Finite Group Databasebeta

← C3×#25808 #10644415

Subgroups — C3×#25808 #10644415

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#577C211yesmaximal, characteristic
2C3×#3156C211yesmaximal, characteristic, complemented
3C2×C3×#497C211yesmaximal, characteristic, complemented
4C2×C3×#473C211yesmaximal, characteristic, complemented
5C2×C3×#456C211yesmaximal, characteristic, complemented
6C2×C3×#455C211yesmaximal, characteristic, complemented
7C3×#3011C211yesmaximal, characteristic, complemented
8C3×#3009C211yesmaximal, characteristic, complemented
9C3×#2020C211yesmaximal, characteristic, complemented
10C3×#2019C211yesmaximal, characteristic, complemented
11C3×#2005C211yesmaximal, characteristic, complemented
12C3×#2003C211yesmaximal, characteristic, complemented
13C3×#1977C211yesmaximal, characteristic, complemented
14C3×#1975C211yesmaximal, characteristic, complemented
15C3×#1765C211yesmaximal, characteristic, complemented
16#25808C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×H(5,𝔽2)C2211yescharacteristic
19C3×#577—24no—
20C3×#577—24no—
21C2×C3×#137—21no—
22C2×C3×#137C2211yescharacteristic
23C2×C3×#137C2211yescharacteristic
24C2×C3×#137C2211yescharacteristic
25C2×C3×#137C2211yescharacteristic
26C2×C3×#137C2211yescharacteristic, complemented
27C2×C3×AGL(1,ℤ/8)—21no—
28C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
29C2×C3×#135—21no—
30C2×C3×#135C2211yescharacteristic
31C22×C3×Q16C2211yescharacteristic, complemented
32C22×C3×Q16C2211yescharacteristic, complemented
33C22×C3×SD16—21no—
34C22×C3×SD16C2211yescharacteristic
35C22×C3×SD16C2211yescharacteristic
36C2×C3×#131C2211yescharacteristic
37C3×#536C2211yescharacteristic
38C3×#536C2211yescharacteristic, complemented
39C2×C3×C4⋊Q8C2211yescharacteristic, complemented
40C2×C3×#124C2211yescharacteristic
41C3×#497—24no—
42C3×#497—21no—
43C3×#497—21no—
44C3×#495—21no—
45C3×#494—21no—
46C3×#473—24no—
47C3×#456—24no—
48C3×#455—24no—
49C3×#452—22no—
50C3×#452—22no—
51C3×#451—22no—
52C3×#450—22no—
53C2×C3×#108C2211yescharacteristic, complemented
54C2×C3×#104C2211yescharacteristic
55C2×C3×#104C2211yescharacteristic
56C2×C3×#104C2211yescharacteristic, complemented
57C3×#419C2211yescharacteristic, complemented
58C3×#418C2211yescharacteristic
59C3×#416C2211yescharacteristic
60C2×C3×#101C2211yescharacteristic, complemented
61C2×C3×#101C2211yescharacteristic, complemented
62C2×C3×#101C2211yescharacteristic, complemented
63C2×C3×#100C2211yescharacteristic
64C3×#408C2211yescharacteristic
65C3×#408C2211yescharacteristic, complemented
66C3×#405C2211yescharacteristic, complemented
67C2×C3×#97C2211yescharacteristic, complemented
68C3×#341C2211yescharacteristic, complemented
69C3×#339C2211yescharacteristic, complemented
70C2×#577C2×C311yescharacteristic
71#3156C2×C311yescharacteristic, complemented
72C2×#497C2×C311yescharacteristic, complemented
73C2×#473C2×C311yescharacteristic, complemented
74C2×#456C2×C311yescharacteristic, complemented
75C2×#455C2×C311yescharacteristic, complemented
76#3011C2×C311yescharacteristic, complemented
77#3009C2×C311yescharacteristic, complemented
78#2020C2×C311yescharacteristic, complemented
79#2019C2×C311yescharacteristic, complemented
80#2005C2×C311yescharacteristic, complemented
81#2003C2×C311yescharacteristic, complemented
82#1977C2×C311yescharacteristic, complemented
83#1975C2×C311yescharacteristic, complemented
84#1765C2×C311yescharacteristic, complemented
85C3×2−1+4—22no—
86C3×2−1+4—22no—
87C3×2−1+4—22no—
88C3×2−1+4—41no—
89C3×H(5,𝔽2)—22no—
90C3×H(5,𝔽2)—22no—
91C3×H(5,𝔽2)—22no—
92C3×H(5,𝔽2)—41no—
93C2×C3×#41—21no—
94C2×C3×#41—21no—
95C2×C3×#41—21no—
96C2×C3×#41—21no—
97C2×C3×#41—41no—
98C2×C3×#41C2311yescharacteristic
99C2×C3×#41C2311yescharacteristic
100C2×C3×#41C2311yescharacteristic
101C22×C3×Q8—21no—
102C22×C3×Q8—21no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2311yescharacteristic
106C22×C3×D4—21no—
107C22×C3×D4—21no—
108C22×C3×D4—41no—
109C22×C3×D4C2311yescharacteristic
110C3×#137—28no—
111C3×#137—22no—
112C3×#137—22no—
113C3×#137—22no—
114C3×#137—22no—
115C3×#137—22no—
116C3×#137—22no—
117C3×#137—22no—
118C3×#137—22no—
119C3×#137—41no—
120C3×#137—41no—
121C3×AGL(1,ℤ/8)—28no—
122C3×AGL(1,ℤ/8)—22no—
123C3×AGL(1,ℤ/8)—22no—
124C3×#135—28no—
125C3×#135—22no—
126C3×#135—22no—
127C2×C3×Q16—21no—
128C2×C3×Q16—22no—
129C2×C3×Q16—21no—
130C2×C3×Q16—21no—
131C2×C3×Q16—21no—
132C2×C3×Q16—21no—
133C2×C3×Q16—22no—
134C2×C3×Q16—22no—
135C2×C3×Q16—21no—
136C2×C3×Q16—21no—
137C2×C3×Q16—22no—
138C2×C3×Q16—41no—
139C2×C3×Q16D411yescharacteristic
140C2×C3×SD16—28no—
141C2×C3×SD16—21no—
142C2×C3×SD16—21no—
143C2×C3×SD16—22no—
144C2×C3×SD16—21no—
145C2×C3×SD16—21no—
146C2×C3×SD16—21no—
147C2×C3×SD16—21no—
148C2×C3×SD16—21no—
149C2×C3×SD16—21no—
150C2×C3×SD16—22no—
151C2×C3×SD16—22no—
152C2×C3×SD16—41no—
153C2×C3×SD16D411yescharacteristic
154C2×C3×SD16D414yes—
155C2×C3×SD16D411yescharacteristic
156C2×C3×D8—21no—
157C2×C3×D8D411yescharacteristic
158C3×#131—22no—
159C3×#131D414yes—
160C2×C3×M16—21no—
161C2×C3×M16C2311yescharacteristic
162C2×C3×M16C2311yescharacteristic
163C2×C3×M16C2311yescharacteristic
164C2×C3×M16C2311yescharacteristic
165C22×C3×C8—21no—
166C22×C3×C8C2311yescharacteristic
167C22×C3×C8C2311yescharacteristic
168C3×C4⋊Q8—22no—
169C3×C4⋊Q8—21no—
170C3×C4⋊Q8—21no—
171C3×C4⋊Q8—22no—
172C3×#124—22no—
173C3×#124—21no—
174C3×#124—21no—
175C3×#124—22no—
176C3×#123—41no—
177C3×#123—41no—
178C3×C22⋊Q8—22no—
179C3×C22⋊Q8—22no—
180C3×#117C2311yescharacteristic
181C2×C3×C4⋊C4—41no—
182C2×C3×C22⋊C4—41no—
183C2×C3×C42C2311yescharacteristic
184C3×#108—22no—
185C3×#104—22no—
186C3×#104—22no—
187C3×#104D414yes—
188C3×#103—22no—
189C3×#103D412yes—
190C3×#102—22no—
191C3×#102D412yes—
192C3×#101—22no—
193C3×#101—22no—
194C3×#101—22no—
195C3×#100—22no—
196C3×C22⋊C8—22no—
197C3×C22⋊C8—22no—
198C3×#97—22no—
199C3×#97—21no—
200C3×C4×C8—21no—
201C2×2−1+4C22×C311yescharacteristic
202C2×H(5,𝔽2)C22×C311yescharacteristic
203#577—24no—
204#577—24no—
205C2×#137—21no—
206C2×#137C22×C311yescharacteristic
207C2×#137C22×C311yescharacteristic
208C2×#137C22×C311yescharacteristic
209C2×#137C22×C311yescharacteristic
210C2×#137C22×C311yescharacteristic, complemented
211C2×AGL(1,ℤ/8)—21no—
212C2×AGL(1,ℤ/8)C22×C311yescharacteristic
213C2×#135—21no—
214C2×#135C22×C311yescharacteristic
215C22×Q16C22×C311yescharacteristic, complemented
216C22×Q16C22×C311yescharacteristic, complemented
217C22×SD16—21no—
218C22×SD16C22×C311yescharacteristic
219C22×SD16C22×C311yescharacteristic
220C2×#131C22×C311yescharacteristic
221#536C22×C311yescharacteristic
222#536C22×C311yescharacteristic, complemented
223C2×C4⋊Q8C22×C311yescharacteristic, complemented
224C2×#124C22×C311yescharacteristic
225#497—24no—
226#497—21no—
227#497—21no—
228#495—21no—
229#494—21no—
230#473—24no—
231#456—24no—
232#455—24no—
233#452—22no—
234#452—22no—
235#451—22no—
236#450—22no—
237C2×#108C22×C311yescharacteristic, complemented
238C2×#104C22×C311yescharacteristic
239C2×#104C22×C311yescharacteristic
240C2×#104C22×C311yescharacteristic, complemented
241#419C22×C311yescharacteristic, complemented
242#418C22×C311yescharacteristic
243#416C22×C311yescharacteristic
244C2×#101C22×C311yescharacteristic, complemented
245C2×#101C22×C311yescharacteristic, complemented
246C2×#101C22×C311yescharacteristic, complemented
247C2×#100C22×C311yescharacteristic
248#408C22×C311yescharacteristic
249#408C22×C311yescharacteristic, complemented
250#405C22×C311yescharacteristic, complemented
251C2×#97C22×C311yescharacteristic, complemented
252#341C22×C311yescharacteristic, complemented
253#339C22×C311yescharacteristic, complemented
254C24×C3—21no—
255C24×C3—41no—
256C3×#41—21no—
257C3×#41—21no—
258C3×#41—24no—
259C3×#41—24no—
260C3×#41—21no—
261C3×#41—21no—
262C3×#41—21no—
263C3×#41—21no—
264C3×#41—21no—
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—42no—
269C3×#41—44no—
270C3×#41—42no—
271C3×#41—42no—
272C3×#41—42no—
273C3×#41—44no—
274C3×#41—42no—
275C3×#41—42no—
276C3×#41C2×D412yes—
277C3×#41C2×D412yes—
278C2×C3×Q8—21no—
279C2×C3×Q8—24no—
280C2×C3×Q8—21no—
281C2×C3×Q8—21no—
282C2×C3×Q8—21no—
283C2×C3×Q8—21no—
284C2×C3×Q8—21no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—21no—
288C2×C3×Q8—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8—21no—
294C2×C3×Q8—21no—
295C2×C3×Q8—21no—
296C2×C3×Q8—41no—
297C2×C3×Q8—42no—
298C2×C3×Q8—42no—
299C2×C3×Q8—42no—
300C2×C3×Q8C2×D411yescharacteristic
301C2×C3×Q8C2×D412yes—
302C2×C3×Q8C2×D411yescharacteristic
303C2×C3×Q8C2×D411yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—24no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—42no—
314C2×C3×D4—41no—
315C2×C3×D4—41no—
316C2×C3×D4—42no—
317C2×C3×D4—44no—
318C2×C3×D4—44no—
319C2×C3×D4—41no—
320C2×C3×D4—42no—
321C2×C3×D4C2×D411yescharacteristic
322C2×C3×D4C2×D411yescharacteristic
323C2×C3×D4C2×D412yes—
324C2×C3×D4C2×D411yescharacteristic
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—21no—
328C22×C3×C4—21no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—21no—
332C22×C3×C4—41no—
333C22×C3×C4—41no—
334C22×C3×C4—41no—
335C22×C3×C4C2411yescharacteristic
336C3×Q16—24no—
337C3×Q16—22no—
338C3×Q16—44no—
339C3×Q16—42no—
340C3×Q16—42no—
341C3×Q16—42no—
342C3×Q16—42no—
343C3×Q16—42no—
344C3×Q16—42no—
345C3×SD16—24no—
346C3×SD16—24no—
347C3×SD16—22no—
348C3×SD16—24no—
349C3×SD16—24no—
350C3×SD16—22no—
351C3×SD16—44no—
352C3×SD16—42no—
353C3×SD16—42no—
354C3×SD16—42no—
355C3×SD16—42no—
356C3×D8—24no—
357C3×D8—22no—
358C3×M16—21no—
359C3×M16—21no—
360C3×M16—24no—
361C3×M16—21no—
362C3×M16—21no—
363C3×M16—21no—
364C3×M16—21no—
365C3×M16C2×D412yes—
366C3×M16C2×D412yes—
367C2×C3×C8—21no—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—21no—
371C2×C3×C8—24no—
372C2×C3×C8—21no—
373C2×C3×C8—21no—
374C2×C3×C8C2×D412yes—
375C2×C3×C8C2×D411yescharacteristic
376C2×C3×C8C2×D411yescharacteristic
377C2×C3×C8C2×D412yes—
378C2×C3×C8C2×D412yes—
379C3×C4⋊C4—44no—
380C3×C4⋊C4—42no—
381C3×C4⋊C4—42no—
382C3×C4⋊C4C2×D412yes—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—44no—
385C3×C22⋊C4—42no—
386C3×C22⋊C4—42no—
387C3×C42—21no—
388C3×C42—21no—
389C3×C42C2×D412yes—
3902−1+4—22no—
3912−1+4—22no—
3922−1+4—22no—
3932−1+4—41no—
394H(5,𝔽2)—22no—
395H(5,𝔽2)—22no—
396H(5,𝔽2)—22no—
397H(5,𝔽2)—41no—
398C2×#41—21no—
399C2×#41—21no—
400C2×#41—21no—
401C2×#41—21no—
402C2×#41—41no—
403C2×#41C23×C311yescharacteristic
404C2×#41C23×C311yescharacteristic
405C2×#41C23×C311yescharacteristic
406C22×Q8—21no—
407C22×Q8—21no—
408C22×Q8C23×C311yescharacteristic
409C22×Q8C23×C311yescharacteristic
410C22×Q8C23×C311yescharacteristic
411C22×D4—21no—
412C22×D4—21no—
413C22×D4—41no—
414C22×D4C23×C311yescharacteristic
415#137—28no—
416#137—22no—
417#137—22no—
418#137—22no—
419#137—22no—
420#137—22no—
421#137—22no—
422#137—22no—
423#137—22no—
424#137—41no—
425#137—41no—
426AGL(1,ℤ/8)—28no—
427AGL(1,ℤ/8)—22no—
428AGL(1,ℤ/8)—22no—
429#135—28no—
430#135—22no—
431#135—22no—
432C2×Q16—21no—
433C2×Q16—22no—
434C2×Q16—21no—
435C2×Q16—21no—
436C2×Q16—21no—
437C2×Q16—21no—
438C2×Q16—22no—
439C2×Q16—22no—
440C2×Q16—21no—
441C2×Q16—21no—
442C2×Q16—22no—
443C2×Q16—41no—
444C2×Q16C3×D411yescharacteristic
445C2×SD16—28no—
446C2×SD16—21no—
447C2×SD16—21no—
448C2×SD16—22no—
449C2×SD16—21no—
450C2×SD16—21no—
451C2×SD16—21no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×SD16—21no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—41no—
458C2×SD16C3×D411yescharacteristic
459C2×SD16C3×D414yes—
460C2×SD16C3×D411yescharacteristic
461C2×D8—21no—
462C2×D8C3×D411yescharacteristic
463#131—22no—
464#131C3×D414yes—
465C2×M16—21no—
466C2×M16C23×C311yescharacteristic
467C2×M16C23×C311yescharacteristic
468C2×M16C23×C311yescharacteristic
469C2×M16C23×C311yescharacteristic
470C22×C8—21no—
471C22×C8C23×C311yescharacteristic
472C22×C8C23×C311yescharacteristic
473C4⋊Q8—22no—
474C4⋊Q8—21no—
475C4⋊Q8—21no—
476C4⋊Q8—22no—
477#124—22no—
478#124—21no—
479#124—21no—
480#124—22no—
481#123—41no—
482#123—41no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485#117C23×C311yescharacteristic
486C2×C4⋊C4—41no—
487C2×C22⋊C4—41no—
488C2×C42C23×C311yescharacteristic
489#108—22no—
490#104—22no—
491#104—22no—
492#104C3×D414yes—
493#103—22no—
494#103C3×D412yes—
495#102—22no—
496#102C3×D412yes—
497#101—22no—
498#101—22no—
499#101—22no—
500#100—22no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503#97—22no—
504#97—21no—
505C4×C8—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—22no—
510C23×C3—44no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—82no—
514C23×C3—162no—
515C23×C3H(5,𝔽2)11yescharacteristic
516C3×Q8—21no—
517C3×Q8—21no—
518C3×Q8—22no—
519C3×Q8—21no—
520C3×Q8—22no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—44no—
524C3×Q8—41no—
525C3×Q8—41no—
526C3×Q8—41no—
527C3×Q8—41no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—41no—
531C3×Q8—41no—
532C3×Q8—41no—
533C3×Q8—41no—
534C3×Q8#12712yes—
535C3×D4—22no—
536C3×D4—22no—
537C3×D4—21no—
538C3×D4—22no—
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—22no—
542C3×D4—21no—
543C3×D4—21no—
544C3×D4—44no—
545C3×D4—44no—
546C3×D4—44no—
547C3×D4—41no—
548C3×D4—41no—
549C3×D4—41no—
550C3×D4—41no—
551C3×D4—41no—
552C3×D4—41no—
553C3×D4#12712yes—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—44no—
563C2×C3×C4—44no—
564C2×C3×C4—42no—
565C2×C3×C4—44no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—41no—
569C2×C3×C4—41no—
570C2×C3×C4—41no—
571C2×C3×C4—41no—
572C2×C3×C4—41no—
573C2×C3×C4—41no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—41no—
578C2×C3×C4C22×D411yescharacteristic
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4H(5,𝔽2)11yescharacteristic
584C3×C8—22no—
585C3×C8—22no—
586C3×C8—22no—
587C3×C8—41no—
588C3×C8—41no—
589C3×C8#12012yes—
590C3×C8#12012yes—
591C24—21no—
592C24—41no—
593#41—21no—
594#41—21no—
595#41—24no—
596#41—24no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—42no—
606#41—44no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—44no—
611#41—42no—
612#41—42no—
613#41C2×C3×D412yes—
614#41C2×C3×D412yes—
615C2×Q8—21no—
616C2×Q8—24no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—41no—
634C2×Q8—42no—
635C2×Q8—42no—
636C2×Q8—42no—
637C2×Q8C2×C3×D411yescharacteristic
638C2×Q8C2×C3×D412yes—
639C2×Q8C2×C3×D411yescharacteristic
640C2×Q8C2×C3×D411yescharacteristic
641C2×D4—21no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—42no—
651C2×D4—41no—
652C2×D4—41no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—41no—
657C2×D4—42no—
658C2×D4C2×C3×D411yescharacteristic
659C2×D4C2×C3×D411yescharacteristic
660C2×D4C2×C3×D412yes—
661C2×D4C2×C3×D411yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—41no—
670C22×C4—41no—
671C22×C4—41no—
672C22×C4C24×C311yescharacteristic
673Q16—24no—
674Q16—22no—
675Q16—44no—
676Q16—42no—
677Q16—42no—
678Q16—42no—
679Q16—42no—
680Q16—42no—
681Q16—42no—
682SD16—24no—
683SD16—24no—
684SD16—22no—
685SD16—24no—
686SD16—24no—
687SD16—22no—
688SD16—44no—
689SD16—42no—
690SD16—42no—
691SD16—42no—
692SD16—42no—
693D8—24no—
694D8—22no—
695M16—21no—
696M16—21no—
697M16—24no—
698M16—21no—
699M16—21no—
700M16—21no—
701M16—21no—
702M16C2×C3×D412yes—
703M16C2×C3×D412yes—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—24no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8C2×C3×D412yes—
712C2×C8C2×C3×D411yescharacteristic
713C2×C8C2×C3×D411yescharacteristic
714C2×C8C2×C3×D412yes—
715C2×C8C2×C3×D412yes—
716C4⋊C4—44no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4C2×C3×D412yes—
720C22⋊C4—21no—
721C22⋊C4—44no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C42—21no—
725C42—21no—
726C42C2×C3×D412yes—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—42no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—42no—
733C22×C3—42no—
734C22×C3—42no—
735C22×C3—82no—
736C22×C3—82no—
737C22×C3—161no—
738C22×C3—164no—
739C22×C3#53511yescharacteristic
740C22×C3D4211yescharacteristic
741C22×C3D4211yescharacteristic
742C3×C4—22no—
743C3×C4—42no—
744C3×C4—41no—
745C3×C4—42no—
746C3×C4—41no—
747C3×C4—42no—
748C3×C4—81no—
749C3×C4—81no—
750C3×C4C2×#12011yescharacteristic
751C3×C4C2×#12711yescharacteristic
752C3×C4D4211yescharacteristic
753C3×C4D4211yescharacteristic
754C23—21no—
755C23—21no—
756C23—21no—
757C23—22no—
758C23—44no—
759C23—41no—
760C23—41no—
761C23—82no—
762C23—162no—
763C23C3×H(5,𝔽2)11yescharacteristic
764Q8—21no—
765Q8—21no—
766Q8—22no—
767Q8—21no—
768Q8—22no—
769Q8—21no—
770Q8—21no—
771Q8—44no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776Q8—41no—
777Q8—41no—
778Q8—41no—
779Q8—41no—
780Q8—41no—
781Q8—41no—
782Q8C3×#12712yes—
783D4—22no—
784D4—22no—
785D4—21no—
786D4—22no—
787D4—21no—
788D4—21no—
789D4—22no—
790D4—21no—
791D4—21no—
792D4—44no—
793D4—44no—
794D4—44no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4C3×#12712yes—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4C22×C3×D411yescharacteristic
827C2×C4C22×C3×D411yescharacteristic
828C2×C4C22×C3×D411yescharacteristic
829C2×C4C22×C3×D411yescharacteristic
830C2×C4C22×C3×D411yescharacteristic
831C2×C4C3×H(5,𝔽2)11yescharacteristic
832C8—22no—
833C8—22no—
834C8—22no—
835C8—41no—
836C8—41no—
837C8C3×#12012yes—
838C8C3×#12012yes—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—42no—
842C2×C3—81no—
843C2×C3—81no—
844C2×C3—82no—
845C2×C3#243311yescharacteristic
846C2×C3#328912yes—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—82no—
856C22—82no—
857C22—161no—
858C22—164no—
859C22C3×#53511yescharacteristic
860C22C3×D4211yescharacteristic
861C22C3×D4211yescharacteristic
862C4—22no—
863C4—42no—
864C4—41no—
865C4—41no—
866C4—42no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4C2×C3×#12011yescharacteristic
871C4C2×C3×#12711yescharacteristic
872C4C3×D4211yescharacteristic
873C4C3×D4211yescharacteristic
874C3#2580811yescharacteristic, direct product factor, Sylow
875C2—21no—
876C2—21no—
877C2—42no—
878C2—81no—
879C2—81no—
880C2—82no—
881C2C3×#243311yescharacteristic
882C2C3×#328912yes—
subgroupG/H
center, socleC22×C3D42
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#577C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3156C2semidirect
3. C2×C3×#497C2semidirect
4. C2×C3×#473C2semidirect
5. C2×C3×#456C2semidirect
6. C2×C3×#455C2semidirect
7. C3×#3011C2semidirect
8. C3×#3009C2semidirect
9. C3×#2020C2semidirect
10. C3×#2019C2semidirect
11. C3×#2005C2semidirect
12. C3×#2003C2semidirect
13. C3×#1977C2semidirect
14. C3×#1975C2semidirect
15. C3×#1765C2semidirect
16. #25808C3direct (N × H)
26. C2×C3×#137C22semidirect
31. C22×C3×Q16C22semidirect
32. C22×C3×Q16C22semidirect
38. C3×#536C22semidirect
39. C2×C3×C4⋊Q8C22semidirect
53. C2×C3×#108C22semidirect
56. C2×C3×#104C22semidirect
57. C3×#419C22semidirect
60. C2×C3×#101C22semidirect
61. C2×C3×#101C22semidirect
62. C2×C3×#101C22semidirect
65. C3×#408C22semidirect
66. C3×#405C22semidirect
67. C2×C3×#97C22semidirect
68. C3×#341C22semidirect
69. C3×#339C22semidirect
71. #3156C2×C3semidirect
72. C2×#497C2×C3semidirect
73. C2×#473C2×C3semidirect
74. C2×#456C2×C3semidirect
75. C2×#455C2×C3semidirect
76. #3011C2×C3semidirect
77. #3009C2×C3semidirect
78. #2020C2×C3semidirect
79. #2019C2×C3semidirect
80. #2005C2×C3semidirect
81. #2003C2×C3semidirect
82. #1977C2×C3semidirect
83. #1975C2×C3semidirect
84. #1765C2×C3semidirect
210. C2×#137C22×C3semidirect
215. C22×Q16C22×C3semidirect
216. C22×Q16C22×C3semidirect
222. #536C22×C3semidirect
223. C2×C4⋊Q8C22×C3semidirect
237. C2×#108C22×C3semidirect
240. C2×#104C22×C3semidirect
241. #419C22×C3semidirect
244. C2×#101C22×C3semidirect
245. C2×#101C22×C3semidirect
246. C2×#101C22×C3semidirect
249. #408C22×C3semidirect
250. #405C22×C3semidirect
251. C2×#97C22×C3semidirect
252. #341C22×C3semidirect
253. #339C22×C3semidirect
874. C3#25808direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5772
C3×#31562
C2×C3×#4972
C2×C3×#4732
C2×C3×#4562
C2×C3×#4552
C3×#30112
C3×#30092
C3×#20202
C3×#20192
C3×#20052
C3×#20032
C3×#19772
C3×#19752
C3×#17652
#258083