Finite Group Databasebeta

← C3×#79262 #11868167

Subgroups — C3×#79262 #11868167

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5748C211yesmaximal, characteristic
2C2×C3×#909C211yesmaximal, characteristic, complemented
3C2×C3×#909C211yesmaximal, characteristic, complemented
4C3×#5745C211yesmaximal, characteristic, complemented
5C32×#430C211yesmaximal, characteristic, complemented
6C2×C3×#824C211yesmaximal, characteristic, complemented
7C3×#5132C211yesmaximal, characteristic, complemented
8C3×#4898C214yesmaximal, complemented
9C3×#4896C214yesmaximal, complemented
10C3×#3069—31nomaximal
11#79262C311yesmaximal, characteristic, direct product factor
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×C32×M16C2211yescharacteristic
17C2×C32×M16C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#909—22no—
20C3×#909—21no—
21C3×#909—22no—
22C3×#909—22no—
23C3×#909C2214yes—
24C3×#909C2212yes—
25C3×#908—21no—
26C3×#908C2212yes—
27C3×#907—22no—
28C3×D3×M16—22no—
29C2×C3×Dic12—21no—
30C2×C3×Dic12C2212yescomplemented
31C3×#904—22no—
32C2×C3×#204—21no—
33C2×C3×#204C2212yescomplemented
34C3×#901C2214yes—
35C32×#108C2214yescomplemented
36C3×#824C2212yescomplemented
37C3×#824C2214yescomplemented
38C3×#823C2212yescomplemented
39C3×#575—31no—
40C2×C3×#137—31no—
41C2×C3×#137—31no—
42C3×#568—31no—
43#5748C2×C311yescharacteristic
44C2×#909C2×C311yescharacteristic, complemented
45C2×#909C2×C311yescharacteristic, complemented
46#5745C2×C311yescharacteristic, complemented
47C3×#473—34no—
48C3×#471—34no—
49C3×#430—21no—
50C3×#430D311yescharacteristic, complemented
51C3×#430C2×C311yescharacteristic, complemented
52C3×#413—31no—
53C2×C3×#101—31no—
54C2×#824C2×C311yescharacteristic, complemented
55#5132C2×C311yescharacteristic, complemented
56#4898C2×C314yescomplemented
57#4896C2×C314yescomplemented
58C22×C32×C4C2311yescharacteristic
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C22×C3×Dic3—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235—21no—
68C3×#235D412yes—
69C3×#235C2312yes—
70C2×C3×D12D411yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D411yescharacteristic
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2311yescharacteristic
82C32×M16—21no—
83C32×M16—21no—
84C32×M16D412yes—
85C32×M16D412yes—
86C32×M16C2312yes—
87C32×M16C2312yes—
88C2×C32×C8—21no—
89C2×C32×C8—21no—
90C2×C32×C8C2312yes—
91C3×#208—21no—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C3×Dic12—22no—
95C3×Dic12—24no—
96C3×Dic12—24no—
97C3×D24—22no—
98C3×#204—24no—
99C3×#204—22no—
100C3×#204—22no—
101C3×#204—24no—
102C3×ΓL(1,𝔽25)—24no—
103C3×D3×C8—24no—
104#3069—31noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×Q8—31no—
108C2×#235C22×C311yescharacteristic
109C2×#235C22×C311yescharacteristic
110C22×Dic6C22×C311yescharacteristic
111C3×#137—34no—
112C3×#137—32no—
113C3×#137—61no—
114C3×#137—62no—
115C3×#137—62no—
116C3×#137—62no—
117C3×AGL(1,ℤ/8)—32no—
118C3×AGL(1,ℤ/8)—61no—
119C3×#135—62no—
120C2×C3×Q16—32no—
121C2×C3×Q16—61no—
122C2×C3×SD16—32no—
123C2×C3×SD16—61no—
124C3×#131—34no—
125C3×#131—62no—
126C2×C3×M16—21no—
127C2×C3×M16—21no—
128C2×C3×M16—21no—
129C2×C3×M16—31no—
130C2×C3×M16—62no—
131C2×C3×M16C2×D311yescharacteristic
132C2×C3×M16C2×D311yescharacteristic
133C2×C3×M16C2×D311yescharacteristic
134C2×C3×M16C22×C311yescharacteristic
135C2×C3×M16C22×C311yescharacteristic
136C2×C3×M16C22×C311yescharacteristic
137C2×#208C22×C311yescharacteristic
138#909—22no—
139#909—21no—
140#909—22no—
141#909—22no—
142#909C22×C312yes—
143#909C22×C314yes—
144#908—21no—
145#908C22×C312yes—
146#907—22no—
147D3×M16—22no—
148C2×Dic12—21no—
149C2×Dic12C22×C312yescomplemented
150#904—22no—
151C2×#204—21no—
152C2×#204C22×C312yescomplemented
153#901C22×C314yes—
154C3×#108—24no—
155C3×#108C2×D314yescomplemented
156C3×#108C22×C314yescomplemented
157C3×#101—34no—
158C3×#101—32no—
159C3×#100—32no—
160#824C22×C312yescomplemented
161#824C22×C314yescomplemented
162#823C22×C312yescomplemented
163C23×C32#4111yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4111yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C3×#67—22no—
173C3×#67—22no—
174C3×#67—41no—
175C3×#67—41no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—41no—
180C2×C3×Dic3—41no—
181C3×D12—21no—
182C3×D12—21no—
183C3×D12—21no—
184C3×D12C2×D412yes—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187C3×C4×D3—41no—
188C3×C4×D3—41no—
189C3×Dic6—21no—
190C3×Dic6—22no—
191C3×Dic6—22no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194C3×Dic6—41no—
195C3×Dic6—41no—
196C3×Dic6C2×D412yes—
197C32×C8—22no—
198C32×C8—22no—
199C32×C8C2×D414yes—
200C3×C3⋊C8—22no—
201#575—31no—
202C2×#137—31no—
203C2×#137—31no—
204#568—31no—
205#473—34no—
206#471—34no—
207#430C3×D311yescharacteristic, complemented
208#413—31no—
209C2×#101—31no—
210C3×#41—32no—
211C3×#41—32no—
212C3×#41—61no—
213C3×#41—61no—
214C3×#41—61no—
215C3×#41—61no—
216C3×#41—61no—
217C3×#41—61no—
218C2×C3×Q8—31no—
219C2×C3×Q8—32no—
220C2×C3×Q8—31no—
221C2×C3×Q8—61no—
222C2×C3×Q8—61no—
223C2×C3×Q8—61no—
224C2×C3×Q8—61no—
225C2×C3×Q8—61no—
226C2×C3×D4—31no—
227C2×C3×D4—31no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C22×C3×C4—21no—
231C22×C3×C4—61no—
232C22×C3×C4—61no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C23×C311yescharacteristic
236C2×#67—21no—
237C2×#67—21no—
238C22×Dic3—21no—
239#235—21no—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—21no—
244#235—21no—
245#235C3×D412yes—
246#235C23×C312yes—
247C2×D12C3×D411yescharacteristic
248C2×D12C23×C311yescharacteristic
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6C3×D411yescharacteristic
257C2×Dic6C23×C312yes—
258C2×Dic6C23×C311yescharacteristic
259C3×Q16—64no—
260C3×Q16—62no—
261C3×Q16—64no—
262C3×SD16—64no—
263C3×SD16—62no—
264C3×SD16—62no—
265C3×SD16—64no—
266C3×D8—62no—
267C3×M16—21no—
268C3×M16—21no—
269C3×M16—21no—
270C3×M16—21no—
271C3×M16—22no—
272C3×M16—22no—
273C3×M16—22no—
274C3×M16—22no—
275C3×M16—32no—
276C3×M16—41no—
277C3×M16—41no—
278C3×M16—61no—
279C3×M16—64no—
280C3×M16D1212yes—
281C3×M16D1212yes—
282C3×M16C3×D412yes—
283C3×M16C3×D412yes—
284C3×M16C22×D312yes—
285C3×M16C22×D312yes—
286C3×M16C23×C312yes—
287C3×M16C23×C312yes—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—22no—
293C2×C3×C8—41no—
294C2×C3×C8—41no—
295C2×C3×C8—61no—
296C2×C3×C8—64no—
297C2×C3×C8C22×D312yes—
298C2×C3×C8C23×C312yes—
299#208—21no—
300#208C23×C312yes—
301C2×C3⋊C8—21no—
302Dic12—22no—
303Dic12—24no—
304Dic12—24no—
305D24—22no—
306#204—24no—
307#204—22no—
308#204—22no—
309#204—24no—
310ΓL(1,𝔽25)—24no—
311D3×C8—24no—
312C22×C32—41no—
313C22×C32#12111yescharacteristic
314C22×C32#12111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C2×C3×D3—22no—
317C2×C3×D3—41no—
318C2×C3×D3—81no—
319C2×C3×D3—81no—
320C32×C4#12111yescharacteristic
321C32×C4#12111yescharacteristic
322C32×C4C22×D411yescharacteristic
323C32×C4C22×D411yescharacteristic
324C3×Dic3—22no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C2×#41—31no—
328C2×#41—31no—
329C22×Q8—31no—
330#137—34no—
331#137—32no—
332#137—61no—
333#137—62no—
334#137—62no—
335#137—62no—
336AGL(1,ℤ/8)—32no—
337AGL(1,ℤ/8)—61no—
338#135—62no—
339C2×Q16—32no—
340C2×Q16—61no—
341C2×SD16—32no—
342C2×SD16—61no—
343#131—34no—
344#131—62no—
345C2×M16—31no—
346C2×M16—62no—
347C2×M16C2×C3×D311yescharacteristic
348C2×M16C2×C3×D311yescharacteristic
349C2×M16C2×C3×D311yescharacteristic
350#108C2×C3×D314yescomplemented
351#101—34no—
352#101—32no—
353#100—32no—
354C23×C3—21no—
355C23×C3—61no—
356C23×C3—61no—
357C23×C3#23911yescharacteristic
358C23×C3C3×#4111yescharacteristic
359C22×D3—21no—
360C22×D3—21no—
361C3×Q8—32no—
362C3×Q8—61no—
363C3×Q8—62no—
364C3×Q8—61no—
365C3×Q8—62no—
366C3×Q8—61no—
367C3×Q8—121no—
368C3×Q8—121no—
369C3×D4—32no—
370C3×D4—62no—
371C3×D4—62no—
372C3×D4—61no—
373C3×D4—61no—
374C3×D4—61no—
375C3×D4—121no—
376C3×D4—121no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—62no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4—121no—
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4C2×D1211yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4#23911yescharacteristic
397C2×C3×C4C2×C3×D411yescharacteristic
398C2×C3×C4C2×C3×D411yescharacteristic
399C2×C3×C4C2×C3×D411yescharacteristic
400C2×C3×C4C2×C3×D411yescharacteristic
401C2×C3×C4C3×#4111yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C24×C311yescharacteristic
404#67—22no—
405#67—22no—
406#67—41no—
407#67—41no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—21no—
411C2×Dic3—41no—
412C2×Dic3—41no—
413D12—21no—
414D12—21no—
415D12—21no—
416D12C2×C3×D412yes—
417C4×D3—22no—
418C4×D3—22no—
419C4×D3—41no—
420C4×D3—41no—
421Dic6—21no—
422Dic6—22no—
423Dic6—22no—
424Dic6—21no—
425Dic6—21no—
426Dic6—41no—
427Dic6—41no—
428Dic6C2×C3×D412yes—
429C3×C8—22no—
430C3×C8—22no—
431C3×C8—22no—
432C3×C8—22no—
433C3×C8—24no—
434C3×C8—42no—
435C3×C8—42no—
436C3×C8—62no—
437C3×C8C2×D1214yes—
438C3×C8C2×C3×D414yes—
439C3⋊C8—22no—
440C2×C32—21no—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32C2×#12111yescharacteristic
444C3×D3—42no—
445C3×D3—81no—
446#41—32no—
447#41—32no—
448#41—61no—
449#41—61no—
450#41—61no—
451#41—61no—
452#41—61no—
453#41—61no—
454C2×Q8—32no—
455C2×Q8—31no—
456C2×Q8—31no—
457C2×Q8—61no—
458C2×Q8—61no—
459C2×Q8—61no—
460C2×Q8—61no—
461C2×Q8—61no—
462C2×D4—31no—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4—61no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4C22×C3×D311yescharacteristic
470Q16—64no—
471Q16—62no—
472Q16—64no—
473SD16—64no—
474SD16—62no—
475SD16—62no—
476SD16—64no—
477D8—62no—
478M16—21no—
479M16—21no—
480M16—32no—
481M16—61no—
482M16—64no—
483M16C3×D1212yes—
484M16C3×D1212yes—
485M16C22×C3×D312yes—
486M16C22×C3×D312yes—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—61no—
490C2×C8—64no—
491C2×C8C22×C3×D312yes—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—62no—
498C22×C3—81no—
499C22×C3—121no—
500C22×C3—241no—
501C22×C3—241no—
502C22×C3#89511yescharacteristic
503C22×C3#89511yescharacteristic
504C22×C3C3×#12111yescharacteristic
505C22×C3C3×#12111yescharacteristic
506C22×C3C2×#23911yescharacteristic
507C22×C3C2×C3×#4111yescharacteristic
508C2×D3—22no—
509C2×D3—41no—
510C2×D3—81no—
511C2×D3—81no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—62no—
517C3×C4—121no—
518C3×C4—122no—
519C3×C4#89511yescharacteristic
520C3×C4#89511yescharacteristic
521C3×C4C3×#12111yescharacteristic
522C3×C4C3×#12111yescharacteristic
523C3×C4C22×D1211yescharacteristic
524C3×C4C2×D3×D411yescharacteristic
525C3×C4C22×C3×D411yescharacteristic
526C3×C4C22×C3×D411yescharacteristic
527Dic3—22no—
528Dic3—42no—
529Dic3—41no—
530C32#306911yescharacteristic, complemented, Sylow
531C23—61no—
532C23—61no—
533C23C3×#23911yescharacteristic
534Q8—32no—
535Q8—61no—
536Q8—62no—
537Q8—61no—
538Q8—62no—
539Q8—61no—
540Q8—121no—
541Q8—121no—
542D4—32no—
543D4—62no—
544D4—62no—
545D4—61no—
546D4—61no—
547D4—61no—
548D4—121no—
549D4—121no—
550C2×C4—61no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—62no—
555C2×C4—121no—
556C2×C4—121no—
557C2×C4—121no—
558C2×C4—121no—
559C2×C4C2×C3×D1211yescharacteristic
560C2×C4C2×C3×D1211yescharacteristic
561C2×C4C3×D3×D411yescharacteristic
562C2×C4C3×D3×D411yescharacteristic
563C2×C4C3×#23911yescharacteristic
564C2×C4C23×C3×D311yescharacteristic
565C8—22no—
566C8—22no—
567C8—62no—
568C8C2×C3×D1214yes—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—41no—
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—122no—
580C2×C3—241no—
581C2×C3C2×#89511yescharacteristic
582C2×C3C2×C3×#12111yescharacteristic
583D3—42no—
584D3—81no—
585C22—41no—
586C22—62no—
587C22—121no—
588C22—241no—
589C22—241no—
590C22C3×#89511yescharacteristic
591C22C3×#89511yescharacteristic
592C22C2×C3×#23911yescharacteristic
593C4—62no—
594C4—121no—
595C4—122no—
596C4C3×#89511yescharacteristic
597C4C3×#89511yescharacteristic
598C4C22×C3×D1211yescharacteristic
599C4C2×C3×D3×D411yescharacteristic
600C3—21no—
601C3#7926211yescharacteristic, direct product factor
602C3C3×#306911yescharacteristic, complemented
603C2—21no—
604C2—21no—
605C2—21no—
606C2—122no—
607C2—241no—
608C2C2×C3×#89511yescharacteristic
subgroupG/H
centerC2×C3C2×#895
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#430C2
socleC2×C32C2×#121
prime radicalC3×#5748C2
hypercenterC3×#430D3
hypocenterC3C3×#3069
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C3 ◁ C22×C3×C4 ◁ C3×#430

Complements

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

NH ≅ G/Ntype
2. C2×C3×#909C2semidirect
3. C2×C3×#909C2semidirect
4. C3×#5745C2semidirect
5. C32×#430C2semidirect
6. C2×C3×#824C2semidirect
7. C3×#5132C2semidirect
8. C3×#4898C2semidirect
9. C3×#4896C2semidirect
11. #79262C3direct (N × H)
30. C2×C3×Dic12C22semidirect
33. C2×C3×#204C22semidirect
35. C32×#108C22semidirect
36. C3×#824C22semidirect
37. C3×#824C22semidirect
38. C3×#823C22semidirect
44. C2×#909C2×C3semidirect
45. C2×#909C2×C3semidirect
46. #5745C2×C3semidirect
50. C3×#430D3semidirect
51. C3×#430C2×C3semidirect
54. C2×#824C2×C3semidirect
55. #5132C2×C3semidirect
56. #4898C2×C3semidirect
57. #4896C2×C3semidirect
149. C2×Dic12C22×C3semidirect
152. C2×#204C22×C3semidirect
155. C3×#108C2×D3semidirect
156. C3×#108C22×C3semidirect
160. #824C22×C3semidirect
161. #824C22×C3semidirect
162. #823C22×C3semidirect
207. #430C3×D3semidirect
350. #108C2×C3×D3semidirect
530. C32#3069semidirect
601. C3#79262direct (N × H)
602. C3C3×#3069semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
C2×C3×#9092
C3×#57452
C32×#4302
C2×C3×#8242
C3×#51322
C3×#48982
C3×#48962
C3×#30693
#792623