Finite Group Databasebeta

← C3×#24246 #10642853

Subgroups — C3×#24246 #10642853

Order 768.

1424 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#452C211yesmaximal, characteristic, complemented
4C2×C3×#451C211yesmaximal, characteristic, complemented
5C2×C3×C4×Q16C211yesmaximal, characteristic, complemented
6C3×#2536C211yesmaximal, characteristic, complemented
7C3×#2036C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2001C211yesmaximal, characteristic, complemented
10C3×#2000C211yesmaximal, characteristic, complemented
11C3×#1958C211yesmaximal, characteristic, complemented
12C3×#1954C211yesmaximal, characteristic, complemented
13C3×#1805C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1787C211yesmaximal, characteristic, complemented
16#24246C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C3×#548—24no—
23C3×#548—24no—
24C2×C3×#124—21no—
25C2×C3×#124C2211yescharacteristic
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×#121—21no—
31C2×C3×#121C2211yescharacteristic
32C2×C3×C4×Q8C2211yescharacteristic
33C2×C3×C4×Q8C2211yescharacteristic
34C2×C3×C4×D4—21no—
35C2×C3×C4×D4C2211yescharacteristic
36C3×#464—24no—
37C3×#452—24no—
38C3×#451—24no—
39C3×C4×Q16—24no—
40C2×C3×#107C2211yescharacteristic
41C2×C3×C4⋊C8C2211yescharacteristic
42C2×C3×#103C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#103C2211yescharacteristic
48C2×C3×#103C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C2×C3×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C2×C3×C4×C8C2211yescharacteristic
57C3×#398—21no—
58C3×#394—21no—
59C3×#388—21no—
60C3×#388—21no—
61C3×#382C2211yescharacteristic
62C3×#380C2211yescharacteristic
63C3×#380C2211yescharacteristic
64C3×#340C2211yescharacteristic
65C3×#340C2211yescharacteristic
66C2×#548C2×C311yescharacteristic
67C2×#464C2×C311yescharacteristic, complemented
68C2×#452C2×C311yescharacteristic, complemented
69C2×#451C2×C311yescharacteristic, complemented
70C2×C4×Q16C2×C311yescharacteristic, complemented
71#2536C2×C311yescharacteristic, complemented
72#2036C2×C311yescharacteristic, complemented
73#2033C2×C311yescharacteristic, complemented
74#2001C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1958C2×C311yescharacteristic, complemented
77#1954C2×C311yescharacteristic, complemented
78#1805C2×C311yescharacteristic, complemented
79#1788C2×C311yescharacteristic, complemented
80#1787C2×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—22no—
88C22×C3×Q8—22no—
89C22×C3×Q8—21no—
90C22×C3×Q8—22no—
91C22×C3×Q8—22no—
92C22×C3×Q8—41no—
93C22×C3×Q8—41no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×Q8C2311yescharacteristic
97C22×C3×D4—21no—
98C22×C3×D4—21no—
99C22×C3×D4D411yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C23×C3×C4—21no—
102C23×C3×C4—21no—
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—41no—
110C2×C3×Q16D414yescomplemented
111C2×C3×SD16—22no—
112C2×C3×SD16—22no—
113C2×C3×SD16—41no—
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C3×#124—28no—
119C3×#124—22no—
120C3×#124D414yes—
121C3×C22⋊Q8—28no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—22no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—41no—
127C3×C22⋊Q8—41no—
128C3×#121—28no—
129C3×#121—22no—
130C3×#121—22no—
131C3×C4×Q8—22no—
132C3×C4×Q8—22no—
133C3×C4×Q8—22no—
134C3×C4×Q8D414yes—
135C3×C4×D4—28no—
136C3×C4×D4—22no—
137C3×C4×D4—22no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4D411yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4D411yescharacteristic
157C2×C3×C22⋊C4D411yescharacteristic
158C2×C3×C42—21no—
159C2×C3×C42—21no—
160C2×C3×C42C2311yescharacteristic
161C3×#107—22no—
162C3×C4⋊C8—22no—
163C3×#103—22no—
164C3×#103—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#103—41no—
170C3×#102—22no—
171C3×#102—22no—
172C3×#102—41no—
173C3×C22⋊C8—22no—
174C3×C22⋊C8—22no—
175C3×C22⋊C8—41no—
176C3×C22⋊C8—41no—
177C3×C4×C8—22no—
178C3×#95—21no—
179C3×#95—21no—
180C3×#95—21no—
181C3×#95—21no—
182C22×#41C22×C311yescharacteristic
183C23×Q8C22×C311yescharacteristic
184C22×Q16C22×C311yescharacteristic
185C22×Q16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187#548—24no—
188#548—24no—
189C2×#124—21no—
190C2×#124C22×C311yescharacteristic
191C2×C22⋊Q8—21no—
192C2×C22⋊Q8C22×C311yescharacteristic
193C2×C22⋊Q8C22×C311yescharacteristic
194C2×C22⋊Q8C22×C311yescharacteristic
195C2×#121—21no—
196C2×#121C22×C311yescharacteristic
197C2×C4×Q8C22×C311yescharacteristic
198C2×C4×Q8C22×C311yescharacteristic
199C2×C4×D4—21no—
200C2×C4×D4C22×C311yescharacteristic
201#464—24no—
202#452—24no—
203#451—24no—
204C4×Q16—24no—
205C2×#107C22×C311yescharacteristic
206C2×C4⋊C8C22×C311yescharacteristic
207C2×#103C22×C311yescharacteristic
208C2×#103C22×C311yescharacteristic
209C2×#103C22×C311yescharacteristic
210C2×#103C22×C311yescharacteristic
211C2×#103C22×C311yescharacteristic
212C2×#103C22×C311yescharacteristic
213C2×#103C22×C311yescharacteristic
214C2×#102C22×C311yescharacteristic
215C2×#102C22×C311yescharacteristic
216C2×#102C22×C311yescharacteristic
217C2×C22⋊C8C22×C311yescharacteristic
218C2×C22⋊C8C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic
220C2×C22⋊C8C22×C311yescharacteristic
221C2×C4×C8C22×C311yescharacteristic
222#398—21no—
223#394—21no—
224#388—21no—
225#388—21no—
226#382C22×C311yescharacteristic
227#380C22×C311yescharacteristic
228#380C22×C311yescharacteristic
229#340C22×C311yescharacteristic
230#340C22×C311yescharacteristic
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C24×C3C2×D411yescharacteristic
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C2×C3×Q8—24no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
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—42no—
253C2×C3×Q8—42no—
254C2×C3×Q8—44no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C2×C3×Q8—44no—
258C2×C3×Q8C2×D412yes—
259C2×C3×Q8C2×D412yes—
260C2×C3×Q8C2×D412yes—
261C2×C3×Q8C2×D412yes—
262C2×C3×Q8#4112yes—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—41no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4C2×D412yes—
278C22×C3×C4—21no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—42no—
300C22×C3×C4—42no—
301C22×C3×C4—42no—
302C22×C3×C4—42no—
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C3×Q16—28no—
309C3×Q16—44no—
310C3×SD16—44no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
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×C8C2×D412yes—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—22no—
326C3×C4⋊C4—21no—
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×C4⋊C4—42no—
336C3×C4⋊C4C2×D412yes—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—24no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—24no—
341C3×C22⋊C4—22no—
342C3×C22⋊C4—22no—
343C3×C22⋊C4—42no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—42no—
346C3×C22⋊C4—42no—
347C3×C42—24no—
348C3×C42—42no—
349C3×C42C2×D412yes—
350C3×C42C2×D412yes—
351C2×#41—22no—
352C2×#41—22no—
353C2×#41—22no—
354C2×#41—22no—
355C2×#41—41no—
356C2×#41—41no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—41no—
363C22×Q8—41no—
364C22×Q8C23×C311yescharacteristic
365C22×Q8C23×C311yescharacteristic
366C22×Q8C23×C311yescharacteristic
367C22×D4—21no—
368C22×D4—21no—
369C22×D4C3×D411yescharacteristic
370C22×D4C23×C311yescharacteristic
371C23×C4—21no—
372C23×C4—21no—
373C23×C4C23×C311yescharacteristic
374C23×C4C23×C311yescharacteristic
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—22no—
378C2×Q16—22no—
379C2×Q16—41no—
380C2×Q16C3×D414yescomplemented
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C22×C8C23×C311yescharacteristic
385C22×C8C23×C311yescharacteristic
386C22×C8C23×C311yescharacteristic
387C22×C8C23×C311yescharacteristic
388#124—28no—
389#124—22no—
390#124C3×D414yes—
391C22⋊Q8—28no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—41no—
397C22⋊Q8—41no—
398#121—28no—
399#121—22no—
400#121—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8C3×D414yes—
405C4×D4—28no—
406C4×D4—22no—
407C4×D4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4C3×D411yescharacteristic
414C2×C4⋊C4C23×C311yescharacteristic
415C2×C4⋊C4C23×C311yescharacteristic
416C2×C4⋊C4C23×C311yescharacteristic
417C2×C4⋊C4C23×C311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4C3×D411yescharacteristic
427C2×C22⋊C4C3×D411yescharacteristic
428C2×C42—21no—
429C2×C42—21no—
430C2×C42C23×C311yescharacteristic
431#107—22no—
432C4⋊C8—22no—
433#103—22no—
434#103—22no—
435#103—22no—
436#103—22no—
437#103—22no—
438#103—22no—
439#103—41no—
440#102—22no—
441#102—22no—
442#102—41no—
443C22⋊C8—22no—
444C22⋊C8—22no—
445C22⋊C8—41no—
446C22⋊C8—41no—
447C4×C8—22no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—22no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3#13512yes—
473C23×C3C22×D411yescharacteristic
474C3×Q8—22no—
475C3×Q8—22no—
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—22no—
479C3×Q8—22no—
480C3×Q8—22no—
481C3×Q8—48no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8#12114yes—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—44no—
490C3×D4—48no—
491C3×D4—48no—
492C3×D4—41no—
493C3×D4—41no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—48no—
511C2×C3×C4—48no—
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—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—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4#12012yes—
536C2×C3×C4#12012yes—
537C2×C3×C4C22×D411yescharacteristic
538C2×C3×C4C22×D411yescharacteristic
539C2×C3×C4C22×D411yescharacteristic
540C2×C3×C4C2×#4111yescharacteristic
541C2×C3×C4H(5,𝔽2)11yescharacteristic
542C2×C3×C4H(5,𝔽2)11yescharacteristic
543C3×C8—22no—
544C3×C8—41no—
545C3×C8—41no—
546C3×C8—41no—
547C24—21no—
548C24C2×C3×D411yescharacteristic
549C24C2×C3×D411yescharacteristic
550#41—44no—
551#41—44no—
552#41—44no—
553#41—44no—
554C2×Q8—24no—
555C2×Q8—21no—
556C2×Q8—21no—
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—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×Q8—44no—
571C2×Q8—44no—
572C2×Q8—44no—
573C2×Q8—44no—
574C2×Q8C2×C3×D412yes—
575C2×Q8C2×C3×D412yes—
576C2×Q8C2×C3×D412yes—
577C2×Q8C2×C3×D412yes—
578C2×Q8C3×#4112yes—
579C2×D4—24no—
580C2×D4—24no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4C2×C3×D412yes—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4C2×C3×D411yescharacteristic
620C22×C4C2×C3×D411yescharacteristic
621C22×C4C2×C3×D411yescharacteristic
622C22×C4C2×C3×D411yescharacteristic
623C22×C4C24×C311yescharacteristic
624Q16—28no—
625Q16—44no—
626SD16—44no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
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×C8C2×C3×D412yes—
639C4⋊C4—24no—
640C4⋊C4—24no—
641C4⋊C4—22no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4C2×C3×D412yes—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C42—24no—
664C42—42no—
665C42C2×C3×D412yes—
666C42C2×C3×D412yes—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—42no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—42no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3C2×#12011yescharacteristic
689C22×C3D4211yescharacteristic
690C22×C3#54611yescharacteristic
691C22×C3C2×#13511yescharacteristic
692C22×C3#57511yescharacteristic
693C22×C3#57811yescharacteristic
694C22×C3#57811yescharacteristic
695C3×C4—24no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—42no—
701C3×C4—42no—
702C3×C4—42no—
703C3×C4—81no—
704C3×C4—81no—
705C3×C4—81no—
706C3×C4C2×#12111yescharacteristic
707C3×C4#53511yescharacteristic
708C3×C4D4211yescharacteristic
709C3×C4#54611yescharacteristic
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—22no—
722C23—21no—
723C23—21no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23C3×#13512yes—
731C23C22×C3×D411yescharacteristic
732Q8—22no—
733Q8—22no—
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8—22no—
738Q8—22no—
739Q8—48no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8C3×#12114yes—
745D4—22no—
746D4—22no—
747D4—44no—
748D4—48no—
749D4—48no—
750D4—41no—
751D4—41no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
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×C4—41no—
792C2×C4—41no—
793C2×C4C3×#12012yes—
794C2×C4C3×#12012yes—
795C2×C4C22×C3×D411yescharacteristic
796C2×C4C22×C3×D411yescharacteristic
797C2×C4C22×C3×D411yescharacteristic
798C2×C4C2×C3×#4111yescharacteristic
799C2×C4C3×H(5,𝔽2)11yescharacteristic
800C2×C4C3×H(5,𝔽2)11yescharacteristic
801C8—22no—
802C8—41no—
803C8—41no—
804C8—41no—
805C2×C3—42no—
806C2×C3—81no—
807C2×C3—82no—
808C2×C3#240811yescharacteristic
809C2×C3#300211yescharacteristic
810C2×C3#301111yescharacteristic
811C2×C3#327711yescharacteristic
812C2×C3#328511yescharacteristic
813C2×C3#330011yescharacteristic
814C2×C3#332711yescharacteristic
815C22—22no—
816C22—22no—
817C22—22no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22C2×C3×#12011yescharacteristic
837C22C3×D4211yescharacteristic
838C22C3×#54611yescharacteristic
839C22C2×C3×#13511yescharacteristic
840C22C3×#57511yescharacteristic
841C22C3×#57811yescharacteristic
842C22C3×#57811yescharacteristic
843C4—24no—
844C4—22no—
845C4—22no—
846C4—41no—
847C4—41no—
848C4—42no—
849C4—42no—
850C4—42no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4C2×C3×#12111yescharacteristic
855C4C3×#53511yescharacteristic
856C4C3×D4211yescharacteristic
857C4C3×#54611yescharacteristic
858C3#2424611yescharacteristic, direct product factor, Sylow
859C2—42no—
860C2—81no—
861C2—82no—
862C2C3×#240811yescharacteristic
863C2C3×#300211yescharacteristic
864C2C3×#301111yescharacteristic
865C2C3×#327711yescharacteristic
866C2C3×#328511yescharacteristic
867C2C3×#330011yescharacteristic
868C2C3×#332711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#548C2
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
2. C2×C3×#464C2semidirect
3. C2×C3×#452C2semidirect
4. C2×C3×#451C2semidirect
5. C2×C3×C4×Q16C2semidirect
6. C3×#2536C2semidirect
7. C3×#2036C2semidirect
8. C3×#2033C2semidirect
9. C3×#2001C2semidirect
10. C3×#2000C2semidirect
11. C3×#1958C2semidirect
12. C3×#1954C2semidirect
13. C3×#1805C2semidirect
14. C3×#1788C2semidirect
15. C3×#1787C2semidirect
16. #24246C3direct (N × H)
67. C2×#464C2×C3semidirect
68. C2×#452C2×C3semidirect
69. C2×#451C2×C3semidirect
70. C2×C4×Q16C2×C3semidirect
71. #2536C2×C3semidirect
72. #2036C2×C3semidirect
73. #2033C2×C3semidirect
74. #2001C2×C3semidirect
75. #2000C2×C3semidirect
76. #1958C2×C3semidirect
77. #1954C2×C3semidirect
78. #1805C2×C3semidirect
79. #1788C2×C3semidirect
80. #1787C2×C3semidirect
110. C2×C3×Q16D4semidirect
380. C2×Q16C3×D4semidirect
858. C3#24246direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C2×C3×#4642
C2×C3×#4522
C2×C3×#4512
C2×C3×C4×Q162
C3×#25362
C3×#20362
C3×#20332
C3×#20012
C3×#20002
C3×#19582
C3×#19542
C3×#18052
C3×#17882
C3×#17872
#242463