Finite Group Databasebeta

← C3×#23956 #10642563

Subgroups — C3×#23956 #10642563

Order 768.

1284 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic, complemented
2C3×#3005C211yesmaximal, characteristic, complemented
3C3×#2896C211yesmaximal, characteristic, complemented
4C3×#2431C211yesmaximal, characteristic, complemented
5C3×#2028C211yesmaximal, characteristic, complemented
6C3×#2027C211yesmaximal, characteristic, complemented
7C3×#2004C211yesmaximal, characteristic, complemented
8C3×#2002C211yesmaximal, characteristic, complemented
9C3×#1900C211yesmaximal, characteristic, complemented
10C3×#1887C211yesmaximal, characteristic, complemented
11C3×#1885C211yesmaximal, characteristic, complemented
12C3×#1883C211yesmaximal, characteristic, complemented
13C3×#1882C211yesmaximal, characteristic, complemented
14C3×#1871C211yesmaximal, characteristic, complemented
15C3×#1826C211yesmaximal, characteristic, complemented
16#23956C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C22×C3×M16C2211yescharacteristic
21C3×#555—21no—
22C3×#553—21no—
23C3×#553—21no—
24C3×#551—22no—
25C3×#547—21no—
26C3×#546—22no—
27C3×#544C2211yescharacteristic
28C3×#542—21no—
29C3×#540—21no—
30C3×#535C2211yescharacteristic
31C3×#532—21no—
32C2×C3×#127C2211yescharacteristic
33C3×#529—21no—
34C2×C3×#124C2211yescharacteristic
35C3×#525C2211yescharacteristic
36C2×C3×#121C2211yescharacteristic
37C3×#520C2211yescharacteristic
38C3×#518C2211yescharacteristic
39C2×C3×#117C2211yescharacteristic
40C3×#452—21no—
41C3×#452—21no—
42C3×#449—21no—
43C3×#449—21no—
44C2×C3×#104C2211yescharacteristic
45C2×C3×#104C2211yescharacteristic
46C3×#419C2211yescharacteristic
47C3×#419C2211yescharacteristic
48C3×#419C2211yescharacteristic
49C3×#418C2211yescharacteristic
50C3×#418C2211yescharacteristic
51C3×#418C2211yescharacteristic
52C3×#417—21no—
53C3×#417—21no—
54C3×#416—21no—
55C3×#416—21no—
56C2×C3×#100C2211yescharacteristic
57C2×C3×#100C2211yescharacteristic
58C3×#407C2211yescharacteristic
59C3×#392—22no—
60C3×#391C2211yescharacteristic
61C3×#390C2211yescharacteristic
62C3×#386—22no—
63C3×C4×C22⋊C4C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3494C2×C311yescharacteristic, complemented
73#3005C2×C311yescharacteristic, complemented
74#2896C2×C311yescharacteristic, complemented
75#2431C2×C311yescharacteristic, complemented
76#2028C2×C311yescharacteristic, complemented
77#2027C2×C311yescharacteristic, complemented
78#2004C2×C311yescharacteristic, complemented
79#2002C2×C311yescharacteristic, complemented
80#1900C2×C311yescharacteristic, complemented
81#1887C2×C311yescharacteristic, complemented
82#1885C2×C311yescharacteristic, complemented
83#1883C2×C311yescharacteristic, complemented
84#1882C2×C311yescharacteristic, complemented
85#1871C2×C311yescharacteristic, complemented
86#1826C2×C311yescharacteristic, complemented
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—22no—
90C2×C3×#41—21no—
91C2×C3×#41—21no—
92C2×C3×#41—21no—
93C2×C3×#41—21no—
94C2×C3×#41—41no—
95C2×C3×#41—41no—
96C2×C3×#41C2311yescharacteristic
97C22×C3×Q8C2311yescharacteristic
98C22×C3×D4—21no—
99C22×C3×D4—22no—
100C22×C3×D4D412yes—
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C3×#137—22no—
106C3×#137—41no—
107C3×AGL(1,ℤ/8)—22no—
108C3×AGL(1,ℤ/8)—41no—
109C2×C3×Q16—21no—
110C2×C3×SD16—21no—
111C2×C3×SD16—21no—
112C2×C3×D8—21no—
113C2×C3×M16—21no—
114C2×C3×M16—41no—
115C2×C3×M16—41no—
116C2×C3×M16C2311yescharacteristic
117C2×C3×M16C2311yescharacteristic
118C2×C3×M16C2311yescharacteristic
119C2×C3×M16C2311yescharacteristic
120C22×C3×C8—21no—
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8—21no—
123C3×#127—21no—
124C3×#127—22no—
125C3×#127—41no—
126C3×#126—22no—
127C3×#126—22no—
128C3×#125—21no—
129C3×#125—21no—
130C3×#124—22no—
131C3×#124—22no—
132C3×#124—21no—
133C3×#124—22no—
134C3×#124—41no—
135C3×#123—22no—
136C3×#123—22no—
137C3×#123—22no—
138C3×#123—22no—
139C3×#123—21no—
140C3×C22⋊Q8—22no—
141C3×C22⋊Q8—22no—
142C3×C22⋊Q8D411yescharacteristic, complemented
143C3×C22⋊Q8D411yescharacteristic, complemented
144C3×#121—22no—
145C3×#121—22no—
146C3×#121—22no—
147C3×#121—21no—
148C3×#121—21no—
149C3×#121—21no—
150C3×#121—21no—
151C3×#121—21no—
152C3×#121—21no—
153C3×#121D411yescharacteristic, complemented
154C3×#121D411yescharacteristic, complemented
155C3×#120—21no—
156C3×#120—22no—
157C3×C4×Q8—21no—
158C3×C4×D4—22no—
159C3×C4×D4—22no—
160C3×C4×D4—21no—
161C3×C4×D4—22no—
162C3×C4×D4—21no—
163C3×C4×D4—21no—
164C3×C4×D4—21no—
165C3×C4×D4—21no—
166C3×C4×D4—21no—
167C3×C4×D4—21no—
168C3×#117—22no—
169C3×#117—21no—
170C3×#117—21no—
171C3×#117—21no—
172C3×#117D411yescharacteristic, complemented
173C3×#117D411yescharacteristic, complemented
174C3×#117C2311yescharacteristic
175C3×#117C2311yescharacteristic
176C3×#117C2311yescharacteristic
177C2×C3×C4⋊C4—21no—
178C2×C3×C4⋊C4D411yescharacteristic, complemented
179C2×C3×C4⋊C4D411yescharacteristic, complemented
180C2×C3×C4⋊C4C2311yescharacteristic
181C2×C3×C22⋊C4—21no—
182C2×C3×C22⋊C4—22no—
183C2×C3×C22⋊C4—21no—
184C2×C3×C22⋊C4—22no—
185C2×C3×C22⋊C4—22no—
186C2×C3×C22⋊C4D412yes—
187C2×C3×C42—21no—
188C2×C3×C42C2311yescharacteristic
189C2×C3×C42C2311yescharacteristic
190C3×#104—41no—
191C3×#104—41no—
192C3×#103—21no—
193C3×#103—21no—
194C3×#103—21no—
195C3×#103—21no—
196C3×#103—21no—
197C3×#103—21no—
198C3×#102—21no—
199C3×#102—21no—
200C3×#102—21no—
201C3×#102—21no—
202C3×#102—21no—
203C3×#102—21no—
204C3×#100—41no—
205C3×#100—41no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—21no—
208C3×#95—21no—
209C3×#95—22no—
210C22×#41C22×C311yescharacteristic
211C2×#137C22×C311yescharacteristic
212C2×AGL(1,ℤ/8)C22×C311yescharacteristic
213C22×M16C22×C311yescharacteristic
214#555—21no—
215#553—21no—
216#553—21no—
217#551—22no—
218#547—21no—
219#546—22no—
220#544C22×C311yescharacteristic
221#542—21no—
222#540—21no—
223#535C22×C311yescharacteristic
224#532—21no—
225C2×#127C22×C311yescharacteristic
226#529—21no—
227C2×#124C22×C311yescharacteristic
228#525C22×C311yescharacteristic
229C2×#121C22×C311yescharacteristic
230#520C22×C311yescharacteristic
231#518C22×C311yescharacteristic
232C2×#117C22×C311yescharacteristic
233#452—21no—
234#452—21no—
235#449—21no—
236#449—21no—
237C2×#104C22×C311yescharacteristic
238C2×#104C22×C311yescharacteristic
239#419C22×C311yescharacteristic
240#419C22×C311yescharacteristic
241#419C22×C311yescharacteristic
242#418C22×C311yescharacteristic
243#418C22×C311yescharacteristic
244#418C22×C311yescharacteristic
245#417—21no—
246#417—21no—
247#416—21no—
248#416—21no—
249C2×#100C22×C311yescharacteristic
250C2×#100C22×C311yescharacteristic
251#407C22×C311yescharacteristic
252#392—22no—
253#391C22×C311yescharacteristic
254#390C22×C311yescharacteristic
255#386—22no—
256C4×C22⋊C4C22×C311yescharacteristic
257#343C22×C311yescharacteristic
258#343C22×C311yescharacteristic
259#339C22×C311yescharacteristic
260#339C22×C311yescharacteristic
261#339C22×C311yescharacteristic
262#339C22×C311yescharacteristic
263#339C22×C311yescharacteristic
264#339C22×C311yescharacteristic
265C24×C3—21no—
266C24×C3C2×D412yes—
267C24×C3C2×D411yescharacteristic
268C3×#41—24no—
269C3×#41—24no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—21no—
274C3×#41—42no—
275C3×#41—42no—
276C3×#41—42no—
277C3×#41—42no—
278C3×#41—42no—
279C3×#41—42no—
280C3×#41—84no—
281C2×C3×Q8—22no—
282C2×C3×Q8—21no—
283C2×C3×Q8—21no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8C2×D411yescharacteristic
288C2×C3×Q8#4112yescomplemented
289C2×C3×D4—21no—
290C2×C3×D4—22no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4—22no—
294C2×C3×D4—21no—
295C2×C3×D4—22no—
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—42no—
308C2×C3×D4—44no—
309C2×C3×D4—42no—
310C2×C3×D4—41no—
311C2×C3×D4—41no—
312C2×C3×D4—44no—
313C2×C3×D4—82no—
314C2×C3×D4—82no—
315C2×C3×D4C2×D411yescharacteristic
316C2×C3×D4#4112yescomplemented
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—42no—
331C22×C3×C4—42no—
332C22×C3×C4—41no—
333C22×C3×C4—41no—
334C22×C3×C4C2×D411yescharacteristic
335C22×C3×C4C2×D411yescharacteristic
336C22×C3×C4C2×D411yescharacteristic
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2×D412yes—
340C22×C3×C4C2411yescharacteristic
341C3×Q16—42no—
342C3×SD16—42no—
343C3×SD16—42no—
344C3×D8—42no—
345C3×M16—21no—
346C3×M16—21no—
347C3×M16—21no—
348C3×M16—21no—
349C3×M16—21no—
350C3×M16—21no—
351C3×M16—21no—
352C3×M16—21no—
353C3×M16—42no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—21no—
357C2×C3×C8—21no—
358C2×C3×C8—42no—
359C3×C4⋊C4—22no—
360C3×C4⋊C4—22no—
361C3×C4⋊C4—22no—
362C3×C4⋊C4—22no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4C2×D411yescharacteristic
370C3×C4⋊C4C2×D411yescharacteristic
371C3×C4⋊C4C2×D411yescharacteristic
372C3×C4⋊C4C2×D411yescharacteristic
373C3×C4⋊C4C2×D411yescharacteristic
374C3×C4⋊C4C2×D411yescharacteristic
375C3×C22⋊C4—22no—
376C3×C22⋊C4—22no—
377C3×C22⋊C4—22no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—22no—
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—22no—
388C3×C22⋊C4—22no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—44no—
392C3×C22⋊C4—42no—
393C3×C22⋊C4—82no—
394C3×C42—22no—
395C3×C42—21no—
396C3×C42—21no—
397C3×C42—21no—
398C3×C42—21no—
399C3×C42—21no—
400C3×C42—21no—
401C3×C42—21no—
402C3×C42—21no—
403C3×C42—21no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—21no—
408C2×#41—21no—
409C2×#41—21no—
410C2×#41—21no—
411C2×#41—41no—
412C2×#41—41no—
413C2×#41C23×C311yescharacteristic
414C22×Q8C23×C311yescharacteristic
415C22×D4—21no—
416C22×D4—22no—
417C22×D4C3×D412yes—
418C22×D4C23×C311yescharacteristic
419C22×D4C23×C311yescharacteristic
420C23×C4—21no—
421C23×C4C23×C311yescharacteristic
422#137—22no—
423#137—41no—
424AGL(1,ℤ/8)—22no—
425AGL(1,ℤ/8)—41no—
426C2×Q16—21no—
427C2×SD16—21no—
428C2×SD16—21no—
429C2×D8—21no—
430C2×M16—21no—
431C2×M16—41no—
432C2×M16—41no—
433C2×M16C23×C311yescharacteristic
434C2×M16C23×C311yescharacteristic
435C2×M16C23×C311yescharacteristic
436C2×M16C23×C311yescharacteristic
437C22×C8—21no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440#127—21no—
441#127—22no—
442#127—41no—
443#126—22no—
444#126—22no—
445#125—21no—
446#125—21no—
447#124—22no—
448#124—22no—
449#124—21no—
450#124—22no—
451#124—41no—
452#123—22no—
453#123—22no—
454#123—22no—
455#123—22no—
456#123—21no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8C3×D411yescharacteristic, complemented
460C22⋊Q8C3×D411yescharacteristic, complemented
461#121—22no—
462#121—22no—
463#121—22no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121C3×D411yescharacteristic, complemented
471#121C3×D411yescharacteristic, complemented
472#120—21no—
473#120—22no—
474C4×Q8—21no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—21no—
478C4×D4—22no—
479C4×D4—21no—
480C4×D4—21no—
481C4×D4—21no—
482C4×D4—21no—
483C4×D4—21no—
484C4×D4—21no—
485#117—22no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117C3×D411yescharacteristic, complemented
490#117C3×D411yescharacteristic, complemented
491#117C23×C311yescharacteristic
492#117C23×C311yescharacteristic
493#117C23×C311yescharacteristic
494C2×C4⋊C4—21no—
495C2×C4⋊C4C3×D411yescharacteristic, complemented
496C2×C4⋊C4C3×D411yescharacteristic, complemented
497C2×C4⋊C4C23×C311yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4C3×D412yes—
504C2×C42—21no—
505C2×C42C23×C311yescharacteristic
506C2×C42C23×C311yescharacteristic
507#104—41no—
508#104—41no—
509#103—21no—
510#103—21no—
511#103—21no—
512#103—21no—
513#103—21no—
514#103—21no—
515#102—21no—
516#102—21no—
517#102—21no—
518#102—21no—
519#102—21no—
520#102—21no—
521#100—41no—
522#100—41no—
523C22⋊C8—21no—
524C22⋊C8—21no—
525#95—21no—
526#95—22no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—22no—
530C23×C3—21no—
531C23×C3—22no—
532C23×C3—22no—
533C23×C3—22no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—42no—
537C23×C3—42no—
538C23×C3—42no—
539C23×C3—42no—
540C23×C3—41no—
541C23×C3—41no—
542C23×C3#12011yescharacteristic
543C23×C3#12011yescharacteristic
544C23×C3C22×D411yescharacteristic
545C3×Q8—22no—
546C3×Q8—21no—
547C3×Q8—22no—
548C3×Q8—21no—
549C3×Q8—41no—
550C3×Q8—41no—
551C3×Q8—82no—
552C3×D4—22no—
553C3×D4—21no—
554C3×D4—22no—
555C3×D4—21no—
556C3×D4—44no—
557C3×D4—42no—
558C3×D4—44no—
559C3×D4—44no—
560C3×D4—41no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—41no—
566C3×D4—41no—
567C3×D4—41no—
568C3×D4—81no—
569C3×D4—82no—
570C3×D4—82no—
571C3×D4—82no—
572C3×D4—88no—
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—21no—
582C2×C3×C4—21no—
583C2×C3×C4—22no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—44no—
594C2×C3×C4—44no—
595C2×C3×C4—41no—
596C2×C3×C4—42no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—42no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—81no—
607C2×C3×C4—82no—
608C2×C3×C4—82no—
609C2×C3×C4—82no—
610C2×C3×C4#12011yescharacteristic
611C2×C3×C4#12011yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C2×#4111yescharacteristic
615C2×C3×C4C2×#4111yescharacteristic
616C2×C3×C4H(5,𝔽2)11yescharacteristic
617C2×C3×C4H(5,𝔽2)11yescharacteristic
618C3×C8—41no—
619C3×C8—41no—
620C3×C8—41no—
621C3×C8—41no—
622C24—21no—
623C24C2×C3×D412yes—
624C24C2×C3×D411yescharacteristic
625#41—24no—
626#41—24no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—42no—
632#41—42no—
633#41—42no—
634#41—42no—
635#41—42no—
636#41—42no—
637#41—84no—
638C2×Q8—22no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8C2×C3×D411yescharacteristic
645C2×Q8C3×#4112yescomplemented
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—22no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—42no—
667C2×D4—41no—
668C2×D4—41no—
669C2×D4—44no—
670C2×D4—82no—
671C2×D4—82no—
672C2×D4C2×C3×D411yescharacteristic
673C2×D4C3×#4112yescomplemented
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4C2×C3×D411yescharacteristic
692C22×C4C2×C3×D411yescharacteristic
693C22×C4C2×C3×D411yescharacteristic
694C22×C4C2×C3×D411yescharacteristic
695C22×C4C2×C3×D411yescharacteristic
696C22×C4C2×C3×D412yes—
697C22×C4C24×C311yescharacteristic
698Q16—42no—
699SD16—42no—
700SD16—42no—
701D8—42no—
702M16—21no—
703M16—21no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—42no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—42no—
716C4⋊C4—22no—
717C4⋊C4—22no—
718C4⋊C4—22no—
719C4⋊C4—22no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4C2×C3×D411yescharacteristic
727C4⋊C4C2×C3×D411yescharacteristic
728C4⋊C4C2×C3×D411yescharacteristic
729C4⋊C4C2×C3×D411yescharacteristic
730C4⋊C4C2×C3×D411yescharacteristic
731C4⋊C4C2×C3×D411yescharacteristic
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—82no—
751C42—22no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42—21no—
757C42—21no—
758C42—21no—
759C42—21no—
760C42—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—44no—
770C22×C3—42no—
771C22×C3—41no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—42no—
777C22×C3—81no—
778C22×C3—81no—
779C22×C3—82no—
780C22×C3—82no—
781C22×C3—82no—
782C22×C3—81no—
783C22×C3—81no—
784C22×C3C2×#12011yescharacteristic
785C22×C3#54611yescharacteristic
786C22×C3#54611yescharacteristic
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—42no—
790C3×C4—42no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—41no—
795C3×C4—41no—
796C3×C4—41no—
797C3×C4—42no—
798C3×C4—41no—
799C3×C4—81no—
800C3×C4#52511yescharacteristic
801C3×C4#53511yescharacteristic
802C3×C4#54611yescharacteristic
803C3×C4#54611yescharacteristic
804C23—21no—
805C23—21no—
806C23—22no—
807C23—21no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—41no—
812C23—41no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—41no—
818C23—41no—
819C23C3×#12011yescharacteristic
820C23C3×#12011yescharacteristic
821C23C22×C3×D411yescharacteristic
822Q8—22no—
823Q8—21no—
824Q8—22no—
825Q8—21no—
826Q8—41no—
827Q8—41no—
828Q8—82no—
829D4—22no—
830D4—21no—
831D4—22no—
832D4—21no—
833D4—44no—
834D4—42no—
835D4—44no—
836D4—44no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—82no—
846D4—81no—
847D4—82no—
848D4—82no—
849D4—88no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—42no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—82no—
885C2×C4—82no—
886C2×C4—82no—
887C2×C4C3×#12011yescharacteristic
888C2×C4C3×#12011yescharacteristic
889C2×C4C22×C3×D411yescharacteristic
890C2×C4C22×C3×D411yescharacteristic
891C2×C4C2×C3×#4111yescharacteristic
892C2×C4C2×C3×#4111yescharacteristic
893C2×C4C3×H(5,𝔽2)11yescharacteristic
894C2×C4C3×H(5,𝔽2)11yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C2×C3—21no—
900C2×C3—21no—
901C2×C3—41no—
902C2×C3—41no—
903C2×C3—81no—
904C2×C3—82no—
905C2×C3—82no—
906C2×C3#240411yescharacteristic
907C2×C3#301811yescharacteristic
908C2×C3#301911yescharacteristic
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—44no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—42no—
925C22—81no—
926C22—81no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—81no—
931C22—81no—
932C22C2×C3×#12011yescharacteristic
933C22C3×#54611yescharacteristic
934C22C3×#54611yescharacteristic
935C4—21no—
936C4—21no—
937C4—42no—
938C4—42no—
939C4—41no—
940C4—41no—
941C4—41no—
942C4—41no—
943C4—41no—
944C4—41no—
945C4—42no—
946C4—41no—
947C4—81no—
948C4C3×#52511yescharacteristic
949C4C3×#53511yescharacteristic
950C4C3×#54611yescharacteristic
951C4C3×#54611yescharacteristic
952C3#2395611yescharacteristic, direct product factor, Sylow
953C2—21no—
954C2—21no—
955C2—41no—
956C2—41no—
957C2—82no—
958C2—82no—
959C2—81no—
960C2C3×#240411yescharacteristic
961C2C3×#301811yescharacteristic
962C2C3×#301911yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3494C2semidirect
2. C3×#3005C2semidirect
3. C3×#2896C2semidirect
4. C3×#2431C2semidirect
5. C3×#2028C2semidirect
6. C3×#2027C2semidirect
7. C3×#2004C2semidirect
8. C3×#2002C2semidirect
9. C3×#1900C2semidirect
10. C3×#1887C2semidirect
11. C3×#1885C2semidirect
12. C3×#1883C2semidirect
13. C3×#1882C2semidirect
14. C3×#1871C2semidirect
15. C3×#1826C2semidirect
16. #23956C3direct (N × H)
72. #3494C2×C3semidirect
73. #3005C2×C3semidirect
74. #2896C2×C3semidirect
75. #2431C2×C3semidirect
76. #2028C2×C3semidirect
77. #2027C2×C3semidirect
78. #2004C2×C3semidirect
79. #2002C2×C3semidirect
80. #1900C2×C3semidirect
81. #1887C2×C3semidirect
82. #1885C2×C3semidirect
83. #1883C2×C3semidirect
84. #1882C2×C3semidirect
85. #1871C2×C3semidirect
86. #1826C2×C3semidirect
142. C3×C22⋊Q8D4semidirect
143. C3×C22⋊Q8D4semidirect
153. C3×#121D4semidirect
154. C3×#121D4semidirect
172. C3×#117D4semidirect
173. C3×#117D4semidirect
178. C2×C3×C4⋊C4D4semidirect
179. C2×C3×C4⋊C4D4semidirect
288. C2×C3×Q8#41semidirect
316. C2×C3×D4#41semidirect
459. C22⋊Q8C3×D4semidirect
460. C22⋊Q8C3×D4semidirect
470. #121C3×D4semidirect
471. #121C3×D4semidirect
489. #117C3×D4semidirect
490. #117C3×D4semidirect
495. C2×C4⋊C4C3×D4semidirect
496. C2×C4⋊C4C3×D4semidirect
645. C2×Q8C3×#41semidirect
673. C2×D4C3×#41semidirect
952. C3#23956direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34942
C3×#30052
C3×#28962
C3×#24312
C3×#20282
C3×#20272
C3×#20042
C3×#20022
C3×#19002
C3×#18872
C3×#18852
C3×#18832
C3×#18822
C3×#18712
C3×#18262
#239563