Finite Group Databasebeta

← C3×#24369 #10642976

Subgroups — C3×#24369 #10642976

Order 768.

1388 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#462C211yesmaximal, characteristic, complemented
4C2×C3×#451C211yesmaximal, characteristic, complemented
5C3×#2432C211yesmaximal, characteristic
6C3×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2055C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#1894C211yesmaximal, characteristic, complemented
12C3×#1880C211yesmaximal, characteristic, complemented
13C3×#1878C211yesmaximal, characteristic, complemented
14C3×#1851C211yesmaximal, characteristic, complemented
15C3×#1788C211yesmaximal, characteristic
16#24369C311yesmaximal, 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×Q16C2211yescharacteristic
25C22×C3×Q16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29C2×C3×C4⋊Q8C2211yescharacteristic
30C2×C3×#124C2211yescharacteristic
31C2×C3×C22⋊Q8C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C3×#464—24no—
35C3×#462—24no—
36C3×#451—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×#103C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C3×#394—21no—
49C3×#394—21no—
50C3×#391—21no—
51C3×#391—21no—
52C3×#391C2211yescharacteristic
53C3×#391C2211yescharacteristic
54C3×#391C2211yescharacteristic
55C3×#390C2211yescharacteristic
56C3×#385—21no—
57C3×#385—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
67C2×#464C2×C311yescharacteristic, complemented
68C2×#462C2×C311yescharacteristic, complemented
69C2×#451C2×C311yescharacteristic, complemented
70#2432C2×C311yescharacteristic
71Q8×C22⋊C4C2×C311yescharacteristic, complemented
72#2056C2×C311yescharacteristic, complemented
73#2055C2×C311yescharacteristic, complemented
74#2016C2×C311yescharacteristic, complemented
75#2015C2×C311yescharacteristic, complemented
76#1894C2×C311yescharacteristic, complemented
77#1880C2×C311yescharacteristic, complemented
78#1878C2×C311yescharacteristic, complemented
79#1851C2×C311yescharacteristic, complemented
80#1788C2×C311yescharacteristic
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×Q8D414yes—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×Q8C2311yescharacteristic
97C22×C3×Q8C2311yescharacteristic
98C22×C3×D4—21no—
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4—21no—
101C23×C3×C4—21no—
102C23×C3×C4C2311yescharacteristic
103C3×#137—232no—
104C2×C3×Q16—22no—
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—22no—
110C2×C3×Q16—22no—
111C2×C3×Q16—22no—
112C2×C3×Q16—22no—
113C2×C3×Q16—41no—
114C2×C3×Q16—41no—
115C2×C3×Q16D414yes—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16—22no—
121C2×C3×SD16D414yes—
122C2×C3×M16—22no—
123C2×C3×M16—22no—
124C2×C3×M16—22no—
125C22×C3×C8C2311yescharacteristic
126C22×C3×C8C2311yescharacteristic
127C22×C3×C8C2311yescharacteristic
128C22×C3×C8C2311yescharacteristic
129C3×C4⋊Q8—22no—
130C3×C4⋊Q8—41no—
131C3×#124—22no—
132C3×#124—41no—
133C3×C22⋊Q8—22no—
134C3×C22⋊Q8—22no—
135C3×C4×Q8—22no—
136C3×C4×Q8—22no—
137C3×C4×Q8—41no—
138C3×C4×Q8—41no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
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⋊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—22no—
165C3×#103—22no—
166C3×#103—41no—
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×Q16C22×C311yescharacteristic
187C22×Q16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic
189C22×SD16C22×C311yescharacteristic
190C22×M16C22×C311yescharacteristic
191C2×C4⋊Q8C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×C22⋊Q8C22×C311yescharacteristic
194C2×C4×Q8C22×C311yescharacteristic
195C2×C4×Q8C22×C311yescharacteristic
196#464—24no—
197#462—24no—
198#451—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×#103C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×C22⋊C8C22×C311yescharacteristic
210#394—21no—
211#394—21no—
212#391—21no—
213#391—21no—
214#391C22×C311yescharacteristic
215#391C22×C311yescharacteristic
216#391C22×C311yescharacteristic
217#390C22×C311yescharacteristic
218#385—21no—
219#385—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×C3C2×D411yescharacteristic
230C3×#41—28no—
231C3×#41—44no—
232C3×#41—44no—
233C3×#41—44no—
234C2×C3×Q8—24no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—28no—
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×Q8—42no—
256C2×C3×Q8—42no—
257C2×C3×Q8—44no—
258C2×C3×Q8—44no—
259C2×C3×Q8—44no—
260C2×C3×Q8C2×D412yes—
261C2×C3×Q8C2×D412yes—
262C2×C3×Q8C2×D412yes—
263C2×C3×Q8C2×D412yes—
264C2×C3×Q8C2×D412yes—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4C2×D412yes—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—24no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
292C22×C3×C4C2×D411yescharacteristic
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4#4112yes—
298C22×C3×C4C2411yescharacteristic
299C3×Q16—28no—
300C3×Q16—28no—
301C3×Q16—44no—
302C3×Q16—44no—
303C3×SD16—28no—
304C3×SD16—28no—
305C3×M16—28no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8C2×D412yes—
317C2×C3×C8C2×D412yes—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—42no—
325C3×C4⋊C4—42no—
326C3×C4⋊C4—42no—
327C3×C4⋊C4—42no—
328C3×C4⋊C4—42no—
329C3×C22⋊C4—22no—
330C3×C22⋊C4—41no—
331C3×C22⋊C4—42no—
332C3×C22⋊C4—42no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C42—21no—
338C3×C42—21no—
339C3×C42—21no—
340C3×C42—21no—
341C3×C42—42no—
342C3×C42—42no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—41no—
348C2×#41—41no—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—41no—
354C22×Q8—41no—
355C22×Q8C3×D414yes—
356C22×Q8C23×C311yescharacteristic
357C22×Q8C23×C311yescharacteristic
358C22×Q8C23×C311yescharacteristic
359C22×Q8C23×C311yescharacteristic
360C22×D4—21no—
361C22×D4C23×C311yescharacteristic
362C23×C4—21no—
363C23×C4—21no—
364C23×C4C23×C311yescharacteristic
365#137—232no—
366C2×Q16—22no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16—41no—
376C2×Q16—41no—
377C2×Q16C3×D414yes—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16C3×D414yes—
384C2×M16—22no—
385C2×M16—22no—
386C2×M16—22no—
387C22×C8C23×C311yescharacteristic
388C22×C8C23×C311yescharacteristic
389C22×C8C23×C311yescharacteristic
390C22×C8C23×C311yescharacteristic
391C4⋊Q8—22no—
392C4⋊Q8—41no—
393#124—22no—
394#124—41no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—41no—
400C4×Q8—41no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4C23×C311yescharacteristic
407C2×C4⋊C4C23×C311yescharacteristic
408C2×C4⋊C4C23×C311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4C3×D411yescharacteristic
416C2×C22⋊C4C3×D411yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C23×C311yescharacteristic
420C2×C42C23×C311yescharacteristic
421C4⋊C8—22no—
422C4⋊C8—22no—
423#103—22no—
424#103—22no—
425#103—22no—
426#103—22no—
427#103—22no—
428#103—41no—
429#102—22no—
430#102—41no—
431C22⋊C8—22no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95C3×D411yescharacteristic
440#95C3×D411yescharacteristic
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—21no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—22no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3#12112yes—
455C23×C3C22×D411yescharacteristic
456C3×Q8—22no—
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8—22no—
461C3×Q8—22no—
462C3×Q8—22no—
463C3×Q8—48no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8#12014yes—
473C3×D4—22no—
474C3×D4—22no—
475C3×D4—48no—
476C3×D4—41no—
477C3×D4—41no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—48no—
501C2×C3×C4—48no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
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#12112yes—
519C2×C3×C4#13712yescomplemented
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C2×#4111yescharacteristic
524C2×C3×C4H(5,𝔽2)11yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C3×C8—22no—
527C3×C8—22no—
528C3×C8—41no—
529C3×C8—41no—
530C24—21no—
531C24C2×C3×D411yescharacteristic
532#41—28no—
533#41—44no—
534#41—44no—
535#41—44no—
536C2×Q8—24no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—28no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8C2×C3×D412yes—
563C2×Q8C2×C3×D412yes—
564C2×Q8C2×C3×D412yes—
565C2×Q8C2×C3×D412yes—
566C2×Q8C2×C3×D412yes—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4C2×C3×D412yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4C2×C3×D411yescharacteristic
594C22×C4C2×C3×D411yescharacteristic
595C22×C4C2×C3×D411yescharacteristic
596C22×C4C2×C3×D411yescharacteristic
597C22×C4C2×C3×D412yes—
598C22×C4C2×C3×D411yescharacteristic
599C22×C4C3×#4112yes—
600C22×C4C24×C311yescharacteristic
601Q16—28no—
602Q16—28no—
603Q16—44no—
604Q16—44no—
605SD16—28no—
606SD16—28no—
607M16—28no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×C3×D412yes—
619C2×C8C2×C3×D412yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C22⋊C4—22no—
632C22⋊C4—41no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—42no—
644C42—42no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3C2×#12111yescharacteristic
660C22×C3D4211yescharacteristic
661C22×C3D4211yescharacteristic
662C22×C3C2×#13711yescharacteristic
663C22×C3#57511yescharacteristic
664C22×C3#57811yescharacteristic
665C22×C3#57811yescharacteristic
666C3×C4—22no—
667C3×C4—24no—
668C3×C4—22no—
669C3×C4—42no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—81no—
678C3×C4C2×#12011yescharacteristic
679C3×C4#53411yescharacteristic
680C3×C4#54611yescharacteristic
681C3×C4#54611yescharacteristic
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23C3×#12112yes—
696C23C22×C3×D411yescharacteristic
697Q8—22no—
698Q8—22no—
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—48no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8C3×#12014yes—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4C3×#12112yes—
760C2×C4C3×#13712yescomplemented
761C2×C4C22×C3×D411yescharacteristic
762C2×C4C22×C3×D411yescharacteristic
763C2×C4C22×C3×D411yescharacteristic
764C2×C4C2×C3×#4111yescharacteristic
765C2×C4C3×H(5,𝔽2)11yescharacteristic
766C2×C4C3×H(5,𝔽2)11yescharacteristic
767C8—22no—
768C8—22no—
769C8—41no—
770C8—41no—
771C2×C3—42no—
772C2×C3—82no—
773C2×C3#241011yescharacteristic
774C2×C3#303711yescharacteristic
775C2×C3#304411yescharacteristic
776C2×C3#326911yescharacteristic
777C2×C3#327011yescharacteristic
778C2×C3#327611yescharacteristic
779C2×C3#327711yescharacteristic
780C22—22no—
781C22—22no—
782C22—22no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22C2×C3×#12111yescharacteristic
795C22C3×D4211yescharacteristic
796C22C3×D4211yescharacteristic
797C22C2×C3×#13711yescharacteristic
798C22C3×#57511yescharacteristic
799C22C3×#57811yescharacteristic
800C22C3×#57811yescharacteristic
801C4—22no—
802C4—24no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4—81no—
813C4C2×C3×#12011yescharacteristic
814C4C3×#53411yescharacteristic
815C4C3×#54611yescharacteristic
816C4C3×#54611yescharacteristic
817C3#2436911yescharacteristic, direct product factor, Sylow
818C2—42no—
819C2—82no—
820C2C3×#241011yescharacteristic
821C2C3×#303711yescharacteristic
822C2C3×#304411yescharacteristic
823C2C3×#326911yescharacteristic
824C2C3×#327011yescharacteristic
825C2C3×#327611yescharacteristic
826C2C3×#327711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#41C22
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×#464C2semidirect
3. C2×C3×#462C2semidirect
4. C2×C3×#451C2semidirect
6. C3×Q8×C22⋊C4C2semidirect
7. C3×#2056C2semidirect
8. C3×#2055C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
11. C3×#1894C2semidirect
12. C3×#1880C2semidirect
13. C3×#1878C2semidirect
14. C3×#1851C2semidirect
16. #24369C3direct (N × H)
67. C2×#464C2×C3semidirect
68. C2×#462C2×C3semidirect
69. C2×#451C2×C3semidirect
71. Q8×C22⋊C4C2×C3semidirect
72. #2056C2×C3semidirect
73. #2055C2×C3semidirect
74. #2016C2×C3semidirect
75. #2015C2×C3semidirect
76. #1894C2×C3semidirect
77. #1880C2×C3semidirect
78. #1878C2×C3semidirect
79. #1851C2×C3semidirect
519. C2×C3×C4#137semidirect
760. C2×C4C3×#137semidirect
817. C3#24369direct (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×#4622
C2×C3×#4512
C3×#24322
C3×Q8×C22⋊C42
C3×#20562
C3×#20552
C3×#20162
C3×#20152
C3×#18942
C3×#18802
C3×#18782
C3×#18512
C3×#17882
#243693