Finite Group Databasebeta

← C3×#30395 #10649002

Subgroups — C3×#30395 #10649002

Order 768.

586 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2647C211yesmaximal, characteristic, complemented
2C3×#2644C211yesmaximal, characteristic
3C3×#2099C211yesmaximal, characteristic, complemented
4C3×#2094C211yesmaximal, characteristic
5C3×#2088C211yesmaximal, characteristic, complemented
6C3×#2088C211yesmaximal, characteristic, complemented
7C3×#2085C211yesmaximal, characteristic, complemented
8C3×#2073C211yesmaximal, characteristic
9C3×#2067C211yesmaximal, characteristic
10C3×#2065C211yesmaximal, characteristic
11C3×#1944C211yesmaximal, characteristic, complemented
12C3×#1941C211yesmaximal, characteristic, complemented
13C3×#1936C211yesmaximal, characteristic
14C3×#1934C211yesmaximal, characteristic
15C3×#1768C211yesmaximal, characteristic, complemented
16#30395C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#107C2211yescharacteristic
18C2×C3×#106C2211yescharacteristic
19C2×C3×#106C2211yescharacteristic
20C2×C3×#106C2211yescharacteristic
21C2×C3×C4⋊C8C2211yescharacteristic
22C2×C3×C4⋊C8C2211yescharacteristic
23C2×C3×#102C2211yescharacteristic
24C2×C3×#102C2211yescharacteristic
25C2×C3×#102C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×#97C2211yescharacteristic
28C2×C3×C4×C8C2211yescharacteristic
29C3×#400—21no—
30C3×#400—21no—
31C3×#398—21no—
32C3×#398—21no—
33C3×#397—21no—
34C3×#397—21no—
35C3×#397—21no—
36C3×#396—21no—
37C3×#390C2211yescharacteristic
38C3×#390C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C3×#389C2211yescharacteristic
41C3×#389C2211yescharacteristic
42C3×#389C2211yescharacteristic
43C3×#389C2211yescharacteristic
44C3×#389C2211yescharacteristic
45C3×#389C2211yescharacteristic
46C3×#389C2211yescharacteristic
47C3×#384C2211yescharacteristic
48C3×#382C2211yescharacteristic
49C3×#376C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2647C2×C311yescharacteristic, complemented
61#2644C2×C311yescharacteristic
62#2099C2×C311yescharacteristic, complemented
63#2094C2×C311yescharacteristic
64#2088C2×C311yescharacteristic, complemented
65#2088C2×C311yescharacteristic, complemented
66#2085C2×C311yescharacteristic, complemented
67#2073C2×C311yescharacteristic
68#2067C2×C311yescharacteristic
69#2065C2×C311yescharacteristic
70#1944C2×C311yescharacteristic, complemented
71#1941C2×C311yescharacteristic, complemented
72#1936C2×C311yescharacteristic
73#1934C2×C311yescharacteristic
74#1768C2×C311yescharacteristic, complemented
75C22×C3×D4C2311yescharacteristic
76C22×C3×C8C2311yescharacteristic
77C22×C3×C8C2311yescharacteristic
78C22×C3×C8C2311yescharacteristic
79C22×C3×C8C2311yescharacteristic
80C2×C3×C4⋊C4—21no—
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⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
102C2×C3×C42C2311yescharacteristic
103C2×C3×C42C2311yescharacteristic
104C2×C3×C42C2311yescharacteristic
105C3×#107—41no—
106C3×#106—22no—
107C3×#106—22no—
108C3×#106—41no—
109C3×C4⋊C8—22no—
110C3×C4⋊C8—22no—
111C3×#102—22no—
112C3×#102—22no—
113C3×#102—41no—
114C3×#102—41no—
115C3×#97—41no—
116C3×C4×C8—41no—
117C3×#95—21no—
118C3×#95—21no—
119C3×#95—21no—
120C3×#95—21no—
121C3×#95—21no—
122C3×#95—21no—
123C3×#95—21no—
124C3×#95—21no—
125C3×#95—21no—
126C3×#95D411yescharacteristic
127C3×#95D411yescharacteristic
128C3×#95D411yescharacteristic
129C3×#95D411yescharacteristic
130C2×#107C22×C311yescharacteristic
131C2×#106C22×C311yescharacteristic
132C2×#106C22×C311yescharacteristic
133C2×#106C22×C311yescharacteristic
134C2×C4⋊C8C22×C311yescharacteristic
135C2×C4⋊C8C22×C311yescharacteristic
136C2×#102C22×C311yescharacteristic
137C2×#102C22×C311yescharacteristic
138C2×#102C22×C311yescharacteristic
139C2×#102C22×C311yescharacteristic
140C2×#97C22×C311yescharacteristic
141C2×C4×C8C22×C311yescharacteristic
142#400—21no—
143#400—21no—
144#398—21no—
145#398—21no—
146#397—21no—
147#397—21no—
148#397—21no—
149#396—21no—
150#390C22×C311yescharacteristic
151#390C22×C311yescharacteristic
152#390C22×C311yescharacteristic
153#389C22×C311yescharacteristic
154#389C22×C311yescharacteristic
155#389C22×C311yescharacteristic
156#389C22×C311yescharacteristic
157#389C22×C311yescharacteristic
158#389C22×C311yescharacteristic
159#389C22×C311yescharacteristic
160#384C22×C311yescharacteristic
161#382C22×C311yescharacteristic
162#376C22×C311yescharacteristic
163#340C22×C311yescharacteristic
164#340C22×C311yescharacteristic
165#340C22×C311yescharacteristic
166#340C22×C311yescharacteristic
167#340C22×C311yescharacteristic
168#340C22×C311yescharacteristic
169#340C22×C311yescharacteristic
170#340C22×C311yescharacteristic
171#336C22×C311yescharacteristic
172#336C22×C311yescharacteristic
173C24×C3—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—
180C22×C3×C4—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×C4C2×D411yescharacteristic
188C22×C3×C4C2×D411yescharacteristic
189C22×C3×C4C2×D411yescharacteristic
190C22×C3×C4C2×D411yescharacteristic
191C22×C3×C4C2×D411yescharacteristic
192C22×C3×C4C2×D411yescharacteristic
193C22×C3×C4C2411yescharacteristic
194C2×C3×C8—21no—
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#4112yes—
205C2×C3×C8#4112yes—
206C3×C4⋊C4—21no—
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—81no—
221C3×C4⋊C4—81no—
222C3×C4⋊C4—81no—
223C3×C4⋊C4—81no—
224C3×C4⋊C4—81no—
225C3×C4⋊C4—81no—
226C3×C4⋊C4—81no—
227C3×C4⋊C4—81no—
228C3×C4⋊C4—81no—
229C3×C22⋊C4—81no—
230C3×C22⋊C4—81no—
231C3×C22⋊C4—81no—
232C3×C22⋊C4—81no—
233C3×C22⋊C4—81no—
234C3×C22⋊C4—81no—
235C3×C42—21no—
236C3×C42—21no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C22×D4C23×C311yescharacteristic
242C22×C8C23×C311yescharacteristic
243C22×C8C23×C311yescharacteristic
244C22×C8C23×C311yescharacteristic
245C22×C8C23×C311yescharacteristic
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C23×C311yescharacteristic
256C2×C4⋊C4C23×C311yescharacteristic
257C2×C4⋊C4C23×C311yescharacteristic
258C2×C4⋊C4C23×C311yescharacteristic
259C2×C4⋊C4C23×C311yescharacteristic
260C2×C4⋊C4C23×C311yescharacteristic
261C2×C4⋊C4C23×C311yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C42C23×C311yescharacteristic
269C2×C42C23×C311yescharacteristic
270C2×C42C23×C311yescharacteristic
271#107—41no—
272#106—22no—
273#106—22no—
274#106—41no—
275C4⋊C8—22no—
276C4⋊C8—22no—
277#102—22no—
278#102—22no—
279#102—41no—
280#102—41no—
281#97—41no—
282C4×C8—41no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—21no—
291#95—21no—
292#95C3×D411yescharacteristic
293#95C3×D411yescharacteristic
294#95C3×D411yescharacteristic
295#95C3×D411yescharacteristic
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—41no—
302C23×C3—41no—
303C23×C3C22×D411yescharacteristic
304C3×D4—41no—
305C3×D4—41no—
306C3×D4—41no—
307C3×D4—41no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
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—41no—
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×C4C2×#4111yescharacteristic
348C2×C3×C4C2×#4111yescharacteristic
349C2×C3×C4H(5,𝔽2)11yescharacteristic
350C2×C3×C42−1+411yescharacteristic
351C2×C3×C42−1+411yescharacteristic
352C2×C3×C42−1+411yescharacteristic
353C3×C8—22no—
354C3×C8—22no—
355C3×C8—41no—
356C3×C8—41no—
357C24—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4C2×C3×D411yescharacteristic
372C22×C4C2×C3×D411yescharacteristic
373C22×C4C2×C3×D411yescharacteristic
374C22×C4C2×C3×D411yescharacteristic
375C22×C4C2×C3×D411yescharacteristic
376C22×C4C2×C3×D411yescharacteristic
377C22×C4C24×C311yescharacteristic
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8C3×#4112yes—
389C2×C8C3×#4112yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
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—81no—
405C4⋊C4—81no—
406C4⋊C4—81no—
407C4⋊C4—81no—
408C4⋊C4—81no—
409C4⋊C4—81no—
410C4⋊C4—81no—
411C4⋊C4—81no—
412C4⋊C4—81no—
413C22⋊C4—81no—
414C22⋊C4—81no—
415C22⋊C4—81no—
416C22⋊C4—81no—
417C22⋊C4—81no—
418C22⋊C4—81no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—21no—
423C42—21no—
424C42—21no—
425C22×C3—81no—
426C22×C3—81no—
427C22×C3—81no—
428C22×C3—81no—
429C22×C3—81no—
430C22×C3—81no—
431C22×C3—81no—
432C22×C3#53211yescharacteristic
433C22×C3#53611yescharacteristic
434C22×C3#53711yescharacteristic
435C22×C3#57611yescharacteristic
436C22×C3#57711yescharacteristic
437C22×C3#57711yescharacteristic
438C22×C3#57711yescharacteristic
439C3×C4—41no—
440C3×C4—41no—
441C3×C4—41no—
442C3×C4—41no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—81no—
446C3×C4—81no—
447C3×C4—81no—
448C3×C4—81no—
449C3×C4—81no—
450C3×C4—81no—
451C3×C4—81no—
452C3×C4#53911yescharacteristic
453C3×C4#53911yescharacteristic
454C3×C4#54111yescharacteristic
455C3×C4#54111yescharacteristic
456C23—41no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23C22×C3×D411yescharacteristic
464D4—41no—
465D4—41no—
466D4—41no—
467D4—41no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
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—41no—
487C2×C4—41no—
488C2×C4—41no—
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×C4C2×C3×#4111yescharacteristic
508C2×C4C2×C3×#4111yescharacteristic
509C2×C4C3×H(5,𝔽2)11yescharacteristic
510C2×C4C3×2−1+411yescharacteristic
511C2×C4C3×2−1+411yescharacteristic
512C2×C4C3×2−1+411yescharacteristic
513C8—22no—
514C8—22no—
515C8—41no—
516C8—41no—
517C2×C3—161no—
518C2×C3#266411yescharacteristic
519C2×C3#317411yescharacteristic
520C2×C3#317911yescharacteristic
521C2×C3#324111yescharacteristic
522C2×C3#324411yescharacteristic
523C2×C3#325711yescharacteristic
524C2×C3#326311yescharacteristic
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22C3×#53211yescharacteristic
533C22C3×#53611yescharacteristic
534C22C3×#53711yescharacteristic
535C22C3×#57611yescharacteristic
536C22C3×#57711yescharacteristic
537C22C3×#57711yescharacteristic
538C22C3×#57711yescharacteristic
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C3×#53911yescharacteristic
553C4C3×#53911yescharacteristic
554C4C3×#54111yescharacteristic
555C4C3×#54111yescharacteristic
556C3#3039511yescharacteristic, direct product factor, Sylow
557C2—161no—
558C2C3×#266411yescharacteristic
559C2C3×#317411yescharacteristic
560C2C3×#317911yescharacteristic
561C2C3×#324111yescharacteristic
562C2C3×#324411yescharacteristic
563C2C3×#325711yescharacteristic
564C2C3×#326311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2647C2semidirect
3. C3×#2099C2semidirect
5. C3×#2088C2semidirect
6. C3×#2088C2semidirect
7. C3×#2085C2semidirect
11. C3×#1944C2semidirect
12. C3×#1941C2semidirect
15. C3×#1768C2semidirect
16. #30395C3direct (N × H)
60. #2647C2×C3semidirect
62. #2099C2×C3semidirect
64. #2088C2×C3semidirect
65. #2088C2×C3semidirect
66. #2085C2×C3semidirect
70. #1944C2×C3semidirect
71. #1941C2×C3semidirect
74. #1768C2×C3semidirect
556. C3#30395direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#26472
C3×#26442
C3×#20992
C3×#20942
C3×#20882
C3×#20852
C3×#20732
C3×#20672
C3×#20652
C3×#19442
C3×#19412
C3×#19362
C3×#19342
C3×#17682
#303953