Finite Group Databasebeta

← C3×#19070 #10637677

Subgroups — C3×#19070 #10637677

Order 768.

844 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3553C211yesmaximal, characteristic, complemented
2C3×#3234C211yesmaximal, characteristic, complemented
3C3×#3219C211yesmaximal, characteristic, complemented
4C3×#3171C211yesmaximal, characteristic, complemented
5C3×#1664C211yesmaximal, characteristic, complemented
6C3×#1663C211yesmaximal, characteristic, complemented
7C3×#1661C211yesmaximal, characteristic, complemented
8C3×#1660C211yesmaximal, characteristic, complemented
9C3×#1658C211yesmaximal, characteristic, complemented
10C3×#1657C211yesmaximal, characteristic, complemented
11C3×#1657C211yesmaximal, characteristic, complemented
12C3×#1656C211yesmaximal, characteristic, complemented
13C3×#1535C211yesmaximal, characteristic, complemented
14C3×#1529C211yesmaximal, characteristic, complemented
15C3×#1528C211yesmaximal, characteristic, complemented
16#19070C311yesmaximal, characteristic, direct product factor, Sylow
17C3×#564C2211yescharacteristic
18C3×#563C2211yescharacteristic
19C3×#563C2211yescharacteristic
20C3×#562C2211yescharacteristic
21C3×#554—21no—
22C3×#554—21no—
23C3×#553—21no—
24C3×#553—21no—
25C3×#552—21no—
26C3×#552—21no—
27C3×#541—21no—
28C3×#541—21no—
29C3×#539—21no—
30C3×#539—21no—
31C3×#539—21no—
32C3×#539—21no—
33C3×#532C2211yescharacteristic
34C3×#529C2211yescharacteristic
35C3×#529C2211yescharacteristic
36C2×C3×#125C2211yescharacteristic
37C3×#501C2211yescharacteristic
38C3×#501C2211yescharacteristic
39C3×#501C2211yescharacteristic
40C3×#497C2211yescharacteristic
41C3×#496C2211yescharacteristic
42C3×#496C2211yescharacteristic
43C3×#491C2211yescharacteristic
44C3×#490C2211yescharacteristic
45C3×#490C2211yescharacteristic
46C3×#490C2211yescharacteristic
47C3×#490C2211yescharacteristic
48C3×#489C2211yescharacteristic
49C3×#481—21no—
50C3×#480—21no—
51C3×#478—21no—
52C3×#478—21no—
53C3×#469—21no—
54C3×#468—21no—
55C3×#464—21no—
56C3×#463—21no—
57C3×#452—21no—
58C3×#449—21no—
59C3×C4×SD16—21no—
60C3×C4×D8—21no—
61C3×#432C2211yescharacteristic
62C3×#432C2211yescharacteristic
63C3×C4×M16C2211yescharacteristic
64C3×#330C2211yescharacteristic
65C3×#330C2211yescharacteristic
66C3×#330C2211yescharacteristic
67C3×#330C2211yescharacteristic
68C3×#330C2211yescharacteristic
69C3×#330C2211yescharacteristic
70C3×#330C2211yescharacteristic
71C3×#330C2211yescharacteristic
72C3×#329C2211yescharacteristic
73C3×#329C2211yescharacteristic
74C3×#329C2211yescharacteristic
75C3×#329C2211yescharacteristic
76#3553C2×C311yescharacteristic, complemented
77#3234C2×C311yescharacteristic, complemented
78#3219C2×C311yescharacteristic, complemented
79#3171C2×C311yescharacteristic, complemented
80#1664C2×C311yescharacteristic, complemented
81#1663C2×C311yescharacteristic, complemented
82#1661C2×C311yescharacteristic, complemented
83#1660C2×C311yescharacteristic, complemented
84#1658C2×C311yescharacteristic, complemented
85#1657C2×C311yescharacteristic, complemented
86#1657C2×C311yescharacteristic, complemented
87#1656C2×C311yescharacteristic, complemented
88#1535C2×C311yescharacteristic, complemented
89#1529C2×C311yescharacteristic, complemented
90#1528C2×C311yescharacteristic, complemented
91C2×C3×#41—21no—
92C2×C3×Q16—21no—
93C2×C3×SD16—21no—
94C2×C3×SD16—21no—
95C2×C3×SD16—21no—
96C2×C3×D8—21no—
97C2×C3×D8—21no—
98C2×C3×M16—21no—
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8C2311yescharacteristic
102C3×#127C2311yescharacteristic
103C3×#126—21no—
104C3×#126—21no—
105C3×#126—21no—
106C3×#126—21no—
107C3×#126—21no—
108C3×#126—21no—
109C3×#126—21no—
110C3×#126—21no—
111C3×#126—21no—
112C3×#126—21no—
113C3×#125—21no—
114C3×#125—21no—
115C3×#125—21no—
116C3×#125—21no—
117C3×#125—21no—
118C3×#125—21no—
119C3×#125—21no—
120C3×#125—21no—
121C3×#125—21no—
122C3×#125—21no—
123C3×#125—21no—
124C3×#125—21no—
125C3×#125D411yescharacteristic
126C3×#125D411yescharacteristic
127C3×#125C2311yescharacteristic
128C3×#125C2311yescharacteristic
129C3×#125C2311yescharacteristic
130C3×#125C2311yescharacteristic
131C3×#124—21no—
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×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⋊Q8—21no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—21no—
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8D411yescharacteristic
157C3×C22⋊Q8D411yescharacteristic
158C3×#121—21no—
159C3×#121—21no—
160C3×#121—21no—
161C3×#121—21no—
162C3×#121—21no—
163C3×#121—21no—
164C3×#121D411yescharacteristic
165C3×#121D411yescharacteristic
166C3×C4×Q8—21no—
167C3×C4×Q8—21no—
168C3×C4×Q8D411yescharacteristic
169C3×C4×Q8D411yescharacteristic
170C3×C4×D4—21no—
171C3×C4×D4—21no—
172C3×C4×D4—21no—
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×D4—21no—
180C3×C4×D4D411yescharacteristic
181C3×C4×D4D411yescharacteristic
182C3×#117—21no—
183C3×#117—21no—
184C3×#117—21no—
185C3×#117—21no—
186C2×C3×C4⋊C4—21no—
187C2×C3×C4⋊C4—21no—
188C2×C3×C4⋊C4—21no—
189C2×C3×C4⋊C4—21no—
190C2×C3×C4⋊C4D411yescharacteristic
191C2×C3×C4⋊C4D411yescharacteristic
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×#102—21no—
205C3×#102—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#564C22×C311yescharacteristic
223#563C22×C311yescharacteristic
224#563C22×C311yescharacteristic
225#562C22×C311yescharacteristic
226#554—21no—
227#554—21no—
228#553—21no—
229#553—21no—
230#552—21no—
231#552—21no—
232#541—21no—
233#541—21no—
234#539—21no—
235#539—21no—
236#539—21no—
237#539—21no—
238#532C22×C311yescharacteristic
239#529C22×C311yescharacteristic
240#529C22×C311yescharacteristic
241C2×#125C22×C311yescharacteristic
242#501C22×C311yescharacteristic
243#501C22×C311yescharacteristic
244#501C22×C311yescharacteristic
245#497C22×C311yescharacteristic
246#496C22×C311yescharacteristic
247#496C22×C311yescharacteristic
248#491C22×C311yescharacteristic
249#490C22×C311yescharacteristic
250#490C22×C311yescharacteristic
251#490C22×C311yescharacteristic
252#490C22×C311yescharacteristic
253#489C22×C311yescharacteristic
254#481—21no—
255#480—21no—
256#478—21no—
257#478—21no—
258#469—21no—
259#468—21no—
260#464—21no—
261#463—21no—
262#452—21no—
263#449—21no—
264C4×SD16—21no—
265C4×D8—21no—
266#432C22×C311yescharacteristic
267#432C22×C311yescharacteristic
268C4×M16C22×C311yescharacteristic
269#330C22×C311yescharacteristic
270#330C22×C311yescharacteristic
271#330C22×C311yescharacteristic
272#330C22×C311yescharacteristic
273#330C22×C311yescharacteristic
274#330C22×C311yescharacteristic
275#330C22×C311yescharacteristic
276#330C22×C311yescharacteristic
277#329C22×C311yescharacteristic
278#329C22×C311yescharacteristic
279#329C22×C311yescharacteristic
280#329C22×C311yescharacteristic
281C3×#41—81no—
282C3×#41—81no—
283C2×C3×Q8—21no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8C2×D411yescharacteristic
287C2×C3×Q8C2×D411yescharacteristic
288C2×C3×D4—21no—
289C2×C3×D4—21no—
290C2×C3×D4—21no—
291C2×C3×D4—21no—
292C2×C3×D4—21no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—41no—
296C2×C3×D4C2×D411yescharacteristic
297C2×C3×D4C2×D411yescharacteristic
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—41no—
307C22×C3×C4C2×D411yescharacteristic
308C22×C3×C4C2×D411yescharacteristic
309C22×C3×C4C2×D411yescharacteristic
310C3×Q16—81no—
311C3×SD16—42no—
312C3×SD16—81no—
313C3×SD16—81no—
314C3×D8—42no—
315C3×D8—81no—
316C3×M16—42no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—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—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4C2×D411yescharacteristic
356C3×C4⋊C4C2×D411yescharacteristic
357C3×C4⋊C4C2×D411yescharacteristic
358C3×C4⋊C4C2×D411yescharacteristic
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—41no—
382C3×C22⋊C4—41no—
383C3×C42—21no—
384C3×C42—21no—
385C3×C42—21no—
386C3×C42—21no—
387C3×C42—21no—
388C3×C42—21no—
389C3×C42C2×D411yescharacteristic
390C3×C42C2×D411yescharacteristic
391C3×C42C2×D411yescharacteristic
392C3×C42C2411yescharacteristic
393C2×#41—21no—
394C2×Q16—21no—
395C2×SD16—21no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×D8—21no—
399C2×D8—21no—
400C2×M16—21no—
401C4⋊Q8—21no—
402C4⋊Q8—21no—
403C4⋊Q8C23×C311yescharacteristic
404#127C23×C311yescharacteristic
405#126—21no—
406#126—21no—
407#126—21no—
408#126—21no—
409#126—21no—
410#126—21no—
411#126—21no—
412#126—21no—
413#126—21no—
414#126—21no—
415#125—21no—
416#125—21no—
417#125—21no—
418#125—21no—
419#125—21no—
420#125—21no—
421#125—21no—
422#125—21no—
423#125—21no—
424#125—21no—
425#125—21no—
426#125—21no—
427#125C3×D411yescharacteristic
428#125C3×D411yescharacteristic
429#125C23×C311yescharacteristic
430#125C23×C311yescharacteristic
431#125C23×C311yescharacteristic
432#125C23×C311yescharacteristic
433#124—21no—
434#124C23×C311yescharacteristic
435#124C23×C311yescharacteristic
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—
445#123—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⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8—21no—
458C22⋊Q8C3×D411yescharacteristic
459C22⋊Q8C3×D411yescharacteristic
460#121—21no—
461#121—21no—
462#121—21no—
463#121—21no—
464#121—21no—
465#121—21no—
466#121C3×D411yescharacteristic
467#121C3×D411yescharacteristic
468C4×Q8—21no—
469C4×Q8—21no—
470C4×Q8C3×D411yescharacteristic
471C4×Q8C3×D411yescharacteristic
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—21no—
478C4×D4—21no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4C3×D411yescharacteristic
483C4×D4C3×D411yescharacteristic
484#117—21no—
485#117—21no—
486#117—21no—
487#117—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4C3×D411yescharacteristic
493C2×C4⋊C4C3×D411yescharacteristic
494C2×C42C23×C311yescharacteristic
495#107—21no—
496#107—21no—
497#107—21no—
498#106—21no—
499#106—21no—
500#106—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503#103—21no—
504#103—21no—
505#103—21no—
506#102—21no—
507#102—21no—
508#102—21no—
509#102—21no—
510#102—21no—
511#102—21no—
512#102—21no—
513#102—21no—
514#102—21no—
515C22⋊C8—21no—
516C22⋊C8—21no—
517#97C23×C311yescharacteristic
518#97C23×C311yescharacteristic
519#97C23×C311yescharacteristic
520#97C23×C311yescharacteristic
521#97C23×C311yescharacteristic
522#97C23×C311yescharacteristic
523C4×C8—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—41no—
527C23×C3#12011yescharacteristic
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—41no—
531C3×Q8—41no—
532C3×Q8—81no—
533C3×Q8—81no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—41no—
537C3×D4—41no—
538C3×D4—41no—
539C3×D4—41no—
540C3×D4—42no—
541C3×D4—42no—
542C3×D4—42no—
543C3×D4—81no—
544C3×D4—81no—
545C3×D4—82no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—41no—
557C2×C3×C4—41no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—81no—
561C2×C3×C4—81no—
562C2×C3×C4—82no—
563C2×C3×C4—81no—
564C2×C3×C4—81no—
565C2×C3×C4—81no—
566C2×C3×C4—81no—
567C2×C3×C4—81no—
568C2×C3×C4—81no—
569C2×C3×C4#12011yescharacteristic
570C2×C3×C4#12011yescharacteristic
571C2×C3×C4#12011yescharacteristic
572C2×C3×C4C22×D411yescharacteristic
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4C22×D411yescharacteristic
575C3×C8—22no—
576C3×C8—41no—
577C3×C8—41no—
578C3×C8—41no—
579C3×C8—41no—
580C3×C8—41no—
581#41—81no—
582#41—81no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×C3×D411yescharacteristic
587C2×Q8C2×C3×D411yescharacteristic
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—41no—
596C2×D4C2×C3×D411yescharacteristic
597C2×D4C2×C3×D411yescharacteristic
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—41no—
607C22×C4C2×C3×D411yescharacteristic
608C22×C4C2×C3×D411yescharacteristic
609C22×C4C2×C3×D411yescharacteristic
610Q16—81no—
611SD16—42no—
612SD16—81no—
613SD16—81no—
614D8—42no—
615D8—81no—
616M16—42no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—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⋊C4C2×C3×D411yescharacteristic
656C4⋊C4C2×C3×D411yescharacteristic
657C4⋊C4C2×C3×D411yescharacteristic
658C4⋊C4C2×C3×D411yescharacteristic
659C4⋊C4C2×C3×D411yescharacteristic
660C4⋊C4C2×C3×D411yescharacteristic
661C4⋊C4C2×C3×D411yescharacteristic
662C4⋊C4C2×C3×D411yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
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—41no—
682C22⋊C4—41no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42C2×C3×D411yescharacteristic
690C42C2×C3×D411yescharacteristic
691C42C2×C3×D411yescharacteristic
692C42C24×C311yescharacteristic
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3C2×#12011yescharacteristic
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—41no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—81no—
723C23—21no—
724C23—21no—
725C23—41no—
726C23C3×#12011yescharacteristic
727Q8—41no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—81no—
732Q8—81no—
733D4—41no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—81no—
743D4—81no—
744D4—82no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—81no—
760C2×C4—81no—
761C2×C4—82no—
762C2×C4—81no—
763C2×C4—81no—
764C2×C4—81no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4C3×#12011yescharacteristic
769C2×C4C3×#12011yescharacteristic
770C2×C4C3×#12011yescharacteristic
771C2×C4C22×C3×D411yescharacteristic
772C2×C4C22×C3×D411yescharacteristic
773C2×C4C22×C3×D411yescharacteristic
774C8—22no—
775C8—41no—
776C8—41no—
777C8—41no—
778C8—41no—
779C8—41no—
780C2×C3—41no—
781C2×C3—81no—
782C2×C3—81no—
783C2×C3—161no—
784C2×C3#301811yescharacteristic
785C2×C3#302011yescharacteristic
786C2×C3#302111yescharacteristic
787C22—21no—
788C22—21no—
789C22—21no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22C2×C3×#12011yescharacteristic
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—81no—
817C3#1907011yescharacteristic, direct product factor, Sylow
818C2—41no—
819C2—81no—
820C2—81no—
821C2—161no—
822C2C3×#301811yescharacteristic
823C2C3×#302011yescharacteristic
824C2C3×#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×#3553C2semidirect
2. C3×#3234C2semidirect
3. C3×#3219C2semidirect
4. C3×#3171C2semidirect
5. C3×#1664C2semidirect
6. C3×#1663C2semidirect
7. C3×#1661C2semidirect
8. C3×#1660C2semidirect
9. C3×#1658C2semidirect
10. C3×#1657C2semidirect
11. C3×#1657C2semidirect
12. C3×#1656C2semidirect
13. C3×#1535C2semidirect
14. C3×#1529C2semidirect
15. C3×#1528C2semidirect
16. #19070C3direct (N × H)
76. #3553C2×C3semidirect
77. #3234C2×C3semidirect
78. #3219C2×C3semidirect
79. #3171C2×C3semidirect
80. #1664C2×C3semidirect
81. #1663C2×C3semidirect
82. #1661C2×C3semidirect
83. #1660C2×C3semidirect
84. #1658C2×C3semidirect
85. #1657C2×C3semidirect
86. #1657C2×C3semidirect
87. #1656C2×C3semidirect
88. #1535C2×C3semidirect
89. #1529C2×C3semidirect
90. #1528C2×C3semidirect
817. C3#19070direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35532
C3×#32342
C3×#32192
C3×#31712
C3×#16642
C3×#16632
C3×#16612
C3×#16602
C3×#16582
C3×#16572
C3×#16562
C3×#15352
C3×#15292
C3×#15282
#190703