Finite Group Databasebeta

← C3×#79678 #11887513

Subgroups — C3×#79678 #11887513

Order 1152.

901 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic
3C32×C4×SD16C211yesmaximal, characteristic, complemented
4C3×#5170C212yesmaximal, complemented
5C3×#5020C211yesmaximal, characteristic, complemented
6C3×#5019C211yesmaximal, characteristic, complemented
7C3×#4862C212yesmaximal, complemented
8C3×D3×#103C212yesmaximal, complemented
9C3×#4778C212yesmaximal, complemented
10C3×C8×D12C211yesmaximal, characteristic, complemented
11C3×#4681C211yesmaximal, characteristic, complemented
12C3×#3298—31nomaximal
13#79678C311yesmaximal, characteristic, direct product factor
14C2×C3×D3×Q8C2212yes—
15C2×C3×#235—21no—
16C2×C32×SD16C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18C32×C4×D4C2211yescharacteristic
19C3×#938C2212yes—
20C2×C3×#214C2212yes—
21C3×#924—21no—
22C2×C3×D3×C8C2212yes—
23C3×#897—22no—
24C3×#897C2212yes—
25C3×D3×C4⋊C4C2212yes—
26C3×#883—22no—
27C3×C4×D12—21no—
28C3×C4×D12C2211yescharacteristic
29C3×#869—21no—
30C3×#869C2211yescharacteristic
31C3×#869C2211yescharacteristic
32C32×#106C2211yescharacteristic
33C32×#103C2211yescharacteristic
34C32×#102C2211yescharacteristic
35C32×C4×C8C2211yescharacteristic
36C3×#835C2212yes—
37C3×(C2×D3)⋊C8C2212yes—
38C3×#816C2212yes—
39C3×#816C2212yes—
40C3×#810C2212yes—
41C3×#808C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43C3×D4×Q8—31no—
44C3×#547—31no—
45Q8×D12C2×C311yescharacteristic, complemented
46#5551C2×C311yescharacteristic
47C3×#487—31no—
48C3×#483—32no—
49C3×#475—31no—
50C3×#465—32no—
51C3×#461—31no—
52C3×#448—32no—
53C3×C4×SD16—21no—
54C3×C4×SD16D311yescharacteristic, complemented
55C3×C4×SD16C2×C311yescharacteristic, complemented
56C3×C8×D4—31no—
57C2×C3×#103—32no—
58#5170C2×C312yescomplemented
59#5020C2×C311yescharacteristic, complemented
60#5019C2×C311yescharacteristic, complemented
61#4862C2×C312yescomplemented
62D3×#103C2×C312yescomplemented
63#4778C2×C312yescomplemented
64C8×D12C2×C311yescharacteristic, complemented
65#4681C2×C311yescharacteristic, complemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2311yescharacteristic
68C22×C32×C4—21no—
69C2×C3×#67—22no—
70C3×D3×Q8—24no—
71C3×D3×Q8—42no—
72C3×#235—44no—
73C2×C3×D12D411yescharacteristic
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3C2312yes—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6C2312yes—
80C32×SD16—22no—
81C2×C32×C8C2311yescharacteristic
82C2×C32×C8C2311yescharacteristic
83C32×C4⋊C4—21no—
84C32×C4⋊C4C2311yescharacteristic
85C32×C4⋊C4C2311yescharacteristic
86C32×C22⋊C4—21no—
87C32×C42—21no—
88C32×C42C2311yescharacteristic
89C3×#217—22no—
90C3×#214—42no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4D412yes—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—22no—
97C3×C4⋊Dic3D411yescharacteristic
98C3×C4⋊Dic3C2312yes—
99C3×Dic3⋊C4—22no—
100C2×C3×C3⋊C8C2312yes—
101C3×D3×C8—42no—
102#3298—31noSylow
103C2×C3×#41—61no—
104C22×C3×Q8—32no—
105C2×D3×Q8C22×C312yes—
106C2×#235—21no—
107C2×C3×SD16—21no—
108C2×C3×SD16—32no—
109C2×C3×SD16C2×D311yescharacteristic
110C2×C3×SD16C22×C311yescharacteristic
111C22×C3×C8—32no—
112C3×C4⋊Q8—31no—
113C3×C4⋊Q8—31no—
114C3×C4⋊Q8—61no—
115C3×#123—62no—
116C3×C22⋊Q8—32no—
117C3×C22⋊Q8—62no—
118C3×C22⋊Q8—61no—
119C3×#121—32no—
120C3×C4×Q8—21no—
121C3×C4×Q8C2×D311yescharacteristic
122C3×C4×Q8C22×C311yescharacteristic
123C3×C4×D4—21no—
124C3×C4×D4—31no—
125C3×C4×D4—61no—
126C3×C4×D4C2×D311yescharacteristic
127C3×C4×D4C22×C311yescharacteristic
128C2×C3×C4⋊C4—32no—
129#938C22×C312yes—
130C2×#214C22×C312yes—
131#924—21no—
132C2×D3×C8C22×C312yes—
133#897—22no—
134#897C22×C312yes—
135D3×C4⋊C4C22×C312yes—
136#883—22no—
137C4×D12—21no—
138C4×D12C22×C311yescharacteristic
139#869—21no—
140#869C22×C311yescharacteristic
141#869C22×C311yescharacteristic
142C3×#106—21no—
143C3×#106—32no—
144C3×#106C2×D311yescharacteristic
145C3×#106C22×C311yescharacteristic
146C3×C4⋊C8—31no—
147C3×#103—21no—
148C3×#103—32no—
149C3×#103—32no—
150C3×#103—32no—
151C3×#103—32no—
152C3×#103C2×D311yescharacteristic
153C3×#103C22×C311yescharacteristic
154C3×#102—21no—
155C3×#102C2×D311yescharacteristic
156C3×#102C22×C311yescharacteristic
157C3×C22⋊C8—32no—
158C3×C4×C8—21no—
159C3×C4×C8C2×D311yescharacteristic
160C3×C4×C8C22×C311yescharacteristic
161#835C22×C312yes—
162(C2×D3)⋊C8C22×C312yes—
163#816C22×C312yes—
164#816C22×C312yes—
165#810C22×C312yes—
166#808C22×C312yes—
167C4⋊(C3⋊C8)C22×C311yescharacteristic
168C23×C32—21no—
169C22×C3×D3C2×D412yes—
170C32×Q8—21no—
171C32×Q8#4112yescomplemented
172C32×D4—21no—
173C32×D4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—42no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C3×#67—44no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3C2×D412yes—
185C3×D12SD1614yescomplemented
186C3×C4×D3—22no—
187C3×C4×D3—22no—
188C3×C4×D3—44no—
189C3×C4×D3—44no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192C3×Dic6—44no—
193C3×Dic6—42no—
194C32×C8—21no—
195C32×C8—21no—
196C3×C3⋊C8—22no—
197D4×Q8—31no—
198#547—31no—
199#487—31no—
200#483—32no—
201#475—31no—
202#465—32no—
203#461—31no—
204#448—32no—
205C4×SD16C3×D311yescharacteristic, complemented
206C8×D4—31no—
207C2×#103—32no—
208C3×#41—124no—
209C2×C3×Q8—21no—
210C2×C3×Q8—32no—
211C2×C3×Q8—62no—
212C2×C3×Q8—61no—
213C2×C3×Q8—64no—
214C2×C3×Q8—122no—
215C2×C3×Q8C22×D311yescharacteristic
216C2×C3×Q8C23×C311yescharacteristic
217C2×C3×D4—21no—
218C2×C3×D4—31no—
219C2×C3×D4—62no—
220C2×C3×D4C22×D311yescharacteristic
221C2×C3×D4C23×C311yescharacteristic
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—32no—
225C22×C3×C4—41no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C2×#67—22no—
229D3×Q8—24no—
230D3×Q8—42no—
231#235—44no—
232C2×D12C3×D411yescharacteristic
233C2×C4×D3—22no—
234C2×C4×D3—22no—
235C2×C4×D3C23×C312yes—
236C2×Dic6—21no—
237C2×Dic6—22no—
238C2×Dic6C23×C312yes—
239C3×SD16—24no—
240C3×SD16—22no—
241C3×SD16—22no—
242C3×SD16—122no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—32no—
246C2×C3×C8—122no—
247C2×C3×C8C22×D311yescharacteristic
248C2×C3×C8C22×D311yescharacteristic
249C2×C3×C8C23×C311yescharacteristic
250C2×C3×C8C23×C311yescharacteristic
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—31no—
256C3×C4⋊C4—32no—
257C3×C4⋊C4—41no—
258C3×C4⋊C4—62no—
259C3×C4⋊C4—62no—
260C3×C4⋊C4—61no—
261C3×C4⋊C4—61no—
262C3×C4⋊C4—61no—
263C3×C4⋊C4C22×D311yescharacteristic
264C3×C4⋊C4C22×D311yescharacteristic
265C3×C4⋊C4C23×C311yescharacteristic
266C3×C4⋊C4C23×C311yescharacteristic
267C3×C22⋊C4—21no—
268C3×C22⋊C4—21no—
269C3×C22⋊C4—32no—
270C3×C22⋊C4—41no—
271C3×C22⋊C4—62no—
272C3×C22⋊C4—62no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—41no—
277C3×C42C22×D311yescharacteristic
278C3×C42C23×C311yescharacteristic
279#217—22no—
280#214—42no—
281(C2×D3)⋊C4—22no—
282(C2×D3)⋊C4C3×D412yes—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—22no—
287C4⋊Dic3C3×D411yescharacteristic
288C4⋊Dic3C23×C312yes—
289Dic3⋊C4—22no—
290C2×C3⋊C8C23×C312yes—
291D3×C8—42no—
292C22×C32—41no—
293C22×C32—41no—
294C22×C32—41no—
295C22×C32C22×D411yescharacteristic
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3C2×SD1614yes—
299C32×C4—22no—
300C32×C4—21no—
301C32×C4—41no—
302C32×C4—41no—
303C32×C4C2×SD1612yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4H(5,𝔽2)11yescharacteristic
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3—42no—
309C2×#41—61no—
310C22×Q8—32no—
311C2×SD16—32no—
312C2×SD16C2×C3×D311yescharacteristic
313C22×C8—32no—
314C4⋊Q8—31no—
315C4⋊Q8—31no—
316C4⋊Q8—61no—
317#123—62no—
318C22⋊Q8—32no—
319C22⋊Q8—62no—
320C22⋊Q8—61no—
321#121—32no—
322C4×Q8C2×C3×D311yescharacteristic
323C4×D4—31no—
324C4×D4—61no—
325C4×D4C2×C3×D311yescharacteristic
326C2×C4⋊C4—32no—
327#106—32no—
328#106C2×C3×D311yescharacteristic
329C4⋊C8—31no—
330#103—32no—
331#103—32no—
332#103—32no—
333#103—32no—
334#103C2×C3×D311yescharacteristic
335#102C2×C3×D311yescharacteristic
336C22⋊C8—32no—
337C4×C8C2×C3×D311yescharacteristic
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—32no—
341C23×C3—41no—
342C22×D3C2×C3×D412yes—
343C3×Q8—21no—
344C3×Q8—21no—
345C3×Q8—22no—
346C3×Q8—41no—
347C3×Q8—62no—
348C3×Q8—62no—
349C3×Q8—124no—
350C3×Q8—122no—
351C3×Q8#23512yescomplemented
352C3×Q8C3×#4112yescomplemented
353C3×D4—22no—
354C3×D4—21no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4—34no—
359C3×D4—41no—
360C3×D4—124no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—32no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—41no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—82no—
381C2×C3×C4—124no—
382C2×C3×C4—124no—
383C2×C3×C4D3×D411yescharacteristic
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4C2×C3×D411yescharacteristic
386C2×C3×C4C2×C3×D411yescharacteristic
387C2×C3×C4C23×D311yescharacteristic
388C2×C3×C4C24×C311yescharacteristic
389#67—44no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3C2×C3×D412yes—
393D12C3×SD1614yescomplemented
394C4×D3—22no—
395C4×D3—22no—
396C4×D3—44no—
397C4×D3—44no—
398Dic6—22no—
399Dic6—22no—
400Dic6—44no—
401Dic6—42no—
402C3×C8—22no—
403C3×C8—21no—
404C3×C8—21no—
405C3×C8—21no—
406C3×C8—21no—
407C3×C8—41no—
408C3×C8—62no—
409C3⋊C8—22no—
410C2×C32—81no—
411C2×C32#54611yescharacteristic
412C2×C32C22×SD1611yescharacteristic
413C2×C32#57811yescharacteristic
414C3×D3—24no—
415#41—124no—
416C2×Q8—32no—
417C2×Q8—62no—
418C2×Q8—61no—
419C2×Q8—64no—
420C2×Q8—122no—
421C2×Q8C22×C3×D311yescharacteristic
422C2×D4—31no—
423C2×D4—62no—
424C2×D4C22×C3×D311yescharacteristic
425C22×C4—21no—
426C22×C4—32no—
427C22×C4—62no—
428C22×C4—62no—
429SD16—22no—
430SD16—122no—
431C2×C8—32no—
432C2×C8—122no—
433C2×C8C22×C3×D311yescharacteristic
434C2×C8C22×C3×D311yescharacteristic
435C4⋊C4—21no—
436C4⋊C4—31no—
437C4⋊C4—32no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4C22×C3×D311yescharacteristic
444C4⋊C4C22×C3×D311yescharacteristic
445C22⋊C4—21no—
446C22⋊C4—32no—
447C22⋊C4—62no—
448C22⋊C4—62no—
449C42—21no—
450C42C22×C3×D311yescharacteristic
451C22×C3—21no—
452C22×C3—34no—
453C22×C3—42no—
454C22×C3—41no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—62no—
461C22×C3—62no—
462C22×C3—81no—
463C22×C3—81no—
464C22×C3C2×D3×D411yescharacteristic
465C22×C3C22×C3×D411yescharacteristic
466C2×D3—22no—
467C2×D3—22no—
468C2×D3C2×C3×SD1614yes—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—41no—
477C3×C4—42no—
478C3×C4—41no—
479C3×C4—41no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—62no—
483C3×C4—81no—
484C3×C4—81no—
485C3×C4—122no—
486C3×C4—122no—
487C3×C4D3×SD1612yes—
488C3×C4C2×C3×SD1612yes—
489C3×C4C2×#23511yescharacteristic
490C3×C4#100911yescharacteristic
491C3×C4C2×C3×#4111yescharacteristic
492C3×C4C3×H(5,𝔽2)11yescharacteristic
493Dic3—22no—
494Dic3—42no—
495Dic3—42no—
496C32#329811yescharacteristic, complemented, Sylow
497C23—21no—
498C23—32no—
499Q8—21no—
500Q8—62no—
501Q8—62no—
502Q8—124no—
503Q8—122no—
504Q8C3×#23512yescomplemented
505D4—21no—
506D4—21no—
507D4—34no—
508D4—124no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—32no—
513C2×C4—42no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—124no—
519C2×C4—124no—
520C2×C4C3×D3×D411yescharacteristic
521C2×C4C3×D3×D411yescharacteristic
522C2×C4C23×C3×D311yescharacteristic
523C8—21no—
524C8—21no—
525C8—62no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—64no—
530C2×C3—82no—
531C2×C3—81no—
532C2×C3—81no—
533C2×C3#555011yescharacteristic
534C2×C3C2×D3×SD1611yescharacteristic
535C2×C3#577111yescharacteristic
536C2×C3C3×#54611yescharacteristic
537C2×C3C22×C3×SD1611yescharacteristic
538C2×C3C3×#57811yescharacteristic
539D3—24no—
540C22—34no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—62no—
545C22—62no—
546C22C2×C3×D3×D411yescharacteristic
547C4—21no—
548C4—22no—
549C4—41no—
550C4—41no—
551C4—62no—
552C4—122no—
553C4—122no—
554C4C3×D3×SD1612yes—
555C4C2×C3×#23511yescharacteristic
556C4C3×#100911yescharacteristic
557C3—21no—
558C3#7967811yescharacteristic, direct product factor
559C3C3×#329811yescharacteristic, complemented
560C2—64no—
561C2—81no—
562C2C3×#555011yescharacteristic
563C2C2×C3×D3×SD1611yescharacteristic
564C2C3×#577111yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC3×#5551C2
hypercenterC3×C4×SD16D3
hypocenterC3C3×#3298
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C3×Q8×D12C2semidirect
3. C32×C4×SD16C2semidirect
4. C3×#5170C2semidirect
5. C3×#5020C2semidirect
6. C3×#5019C2semidirect
7. C3×#4862C2semidirect
8. C3×D3×#103C2semidirect
9. C3×#4778C2semidirect
10. C3×C8×D12C2semidirect
11. C3×#4681C2semidirect
13. #79678C3direct (N × H)
45. Q8×D12C2×C3semidirect
54. C3×C4×SD16D3semidirect
55. C3×C4×SD16C2×C3semidirect
58. #5170C2×C3semidirect
59. #5020C2×C3semidirect
60. #5019C2×C3semidirect
61. #4862C2×C3semidirect
62. D3×#103C2×C3semidirect
63. #4778C2×C3semidirect
64. C8×D12C2×C3semidirect
65. #4681C2×C3semidirect
171. C32×Q8#41semidirect
185. C3×D12SD16semidirect
205. C4×SD16C3×D3semidirect
351. C3×Q8#235semidirect
352. C3×Q8C3×#41semidirect
393. D12C3×SD16semidirect
496. C32#3298semidirect
504. Q8C3×#235semidirect
558. C3#79678direct (N × H)
559. C3C3×#3298semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
C3×#55512
C32×C4×SD162
C3×#51702
C3×#50202
C3×#50192
C3×#48622
C3×D3×#1032
C3×#47782
C3×C8×D122
C3×#46812
C3×#32983
#796783