Finite Group Databasebeta

← C3×#26744 #10645351

Subgroups — C3×#26744 #10645351

Order 768.

854 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2491C211yesmaximal, characteristic, complemented
2C3×#2363C211yesmaximal, characteristic, complemented
3C3×#2054C211yesmaximal, characteristic, complemented
4C3×#2034C211yesmaximal, characteristic, complemented
5C3×#2023C211yesmaximal, characteristic, complemented
6C3×#1999C211yesmaximal, characteristic
7C3×#1988C211yesmaximal, characteristic, complemented
8C3×#1936C211yesmaximal, characteristic, complemented
9C3×#1926C211yesmaximal, characteristic, complemented
10C3×#1924C211yesmaximal, characteristic, complemented
11C3×#1919C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1875C211yesmaximal, characteristic, complemented
14C3×#1825C211yesmaximal, characteristic, complemented
15C3×#1762C211yesmaximal, characteristic, complemented
16#26744C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×D8C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×C3×#124—21no—
20C2×C3×#121C2211yescharacteristic
21C2×C3×#121C2211yescharacteristic
22C2×C3×C4×D4C2211yescharacteristic
23C2×C3×#117C2211yescharacteristic
24C2×C3×#106C2211yescharacteristic
25C2×C3×C4⋊C8C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×#102C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×C22⋊C8C2211yescharacteristic
33C2×C3×C22⋊C8C2211yescharacteristic
34C2×C3×#97C2211yescharacteristic
35C3×#394—21no—
36C3×#393—21no—
37C3×#390—21no—
38C3×#390C2211yescharacteristic
39C3×#390C2211yescharacteristic
40C3×#390C2211yescharacteristic
41C3×#389C2211yescharacteristic
42C3×#388—21no—
43C3×#388—21no—
44C3×#386—21no—
45C3×#380C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C4⋊C4C2211yescharacteristic
48C3×C4×C22⋊C4—21no—
49C3×C4×C22⋊C4C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2491C2×C311yescharacteristic, complemented
61#2363C2×C311yescharacteristic, complemented
62#2054C2×C311yescharacteristic, complemented
63#2034C2×C311yescharacteristic, complemented
64#2023C2×C311yescharacteristic, complemented
65#1999C2×C311yescharacteristic
66#1988C2×C311yescharacteristic, complemented
67#1936C2×C311yescharacteristic, complemented
68#1926C2×C311yescharacteristic, complemented
69#1924C2×C311yescharacteristic, complemented
70#1919C2×C311yescharacteristic, complemented
71#1879C2×C311yescharacteristic, complemented
72#1875C2×C311yescharacteristic, complemented
73#1825C2×C311yescharacteristic, complemented
74#1762C2×C311yescharacteristic, complemented
75C22×C3×Q8—21no—
76C22×C3×D4—21no—
77C22×C3×D4—21no—
78C22×C3×D4C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C23×C3×C4C2311yescharacteristic
82C2×C3×D8—22no—
83C2×C3×D8—41no—
84C2×C3×D8—41no—
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C4⋊Q8—22no—
90C3×C4⋊Q8—41no—
91C3×#124—44no—
92C3×#121—22no—
93C3×#121—22no—
94C3×#121—22no—
95C3×#121—41no—
96C3×C4×D4—22no—
97C3×C4×D4—41no—
98C3×#117—22no—
99C3×#117—41no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C42—21no—
122C2×C3×C42—21no—
123C2×C3×C42—21no—
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C3×#106—22no—
127C3×C4⋊C8—41no—
128C3×#102—22no—
129C3×#102—22no—
130C3×#102—22no—
131C3×#102—22no—
132C3×#102—41no—
133C3×#102—41no—
134C3×C22⋊C8—41no—
135C3×C22⋊C8—41no—
136C3×#97—41no—
137C3×#95—21no—
138C3×#95—21no—
139C3×#95—21no—
140C3×#95—21no—
141C3×#95D411yescharacteristic
142C3×#95D411yescharacteristic
143C22×D8C22×C311yescharacteristic
144C2×C4⋊Q8C22×C311yescharacteristic
145C2×#124—21no—
146C2×#121C22×C311yescharacteristic
147C2×#121C22×C311yescharacteristic
148C2×C4×D4C22×C311yescharacteristic
149C2×#117C22×C311yescharacteristic
150C2×#106C22×C311yescharacteristic
151C2×C4⋊C8C22×C311yescharacteristic
152C2×#102C22×C311yescharacteristic
153C2×#102C22×C311yescharacteristic
154C2×#102C22×C311yescharacteristic
155C2×#102C22×C311yescharacteristic
156C2×#102C22×C311yescharacteristic
157C2×#102C22×C311yescharacteristic
158C2×C22⋊C8C22×C311yescharacteristic
159C2×C22⋊C8C22×C311yescharacteristic
160C2×#97C22×C311yescharacteristic
161#394—21no—
162#393—21no—
163#390—21no—
164#390C22×C311yescharacteristic
165#390C22×C311yescharacteristic
166#390C22×C311yescharacteristic
167#389C22×C311yescharacteristic
168#388—21no—
169#388—21no—
170#386—21no—
171#380C22×C311yescharacteristic
172C4×C4⋊C4C22×C311yescharacteristic
173C4×C4⋊C4C22×C311yescharacteristic
174C4×C22⋊C4—21no—
175C4×C22⋊C4C22×C311yescharacteristic
176#340C22×C311yescharacteristic
177#340C22×C311yescharacteristic
178#340C22×C311yescharacteristic
179#340C22×C311yescharacteristic
180#340C22×C311yescharacteristic
181#340C22×C311yescharacteristic
182#340C22×C311yescharacteristic
183#340C22×C311yescharacteristic
184#336C22×C311yescharacteristic
185#336C22×C311yescharacteristic
186C24×C3—21no—
187C24×C3—21no—
188C24×C3C2×D411yescharacteristic
189C2×C3×Q8—42no—
190C2×C3×Q8—42no—
191C2×C3×Q8—81no—
192C2×C3×D4—24no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
204C2×C3×D4—42no—
205C2×C3×D4—42no—
206C2×C3×D4—81no—
207C2×C3×D4—81no—
208C2×C3×D4—81no—
209C2×C3×D4#4112yes—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—42no—
223C22×C3×C4—42no—
224C22×C3×C4—81no—
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2411yescharacteristic
231C3×D8—44no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—42no—
254C3×C4⋊C4—81no—
255C3×C4⋊C4#4112yes—
256C3×C4⋊C4#4112yes—
257C3×C4⋊C4#4112yes—
258C3×C22⋊C4—24no—
259C3×C22⋊C4—22no—
260C3×C22⋊C4—41no—
261C3×C22⋊C4—42no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—42no—
264C3×C22⋊C4—42no—
265C3×C22⋊C4—42no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—81no—
270C3×C22⋊C4—81no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—42no—
276C3×C42—42no—
277C3×C42—81no—
278C22×Q8—21no—
279C22×D4—21no—
280C22×D4—21no—
281C22×D4C23×C311yescharacteristic
282C22×D4C23×C311yescharacteristic
283C23×C4—21no—
284C23×C4C23×C311yescharacteristic
285C2×D8—22no—
286C2×D8—41no—
287C2×D8—41no—
288C22×C8C23×C311yescharacteristic
289C22×C8C23×C311yescharacteristic
290C22×C8C23×C311yescharacteristic
291C22×C8C23×C311yescharacteristic
292C4⋊Q8—22no—
293C4⋊Q8—41no—
294#124—44no—
295#121—22no—
296#121—22no—
297#121—22no—
298#121—41no—
299C4×D4—22no—
300C4×D4—41no—
301#117—22no—
302#117—41no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4C23×C311yescharacteristic
306C2×C4⋊C4C23×C311yescharacteristic
307C2×C4⋊C4C23×C311yescharacteristic
308C2×C4⋊C4C23×C311yescharacteristic
309C2×C4⋊C4C23×C311yescharacteristic
310C2×C4⋊C4C23×C311yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4C3×D411yescharacteristic
323C2×C22⋊C4C3×D411yescharacteristic
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42C23×C311yescharacteristic
328C2×C42C23×C311yescharacteristic
329#106—22no—
330C4⋊C8—41no—
331#102—22no—
332#102—22no—
333#102—22no—
334#102—22no—
335#102—41no—
336#102—41no—
337C22⋊C8—41no—
338C22⋊C8—41no—
339#97—41no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95C3×D411yescharacteristic
345#95C3×D411yescharacteristic
346C23×C3—22no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—21no—
352C23×C3—21no—
353C23×C3—21no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3C22×D411yescharacteristic
368C3×Q8—84no—
369C3×D4—22no—
370C3×D4—22no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—41no—
374C3×D4—41no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4—84no—
378C3×D4—84no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—84no—
416C2×C3×C4AGL(1,ℤ/8)12yes—
417C2×C3×C4C2×#4111yescharacteristic
418C2×C3×C4C2×#4111yescharacteristic
419C2×C3×C4C2×#4111yescharacteristic
420C2×C3×C4C2×#4111yescharacteristic
421C2×C3×C4H(5,𝔽2)11yescharacteristic
422C2×C3×C4H(5,𝔽2)11yescharacteristic
423C3×C8—41no—
424C3×C8—41no—
425C3×C8—41no—
426C3×C8—41no—
427C24—21no—
428C24—21no—
429C24C2×C3×D411yescharacteristic
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×D4—24no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—42no—
446C2×D4—42no—
447C2×D4—81no—
448C2×D4—81no—
449C2×D4—81no—
450C2×D4C3×#4112yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D411yescharacteristic
468C22×C4C2×C3×D411yescharacteristic
469C22×C4C2×C3×D411yescharacteristic
470C22×C4C2×C3×D411yescharacteristic
471C22×C4C24×C311yescharacteristic
472D8—44no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—81no—
496C4⋊C4C3×#4112yes—
497C4⋊C4C3×#4112yes—
498C4⋊C4C3×#4112yes—
499C22⋊C4—24no—
500C22⋊C4—22no—
501C22⋊C4—41no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—42no—
506C22⋊C4—42no—
507C22⋊C4—42no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—81no—
511C22⋊C4—81no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C42—42no—
518C42—81no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—42no—
522C22×C3—41no—
523C22×C3—42no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—81no—
530C22×C3—81no—
531C22×C3—81no—
532C22×C3—81no—
533C22×C3—81no—
534C22×C3—81no—
535C22×C3—81no—
536C22×C3—81no—
537C22×C3—81no—
538C22×C3—81no—
539C22×C3—81no—
540C22×C3#52511yescharacteristic
541C22×C3#54611yescharacteristic
542C22×C3#54611yescharacteristic
543C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
544C22×C3#57511yescharacteristic
545C22×C3#57611yescharacteristic
546C22×C3#57711yescharacteristic
547C3×C4—22no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—41no—
551C3×C4—42no—
552C3×C4—41no—
553C3×C4—42no—
554C3×C4—41no—
555C3×C4—81no—
556C3×C4—81no—
557C3×C4—81no—
558C3×C4#52911yescharacteristic
559C3×C4#53811yescharacteristic
560C3×C4#55511yescharacteristic
561C3×C4#55911yescharacteristic
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—22no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C22×C3×D411yescharacteristic
584Q8—84no—
585D4—22no—
586D4—22no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—84no—
594D4—84no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4C3×AGL(1,ℤ/8)12yes—
633C2×C4C2×C3×#4111yescharacteristic
634C2×C4C2×C3×#4111yescharacteristic
635C2×C4C2×C3×#4111yescharacteristic
636C2×C4C2×C3×#4111yescharacteristic
637C2×C4C3×H(5,𝔽2)11yescharacteristic
638C2×C4C3×H(5,𝔽2)11yescharacteristic
639C8—41no—
640C8—41no—
641C8—41no—
642C8—41no—
643C2×C3—81no—
644C2×C3—82no—
645C2×C3—161no—
646C2×C3#245911yescharacteristic
647C2×C3#311511yescharacteristic
648C2×C3#311811yescharacteristic
649C2×C3#331811yescharacteristic
650C2×C3#331911yescharacteristic
651C2×C3#332111yescharacteristic
652C2×C3#333211yescharacteristic
653C22—41no—
654C22—42no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22C3×#52511yescharacteristic
675C22C3×#54611yescharacteristic
676C22C3×#54611yescharacteristic
677C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
678C22C3×#57511yescharacteristic
679C22C3×#57611yescharacteristic
680C22C3×#57711yescharacteristic
681C4—22no—
682C4—41no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—41no—
688C4—42no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4C3×#52911yescharacteristic
693C4C3×#53811yescharacteristic
694C4C3×#55511yescharacteristic
695C4C3×#55911yescharacteristic
696C3#2674411yescharacteristic, direct product factor, Sylow
697C2—81no—
698C2—82no—
699C2—161no—
700C2C3×#245911yescharacteristic
701C2C3×#311511yescharacteristic
702C2C3×#311811yescharacteristic
703C2C3×#331811yescharacteristic
704C2C3×#331911yescharacteristic
705C2C3×#332111yescharacteristic
706C2C3×#333211yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2491C2semidirect
2. C3×#2363C2semidirect
3. C3×#2054C2semidirect
4. C3×#2034C2semidirect
5. C3×#2023C2semidirect
7. C3×#1988C2semidirect
8. C3×#1936C2semidirect
9. C3×#1926C2semidirect
10. C3×#1924C2semidirect
11. C3×#1919C2semidirect
12. C3×#1879C2semidirect
13. C3×#1875C2semidirect
14. C3×#1825C2semidirect
15. C3×#1762C2semidirect
16. #26744C3direct (N × H)
60. #2491C2×C3semidirect
61. #2363C2×C3semidirect
62. #2054C2×C3semidirect
63. #2034C2×C3semidirect
64. #2023C2×C3semidirect
66. #1988C2×C3semidirect
67. #1936C2×C3semidirect
68. #1926C2×C3semidirect
69. #1924C2×C3semidirect
70. #1919C2×C3semidirect
71. #1879C2×C3semidirect
72. #1875C2×C3semidirect
73. #1825C2×C3semidirect
74. #1762C2×C3semidirect
696. C3#26744direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#24912
C3×#23632
C3×#20542
C3×#20342
C3×#20232
C3×#19992
C3×#19882
C3×#19362
C3×#19262
C3×#19242
C3×#19192
C3×#18792
C3×#18752
C3×#18252
C3×#17622
#267443