Finite Group Databasebeta

← C3×#19069 #10637676

Subgroups — C3×#19069 #10637676

Order 768.

886 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3545C211yesmaximal, characteristic
2C3×#3240C211yesmaximal, characteristic, complemented
3C3×#3215C211yesmaximal, characteristic, complemented
4C3×#3172C211yesmaximal, characteristic, complemented
5C3×#1664C211yesmaximal, characteristic, complemented
6C3×#1662C211yesmaximal, characteristic, complemented
7C3×#1661C211yesmaximal, characteristic, complemented
8C3×#1661C211yesmaximal, characteristic, complemented
9C3×#1661C211yesmaximal, characteristic, complemented
10C3×#1660C211yesmaximal, characteristic, complemented
11C3×#1659C211yesmaximal, characteristic, complemented
12C3×#1659C211yesmaximal, characteristic, complemented
13C3×#1535C211yesmaximal, characteristic, complemented
14C3×#1529C211yesmaximal, characteristic, complemented
15C3×#1527C211yesmaximal, characteristic, complemented
16#19069C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#563C2211yescharacteristic
18C3×#562C2211yescharacteristic
19C3×#562C2211yescharacteristic
20C3×H(3,𝔽4)C2211yescharacteristic
21C3×#555—21no—
22C3×#551—21no—
23C3×#551—21no—
24C3×#551—21no—
25C3×#546—21no—
26C3×#546—21no—
27C3×#542—21no—
28C3×#542—21no—
29C3×#538—21no—
30C3×#538—21no—
31C3×#536—21no—
32C3×#534—21no—
33C3×#533C2211yescharacteristic, complemented
34C3×#529C2211yescharacteristic
35C3×#529C2211yescharacteristic
36C2×C3×#124C2211yescharacteristic
37C3×#501C2211yescharacteristic, complemented
38C3×#501C2211yescharacteristic, complemented
39C3×#501C2211yescharacteristic, complemented
40C3×#497C2211yescharacteristic
41C3×#497C2211yescharacteristic, complemented
42C3×#497C2211yescharacteristic, complemented
43C3×#491C2211yescharacteristic, complemented
44C3×#489C2211yescharacteristic
45C3×#489C2211yescharacteristic, complemented
46C3×#489C2211yescharacteristic, complemented
47C3×#489C2211yescharacteristic, complemented
48C3×#489C2211yescharacteristic, complemented
49C3×#485—21no—
50C3×#482—21no—
51C3×#479—21no—
52C3×#478—21no—
53C3×#470—21no—
54C3×#468—21no—
55C3×#464—21no—
56C3×#464—21no—
57C3×#451—21no—
58C3×#450—21no—
59C3×C4×Q16—21no—
60C3×C4×SD16—21no—
61C3×#432C2211yescharacteristic, complemented
62C3×#432C2211yescharacteristic, complemented
63C3×C4×M16C2211yescharacteristic, complemented
64C3×#330C2211yescharacteristic, complemented
65C3×#330C2211yescharacteristic, complemented
66C3×#330C2211yescharacteristic, complemented
67C3×#330C2211yescharacteristic, complemented
68C3×#329C2211yescharacteristic
69C3×#329C2211yescharacteristic
70C3×#329C2211yescharacteristic, complemented
71C3×#329C2211yescharacteristic, complemented
72C3×#329C2211yescharacteristic, complemented
73C3×#329C2211yescharacteristic, complemented
74C3×#329C2211yescharacteristic, complemented
75C3×#329C2211yescharacteristic, complemented
76#3545C2×C311yescharacteristic
77#3240C2×C311yescharacteristic, complemented
78#3215C2×C311yescharacteristic, complemented
79#3172C2×C311yescharacteristic, complemented
80#1664C2×C311yescharacteristic, complemented
81#1662C2×C311yescharacteristic, complemented
82#1661C2×C311yescharacteristic, complemented
83#1661C2×C311yescharacteristic, complemented
84#1661C2×C311yescharacteristic, complemented
85#1660C2×C311yescharacteristic, complemented
86#1659C2×C311yescharacteristic, complemented
87#1659C2×C311yescharacteristic, complemented
88#1535C2×C311yescharacteristic, complemented
89#1529C2×C311yescharacteristic, complemented
90#1527C2×C311yescharacteristic, complemented
91C2×C3×#41—21no—
92C22×C3×Q8D411yescharacteristic
93C22×C3×D4—21no—
94C22×C3×D4D411yescharacteristic
95C2×C3×Q16—21no—
96C2×C3×Q16—21no—
97C2×C3×Q16—21no—
98C2×C3×SD16—21no—
99C2×C3×SD16—21no—
100C2×C3×SD16—21no—
101C2×C3×M16—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8C2311yescharacteristic
105C3×C4⋊Q8C2311yescharacteristic
106C3×#126—21no—
107C3×#126—21no—
108C3×#126—21no—
109C3×#126—21no—
110C3×#126—21no—
111C3×#126—21no—
112C3×#125—21no—
113C3×#125C2311yescharacteristic
114C3×#125C2311yescharacteristic
115C3×#124—21no—
116C3×#124—21no—
117C3×#124—21no—
118C3×#124—21no—
119C3×#124—21no—
120C3×#124—21no—
121C3×#124—21no—
122C3×#124—21no—
123C3×#124D411yescharacteristic
124C3×#124D411yescharacteristic
125C3×#124C2311yescharacteristic
126C3×#124C2311yescharacteristic
127C3×#124C2311yescharacteristic
128C3×#124C2311yescharacteristic
129C3×#123—21no—
130C3×#123—21no—
131C3×#123—21no—
132C3×#123—21no—
133C3×#123—21no—
134C3×#123—21no—
135C3×#123—21no—
136C3×#123—21no—
137C3×#123—21no—
138C3×#123—21no—
139C3×#123—21no—
140C3×#123—21no—
141C3×C22⋊Q8—21no—
142C3×C22⋊Q8—21no—
143C3×C22⋊Q8—21no—
144C3×C22⋊Q8—21no—
145C3×C22⋊Q8—21no—
146C3×C22⋊Q8—21no—
147C3×C22⋊Q8—21no—
148C3×C22⋊Q8—21no—
149C3×C22⋊Q8—21no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8D411yescharacteristic
152C3×C22⋊Q8D411yescharacteristic
153C3×#121—21no—
154C3×#121—21no—
155C3×#121—21no—
156C3×#121—21no—
157C3×#121—21no—
158C3×#121—21no—
159C3×#121—21no—
160C3×#121—21no—
161C3×#121D411yescharacteristic
162C3×#121D411yescharacteristic
163C3×#120—21no—
164C3×#120—21no—
165C3×#120—21no—
166C3×#120—21no—
167C3×#120—21no—
168C3×#120—21no—
169C3×C4×Q8—21no—
170C3×C4×Q8—21no—
171C3×C4×Q8D411yescharacteristic
172C3×C4×Q8D411yescharacteristic
173C3×C4×D4—21no—
174C3×C4×D4—21no—
175C3×C4×D4—21no—
176C3×C4×D4—21no—
177C3×C4×D4—21no—
178C3×C4×D4—21no—
179C3×C4×D4D411yescharacteristic
180C3×C4×D4D411yescharacteristic
181C3×#117—21no—
182C3×#117—21no—
183C3×#117—21no—
184C3×#117—21no—
185C3×#117—21no—
186C3×#117—21no—
187C2×C3×C22⋊C4—21no—
188C2×C3×C22⋊C4—21no—
189C2×C3×C22⋊C4—21no—
190C2×C3×C22⋊C4—21no—
191C2×C3×C22⋊C4—21no—
192C2×C3×C42C2311yescharacteristic
193C3×#107—21no—
194C3×#107—21no—
195C3×#107—21no—
196C3×#106—21no—
197C3×#106—21no—
198C3×#106—21no—
199C3×C4⋊C8—21no—
200C3×C4⋊C8—21no—
201C3×#103—21no—
202C3×#103—21no—
203C3×#103—21no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—21no—
208C3×#102—21no—
209C3×#102—21no—
210C3×#102—21no—
211C3×#102—21no—
212C3×#102—21no—
213C3×C22⋊C8—21no—
214C3×C22⋊C8—21no—
215C3×#97C2311yescharacteristic
216C3×#97C2311yescharacteristic
217C3×#97C2311yescharacteristic
218C3×#97C2311yescharacteristic
219C3×#97C2311yescharacteristic
220C3×#97C2311yescharacteristic
221C3×C4×C8—21no—
222#563C22×C311yescharacteristic
223#562C22×C311yescharacteristic
224#562C22×C311yescharacteristic
225H(3,𝔽4)C22×C311yescharacteristic
226#555—21no—
227#551—21no—
228#551—21no—
229#551—21no—
230#546—21no—
231#546—21no—
232#542—21no—
233#542—21no—
234#538—21no—
235#538—21no—
236#536—21no—
237#534—21no—
238#533C22×C311yescharacteristic, complemented
239#529C22×C311yescharacteristic
240#529C22×C311yescharacteristic
241C2×#124C22×C311yescharacteristic
242#501C22×C311yescharacteristic, complemented
243#501C22×C311yescharacteristic, complemented
244#501C22×C311yescharacteristic, complemented
245#497C22×C311yescharacteristic
246#497C22×C311yescharacteristic, complemented
247#497C22×C311yescharacteristic, complemented
248#491C22×C311yescharacteristic, complemented
249#489C22×C311yescharacteristic
250#489C22×C311yescharacteristic, complemented
251#489C22×C311yescharacteristic, complemented
252#489C22×C311yescharacteristic, complemented
253#489C22×C311yescharacteristic, complemented
254#485—21no—
255#482—21no—
256#479—21no—
257#478—21no—
258#470—21no—
259#468—21no—
260#464—21no—
261#464—21no—
262#451—21no—
263#450—21no—
264C4×Q16—21no—
265C4×SD16—21no—
266#432C22×C311yescharacteristic, complemented
267#432C22×C311yescharacteristic, complemented
268C4×M16C22×C311yescharacteristic, complemented
269#330C22×C311yescharacteristic, complemented
270#330C22×C311yescharacteristic, complemented
271#330C22×C311yescharacteristic, complemented
272#330C22×C311yescharacteristic, complemented
273#329C22×C311yescharacteristic
274#329C22×C311yescharacteristic
275#329C22×C311yescharacteristic, complemented
276#329C22×C311yescharacteristic, complemented
277#329C22×C311yescharacteristic, complemented
278#329C22×C311yescharacteristic, complemented
279#329C22×C311yescharacteristic, complemented
280#329C22×C311yescharacteristic, complemented
281C24×C3—21no—
282C24×C3—21no—
283C3×#41—82no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—81no—
289C2×C3×Q8C2×D411yescharacteristic
290C2×C3×Q8C2×D411yescharacteristic
291C2×C3×Q8C2×D411yescharacteristic
292C2×C3×Q8C2×D411yescharacteristic
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—21no—
298C2×C3×D4—21no—
299C2×C3×D4—21no—
300C2×C3×D4—21no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—81no—
304C2×C3×D4—82no—
305C2×C3×D4C2×D411yescharacteristic
306C2×C3×D4C2×D411yescharacteristic
307C2×C3×D4C2×D411yescharacteristic
308C2×C3×D4C2×D411yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D411yescharacteristic
319C22×C3×C4C2×D411yescharacteristic
320C3×Q16—42no—
321C3×Q16—81no—
322C3×Q16—81no—
323C3×SD16—42no—
324C3×SD16—81no—
325C3×SD16—81no—
326C3×M16—42no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4C2×D411yescharacteristic
354C3×C4⋊C4C2×D411yescharacteristic
355C3×C4⋊C4C2×D411yescharacteristic
356C3×C4⋊C4C2×D411yescharacteristic
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—21no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4—21no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—41no—
386C3×C42—21no—
387C3×C42—21no—
388C3×C42—21no—
389C3×C42—21no—
390C3×C42—41no—
391C3×C42C2×D411yescharacteristic
392C3×C42C2×D411yescharacteristic
393C3×C42C2×D411yescharacteristic
394C3×C42C2411yescharacteristic
395C2×#41—21no—
396C22×Q8C3×D411yescharacteristic
397C22×D4—21no—
398C22×D4C3×D411yescharacteristic
399C2×Q16—21no—
400C2×Q16—21no—
401C2×Q16—21no—
402C2×SD16—21no—
403C2×SD16—21no—
404C2×SD16—21no—
405C2×M16—21no—
406C4⋊Q8—21no—
407C4⋊Q8—21no—
408C4⋊Q8C23×C311yescharacteristic
409C4⋊Q8C23×C311yescharacteristic
410#126—21no—
411#126—21no—
412#126—21no—
413#126—21no—
414#126—21no—
415#126—21no—
416#125—21no—
417#125C23×C311yescharacteristic
418#125C23×C311yescharacteristic
419#124—21no—
420#124—21no—
421#124—21no—
422#124—21no—
423#124—21no—
424#124—21no—
425#124—21no—
426#124—21no—
427#124C3×D411yescharacteristic
428#124C3×D411yescharacteristic
429#124C23×C311yescharacteristic
430#124C23×C311yescharacteristic
431#124C23×C311yescharacteristic
432#124C23×C311yescharacteristic
433#123—21no—
434#123—21no—
435#123—21no—
436#123—21no—
437#123—21no—
438#123—21no—
439#123—21no—
440#123—21no—
441#123—21no—
442#123—21no—
443#123—21no—
444#123—21no—
445C22⋊Q8—21no—
446C22⋊Q8—21no—
447C22⋊Q8—21no—
448C22⋊Q8—21no—
449C22⋊Q8—21no—
450C22⋊Q8—21no—
451C22⋊Q8—21no—
452C22⋊Q8—21no—
453C22⋊Q8—21no—
454C22⋊Q8—21no—
455C22⋊Q8C3×D411yescharacteristic
456C22⋊Q8C3×D411yescharacteristic
457#121—21no—
458#121—21no—
459#121—21no—
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121C3×D411yescharacteristic
466#121C3×D411yescharacteristic
467#120—21no—
468#120—21no—
469#120—21no—
470#120—21no—
471#120—21no—
472#120—21no—
473C4×Q8—21no—
474C4×Q8—21no—
475C4×Q8C3×D411yescharacteristic
476C4×Q8C3×D411yescharacteristic
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4C3×D411yescharacteristic
484C4×D4C3×D411yescharacteristic
485#117—21no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117—21no—
490#117—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C42C23×C311yescharacteristic
497#107—21no—
498#107—21no—
499#107—21no—
500#106—21no—
501#106—21no—
502#106—21no—
503C4⋊C8—21no—
504C4⋊C8—21no—
505#103—21no—
506#103—21no—
507#103—21no—
508#103—21no—
509#103—21no—
510#103—21no—
511#103—21no—
512#102—21no—
513#102—21no—
514#102—21no—
515#102—21no—
516#102—21no—
517C22⋊C8—21no—
518C22⋊C8—21no—
519#97C23×C311yescharacteristic
520#97C23×C311yescharacteristic
521#97C23×C311yescharacteristic
522#97C23×C311yescharacteristic
523#97C23×C311yescharacteristic
524#97C23×C311yescharacteristic
525C4×C8—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—42no—
531C23×C3—81no—
532C23×C3—81no—
533C23×C3—81no—
534C23×C3—81no—
535C23×C3—81no—
536C23×C3#12011yescharacteristic
537C3×Q8—41no—
538C3×Q8—41no—
539C3×Q8—41no—
540C3×Q8—41no—
541C3×Q8—41no—
542C3×Q8—41no—
543C3×Q8—41no—
544C3×Q8—41no—
545C3×Q8—81no—
546C3×Q8—81no—
547C3×D4—41no—
548C3×D4—41no—
549C3×D4—41no—
550C3×D4—41no—
551C3×D4—42no—
552C3×D4—42no—
553C3×D4—81no—
554C3×D4—81no—
555C3×D4—81no—
556C3×D4—81no—
557C3×D4—81no—
558C3×D4—81no—
559C3×D4—81no—
560C3×D4—81no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—42no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—81no—
576C2×C3×C4—81no—
577C2×C3×C4—81no—
578C2×C3×C4—81no—
579C2×C3×C4—81no—
580C2×C3×C4—81no—
581C2×C3×C4—81no—
582C2×C3×C4#12011yescharacteristic
583C2×C3×C4#12011yescharacteristic
584C2×C3×C4#12011yescharacteristic
585C2×C3×C4C22×D411yescharacteristic
586C2×C3×C4C22×D411yescharacteristic
587C2×C3×C4C22×D411yescharacteristic
588C3×C8—22no—
589C3×C8—41no—
590C3×C8—41no—
591C3×C8—41no—
592C3×C8—41no—
593C3×C8—41no—
594C24—21no—
595C24—21no—
596#41—82no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—81no—
602C2×Q8C2×C3×D411yescharacteristic
603C2×Q8C2×C3×D411yescharacteristic
604C2×Q8C2×C3×D411yescharacteristic
605C2×Q8C2×C3×D411yescharacteristic
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—81no—
617C2×D4—82no—
618C2×D4C2×C3×D411yescharacteristic
619C2×D4C2×C3×D411yescharacteristic
620C2×D4C2×C3×D411yescharacteristic
621C2×D4C2×C3×D411yescharacteristic
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4C2×C3×D411yescharacteristic
631C22×C4C2×C3×D411yescharacteristic
632C22×C4C2×C3×D411yescharacteristic
633Q16—42no—
634Q16—81no—
635Q16—81no—
636SD16—42no—
637SD16—81no—
638SD16—81no—
639M16—42no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4C2×C3×D411yescharacteristic
667C4⋊C4C2×C3×D411yescharacteristic
668C4⋊C4C2×C3×D411yescharacteristic
669C4⋊C4C2×C3×D411yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—41no—
704C42C2×C3×D411yescharacteristic
705C42C2×C3×D411yescharacteristic
706C42C2×C3×D411yescharacteristic
707C42C24×C311yescharacteristic
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—162no—
724C22×C3—162no—
725C22×C3C2×#12011yescharacteristic
726C3×C4—21no—
727C3×C4—21no—
728C3×C4—21no—
729C3×C4—21no—
730C3×C4—21no—
731C3×C4—21no—
732C3×C4—41no—
733C3×C4—41no—
734C3×C4—41no—
735C3×C4—41no—
736C3×C4—41no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—81no—
741C3×C4—81no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—42no—
747C23—81no—
748C23—81no—
749C23—81no—
750C23—81no—
751C23—81no—
752C23C3×#12011yescharacteristic
753Q8—41no—
754Q8—41no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—41no—
761Q8—81no—
762Q8—81no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—42no—
768D4—42no—
769D4—81no—
770D4—81no—
771D4—81no—
772D4—81no—
773D4—81no—
774D4—81no—
775D4—81no—
776D4—81no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—81no—
797C2×C4—81no—
798C2×C4C3×#12011yescharacteristic
799C2×C4C3×#12011yescharacteristic
800C2×C4C3×#12011yescharacteristic
801C2×C4C22×C3×D411yescharacteristic
802C2×C4C22×C3×D411yescharacteristic
803C2×C4C22×C3×D411yescharacteristic
804C8—22no—
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C2×C3—41no—
811C2×C3—81no—
812C2×C3—81no—
813C2×C3—81no—
814C2×C3—81no—
815C2×C3#301811yescharacteristic
816C2×C3#301911yescharacteristic
817C2×C3#302211yescharacteristic
818C22—21no—
819C22—21no—
820C22—21no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—162no—
834C22—162no—
835C22C2×C3×#12011yescharacteristic
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—41no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—81no—
851C4—81no—
852C3#1906911yescharacteristic, direct product factor, Sylow
853C2—41no—
854C2—81no—
855C2—81no—
856C2—81no—
857C2—81no—
858C2C3×#301811yescharacteristic
859C2C3×#301911yescharacteristic
860C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
prime radicalC3×#3545C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3240C2semidirect
3. C3×#3215C2semidirect
4. C3×#3172C2semidirect
5. C3×#1664C2semidirect
6. C3×#1662C2semidirect
7. C3×#1661C2semidirect
8. C3×#1661C2semidirect
9. C3×#1661C2semidirect
10. C3×#1660C2semidirect
11. C3×#1659C2semidirect
12. C3×#1659C2semidirect
13. C3×#1535C2semidirect
14. C3×#1529C2semidirect
15. C3×#1527C2semidirect
16. #19069C3direct (N × H)
33. C3×#533C22semidirect
37. C3×#501C22semidirect
38. C3×#501C22semidirect
39. C3×#501C22semidirect
41. C3×#497C22semidirect
42. C3×#497C22semidirect
43. C3×#491C22semidirect
45. C3×#489C22semidirect
46. C3×#489C22semidirect
47. C3×#489C22semidirect
48. C3×#489C22semidirect
61. C3×#432C22semidirect
62. C3×#432C22semidirect
63. C3×C4×M16C22semidirect
64. C3×#330C22semidirect
65. C3×#330C22semidirect
66. C3×#330C22semidirect
67. C3×#330C22semidirect
70. C3×#329C22semidirect
71. C3×#329C22semidirect
72. C3×#329C22semidirect
73. C3×#329C22semidirect
74. C3×#329C22semidirect
75. C3×#329C22semidirect
77. #3240C2×C3semidirect
78. #3215C2×C3semidirect
79. #3172C2×C3semidirect
80. #1664C2×C3semidirect
81. #1662C2×C3semidirect
82. #1661C2×C3semidirect
83. #1661C2×C3semidirect
84. #1661C2×C3semidirect
85. #1660C2×C3semidirect
86. #1659C2×C3semidirect
87. #1659C2×C3semidirect
88. #1535C2×C3semidirect
89. #1529C2×C3semidirect
90. #1527C2×C3semidirect
238. #533C22×C3semidirect
242. #501C22×C3semidirect
243. #501C22×C3semidirect
244. #501C22×C3semidirect
246. #497C22×C3semidirect
247. #497C22×C3semidirect
248. #491C22×C3semidirect
250. #489C22×C3semidirect
251. #489C22×C3semidirect
252. #489C22×C3semidirect
253. #489C22×C3semidirect
266. #432C22×C3semidirect
267. #432C22×C3semidirect
268. C4×M16C22×C3semidirect
269. #330C22×C3semidirect
270. #330C22×C3semidirect
271. #330C22×C3semidirect
272. #330C22×C3semidirect
275. #329C22×C3semidirect
276. #329C22×C3semidirect
277. #329C22×C3semidirect
278. #329C22×C3semidirect
279. #329C22×C3semidirect
280. #329C22×C3semidirect
852. C3#19069direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35452
C3×#32402
C3×#32152
C3×#31722
C3×#16642
C3×#16622
C3×#16612
C3×#16602
C3×#16592
C3×#15352
C3×#15292
C3×#15272
#190693