Finite Group Databasebeta

← C3×#19068 #10637675

Subgroups — C3×#19068 #10637675

Order 768.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3545C211yesmaximal, characteristic, complemented
2C3×#3219C211yesmaximal, characteristic, complemented
3C3×#3213C211yesmaximal, characteristic, complemented
4C3×#3171C211yesmaximal, characteristic, complemented
5C3×#1664C211yesmaximal, characteristic, complemented
6C3×#1662C211yesmaximal, characteristic, complemented
7C3×#1661C211yesmaximal, characteristic, complemented
8C3×#1659C211yesmaximal, characteristic, complemented
9C3×#1657C211yesmaximal, characteristic, complemented
10C3×#1656C211yesmaximal, characteristic, complemented
11C3×#1656C211yesmaximal, characteristic, complemented
12C3×#1655C211yesmaximal, characteristic, complemented
13C3×#1535C211yesmaximal, characteristic, complemented
14C3×#1529C211yesmaximal, characteristic, complemented
15C3×#1527C211yesmaximal, characteristic, complemented
16#19068C311yesmaximal, 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×#532C2211yescharacteristic, complemented
34C3×#529C2211yescharacteristic
35C3×#529C2211yescharacteristic
36C2×C3×#124C2211yescharacteristic
37C3×#501C2211yescharacteristic, complemented
38C3×#497C2211yescharacteristic, complemented
39C3×#496C2211yescharacteristic
40C3×#496C2211yescharacteristic, complemented
41C3×#496C2211yescharacteristic, complemented
42C3×#496C2211yescharacteristic, complemented
43C3×#491C2211yescharacteristic, complemented
44C3×#490C2211yescharacteristic, complemented
45C3×#490C2211yescharacteristic, complemented
46C3×#489C2211yescharacteristic
47C3×#489C2211yescharacteristic, complemented
48C3×#489C2211yescharacteristic, complemented
49C3×#469—21no—
50C3×#468—21no—
51C3×#464—21no—
52C3×#463—21no—
53C3×#463—21no—
54C3×#463—21no—
55C3×#452—21no—
56C3×#449—21no—
57C3×#448—21no—
58C3×#447—21no—
59C3×C4×SD16—21no—
60C3×C4×D8—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, complemented
77#3219C2×C311yescharacteristic, complemented
78#3213C2×C311yescharacteristic, complemented
79#3171C2×C311yescharacteristic, complemented
80#1664C2×C311yescharacteristic, complemented
81#1662C2×C311yescharacteristic, complemented
82#1661C2×C311yescharacteristic, complemented
83#1659C2×C311yescharacteristic, complemented
84#1657C2×C311yescharacteristic, complemented
85#1656C2×C311yescharacteristic, complemented
86#1656C2×C311yescharacteristic, complemented
87#1655C2×C311yescharacteristic, complemented
88#1535C2×C311yescharacteristic, complemented
89#1529C2×C311yescharacteristic, complemented
90#1527C2×C311yescharacteristic, complemented
91C2×C3×#41—21no—
92C2×C3×#41—21no—
93C22×C3×Q8D411yescharacteristic
94C22×C3×D4—21no—
95C22×C3×D4D411yescharacteristic
96C2×C3×Q16—21no—
97C2×C3×SD16—21no—
98C2×C3×SD16—21no—
99C2×C3×SD16—21no—
100C2×C3×SD16—21no—
101C2×C3×SD16—21no—
102C2×C3×D8—21no—
103C2×C3×D8—21no—
104C2×C3×D8—21no—
105C2×C3×D8—21no—
106C2×C3×M16—21no—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8C2311yescharacteristic
110C3×#127C2311yescharacteristic
111C3×#126—21no—
112C3×#126—21no—
113C3×#126—21no—
114C3×#126—21no—
115C3×#126—21no—
116C3×#126—21no—
117C3×#125C2311yescharacteristic
118C3×#125C2311yescharacteristic
119C3×#124—21no—
120C3×#124—21no—
121C3×#124—21no—
122C3×#124—21no—
123C3×#124—21no—
124C3×#124—21no—
125C3×#124—21no—
126C3×#124—21no—
127C3×#124—21no—
128C3×#124D411yescharacteristic
129C3×#124D411yescharacteristic
130C3×#124C2311yescharacteristic
131C3×#124C2311yescharacteristic
132C3×#124C2311yescharacteristic
133C3×#124C2311yescharacteristic
134C3×#123—21no—
135C3×#123—21no—
136C3×#123—21no—
137C3×#123—21no—
138C3×#123—21no—
139C3×#123—21no—
140C3×#123—21no—
141C3×#123—21no—
142C3×#123—21no—
143C3×#123—21no—
144C3×#123—21no—
145C3×#123—21no—
146C3×C22⋊Q8—21no—
147C3×C22⋊Q8—21no—
148C3×C22⋊Q8—21no—
149C3×C22⋊Q8—21no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8—21no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8D411yescharacteristic
155C3×C22⋊Q8D411yescharacteristic
156C3×#121—21no—
157C3×#121—21no—
158C3×#121—21no—
159C3×#121—21no—
160C3×#121—21no—
161C3×#121—21no—
162C3×#121—21no—
163C3×#121—21no—
164C3×#121—21no—
165C3×#121—21no—
166C3×#121D411yescharacteristic
167C3×#121D411yescharacteristic
168C3×#120—21no—
169C3×#120—21no—
170C3×#120—21no—
171C3×#120—21no—
172C3×#120—21no—
173C3×#120—21no—
174C3×C4×Q8D411yescharacteristic
175C3×C4×Q8D411yescharacteristic
176C3×C4×D4—21no—
177C3×C4×D4—21no—
178C3×C4×D4—21no—
179C3×C4×D4—21no—
180C3×C4×D4—21no—
181C3×C4×D4—21no—
182C3×C4×D4—21no—
183C3×C4×D4—21no—
184C3×C4×D4D411yescharacteristic
185C3×C4×D4D411yescharacteristic
186C3×#117—21no—
187C3×#117—21no—
188C3×#117—21no—
189C3×#117—21no—
190C3×#117—21no—
191C2×C3×C22⋊C4—21no—
192C2×C3×C22⋊C4—21no—
193C2×C3×C22⋊C4—21no—
194C2×C3×C22⋊C4—21no—
195C2×C3×C22⋊C4—21no—
196C2×C3×C42C2311yescharacteristic
197C3×#107—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×#102—21no—
207C3×#102—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#532C22×C311yescharacteristic, complemented
239#529C22×C311yescharacteristic
240#529C22×C311yescharacteristic
241C2×#124C22×C311yescharacteristic
242#501C22×C311yescharacteristic, complemented
243#497C22×C311yescharacteristic, complemented
244#496C22×C311yescharacteristic
245#496C22×C311yescharacteristic, complemented
246#496C22×C311yescharacteristic, complemented
247#496C22×C311yescharacteristic, complemented
248#491C22×C311yescharacteristic, complemented
249#490C22×C311yescharacteristic, complemented
250#490C22×C311yescharacteristic, complemented
251#489C22×C311yescharacteristic
252#489C22×C311yescharacteristic, complemented
253#489C22×C311yescharacteristic, complemented
254#469—21no—
255#468—21no—
256#464—21no—
257#463—21no—
258#463—21no—
259#463—21no—
260#452—21no—
261#449—21no—
262#448—21no—
263#447—21no—
264C4×SD16—21no—
265C4×D8—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—
284C3×#41—81no—
285C3×#41—81no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—81no—
290C2×C3×Q8C2×D411yescharacteristic
291C2×C3×Q8C2×D411yescharacteristic
292C2×C3×Q8C2×D411yescharacteristic
293C2×C3×Q8C2×D411yescharacteristic
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—21no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—41no—
308C2×C3×D4—81no—
309C2×C3×D4—82no—
310C2×C3×D4C2×D411yescharacteristic
311C2×C3×D4C2×D411yescharacteristic
312C2×C3×D4C2×D411yescharacteristic
313C2×C3×D4C2×D411yescharacteristic
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—41no—
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C3×Q16—81no—
327C3×SD16—42no—
328C3×SD16—81no—
329C3×SD16—81no—
330C3×SD16—81no—
331C3×SD16—81no—
332C3×D8—42no—
333C3×D8—81no—
334C3×D8—81no—
335C3×D8—81no—
336C3×M16—42no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—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—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4C2×D411yescharacteristic
360C3×C4⋊C4C2×D411yescharacteristic
361C3×C4⋊C4C2×D411yescharacteristic
362C3×C4⋊C4C2×D411yescharacteristic
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—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—41no—
392C3×C22⋊C4—41no—
393C3×C42—21no—
394C3×C42—21no—
395C3×C42—21no—
396C3×C42—21no—
397C3×C42C2×D411yescharacteristic
398C3×C42C2×D411yescharacteristic
399C3×C42C2×D411yescharacteristic
400C3×C42C2411yescharacteristic
401C2×#41—21no—
402C2×#41—21no—
403C22×Q8C3×D411yescharacteristic
404C22×D4—21no—
405C22×D4C3×D411yescharacteristic
406C2×Q16—21no—
407C2×SD16—21no—
408C2×SD16—21no—
409C2×SD16—21no—
410C2×SD16—21no—
411C2×SD16—21no—
412C2×D8—21no—
413C2×D8—21no—
414C2×D8—21no—
415C2×D8—21no—
416C2×M16—21no—
417C4⋊Q8—21no—
418C4⋊Q8—21no—
419C4⋊Q8C23×C311yescharacteristic
420#127C23×C311yescharacteristic
421#126—21no—
422#126—21no—
423#126—21no—
424#126—21no—
425#126—21no—
426#126—21no—
427#125C23×C311yescharacteristic
428#125C23×C311yescharacteristic
429#124—21no—
430#124—21no—
431#124—21no—
432#124—21no—
433#124—21no—
434#124—21no—
435#124—21no—
436#124—21no—
437#124—21no—
438#124C3×D411yescharacteristic
439#124C3×D411yescharacteristic
440#124C23×C311yescharacteristic
441#124C23×C311yescharacteristic
442#124C23×C311yescharacteristic
443#124C23×C311yescharacteristic
444#123—21no—
445#123—21no—
446#123—21no—
447#123—21no—
448#123—21no—
449#123—21no—
450#123—21no—
451#123—21no—
452#123—21no—
453#123—21no—
454#123—21no—
455#123—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8—21no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—21no—
462C22⋊Q8—21no—
463C22⋊Q8—21no—
464C22⋊Q8C3×D411yescharacteristic
465C22⋊Q8C3×D411yescharacteristic
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—21no—
471#121—21no—
472#121—21no—
473#121—21no—
474#121—21no—
475#121—21no—
476#121C3×D411yescharacteristic
477#121C3×D411yescharacteristic
478#120—21no—
479#120—21no—
480#120—21no—
481#120—21no—
482#120—21no—
483#120—21no—
484C4×Q8C3×D411yescharacteristic
485C4×Q8C3×D411yescharacteristic
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4C3×D411yescharacteristic
495C4×D4C3×D411yescharacteristic
496#117—21no—
497#117—21no—
498#117—21no—
499#117—21no—
500#117—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C42C23×C311yescharacteristic
507#107—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511#103—21no—
512#103—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#102—21no—
517#102—21no—
518#102—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522#102—21no—
523C22⋊C8—21no—
524C22⋊C8—21no—
525#97C23×C311yescharacteristic
526#97C23×C311yescharacteristic
527#97C23×C311yescharacteristic
528#97C23×C311yescharacteristic
529#97C23×C311yescharacteristic
530#97C23×C311yescharacteristic
531C4×C8—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—42no—
537C23×C3—41no—
538C23×C3—81no—
539C23×C3—81no—
540C23×C3—81no—
541C23×C3—81no—
542C23×C3—81no—
543C23×C3#12011yescharacteristic
544C3×Q8—41no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—41no—
548C3×Q8—41no—
549C3×Q8—41no—
550C3×Q8—81no—
551C3×Q8—81no—
552C3×D4—41no—
553C3×D4—41no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—41no—
557C3×D4—41no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—41no—
561C3×D4—41no—
562C3×D4—42no—
563C3×D4—42no—
564C3×D4—81no—
565C3×D4—81no—
566C3×D4—81no—
567C3×D4—81no—
568C3×D4—81no—
569C3×D4—81no—
570C3×D4—81no—
571C3×D4—81no—
572C3×D4—82no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—42no—
585C2×C3×C4—41no—
586C2×C3×C4—81no—
587C2×C3×C4—81no—
588C2×C3×C4—82no—
589C2×C3×C4—81no—
590C2×C3×C4—81no—
591C2×C3×C4—81no—
592C2×C3×C4—81no—
593C2×C3×C4—81no—
594C2×C3×C4#12011yescharacteristic
595C2×C3×C4#12011yescharacteristic
596C2×C3×C4#12011yescharacteristic
597C2×C3×C4C22×D411yescharacteristic
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C3×C8—22no—
601C3×C8—41no—
602C3×C8—41no—
603C3×C8—41no—
604C3×C8—41no—
605C3×C8—41no—
606C24—21no—
607C24—21no—
608#41—82no—
609#41—81no—
610#41—81no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—81no—
615C2×Q8C2×C3×D411yescharacteristic
616C2×Q8C2×C3×D411yescharacteristic
617C2×Q8C2×C3×D411yescharacteristic
618C2×Q8C2×C3×D411yescharacteristic
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—41no—
633C2×D4—81no—
634C2×D4—82no—
635C2×D4C2×C3×D411yescharacteristic
636C2×D4C2×C3×D411yescharacteristic
637C2×D4C2×C3×D411yescharacteristic
638C2×D4C2×C3×D411yescharacteristic
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—41no—
648C22×C4C2×C3×D411yescharacteristic
649C22×C4C2×C3×D411yescharacteristic
650C22×C4C2×C3×D411yescharacteristic
651Q16—81no—
652SD16—42no—
653SD16—81no—
654SD16—81no—
655SD16—81no—
656SD16—81no—
657D8—42no—
658D8—81no—
659D8—81no—
660D8—81no—
661M16—42no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4C2×C3×D411yescharacteristic
685C4⋊C4C2×C3×D411yescharacteristic
686C4⋊C4C2×C3×D411yescharacteristic
687C4⋊C4C2×C3×D411yescharacteristic
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—21no—
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—41no—
717C22⋊C4—41no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42C2×C3×D411yescharacteristic
723C42C2×C3×D411yescharacteristic
724C42C2×C3×D411yescharacteristic
725C42C24×C311yescharacteristic
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—162no—
745C22×C3—162no—
746C22×C3C2×#12011yescharacteristic
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—41no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—81no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—42no—
767C23—41no—
768C23—81no—
769C23—81no—
770C23—81no—
771C23—81no—
772C23—81no—
773C23C3×#12011yescharacteristic
774Q8—41no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—81no—
781Q8—81no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—42no—
793D4—42no—
794D4—81no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—82no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—82no—
819C2×C4—81no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—81no—
823C2×C4—81no—
824C2×C4C3×#12011yescharacteristic
825C2×C4C3×#12011yescharacteristic
826C2×C4C3×#12011yescharacteristic
827C2×C4C22×C3×D411yescharacteristic
828C2×C4C22×C3×D411yescharacteristic
829C2×C4C22×C3×D411yescharacteristic
830C8—22no—
831C8—41no—
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C2×C3—41no—
837C2×C3—81no—
838C2×C3—81no—
839C2×C3—81no—
840C2×C3—81no—
841C2×C3—161no—
842C2×C3#301811yescharacteristic
843C2×C3#301911yescharacteristic
844C2×C3#302111yescharacteristic
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—162no—
864C22—162no—
865C22C2×C3×#12011yescharacteristic
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—81no—
881C3#1906811yescharacteristic, direct product factor, Sylow
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C3×#301811yescharacteristic
889C2C3×#301911yescharacteristic
890C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC42C24×C3
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
1. C3×#3545C2semidirect
2. C3×#3219C2semidirect
3. C3×#3213C2semidirect
4. C3×#3171C2semidirect
5. C3×#1664C2semidirect
6. C3×#1662C2semidirect
7. C3×#1661C2semidirect
8. C3×#1659C2semidirect
9. C3×#1657C2semidirect
10. C3×#1656C2semidirect
11. C3×#1656C2semidirect
12. C3×#1655C2semidirect
13. C3×#1535C2semidirect
14. C3×#1529C2semidirect
15. C3×#1527C2semidirect
16. #19068C3direct (N × H)
33. C3×#532C22semidirect
37. C3×#501C22semidirect
38. C3×#497C22semidirect
40. C3×#496C22semidirect
41. C3×#496C22semidirect
42. C3×#496C22semidirect
43. C3×#491C22semidirect
44. C3×#490C22semidirect
45. C3×#490C22semidirect
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
76. #3545C2×C3semidirect
77. #3219C2×C3semidirect
78. #3213C2×C3semidirect
79. #3171C2×C3semidirect
80. #1664C2×C3semidirect
81. #1662C2×C3semidirect
82. #1661C2×C3semidirect
83. #1659C2×C3semidirect
84. #1657C2×C3semidirect
85. #1656C2×C3semidirect
86. #1656C2×C3semidirect
87. #1655C2×C3semidirect
88. #1535C2×C3semidirect
89. #1529C2×C3semidirect
90. #1527C2×C3semidirect
238. #532C22×C3semidirect
242. #501C22×C3semidirect
243. #497C22×C3semidirect
245. #496C22×C3semidirect
246. #496C22×C3semidirect
247. #496C22×C3semidirect
248. #491C22×C3semidirect
249. #490C22×C3semidirect
250. #490C22×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
881. C3#19068direct (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×#32192
C3×#32132
C3×#31712
C3×#16642
C3×#16622
C3×#16612
C3×#16592
C3×#16572
C3×#16562
C3×#16552
C3×#15352
C3×#15292
C3×#15272
#190683