Finite Group Databasebeta

← C3×#69826 #11791129

Subgroups — C3×#69826 #11791129

Order 1152.

753 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic
2C2×C32×#97C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4C2×C3×#818C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C3×#4939C211yesmaximal, characteristic
7C3×#4929C211yesmaximal, characteristic, complemented
8C3×#1973—31nomaximal
9#69826C311yesmaximal, characteristic, direct product factor
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—22no—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#204—22no—
19C2×C3×#204—22no—
20C2×C3×#204C414yescomplemented
21C32×#97—22no—
22C3×C3⋊#95—22no—
23C3×#821—22no—
24C3×#818—22no—
25C3×#816—22no—
26C22×C3×SD16—31no—
27C22×#204C2×C311yescharacteristic
28C2×C3×#107—31no—
29C2×C3×#103—31no—
30C2×C3×#102—31no—
31C2×C3×#97—21no—
32C2×C3×#97D311yescharacteristic, complemented
33C2×C3×#97C2×C311yescharacteristic, complemented
34C3×#391—31no—
35C3×#390—31no—
36C2×#821C2×C311yescharacteristic
37C2×#818C2×C311yescharacteristic, complemented
38C2×#816C2×C311yescharacteristic, complemented
39#4939C2×C311yescharacteristic
40#4929C2×C311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4D412yes—
43C22×C32×C4C2311yescharacteristic
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12C2×C412yes—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6C2×C412yes—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8C2×C412yes—
62C2×C32×C8D412yes—
63C2×C32×C8D412yes—
64C2×C32×C8D412yes—
65C32×C42—21no—
66C32×C42—21no—
67C3×(C2×D3)⋊C4—44no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×#204—28no—
73#1973—31noSylow
74C22×C3×Q8—31no—
75C22×C3×D4—31no—
76C22×D12C22×C311yescharacteristic
77C22×Dic6C22×C311yescharacteristic
78C2×C3×SD16—34no—
79C2×C3×SD16—62no—
80C2×C3×SD16—62no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D311yescharacteristic
85C22×C3×C8C22×C311yescharacteristic
86C22×C3×C8C22×C311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C22⋊C4—62no—
90C2×C3×C42—21no—
91C2×C3×C42C2×D311yescharacteristic
92C2×C3×C42C22×C311yescharacteristic
93C2×(C2×D3)⋊C4—22no—
94C2×C4⋊Dic3C22×C311yescharacteristic
95C2×C4⋊Dic3C22×C311yescharacteristic
96C2×#204—22no—
97C2×#204—22no—
98C2×#204C3×C414yescomplemented
99C3×#107—62no—
100C3×#103—62no—
101C3×#102—62no—
102C3×#97—24no—
103C3×#97—22no—
104C3×#97—22no—
105C3×#95—62no—
106C3⋊#95—22no—
107#821—22no—
108#818—22no—
109#816—22no—
110C23×C32C2×D411yescharacteristic
111C22×C3×D3—22no—
112C22×C3×D3—41no—
113C22×C3×D3—41no—
114C22×C3×D3—42no—
115C22×C3×D3—42no—
116C2×C32×C4—22no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—42no—
131C2×C3×Dic3—42no—
132C3×D12—22no—
133C3×D12—22no—
134C3×D12—41no—
135C3×D12—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C32×C8—22no—
141C32×C8C22⋊C414yescomplemented
142C22×SD16—31no—
143C2×#107—31no—
144C2×#103—31no—
145C2×#102—31no—
146C2×#97C3×D311yescharacteristic, complemented
147#391—31no—
148#390—31no—
149C24×C3—61no—
150C23×D3—21no—
151C2×C3×Q8—32no—
152C2×C3×Q8—61no—
153C2×C3×Q8—61no—
154C2×C3×Q8—61no—
155C2×C3×Q8—61no—
156C2×C3×Q8—61no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—22no—
164C22×C3×C4—21no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4D1212yes—
169C22×C3×C4C3×D412yes—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C23×C311yescharacteristic
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C2×D12—21no—
176C2×D12—21no—
177C2×D12—21no—
178C2×D12—21no—
179C2×D12—21no—
180C2×D12C2×C3×C412yes—
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6C2×C3×C412yes—
187C3×SD16—68no—
188C2×C3×C8—22no—
189C2×C3×C8—22no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—22no—
195C2×C3×C8—22no—
196C2×C3×C8—22no—
197C2×C3×C8—22no—
198C2×C3×C8C4×D312yes—
199C2×C3×C8D1212yes—
200C2×C3×C8D1212yes—
201C2×C3×C8#6712yes—
202C2×C3×C8C2×C3×C412yes—
203C2×C3×C8C3×D412yes—
204C2×C3×C8C3×D412yes—
205C2×C3×C8C3×D412yes—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C22⋊C4—124no—
211C3×C42—22no—
212C3×C42—22no—
213C3×C42—21no—
214C3×C42—21no—
215C3×C42—21no—
216C3×C42—21no—
217(C2×D3)⋊C4—44no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222#204—28no—
223C22×C32C4×D411yescharacteristic
224C22×C32#12111yescharacteristic
225C22×C32#12711yescharacteristic
226C22×C32AGL(1,ℤ/8)12yes—
227C22×C32#13712yes—
228C2×C3×D3—42no—
229C2×C3×D3—44no—
230C2×C3×D3—82no—
231C2×C3×D3—81no—
232C2×C3×D3—81no—
233C32×C4—42no—
234C32×C4C2×C22⋊C411yescharacteristic
235C32×C4C4×D411yescharacteristic
236C32×C4#12111yescharacteristic
237C32×C4#12411yescharacteristic
238C3×Dic3—42no—
239C3×Dic3—81no—
240C3×Dic3—81no—
241C22×Q8—31no—
242C22×D4—31no—
243C2×SD16—34no—
244C2×SD16—62no—
245C2×SD16—62no—
246C22×C8C2×C3×D311yescharacteristic
247C22×C8C2×C3×D311yescharacteristic
248C2×C4⋊C4—31no—
249C2×C4⋊C4—31no—
250C2×C22⋊C4—62no—
251C2×C42C2×C3×D311yescharacteristic
252#107—62no—
253#103—62no—
254#102—62no—
255#97—22no—
256#95—62no—
257C23×C3—21no—
258C23×C3—62no—
259C23×C3—121no—
260C23×C3—122no—
261C23×C3—122no—
262C23×C3—121no—
263C23×C3C2×D1211yescharacteristic
264C23×C3C2×C3×D411yescharacteristic
265C22×D3—22no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—42no—
269C22×D3—42no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—121no—
273C3×Q8—121no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—24no—
279C2×C3×C4—22no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—42no—
292C2×C3×C4—42no—
293C2×C3×C4—62no—
294C2×C3×C4—121no—
295C2×C3×C4—121no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—122no—
299C2×C3×C4—122no—
300C2×C3×C4C2×C4×D311yescharacteristic
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4C2×D1211yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×C3×C4C22×C3×C411yescharacteristic
307C2×C3×C4C2×C3×D411yescharacteristic
308C2×C3×C4C2×C3×D411yescharacteristic
309C2×C3×C4C2×C3×D411yescharacteristic
310C2×C3×C4C3×#4111yescharacteristic
311C2×C3×C4C3×#4111yescharacteristic
312C2×Dic3—22no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3—41no—
316C2×Dic3—41no—
317C2×Dic3—42no—
318C2×Dic3—42no—
319D12—22no—
320D12—22no—
321D12—41no—
322D12—41no—
323Dic6—22no—
324Dic6—22no—
325Dic6—41no—
326Dic6—41no—
327C3×C8—24no—
328C3×C8—22no—
329C3×C8—22no—
330C3×C8—24no—
331C3×C8(C2×D3)⋊C414yescomplemented
332C3×C8C3×C22⋊C414yescomplemented
333C2×C32#39011yescharacteristic
334C2×C32#44012yes—
335C2×C32#46812yes—
336C2×C32#49611yescharacteristic
337C2×C32#49711yescharacteristic
338C3×D3—82no—
339C24—61no—
340C2×Q8—32no—
341C2×Q8—61no—
342C2×Q8—61no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4C3×D1212yes—
356C22×C4C22×C3×D311yescharacteristic
357SD16—68no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8C3×C4×D312yes—
361C2×C8C3×D1212yes—
362C2×C8C3×D1212yes—
363C2×C8C3×#6712yes—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C22⋊C4—124no—
369C42—21no—
370C42—21no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—122no—
377C22×C3—124no—
378C22×C3—242no—
379C22×C3—241no—
380C22×C3—241no—
381C22×C3C4×D1211yescharacteristic
382C22×C3#87411yescharacteristic
383C22×C3#90812yes—
384C22×C3#90912yes—
385C22×C3#93011yescharacteristic
386C22×C3C3×C4×D411yescharacteristic
387C22×C3C3×#12111yescharacteristic
388C22×C3C3×#12711yescharacteristic
389C22×C3C3×AGL(1,ℤ/8)12yes—
390C22×C3C3×#13712yes—
391C2×D3—42no—
392C2×D3—44no—
393C2×D3—82no—
394C2×D3—81no—
395C2×D3—81no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—44no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—122no—
404C3×C4—241no—
405C3×C4—241no—
406C3×C4C4×D1211yescharacteristic
407C3×C4#87511yescharacteristic
408C3×C4C2×(C2×D3)⋊C411yescharacteristic
409C3×C4#93011yescharacteristic
410C3×C4C2×C3×C22⋊C411yescharacteristic
411C3×C4C3×C4×D411yescharacteristic
412C3×C4C3×#12111yescharacteristic
413C3×C4C3×#12411yescharacteristic
414Dic3—42no—
415Dic3—81no—
416Dic3—81no—
417C32#197311yescharacteristic, complemented, Sylow
418C23—62no—
419C23—122no—
420C23—122no—
421C23—121no—
422C23—121no—
423C23C2×C3×D1211yescharacteristic
424Q8—62no—
425Q8—62no—
426Q8—121no—
427Q8—121no—
428D4—62no—
429D4—62no—
430D4—121no—
431D4—121no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—62no—
436C2×C4—121no—
437C2×C4—121no—
438C2×C4—122no—
439C2×C4—122no—
440C2×C4—121no—
441C2×C4—121no—
442C2×C4C2×C3×C4×D311yescharacteristic
443C2×C4C2×C3×D1211yescharacteristic
444C2×C4C2×C3×D1211yescharacteristic
445C2×C4C3×#23511yescharacteristic
446C2×C4C3×#23511yescharacteristic
447C2×C4C2×C3×#6711yescharacteristic
448C8—22no—
449C8C3×(C2×D3)⋊C414yescomplemented
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—22no—
455C2×C3—242no—
456C2×C3#471012yes—
457C2×C3#471211yescharacteristic
458C2×C3#471511yescharacteristic
459C2×C3#493911yescharacteristic
460C2×C3#513412yes—
461C2×C3C3×#39011yescharacteristic
462C2×C3C3×#44012yes—
463C2×C3C3×#46812yes—
464C2×C3C3×#49611yescharacteristic
465C2×C3C3×#49711yescharacteristic
466D3—82no—
467C22—122no—
468C22—124no—
469C22—241no—
470C22—241no—
471C22—242no—
472C22C3×C4×D1211yescharacteristic
473C22C3×#87411yescharacteristic
474C22C3×#90812yes—
475C22C3×#90912yes—
476C22C3×#93011yescharacteristic
477C4—42no—
478C4—122no—
479C4—241no—
480C4—241no—
481C4C3×C4×D1211yescharacteristic
482C4C3×#87511yescharacteristic
483C4C2×C3×(C2×D3)⋊C411yescharacteristic
484C4C3×#93011yescharacteristic
485C3—21no—
486C3#6982611yescharacteristic, direct product factor
487C3C3×#197311yescharacteristic, complemented
488C2—242no—
489C2C3×#471012yes—
490C2C3×#471211yescharacteristic
491C2C3×#471511yescharacteristic
492C2C3×#493911yescharacteristic
493C2C3×#513412yes—
subgroupG/H
centerC23×C3C2×D12
commutatorC2×C3×C4C22×C3×C4
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#97C2
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C3×C4C23×C3
hypercenterC2×C3×#97D3
hypocenterC3C3×#1973
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C42 ◁ C2×C3×#97

Complements

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

NH ≅ G/Ntype
2. C2×C32×#97C2semidirect
4. C2×C3×#818C2semidirect
5. C2×C3×#816C2semidirect
7. C3×#4929C2semidirect
9. #69826C3direct (N × H)
20. C2×C3×#204C4semidirect
32. C2×C3×#97D3semidirect
33. C2×C3×#97C2×C3semidirect
37. C2×#818C2×C3semidirect
38. C2×#816C2×C3semidirect
40. #4929C2×C3semidirect
98. C2×#204C3×C4semidirect
141. C32×C8C22⋊C4semidirect
146. C2×#97C3×D3semidirect
331. C3×C8(C2×D3)⋊C4semidirect
332. C3×C8C3×C22⋊C4semidirect
417. C32#1973semidirect
449. C8C3×(C2×D3)⋊C4semidirect
486. C3#69826direct (N × H)
487. C3C3×#1973semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×C32×#972
C2×C3×#8212
C2×C3×#8182
C2×C3×#8162
C3×#49392
C3×#49292
C3×#19733
#698263