Finite Group Databasebeta

← C3×#24368 #10642975

Subgroups — C3×#24368 #10642975

Order 768.

1446 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic, complemented
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#460C211yesmaximal, characteristic, complemented
4C2×C3×#448C211yesmaximal, characteristic, complemented
5C3×#2431C211yesmaximal, characteristic
6C3×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2055C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2014C211yesmaximal, characteristic, complemented
11C3×#1895C211yesmaximal, characteristic, complemented
12C3×#1880C211yesmaximal, characteristic, complemented
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1851C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic, complemented
16#24368C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C2×C3×#137—24no—
20C2×C3×#137—24no—
21C2×C3×#137—24no—
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29C2×C3×#127C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C3×#464—24no—
35C3×#460—24no—
36C3×#448—24no—
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×C4⋊C8C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#103C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C3×#392—21no—
49C3×#392—21no—
50C3×#391—21no—
51C3×#391—21no—
52C3×#391C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#391C2211yescharacteristic
55C3×#390C2211yescharacteristic
56C3×#386—21no—
57C3×#386—21no—
58C3×#380—21no—
59C3×#380C2211yescharacteristic
60C3×C4×C22⋊C4—21no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C3×#336C2211yescharacteristic
65C3×#336C2211yescharacteristic
66C22×#137C2×C311yescharacteristic, complemented
67C2×#464C2×C311yescharacteristic, complemented
68C2×#460C2×C311yescharacteristic, complemented
69C2×#448C2×C311yescharacteristic, complemented
70#2431C2×C311yescharacteristic
71Q8×C22⋊C4C2×C311yescharacteristic, complemented
72#2056C2×C311yescharacteristic, complemented
73#2055C2×C311yescharacteristic, complemented
74#2015C2×C311yescharacteristic, complemented
75#2014C2×C311yescharacteristic, complemented
76#1895C2×C311yescharacteristic, complemented
77#1880C2×C311yescharacteristic, complemented
78#1878C2×C311yescharacteristic, complemented
79#1851C2×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—41no—
86C2×C3×#41—41no—
87C22×C3×Q8—21no—
88C22×C3×Q8—22no—
89C22×C3×Q8—22no—
90C22×C3×Q8—22no—
91C22×C3×Q8—41no—
92C22×C3×Q8—41no—
93C22×C3×Q8D414yescomplemented
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4—21no—
105C23×C3×C4C2311yescharacteristic
106C3×#137—232no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—22no—
110C2×C3×Q16—22no—
111C2×C3×Q16—22no—
112C2×C3×Q16D414yescomplemented
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×SD16—22no—
121C2×C3×SD16—22no—
122C2×C3×SD16—41no—
123C2×C3×SD16—41no—
124C2×C3×SD16D414yescomplemented
125C2×C3×M16—22no—
126C2×C3×M16—22no—
127C2×C3×M16—22no—
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C22×C3×C8C2311yescharacteristic
132C3×#127—22no—
133C3×#127—41no—
134C3×#124—22no—
135C3×#124—41no—
136C3×#121—22no—
137C3×#121—22no—
138C3×C4×Q8—22no—
139C3×C4×Q8—22no—
140C3×C4×Q8—41no—
141C3×C4×Q8—41no—
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⋊C4D411yescharacteristic
154C2×C3×C22⋊C4D411yescharacteristic
155C2×C3×C42—21no—
156C2×C3×C42—21no—
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—41no—
165C3×#102—22no—
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
180C23×Q8C22×C311yescharacteristic
181C2×#137—24no—
182C2×#137—24no—
183C2×#137—24no—
184C22×Q16C22×C311yescharacteristic
185C22×Q16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic
189C22×SD16C22×C311yescharacteristic
190C22×M16C22×C311yescharacteristic
191C2×#127C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#121C22×C311yescharacteristic
194C2×C4×Q8C22×C311yescharacteristic
195C2×C4×Q8C22×C311yescharacteristic
196#464—24no—
197#460—24no—
198#448—24no—
199C2×C4⋊C8C22×C311yescharacteristic
200C2×C4⋊C8C22×C311yescharacteristic
201C2×#103C22×C311yescharacteristic
202C2×#103C22×C311yescharacteristic
203C2×#103C22×C311yescharacteristic
204C2×#103C22×C311yescharacteristic
205C2×#102C22×C311yescharacteristic
206C2×#102C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×C22⋊C8C22×C311yescharacteristic
210#392—21no—
211#392—21no—
212#391—21no—
213#391—21no—
214#391C22×C311yescharacteristic
215#391C22×C311yescharacteristic
216#391C22×C311yescharacteristic
217#390C22×C311yescharacteristic
218#386—21no—
219#386—21no—
220#380—21no—
221#380C22×C311yescharacteristic
222C4×C22⋊C4—21no—
223C4×C22⋊C4C22×C311yescharacteristic
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—44no—
233C3×#41—44no—
234C3×#41—44no—
235C2×C3×Q8—24no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—28no—
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—42no—
251C2×C3×Q8—42no—
252C2×C3×Q8—44no—
253C2×C3×Q8—44no—
254C2×C3×Q8—44no—
255C2×C3×Q8C2×D412yes—
256C2×C3×Q8C2×D412yes—
257C2×C3×Q8C2×D412yes—
258C2×C3×Q8C2×D412yes—
259C2×C3×Q8C2×D412yes—
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—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—81no—
280C2×C3×D4—81no—
281C2×C3×D4—81no—
282C2×C3×D4—81no—
283C2×C3×D4C2×D412yes—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—24no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—42no—
299C22×C3×C4—42no—
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4#4112yes—
307C22×C3×C4C2411yescharacteristic
308C3×Q16—28no—
309C3×Q16—28no—
310C3×SD16—28no—
311C3×SD16—28no—
312C3×SD16—44no—
313C3×SD16—44no—
314C3×M16—28no—
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×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8C2×D412yes—
326C2×C3×C8C2×D412yes—
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—42no—
334C3×C4⋊C4—42no—
335C3×C22⋊C4—22no—
336C3×C22⋊C4—41no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—42no—
340C3×C22⋊C4—42no—
341C3×C22⋊C4—81no—
342C3×C22⋊C4—81no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42—21no—
347C3×C42—42no—
348C3×C42—42no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—41no—
354C2×#41—41no—
355C22×Q8—21no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—41no—
360C22×Q8—41no—
361C22×Q8C3×D414yescomplemented
362C22×Q8C23×C311yescharacteristic
363C22×Q8C23×C311yescharacteristic
364C22×Q8C23×C311yescharacteristic
365C22×D4—21no—
366C22×D4—21no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4C23×C311yescharacteristic
370C22×D4C23×C311yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C23×C311yescharacteristic
374#137—232no—
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—22no—
378C2×Q16—22no—
379C2×Q16—22no—
380C2×Q16C3×D414yescomplemented
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—22no—
388C2×SD16—22no—
389C2×SD16—22no—
390C2×SD16—41no—
391C2×SD16—41no—
392C2×SD16C3×D414yescomplemented
393C2×M16—22no—
394C2×M16—22no—
395C2×M16—22no—
396C22×C8C23×C311yescharacteristic
397C22×C8C23×C311yescharacteristic
398C22×C8C23×C311yescharacteristic
399C22×C8C23×C311yescharacteristic
400#127—22no—
401#127—41no—
402#124—22no—
403#124—41no—
404#121—22no—
405#121—22no—
406C4×Q8—22no—
407C4×Q8—22no—
408C4×Q8—41no—
409C4×Q8—41no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4C23×C311yescharacteristic
413C2×C4⋊C4C23×C311yescharacteristic
414C2×C4⋊C4C23×C311yescharacteristic
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×C42—21no—
424C2×C42—21no—
425C2×C42C23×C311yescharacteristic
426C2×C42C23×C311yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429#103—22no—
430#103—22no—
431#103—22no—
432#103—41no—
433#102—22no—
434#102—22no—
435#102—22no—
436#102—41no—
437C22⋊C8—22no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95C3×D411yescharacteristic
446#95C3×D411yescharacteristic
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—22no—
454C23×C3—41no—
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—41no—
466C23×C3—41no—
467C23×C3#12112yes—
468C23×C3C22×D411yescharacteristic
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—22no—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—22no—
475C3×Q8—22no—
476C3×Q8—48no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8#12014yes—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—48no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—84no—
492C3×D4—84no—
493C3×D4—84no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
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—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—48no—
517C2×C3×C4—48no—
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—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4#12112yes—
532C2×C3×C4#13712yescomplemented
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4C22×D411yescharacteristic
536C2×C3×C4C2×#4111yescharacteristic
537C2×C3×C4H(5,𝔽2)11yescharacteristic
538C2×C3×C4H(5,𝔽2)11yescharacteristic
539C3×C8—22no—
540C3×C8—22no—
541C3×C8—41no—
542C3×C8—41no—
543C24—21no—
544C24—21no—
545C24C2×C3×D411yescharacteristic
546#41—28no—
547#41—44no—
548#41—44no—
549#41—44no—
550C2×Q8—24no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—28no—
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—42no—
566C2×Q8—42no—
567C2×Q8—44no—
568C2×Q8—44no—
569C2×Q8—44no—
570C2×Q8C2×C3×D412yes—
571C2×Q8C2×C3×D412yes—
572C2×Q8C2×C3×D412yes—
573C2×Q8C2×C3×D412yes—
574C2×Q8C2×C3×D412yes—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—81no—
595C2×D4—81no—
596C2×D4—81no—
597C2×D4—81no—
598C2×D4C2×C3×D412yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4C2×C3×D411yescharacteristic
616C22×C4C2×C3×D411yescharacteristic
617C22×C4C2×C3×D411yescharacteristic
618C22×C4C2×C3×D411yescharacteristic
619C22×C4C2×C3×D412yes—
620C22×C4C2×C3×D411yescharacteristic
621C22×C4C3×#4112yes—
622C22×C4C24×C311yescharacteristic
623Q16—28no—
624Q16—28no—
625SD16—28no—
626SD16—28no—
627SD16—44no—
628SD16—44no—
629M16—28no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8C2×C3×D412yes—
641C2×C8C2×C3×D412yes—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—81no—
657C22⋊C4—81no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—42no—
663C42—42no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—22no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—42no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—81no—
680C22×C3—81no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3C2×#12111yescharacteristic
686C22×C3D4211yescharacteristic
687C22×C3D4211yescharacteristic
688C22×C3C2×#13711yescharacteristic
689C22×C3#57511yescharacteristic
690C22×C3#57711yescharacteristic
691C22×C3#57711yescharacteristic
692C3×C4—22no—
693C3×C4—24no—
694C3×C4—22no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—81no—
701C3×C4—81no—
702C3×C4—81no—
703C3×C4C2×#12011yescharacteristic
704C3×C4#53411yescharacteristic
705C3×C4#54611yescharacteristic
706C3×C4#54611yescharacteristic
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23C3×#12112yes—
728C23C22×C3×D411yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—22no—
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—48no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8C3×#12014yes—
742D4—22no—
743D4—22no—
744D4—48no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—84no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—48no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4C3×#12112yes—
792C2×C4C3×#13712yescomplemented
793C2×C4C22×C3×D411yescharacteristic
794C2×C4C22×C3×D411yescharacteristic
795C2×C4C22×C3×D411yescharacteristic
796C2×C4C2×C3×#4111yescharacteristic
797C2×C4C3×H(5,𝔽2)11yescharacteristic
798C2×C4C3×H(5,𝔽2)11yescharacteristic
799C8—22no—
800C8—22no—
801C8—41no—
802C8—41no—
803C2×C3—42no—
804C2×C3—82no—
805C2×C3—161no—
806C2×C3#241011yescharacteristic
807C2×C3#303711yescharacteristic
808C2×C3#304311yescharacteristic
809C2×C3#326611yescharacteristic
810C2×C3#327111yescharacteristic
811C2×C3#327511yescharacteristic
812C2×C3#327811yescharacteristic
813C22—22no—
814C22—22no—
815C22—22no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22C2×C3×#12111yescharacteristic
835C22C3×D4211yescharacteristic
836C22C3×D4211yescharacteristic
837C22C2×C3×#13711yescharacteristic
838C22C3×#57511yescharacteristic
839C22C3×#57711yescharacteristic
840C22C3×#57711yescharacteristic
841C4—22no—
842C4—24no—
843C4—22no—
844C4—42no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4C2×C3×#12011yescharacteristic
853C4C3×#53411yescharacteristic
854C4C3×#54611yescharacteristic
855C4C3×#54611yescharacteristic
856C3#2436811yescharacteristic, direct product factor, Sylow
857C2—42no—
858C2—82no—
859C2—161no—
860C2C3×#241011yescharacteristic
861C2C3×#303711yescharacteristic
862C2C3×#304311yescharacteristic
863C2C3×#326611yescharacteristic
864C2C3×#327111yescharacteristic
865C2C3×#327511yescharacteristic
866C2C3×#327811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2431C2
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
1. C22×C3×#137C2semidirect
2. C2×C3×#464C2semidirect
3. C2×C3×#460C2semidirect
4. C2×C3×#448C2semidirect
6. C3×Q8×C22⋊C4C2semidirect
7. C3×#2056C2semidirect
8. C3×#2055C2semidirect
9. C3×#2015C2semidirect
10. C3×#2014C2semidirect
11. C3×#1895C2semidirect
12. C3×#1880C2semidirect
13. C3×#1878C2semidirect
14. C3×#1851C2semidirect
15. C3×#1788C2semidirect
16. #24368C3direct (N × H)
66. C22×#137C2×C3semidirect
67. C2×#464C2×C3semidirect
68. C2×#460C2×C3semidirect
69. C2×#448C2×C3semidirect
71. Q8×C22⋊C4C2×C3semidirect
72. #2056C2×C3semidirect
73. #2055C2×C3semidirect
74. #2015C2×C3semidirect
75. #2014C2×C3semidirect
76. #1895C2×C3semidirect
77. #1880C2×C3semidirect
78. #1878C2×C3semidirect
79. #1851C2×C3semidirect
80. #1788C2×C3semidirect
93. C22×C3×Q8D4semidirect
112. C2×C3×Q16D4semidirect
124. C2×C3×SD16D4semidirect
361. C22×Q8C3×D4semidirect
380. C2×Q16C3×D4semidirect
392. C2×SD16C3×D4semidirect
532. C2×C3×C4#137semidirect
792. C2×C4C3×#137semidirect
856. C3#24368direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1372
C2×C3×#4642
C2×C3×#4602
C2×C3×#4482
C3×#24312
C3×Q8×C22⋊C42
C3×#20562
C3×#20552
C3×#20152
C3×#20142
C3×#18952
C3×#18802
C3×#18782
C3×#18512
C3×#17882
#243683