Finite Group Databasebeta

← C3×#68967 #11793133

Subgroups — C3×#68967 #11793133

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5483C211yesmaximal, characteristic, complemented
2C2×C3×#806C211yesmaximal, characteristic
3C2×C3×#806C211yesmaximal, characteristic
4C2×C3×#806C211yesmaximal, characteristic
5C32×#342C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7C3×#4526C211yesmaximal, characteristic, complemented
8C3×#2032—31nomaximal
9#68967C311yesmaximal, characteristic, direct product factor
10C22×C3×#67C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×C32×C22⋊C4C2211yescharacteristic
14C2×C3×#217C2211yescharacteristic
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C3×#924—22no—
18C3×#878—22no—
19C3×#878—22no—
20C3×#806—22no—
21C3×#806—22no—
22C3×#806—22no—
23C3×#543—31no—
24#5483C2×C311yescharacteristic, complemented
25C2×C3×#99—31no—
26C2×C3×#99—31no—
27C2×C3×#99—31no—
28C2×#806C2×C311yescharacteristic
29C2×#806C2×C311yescharacteristic
30C2×#806C2×C311yescharacteristic
31C3×#342—21no—
32C3×#342—31no—
33C3×#342—31no—
34C3×#342D311yescharacteristic, complemented
35C3×#342C2×C311yescharacteristic, complemented
36#4527C2×C311yescharacteristic, complemented
37#4526C2×C311yescharacteristic, complemented
38C24×C32C2311yescharacteristic
39C23×C3×D3Q811yescharacteristic, complemented
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C2×C3×#67—21no—
44C2×C3×#67—21no—
45C2×C3×#67—21no—
46C2×C3×#67—21no—
47C2×C3×#67—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3Q811yescharacteristic, complemented
53C2×C3×Dic6—22no—
54C32×C22⋊C4—21no—
55C32×C22⋊C4—21no—
56C32×C22⋊C4—21no—
57C32×C22⋊C4—21no—
58C32×C22⋊C4—21no—
59C32×C22⋊C4D412yes—
60C3×#217—21no—
61C3×#217—21no—
62C3×#217—21no—
63C3×#217—21no—
64C3×#217D412yes—
65C3×#217D412yes—
66C3×C4⋊Dic3—22no—
67C3×Dic3⋊C4—24no—
68#2032—31noSylow
69C22×C3×D4—31no—
70C22×#67C22×C311yescharacteristic
71C3×C22⋊Q8—62no—
72C3×C22⋊Q8—62no—
73C3×C22⋊Q8—62no—
74C2×C3×C22⋊C4—21no—
75C2×C3×C22⋊C4—21no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—31no—
78C2×C3×C22⋊C4—31no—
79C2×C3×C22⋊C4—31no—
80C2×C3×C22⋊C4C2×D311yescharacteristic
81C2×C3×C22⋊C4C2×D311yescharacteristic
82C2×C3×C22⋊C4C2×D311yescharacteristic
83C2×C3×C22⋊C4C22×C311yescharacteristic
84C2×C3×C22⋊C4C22×C311yescharacteristic
85C2×C3×C22⋊C4C22×C311yescharacteristic
86C2×#217C22×C311yescharacteristic
87C2×#217C22×C311yescharacteristic
88C2×#217C22×C311yescharacteristic
89#924—22no—
90#878—22no—
91#878—22no—
92C3×#99—62no—
93C3×#99—62no—
94C3×#99—62no—
95#806—22no—
96#806—22no—
97#806—22no—
98C23×C32—81no—
99C23×C32C2×D411yescharacteristic
100C23×C32C2×D411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C23×C32C2×Q811yescharacteristic
103C23×C32#4111yescharacteristic
104C23×C32#4111yescharacteristic
105C23×C32#4111yescharacteristic
106C22×C3×D3—21no—
107C22×C3×D3—21no—
108C22×C3×D3—21no—
109C22×C3×D3—81no—
110C2×C32×C4—22no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—81no—
114C2×C32×C4—81no—
115C2×C32×C4—81no—
116C3×#67—41no—
117C3×#67—41no—
118C3×#67—41no—
119C3×#67—41no—
120C2×C3×Dic3—22no—
121C2×C3×Dic3—22no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—81no—
127C2×C3×Dic3—81no—
128C2×C3×Dic3—81no—
129C3×Dic6—82no—
130#543—31no—
131C2×#99—31no—
132C2×#99—31no—
133C2×#99—31no—
134#342—31no—
135#342—31no—
136#342C3×D311yescharacteristic, complemented
137C24×C3—21no—
138C24×C3—31no—
139C24×C3C22×D311yescharacteristic
140C24×C3C23×C311yescharacteristic
141C23×D3C3×Q811yescharacteristic, complemented
142C2×C3×Q8—62no—
143C2×C3×D4—61no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—41no—
158C22×C3×C4—41no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C2×#67—21no—
163C2×#67—21no—
164C2×#67—21no—
165C2×#67—21no—
166C2×#67—21no—
167C2×#67—21no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3C3×Q811yescharacteristic, complemented
172C2×Dic6—22no—
173C3×C4⋊C4—64no—
174C3×C4⋊C4—62no—
175C3×C22⋊C4—21no—
176C3×C22⋊C4—21no—
177C3×C22⋊C4—22no—
178C3×C22⋊C4—21no—
179C3×C22⋊C4—21no—
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—21no—
185C3×C22⋊C4—21no—
186C3×C22⋊C4—22no—
187C3×C22⋊C4—32no—
188C3×C22⋊C4—32no—
189C3×C22⋊C4—41no—
190C3×C22⋊C4—41no—
191C3×C22⋊C4—41no—
192C3×C22⋊C4—41no—
193C3×C22⋊C4—61no—
194C3×C22⋊C4—61no—
195C3×C22⋊C4—61no—
196C3×C22⋊C4—61no—
197C3×C22⋊C4D1212yes—
198C3×C22⋊C4C3×D412yes—
199#217—21no—
200#217—21no—
201#217—21no—
202#217—21no—
203#217C3×D412yes—
204#217C3×D412yes—
205C4⋊Dic3—22no—
206Dic3⋊C4—24no—
207C22×C32—41no—
208C22×C32—41no—
209C22×C32—41no—
210C22×C32—41no—
211C22×C32—41no—
212C22×C32—41no—
213C22×C32—41no—
214C22×C32#12011yescharacteristic
215C22×C32C22⋊Q811yescharacteristic
216C22×C32C22⋊Q811yescharacteristic
217C22×C32C22⋊Q811yescharacteristic
218C22×C32#12411yescharacteristic
219C22×C32#12411yescharacteristic
220C22×C32#12411yescharacteristic
221C2×C3×D3—41no—
222C2×C3×D3—81no—
223C2×C3×D3—81no—
224C2×C3×D3—81no—
225C32×C4—42no—
226C32×C4—81no—
227C32×C4—81no—
228C3×Dic3—42no—
229C3×Dic3—42no—
230C3×Dic3—41no—
231C3×Dic3—81no—
232C22×D4—31no—
233C22⋊Q8—62no—
234C22⋊Q8—62no—
235C22⋊Q8—62no—
236C2×C22⋊C4—31no—
237C2×C22⋊C4—31no—
238C2×C22⋊C4—31no—
239C2×C22⋊C4C2×C3×D311yescharacteristic
240C2×C22⋊C4C2×C3×D311yescharacteristic
241C2×C22⋊C4C2×C3×D311yescharacteristic
242#99—62no—
243#99—62no—
244#99—62no—
245C23×C3—21no—
246C23×C3—21no—
247C23×C3—21no—
248C23×C3—21no—
249C23×C3—21no—
250C23×C3—21no—
251C23×C3—21no—
252C23×C3—61no—
253C23×C3—61no—
254C23×C3—61no—
255C23×C3—81no—
256C23×C3—81no—
257C23×C3—82no—
258C23×C3—241no—
259C23×C3C2×D1211yescharacteristic
260C23×C3#23511yescharacteristic
261C23×C3#23511yescharacteristic
262C23×C3D3×D411yescharacteristic
263C23×C3D3×D411yescharacteristic
264C23×C3#23711yescharacteristic
265C23×C3D3×Q811yescharacteristic
266C23×C3C2×C3×D411yescharacteristic
267C23×C3C2×C3×D411yescharacteristic
268C23×C3C2×C3×D411yescharacteristic
269C23×C3C2×C3×Q811yescharacteristic
270C23×C3C3×#4111yescharacteristic
271C23×C3C3×#4111yescharacteristic
272C23×C3C3×#4111yescharacteristic
273C22×D3—21no—
274C22×D3—21no—
275C22×D3—21no—
276C22×D3—81no—
277C3×Q8—242no—
278C3×D4—121no—
279C3×D4—121no—
280C3×D4—121no—
281C3×D4—121no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—42no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—81no—
297C2×C3×C4—81no—
298C2×C3×C4—82no—
299C2×C3×C4—82no—
300C2×C3×C4—81no—
301C2×C3×C4—81no—
302C2×C3×C4—81no—
303C2×C3×C4—81no—
304C2×C3×C4—82no—
305C2×C3×C4—121no—
306C2×C3×C4—241no—
307C2×C3×C4—241no—
308C2×C3×C4—241no—
309#67—41no—
310#67—41no—
311#67—41no—
312#67—41no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—41no—
319C2×Dic3—81no—
320C2×Dic3—81no—
321C2×Dic3—81no—
322Dic6—82no—
323C2×C32—21no—
324C2×C32—21no—
325C2×C32—21no—
326C2×C32—21no—
327C2×C32—21no—
328C2×C32—21no—
329C2×C32—21no—
330C2×C32#39311yescharacteristic
331C3×D3—81no—
332C24—31no—
333C24C22×C3×D311yescharacteristic
334C2×Q8—62no—
335C2×D4—61no—
336C2×D4—61no—
337C2×D4—61no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—31no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—61no—
348C4⋊C4—64no—
349C4⋊C4—62no—
350C22⋊C4—21no—
351C22⋊C4—21no—
352C22⋊C4—21no—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—32no—
356C22⋊C4—32no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4C3×D1212yes—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3—41no—
380C22×C3—41no—
381C22×C3—41no—
382C22×C3—41no—
383C22×C3—42no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—81no—
387C22×C3—81no—
388C22×C3—81no—
389C22×C3—81no—
390C22×C3—121no—
391C22×C3—241no—
392C22×C3—241no—
393C22×C3—241no—
394C22×C3#87511yescharacteristic
395C22×C3#88211yescharacteristic
396C22×C3#88511yescharacteristic
397C22×C3#88511yescharacteristic
398C22×C3#89611yescharacteristic
399C22×C3#89611yescharacteristic
400C22×C3#89711yescharacteristic
401C22×C3C3×#12011yescharacteristic
402C22×C3C3×C22⋊Q811yescharacteristic
403C22×C3C3×C22⋊Q811yescharacteristic
404C22×C3C3×C22⋊Q811yescharacteristic
405C22×C3C3×#12411yescharacteristic
406C22×C3C3×#12411yescharacteristic
407C22×C3C3×#12411yescharacteristic
408C2×D3—41no—
409C2×D3—81no—
410C2×D3—81no—
411C2×D3—81no—
412C3×C4—42no—
413C3×C4—42no—
414C3×C4—82no—
415C3×C4—82no—
416C3×C4—81no—
417C3×C4—81no—
418C3×C4—81no—
419C3×C4—81no—
420C3×C4—82no—
421C3×C4—122no—
422C3×C4—122no—
423C3×C4—121no—
424C3×C4—241no—
425Dic3—42no—
426Dic3—42no—
427Dic3—41no—
428Dic3—81no—
429C32#203211yescharacteristic, complemented, Sylow
430C23—61no—
431C23—61no—
432C23—61no—
433C23—81no—
434C23—241no—
435C23C2×C3×D1211yescharacteristic
436C23C3×#23511yescharacteristic
437C23C3×#23511yescharacteristic
438C23C3×D3×D411yescharacteristic
439C23C3×D3×D411yescharacteristic
440C23C3×#23711yescharacteristic
441C23C3×D3×Q811yescharacteristic
442Q8—242no—
443D4—121no—
444D4—121no—
445D4—121no—
446D4—121no—
447C2×C4—22no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—81no—
458C2×C4—121no—
459C2×C4—241no—
460C2×C4—241no—
461C2×C4—241no—
462C2×C3—22no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—41no—
479C2×C3—41no—
480C2×C3—41no—
481C2×C3—41no—
482C2×C3—41no—
483C2×C3—41no—
484C2×C3—241no—
485C2×C3#467311yescharacteristic
486C2×C3C3×#39311yescharacteristic
487D3—81no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—121no—
496C22—241no—
497C22—241no—
498C22—241no—
499C22C3×#87511yescharacteristic
500C22C3×#88211yescharacteristic
501C22C3×#88511yescharacteristic
502C22C3×#88511yescharacteristic
503C22C3×#89611yescharacteristic
504C22C3×#89611yescharacteristic
505C22C3×#89711yescharacteristic
506C4—42no—
507C4—81no—
508C4—81no—
509C4—122no—
510C4—122no—
511C4—121no—
512C4—241no—
513C3—21no—
514C3#6896711yescharacteristic, direct product factor
515C3C3×#203211yescharacteristic, complemented
516C2—21no—
517C2—21no—
518C2—21no—
519C2—21no—
520C2—21no—
521C2—21no—
522C2—21no—
523C2—241no—
524C2C3×#467311yescharacteristic
subgroupG/H
centerC2×C3#4673
commutator, cosocleC24×C3C23×C3
FrattiniC24C22×C3×D3
FittingC32×#342C2
socleC2×C32#393
prime radicalC22×C3×#67C22
hypercenterC3×#342D3
hypocenterC3C3×#2032
LCSG ▷ C24×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C24×C3 ◁ C3×#342

Complements

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

NH ≅ G/Ntype
1. C3×#5483C2semidirect
5. C32×#342C2semidirect
6. C3×#4527C2semidirect
7. C3×#4526C2semidirect
9. #68967C3direct (N × H)
24. #5483C2×C3semidirect
34. C3×#342D3semidirect
35. C3×#342C2×C3semidirect
36. #4527C2×C3semidirect
37. #4526C2×C3semidirect
39. C23×C3×D3Q8semidirect
52. C22×C3×Dic3Q8semidirect
136. #342C3×D3semidirect
141. C23×D3C3×Q8semidirect
171. C22×Dic3C3×Q8semidirect
429. C32#2032semidirect
514. C3#68967direct (N × H)
515. C3C3×#2032semidirect

Maximal subgroups

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

subgroupindex
C3×#54832
C2×C3×#8062
C32×#3422
C3×#45272
C3×#45262
C3×#20323
#689673