Finite Group Databasebeta

← C3×#83551 #11887609

Subgroups — C3×#83551 #11887609

Order 1152.

916 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×D4×Q8C211yesmaximal, characteristic
2C3×#5543C211yesmaximal, characteristic
3C3×#5228C212yesmaximal, complemented
4C2×C3×#835C212yesmaximal, complemented
5C3×#5090C211yesmaximal, characteristic, complemented
6C3×#5079C211yesmaximal, characteristic, complemented
7C3×#5051C212yesmaximal, complemented
8C3×#5044C212yesmaximal, complemented
9C3×C4×#216C211yesmaximal, characteristic, complemented
10C3×#5021C211yesmaximal, characteristic, complemented
11C3×D4×C3⋊C8C211yesmaximal, characteristic
12C3×#3299—31nomaximal
13#83551C311yesmaximal, characteristic, direct product factor
14C22×C32×Q8C2212yes—
15C32×C4⋊Q8—21no—
16C32×C4⋊Q8C2211yescharacteristic
17C32×C22⋊Q8—22no—
18C32×C22⋊Q8C2212yes—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4—21no—
21C32×C4×D4C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#216C2212yes—
24C3×D4×Dic3—21no—
25C2×C3×C4⋊Dic3C2212yes—
26C3×#924C2212yes—
27C22×C3×C3⋊C8C2212yes—
28C3×#890—21no—
29C3×#878—22no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×#835C2211yescharacteristic
33C3×#835C2212yes—
34C3×#835C2212yes—
35C3×#835C2212yes—
36C3×#835C2212yes—
37C3×#830C2212yes—
38C3×#810C2211yescharacteristic
39C3×#807C2212yes—
40C3×#807C2211yescharacteristic
41C3×C4⋊(C3⋊C8)C2211yescharacteristic
42C3×C4×C3⋊C8C2211yescharacteristic
43C3×#554—31no—
44C3×D4×Q8—21no—
45C3×D4×Q8D311yescharacteristic
46C3×D4×Q8C2×C311yescharacteristic
47#5543C2×C311yescharacteristic
48C3×#487—31no—
49C3×#484—32no—
50C3×#477—31no—
51C3×#467—32no—
52C3×#462—31no—
53C3×#451—32no—
54C3×C4×Q16—31no—
55C3×C8×D4—31no—
56C2×C3×#103—32no—
57#5228C2×C312yescomplemented
58C2×#835C2×C312yescomplemented
59#5090C2×C311yescharacteristic, complemented
60#5079C2×C311yescharacteristic, complemented
61#5051C2×C312yescomplemented
62#5044C2×C312yescomplemented
63C4×#216C2×C311yescharacteristic, complemented
64#5021C2×C311yescharacteristic, complemented
65D4×C3⋊C8C2×C311yescharacteristic
66C2×C32×Q8—22no—
67C2×C32×Q8—24no—
68C2×C32×Q8—42no—
69C2×C32×Q8C2312yes—
70C2×C32×Q8C2311yescharacteristic
71C2×C32×D4D411yescharacteristic
72C22×C32×C4—22no—
73C22×C32×C4C2312yes—
74C22×C3×Dic3—22no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6C2311yescharacteristic
77C32×C4⋊C4—21no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4—21no—
80C32×C4⋊C4—22no—
81C32×C4⋊C4D411yescharacteristic
82C32×C4⋊C4C2311yescharacteristic
83C32×C22⋊C4—22no—
84C32×C22⋊C4D412yes—
85C32×C42—21no—
86C32×C42C2311yescharacteristic
87C3×#217—22no—
88C3×#216—22no—
89C3×#216—42no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2311yescharacteristic
94C3×Dic3⋊C4—21no—
95C3×Dic3⋊C4—22no—
96C3×C4×Dic3—21no—
97C2×C3×C3⋊C8—42no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2311yescharacteristic
101#3299—31noSylow
102C22×C3×Q8—22no—
103C22×C3×Q8C2×D312yes—
104C22×C3×Q8C22×C312yes—
105C2×C3×Q16—31no—
106C2×C3×Q16—32no—
107C22×C3×C8—32no—
108C3×C4⋊Q8—22no—
109C3×C4⋊Q8—21no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8—21no—
112C3×C4⋊Q8—31no—
113C3×C4⋊Q8C2×D311yescharacteristic
114C3×C4⋊Q8C22×C311yescharacteristic
115C3×#125—61no—
116C3×C22⋊Q8—24no—
117C3×C22⋊Q8—22no—
118C3×C22⋊Q8—22no—
119C3×C22⋊Q8—22no—
120C3×C22⋊Q8—32no—
121C3×C22⋊Q8—62no—
122C3×C22⋊Q8C2×D312yes—
123C3×C22⋊Q8C22×C312yes—
124C3×C4×Q8—21no—
125C3×C4×Q8—31no—
126C3×C4×Q8C2×D311yescharacteristic
127C3×C4×Q8C22×C311yescharacteristic
128C3×C4×D4—22no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×C4×D4—21no—
132C3×C4×D4—61no—
133C3×C4×D4C2×D311yescharacteristic
134C3×C4×D4C22×C311yescharacteristic
135C2×C3×C4⋊C4—32no—
136C2×#216C22×C311yescharacteristic
137C2×#216C22×C312yes—
138D4×Dic3—21no—
139C2×C4⋊Dic3C22×C312yes—
140#924C22×C312yes—
141C22×C3⋊C8C22×C312yes—
142#890—21no—
143#878—22no—
144#869C22×C311yescharacteristic
145C4×Dic6C22×C311yescharacteristic
146C3×#107—31no—
147C3×#107—32no—
148C3×C4⋊C8—31no—
149C3×#103—31no—
150C3×#103—32no—
151C3×#103—32no—
152C3×#103—32no—
153C3×#103—32no—
154C3×#103—31no—
155C3×C22⋊C8—32no—
156C3×C4×C8—31no—
157#835C22×C311yescharacteristic
158#835C22×C312yes—
159#835C22×C312yes—
160#835C22×C312yes—
161#835C22×C312yes—
162#830C22×C312yes—
163#810C22×C311yescharacteristic
164#807C22×C312yes—
165#807C22×C311yescharacteristic
166C4⋊(C3⋊C8)C22×C311yescharacteristic
167C4×C3⋊C8C22×C311yescharacteristic
168C23×C32C2×D412yes—
169C32×Q8—21no—
170C32×Q8—22no—
171C32×Q8—22no—
172C32×Q8—44no—
173C32×Q8#4112yes—
174C32×D4Q1614yescomplemented
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—44no—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—82no—
189C3×Dic6—21no—
190C3×Dic6—21no—
191C3×Dic6—81no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195#554—31no—
196D4×Q8C3×D311yescharacteristic
197#487—31no—
198#484—32no—
199#477—31no—
200#467—32no—
201#462—31no—
202#451—32no—
203C4×Q16—31no—
204C8×D4—31no—
205C2×#103—32no—
206C2×C3×Q8—24no—
207C2×C3×Q8—22no—
208C2×C3×Q8—22no—
209C2×C3×Q8—24no—
210C2×C3×Q8—24no—
211C2×C3×Q8—21no—
212C2×C3×Q8—22no—
213C2×C3×Q8—31no—
214C2×C3×Q8—44no—
215C2×C3×Q8—42no—
216C2×C3×Q8—42no—
217C2×C3×Q8—44no—
218C2×C3×Q8—61no—
219C2×C3×Q8C22×D312yes—
220C2×C3×Q8C22×D311yescharacteristic
221C2×C3×Q8C23×C312yes—
222C2×C3×Q8C23×C311yescharacteristic
223C2×C3×D4—21no—
224C2×C3×D4#6711yescharacteristic
225C2×C3×D4C3×D411yescharacteristic
226C22×C3×C4—24no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—62no—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C23×C312yes—
233C22×Dic3—22no—
234C2×Dic6—21no—
235C2×Dic6C23×C311yescharacteristic
236C3×Q16—62no—
237C3×Q16—122no—
238C2×C3×C8—31no—
239C2×C3×C8—31no—
240C2×C3×C8—32no—
241C2×C3×C8—122no—
242C3×C4⋊C4—22no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—31no—
257C3×C4⋊C4—32no—
258C3×C4⋊C4—61no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4#6711yescharacteristic
263C3×C4⋊C4C3×D411yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C23×C311yescharacteristic
266C3×C22⋊C4—24no—
267C3×C22⋊C4—22no—
268C3×C22⋊C4—22no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—62no—
271C3×C22⋊C4#6712yes—
272C3×C22⋊C4C3×D412yes—
273C3×C42—22no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—61no—
278C3×C42C22×D311yescharacteristic
279C3×C42C23×C311yescharacteristic
280#217—22no—
281#216—22no—
282#216—42no—
283C4⋊Dic3—21no—
284C4⋊Dic3—22no—
285C4⋊Dic3C23×C311yescharacteristic
286C4⋊Dic3C23×C312yes—
287Dic3⋊C4—21no—
288Dic3⋊C4—22no—
289C4×Dic3—21no—
290C2×C3⋊C8—42no—
291C2×C3⋊C8C23×C311yescharacteristic
292C2×C3⋊C8C23×C311yescharacteristic
293C2×C3⋊C8C23×C312yes—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32C2×Q1614yes—
297C22×C32C22×D411yescharacteristic
298C32×C4—22no—
299C32×C4—22no—
300C32×C4—21no—
301C32×C4—42no—
302C32×C4—41no—
303C32×C4C2×Q1612yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4H(5,𝔽2)11yescharacteristic
306C3×Dic3—41no—
307C3×Dic3—42no—
308C3×Dic3—41no—
309C22×Q8C2×C3×D312yes—
310C2×Q16—31no—
311C2×Q16—32no—
312C22×C8—32no—
313C4⋊Q8—21no—
314C4⋊Q8—31no—
315C4⋊Q8C2×C3×D311yescharacteristic
316#125—61no—
317C22⋊Q8—22no—
318C22⋊Q8—32no—
319C22⋊Q8—62no—
320C22⋊Q8C2×C3×D312yes—
321C4×Q8—31no—
322C4×Q8C2×C3×D311yescharacteristic
323C4×D4—21no—
324C4×D4—61no—
325C4×D4C2×C3×D311yescharacteristic
326C2×C4⋊C4—32no—
327#107—31no—
328#107—32no—
329C4⋊C8—31no—
330#103—31no—
331#103—32no—
332#103—32no—
333#103—32no—
334#103—32no—
335#103—31no—
336C22⋊C8—32no—
337C4×C8—31no—
338C23×C3—22no—
339C23×C3C2×#6712yes—
340C23×C3C2×C3×D412yes—
341C3×Q8—22no—
342C3×Q8—21no—
343C3×Q8—21no—
344C3×Q8—22no—
345C3×Q8—22no—
346C3×Q8—22no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—42no—
350C3×Q8—42no—
351C3×Q8—44no—
352C3×Q8—44no—
353C3×Q8—48no—
354C3×Q8—61no—
355C3×Q8—61no—
356C3×Q8—241no—
357C3×Q8#23712yes—
358C3×Q8C3×#4112yes—
359C3×D4—24no—
360C3×D4#21614yescomplemented
361C3×D4C3×Q1614yescomplemented
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—22no—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—21no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—22no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—44no—
382C2×C3×C4—44no—
383C2×C3×C4—48no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—62no—
387C2×C3×C4—242no—
388C2×C3×C4C2×#6711yescharacteristic
389C2×C3×C4C2×#6712yes—
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×C3×D412yes—
392C2×C3×C4C2×C3×D411yescharacteristic
393C2×C3×C4C2×C3×D411yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C24×C311yescharacteristic
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—82no—
400Dic6—21no—
401Dic6—21no—
402Dic6—81no—
403C3×C8—61no—
404C3×C8—61no—
405C3×C8—62no—
406C3⋊C8—21no—
407C3⋊C8—21no—
408C3⋊C8—22no—
409C2×C32—24no—
410C2×C32#54611yescharacteristic
411C2×C32C22×Q1611yescharacteristic
412C2×C32#57711yescharacteristic
413C2×Q8—22no—
414C2×Q8—24no—
415C2×Q8—31no—
416C2×Q8—42no—
417C2×Q8—61no—
418C2×Q8C22×C3×D312yes—
419C2×Q8C22×C3×D311yescharacteristic
420C2×D4C3×#6711yescharacteristic
421C22×C4—22no—
422C22×C4—62no—
423C22×C4C22×C3×D312yes—
424Q16—62no—
425Q16—122no—
426C2×C8—31no—
427C2×C8—31no—
428C2×C8—32no—
429C2×C8—122no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—31no—
435C4⋊C4—32no—
436C4⋊C4—62no—
437C4⋊C4—61no—
438C4⋊C4—61no—
439C4⋊C4—62no—
440C4⋊C4C3×#6711yescharacteristic
441C4⋊C4C22×C3×D311yescharacteristic
442C22⋊C4—22no—
443C22⋊C4—62no—
444C22⋊C4C3×#6712yes—
445C42—21no—
446C42—61no—
447C42C22×C3×D311yescharacteristic
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—24no—
453C22×C3—21no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3C2×#21614yes—
457C22×C3C2×C3×Q1614yes—
458C22×C3C22×#6711yescharacteristic
459C22×C3C22×C3×D411yescharacteristic
460C3×C4—24no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—22no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—42no—
471C3×C4—41no—
472C3×C4—44no—
473C3×C4—42no—
474C3×C4—41no—
475C3×C4—42no—
476C3×C4—41no—
477C3×C4—42no—
478C3×C4—121no—
479C3×C4—121no—
480C3×C4—122no—
481C3×C4C2×#21612yes—
482C3×C4C2×C3×Q1612yes—
483C3×C4C2×#23711yescharacteristic
484C3×C4#100411yescharacteristic
485C3×C4C2×C3×#4111yescharacteristic
486C3×C4C3×H(5,𝔽2)11yescharacteristic
487Dic3—42no—
488Dic3—41no—
489Dic3—41no—
490C32#329911yescharacteristic, complemented, Sylow
491C23C2×C3×#6712yes—
492Q8—21no—
493Q8—22no—
494Q8—22no—
495Q8—44no—
496Q8—61no—
497Q8—61no—
498Q8—241no—
499Q8C3×#23712yes—
500D4C3×#21614yescomplemented
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—44no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—62no—
510C2×C4—242no—
511C2×C4C2×C3×#6711yescharacteristic
512C2×C4C2×C3×#6712yes—
513C2×C4C2×C3×#6711yescharacteristic
514C2×C4C23×C3×D311yescharacteristic
515C8—61no—
516C8—61no—
517C8—62no—
518C2×C3—24no—
519C2×C3—24no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—44no—
524C2×C3#580611yescharacteristic
525C2×C3C22×#21611yescharacteristic
526C2×C3#583711yescharacteristic
527C2×C3C3×#54611yescharacteristic
528C2×C3C22×C3×Q1611yescharacteristic
529C2×C3C3×#57711yescharacteristic
530C22—22no—
531C22—22no—
532C22C2×C3×#21614yes—
533C22C22×C3×#6711yescharacteristic
534C4—22no—
535C4—22no—
536C4—21no—
537C4—42no—
538C4—41no—
539C4—121no—
540C4—121no—
541C4—122no—
542C4C2×C3×#21612yes—
543C4C2×C3×#23711yescharacteristic
544C4C3×#100411yescharacteristic
545C3—21no—
546C3#8355111yescharacteristic, direct product factor
547C3C3×#329911yescharacteristic, complemented
548C2—24no—
549C2C3×#580611yescharacteristic
550C2C22×C3×#21611yescharacteristic
551C2C3×#583711yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×D4×Q8C2
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC3×D4×Q8D3
hypocenterC3C3×#3299
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
3. C3×#5228C2semidirect
4. C2×C3×#835C2semidirect
5. C3×#5090C2semidirect
6. C3×#5079C2semidirect
7. C3×#5051C2semidirect
8. C3×#5044C2semidirect
9. C3×C4×#216C2semidirect
10. C3×#5021C2semidirect
13. #83551C3direct (N × H)
57. #5228C2×C3semidirect
58. C2×#835C2×C3semidirect
59. #5090C2×C3semidirect
60. #5079C2×C3semidirect
61. #5051C2×C3semidirect
62. #5044C2×C3semidirect
63. C4×#216C2×C3semidirect
64. #5021C2×C3semidirect
174. C32×D4Q16semidirect
360. C3×D4#216semidirect
361. C3×D4C3×Q16semidirect
490. C32#3299semidirect
500. D4C3×#216semidirect
546. C3#83551direct (N × H)
547. C3C3×#3299semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
C3×#55432
C3×#52282
C2×C3×#8352
C3×#50902
C3×#50792
C3×#50512
C3×#50442
C3×C4×#2162
C3×#50212
C3×D4×C3⋊C82
C3×#32993
#835513