Finite Group Databasebeta

← C3×#10953 #10629560

Subgroups — C3×#10953 #10629560

Order 768.

1018 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#418C211yesmaximal, characteristic
2C2×C3×#418C211yesmaximal, characteristic
3C22×C3×#100C211yesmaximal, characteristic
4C3×#2873C211yesmaximal, characteristic, complemented
5C2×C3×#344C211yesmaximal, characteristic, complemented
6C3×#1733C211yesmaximal, characteristic, complemented
7C2×C3×#338C211yesmaximal, characteristic, complemented
8#10953C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×D4C2211yescharacteristic
10C22×C3×M16C2211yescharacteristic
11C22×C3×M16C2211yescharacteristic
12C22×C3×M16C2211yescharacteristic
13C22×C3×M16C2211yescharacteristic
14C2×C3×#117C2211yescharacteristic
15C2×C3×#117C2211yescharacteristic
16C3×#418—22no—
17C3×#418—22no—
18C3×#418—22no—
19C3×#418C414yescomplemented
20C2×C3×#102—22no—
21C2×C3×#102C414yescomplemented
22C2×C3×#100—22no—
23C2×C3×#100—22no—
24C2×C3×#100C414yescomplemented
25C3×#405—22no—
26C3×#405—22no—
27C3×C4×M16—22no—
28C3×#344—22no—
29C3×#339—22no—
30C3×#338—22no—
31C2×#418C2×C311yescharacteristic
32C2×#418C2×C311yescharacteristic
33C22×#100C2×C311yescharacteristic
34#2873C2×C311yescharacteristic, complemented
35C2×#344C2×C311yescharacteristic, complemented
36#1733C2×C311yescharacteristic, complemented
37C2×#338C2×C311yescharacteristic, complemented
38C25×C3—21no—
39C22×C3×D4—21no—
40C22×C3×D4—21no—
41C22×C3×D4—21no—
42C22×C3×D4—21no—
43C22×C3×D4—21no—
44C22×C3×D4—21no—
45C22×C3×D4—21no—
46C22×C3×D4—21no—
47C22×C3×D4—21no—
48C22×C3×D4—21no—
49C22×C3×D4—21no—
50C22×C3×D4C2×C412yes—
51C22×C3×D4C2×C412yes—
52C22×C3×D4C2×C412yes—
53C23×C3×C4C2311yescharacteristic
54C2×C3×M16—21no—
55C2×C3×M16—21no—
56C2×C3×M16—21no—
57C2×C3×M16—21no—
58C2×C3×M16—21no—
59C2×C3×M16—21no—
60C2×C3×M16—21no—
61C2×C3×M16—21no—
62C2×C3×M16—21no—
63C2×C3×M16—21no—
64C2×C3×M16—21no—
65C2×C3×M16—21no—
66C2×C3×M16—21no—
67C2×C3×M16—21no—
68C2×C3×M16—21no—
69C2×C3×M16—21no—
70C2×C3×M16—21no—
71C2×C3×M16—21no—
72C2×C3×M16C2×C412yes—
73C2×C3×M16C2×C412yes—
74C2×C3×M16C2×C412yes—
75C2×C3×M16D412yes—
76C2×C3×M16D412yes—
77C2×C3×M16D412yes—
78C22×C3×C8—21no—
79C22×C3×C8—21no—
80C22×C3×C8C2×C412yes—
81C22×C3×C8D412yes—
82C3×#117—21no—
83C3×#117—21no—
84C3×#117—21no—
85C3×#117—21no—
86C3×#117—21no—
87C3×#117C2×C412yes—
88C3×#117D412yes—
89C3×#117D412yes—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4C2×C412yes—
92C2×C3×C22⋊C4—21no—
93C2×C3×C22⋊C4—21no—
94C2×C3×C42—21no—
95C2×C3×C42—21no—
96C3×#102—28no—
97C3×#102—28no—
98C3×#100—28no—
99C3×#97—24no—
100C3×C4×C8—24no—
101C23×D4C22×C311yescharacteristic
102C22×M16C22×C311yescharacteristic
103C22×M16C22×C311yescharacteristic
104C22×M16C22×C311yescharacteristic
105C22×M16C22×C311yescharacteristic
106C2×#117C22×C311yescharacteristic
107C2×#117C22×C311yescharacteristic
108#418—22no—
109#418—22no—
110#418—22no—
111#418C3×C414yescomplemented
112C2×#102—22no—
113C2×#102C3×C414yescomplemented
114C2×#100—22no—
115C2×#100—22no—
116C2×#100C3×C414yescomplemented
117#405—22no—
118#405—22no—
119C4×M16—22no—
120#344—22no—
121#339—22no—
122#338—22no—
123C24×C3—22no—
124C24×C3—22no—
125C24×C3—22no—
126C24×C3—41no—
127C24×C3—41no—
128C24×C3—41no—
129C24×C3—41no—
130C24×C3—84no—
131C24×C3#4111yescharacteristic
132C2×C3×D4—22no—
133C2×C3×D4—22no—
134C2×C3×D4—22no—
135C2×C3×D4—22no—
136C2×C3×D4—22no—
137C2×C3×D4—22no—
138C2×C3×D4—22no—
139C2×C3×D4—22no—
140C2×C3×D4—22no—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4—22no—
144C2×C3×D4—22no—
145C2×C3×D4—22no—
146C2×C3×D4—22no—
147C2×C3×D4—41no—
148C2×C3×D4—41no—
149C2×C3×D4—41no—
150C2×C3×D4—41no—
151C2×C3×D4—41no—
152C2×C3×D4—41no—
153C2×C3×D4—41no—
154C2×C3×D4—41no—
155C2×C3×D4—41no—
156C2×C3×D4—41no—
157C2×C3×D4—41no—
158C2×C3×D4—41no—
159C2×C3×D4C4214yes—
160C22×C3×C4—22no—
161C22×C3×C4—41no—
162C22×C3×C4C22×C411yescharacteristic
163C22×C3×C4C22×C411yescharacteristic
164C22×C3×C4C22×C411yescharacteristic
165C22×C3×C4C2×D411yescharacteristic
166C22×C3×C4C2×D411yescharacteristic
167C22×C3×C4C2×D411yescharacteristic
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2×D411yescharacteristic
170C22×C3×C4C2×D411yescharacteristic
171C22×C3×C4#4111yescharacteristic
172C22×C3×C4#4111yescharacteristic
173C22×C3×C4#4111yescharacteristic
174C22×C3×C4#4111yescharacteristic
175C22×C3×C4#4111yescharacteristic
176C3×M16—22no—
177C3×M16—22no—
178C3×M16—22no—
179C3×M16—22no—
180C3×M16—22no—
181C3×M16—22no—
182C3×M16—22no—
183C3×M16—22no—
184C3×M16—22no—
185C3×M16—41no—
186C3×M16—41no—
187C3×M16—41no—
188C3×M16—41no—
189C3×M16—41no—
190C3×M16—41no—
191C3×M16C22⋊C414yes—
192C2×C3×C8—22no—
193C2×C3×C8—22no—
194C2×C3×C8—22no—
195C2×C3×C8—22no—
196C2×C3×C8—22no—
197C2×C3×C8—22no—
198C2×C3×C8—22no—
199C2×C3×C8—22no—
200C2×C3×C8—22no—
201C2×C3×C8—41no—
202C2×C3×C8—41no—
203C2×C3×C8C22⋊C414yes—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—22no—
206C3×C4⋊C4—41no—
207C3×C4⋊C4C22⋊C414yes—
208C3×C22⋊C4—22no—
209C3×C22⋊C4—22no—
210C3×C22⋊C4—22no—
211C3×C22⋊C4—41no—
212C3×C42—22no—
213C3×C42—22no—
214C3×C42—22no—
215C3×C42—41no—
216C25—21no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4—21no—
227C22×D4—21no—
228C22×D4C2×C3×C412yes—
229C22×D4C2×C3×C412yes—
230C22×D4C2×C3×C412yes—
231C23×C4C23×C311yescharacteristic
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16C2×C3×C412yes—
251C2×M16C2×C3×C412yes—
252C2×M16C2×C3×C412yes—
253C2×M16C3×D412yes—
254C2×M16C3×D412yes—
255C2×M16C3×D412yes—
256C22×C8—21no—
257C22×C8—21no—
258C22×C8C2×C3×C412yes—
259C22×C8C3×D412yes—
260#117—21no—
261#117—21no—
262#117—21no—
263#117—21no—
264#117—21no—
265#117C2×C3×C412yes—
266#117C3×D412yes—
267#117C3×D412yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4C2×C3×C412yes—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C42—21no—
273C2×C42—21no—
274#102—28no—
275#102—28no—
276#100—28no—
277#97—24no—
278C4×C8—24no—
279C23×C3—24no—
280C23×C3—42no—
281C23×C3—42no—
282C23×C3—42no—
283C23×C3—42no—
284C23×C3—42no—
285C23×C3—42no—
286C23×C3—42no—
287C23×C3—84no—
288C23×C3—84no—
289C23×C3—84no—
290C23×C3—84no—
291C23×C3—84no—
292C23×C3—84no—
293C23×C3—84no—
294C23×C3#11711yescharacteristic
295C23×C3C4×D411yescharacteristic
296C23×C3C4×D411yescharacteristic
297C23×C3#12111yescharacteristic
298C23×C3#12311yescharacteristic
299C23×C3#12411yescharacteristic
300C23×C3#12611yescharacteristic
301C3×D4—24no—
302C3×D4—24no—
303C3×D4—42no—
304C3×D4—42no—
305C3×D4—42no—
306C3×D4—42no—
307C3×D4—42no—
308C3×D4—42no—
309C2×C3×C4—24no—
310C2×C3×C4—42no—
311C2×C3×C4—82no—
312C2×C3×C4—82no—
313C2×C3×C4C2×C4211yescharacteristic
314C2×C3×C4C2×C22⋊C411yescharacteristic
315C2×C3×C4C2×C22⋊C411yescharacteristic
316C2×C3×C4C2×C22⋊C411yescharacteristic
317C2×C3×C4#11711yescharacteristic
318C2×C3×C4#11711yescharacteristic
319C2×C3×C4C4×D411yescharacteristic
320C2×C3×C4C4×D411yescharacteristic
321C2×C3×C4C4×D411yescharacteristic
322C2×C3×C4C4×D411yescharacteristic
323C2×C3×C4C4×D411yescharacteristic
324C2×C3×C4C4×D411yescharacteristic
325C2×C3×C4C4×D411yescharacteristic
326C2×C3×C4C4×D411yescharacteristic
327C2×C3×C4C4×D411yescharacteristic
328C2×C3×C4C4×D411yescharacteristic
329C2×C3×C4#12011yescharacteristic
330C2×C3×C4#12111yescharacteristic
331C2×C3×C4#12111yescharacteristic
332C2×C3×C4#12111yescharacteristic
333C2×C3×C4#12111yescharacteristic
334C2×C3×C4#12111yescharacteristic
335C2×C3×C4#12311yescharacteristic
336C2×C3×C4#12311yescharacteristic
337C2×C3×C4#12411yescharacteristic
338C2×C3×C4#12411yescharacteristic
339C2×C3×C4#12611yescharacteristic
340C2×C3×C4#12711yescharacteristic
341C3×C8—24no—
342C3×C8—24no—
343C3×C8—42no—
344C3×C8—42no—
345C24—22no—
346C24—22no—
347C24—22no—
348C24—41no—
349C24—41no—
350C24—41no—
351C24—41no—
352C24—84no—
353C24C3×#4111yescharacteristic
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4C3×C4214yes—
382C22×C4—22no—
383C22×C4—41no—
384C22×C4C22×C3×C411yescharacteristic
385C22×C4C22×C3×C411yescharacteristic
386C22×C4C22×C3×C411yescharacteristic
387C22×C4C2×C3×D411yescharacteristic
388C22×C4C2×C3×D411yescharacteristic
389C22×C4C2×C3×D411yescharacteristic
390C22×C4C2×C3×D411yescharacteristic
391C22×C4C2×C3×D411yescharacteristic
392C22×C4C2×C3×D411yescharacteristic
393C22×C4C3×#4111yescharacteristic
394C22×C4C3×#4111yescharacteristic
395C22×C4C3×#4111yescharacteristic
396C22×C4C3×#4111yescharacteristic
397C22×C4C3×#4111yescharacteristic
398M16—22no—
399M16—22no—
400M16—22no—
401M16—22no—
402M16—22no—
403M16—22no—
404M16—22no—
405M16—22no—
406M16—22no—
407M16—41no—
408M16—41no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16C3×C22⋊C414yes—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—41no—
424C2×C8—41no—
425C2×C8C3×C22⋊C414yes—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—41no—
429C4⋊C4C3×C22⋊C414yes—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—22no—
433C22⋊C4—41no—
434C42—22no—
435C42—22no—
436C42—22no—
437C42—41no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—41no—
442C22×C3—41no—
443C22×C3—41no—
444C22×C3—41no—
445C22×C3—44no—
446C22×C3—84no—
447C22×C3—84no—
448C22×C3—84no—
449C22×C3—84no—
450C22×C3—84no—
451C22×C3—84no—
452C22×C3—84no—
453C22×C3C4×C22⋊C411yescharacteristic
454C22×C3#38611yescharacteristic
455C22×C3#38811yescharacteristic
456C22×C3#38811yescharacteristic
457C22×C3#38811yescharacteristic
458C22×C3#38811yescharacteristic
459C22×C3#39011yescharacteristic
460C3×C4—44no—
461C3×C4—82no—
462C3×C4C4×C22⋊C411yescharacteristic
463C3×C4C4×C22⋊C411yescharacteristic
464C3×C4#38611yescharacteristic
465C3×C4#38611yescharacteristic
466C3×C4#38811yescharacteristic
467C3×C4#38811yescharacteristic
468C3×C4#39011yescharacteristic
469C3×C4#39011yescharacteristic
470C23—24no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—84no—
479C23—84no—
480C23—84no—
481C23—84no—
482C23—84no—
483C23—84no—
484C23—84no—
485C23C3×#11711yescharacteristic
486C23C3×C4×D411yescharacteristic
487C23C3×C4×D411yescharacteristic
488C23C3×#12111yescharacteristic
489C23C3×#12311yescharacteristic
490C23C3×#12411yescharacteristic
491C23C3×#12611yescharacteristic
492D4—24no—
493D4—24no—
494D4—42no—
495D4—42no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—42no—
500C2×C4—24no—
501C2×C4—42no—
502C2×C4—82no—
503C2×C4—82no—
504C2×C4C2×C3×C4211yescharacteristic
505C2×C4C2×C3×C22⋊C411yescharacteristic
506C2×C4C2×C3×C22⋊C411yescharacteristic
507C2×C4C2×C3×C22⋊C411yescharacteristic
508C2×C4C3×#11711yescharacteristic
509C2×C4C3×#11711yescharacteristic
510C2×C4C3×C4×D411yescharacteristic
511C2×C4C3×C4×D411yescharacteristic
512C2×C4C3×C4×D411yescharacteristic
513C2×C4C3×C4×D411yescharacteristic
514C2×C4C3×C4×D411yescharacteristic
515C2×C4C3×C4×D411yescharacteristic
516C2×C4C3×C4×D411yescharacteristic
517C2×C4C3×C4×D411yescharacteristic
518C2×C4C3×C4×D411yescharacteristic
519C2×C4C3×C4×D411yescharacteristic
520C2×C4C3×#12011yescharacteristic
521C2×C4C3×#12111yescharacteristic
522C2×C4C3×#12111yescharacteristic
523C2×C4C3×#12111yescharacteristic
524C2×C4C3×#12111yescharacteristic
525C2×C4C3×#12111yescharacteristic
526C2×C4C3×#12311yescharacteristic
527C2×C4C3×#12311yescharacteristic
528C2×C4C3×#12411yescharacteristic
529C2×C4C3×#12411yescharacteristic
530C2×C4C3×#12611yescharacteristic
531C2×C4C3×#12711yescharacteristic
532C8—24no—
533C8—24no—
534C8—42no—
535C8—42no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—84no—
543C2×C3#143711yescharacteristic
544C2×C3#190312yes—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—44no—
553C22—84no—
554C22—84no—
555C22—84no—
556C22—84no—
557C22—84no—
558C22—84no—
559C22—84no—
560C22C3×C4×C22⋊C411yescharacteristic
561C22C3×#38611yescharacteristic
562C22C3×#38811yescharacteristic
563C22C3×#38811yescharacteristic
564C22C3×#38811yescharacteristic
565C22C3×#38811yescharacteristic
566C22C3×#39011yescharacteristic
567C4—44no—
568C4—82no—
569C4C3×C4×C22⋊C411yescharacteristic
570C4C3×C4×C22⋊C411yescharacteristic
571C4C3×#38611yescharacteristic
572C4C3×#38611yescharacteristic
573C4C3×#38811yescharacteristic
574C4C3×#38811yescharacteristic
575C4C3×#39011yescharacteristic
576C4C3×#39011yescharacteristic
577C3#1095311yescharacteristic, direct product factor, Sylow
578C2—21no—
579C2—21no—
580C2—21no—
581C2—21no—
582C2—21no—
583C2—21no—
584C2—84no—
585C2C3×#143711yescharacteristic
586C2C3×#190312yes—
subgroupG/H
center, socleC22×C3#386
commutatorC2×C4C2×C3×C42
Frattini, cosocleC23×C4C23×C3
prime radicalC23×C3×D4C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C3×#2873C2semidirect
5. C2×C3×#344C2semidirect
6. C3×#1733C2semidirect
7. C2×C3×#338C2semidirect
8. #10953C3direct (N × H)
19. C3×#418C4semidirect
21. C2×C3×#102C4semidirect
24. C2×C3×#100C4semidirect
34. #2873C2×C3semidirect
35. C2×#344C2×C3semidirect
36. #1733C2×C3semidirect
37. C2×#338C2×C3semidirect
111. #418C3×C4semidirect
113. C2×#102C3×C4semidirect
116. C2×#100C3×C4semidirect
577. C3#10953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4182
C22×C3×#1002
C3×#28732
C2×C3×#3442
C3×#17332
C2×C3×#3382
#109533