Finite Group Databasebeta

← C3×#24221 #10642828

Subgroups — C3×#24221 #10642828

Order 768.

1364 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#536C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#462C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic
5C2×C3×#451C211yesmaximal, characteristic, complemented
6C3×#2323C211yesmaximal, characteristic, complemented
7C3×#2043C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#1983C211yesmaximal, characteristic, complemented
12C3×#1981C211yesmaximal, characteristic, complemented
13C3×#1798C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic
15C3×#1787C211yesmaximal, characteristic, complemented
16#24221C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×Q16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C3×#536—24no—
24C3×#536—24no—
25C2×C3×C4⋊Q8C2211yescharacteristic
26C2×C3×C4⋊Q8C2211yescharacteristic
27C2×C3×#124C2211yescharacteristic
28C2×C3×#124C2211yescharacteristic
29C2×C3×#123—21no—
30C2×C3×#123—21no—
31C2×C3×C22⋊Q8—21no—
32C2×C3×C22⋊Q8—21no—
33C2×C3×C22⋊Q8C2211yescharacteristic
34C2×C3×C4×Q8C2211yescharacteristic
35C2×C3×#117C2211yescharacteristic
36C3×#464—24no—
37C3×#462—24no—
38C3×#452—24no—
39C3×#451—24no—
40C2×C3×C4⋊C8C2211yescharacteristic
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×#103C2211yescharacteristic
50C2×C3×#103C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×#102C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×C22⋊C8C2211yescharacteristic
56C3×#391C2211yescharacteristic
57C3×#389—21no—
58C3×#389C2211yescharacteristic
59C3×#388—21no—
60C3×#388—21no—
61C3×#387—21no—
62C3×#380C2211yescharacteristic
63C3×C4×C4⋊C4C2211yescharacteristic
64C3×#336C2211yescharacteristic
65C3×#336C2211yescharacteristic
66C2×#536C2×C311yescharacteristic
67C2×#464C2×C311yescharacteristic, complemented
68C2×#462C2×C311yescharacteristic, complemented
69C2×#452C2×C311yescharacteristic
70C2×#451C2×C311yescharacteristic, complemented
71#2323C2×C311yescharacteristic, complemented
72#2043C2×C311yescharacteristic, complemented
73#2042C2×C311yescharacteristic, complemented
74#2016C2×C311yescharacteristic, complemented
75#2015C2×C311yescharacteristic, complemented
76#1983C2×C311yescharacteristic, complemented
77#1981C2×C311yescharacteristic, complemented
78#1798C2×C311yescharacteristic, complemented
79#1788C2×C311yescharacteristic
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×Q8C2311yescharacteristic
98C22×C3×D4—21no—
99C22×C3×D4C2311yescharacteristic
100C23×C3×C4—21no—
101C23×C3×C4—21no—
102C23×C3×C4C2311yescharacteristic
103C2×C3×Q16—22no—
104C2×C3×Q16—22no—
105C2×C3×Q16—22no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—41no—
110C2×C3×Q16—41no—
111C2×C3×Q16—41no—
112C2×C3×SD16—22no—
113C2×C3×SD16—22no—
114C2×C3×SD16—41no—
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C3×C4⋊Q8—22no—
120C3×C4⋊Q8—22no—
121C3×C4⋊Q8—22no—
122C3×C4⋊Q8D414yes—
123C3×#124—22no—
124C3×#124—22no—
125C3×#124—22no—
126C3×#124D414yes—
127C3×#123—28no—
128C3×#123—28no—
129C3×C22⋊Q8—28no—
130C3×C22⋊Q8—28no—
131C3×C22⋊Q8—22no—
132C3×C22⋊Q8D414yes—
133C3×C4×Q8—22no—
134C3×C4×Q8—22no—
135C3×#117—22no—
136C3×#117—22no—
137C2×C3×C4⋊C4—21no—
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⋊C4—21no—
144C2×C3×C4⋊C4D411yescharacteristic
145C2×C3×C4⋊C4D411yescharacteristic
146C2×C3×C4⋊C4C2311yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
156C2×C3×C22⋊C4D411yescharacteristic
157C2×C3×C42—21no—
158C2×C3×C42—21no—
159C2×C3×C42C2311yescharacteristic
160C2×C3×C42C2311yescharacteristic
161C3×C4⋊C8—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×#103—41no—
171C3×#103—41no—
172C3×#102—22no—
173C3×#102—22no—
174C3×#102—41no—
175C3×C22⋊C8—22no—
176C3×C22⋊C8—22no—
177C3×#95—21no—
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×Q16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic
188#536—24no—
189#536—24no—
190C2×C4⋊Q8C22×C311yescharacteristic
191C2×C4⋊Q8C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#124C22×C311yescharacteristic
194C2×#123—21no—
195C2×#123—21no—
196C2×C22⋊Q8—21no—
197C2×C22⋊Q8—21no—
198C2×C22⋊Q8C22×C311yescharacteristic
199C2×C4×Q8C22×C311yescharacteristic
200C2×#117C22×C311yescharacteristic
201#464—24no—
202#462—24no—
203#452—24no—
204#451—24no—
205C2×C4⋊C8C22×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×#103C22×C311yescharacteristic
215C2×#103C22×C311yescharacteristic
216C2×#102C22×C311yescharacteristic
217C2×#102C22×C311yescharacteristic
218C2×#102C22×C311yescharacteristic
219C2×C22⋊C8C22×C311yescharacteristic
220C2×C22⋊C8C22×C311yescharacteristic
221#391C22×C311yescharacteristic
222#389—21no—
223#389C22×C311yescharacteristic
224#388—21no—
225#388—21no—
226#387—21no—
227#380C22×C311yescharacteristic
228C4×C4⋊C4C22×C311yescharacteristic
229#336C22×C311yescharacteristic
230#336C22×C311yescharacteristic
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C3×#41—44no—
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C2×C3×Q8—24no—
238C2×C3×Q8—21no—
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—21no—
253C2×C3×Q8—21no—
254C2×C3×Q8—21no—
255C2×C3×Q8—21no—
256C2×C3×Q8—21no—
257C2×C3×Q8—21no—
258C2×C3×Q8—44no—
259C2×C3×Q8—44no—
260C2×C3×Q8—44no—
261C2×C3×Q8—44no—
262C2×C3×Q8—42no—
263C2×C3×Q8—42no—
264C2×C3×Q8C2×D412yes—
265C2×C3×Q8C2×D412yes—
266C2×C3×Q8C2×D412yes—
267C2×C3×Q8C2×D412yes—
268C2×C3×D4—24no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—42no—
275C2×C3×D4—42no—
276C2×C3×D4C2×D412yes—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
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—42no—
291C22×C3×C4—42no—
292C22×C3×C4—42no—
293C22×C3×C4—42no—
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2×D411yescharacteristic
296C22×C3×C4C2×D411yescharacteristic
297C22×C3×C4C2×D411yescharacteristic
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D412yes—
300C22×C3×C4#4112yes—
301C22×C3×C4C2411yescharacteristic
302C3×Q16—44no—
303C3×Q16—44no—
304C3×Q16—44no—
305C3×SD16—44no—
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×C8—21no—
317C2×C3×C8—21no—
318C3×C4⋊C4—24no—
319C3×C4⋊C4—24no—
320C3×C4⋊C4—24no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—22no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—42no—
331C3×C4⋊C4—81no—
332C3×C4⋊C4C2×D412yes—
333C3×C22⋊C4—24no—
334C3×C22⋊C4—24no—
335C3×C22⋊C4—24no—
336C3×C22⋊C4—24no—
337C3×C22⋊C4—24no—
338C3×C22⋊C4—22no—
339C3×C22⋊C4—22no—
340C3×C22⋊C4—81no—
341C3×C42—21no—
342C3×C42—21no—
343C3×C42—42no—
344C3×C42—81no—
345C3×C42C2×D412yes—
346C3×C42C2×D412yes—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41—41no—
352C2×#41—41no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—21no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—41no—
359C22×Q8—41no—
360C22×Q8C23×C311yescharacteristic
361C22×Q8C23×C311yescharacteristic
362C22×Q8C23×C311yescharacteristic
363C22×Q8C23×C311yescharacteristic
364C22×D4—21no—
365C22×D4C23×C311yescharacteristic
366C23×C4—21no—
367C23×C4—21no—
368C23×C4C23×C311yescharacteristic
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×Q16—41no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—41no—
381C22×C8C23×C311yescharacteristic
382C22×C8C23×C311yescharacteristic
383C22×C8C23×C311yescharacteristic
384C22×C8C23×C311yescharacteristic
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4⋊Q8—22no—
388C4⋊Q8C3×D414yes—
389#124—22no—
390#124—22no—
391#124—22no—
392#124C3×D414yes—
393#123—28no—
394#123—28no—
395C22⋊Q8—28no—
396C22⋊Q8—28no—
397C22⋊Q8—22no—
398C22⋊Q8C3×D414yes—
399C4×Q8—22no—
400C4×Q8—22no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4C3×D411yescharacteristic
411C2×C4⋊C4C3×D411yescharacteristic
412C2×C4⋊C4C23×C311yescharacteristic
413C2×C4⋊C4C23×C311yescharacteristic
414C2×C4⋊C4C23×C311yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4C3×D411yescharacteristic
422C2×C22⋊C4C3×D411yescharacteristic
423C2×C42—21no—
424C2×C42—21no—
425C2×C42C23×C311yescharacteristic
426C2×C42C23×C311yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429#103—22no—
430#103—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—22no—
435#103—41no—
436#103—41no—
437#103—41no—
438#102—22no—
439#102—22no—
440#102—41no—
441C22⋊C8—22no—
442C22⋊C8—22no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—22no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3#12112yes—
462C23×C3C22×D411yescharacteristic
463C3×Q8—22no—
464C3×Q8—22no—
465C3×Q8—22no—
466C3×Q8—22no—
467C3×Q8—22no—
468C3×Q8—22no—
469C3×Q8—22no—
470C3×Q8—22no—
471C3×Q8—48no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×Q8—41no—
476C3×Q8—41no—
477C3×Q8—41no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—48no—
483C3×D4—41no—
484C3×D4—41no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—48no—
507C2×C3×C4—48no—
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—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4#12012yes—
525C2×C3×C4#12012yes—
526C2×C3×C4#12112yes—
527C2×C3×C4C22×D411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C2×#4111yescharacteristic
531C2×C3×C4H(5,𝔽2)11yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533C3×C8—41no—
534C3×C8—41no—
535C3×C8—41no—
536C3×C8—41no—
537C24—21no—
538C24C2×C3×D411yescharacteristic
539#41—44no—
540#41—44no—
541#41—44no—
542#41—44no—
543C2×Q8—24no—
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—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—44no—
568C2×Q8—42no—
569C2×Q8—42no—
570C2×Q8C2×C3×D412yes—
571C2×Q8C2×C3×D412yes—
572C2×Q8C2×C3×D412yes—
573C2×Q8C2×C3×D412yes—
574C2×D4—24no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4C2×C3×D412yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4C2×C3×D411yescharacteristic
601C22×C4C2×C3×D411yescharacteristic
602C22×C4C2×C3×D411yescharacteristic
603C22×C4C2×C3×D411yescharacteristic
604C22×C4C2×C3×D411yescharacteristic
605C22×C4C2×C3×D412yes—
606C22×C4C3×#4112yes—
607C22×C4C24×C311yescharacteristic
608Q16—44no—
609Q16—44no—
610Q16—44no—
611SD16—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—24no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—42no—
637C4⋊C4—81no—
638C4⋊C4C2×C3×D412yes—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—81no—
651C42C2×C3×D412yes—
652C42C2×C3×D412yes—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3C2×#12011yescharacteristic
668C22×C3C2×#12111yescharacteristic
669C22×C3#53511yescharacteristic
670C22×C3#57711yescharacteristic
671C22×C3#57811yescharacteristic
672C22×C3#57811yescharacteristic
673C22×C3#57811yescharacteristic
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—42no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—42no—
684C3×C4—81no—
685C3×C4—81no—
686C3×C4D4211yescharacteristic
687C3×C4D4211yescharacteristic
688C3×C4#54611yescharacteristic
689C3×C4#54611yescharacteristic
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23C3×#12112yes—
704C23C22×C3×D411yescharacteristic
705Q8—22no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—48no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—41no—
726D4—41no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—48no—
749C2×C4—48no—
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×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4C3×#12012yes—
767C2×C4C3×#12012yes—
768C2×C4C3×#12112yes—
769C2×C4C22×C3×D411yescharacteristic
770C2×C4C22×C3×D411yescharacteristic
771C2×C4C22×C3×D411yescharacteristic
772C2×C4C2×C3×#4111yescharacteristic
773C2×C4C3×H(5,𝔽2)11yescharacteristic
774C2×C4C3×H(5,𝔽2)11yescharacteristic
775C8—41no—
776C8—41no—
777C8—41no—
778C8—41no—
779C2×C3—42no—
780C2×C3—82no—
781C2×C3#240811yescharacteristic
782C2×C3#301111yescharacteristic
783C2×C3#301311yescharacteristic
784C2×C3#304411yescharacteristic
785C2×C3#304611yescharacteristic
786C2×C3#322311yescharacteristic
787C2×C3#322511yescharacteristic
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C2×C3×#12011yescharacteristic
803C22C2×C3×#12111yescharacteristic
804C22C3×#53511yescharacteristic
805C22C3×#57711yescharacteristic
806C22C3×#57811yescharacteristic
807C22C3×#57811yescharacteristic
808C22C3×#57811yescharacteristic
809C4—22no—
810C4—22no—
811C4—22no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—41no—
817C4—41no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4C3×D4211yescharacteristic
822C4C3×D4211yescharacteristic
823C4C3×#54611yescharacteristic
824C4C3×#54611yescharacteristic
825C3#2422111yescharacteristic, direct product factor, Sylow
826C2—42no—
827C2—82no—
828C2C3×#240811yescharacteristic
829C2C3×#301111yescharacteristic
830C2C3×#301311yescharacteristic
831C2C3×#304411yescharacteristic
832C2C3×#304611yescharacteristic
833C2C3×#322311yescharacteristic
834C2C3×#322511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×#41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#464C2semidirect
3. C2×C3×#462C2semidirect
5. C2×C3×#451C2semidirect
6. C3×#2323C2semidirect
7. C3×#2043C2semidirect
8. C3×#2042C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
11. C3×#1983C2semidirect
12. C3×#1981C2semidirect
13. C3×#1798C2semidirect
15. C3×#1787C2semidirect
16. #24221C3direct (N × H)
67. C2×#464C2×C3semidirect
68. C2×#462C2×C3semidirect
70. C2×#451C2×C3semidirect
71. #2323C2×C3semidirect
72. #2043C2×C3semidirect
73. #2042C2×C3semidirect
74. #2016C2×C3semidirect
75. #2015C2×C3semidirect
76. #1983C2×C3semidirect
77. #1981C2×C3semidirect
78. #1798C2×C3semidirect
80. #1787C2×C3semidirect
825. C3#24221direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5362
C2×C3×#4642
C2×C3×#4622
C2×C3×#4522
C2×C3×#4512
C3×#23232
C3×#20432
C3×#20422
C3×#20162
C3×#20152
C3×#19832
C3×#19812
C3×#17982
C3×#17882
C3×#17872
#242213