Finite Group Databasebeta

← C3×#70212 #11794008

Subgroups — C3×#70212 #11794008

Order 1152.

821 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#213C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic, complemented
3C3×#5221C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8C3×#2054—31nomaximal
9#70212C311yesmaximal, characteristic, direct product factor
10C22×C32×D4C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C3×#217—21no—
15C2×C3×#217—21no—
16C2×C3×#213—22no—
17C2×C3×#213—22no—
18C2×C3×#213—22no—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C32×#102—22no—
25C3×#821—22no—
26C3×Dic3⋊C8—22no—
27C22×C3×D8—31no—
28C22×#213C2×C311yescharacteristic
29C2×C3×C4⋊C8—31no—
30C2×C3×#102—21no—
31C2×C3×#102—31no—
32C2×C3×#102D311yescharacteristic, complemented
33C2×C3×#102C2×C311yescharacteristic, complemented
34C3×#390—31no—
35C3×#390—31no—
36#5221C2×C311yescharacteristic, complemented
37C2×#821C2×C311yescharacteristic, complemented
38C2×Dic3⋊C8C2×C311yescharacteristic, complemented
39#4988C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4529C2×C311yescharacteristic, complemented
42C24×C32—21no—
43C23×C3×D3—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4D412yes—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12D412yes—
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×#213—28no—
69C3×(C2×D3)⋊C4—42no—
70C3×(C2×D3)⋊C4—42no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D412yes—
78#2054—31noSylow
79C22×C3×D4—21no—
80C22×C3×D4—31no—
81C22×C3×D4C2×D311yescharacteristic
82C22×C3×D4C22×C311yescharacteristic
83C22×D12C22×C311yescharacteristic
84C2×C3×D8—62no—
85C2×C3×D8—62no—
86C2×C3×D8—62no—
87C22×C3×C8—21no—
88C22×C3×C8—31no—
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C22×C311yescharacteristic
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C22×C311yescharacteristic
95C2×C3×C22⋊C4—61no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C22⋊C4—61no—
99C2×C3×C42—31no—
100C2×#217—21no—
101C2×#217—21no—
102C2×#213—22no—
103C2×#213—22no—
104C2×#213—22no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×C4⋊Dic3C22×C311yescharacteristic
108C2×C4×Dic3C22×C311yescharacteristic
109C22×C3⋊C8C22×C311yescharacteristic
110C3×C4⋊C8—62no—
111C3×#102—24no—
112C3×#102—22no—
113C3×#102—22no—
114C3×#102—62no—
115#821—22no—
116Dic3⋊C8—22no—
117C23×C32—22no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32—41no—
121C23×C32—41no—
122C23×C32—41no—
123C23×C32—41no—
124C23×C32C2×D411yescharacteristic
125C22×C3×D3—22no—
126C22×C3×D3—41no—
127C22×C3×D3—41no—
128C22×C3×D3—41no—
129C22×C3×D3—41no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—41no—
135C32×D4—41no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C3×Dic3—21no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3D812yescomplemented
154C3×D12—22no—
155C3×D12—22no—
156C3×D12—41no—
157C3×D12—41no—
158C32×C8—41no—
159C3×C3⋊C8—22no—
160C22×D8—31no—
161C2×C4⋊C8—31no—
162C2×#102—31no—
163C2×#102C3×D311yescharacteristic, complemented
164#390—31no—
165#390—31no—
166#340—31no—
167C24×C3—21no—
168C24×C3—21no—
169C24×C3—41no—
170C24×C3—61no—
171C23×D3—21no—
172C2×C3×D4—22no—
173C2×C3×D4—22no—
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—21no—
183C2×C3×D4—21no—
184C2×C3×D4—22no—
185C2×C3×D4—32no—
186C2×C3×D4—41no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C2×C3×D4—61no—
194C2×C3×D4#6712yes—
195C2×C3×D4C3×D412yes—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C23×C311yescharacteristic
205C22×Dic3—21no—
206C22×Dic3C3×D411yescharacteristic
207C22×Dic3C3×D411yescharacteristic
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12C3×D412yes—
214C3×D8—68no—
215C2×C3×C8—22no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—21no—
222C2×C3×C8—32no—
223C2×C3×C8—41no—
224C2×C3×C8—41no—
225C2×C3×C8—61no—
226C2×C3×C8—61no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—21no—
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—41no—
233C3×C4⋊C4—61no—
234C3×C4⋊C4—61no—
235C3×C22⋊C4—122no—
236C3×C22⋊C4—122no—
237C3×C22⋊C4—122no—
238C3×C22⋊C4—122no—
239C3×C42—61no—
240C3×C42—61no—
241#217—42no—
242#217—42no—
243#213—28no—
244(C2×D3)⋊C4—42no—
245(C2×D3)⋊C4—42no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4×Dic3—21no—
249C4×Dic3—21no—
250C2×C3⋊C8—21no—
251C2×C3⋊C8—21no—
252C2×C3⋊C8C3×D412yes—
253C22×C32—42no—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—81no—
257C22×C32—81no—
258C22×C32—81no—
259C22×C32—81no—
260C22×C32#12111yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32C2×D811yescharacteristic
264C22×C32#13511yescharacteristic
265C22×C32AGL(1,ℤ/8)11yescharacteristic
266C22×C32AGL(1,ℤ/8)11yescharacteristic
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C2×C3×D3—42no—
270C2×C3×D3—81no—
271C2×C3×D3—81no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C32×C4—81no—
275C32×C4#12011yescharacteristic
276C32×C4#12311yescharacteristic
277C32×C4#12311yescharacteristic
278C32×C4#12411yescharacteristic
279C3×Dic3—22no—
280C3×Dic3—41no—
281C3×Dic3—81no—
282C22×D4—31no—
283C22×D4C2×C3×D311yescharacteristic
284C2×D8—62no—
285C2×D8—62no—
286C2×D8—62no—
287C22×C8—31no—
288C22×C8C2×C3×D311yescharacteristic
289C2×C4⋊C4—31no—
290C2×C4⋊C4C2×C3×D311yescharacteristic
291C2×C22⋊C4—61no—
292C2×C22⋊C4—61no—
293C2×C22⋊C4—61no—
294C2×C22⋊C4—61no—
295C2×C42—31no—
296C4⋊C8—62no—
297#102—22no—
298#102—62no—
299C23×C3—22no—
300C23×C3—22no—
301C23×C3—21no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3—41no—
308C23×C3—41no—
309C23×C3—41no—
310C23×C3—41no—
311C23×C3—41no—
312C23×C3—41no—
313C23×C3—41no—
314C23×C3—41no—
315C23×C3—41no—
316C23×C3—41no—
317C23×C3—62no—
318C23×C3—81no—
319C23×C3—81no—
320C23×C3—81no—
321C23×C3—81no—
322C23×C3—121no—
323C23×C3—121no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3D3×D411yescharacteristic
329C23×C3C2×C3×D411yescharacteristic
330C22×D3—22no—
331C22×D3—41no—
332C22×D3—41no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C3×D4—24no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4—22no—
342C3×D4—42no—
343C3×D4—42no—
344C3×D4—42no—
345C3×D4—41no—
346C3×D4—41no—
347C3×D4—41no—
348C3×D4—41no—
349C3×D4—62no—
350C3×D4—62no—
351C3×D4—121no—
352C3×D4—121no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—32no—
360C2×C3×C4—42no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—61no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—81no—
373C2×C3×C4—81no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4#23511yescharacteristic
378C2×C3×C4#23511yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4#23711yescharacteristic
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×C3×D411yescharacteristic
384C2×C3×C4C2×C3×D411yescharacteristic
385C2×C3×C4C2×C3×D411yescharacteristic
386C2×C3×C4C3×#4111yescharacteristic
387C2×C3×C4C3×#4111yescharacteristic
388C2×C3×C4C3×#4111yescharacteristic
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3C3×D812yescomplemented
398D12—22no—
399D12—22no—
400D12—41no—
401D12—41no—
402C3×C8—42no—
403C3×C8—41no—
404C3×C8—41no—
405C3×C8—62no—
406C3⋊C8—22no—
407C2×C32—82no—
408C2×C32#39411yescharacteristic
409C2×C32#45911yescharacteristic
410C2×C32#45911yescharacteristic
411C2×C32#46311yescharacteristic
412C2×C32#46311yescharacteristic
413C2×C32#46611yescharacteristic
414C2×C32#46911yescharacteristic
415C3×D3—82no—
416C24—21no—
417C24—61no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—32no—
424C2×D4—61no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4C3×#6712yes—
430C22×C4—21no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—61no—
434C22×C4C22×C3×D311yescharacteristic
435D8—68no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—32no—
440C2×C8—61no—
441C2×C8—61no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—61no—
445C4⋊C4—61no—
446C22⋊C4—122no—
447C22⋊C4—122no—
448C22⋊C4—122no—
449C22⋊C4—122no—
450C42—61no—
451C42—61no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—44no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—82no—
467C22×C3—82no—
468C22×C3—82no—
469C22×C3—82no—
470C22×C3—82no—
471C22×C3—82no—
472C22×C3—81no—
473C22×C3—81no—
474C22×C3—81no—
475C22×C3—81no—
476C22×C3—81no—
477C22×C3—81no—
478C22×C3—81no—
479C22×C3—81no—
480C22×C3—122no—
481C22×C3—122no—
482C22×C3—122no—
483C22×C3—241no—
484C22×C3—241no—
485C22×C3—241no—
486C22×C3—241no—
487C22×C3#88411yescharacteristic
488C22×C3#88411yescharacteristic
489C22×C3D3×D811yescharacteristic
490C22×C3#91111yescharacteristic
491C22×C3#91411yescharacteristic
492C22×C3#91611yescharacteristic
493C22×C3#93911yescharacteristic
494C22×C3C3×#12111yescharacteristic
495C22×C3C3×#12111yescharacteristic
496C22×C3C3×#12111yescharacteristic
497C22×C3C2×C3×D811yescharacteristic
498C22×C3C3×#13511yescharacteristic
499C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
500C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
501C2×D3—42no—
502C2×D3—42no—
503C2×D3—42no—
504C2×D3—81no—
505C2×D3—81no—
506C2×D3—81no—
507C2×D3—81no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—21no—
511C3×C4—21no—
512C3×C4—62no—
513C3×C4—82no—
514C3×C4—81no—
515C3×C4—81no—
516C3×C4—121no—
517C3×C4—241no—
518C3×C4#88311yescharacteristic
519C3×C4#88511yescharacteristic
520C3×C4#92911yescharacteristic
521C3×C4#93711yescharacteristic
522C3×C4C3×#12011yescharacteristic
523C3×C4C3×#12311yescharacteristic
524C3×C4C3×#12311yescharacteristic
525C3×C4C3×#12411yescharacteristic
526Dic3—22no—
527Dic3—41no—
528Dic3—81no—
529C32#205411yescharacteristic, complemented, Sylow
530C23—22no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—62no—
538C23—121no—
539C23—121no—
540C23—121no—
541C23—121no—
542C23—121no—
543C23—121no—
544C23C3×D3×D411yescharacteristic
545D4—22no—
546D4—22no—
547D4—41no—
548D4—41no—
549D4—62no—
550D4—62no—
551D4—121no—
552D4—121no—
553C2×C4—32no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4C3×#23511yescharacteristic
566C2×C4C3×#23511yescharacteristic
567C2×C4C3×D3×D411yescharacteristic
568C2×C4C3×D3×D411yescharacteristic
569C2×C4C3×#23711yescharacteristic
570C2×C4C2×C3×#6711yescharacteristic
571C8—41no—
572C8—62no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—84no—
581C2×C3—82no—
582C2×C3—82no—
583C2×C3—242no—
584C2×C3#477511yescharacteristic
585C2×C3#478211yescharacteristic
586C2×C3#478611yescharacteristic
587C2×C3#478711yescharacteristic
588C2×C3#495911yescharacteristic
589C2×C3#515011yescharacteristic
590C2×C3#516511yescharacteristic
591C2×C3C3×#39411yescharacteristic
592C2×C3C3×#45911yescharacteristic
593C2×C3C3×#45911yescharacteristic
594C2×C3C3×#46311yescharacteristic
595C2×C3C3×#46311yescharacteristic
596C2×C3C3×#46611yescharacteristic
597C2×C3C3×#46911yescharacteristic
598D3—82no—
599C22—42no—
600C22—42no—
601C22—42no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—122no—
607C22—122no—
608C22—122no—
609C22—241no—
610C22—241no—
611C22—241no—
612C22—241no—
613C22C3×#88411yescharacteristic
614C22C3×#88411yescharacteristic
615C22C3×D3×D811yescharacteristic
616C22C3×#91111yescharacteristic
617C22C3×#91411yescharacteristic
618C22C3×#91611yescharacteristic
619C22C3×#93911yescharacteristic
620C4—62no—
621C4—81no—
622C4—121no—
623C4—241no—
624C4C3×#88311yescharacteristic
625C4C3×#88511yescharacteristic
626C4C3×#92911yescharacteristic
627C4C3×#93711yescharacteristic
628C3—21no—
629C3#7021211yescharacteristic, direct product factor
630C3C3×#205411yescharacteristic, complemented
631C2—82no—
632C2—242no—
633C2C3×#477511yescharacteristic
634C2C3×#478211yescharacteristic
635C2C3×#478611yescharacteristic
636C2C3×#478711yescharacteristic
637C2C3×#495911yescharacteristic
638C2C3×#515011yescharacteristic
639C2C3×#516511yescharacteristic
subgroupG/H
centerC23×C3D3×D4
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
hypercenterC2×C3×#102D3
hypocenterC3C3×#2054
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
2. C2×C32×#102C2semidirect
3. C3×#5221C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C3×#4988C2semidirect
7. C3×#4529C2semidirect
9. #70212C3direct (N × H)
32. C2×C3×#102D3semidirect
33. C2×C3×#102C2×C3semidirect
36. #5221C2×C3semidirect
37. C2×#821C2×C3semidirect
38. C2×Dic3⋊C8C2×C3semidirect
39. #4988C2×C3semidirect
41. #4529C2×C3semidirect
153. C2×C3×Dic3D8semidirect
163. C2×#102C3×D3semidirect
397. C2×Dic3C3×D8semidirect
529. C32#2054semidirect
629. C3#70212direct (N × H)
630. C3C3×#2054semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2132
C2×C32×#1022
C3×#52212
C2×C3×#8212
C2×C3×Dic3⋊C82
C3×#49882
C3×#45292
C3×#20543
#702123