Finite Group Databasebeta

← C3×#70217 #11794046

Subgroups — C3×#70217 #11794046

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#214C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic
3C3×#5221C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C3×#4973C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2055—31nomaximal
9#70217C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#217—21no—
16C2×C3×#214—22no—
17C2×C3×#214—22no—
18C2×C3×#214—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C32×#102—22no—
23C3×C3⋊#95—21no—
24C3×C3⋊#95—21no—
25C3×#816—22no—
26C3×Dic3⋊C8—22no—
27C22×C3×SD16—31no—
28C22×#214C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×#103—31no—
31C2×C3×#102—21no—
32C2×C3×#102D311yescharacteristic
33C2×C3×#102C2×C311yescharacteristic
34C3×#391—31no—
35C3×#390—31no—
36#5221C2×C311yescharacteristic
37C2×#816C2×C311yescharacteristic, complemented
38C2×Dic3⋊C8C2×C311yescharacteristic, complemented
39#4973C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4529C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66C3×#217—42no—
67C3×#217—42no—
68C3×#214—28no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D412yes—
76#2055—31noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—21no—
79C22×C3×D4C2×D311yescharacteristic
80C22×C3×D4C22×C311yescharacteristic
81C22×Dic6C22×C311yescharacteristic
82C2×C3×SD16—62no—
83C2×C3×SD16—62no—
84C2×C3×SD16—62no—
85C22×C3×C8—21no—
86C22×C3×C8—31no—
87C22×C3×C8C2×D311yescharacteristic
88C22×C3×C8C22×C311yescharacteristic
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C4⋊C4C22×C311yescharacteristic
93C2×C3×C22⋊C4—61no—
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—31no—
96C2×#217—21no—
97C2×#217—21no—
98C2×#214—22no—
99C2×#214—22no—
100C2×#214—22no—
101C2×C4⋊Dic3C22×C311yescharacteristic
102C2×C4×Dic3C22×C311yescharacteristic
103C22×C3⋊C8C22×C311yescharacteristic
104C3×C4⋊C8—62no—
105C3×#103—62no—
106C3×#102—24no—
107C3×#102—22no—
108C3×#102—22no—
109C3×#95—61no—
110C3×#95—61no—
111C3⋊#95—21no—
112C3⋊#95—21no—
113#816—22no—
114Dic3⋊C8—22no—
115C23×C32—22no—
116C23×C32—41no—
117C23×C32—41no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32C2×D411yescharacteristic
123C32×D4—22no—
124C32×D4—22no—
125C32×D4—41no—
126C32×D4—41no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—21no—
141C2×C3×Dic3—21no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3SD1612yescomplemented
148C3×Dic6—22no—
149C3×Dic6—22no—
150C3×Dic6—41no—
151C3×Dic6—41no—
152C32×C8—41no—
153C3×C3⋊C8—22no—
154C22×SD16—31no—
155C2×C4⋊C8—31no—
156C2×#103—31no—
157C2×#102C3×D311yescharacteristic
158#391—31no—
159#390—31no—
160#340—31no—
161C24×C3—21no—
162C24×C3—21no—
163C24×C3—41no—
164C2×C3×Q8—32no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×D4—22no—
171C2×C3×D4—22no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—22no—
183C2×C3×D4—41no—
184C2×C3×D4—41no—
185C2×C3×D4—41no—
186C2×C3×D4#6712yes—
187C2×C3×D4C3×D412yes—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—41no—
194C22×C3×C4—61no—
195C22×C3×C4—61no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C23×C311yescharacteristic
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3C3×D411yescharacteristic
201C22×Dic3C3×D411yescharacteristic
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6—21no—
207C2×Dic6C3×D412yes—
208C3×SD16—68no—
209C2×C3×C8—22no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C2×C3×C8—32no—
217C2×C3×C8—41no—
218C2×C3×C8—41no—
219C2×C3×C8—61no—
220C2×C3×C8—61no—
221C3×C4⋊C4—22no—
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—41no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—122no—
230C3×C22⋊C4—122no—
231C3×C42—61no—
232C3×C42—61no—
233#217—42no—
234#217—42no—
235#214—28no—
236C4⋊Dic3—21no—
237C4⋊Dic3—21no—
238C4×Dic3—21no—
239C4×Dic3—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8C3×D412yes—
243C22×C32—42no—
244C22×C32—42no—
245C22×C32—42no—
246C22×C32—81no—
247C22×C32—81no—
248C22×C32—81no—
249C22×C32—81no—
250C22×C32#12111yescharacteristic
251C22×C32#12111yescharacteristic
252C22×C32#12111yescharacteristic
253C22×C32C2×SD1611yescharacteristic
254C22×C32#13511yescharacteristic
255C22×C32AGL(1,ℤ/8)11yescharacteristic
256C22×C32#13711yescharacteristic
257C32×C4—81no—
258C32×C4#12011yescharacteristic
259C32×C4#12311yescharacteristic
260C32×C4#12311yescharacteristic
261C32×C4#12411yescharacteristic
262C3×Dic3—22no—
263C3×Dic3—42no—
264C3×Dic3—41no—
265C3×Dic3—81no—
266C22×Q8—31no—
267C22×D4C2×C3×D311yescharacteristic
268C2×SD16—62no—
269C2×SD16—62no—
270C2×SD16—62no—
271C22×C8—31no—
272C22×C8C2×C3×D311yescharacteristic
273C2×C4⋊C4—31no—
274C2×C4⋊C4C2×C3×D311yescharacteristic
275C2×C22⋊C4—61no—
276C2×C22⋊C4—61no—
277C2×C42—31no—
278C4⋊C8—62no—
279#103—62no—
280#102—22no—
281#95—61no—
282#95—61no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—21no—
286C23×C3—42no—
287C23×C3—42no—
288C23×C3—42no—
289C23×C3—41no—
290C23×C3—41no—
291C23×C3—41no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—81no—
302C23×C3—81no—
303C23×C3—81no—
304C23×C3—81no—
305C23×C3D3×D411yescharacteristic
306C23×C3C2×C3×D411yescharacteristic
307C3×Q8—62no—
308C3×Q8—62no—
309C3×Q8—121no—
310C3×Q8—121no—
311C3×D4—24no—
312C3×D4—22no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—42no—
317C3×D4—42no—
318C3×D4—42no—
319C3×D4—41no—
320C3×D4—41no—
321C3×D4—41no—
322C3×D4—41no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—32no—
330C2×C3×C4—42no—
331C2×C3×C4—41no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—41no—
337C2×C3×C4—61no—
338C2×C3×C4—61no—
339C2×C3×C4—61no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—81no—
344C2×C3×C4—81no—
345C2×C3×C4—121no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4—121no—
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4#23511yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×C3×D411yescharacteristic
357C2×C3×C4C2×C3×D411yescharacteristic
358C2×C3×C4C2×C3×D411yescharacteristic
359C2×C3×C4C3×#4111yescharacteristic
360C2×C3×C4C3×#4111yescharacteristic
361C2×C3×C4C3×#4111yescharacteristic
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—22no—
366C2×Dic3—21no—
367C2×Dic3—21no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3C3×SD1612yescomplemented
374Dic6—22no—
375Dic6—22no—
376Dic6—41no—
377Dic6—41no—
378C3×C8—42no—
379C3×C8—41no—
380C3×C8—41no—
381C3×C8—62no—
382C3⋊C8—22no—
383C2×C32—82no—
384C2×C32#39411yescharacteristic
385C2×C32#46011yescharacteristic
386C2×C32#46111yescharacteristic
387C2×C32#46311yescharacteristic
388C2×C32#46411yescharacteristic
389C2×C32#46511yescharacteristic
390C2×C32#46811yescharacteristic
391C24—21no—
392C2×Q8—32no—
393C2×Q8—61no—
394C2×Q8—61no—
395C2×Q8—61no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4C3×#6712yes—
404C22×C4—21no—
405C22×C4—31no—
406C22×C4—31no—
407C22×C4—61no—
408C22×C4—61no—
409C22×C4C22×C3×D311yescharacteristic
410SD16—68no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—32no—
415C2×C8—61no—
416C2×C8—61no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—61no—
420C4⋊C4—61no—
421C22⋊C4—122no—
422C22⋊C4—122no—
423C42—61no—
424C42—61no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—44no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—82no—
440C22×C3—82no—
441C22×C3—82no—
442C22×C3—82no—
443C22×C3—82no—
444C22×C3—82no—
445C22×C3—81no—
446C22×C3—81no—
447C22×C3—81no—
448C22×C3—81no—
449C22×C3—81no—
450C22×C3—81no—
451C22×C3—81no—
452C22×C3—81no—
453C22×C3#88411yescharacteristic
454C22×C3#88411yescharacteristic
455C22×C3#91111yescharacteristic
456C22×C3#91211yescharacteristic
457C22×C3D3×SD1611yescharacteristic
458C22×C3#91511yescharacteristic
459C22×C3#93911yescharacteristic
460C22×C3C3×#12111yescharacteristic
461C22×C3C3×#12111yescharacteristic
462C22×C3C3×#12111yescharacteristic
463C22×C3C2×C3×SD1611yescharacteristic
464C22×C3C3×#13511yescharacteristic
465C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
466C22×C3C3×#13711yescharacteristic
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—62no—
472C3×C4—82no—
473C3×C4—81no—
474C3×C4—81no—
475C3×C4—122no—
476C3×C4—121no—
477C3×C4—241no—
478C3×C4#88311yescharacteristic
479C3×C4#88511yescharacteristic
480C3×C4#92911yescharacteristic
481C3×C4#93711yescharacteristic
482C3×C4C3×#12011yescharacteristic
483C3×C4C3×#12311yescharacteristic
484C3×C4C3×#12311yescharacteristic
485C3×C4C3×#12411yescharacteristic
486Dic3—22no—
487Dic3—42no—
488Dic3—41no—
489Dic3—81no—
490C32#205511yescharacteristic, complemented, Sylow
491C23—22no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23C3×D3×D411yescharacteristic
499Q8—62no—
500Q8—62no—
501Q8—121no—
502Q8—121no—
503D4—22no—
504D4—22no—
505D4—41no—
506D4—41no—
507C2×C4—32no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—62no—
515C2×C4—61no—
516C2×C4—61no—
517C2×C4—121no—
518C2×C4—121no—
519C2×C4—121no—
520C2×C4—121no—
521C2×C4—121no—
522C2×C4C3×#23511yescharacteristic
523C2×C4C3×#23511yescharacteristic
524C2×C4C3×D3×D411yescharacteristic
525C2×C4C3×D3×D411yescharacteristic
526C2×C4C3×#23711yescharacteristic
527C2×C4C2×C3×#6711yescharacteristic
528C8—41no—
529C8—62no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—84no—
538C2×C3—82no—
539C2×C3—82no—
540C2×C3#476211yescharacteristic
541C2×C3#476711yescharacteristic
542C2×C3#477811yescharacteristic
543C2×C3#478011yescharacteristic
544C2×C3#495911yescharacteristic
545C2×C3#515311yescharacteristic
546C2×C3#516211yescharacteristic
547C2×C3C3×#39411yescharacteristic
548C2×C3C3×#46011yescharacteristic
549C2×C3C3×#46111yescharacteristic
550C2×C3C3×#46311yescharacteristic
551C2×C3C3×#46411yescharacteristic
552C2×C3C3×#46511yescharacteristic
553C2×C3C3×#46811yescharacteristic
554C22—42no—
555C22—42no—
556C22—42no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C3×#88411yescharacteristic
562C22C3×#88411yescharacteristic
563C22C3×#91111yescharacteristic
564C22C3×#91211yescharacteristic
565C22C3×D3×SD1611yescharacteristic
566C22C3×#91511yescharacteristic
567C22C3×#93911yescharacteristic
568C4—62no—
569C4—81no—
570C4—122no—
571C4—121no—
572C4—241no—
573C4C3×#88311yescharacteristic
574C4C3×#88511yescharacteristic
575C4C3×#92911yescharacteristic
576C4C3×#93711yescharacteristic
577C3—21no—
578C3#7021711yescharacteristic, direct product factor
579C3C3×#205511yescharacteristic, complemented
580C2—82no—
581C2C3×#476211yescharacteristic
582C2C3×#476711yescharacteristic
583C2C3×#477811yescharacteristic
584C2C3×#478011yescharacteristic
585C2C3×#495911yescharacteristic
586C2C3×#515311yescharacteristic
587C2C3×#516211yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C32×D4C22
hypercenterC2×C3×#102D3
hypocenterC3C3×#2055
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C2×C3×#102

Complements

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

NH ≅ G/Ntype
4. C2×C3×#816C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C3×#4973C2semidirect
7. C3×#4529C2semidirect
9. #70217C3direct (N × H)
37. C2×#816C2×C3semidirect
38. C2×Dic3⋊C8C2×C3semidirect
39. #4973C2×C3semidirect
41. #4529C2×C3semidirect
147. C2×C3×Dic3SD16semidirect
373. C2×Dic3C3×SD16semidirect
490. C32#2055semidirect
578. C3#70217direct (N × H)
579. C3C3×#2055semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2142
C2×C32×#1022
C3×#52212
C2×C3×#8162
C2×C3×Dic3⋊C82
C3×#49732
C3×#45292
C3×#20553
#702173