Finite Group Databasebeta

← C3×#25543 #10644150

Subgroups — C3×#25543 #10644150

Order 768.

1228 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#554C211yesmaximal, characteristic, complemented
2C2×C3×#481C211yesmaximal, characteristic, complemented
3C2×C3×#465C211yesmaximal, characteristic, complemented
4C3×#2416C211yesmaximal, characteristic
5C3×#2058C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2023C211yesmaximal, characteristic, complemented
8C3×#2000C211yesmaximal, characteristic, complemented
9C3×#1880C211yesmaximal, characteristic, complemented
10C3×#1874C211yesmaximal, characteristic, complemented
11C3×#1872C211yesmaximal, characteristic, complemented
12C3×#1869C211yesmaximal, characteristic, complemented
13C3×#1865C211yesmaximal, characteristic, complemented
14C3×#1853C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#25543C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C23×C3×C8C2211yescharacteristic
19C3×#554—24no—
20C3×#554—24no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#125—21no—
23C2×C3×C22⋊Q8—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C22×C3×C4⋊C4C2211yescharacteristic
34C22×C3×C4⋊C4C2211yescharacteristic
35C22×C3×C4⋊C4C2211yescharacteristic
36C3×#481—24no—
37C3×#465—24no—
38C2×C3×#106C2211yescharacteristic
39C2×C3×#106C2211yescharacteristic
40C2×C3×#106C2211yescharacteristic
41C2×C3×#103C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×#102C2211yescharacteristic
46C2×C3×#102C2211yescharacteristic
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C3×#396—21no—
51C3×#394—21no—
52C3×#390C2211yescharacteristic
53C3×#389C2211yescharacteristic
54C3×#386—21no—
55C3×#380C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#554C2×C311yescharacteristic, complemented
65C2×#481C2×C311yescharacteristic, complemented
66C2×#465C2×C311yescharacteristic, complemented
67#2416C2×C311yescharacteristic
68#2058C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2023C2×C311yescharacteristic, complemented
71#2000C2×C311yescharacteristic, complemented
72#1880C2×C311yescharacteristic, complemented
73#1874C2×C311yescharacteristic, complemented
74#1872C2×C311yescharacteristic, complemented
75#1869C2×C311yescharacteristic, complemented
76#1865C2×C311yescharacteristic, complemented
77#1853C2×C311yescharacteristic, complemented
78C2×#340C2×C311yescharacteristic, complemented
79C22×C3×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4—21no—
83C22×C3×D4D411yescharacteristic
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C23×C3×C4—21no—
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—41no—
93C22×C3×C8—22no—
94C22×C3×C8—22no—
95C22×C3×C8—41no—
96C22×C3×C8C2311yescharacteristic
97C22×C3×C8C2311yescharacteristic
98C22×C3×C8C2311yescharacteristic
99C22×C3×C8C2311yescharacteristic
100C3×C4⋊Q8—22no—
101C3×C4⋊Q8—22no—
102C3×#125—28no—
103C3×C22⋊Q8—28no—
104C3×C22⋊Q8—28no—
105C3×C22⋊Q8—22no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8D414yescomplemented
109C3×#121—22no—
110C3×#121—22no—
111C3×#121—22no—
112C3×#121—41no—
113C3×#121—44no—
114C3×C4×Q8—22no—
115C3×C4×Q8—22no—
116C3×C4×D4—28no—
117C3×C4×D4—22no—
118C3×C4×D4—22no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—21no—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—22no—
127C2×C3×C4⋊C4—22no—
128C2×C3×C4⋊C4—22no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—41no—
132C2×C3×C4⋊C4D411yescharacteristic
133C2×C3×C4⋊C4D414yescomplemented
134C2×C3×C4⋊C4C2311yescharacteristic
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C22⋊C4—21no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4D411yescharacteristic
148C2×C3×C22⋊C4D411yescharacteristic
149C2×C3×C42—21no—
150C2×C3×C42C2311yescharacteristic
151C3×#106—22no—
152C3×#106—22no—
153C3×#106—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—41no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—22no—
160C3×C22⋊C8—22no—
161C3×C22⋊C8—22no—
162C3×C22⋊C8—41no—
163C3×#95—21no—
164C3×#95—21no—
165C22×SD16C22×C311yescharacteristic
166C23×C8C22×C311yescharacteristic
167#554—24no—
168#554—24no—
169C2×C4⋊Q8C22×C311yescharacteristic
170C2×#125—21no—
171C2×C22⋊Q8—21no—
172C2×C22⋊Q8—21no—
173C2×C22⋊Q8C22×C311yescharacteristic
174C2×C22⋊Q8C22×C311yescharacteristic
175C2×#121—21no—
176C2×#121C22×C311yescharacteristic
177C2×#121C22×C311yescharacteristic
178C2×C4×Q8C22×C311yescharacteristic
179C2×C4×D4—21no—
180C2×C4×D4C22×C311yescharacteristic
181C22×C4⋊C4C22×C311yescharacteristic
182C22×C4⋊C4C22×C311yescharacteristic
183C22×C4⋊C4C22×C311yescharacteristic
184#481—24no—
185#465—24no—
186C2×#106C22×C311yescharacteristic
187C2×#106C22×C311yescharacteristic
188C2×#106C22×C311yescharacteristic
189C2×#103C22×C311yescharacteristic
190C2×#103C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#102C22×C311yescharacteristic
193C2×#102C22×C311yescharacteristic
194C2×#102C22×C311yescharacteristic
195C2×C22⋊C8C22×C311yescharacteristic
196C2×C22⋊C8C22×C311yescharacteristic
197C2×C22⋊C8C22×C311yescharacteristic
198#396—21no—
199#394—21no—
200#390C22×C311yescharacteristic
201#389C22×C311yescharacteristic
202#386—21no—
203#380C22×C311yescharacteristic
204#340C22×C311yescharacteristic
205#340C22×C311yescharacteristic
206#340C22×C311yescharacteristic
207#340C22×C311yescharacteristic
208#340C22×C311yescharacteristic
209#340C22×C311yescharacteristic
210#336C22×C311yescharacteristic
211#336C22×C311yescharacteristic
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D411yescharacteristic
215C2×C3×Q8—24no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—81no—
222C2×C3×Q8—81no—
223C2×C3×Q8C2×D412yes—
224C2×C3×D4—22no—
225C2×C3×D4—22no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—42no—
235C2×C3×D4—42no—
236C2×C3×D4—42no—
237C2×C3×D4—81no—
238C2×C3×D4SD1614yescomplemented
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—24no—
249C22×C3×C4—24no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—42no—
259C22×C3×C4—42no—
260C22×C3×C4—81no—
261C22×C3×C4—81no—
262C22×C3×C4—81no—
263C22×C3×C4—81no—
264C22×C3×C4—81no—
265C22×C3×C4C2×D411yescharacteristic
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2×D411yescharacteristic
268C22×C3×C4C2×D412yes—
269C22×C3×C4C2×D412yes—
270C22×C3×C4C2×D411yescharacteristic
271C22×C3×C4C2411yescharacteristic
272C3×SD16—44no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—44no—
285C2×C3×C8#4112yes—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—24no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C4⋊C4—21no—
296C3×C4⋊C4—21no—
297C3×C4⋊C4—21no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—21no—
301C3×C4⋊C4—42no—
302C3×C4⋊C4—42no—
303C3×C4⋊C4C2×D412yes—
304C3×C4⋊C4C2×D412yes—
305C3×C4⋊C4C2×D412yes—
306C3×C4⋊C4#4112yes—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—24no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—42no—
312C3×C22⋊C4—42no—
313C3×C22⋊C4—42no—
314C3×C22⋊C4—42no—
315C3×C22⋊C4—81no—
316C3×C42—24no—
317C3×C42—21no—
318C3×C42—21no—
319C22×Q8—21no—
320C22×Q8C23×C311yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C3×D411yescharacteristic
324C22×D4C23×C311yescharacteristic
325C23×C4—21no—
326C23×C4—21no—
327C23×C4—21no—
328C23×C4C23×C311yescharacteristic
329C23×C4C23×C311yescharacteristic
330C2×SD16—22no—
331C2×SD16—22no—
332C2×SD16—41no—
333C22×C8—22no—
334C22×C8—22no—
335C22×C8—41no—
336C22×C8C23×C311yescharacteristic
337C22×C8C23×C311yescharacteristic
338C22×C8C23×C311yescharacteristic
339C22×C8C23×C311yescharacteristic
340C4⋊Q8—22no—
341C4⋊Q8—22no—
342#125—28no—
343C22⋊Q8—28no—
344C22⋊Q8—28no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8C3×D414yescomplemented
349#121—22no—
350#121—22no—
351#121—22no—
352#121—41no—
353#121—44no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—28no—
357C4×D4—22no—
358C4×D4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4C3×D411yescharacteristic
373C2×C4⋊C4C3×D414yescomplemented
374C2×C4⋊C4C23×C311yescharacteristic
375C2×C4⋊C4C23×C311yescharacteristic
376C2×C4⋊C4C23×C311yescharacteristic
377C2×C4⋊C4C23×C311yescharacteristic
378C2×C4⋊C4C23×C311yescharacteristic
379C2×C4⋊C4C23×C311yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4C3×D411yescharacteristic
388C2×C22⋊C4C3×D411yescharacteristic
389C2×C42—21no—
390C2×C42C23×C311yescharacteristic
391#106—22no—
392#106—22no—
393#106—22no—
394#103—22no—
395#103—22no—
396#103—41no—
397#102—22no—
398#102—22no—
399#102—22no—
400C22⋊C8—22no—
401C22⋊C8—22no—
402C22⋊C8—41no—
403#95—21no—
404#95—21no—
405C23×C3—21no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—41no—
416C23×C3—41no—
417C23×C3—41no—
418C23×C3—41no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3#12012yes—
423C23×C3C2×SD1612yes—
424C23×C3C2×SD1612yes—
425C23×C3#13712yes—
426C23×C3C22×D411yescharacteristic
427C3×Q8—22no—
428C3×Q8—22no—
429C3×Q8—41no—
430C3×Q8—41no—
431C3×Q8—84no—
432C3×D4—28no—
433C3×D4—41no—
434C3×D4—41no—
435C3×D4—41no—
436C3×D4—41no—
437C3×D4—84no—
438C3×D4—84no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—22no—
450C2×C3×C4—21no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—84no—
479C2×C3×C4—84no—
480C2×C3×C4—84no—
481C2×C3×C4#12012yes—
482C2×C3×C4C2×SD1612yes—
483C2×C3×C4C22×D411yescharacteristic
484C2×C3×C4C22×D411yescharacteristic
485C2×C3×C4C2×#4111yescharacteristic
486C2×C3×C4C2×#4111yescharacteristic
487C2×C3×C4H(5,𝔽2)11yescharacteristic
488C2×C3×C42−1+411yescharacteristic
489C3×C8—22no—
490C3×C8—41no—
491C3×C8—41no—
492C3×C8—41no—
493C24—21no—
494C24C2×C3×D411yescharacteristic
495C24C2×C3×D411yescharacteristic
496C2×Q8—24no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—81no—
503C2×Q8—81no—
504C2×Q8C2×C3×D412yes—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—42no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4C3×SD1614yescomplemented
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—81no—
546C22×C4C2×C3×D411yescharacteristic
547C22×C4C2×C3×D411yescharacteristic
548C22×C4C2×C3×D411yescharacteristic
549C22×C4C2×C3×D412yes—
550C22×C4C2×C3×D412yes—
551C22×C4C2×C3×D411yescharacteristic
552C22×C4C24×C311yescharacteristic
553SD16—44no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—44no—
566C2×C8C3×#4112yes—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4C2×C3×D412yes—
585C4⋊C4C2×C3×D412yes—
586C4⋊C4C2×C3×D412yes—
587C4⋊C4C3×#4112yes—
588C22⋊C4—24no—
589C22⋊C4—24no—
590C22⋊C4—22no—
591C22⋊C4—22no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—42no—
596C22⋊C4—81no—
597C42—24no—
598C42—21no—
599C42—21no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—81no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—81no—
617C22×C3—81no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3#44814yes—
621C22×C3C2×#12011yescharacteristic
622C22×C3#54611yescharacteristic
623C22×C3#54711yescharacteristic
624C22×C3C22×SD1611yescharacteristic
625C22×C3C2×#13711yescharacteristic
626C22×C3#57611yescharacteristic
627C22×C3#57711yescharacteristic
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—41no—
631C3×C4—42no—
632C3×C4—41no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4—42no—
637C3×C4—81no—
638C3×C4—81no—
639C3×C4#53211yescharacteristic
640C3×C4#53711yescharacteristic
641C3×C4#54611yescharacteristic
642C3×C4#54711yescharacteristic
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23C3×#12012yes—
661C23C2×C3×SD1612yes—
662C23C2×C3×SD1612yes—
663C23C3×#13712yes—
664C23C22×C3×D411yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—41no—
668Q8—41no—
669Q8—84no—
670D4—28no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—84no—
676D4—84no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4C3×#12012yes—
720C2×C4C2×C3×SD1612yes—
721C2×C4C22×C3×D411yescharacteristic
722C2×C4C22×C3×D411yescharacteristic
723C2×C4C2×C3×#4111yescharacteristic
724C2×C4C2×C3×#4111yescharacteristic
725C2×C4C3×H(5,𝔽2)11yescharacteristic
726C2×C4C3×2−1+411yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C2×C3—24no—
732C2×C3—42no—
733C2×C3—161no—
734C2×C3#243011yescharacteristic
735C2×C3C2×#44811yescharacteristic
736C2×C3#301211yescharacteristic
737C2×C3#329511yescharacteristic
738C2×C3#331611yescharacteristic
739C2×C3#333511yescharacteristic
740C2×C3#334611yescharacteristic
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22C3×#44814yes—
762C22C2×C3×#12011yescharacteristic
763C22C3×#54611yescharacteristic
764C22C3×#54711yescharacteristic
765C22C22×C3×SD1611yescharacteristic
766C22C2×C3×#13711yescharacteristic
767C22C3×#57611yescharacteristic
768C22C3×#57711yescharacteristic
769C4—22no—
770C4—22no—
771C4—41no—
772C4—42no—
773C4—41no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—81no—
779C4—81no—
780C4C3×#53211yescharacteristic
781C4C3×#53711yescharacteristic
782C4C3×#54611yescharacteristic
783C4C3×#54711yescharacteristic
784C3#2554311yescharacteristic, direct product factor, Sylow
785C2—24no—
786C2—42no—
787C2—161no—
788C2C3×#243011yescharacteristic
789C2C2×C3×#44811yescharacteristic
790C2C3×#301211yescharacteristic
791C2C3×#329511yescharacteristic
792C2C3×#331611yescharacteristic
793C2C3×#333511yescharacteristic
794C2C3×#334611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2416C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#554C2semidirect
2. C2×C3×#481C2semidirect
3. C2×C3×#465C2semidirect
5. C3×#2058C2semidirect
6. C3×#2035C2semidirect
7. C3×#2023C2semidirect
8. C3×#2000C2semidirect
9. C3×#1880C2semidirect
10. C3×#1874C2semidirect
11. C3×#1872C2semidirect
12. C3×#1869C2semidirect
13. C3×#1865C2semidirect
14. C3×#1853C2semidirect
15. C2×C3×#340C2semidirect
16. #25543C3direct (N × H)
64. C2×#554C2×C3semidirect
65. C2×#481C2×C3semidirect
66. C2×#465C2×C3semidirect
68. #2058C2×C3semidirect
69. #2035C2×C3semidirect
70. #2023C2×C3semidirect
71. #2000C2×C3semidirect
72. #1880C2×C3semidirect
73. #1874C2×C3semidirect
74. #1872C2×C3semidirect
75. #1869C2×C3semidirect
76. #1865C2×C3semidirect
77. #1853C2×C3semidirect
78. C2×#340C2×C3semidirect
108. C3×C22⋊Q8D4semidirect
133. C2×C3×C4⋊C4D4semidirect
238. C2×C3×D4SD16semidirect
348. C22⋊Q8C3×D4semidirect
373. C2×C4⋊C4C3×D4semidirect
519. C2×D4C3×SD16semidirect
784. C3#25543direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5542
C2×C3×#4812
C2×C3×#4652
C3×#24162
C3×#20582
C3×#20352
C3×#20232
C3×#20002
C3×#18802
C3×#18742
C3×#18722
C3×#18692
C3×#18652
C3×#18532
C2×C3×#3402
#255433