Finite Group Databasebeta

← C3×#24365 #10642972

Subgroups — C3×#24365 #10642972

Order 768.

1454 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
1C22×C3×#135C211yesmaximal, characteristic
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#461C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C3×#2432C211yesmaximal, characteristic, complemented
6C3×#2339C211yesmaximal, characteristic, complemented
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2055C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#1892C211yesmaximal, characteristic, complemented
12C3×#1879C211yesmaximal, characteristic, complemented
13C3×#1877C211yesmaximal, characteristic, complemented
14C3×#1850C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24365C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C2×C3×#135—24no—
20C2×C3×#135—24no—
21C2×C3×#135—24no—
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×D8C2211yescharacteristic
28C23×C3×C8C2211yescharacteristic
29C2×C3×C4⋊Q8C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic
31C2×C3×C22⋊Q8C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×C4×D4C2211yescharacteristic
34C3×#463—24no—
35C3×#461—24no—
36C3×#452—24no—
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C3×#394—21no—
49C3×#394—21no—
50C3×#391C2211yescharacteristic
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#386—21no—
55C3×#386—21no—
56C3×#385—21no—
57C3×#385—21no—
58C3×#381—21no—
59C3×#380C2211yescharacteristic
60C3×C4×C22⋊C4C2211yescharacteristic
61C2×C3×#95—21no—
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C3×#336C2211yescharacteristic
65C3×#336C2211yescharacteristic
66C22×#135C2×C311yescharacteristic
67C2×#463C2×C311yescharacteristic, complemented
68C2×#461C2×C311yescharacteristic, complemented
69C2×#452C2×C311yescharacteristic, complemented
70#2432C2×C311yescharacteristic, complemented
71#2339C2×C311yescharacteristic, complemented
72#2056C2×C311yescharacteristic, complemented
73#2055C2×C311yescharacteristic, complemented
74#2016C2×C311yescharacteristic, complemented
75#2015C2×C311yescharacteristic, complemented
76#1892C2×C311yescharacteristic, complemented
77#1879C2×C311yescharacteristic, complemented
78#1877C2×C311yescharacteristic, complemented
79#1850C2×C311yescharacteristic, complemented
80#1788C2×C311yescharacteristic, complemented
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—22no—
87C2×C3×#41—22no—
88C2×C3×#41—41no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C2×C3×#41—41no—
92C2×C3×#41D414yes—
93C22×C3×Q8C2311yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4C2311yescharacteristic
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4—21no—
101C23×C3×C4—21no—
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C3×#135—232no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—22no—
110C2×C3×Q16—41no—
111C2×C3×Q16—41no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16D414yes—
121C2×C3×D8—22no—
122C2×C3×D8—22no—
123C2×C3×D8D414yes—
124C22×C3×C8—22no—
125C22×C3×C8—22no—
126C22×C3×C8—22no—
127C22×C3×C8C2311yescharacteristic
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×C4⋊Q8—22no—
132C3×C4⋊Q8—41no—
133C3×#124—22no—
134C3×#124—41no—
135C3×C22⋊Q8—22no—
136C3×C22⋊Q8—22no—
137C3×C4×D4—22no—
138C3×C4×D4—22no—
139C3×C4×D4—41no—
140C3×C4×D4—41no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4D411yescharacteristic
156C2×C3×C22⋊C4D411yescharacteristic
157C2×C3×C42C2311yescharacteristic
158C2×C3×C42C2311yescharacteristic
159C3×C4⋊C8—22no—
160C3×C4⋊C8—22no—
161C3×#103—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×#103—22no—
165C3×#103—41no—
166C3×#102—22no—
167C3×#102—22no—
168C3×#102—41no—
169C3×C22⋊C8—22no—
170C3×#95—21no—
171C3×#95—21no—
172C3×#95—21no—
173C3×#95—21no—
174C3×#95—21no—
175C3×#95—21no—
176C3×#95—21no—
177C3×#95D411yescharacteristic
178C3×#95D411yescharacteristic
179C22×#41C22×C311yescharacteristic
180C22×#41C22×C311yescharacteristic
181C2×#135—24no—
182C2×#135—24no—
183C2×#135—24no—
184C22×Q16C22×C311yescharacteristic
185C22×Q16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C23×C8C22×C311yescharacteristic
191C2×C4⋊Q8C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×C22⋊Q8C22×C311yescharacteristic
194C2×C4×D4C22×C311yescharacteristic
195C2×C4×D4C22×C311yescharacteristic
196#463—24no—
197#461—24no—
198#452—24no—
199C2×C4⋊C8C22×C311yescharacteristic
200C2×C4⋊C8C22×C311yescharacteristic
201C2×#103C22×C311yescharacteristic
202C2×#103C22×C311yescharacteristic
203C2×#103C22×C311yescharacteristic
204C2×#103C22×C311yescharacteristic
205C2×#103C22×C311yescharacteristic
206C2×#102C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×C22⋊C8C22×C311yescharacteristic
210#394—21no—
211#394—21no—
212#391C22×C311yescharacteristic
213#391C22×C311yescharacteristic
214#391C22×C311yescharacteristic
215#390C22×C311yescharacteristic
216#386—21no—
217#386—21no—
218#385—21no—
219#385—21no—
220#381—21no—
221#380C22×C311yescharacteristic
222C4×C22⋊C4C22×C311yescharacteristic
223C2×#95—21no—
224#340C22×C311yescharacteristic
225#340C22×C311yescharacteristic
226#336C22×C311yescharacteristic
227#336C22×C311yescharacteristic
228C24×C3—21no—
229C24×C3—21no—
230C24×C3C2×D411yescharacteristic
231C3×#41—28no—
232C3×#41—28no—
233C3×#41—44no—
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C3×#41—44no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8C2×D412yes—
256C2×C3×Q8C2×D412yes—
257C2×C3×D4—24no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4C2×D412yes—
272C2×C3×D4C2×D412yes—
273C2×C3×D4C2×D412yes—
274C2×C3×D4C2×D412yes—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—24no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—42no—
287C22×C3×C4—42no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4—42no—
291C22×C3×C4—42no—
292C22×C3×C4—42no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4—81no—
296C22×C3×C4—81no—
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4#4112yes—
304C22×C3×C4C2411yescharacteristic
305C3×Q16—28no—
306C3×Q16—44no—
307C3×SD16—28no—
308C3×SD16—28no—
309C3×SD16—44no—
310C3×D8—28no—
311C2×C3×C8—28no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8C2×D412yes—
323C2×C3×C8C2×D412yes—
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—42no—
331C3×C4⋊C4—42no—
332C3×C4⋊C4—42no—
333C3×C22⋊C4—22no—
334C3×C22⋊C4—41no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—42no—
340C3×C22⋊C4—42no—
341C3×C22⋊C4—42no—
342C3×C22⋊C4—81no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42—21no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—41no—
355C2×#41—41no—
356C2×#41—41no—
357C2×#41—41no—
358C2×#41C3×D414yes—
359C22×Q8C23×C311yescharacteristic
360C22×Q8C23×C311yescharacteristic
361C22×Q8C23×C311yescharacteristic
362C22×D4—21no—
363C22×D4—21no—
364C22×D4C23×C311yescharacteristic
365C22×D4C23×C311yescharacteristic
366C23×C4—21no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4C23×C311yescharacteristic
371#135—232no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16—22no—
376C2×Q16—41no—
377C2×Q16—41no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16C3×D414yes—
387C2×D8—22no—
388C2×D8—22no—
389C2×D8C3×D414yes—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8C23×C311yescharacteristic
394C22×C8C23×C311yescharacteristic
395C22×C8C23×C311yescharacteristic
396C22×C8C23×C311yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—41no—
399#124—22no—
400#124—41no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—41no—
406C4×D4—41no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C23×C311yescharacteristic
411C2×C4⋊C4C23×C311yescharacteristic
412C2×C4⋊C4C23×C311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4C3×D411yescharacteristic
422C2×C22⋊C4C3×D411yescharacteristic
423C2×C42C23×C311yescharacteristic
424C2×C42C23×C311yescharacteristic
425C4⋊C8—22no—
426C4⋊C8—22no—
427#103—22no—
428#103—22no—
429#103—22no—
430#103—22no—
431#103—41no—
432#102—22no—
433#102—22no—
434#102—41no—
435C22⋊C8—22no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95C3×D411yescharacteristic
444#95C3×D411yescharacteristic
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—22no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3#12112yes—
466C23×C3C22×D411yescharacteristic
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×Q8—41no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×D4—22no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—48no—
485C3×D4—48no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4#12014yes—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—48no—
509C2×C3×C4—48no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—84no—
527C2×C3×C4—84no—
528C2×C3×C4#12112yes—
529C2×C3×C4#13512yescomplemented
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C22×D411yescharacteristic
533C2×C3×C4C2×#4111yescharacteristic
534C2×C3×C4H(5,𝔽2)11yescharacteristic
535C2×C3×C4H(5,𝔽2)11yescharacteristic
536C3×C8—22no—
537C3×C8—22no—
538C3×C8—41no—
539C3×C8—41no—
540C24—21no—
541C24—21no—
542C24C2×C3×D411yescharacteristic
543#41—28no—
544#41—28no—
545#41—44no—
546#41—44no—
547#41—44no—
548#41—44no—
549#41—44no—
550#41—44no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C2×C3×D412yes—
568C2×Q8C2×C3×D412yes—
569C2×D4—24no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4C2×C3×D412yes—
584C2×D4C2×C3×D412yes—
585C2×D4C2×C3×D412yes—
586C2×D4C2×C3×D412yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—81no—
608C22×C4—81no—
609C22×C4C2×C3×D411yescharacteristic
610C22×C4C2×C3×D411yescharacteristic
611C22×C4C2×C3×D411yescharacteristic
612C22×C4C2×C3×D411yescharacteristic
613C22×C4C2×C3×D412yes—
614C22×C4C2×C3×D411yescharacteristic
615C22×C4C3×#4112yes—
616C22×C4C24×C311yescharacteristic
617Q16—28no—
618Q16—44no—
619SD16—28no—
620SD16—28no—
621SD16—44no—
622D8—28no—
623C2×C8—28no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8C2×C3×D412yes—
635C2×C8C2×C3×D412yes—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—42no—
644C4⋊C4—42no—
645C22⋊C4—22no—
646C22⋊C4—41no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C22×C3—22no—
660C22×C3—24no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—42no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—42no—
667C22×C3—42no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—42no—
675C22×C3—42no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3C2×#12111yescharacteristic
681C22×C3D4211yescharacteristic
682C22×C3D4211yescharacteristic
683C22×C3C2×#13511yescharacteristic
684C22×C3#57511yescharacteristic
685C22×C3#57711yescharacteristic
686C22×C3#57811yescharacteristic
687C3×C4—22no—
688C3×C4—22no—
689C3×C4—42no—
690C3×C4—42no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—81no—
695C3×C4—81no—
696C3×C4—81no—
697C3×C4—81no—
698C3×C4C2×#12011yescharacteristic
699C3×C4#53411yescharacteristic
700C3×C4#54611yescharacteristic
701C3×C4#54611yescharacteristic
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23C3×#12112yes—
723C23C22×C3×D411yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—48no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4C3×#12014yes—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—48no—
766C2×C4—48no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C3×#12112yes—
786C2×C4C3×#13512yescomplemented
787C2×C4C22×C3×D411yescharacteristic
788C2×C4C22×C3×D411yescharacteristic
789C2×C4C22×C3×D411yescharacteristic
790C2×C4C2×C3×#4111yescharacteristic
791C2×C4C3×H(5,𝔽2)11yescharacteristic
792C2×C4C3×H(5,𝔽2)11yescharacteristic
793C8—22no—
794C8—22no—
795C8—41no—
796C8—41no—
797C2×C3—42no—
798C2×C3—44no—
799C2×C3—82no—
800C2×C3#241011yescharacteristic
801C2×C3#303511yescharacteristic
802C2×C3#304611yescharacteristic
803C2×C3#326711yescharacteristic
804C2×C3#326911yescharacteristic
805C2×C3#328211yescharacteristic
806C2×C3#328311yescharacteristic
807C22—22no—
808C22—24no—
809C22—22no—
810C22—22no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22C2×C3×#12111yescharacteristic
829C22C3×D4211yescharacteristic
830C22C3×D4211yescharacteristic
831C22C2×C3×#13511yescharacteristic
832C22C3×#57511yescharacteristic
833C22C3×#57711yescharacteristic
834C22C3×#57811yescharacteristic
835C4—22no—
836C4—22no—
837C4—42no—
838C4—42no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—81no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4C2×C3×#12011yescharacteristic
847C4C3×#53411yescharacteristic
848C4C3×#54611yescharacteristic
849C4C3×#54611yescharacteristic
850C3#2436511yescharacteristic, direct product factor, Sylow
851C2—42no—
852C2—44no—
853C2—82no—
854C2C3×#241011yescharacteristic
855C2C3×#303511yescharacteristic
856C2C3×#304611yescharacteristic
857C2C3×#326711yescharacteristic
858C2C3×#326911yescharacteristic
859C2C3×#328211yescharacteristic
860C2C3×#328311yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#135C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#463C2semidirect
3. C2×C3×#461C2semidirect
4. C2×C3×#452C2semidirect
5. C3×#2432C2semidirect
6. C3×#2339C2semidirect
7. C3×#2056C2semidirect
8. C3×#2055C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
11. C3×#1892C2semidirect
12. C3×#1879C2semidirect
13. C3×#1877C2semidirect
14. C3×#1850C2semidirect
15. C3×#1788C2semidirect
16. #24365C3direct (N × H)
67. C2×#463C2×C3semidirect
68. C2×#461C2×C3semidirect
69. C2×#452C2×C3semidirect
70. #2432C2×C3semidirect
71. #2339C2×C3semidirect
72. #2056C2×C3semidirect
73. #2055C2×C3semidirect
74. #2016C2×C3semidirect
75. #2015C2×C3semidirect
76. #1892C2×C3semidirect
77. #1879C2×C3semidirect
78. #1877C2×C3semidirect
79. #1850C2×C3semidirect
80. #1788C2×C3semidirect
529. C2×C3×C4#135semidirect
786. C2×C4C3×#135semidirect
850. C3#24365direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1352
C2×C3×#4632
C2×C3×#4612
C2×C3×#4522
C3×#24322
C3×#23392
C3×#20562
C3×#20552
C3×#20162
C3×#20152
C3×#18922
C3×#18792
C3×#18772
C3×#18502
C3×#17882
#243653