Finite Group Databasebeta

← C3×#27783 #10646390

Subgroups — C3×#27783 #10646390

Order 768.

892 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#489C211yesmaximal, characteristic, complemented
2C2×C3×#486C211yesmaximal, characteristic
3C3×#2551C211yesmaximal, characteristic, complemented
4C3×#2544C211yesmaximal, characteristic
5C3×#2042C211yesmaximal, characteristic, complemented
6C3×#2041C211yesmaximal, characteristic
7C3×#2024C211yesmaximal, characteristic, complemented
8C3×#2023C211yesmaximal, characteristic, complemented
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1959C211yesmaximal, characteristic, complemented
11C3×#1936C211yesmaximal, characteristic, complemented
12C3×#1933C211yesmaximal, characteristic, complemented
13C3×#1802C211yesmaximal, characteristic, complemented
14C3×#1771C211yesmaximal, characteristic, complemented
15C3×#1762C211yesmaximal, characteristic, complemented
16#27783C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×C4⋊Q8—21no—
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#127C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C4×D4C2211yescharacteristic
24C3×#489—24no—
25C3×#486—24no—
26C2×C3×C4⋊C8C2211yescharacteristic
27C2×C3×#103C2211yescharacteristic
28C2×C3×#103C2211yescharacteristic
29C2×C3×#103C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#97C2211yescharacteristic
40C2×C3×#97C2211yescharacteristic
41C2×C3×C4×C8C2211yescharacteristic
42C3×#395—21no—
43C3×#395—21no—
44C3×#394—21no—
45C3×#394—21no—
46C3×#391C2211yescharacteristic
47C3×#390C2211yescharacteristic
48C3×#389—21no—
49C3×#389C2211yescharacteristic
50C3×#389C2211yescharacteristic
51C3×#386—21no—
52C3×#386—21no—
53C3×#384C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#489C2×C311yescharacteristic, complemented
63C2×#486C2×C311yescharacteristic
64#2551C2×C311yescharacteristic, complemented
65#2544C2×C311yescharacteristic
66#2042C2×C311yescharacteristic, complemented
67#2041C2×C311yescharacteristic
68#2024C2×C311yescharacteristic, complemented
69#2023C2×C311yescharacteristic, complemented
70#1983C2×C311yescharacteristic, complemented
71#1959C2×C311yescharacteristic, complemented
72#1936C2×C311yescharacteristic, complemented
73#1933C2×C311yescharacteristic, complemented
74#1802C2×C311yescharacteristic, complemented
75#1771C2×C311yescharacteristic, complemented
76#1762C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×Q8—21no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C4⋊Q8—22no—
90C3×C4⋊Q8—22no—
91C3×C4⋊Q8—41no—
92C3×C4⋊Q8—41no—
93C3×C4⋊Q8—44no—
94C3×#127—22no—
95C3×#127—41no—
96C3×#124—22no—
97C3×#124—22no—
98C3×#124—22no—
99C3×#124—41no—
100C3×C4×D4—22no—
101C3×C4×D4—22no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4D411yescharacteristic
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C42—21no—
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C3×C4⋊C8—22no—
127C3×#103—22no—
128C3×#103—22no—
129C3×#103—22no—
130C3×#103—41no—
131C3×#102—22no—
132C3×#102—22no—
133C3×#102—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102—22no—
137C3×#102—41no—
138C3×#102D414yes—
139C3×#97—22no—
140C3×#97—22no—
141C3×C4×C8—22no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95D411yescharacteristic
148C3×#95D411yescharacteristic
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8C22×C311yescharacteristic
151C2×C4⋊Q8C22×C311yescharacteristic
152C2×#127C22×C311yescharacteristic
153C2×#124C22×C311yescharacteristic
154C2×#124C22×C311yescharacteristic
155C2×C4×D4C22×C311yescharacteristic
156#489—24no—
157#486—24no—
158C2×C4⋊C8C22×C311yescharacteristic
159C2×#103C22×C311yescharacteristic
160C2×#103C22×C311yescharacteristic
161C2×#103C22×C311yescharacteristic
162C2×#103C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×#102C22×C311yescharacteristic
171C2×#97C22×C311yescharacteristic
172C2×#97C22×C311yescharacteristic
173C2×C4×C8C22×C311yescharacteristic
174#395—21no—
175#395—21no—
176#394—21no—
177#394—21no—
178#391C22×C311yescharacteristic
179#390C22×C311yescharacteristic
180#389—21no—
181#389C22×C311yescharacteristic
182#389C22×C311yescharacteristic
183#386—21no—
184#386—21no—
185#384C22×C311yescharacteristic
186C4×C4⋊C4C22×C311yescharacteristic
187C4×C4⋊C4C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193#336C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×Q8—42no—
203C2×C3×Q8—42no—
204C2×C3×Q8—42no—
205C2×C3×Q8—42no—
206C2×C3×Q8—81no—
207C2×C3×Q8—81no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—42no—
220C2×C3×D4—42no—
221C2×C3×D4—42no—
222C2×C3×D4—42no—
223C2×C3×D4—81no—
224C2×C3×D4—81no—
225C2×C3×D4C2×D412yes—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—42no—
233C22×C3×C4—81no—
234C22×C3×C4—81no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2411yescharacteristic
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—21no—
250C2×C3×C8—21no—
251C2×C3×C8—21no—
252C2×C3×C8—21no—
253C2×C3×C8C2×D412yes—
254C3×C4⋊C4—22no—
255C3×C4⋊C4—22no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4—42no—
266C3×C4⋊C4—42no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4—42no—
269C3×C4⋊C4—81no—
270C3×C4⋊C4C2×D412yes—
271C3×C4⋊C4#4112yes—
272C3×C22⋊C4—42no—
273C3×C22⋊C4—42no—
274C3×C22⋊C4—42no—
275C3×C22⋊C4—42no—
276C3×C22⋊C4—42no—
277C3×C22⋊C4—81no—
278C3×C22⋊C4—81no—
279C3×C42—21no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—42no—
284C3×C42#4112yes—
285C3×C42#4112yes—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×Q8C23×C311yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C23×C311yescharacteristic
292C22×D4C23×C311yescharacteristic
293C23×C4—21no—
294C22×C8C23×C311yescharacteristic
295C22×C8C23×C311yescharacteristic
296C22×C8C23×C311yescharacteristic
297C22×C8C23×C311yescharacteristic
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8—41no—
301C4⋊Q8—41no—
302C4⋊Q8—44no—
303#127—22no—
304#127—41no—
305#124—22no—
306#124—22no—
307#124—22no—
308#124—41no—
309C4×D4—22no—
310C4×D4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4C3×D411yescharacteristic
318C2×C4⋊C4C3×D411yescharacteristic
319C2×C4⋊C4C23×C311yescharacteristic
320C2×C4⋊C4C23×C311yescharacteristic
321C2×C4⋊C4C23×C311yescharacteristic
322C2×C4⋊C4C23×C311yescharacteristic
323C2×C4⋊C4C23×C311yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C42—21no—
332C2×C42C23×C311yescharacteristic
333C2×C42C23×C311yescharacteristic
334C2×C42C23×C311yescharacteristic
335C4⋊C8—22no—
336#103—22no—
337#103—22no—
338#103—22no—
339#103—41no—
340#102—22no—
341#102—22no—
342#102—22no—
343#102—22no—
344#102—22no—
345#102—22no—
346#102—41no—
347#102C3×D414yes—
348#97—22no—
349#97—22no—
350C4×C8—22no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95C3×D411yescharacteristic
357#95C3×D411yescharacteristic
358C23×C3—22no—
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×C3—41no—
368C23×C3—41no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3C22×D411yescharacteristic
373C3×Q8—41no—
374C3×Q8—41no—
375C3×Q8—41no—
376C3×Q8—41no—
377C3×Q8—84no—
378C3×Q8—84no—
379C3×D4—22no—
380C3×D4—22no—
381C3×D4—41no—
382C3×D4—41no—
383C3×D4—41no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—41no—
387C3×D4—84no—
388C3×D4—84no—
389C2×C3×C4—21no—
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—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
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—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—84no—
422C2×C3×C4#12412yes—
423C2×C3×C4#12412yes—
424C2×C3×C4AGL(1,ℤ/8)12yes—
425C2×C3×C4#13712yes—
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C4C2×#4111yescharacteristic
430C2×C3×C4H(5,𝔽2)11yescharacteristic
431C2×C3×C42−1+411yescharacteristic
432C3×C8—22no—
433C3×C8—41no—
434C3×C8—41no—
435C3×C8—41no—
436C24—21no—
437C24—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8—42no—
447C2×Q8—42no—
448C2×Q8—81no—
449C2×Q8—81no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—81no—
466C2×D4—81no—
467C2×D4C2×C3×D412yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—81no—
476C22×C4—81no—
477C22×C4C2×C3×D411yescharacteristic
478C22×C4C2×C3×D411yescharacteristic
479C22×C4C2×C3×D411yescharacteristic
480C22×C4C2×C3×D411yescharacteristic
481C22×C4C2×C3×D411yescharacteristic
482C22×C4C2×C3×D411yescharacteristic
483C22×C4C24×C311yescharacteristic
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8C2×C3×D412yes—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—81no—
512C4⋊C4C2×C3×D412yes—
513C4⋊C4C3×#4112yes—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—81no—
520C22⋊C4—81no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42C3×#4112yes—
527C42C3×#4112yes—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—42no—
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—81no—
541C22×C3—81no—
542C22×C3C2×#12411yescharacteristic
543C22×C3D4211yescharacteristic
544C22×C3#54811yescharacteristic
545C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
546C22×C3C2×#13711yescharacteristic
547C22×C3#57611yescharacteristic
548C22×C3#57711yescharacteristic
549C3×C4—22no—
550C3×C4—22no—
551C3×C4—22no—
552C3×C4—22no—
553C3×C4—42no—
554C3×C4—41no—
555C3×C4—42no—
556C3×C4—41no—
557C3×C4—81no—
558C3×C4—81no—
559C3×C4—81no—
560C3×C4—81no—
561C3×C4#53211yescharacteristic
562C3×C4#54211yescharacteristic
563C3×C4#54711yescharacteristic
564C3×C4#55511yescharacteristic
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C22×C3×D411yescharacteristic
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—41no—
584Q8—84no—
585Q8—84no—
586D4—22no—
587D4—22no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—84no—
595D4—84no—
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—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
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—84no—
629C2×C4C3×#12412yes—
630C2×C4C3×#12412yes—
631C2×C4C3×AGL(1,ℤ/8)12yes—
632C2×C4C3×#13712yes—
633C2×C4C22×C3×D411yescharacteristic
634C2×C4C2×C3×#4111yescharacteristic
635C2×C4C2×C3×#4111yescharacteristic
636C2×C4C2×C3×#4111yescharacteristic
637C2×C4C3×H(5,𝔽2)11yescharacteristic
638C2×C4C3×2−1+411yescharacteristic
639C8—22no—
640C8—41no—
641C8—41no—
642C8—41no—
643C2×C3—82no—
644C2×C3—161no—
645C2×C3#249111yescharacteristic
646C2×C3#313611yescharacteristic
647C2×C3#314111yescharacteristic
648C2×C3#326411yescharacteristic
649C2×C3#326611yescharacteristic
650C2×C3#337311yescharacteristic
651C2×C3#337511yescharacteristic
652C22—42no—
653C22—42no—
654C22—42no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22C2×C3×#12411yescharacteristic
667C22C3×D4211yescharacteristic
668C22C3×#54811yescharacteristic
669C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
670C22C2×C3×#13711yescharacteristic
671C22C3×#57611yescharacteristic
672C22C3×#57711yescharacteristic
673C4—22no—
674C4—22no—
675C4—22no—
676C4—22no—
677C4—41no—
678C4—42no—
679C4—41no—
680C4—42no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4—81no—
685C4C3×#53211yescharacteristic
686C4C3×#54211yescharacteristic
687C4C3×#54711yescharacteristic
688C4C3×#55511yescharacteristic
689C3#2778311yescharacteristic, direct product factor, Sylow
690C2—82no—
691C2—161no—
692C2C3×#249111yescharacteristic
693C2C3×#313611yescharacteristic
694C2C3×#314111yescharacteristic
695C2C3×#326411yescharacteristic
696C2C3×#326611yescharacteristic
697C2C3×#337311yescharacteristic
698C2C3×#337511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#489C2semidirect
3. C3×#2551C2semidirect
5. C3×#2042C2semidirect
7. C3×#2024C2semidirect
8. C3×#2023C2semidirect
9. C3×#1983C2semidirect
10. C3×#1959C2semidirect
11. C3×#1936C2semidirect
12. C3×#1933C2semidirect
13. C3×#1802C2semidirect
14. C3×#1771C2semidirect
15. C3×#1762C2semidirect
16. #27783C3direct (N × H)
62. C2×#489C2×C3semidirect
64. #2551C2×C3semidirect
66. #2042C2×C3semidirect
68. #2024C2×C3semidirect
69. #2023C2×C3semidirect
70. #1983C2×C3semidirect
71. #1959C2×C3semidirect
72. #1936C2×C3semidirect
73. #1933C2×C3semidirect
74. #1802C2×C3semidirect
75. #1771C2×C3semidirect
76. #1762C2×C3semidirect
689. C3#27783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4892
C2×C3×#4862
C3×#25512
C3×#25442
C3×#20422
C3×#20412
C3×#20242
C3×#20232
C3×#19832
C3×#19592
C3×#19362
C3×#19332
C3×#18022
C3×#17712
C3×#17622
#277833