no—
427C8—62no—
428C8—121no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—62no—
433C2×C3—81no—
434C2×C3—81no—
435C2×C3—161no—
436C2×C3—241no—
437C2×C3D3×#10011yescharacteristic
438C2×C3D3×#10411yescharacteristic
439C2×C3#482111yescharacteristic
440C2×C3C2×C3×#10011yescharacteristic
441C2×C3C2×C3×#10411yescharacteristic
442C2×C3C3×#42111yescharacteristic
443D3—22no—
444D3—81no—
445C22—32no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—61no—
450C22—61no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22C3×D3×C22⋊C411yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—32no—
459C4—41no—
460C4—61no—
461C4—61no—
462C4—121no—
463C3—21no—
464C3#6834511yescharacteristic, direct product factor
465C3C3×#153011yescharacteristic, complemented
466C2—62no—
467C2—81no—
468C2—241no—
469C2C3×D3×#10011yescharacteristic
470C2C3×D3×#10411yescharacteristic
471C2C3×#482111yescharacteristic
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC2×C3×C4C22×C3×C4
FrattiniC42C22×C3×D3
FittingC32×#329C2
socleC22×C32C2×C22⋊C4
prime radicalC3×#5668C2
cosocleC3×C42C23×C3
hypercenterC3×#329D3
hypocenterC3C3×#1530
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#329

Complements

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

NH ≅ G/Ntype
2. C3×#4705C2semidirect
3. C3×D3×#97C2semidirect
4. C32×#329C2semidirect
5. C3×#4540C2semidirect
6. C3×#4464C2semidirect
7. C3×#4464C2semidirect
9. #68345C3direct (N × H)
33. #4705C2×C3semidirect
34. D3×#97C2×C3semidirect
39. C3×#329D3semidirect
40. C3×#329C2×C3semidirect
41. #4540C2×C3semidirect
42. #4464C2×C3semidirect
43. #4464C2×C3semidirect
150. #329C3×D3semidirect
400. C32#1530semidirect
464. C3#68345direct (N × H)
465. C3C3×#1530semidirect

Maximal subgroups

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

subgroupindex
C3×#56682
C3×#47052
C3×D3×#972
C32×#3292
C3×#45402
C3×#44642
C3×#15303
#683453