Finite Group Databasebeta

← C3×#30381 #10648988

Subgroups — C3×#30381 #10648988

Order 768.

642 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2864C211yesmaximal, characteristic, complemented
2C3×#2860C211yesmaximal, characteristic
3C3×#2101C211yesmaximal, characteristic, complemented
4C3×#2092C211yesmaximal, characteristic
5C3×#2088C211yesmaximal, characteristic, complemented
6C3×#2087C211yesmaximal, characteristic, complemented
7C3×#2085C211yesmaximal, characteristic, complemented
8C3×#2073C211yesmaximal, characteristic
9C3×#2067C211yesmaximal, characteristic
10C3×#2065C211yesmaximal, characteristic
11C3×#1942C211yesmaximal, characteristic, complemented
12C3×#1941C211yesmaximal, characteristic, complemented
13C3×#1934C211yesmaximal, characteristic
14C3×#1934C211yesmaximal, characteristic
15C3×C4×C4⋊C8C211yesmaximal, characteristic, complemented
16#30381C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#126—21no—
18C2×C3×#107C2211yescharacteristic
19C2×C3×#107C2211yescharacteristic
20C2×C3×#106C2211yescharacteristic
21C2×C3×#106C2211yescharacteristic
22C2×C3×C4⋊C8C2211yescharacteristic
23C2×C3×C4⋊C8C2211yescharacteristic
24C2×C3×#102C2211yescharacteristic
25C2×C3×#102C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×C4×C8C2211yescharacteristic
29C2×C3×C4×C8C2211yescharacteristic
30C3×#390C2211yescharacteristic
31C3×#390C2211yescharacteristic
32C3×#390C2211yescharacteristic
33C3×#389C2211yescharacteristic
34C3×#389C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C3×#389C2211yescharacteristic
40C3×#388—21no—
41C3×#388—21no—
42C3×#388—21no—
43C3×#387—21no—
44C3×#387—21no—
45C3×#387—21no—
46C3×#387—21no—
47C3×#382C2211yescharacteristic
48C3×#382C2211yescharacteristic
49C3×C43C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2864C2×C311yescharacteristic, complemented
61#2860C2×C311yescharacteristic
62#2101C2×C311yescharacteristic, complemented
63#2092C2×C311yescharacteristic
64#2088C2×C311yescharacteristic, complemented
65#2087C2×C311yescharacteristic, complemented
66#2085C2×C311yescharacteristic, complemented
67#2073C2×C311yescharacteristic
68#2067C2×C311yescharacteristic
69#2065C2×C311yescharacteristic
70#1942C2×C311yescharacteristic, complemented
71#1941C2×C311yescharacteristic, complemented
72#1934C2×C311yescharacteristic
73#1934C2×C311yescharacteristic
74C4×C4⋊C8C2×C311yescharacteristic, complemented
75C22×C3×D4C2311yescharacteristic
76C22×C3×C8C2311yescharacteristic
77C22×C3×C8C2311yescharacteristic
78C22×C3×C8C2311yescharacteristic
79C22×C3×C8C2311yescharacteristic
80C3×#126—44no—
81C2×C3×C4⋊C4—21no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4C2311yescharacteristic
89C2×C3×C4⋊C4C2311yescharacteristic
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—21no—
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C42D411yescharacteristic
102C2×C3×C42D411yescharacteristic
103C2×C3×C42D411yescharacteristic
104C2×C3×C42D411yescharacteristic
105C2×C3×C42C2311yescharacteristic
106C2×C3×C42C2311yescharacteristic
107C2×C3×C42C2311yescharacteristic
108C3×#107—22no—
109C3×#107—41no—
110C3×#106—22no—
111C3×#106—41no—
112C3×C4⋊C8—22no—
113C3×C4⋊C8—22no—
114C3×#102—22no—
115C3×#102—22no—
116C3×#102—41no—
117C3×#102—41no—
118C3×C4×C8—41no—
119C3×C4×C8—41no—
120C3×#95—21no—
121C3×#95—21no—
122C3×#95—21no—
123C3×#95—21no—
124C3×#95—21no—
125C3×#95—21no—
126C3×#95—21no—
127C3×#95—21no—
128C3×#95—21no—
129C3×#95—21no—
130C3×#95—21no—
131C2×#126—21no—
132C2×#107C22×C311yescharacteristic
133C2×#107C22×C311yescharacteristic
134C2×#106C22×C311yescharacteristic
135C2×#106C22×C311yescharacteristic
136C2×C4⋊C8C22×C311yescharacteristic
137C2×C4⋊C8C22×C311yescharacteristic
138C2×#102C22×C311yescharacteristic
139C2×#102C22×C311yescharacteristic
140C2×#102C22×C311yescharacteristic
141C2×#102C22×C311yescharacteristic
142C2×C4×C8C22×C311yescharacteristic
143C2×C4×C8C22×C311yescharacteristic
144#390C22×C311yescharacteristic
145#390C22×C311yescharacteristic
146#390C22×C311yescharacteristic
147#389C22×C311yescharacteristic
148#389C22×C311yescharacteristic
149#389C22×C311yescharacteristic
150#389C22×C311yescharacteristic
151#389C22×C311yescharacteristic
152#389C22×C311yescharacteristic
153#389C22×C311yescharacteristic
154#388—21no—
155#388—21no—
156#388—21no—
157#387—21no—
158#387—21no—
159#387—21no—
160#387—21no—
161#382C22×C311yescharacteristic
162#382C22×C311yescharacteristic
163C43C22×C311yescharacteristic
164#340C22×C311yescharacteristic
165#340C22×C311yescharacteristic
166#340C22×C311yescharacteristic
167#340C22×C311yescharacteristic
168#340C22×C311yescharacteristic
169#340C22×C311yescharacteristic
170#340C22×C311yescharacteristic
171#340C22×C311yescharacteristic
172#336C22×C311yescharacteristic
173#336C22×C311yescharacteristic
174C24×C3—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—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4C2×D411yescharacteristic
189C22×C3×C4C2×D411yescharacteristic
190C22×C3×C4C2×D411yescharacteristic
191C22×C3×C4C2×D411yescharacteristic
192C22×C3×C4C2×D411yescharacteristic
193C22×C3×C4C2×D411yescharacteristic
194C22×C3×C4C2411yescharacteristic
195C2×C3×C8—21no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—21no—
201C2×C3×C8—21no—
202C2×C3×C8—21no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8#4112yes—
206C2×C3×C8#4112yes—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—21no—
221C3×C4⋊C4—42no—
222C3×C4⋊C4—42no—
223C3×C4⋊C4—42no—
224C3×C4⋊C4—42no—
225C3×C4⋊C4—42no—
226C3×C4⋊C4—42no—
227C3×C4⋊C4—42no—
228C3×C22⋊C4—42no—
229C3×C22⋊C4—42no—
230C3×C22⋊C4—42no—
231C3×C22⋊C4—42no—
232C3×C22⋊C4—42no—
233C3×C22⋊C4—42no—
234C3×C42—22no—
235C3×C42—22no—
236C3×C42—22no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42—21no—
242C3×C42—21no—
243C3×C42—41no—
244C22×D4C23×C311yescharacteristic
245C22×C8C23×C311yescharacteristic
246C22×C8C23×C311yescharacteristic
247C22×C8C23×C311yescharacteristic
248C22×C8C23×C311yescharacteristic
249#126—44no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4C23×C311yescharacteristic
258C2×C4⋊C4C23×C311yescharacteristic
259C2×C4⋊C4C23×C311yescharacteristic
260C2×C4⋊C4C23×C311yescharacteristic
261C2×C4⋊C4C23×C311yescharacteristic
262C2×C4⋊C4C23×C311yescharacteristic
263C2×C4⋊C4C23×C311yescharacteristic
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42C3×D411yescharacteristic
271C2×C42C3×D411yescharacteristic
272C2×C42C3×D411yescharacteristic
273C2×C42C3×D411yescharacteristic
274C2×C42C23×C311yescharacteristic
275C2×C42C23×C311yescharacteristic
276C2×C42C23×C311yescharacteristic
277#107—22no—
278#107—41no—
279#106—22no—
280#106—41no—
281C4⋊C8—22no—
282C4⋊C8—22no—
283#102—22no—
284#102—22no—
285#102—41no—
286#102—41no—
287C4×C8—41no—
288C4×C8—41no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95—21no—
299#95—21no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3—41no—
304C23×C3—41no—
305C23×C3—41no—
306C23×C3—41no—
307C23×C3C22×D411yescharacteristic
308C3×D4—41no—
309C3×D4—41no—
310C3×D4—41no—
311C3×D4—41no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—41no—
328C2×C3×C4—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
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—41no—
338C2×C3×C4—41no—
339C2×C3×C4—41no—
340C2×C3×C4—41no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4#13512yes—
349C2×C3×C4#13512yes—
350C2×C3×C4AGL(1,ℤ/8)12yes—
351C2×C3×C4C2×#4111yescharacteristic
352C2×C3×C4C2×#4111yescharacteristic
353C2×C3×C4H(5,𝔽2)11yescharacteristic
354C2×C3×C42−1+411yescharacteristic
355C2×C3×C42−1+411yescharacteristic
356C2×C3×C42−1+411yescharacteristic
357C3×C8—22no—
358C3×C8—22no—
359C3×C8—41no—
360C3×C8—41no—
361C24—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4C2×C3×D411yescharacteristic
376C22×C4C2×C3×D411yescharacteristic
377C22×C4C2×C3×D411yescharacteristic
378C22×C4C2×C3×D411yescharacteristic
379C22×C4C2×C3×D411yescharacteristic
380C22×C4C2×C3×D411yescharacteristic
381C22×C4C24×C311yescharacteristic
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8C3×#4112yes—
393C2×C8C3×#4112yes—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—42no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—42no—
418C22⋊C4—42no—
419C22⋊C4—42no—
420C22⋊C4—42no—
421C42—22no—
422C42—22no—
423C42—22no—
424C42—21no—
425C42—21no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—21no—
430C42—41no—
431C22×C3—81no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—81no—
436C22×C3—81no—
437C22×C3—81no—
438C22×C3#53211yescharacteristic
439C22×C3#53611yescharacteristic
440C22×C3#53711yescharacteristic
441C22×C3C2×#13511yescharacteristic
442C22×C3C2×#13511yescharacteristic
443C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C3#57511yescharacteristic
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—41no—
451C3×C4—81no—
452C3×C4—81no—
453C3×C4—81no—
454C3×C4—81no—
455C3×C4—81no—
456C3×C4—81no—
457C3×C4—81no—
458C3×C4#53911yescharacteristic
459C3×C4#53911yescharacteristic
460C3×C4#54111yescharacteristic
461C3×C4#54111yescharacteristic
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23C22×C3×D411yescharacteristic
470D4—41no—
471D4—41no—
472D4—41no—
473D4—41no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4C3×#13512yes—
511C2×C4C3×#13512yes—
512C2×C4C3×AGL(1,ℤ/8)12yes—
513C2×C4C2×C3×#4111yescharacteristic
514C2×C4C2×C3×#4111yescharacteristic
515C2×C4C3×H(5,𝔽2)11yescharacteristic
516C2×C4C3×2−1+411yescharacteristic
517C2×C4C3×2−1+411yescharacteristic
518C2×C4C3×2−1+411yescharacteristic
519C8—22no—
520C8—22no—
521C8—41no—
522C8—41no—
523C2×C3—161no—
524C2×C3#266411yescharacteristic
525C2×C3#316811yescharacteristic
526C2×C3#317111yescharacteristic
527C2×C3#322811yescharacteristic
528C2×C3#323311yescharacteristic
529C2×C3#324711yescharacteristic
530C2×C3#325011yescharacteristic
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22C3×#53211yescharacteristic
539C22C3×#53611yescharacteristic
540C22C3×#53711yescharacteristic
541C22C2×C3×#13511yescharacteristic
542C22C2×C3×#13511yescharacteristic
543C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
544C22C3×#57511yescharacteristic
545C4—22no—
546C4—22no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C3×#53911yescharacteristic
559C4C3×#53911yescharacteristic
560C4C3×#54111yescharacteristic
561C4C3×#54111yescharacteristic
562C3#3038111yescharacteristic, direct product factor, Sylow
563C2—161no—
564C2C3×#266411yescharacteristic
565C2C3×#316811yescharacteristic
566C2C3×#317111yescharacteristic
567C2C3×#322811yescharacteristic
568C2C3×#323311yescharacteristic
569C2C3×#324711yescharacteristic
570C2C3×#325011yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2864C2semidirect
3. C3×#2101C2semidirect
5. C3×#2088C2semidirect
6. C3×#2087C2semidirect
7. C3×#2085C2semidirect
11. C3×#1942C2semidirect
12. C3×#1941C2semidirect
15. C3×C4×C4⋊C8C2semidirect
16. #30381C3direct (N × H)
60. #2864C2×C3semidirect
62. #2101C2×C3semidirect
64. #2088C2×C3semidirect
65. #2087C2×C3semidirect
66. #2085C2×C3semidirect
70. #1942C2×C3semidirect
71. #1941C2×C3semidirect
74. C4×C4⋊C8C2×C3semidirect
562. C3#30381direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#28642
C3×#28602
C3×#21012
C3×#20922
C3×#20882
C3×#20872
C3×#20852
C3×#20732
C3×#20672
C3×#20652
C3×#19422
C3×#19412
C3×#19342
C3×C4×C4⋊C82
#303813