Finite Group Databasebeta

← C3×#24324 #10642931

Subgroups — C3×#24324 #10642931

Order 768.

1008 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3504C211yesmaximal, characteristic, complemented
2C3×#3077C211yesmaximal, characteristic, complemented
3C3×C4×AGL(1,ℤ/8)C211yesmaximal, characteristic
4C3×#2566C211yesmaximal, characteristic, complemented
5C3×#2061C211yesmaximal, characteristic, complemented
6C3×#2060C211yesmaximal, characteristic, complemented
7C3×#2027C211yesmaximal, characteristic, complemented
8C3×#2027C211yesmaximal, characteristic, complemented
9C3×#1998C211yesmaximal, characteristic, complemented
10C3×#1986C211yesmaximal, characteristic, complemented
11C3×#1883C211yesmaximal, characteristic
12C3×#1883C211yesmaximal, characteristic
13C3×#1860C211yesmaximal, characteristic, complemented
14C3×#1859C211yesmaximal, characteristic, complemented
15C3×#1806C211yesmaximal, characteristic, complemented
16#24324C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
18C3×#557—21no—
19C3×#557—21no—
20C3×#554—21no—
21C3×#554—21no—
22C3×#554—22no—
23C3×#554—22no—
24C3×#544—21no—
25C3×#544—21no—
26C3×#544C2211yescharacteristic
27C3×#544C2211yescharacteristic
28C3×#533—21no—
29C3×#533C2211yescharacteristic
30C2×C3×#125—21no—
31C2×C3×#125C2211yescharacteristic
32C3×#520C2211yescharacteristic
33C3×#520C2211yescharacteristic
34C3×C4×#41C2211yescharacteristic
35C2×C3×C4×D4C2211yescharacteristic
36C3×#478—21no—
37C3×#478—21no—
38C3×#476—21no—
39C3×#474—21no—
40C3×#442—21no—
41C3×#440—21no—
42C3×C4×SD16—21no—
43C3×C4×D8—21no—
44C3×#428C2211yescharacteristic
45C3×#428C2211yescharacteristic
46C3×#428C2211yescharacteristic
47C3×#423C2211yescharacteristic
48C2×C3×#104C2211yescharacteristic
49C2×C3×#104C2211yescharacteristic
50C3×#418C2211yescharacteristic
51C3×#418C2211yescharacteristic
52C3×#418C2211yescharacteristic
53C3×#417C2211yescharacteristic
54C3×C4×M16C2211yescharacteristic
55C3×#396—22no—
56C3×#390C2211yescharacteristic
57C3×#390C2211yescharacteristic
58C3×#385—22no—
59C3×#384C2211yescharacteristic
60C3×#382C2211yescharacteristic
61C3×C4×C4⋊C4C2211yescharacteristic
62C3×#343C2211yescharacteristic
63C3×#343C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#339C2211yescharacteristic
67C3×#339C2211yescharacteristic
68C3×#339C2211yescharacteristic
69C3×#339C2211yescharacteristic
70C3×#339C2211yescharacteristic
71C3×#339C2211yescharacteristic
72#3504C2×C311yescharacteristic, complemented
73#3077C2×C311yescharacteristic, complemented
74C4×AGL(1,ℤ/8)C2×C311yescharacteristic
75#2566C2×C311yescharacteristic, complemented
76#2061C2×C311yescharacteristic, complemented
77#2060C2×C311yescharacteristic, complemented
78#2027C2×C311yescharacteristic, complemented
79#2027C2×C311yescharacteristic, complemented
80#1998C2×C311yescharacteristic, complemented
81#1986C2×C311yescharacteristic, complemented
82#1883C2×C311yescharacteristic
83#1883C2×C311yescharacteristic
84#1860C2×C311yescharacteristic, complemented
85#1859C2×C311yescharacteristic, complemented
86#1806C2×C311yescharacteristic, complemented
87C2×C3×#41C2311yescharacteristic
88C22×C3×D4C2311yescharacteristic
89C23×C3×C4—21no—
90C3×AGL(1,ℤ/8)—22no—
91C3×AGL(1,ℤ/8)Q814yescomplemented
92C2×C3×SD16—21no—
93C2×C3×D8—21no—
94C2×C3×M16C2311yescharacteristic
95C2×C3×M16C2311yescharacteristic
96C2×C3×M16C2311yescharacteristic
97C2×C3×M16C2311yescharacteristic
98C3×C4⋊Q8—22no—
99C3×C4⋊Q8—22no—
100C3×C4⋊Q8—21no—
101C3×C4⋊Q8—21no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—21no—
104C3×C4⋊Q8D411yescharacteristic
105C3×C4⋊Q8D411yescharacteristic
106C3×#125—22no—
107C3×#125—22no—
108C3×#125—22no—
109C3×#125—22no—
110C3×#125—21no—
111C3×#125—21no—
112C3×#125—21no—
113C3×#125—21no—
114C3×#125—21no—
115C3×#125—21no—
116C3×#125—21no—
117C3×#125—21no—
118C3×#125D411yescharacteristic
119C3×#125D411yescharacteristic
120C3×C22⋊Q8—22no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—21no—
127C3×C22⋊Q8—21no—
128C3×C22⋊Q8—22no—
129C3×C22⋊Q8—22no—
130C3×C4×Q8—22no—
131C3×C4×Q8—22no—
132C3×C4×Q8—21no—
133C3×C4×Q8—21no—
134C3×C4×Q8—21no—
135C3×C4×Q8—21no—
136C3×C4×Q8D411yescharacteristic
137C3×C4×Q8D411yescharacteristic
138C3×C4×D4—21no—
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×C4×D4—21no—
142C3×C4×D4—22no—
143C3×C4×D4—22no—
144C3×C4×D4—21no—
145C3×C4×D4—21no—
146C3×C4×D4—21no—
147C3×C4×D4—21no—
148C3×C4×D4D411yescharacteristic
149C3×C4×D4D411yescharacteristic
150C3×#117—21no—
151C3×#117—21no—
152C3×#117—21no—
153C3×#117C2311yescharacteristic
154C3×#117C2311yescharacteristic
155C3×#117C2311yescharacteristic
156C2×C3×C4⋊C4—22no—
157C2×C3×C4⋊C4—22no—
158C2×C3×C4⋊C4—21no—
159C2×C3×C4⋊C4—21no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—22no—
162C2×C3×C4⋊C4D412yes—
163C2×C3×C4⋊C4D412yes—
164C2×C3×C4⋊C4C2311yescharacteristic
165C2×C3×C4⋊C4C2311yescharacteristic
166C2×C3×C4⋊C4C2311yescharacteristic
167C2×C3×C22⋊C4—22no—
168C2×C3×C22⋊C4—21no—
169C2×C3×C22⋊C4—22no—
170C2×C3×C42—21no—
171C2×C3×C42C2311yescharacteristic
172C2×C3×C42C2311yescharacteristic
173C2×C3×C42C2311yescharacteristic
174C3×#107—21no—
175C3×#107—21no—
176C3×#107—21no—
177C3×#106—21no—
178C3×#106—21no—
179C3×#106—21no—
180C3×C4⋊C8—21no—
181C3×C4⋊C8—21no—
182C3×#104—22no—
183C3×#104—22no—
184C3×#103—21no—
185C3×#102—21no—
186C3×#102—21no—
187C3×#102—21no—
188C3×#102—21no—
189C3×#102—21no—
190C3×#102—21no—
191C3×#102—21no—
192C3×#97—21no—
193C3×C4×C8—21no—
194C3×#95—21no—
195C3×#95—22no—
196C2×AGL(1,ℤ/8)C22×C311yescharacteristic
197#557—21no—
198#557—21no—
199#554—21no—
200#554—21no—
201#554—22no—
202#554—22no—
203#544—21no—
204#544—21no—
205#544C22×C311yescharacteristic
206#544C22×C311yescharacteristic
207#533—21no—
208#533C22×C311yescharacteristic
209C2×#125—21no—
210C2×#125C22×C311yescharacteristic
211#520C22×C311yescharacteristic
212#520C22×C311yescharacteristic
213C4×#41C22×C311yescharacteristic
214C2×C4×D4C22×C311yescharacteristic
215#478—21no—
216#478—21no—
217#476—21no—
218#474—21no—
219#442—21no—
220#440—21no—
221C4×SD16—21no—
222C4×D8—21no—
223#428C22×C311yescharacteristic
224#428C22×C311yescharacteristic
225#428C22×C311yescharacteristic
226#423C22×C311yescharacteristic
227C2×#104C22×C311yescharacteristic
228C2×#104C22×C311yescharacteristic
229#418C22×C311yescharacteristic
230#418C22×C311yescharacteristic
231#418C22×C311yescharacteristic
232#417C22×C311yescharacteristic
233C4×M16C22×C311yescharacteristic
234#396—22no—
235#390C22×C311yescharacteristic
236#390C22×C311yescharacteristic
237#385—22no—
238#384C22×C311yescharacteristic
239#382C22×C311yescharacteristic
240C4×C4⋊C4C22×C311yescharacteristic
241#343C22×C311yescharacteristic
242#343C22×C311yescharacteristic
243#343C22×C311yescharacteristic
244#343C22×C311yescharacteristic
245#339C22×C311yescharacteristic
246#339C22×C311yescharacteristic
247#339C22×C311yescharacteristic
248#339C22×C311yescharacteristic
249#339C22×C311yescharacteristic
250#339C22×C311yescharacteristic
251C24×C3—21no—
252C3×#41—21no—
253C3×#41—21no—
254C3×#41C2×Q812yes—
255C3×#41#4112yes—
256C2×C3×Q8—22no—
257C2×C3×Q8—22no—
258C2×C3×Q8—21no—
259C2×C3×Q8—21no—
260C2×C3×Q8C2×D411yescharacteristic
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×D4C2×D411yescharacteristic
268C2×C3×D4C2×Q812yes—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—41no—
278C22×C3×C4—41no—
279C22×C3×C4—82no—
280C22×C3×C4C2×D412yes—
281C22×C3×C4C2×D412yes—
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C3×SD16—24no—
286C3×D8—24no—
287C3×M16—21no—
288C3×M16—21no—
289C3×M16—21no—
290C3×M16—21no—
291C3×M16—21no—
292C3×M16—21no—
293C3×M16—21no—
294C3×M16C2×Q812yes—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C3×C4⋊C4—22no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—22no—
302C3×C4⋊C4—22no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—22no—
306C3×C4⋊C4—22no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—22no—
312C3×C4⋊C4—22no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
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—21no—
325C3×C4⋊C4—42no—
326C3×C4⋊C4—82no—
327C3×C4⋊C4C2×D411yescharacteristic
328C3×C4⋊C4C2×D411yescharacteristic
329C3×C4⋊C4C2×D411yescharacteristic
330C3×C4⋊C4C2×D411yescharacteristic
331C3×C4⋊C4C2×D411yescharacteristic
332C3×C4⋊C4C2×D411yescharacteristic
333C3×C22⋊C4—22no—
334C3×C22⋊C4—22no—
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—41no—
343C3×C22⋊C4—82no—
344C3×C42—22no—
345C3×C42—22no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—21no—
352C3×C42—21no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42C2×D411yescharacteristic
356C3×C42C2×D411yescharacteristic
357C3×C42C2×D411yescharacteristic
358C3×C42C2×D411yescharacteristic
359C2×#41C23×C311yescharacteristic
360C22×D4C23×C311yescharacteristic
361C23×C4—21no—
362AGL(1,ℤ/8)—22no—
363AGL(1,ℤ/8)C3×Q814yescomplemented
364C2×SD16—21no—
365C2×D8—21no—
366C2×M16C23×C311yescharacteristic
367C2×M16C23×C311yescharacteristic
368C2×M16C23×C311yescharacteristic
369C2×M16C23×C311yescharacteristic
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8C3×D411yescharacteristic
377C4⋊Q8C3×D411yescharacteristic
378#125—22no—
379#125—22no—
380#125—22no—
381#125—22no—
382#125—21no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387#125—21no—
388#125—21no—
389#125—21no—
390#125C3×D411yescharacteristic
391#125C3×D411yescharacteristic
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8C3×D411yescharacteristic
409C4×Q8C3×D411yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4C3×D411yescharacteristic
421C4×D4C3×D411yescharacteristic
422#117—21no—
423#117—21no—
424#117—21no—
425#117C23×C311yescharacteristic
426#117C23×C311yescharacteristic
427#117C23×C311yescharacteristic
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4C3×D412yes—
435C2×C4⋊C4C3×D412yes—
436C2×C4⋊C4C23×C311yescharacteristic
437C2×C4⋊C4C23×C311yescharacteristic
438C2×C4⋊C4C23×C311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C42—21no—
443C2×C42C23×C311yescharacteristic
444C2×C42C23×C311yescharacteristic
445C2×C42C23×C311yescharacteristic
446#107—21no—
447#107—21no—
448#107—21no—
449#106—21no—
450#106—21no—
451#106—21no—
452C4⋊C8—21no—
453C4⋊C8—21no—
454#104—22no—
455#104—22no—
456#103—21no—
457#102—21no—
458#102—21no—
459#102—21no—
460#102—21no—
461#102—21no—
462#102—21no—
463#102—21no—
464#97—21no—
465C4×C8—21no—
466#95—21no—
467#95—22no—
468C23×C3—21no—
469C23×C3—22no—
470C23×C3—42no—
471C23×C3—42no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3C22×D411yescharacteristic
475C3×Q8—21no—
476C3×Q8—81no—
477C3×Q8—81no—
478C3×Q8—82no—
479C3×Q8—82no—
480C3×Q8C22⋊Q812yes—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—21no—
485C3×D4—22no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4C22⋊Q812yes—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—42no—
506C2×C3×C4—42no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—42no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—81no—
513C2×C3×C4—81no—
514C2×C3×C4—82no—
515C2×C3×C4—82no—
516C2×C3×C4—82no—
517C2×C3×C4—82no—
518C2×C3×C4#12011yescharacteristic
519C2×C3×C4#12011yescharacteristic
520C2×C3×C4#12011yescharacteristic
521C2×C3×C4#12011yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C22×Q811yescharacteristic
525C2×C3×C4C2×#4111yescharacteristic
526C2×C3×C42−1+411yescharacteristic
527C2×C3×C42−1+411yescharacteristic
528C3×C8—22no—
529C3×C8—41no—
530C3×C8—41no—
531C3×C8—41no—
532C24—21no—
533#41—21no—
534#41—21no—
535#41C2×C3×Q812yes—
536#41C3×#4112yes—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C2×C3×D411yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4C2×C3×D411yescharacteristic
549C2×D4C2×C3×Q812yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—82no—
561C22×C4C2×C3×D412yes—
562C22×C4C2×C3×D412yes—
563C22×C4C2×C3×D411yescharacteristic
564C22×C4C2×C3×D411yescharacteristic
565C22×C4C24×C311yescharacteristic
566SD16—24no—
567D8—24no—
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16—21no—
573M16—21no—
574M16—21no—
575M16C2×C3×Q812yes—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—42no—
607C4⋊C4—82no—
608C4⋊C4C2×C3×D411yescharacteristic
609C4⋊C4C2×C3×D411yescharacteristic
610C4⋊C4C2×C3×D411yescharacteristic
611C4⋊C4C2×C3×D411yescharacteristic
612C4⋊C4C2×C3×D411yescharacteristic
613C4⋊C4C2×C3×D411yescharacteristic
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—44no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—82no—
625C42—22no—
626C42—22no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42C2×C3×D411yescharacteristic
637C42C2×C3×D411yescharacteristic
638C42C2×C3×D411yescharacteristic
639C42C2×C3×D411yescharacteristic
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—22no—
643C22×C3—44no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—82no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3C2×#12011yescharacteristic
651C22×C3#54811yescharacteristic
652C22×C3D4×Q811yescharacteristic
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—42no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4C2×C22⋊Q811yescharacteristic
670C3×C4#53611yescharacteristic
671C3×C4#54811yescharacteristic
672C3×C4D4×Q811yescharacteristic
673C23—21no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23C22×C3×D411yescharacteristic
680Q8—21no—
681Q8—81no—
682Q8—81no—
683Q8—82no—
684Q8—82no—
685Q8C3×C22⋊Q812yes—
686D4—22no—
687D4—22no—
688D4—22no—
689D4—21no—
690D4—22no—
691D4—41no—
692D4—41no—
693D4C3×C22⋊Q812yes—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4—82no—
723C2×C4C3×#12011yescharacteristic
724C2×C4C3×#12011yescharacteristic
725C2×C4C3×#12011yescharacteristic
726C2×C4C3×#12011yescharacteristic
727C2×C4C22×C3×D411yescharacteristic
728C2×C4C22×C3×D411yescharacteristic
729C2×C4C22×C3×Q811yescharacteristic
730C2×C4C2×C3×#4111yescharacteristic
731C2×C4C3×2−1+411yescharacteristic
732C2×C4C3×2−1+411yescharacteristic
733C8—22no—
734C8—41no—
735C8—41no—
736C8—41no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—82no—
741C2×C3#240911yescharacteristic
742C2×C3#301811yescharacteristic
743C2×C3#302111yescharacteristic
744C22—21no—
745C22—21no—
746C22—22no—
747C22—44no—
748C22—41no—
749C22—41no—
750C22—42no—
751C22—82no—
752C22—81no—
753C22—81no—
754C22C2×C3×#12011yescharacteristic
755C22C3×#54811yescharacteristic
756C22C3×D4×Q811yescharacteristic
757C4—22no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—42no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—81no—
772C4—81no—
773C4C2×C3×C22⋊Q811yescharacteristic
774C4C3×#53611yescharacteristic
775C4C3×#54811yescharacteristic
776C4C3×D4×Q811yescharacteristic
777C3#2432411yescharacteristic, direct product factor, Sylow
778C2—21no—
779C2—21no—
780C2—42no—
781C2—82no—
782C2C3×#240911yescharacteristic
783C2C3×#301811yescharacteristic
784C2C3×#302111yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#3504C2semidirect
2. C3×#3077C2semidirect
4. C3×#2566C2semidirect
5. C3×#2061C2semidirect
6. C3×#2060C2semidirect
7. C3×#2027C2semidirect
8. C3×#2027C2semidirect
9. C3×#1998C2semidirect
10. C3×#1986C2semidirect
13. C3×#1860C2semidirect
14. C3×#1859C2semidirect
15. C3×#1806C2semidirect
16. #24324C3direct (N × H)
72. #3504C2×C3semidirect
73. #3077C2×C3semidirect
75. #2566C2×C3semidirect
76. #2061C2×C3semidirect
77. #2060C2×C3semidirect
78. #2027C2×C3semidirect
79. #2027C2×C3semidirect
80. #1998C2×C3semidirect
81. #1986C2×C3semidirect
84. #1860C2×C3semidirect
85. #1859C2×C3semidirect
86. #1806C2×C3semidirect
91. C3×AGL(1,ℤ/8)Q8semidirect
363. AGL(1,ℤ/8)C3×Q8semidirect
777. C3#24324direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35042
C3×#30772
C3×C4×AGL(1,ℤ/8)2
C3×#25662
C3×#20612
C3×#20602
C3×#20272
C3×#19982
C3×#19862
C3×#18832
C3×#18602
C3×#18592
C3×#18062
#243243