Finite Group Databasebeta

← C3×#107130 #72270331

Subgroups — C3×#107130 #72270331

Order 1536.

5764 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#34171C211yesmaximal, characteristic
2C2×C3×#1783C211yesmaximal, characteristic
3C2×C3×#1438C211yesmaximal, characteristic
4C3×#8020C214yesmaximal, complemented
5#107130C311yesmaximal, characteristic, direct product factor, Sylow
6C24×C3×D4C2211yescharacteristic
7C2×C3×#518C412yescomplemented
8C23×C3×C22⋊C4—22no—
9C22×C3×#100—22no—
10C2×C3×#407C2212yes—
11C3×D4×C22⋊C4—28no—
12C3×#2309C412yescomplemented
13C3×#2308—22no—
14C3×#2280C2212yes—
15C2×C3×#379—22no—
16C22×C3×#95C2212yes—
17C3×#1783—22no—
18C3×#1783C414yescomplemented
19C3×#1438—22no—
20C3×#1438C414yescomplemented
21C3×#1294—28no—
22#34171C2×C311yescharacteristic
23C2×#1783C2×C311yescharacteristic
24C2×#1438C2×C311yescharacteristic
25#8020C2×C314yescomplemented
26C26×C3D412yes—
27C23×C3×D4—24no—
28C23×C3×D4—24no—
29C23×C3×D4—48no—
30C23×C3×D4C2×C411yescharacteristic
31C23×C3×D4C2×C411yescharacteristic
32C23×C3×D4C2×C412yes—
33C23×C3×D4C2×C412yes—
34C23×C3×D4D412yes—
35C23×C3×D4D412yes—
36C23×C3×D4Q812yes—
37C24×C3×C4—22no—
38C24×C3×C4C2311yescharacteristic
39C22×C3×M16—22no—
40C3×#518—48no—
41C2×C3×C4×D4—28no—
42C2×C3×#117C2×C414yes—
43C22×C3×C22⋊C4—28no—
44C22×C3×C22⋊C4—24no—
45C22×C3×C22⋊C4—28no—
46C22×C3×C22⋊C4—48no—
47C22×C3×C22⋊C4—416no—
48C2×C3×#100—28no—
49C2×C3×#100—48no—
50C3×#407—24no—
51C3×#407—22no—
52C3×#407C2×C414yescomplemented
53C2×C3×C22⋊C8—24no—
54C3×#390—28no—
55C3×#386—216no—
56C3×#381—22no—
57C3×#380D418yes—
58C3×#379—28no—
59C3×#379—24no—
60C3×#379—22no—
61C3×C4×C22⋊C4—24no—
62C2×C3×#95—24no—
63C2×C3×#95—24no—
64C2×C3×#95—22no—
65C2×C3×#95C2×C414yescomplemented
66C24×D4C22×C311yescharacteristic
67C2×#518C3×C412yescomplemented
68C23×C22⋊C4—22no—
69C22×#100—22no—
70C2×#407C22×C312yes—
71D4×C22⋊C4—28no—
72#2309C3×C412yescomplemented
73#2308—22no—
74#2280C22×C312yes—
75C2×#379—22no—
76C22×#95C22×C312yes—
77#1783—22no—
78#1783C3×C414yescomplemented
79#1438—22no—
80#1438C3×C414yescomplemented
81#1294—28no—
82C25×C3—28no—
83C25×C3—24no—
84C25×C3—24no—
85C25×C3—44no—
86C25×C3—48no—
87C25×C3—48no—
88C25×C3C22⋊C412yes—
89C25×C3C22⋊C414yes—
90C25×C3C22⋊C412yes—
91C25×C3C4⋊C414yes—
92C25×C3C2×D411yescharacteristic
93C22×C3×D4—28no—
94C22×C3×D4—28no—
95C22×C3×D4—22no—
96C22×C3×D4—22no—
97C22×C3×D4—22no—
98C22×C3×D4—22no—
99C22×C3×D4—28no—
100C22×C3×D4—28no—
101C22×C3×D4—24no—
102C22×C3×D4—28no—
103C22×C3×D4—28no—
104C22×C3×D4—24no—
105C22×C3×D4—44no—
106C22×C3×D4—44no—
107C22×C3×D4—48no—
108C22×C3×D4—48no—
109C22×C3×D4—48no—
110C22×C3×D4—48no—
111C22×C3×D4—432no—
112C22×C3×D4—432no—
113C22×C3×D4C4212yes—
114C22×C3×D4C4212yes—
115C22×C3×D4C22⋊C414yes—
116C22×C3×D4C4⋊C412yes—
117C22×C3×D4C4⋊C414yes—
118C22×C3×D4C4⋊C412yes—
119C23×C3×C4—28no—
120C23×C3×C4—24no—
121C23×C3×C4—28no—
122C23×C3×C4—44no—
123C23×C3×C4—44no—
124C23×C3×C4—48no—
125C23×C3×C4—48no—
126C23×C3×C4—42no—
127C23×C3×C4—42no—
128C23×C3×C4C22×C411yescharacteristic
129C23×C3×C4C22×C411yescharacteristic
130C23×C3×C4C22×C411yescharacteristic
131C23×C3×C4C2×D411yescharacteristic
132C23×C3×C4C2×D411yescharacteristic
133C23×C3×C4C2×D414yes—
134C23×C3×C4C2×Q811yescharacteristic
135C23×C3×C4#4114yes—
136C2×C3×M16—24no—
137C2×C3×M16—42no—
138C2×C3×M16—48no—
139C22×C3×C8—42no—
140C3×C4×D4—432no—
141C3×#117—48no—
142C2×C3×C4⋊C4C22⋊C418yescomplemented
143C2×C3×C22⋊C4—28no—
144C2×C3×C22⋊C4—24no—
145C2×C3×C22⋊C4—28no—
146C2×C3×C22⋊C4—216no—
147C2×C3×C22⋊C4—432no—
148C2×C3×C22⋊C4—416no—
149C2×C3×C22⋊C4—48no—
150C2×C3×C22⋊C4—464no—
151C2×C3×C22⋊C4—48no—
152C2×C3×C22⋊C4—88no—
153C2×C3×C22⋊C4—88no—
154C2×C3×C42—24no—
155C3×#100—416no—
156C3×C22⋊C8—28no—
157C3×C22⋊C8—44no—
158C3×#95—28no—
159C3×#95—28no—
160C3×#95—44no—
161C26C3×D412yes—
162C23×D4—24no—
163C23×D4—24no—
164C23×D4—48no—
165C23×D4C2×C3×C411yescharacteristic
166C23×D4C2×C3×C412yes—
167C23×D4C2×C3×C411yescharacteristic
168C23×D4C2×C3×C412yes—
169C23×D4C3×D412yes—
170C23×D4C3×D412yes—
171C23×D4C3×Q812yes—
172C24×C4—22no—
173C24×C4C23×C311yescharacteristic
174C22×M16—22no—
175#518—48no—
176C2×C4×D4—28no—
177C2×#117C2×C3×C414yes—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—28no—
180C22×C22⋊C4—28no—
181C22×C22⋊C4—416no—
182C22×C22⋊C4—48no—
183C2×#100—28no—
184C2×#100—48no—
185#407—24no—
186#407—22no—
187#407C2×C3×C414yescomplemented
188C2×C22⋊C8—24no—
189#390—28no—
190#386—216no—
191#381—22no—
192#380C3×D418yes—
193#379—28no—
194#379—24no—
195#379—22no—
196C4×C22⋊C4—24no—
197C2×#95—24no—
198C2×#95—24no—
199C2×#95—22no—
200C2×#95C2×C3×C414yescomplemented
201C24×C3—24no—
202C24×C3—24no—
203C24×C3—24no—
204C24×C3—22no—
205C24×C3—22no—
206C24×C3—24no—
207C24×C3—28no—
208C24×C3—28no—
209C24×C3—22no—
210C24×C3—24no—
211C24×C3—28no—
212C24×C3—28no—
213C24×C3—22no—
214C24×C3—24no—
215C24×C3—44no—
216C24×C3—44no—
217C24×C3—416no—
218C24×C3—416no—
219C24×C3—48no—
220C24×C3—48no—
221C24×C3—48no—
222C24×C3—48no—
223C24×C3—416no—
224C24×C3—432no—
225C24×C3—416no—
226C24×C3—416no—
227C24×C3—48no—
228C24×C3—48no—
229C24×C3—88no—
230C24×C3—88no—
231C24×C3—84no—
232C24×C3—84no—
233C24×C3—88no—
234C24×C3—816no—
235C24×C3—88no—
236C24×C3#9514yes—
237C24×C3#9514yes—
238C24×C3#9918yes—
239C24×C3C2×C22⋊C411yescharacteristic
240C24×C3C2×C22⋊C411yescharacteristic
241C24×C3C2×C4⋊C411yescharacteristic
242C24×C3#12012yes—
243C24×C3#12312yes—
244C2×C3×D4—216no—
245C2×C3×D4—216no—
246C2×C3×D4—28no—
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—28no—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—28no—
255C2×C3×D4—28no—
256C2×C3×D4—44no—
257C2×C3×D4—44no—
258C2×C3×D4—44no—
259C2×C3×D4—44no—
260C2×C3×D4—416no—
261C2×C3×D4—416no—
262C2×C3×D4—48no—
263C2×C3×D4—48no—
264C2×C3×D4—432no—
265C2×C3×D4—432no—
266C2×C3×D4—432no—
267C2×C3×D4—432no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—28no—
271C22×C3×C4—28no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—48no—
276C22×C3×C4—42no—
277C22×C3×C4—48no—
278C22×C3×C4—432no—
279C22×C3×C4—48no—
280C22×C3×C4—48no—
281C22×C3×C4—48no—
282C22×C3×C4—48no—
283C22×C3×C4—44no—
284C22×C3×C4—44no—
285C22×C3×C4—416no—
286C22×C3×C4—816no—
287C22×C3×C4—816no—
288C22×C3×C4—84no—
289C22×C3×C4—84no—
290C22×C3×C4—84no—
291C22×C3×C4—84no—
292C22×C3×C4C2×C4211yescharacteristic
293C22×C3×C4C2×C22⋊C412yes—
294C22×C3×C4C2×C22⋊C411yescharacteristic
295C22×C3×C4C2×C4⋊C411yescharacteristic
296C22×C3×C4C2×C4⋊C411yescharacteristic
297C22×C3×C4#11712yes—
298C22×C3×C4C4×D414yes—
299C22×C3×C4C4×D414yes—
300C22×C3×C4#12012yes—
301C22×C3×C4#12114yes—
302C22×C3×C4C22⋊Q814yes—
303C22×C3×C4#12312yes—
304C3×M16—48no—
305C3×M16—84no—
306C2×C3×C8—44no—
307C2×C3×C8—84no—
308C3×C4⋊C4—48no—
309C3×C22⋊C4—416no—
310C3×C22⋊C4—464no—
311C3×C22⋊C4—48no—
312C3×C22⋊C4—48no—
313C3×C22⋊C4—48no—
314C3×C22⋊C4—816no—
315C3×C42—48no—
316C25—28no—
317C25—24no—
318C25—24no—
319C25—44no—
320C25—48no—
321C25—48no—
322C25C3×C22⋊C412yes—
323C25C3×C22⋊C414yes—
324C25C3×C22⋊C412yes—
325C25C3×C4⋊C414yes—
326C25C2×C3×D411yescharacteristic
327C22×D4—28no—
328C22×D4—28no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—22no—
333C22×D4—28no—
334C22×D4—28no—
335C22×D4—24no—
336C22×D4—28no—
337C22×D4—28no—
338C22×D4—24no—
339C22×D4—44no—
340C22×D4—44no—
341C22×D4—48no—
342C22×D4—48no—
343C22×D4—48no—
344C22×D4—48no—
345C22×D4—432no—
346C22×D4—432no—
347C22×D4C3×C4212yes—
348C22×D4C3×C4212yes—
349C22×D4C3×C22⋊C414yes—
350C22×D4C3×C4⋊C412yes—
351C22×D4C3×C4⋊C414yes—
352C22×D4C3×C4⋊C412yes—
353C23×C4—28no—
354C23×C4—24no—
355C23×C4—28no—
356C23×C4—44no—
357C23×C4—48no—
358C23×C4—48no—
359C23×C4—44no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4C22×C3×C411yescharacteristic
363C23×C4C22×C3×C411yescharacteristic
364C23×C4C22×C3×C411yescharacteristic
365C23×C4C2×C3×D411yescharacteristic
366C23×C4C2×C3×D411yescharacteristic
367C23×C4C2×C3×D414yes—
368C23×C4C2×C3×Q811yescharacteristic
369C23×C4C3×#4114yes—
370C2×M16—24no—
371C2×M16—42no—
372C2×M16—48no—
373C22×C8—42no—
374C4×D4—432no—
375#117—48no—
376C2×C4⋊C4C3×C22⋊C418yescomplemented
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—216no—
381C2×C22⋊C4—432no—
382C2×C22⋊C4—416no—
383C2×C22⋊C4—48no—
384C2×C22⋊C4—464no—
385C2×C22⋊C4—48no—
386C2×C22⋊C4—88no—
387C2×C22⋊C4—88no—
388C2×C42—24no—
389#100—416no—
390C22⋊C8—28no—
391C22⋊C8—44no—
392#95—28no—
393#95—28no—
394#95—44no—
395C23×C3—28no—
396C23×C3—216no—
397C23×C3—28no—
398C23×C3—24no—
399C23×C3—24no—
400C23×C3—24no—
401C23×C3—24no—
402C23×C3—24no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—22no—
408C23×C3—22no—
409C23×C3—24no—
410C23×C3—24no—
411C23×C3—28no—
412C23×C3—28no—
413C23×C3—24no—
414C23×C3—24no—
415C23×C3—24no—
416C23×C3—24no—
417C23×C3—416no—
418C23×C3—416no—
419C23×C3—48no—
420C23×C3—48no—
421C23×C3—416no—
422C23×C3—48no—
423C23×C3—416no—
424C23×C3—48no—
425C23×C3—432no—
426C23×C3—416no—
427C23×C3—48no—
428C23×C3—48no—
429C23×C3—44no—
430C23×C3—416no—
431C23×C3—48no—
432C23×C3—48no—
433C23×C3—44no—
434C23×C3—88no—
435C23×C3—88no—
436C23×C3—84no—
437C23×C3—84no—
438C23×C3—88no—
439C23×C3—832no—
440C23×C3—832no—
441C23×C3—88no—
442C23×C3—84no—
443C23×C3—88no—
444C23×C3—832no—
445C23×C3—84no—
446C23×C3—816no—
447C23×C3—832no—
448C23×C3#34218yes—
449C23×C3C2×#9511yescharacteristic
450C23×C3#37911yescharacteristic
451C23×C3#38111yescharacteristic
452C23×C3#38512yes—
453C23×C3#38612yes—
454C23×C3C2×#9914yes—
455C23×C3#45314yes—
456C23×C3#45514yes—
457C3×D4—216no—
458C3×D4—216no—
459C3×D4—416no—
460C3×D4—416no—
461C3×D4—48no—
462C3×D4—48no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—24no—
470C2×C3×C4—24no—
471C2×C3×C4—44no—
472C2×C3×C4—44no—
473C2×C3×C4—44no—
474C2×C3×C4—44no—
475C2×C3×C4—416no—
476C2×C3×C4—48no—
477C2×C3×C4—416no—
478C2×C3×C4—48no—
479C2×C3×C4—88no—
480C2×C3×C4—816no—
481C2×C3×C4—816no—
482C2×C3×C4—84no—
483C2×C3×C4—84no—
484C2×C3×C4—1616no—
485C2×C3×C4C4×C22⋊C412yes—
486C2×C3×C4#38012yes—
487C2×C3×C4#38512yes—
488C2×C3×C4#38612yes—
489C3×C8—84no—
490C24—24no—
491C24—24no—
492C24—24no—
493C24—22no—
494C24—22no—
495C24—24no—
496C24—22no—
497C24—24no—
498C24—28no—
499C24—28no—
500C24—28no—
501C24—28no—
502C24—22no—
503C24—24no—
504C24—44no—
505C24—44no—
506C24—416no—
507C24—416no—
508C24—48no—
509C24—48no—
510C24—48no—
511C24—48no—
512C24—416no—
513C24—416no—
514C24—432no—
515C24—416no—
516C24—48no—
517C24—48no—
518C24—88no—
519C24—88no—
520C24—84no—
521C24—84no—
522C24—88no—
523C24—816no—
524C24—88no—
525C24C3×#9514yes—
526C24C3×#9514yes—
527C24C3×#9918yes—
528C24C2×C3×C22⋊C411yescharacteristic
529C24C2×C3×C22⋊C411yescharacteristic
530C24C2×C3×C4⋊C411yescharacteristic
531C24C3×#12012yes—
532C24C3×#12312yes—
533C2×D4—216no—
534C2×D4—216no—
535C2×D4—28no—
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—24no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—24no—
543C2×D4—28no—
544C2×D4—28no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—416no—
550C2×D4—416no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—432no—
554C2×D4—432no—
555C2×D4—432no—
556C2×D4—432no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—28no—
560C22×C4—28no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—48no—
565C22×C4—42no—
566C22×C4—48no—
567C22×C4—432no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—416no—
575C22×C4—816no—
576C22×C4—816no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4C2×C3×C4211yescharacteristic
582C22×C4C2×C3×C22⋊C412yes—
583C22×C4C2×C3×C22⋊C411yescharacteristic
584C22×C4C2×C3×C4⋊C411yescharacteristic
585C22×C4C2×C3×C4⋊C411yescharacteristic
586C22×C4C3×#11712yes—
587C22×C4C3×C4×D414yes—
588C22×C4C3×C4×D414yes—
589C22×C4C3×#12012yes—
590C22×C4C3×#12114yes—
591C22×C4C3×C22⋊Q814yes—
592C22×C4C3×#12312yes—
593M16—48no—
594M16—84no—
595C2×C8—44no—
596C2×C8—84no—
597C4⋊C4—48no—
598C22⋊C4—416no—
599C22⋊C4—464no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—816no—
604C42—48no—
605C22×C3—22no—
606C22×C3—24no—
607C22×C3—28no—
608C22×C3—28no—
609C22×C3—22no—
610C22×C3—28no—
611C22×C3—28no—
612C22×C3—28no—
613C22×C3—28no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—28no—
621C22×C3—48no—
622C22×C3—48no—
623C22×C3—416no—
624C22×C3—48no—
625C22×C3—44no—
626C22×C3—48no—
627C22×C3—84no—
628C22×C3—88no—
629C22×C3—816no—
630C22×C3—832no—
631C22×C3—816no—
632C22×C3—84no—
633C22×C3—88no—
634C22×C3—88no—
635C22×C3C22⋊#9511yescharacteristic
636C22×C3C2×#34212yes—
637C22×C3#178112yes—
638C22×C3#179214yes—
639C22×C3#181912yes—
640C22×C3#185614yes—
641C22×C3#188512yes—
642C22×C3#188712yes—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—88no—
648C3×C4—88no—
649C23—28no—
650C23—216no—
651C23—28no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—28no—
665C23—24no—
666C23—24no—
667C23—28no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—416no—
672C23—416no—
673C23—48no—
674C23—48no—
675C23—416no—
676C23—48no—
677C23—416no—
678C23—48no—
679C23—432no—
680C23—416no—
681C23—48no—
682C23—44no—
683C23—48no—
684C23—44no—
685C23—416no—
686C23—48no—
687C23—48no—
688C23—88no—
689C23—84no—
690C23—84no—
691C23—88no—
692C23—88no—
693C23—832no—
694C23—832no—
695C23—88no—
696C23—84no—
697C23—88no—
698C23—832no—
699C23—84no—
700C23—816no—
701C23—832no—
702C23C3×#34218yes—
703C23C2×C3×#9511yescharacteristic
704C23C3×#37911yescharacteristic
705C23C3×#38111yescharacteristic
706C23C3×#38512yes—
707C23C3×#38612yes—
708C23C2×C3×#9914yes—
709C23C3×#45314yes—
710C23C3×#45514yes—
711D4—216no—
712D4—216no—
713D4—416no—
714D4—416no—
715D4—48no—
716D4—48no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—416no—
730C2×C4—48no—
731C2×C4—48no—
732C2×C4—416no—
733C2×C4—88no—
734C2×C4—816no—
735C2×C4—84no—
736C2×C4—816no—
737C2×C4—84no—
738C2×C4—1616no—
739C2×C4C3×C4×C22⋊C412yes—
740C2×C4C3×#38012yes—
741C2×C4C3×#38512yes—
742C2×C4C3×#38612yes—
743C8—84no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—22no—
747C2×C3—24no—
748C2×C3—22no—
749C2×C3—48no—
750C2×C3—84no—
751C2×C3#845314yes—
752C2×C3#1072511yescharacteristic
753C2×C3#1074912yes—
754C22—22no—
755C22—24no—
756C22—28no—
757C22—28no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—28no—
767C22—28no—
768C22—28no—
769C22—28no—
770C22—48no—
771C22—48no—
772C22—48no—
773C22—416no—
774C22—44no—
775C22—48no—
776C22—84no—
777C22—88no—
778C22—816no—
779C22—832no—
780C22—816no—
781C22—84no—
782C22—88no—
783C22—88no—
784C22C3×C22⋊#9511yescharacteristic
785C22C2×C3×#34212yes—
786C22C3×#178112yes—
787C22C3×#179214yes—
788C22C3×#181912yes—
789C22C3×#185614yes—
790C22C3×#188512yes—
791C22C3×#188712yes—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—88no—
797C4—88no—
798C3#10713011yescharacteristic, direct product factor, Sylow
799C2—22no—
800C2—22no—
801C2—22no—
802C2—24no—
803C2—22no—
804C2—48no—
805C2—84no—
806C2C3×#845314yes—
807C2C3×#1072511yescharacteristic
808C2C3×#1074912yes—
subgroupG/H
center, socleC23×C3#379
commutatorC22×C4C2×C3×C42
Frattini, cosocleC24×C4C23×C3
prime radicalC24×C3×D4C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C3×#8020C2semidirect
5. #107130C3direct (N × H)
7. C2×C3×#518C4semidirect
12. C3×#2309C4semidirect
18. C3×#1783C4semidirect
20. C3×#1438C4semidirect
25. #8020C2×C3semidirect
52. C3×#407C2×C4semidirect
65. C2×C3×#95C2×C4semidirect
67. C2×#518C3×C4semidirect
72. #2309C3×C4semidirect
78. #1783C3×C4semidirect
80. #1438C3×C4semidirect
142. C2×C3×C4⋊C4C22⋊C4semidirect
187. #407C2×C3×C4semidirect
200. C2×#95C2×C3×C4semidirect
376. C2×C4⋊C4C3×C22⋊C4semidirect
798. C3#107130direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#341712
C2×C3×#17832
C2×C3×#14382
C3×#80202
#1071303