Finite Group Databasebeta

← C3×#69934 #11793158

Subgroups — C3×#69934 #11793158

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C2×C32×C22⋊C8C211yesmaximal, characteristic, complemented
3C3×#5212C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×#818C211yesmaximal, characteristic, complemented
7C3×#4551C211yesmaximal, characteristic, complemented
8C3×#2033—31nomaximal
9#69934C311yesmaximal, characteristic, direct product factor
10C23×C32×C4C2211yescharacteristic
11C22×C3×#67—21no—
12C22×C3×D12C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×C3×#217—21no—
16C3×#930—22no—
17C3×#930—22no—
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C32×C22⋊C8—22no—
23C3×C3⋊#95—21no—
24C3×#821—22no—
25C3×#821—22no—
26C3×#818—22no—
27C2×C3×#121—31no—
28C2×#930C2×C311yescharacteristic
29C2×C3×#107—31no—
30C2×C3×#102—31no—
31C2×C3×#102—31no—
32C2×C3×C22⋊C8—21no—
33C2×C3×C22⋊C8D311yescharacteristic, complemented
34C2×C3×C22⋊C8C2×C311yescharacteristic, complemented
35C3×#380—31no—
36#5212C2×C311yescharacteristic, complemented
37C2×#821C2×C311yescharacteristic, complemented
38C2×#821C2×C311yescharacteristic, complemented
39C2×#818C2×C311yescharacteristic, complemented
40C3×#340—31no—
41#4551C2×C311yescharacteristic, complemented
42C24×C32D411yescharacteristic
43C23×C3×D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4—21no—
47C22×C32×C4—21no—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4D411yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C2×C3×#67—24no—
53C2×C3×#67—42no—
54C2×C3×#67—42no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12—21no—
62C2×C3×D12—21no—
63C2×C3×D12D412yes—
64C2×C32×C8—21no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8—21no—
68C2×C32×C8—21no—
69C2×C32×C8D412yescomplemented
70C3×#217—42no—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3D412yes—
78#2033—31noSylow
79C22×C3×D4—31no—
80C22×C3×D4—61no—
81C23×C3×C4—21no—
82C23×C3×C4C2×D311yescharacteristic
83C23×C3×C4C22×C311yescharacteristic
84C22×#67—21no—
85C22×D12C22×C311yescharacteristic
86C22×C3×C8—21no—
87C22×C3×C8—21no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C2×D311yescharacteristic
90C22×C3×C8C22×C311yescharacteristic
91C22×C3×C8C22×C311yescharacteristic
92C3×#121—62no—
93C3×#121—62no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C22⋊C4—61no—
99C2×#217—21no—
100#930—22no—
101#930—22no—
102C2×(C2×D3)⋊C4—21no—
103C2×C4⋊Dic3C22×C311yescharacteristic
104C2×C4⋊Dic3C22×C311yescharacteristic
105C2×C4⋊Dic3C22×C311yescharacteristic
106C3×#107—62no—
107C3×#102—62no—
108C3×#102—62no—
109C3×C22⋊C8—24no—
110C3×C22⋊C8—22no—
111C3×C22⋊C8—22no—
112C3×#95—61no—
113C3⋊#95—21no—
114#821—22no—
115#821—22no—
116#818—22no—
117C23×C32—21no—
118C23×C32—21no—
119C23×C32—21no—
120C23×C32—21no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32D812yes—
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—
132C2×C32×C4—21no—
133C2×C32×C4—21no—
134C2×C32×C4—21no—
135C2×C32×C4—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
145C3×#67—48no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—41no—
148C2×C3×Dic3—41no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—41no—
158C3×D12—41no—
159C32×C8—22no—
160C32×C8—41no—
161C2×#121—31no—
162C2×#107—31no—
163C2×#102—31no—
164C2×#102—31no—
165C2×C22⋊C8C3×D311yescharacteristic, complemented
166#380—31no—
167#340—31no—
168C24×C3—21no—
169C24×C3—61no—
170C24×C3D1211yescharacteristic
171C24×C3C3×D411yescharacteristic
172C23×D3—21no—
173C2×C3×D4—32no—
174C2×C3×D4—64no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4—122no—
181C2×C3×D4—122no—
182C22×C3×C4—22no—
183C22×C3×C4—22no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—41no—
199C22×C3×C4—41no—
200C22×C3×C4—41no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4—61no—
204C22×C3×C4—61no—
205C22×C3×C4D1211yescharacteristic
206C22×C3×C4C3×D411yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C23×C311yescharacteristic
209C2×#67—24no—
210C2×#67—42no—
211C2×#67—42no—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—21no—
220C2×D12C3×D412yes—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—22no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—22no—
233C2×C3×C8—41no—
234C2×C3×C8—41no—
235C2×C3×C8—41no—
236C2×C3×C8—41no—
237C2×C3×C8#6712yescomplemented
238C2×C3×C8C3×D412yescomplemented
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C22⋊C4—64no—
246C3×C22⋊C4—122no—
247#217—42no—
248(C2×D3)⋊C4—24no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—21no—
254C4⋊Dic3C3×D412yes—
255C22×C32—22no—
256C22×C32—22no—
257C22×C32—22no—
258C22×C32—41no—
259C22×C32—41no—
260C22×C32—41no—
261C22×C32—41no—
262C22×C32#12011yescharacteristic
263C22×C32#12111yescharacteristic
264C22×C32#12311yescharacteristic
265C22×C32C2×D811yescharacteristic
266C22×C32#13511yescharacteristic
267C22×C32AGL(1,ℤ/8)11yescharacteristic
268C22×C32#13711yescharacteristic
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—81no—
273C2×C3×D3—81no—
274C2×C3×D3—81no—
275C2×C3×D3—81no—
276C32×C4—41no—
277C32×C4#12111yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12311yescharacteristic
280C32×C4#12411yescharacteristic
281C3×Dic3—42no—
282C3×Dic3—81no—
283C3×Dic3—81no—
284C22×D4—31no—
285C22×D4—61no—
286C23×C4C2×C3×D311yescharacteristic
287C22×C8C2×C3×D311yescharacteristic
288C22×C8C2×C3×D311yescharacteristic
289#121—62no—
290#121—62no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—31no—
294C2×C22⋊C4—61no—
295C2×C22⋊C4—61no—
296#107—62no—
297#102—62no—
298#102—62no—
299C22⋊C8—22no—
300#95—61no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—21no—
306C23×C3—21no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—21no—
310C23×C3—21no—
311C23×C3—21no—
312C23×C3—21no—
313C23×C3—21no—
314C23×C3—21no—
315C23×C3—22no—
316C23×C3—21no—
317C23×C3—41no—
318C23×C3—41no—
319C23×C3—41no—
320C23×C3—41no—
321C23×C3—62no—
322C23×C3—121no—
323C23×C3—121no—
324C23×C3—121no—
325C23×C3—121no—
326C23×C3—121no—
327C23×C3—121no—
328C23×C3D2412yes—
329C23×C3C3×D812yes—
330C23×C3C2×D1211yescharacteristic
331C23×C3C2×C3×D411yescharacteristic
332C22×D3—22no—
333C22×D3—41no—
334C22×D3—41no—
335C22×D3—41no—
336C22×D3—41no—
337C22×D3—41no—
338C22×D3—41no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—128no—
342C3×D4—121no—
343C3×D4—121no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—41no—
358C2×C3×C4—41no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—62no—
372C2×C3×C4—121no—
373C2×C3×C4—121no—
374C2×C3×C4—121no—
375C2×C3×C4—121no—
376C2×C3×C4—121no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4#23511yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4D3×D411yescharacteristic
383C2×C3×C4#23711yescharacteristic
384C2×C3×C4#23711yescharacteristic
385C2×C3×C4C2×#6711yescharacteristic
386C2×C3×C4C2×C3×D411yescharacteristic
387C2×C3×C4C2×C3×D411yescharacteristic
388C2×C3×C4C2×C3×D411yescharacteristic
389C2×C3×C4C3×#4111yescharacteristic
390C2×C3×C4C3×#4111yescharacteristic
391C2×C3×C4C3×#4111yescharacteristic
392#67—48no—
393C2×Dic3—22no—
394C2×Dic3—41no—
395C2×Dic3—41no—
396C2×Dic3—41no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399C2×Dic3—41no—
400C2×Dic3—41no—
401C2×Dic3—41no—
402D12—22no—
403D12—22no—
404D12—41no—
405D12—41no—
406C3×C8—22no—
407C3×C8—22no—
408C3×C8—42no—
409C3×C8—42no—
410C3×C8—41no—
411C3×C8—41no—
412C2×C32—42no—
413C2×C32#39411yescharacteristic
414C2×C32#44711yescharacteristic
415C2×C32#45211yescharacteristic
416C2×C32#46611yescharacteristic
417C2×C32#46811yescharacteristic
418C2×C32#48011yescharacteristic
419C2×C32#48211yescharacteristic
420C3×D3—82no—
421C24—61no—
422C24C3×D1211yescharacteristic
423C2×D4—32no—
424C2×D4—64no—
425C2×D4—61no—
426C2×D4—61no—
427C2×D4—61no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—122no—
431C2×D4—122no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—61no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4C3×D1211yescharacteristic
442C22×C4C22×C3×D311yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8C3×#6712yescomplemented
449C4⋊C4—32no—
450C4⋊C4—61no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C22⋊C4—64no—
456C22⋊C4—122no—
457C22×C3—24no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—42no—
472C22×C3—42no—
473C22×C3—42no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—241no—
489C22×C3—241no—
490C22×C3—241no—
491C22×C3—241no—
492C22×C3#88211yescharacteristic
493C22×C3#88611yescharacteristic
494C22×C3C2×D2411yescharacteristic
495C22×C3#90411yescharacteristic
496C22×C3#90811yescharacteristic
497C22×C3#90911yescharacteristic
498C22×C3#93011yescharacteristic
499C22×C3C3×#12011yescharacteristic
500C22×C3C3×#12111yescharacteristic
501C22×C3C3×#12311yescharacteristic
502C22×C3C2×C3×D811yescharacteristic
503C22×C3C3×#13511yescharacteristic
504C22×C3C3×AGL(1,ℤ/8)11yescharacteristic
505C22×C3C3×#13711yescharacteristic
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—81no—
510C2×D3—81no—
511C2×D3—81no—
512C2×D3—81no—
513C3×C4—21no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—21no—
517C3×C4—42no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—122no—
521C3×C4—241no—
522C3×C4—241no—
523C3×C4#88311yescharacteristic
524C3×C4#88511yescharacteristic
525C3×C4#93811yescharacteristic
526C3×C4#93911yescharacteristic
527C3×C4C3×#12111yescharacteristic
528C3×C4C3×#12111yescharacteristic
529C3×C4C3×#12311yescharacteristic
530C3×C4C3×#12411yescharacteristic
531Dic3—42no—
532Dic3—81no—
533Dic3—81no—
534C32#203311yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—62no—
542C23—121no—
543C23—121no—
544C23—121no—
545C23—121no—
546C23—121no—
547C23—121no—
548C23C3×D2412yes—
549C23C2×C3×D1211yescharacteristic
550D4—62no—
551D4—62no—
552D4—128no—
553D4—121no—
554D4—121no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—62no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—121no—
567C2×C4—121no—
568C2×C4—121no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4C3×#23511yescharacteristic
572C2×C4C3×D3×D411yescharacteristic
573C2×C4C3×D3×D411yescharacteristic
574C2×C4C3×#23711yescharacteristic
575C2×C4C3×#23711yescharacteristic
576C2×C4C2×C3×#6711yescharacteristic
577C8—22no—
578C8—41no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—44no—
587C2×C3—42no—
588C2×C3—42no—
589C2×C3—242no—
590C2×C3#473211yescharacteristic
591C2×C3#473311yescharacteristic
592C2×C3#473611yescharacteristic
593C2×C3#473711yescharacteristic
594C2×C3#496111yescharacteristic
595C2×C3#511511yescharacteristic
596C2×C3#513411yescharacteristic
597C2×C3C3×#39411yescharacteristic
598C2×C3C3×#44711yescharacteristic
599C2×C3C3×#45211yescharacteristic
600C2×C3C3×#46611yescharacteristic
601C2×C3C3×#46811yescharacteristic
602C2×C3C3×#48011yescharacteristic
603C2×C3C3×#48211yescharacteristic
604D3—82no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—122no—
613C22—122no—
614C22—122no—
615C22—241no—
616C22—241no—
617C22—241no—
618C22—241no—
619C22C3×#88211yescharacteristic
620C22C3×#88611yescharacteristic
621C22C2×C3×D2411yescharacteristic
622C22C3×#90411yescharacteristic
623C22C3×#90811yescharacteristic
624C22C3×#90911yescharacteristic
625C22C3×#93011yescharacteristic
626C4—41no—
627C4—122no—
628C4—241no—
629C4—241no—
630C4C3×#88311yescharacteristic
631C4C3×#88511yescharacteristic
632C4C3×#93811yescharacteristic
633C4C3×#93911yescharacteristic
634C3—21no—
635C3#6993411yescharacteristic, direct product factor
636C3C3×#203311yescharacteristic, complemented
637C2—42no—
638C2—242no—
639C2C3×#473211yescharacteristic
640C2C3×#473311yescharacteristic
641C2C3×#473611yescharacteristic
642C2C3×#473711yescharacteristic
643C2C3×#496111yescharacteristic
644C2C3×#511511yescharacteristic
645C2C3×#513411yescharacteristic
subgroupG/H
centerC23×C3C2×D12
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×C22⋊C8C2
socleC23×C32C2×D4
prime radicalC2×C3×#930C2
hypercenterC2×C3×C22⋊C8D3
hypocenterC3C3×#2033
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ C2×C3×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C22⋊C8C2semidirect
3. C3×#5212C2semidirect
4. C2×C3×#821C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×#818C2semidirect
7. C3×#4551C2semidirect
9. #69934C3direct (N × H)
33. C2×C3×C22⋊C8D3semidirect
34. C2×C3×C22⋊C8C2×C3semidirect
36. #5212C2×C3semidirect
37. C2×#821C2×C3semidirect
38. C2×#821C2×C3semidirect
39. C2×#818C2×C3semidirect
41. #4551C2×C3semidirect
69. C2×C32×C8D4semidirect
165. C2×C22⋊C8C3×D3semidirect
237. C2×C3×C8#67semidirect
238. C2×C3×C8C3×D4semidirect
448. C2×C8C3×#67semidirect
534. C32#2033semidirect
635. C3#69934direct (N × H)
636. C3C3×#2033semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C2×C32×C22⋊C82
C3×#52122
C2×C3×#8212
C2×C3×#8182
C3×#45512
C3×#20333
#699343