Finite Group Databasebeta

← C3×#32919 #10651526

Subgroups — C3×#32919 #10651526

Order 768.

1448 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic, complemented
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#463C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic
6C3×#2620C211yesmaximal, characteristic, complemented
7C3×#1880C211yesmaximal, characteristic, complemented
8C3×#1879C211yesmaximal, characteristic, complemented
9C3×#1878C211yesmaximal, characteristic, complemented
10C3×#1877C211yesmaximal, characteristic, complemented
11C3×#1874C211yesmaximal, characteristic, complemented
12C3×#1872C211yesmaximal, characteristic, complemented
13C3×#1803C211yesmaximal, characteristic, complemented
14C3×#1802C211yesmaximal, characteristic, complemented
15C3×#1798C211yesmaximal, characteristic, complemented
16#32919C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C3×#520—24no—
26C3×#520—24no—
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4—21no—
30C2×C3×C4×D4—21no—
31C2×C3×C4×D4C2211yescharacteristic
32C2×C3×C4×D4C2211yescharacteristic
33C2×C3×#117—21no—
34C2×C3×#117C2211yescharacteristic
35C22×C3×C4⋊C4—21no—
36C22×C3×C4⋊C4C2211yescharacteristic
37C3×#464—24no—
38C3×#463—24no—
39C3×#452—24no—
40C3×#449—24no—
41C2×C3×C4⋊C8C2211yescharacteristic
42C2×C3×C4⋊C8C2211yescharacteristic
43C2×C3×#103C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×#102C2211yescharacteristic
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C3×#396—21no—
54C3×#396—21no—
55C3×#394—21no—
56C3×#394—21no—
57C3×#391C2211yescharacteristic
58C3×#390C2211yescharacteristic
59C3×#384C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#340C2211yescharacteristic
63C3×#340C2211yescharacteristic
64C3×#336C2211yescharacteristic
65C3×#336C2211yescharacteristic
66C2×#520C2×C311yescharacteristic, complemented
67C2×#464C2×C311yescharacteristic, complemented
68C2×#463C2×C311yescharacteristic, complemented
69C2×#452C2×C311yescharacteristic, complemented
70C2×#449C2×C311yescharacteristic
71#2620C2×C311yescharacteristic, complemented
72#1880C2×C311yescharacteristic, complemented
73#1879C2×C311yescharacteristic, complemented
74#1878C2×C311yescharacteristic, complemented
75#1877C2×C311yescharacteristic, complemented
76#1874C2×C311yescharacteristic, complemented
77#1872C2×C311yescharacteristic, complemented
78#1803C2×C311yescharacteristic, complemented
79#1802C2×C311yescharacteristic, complemented
80#1798C2×C311yescharacteristic, complemented
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41D414yes—
87C22×C3×Q8C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4C2311yescharacteristic
92C22×C3×D4C2311yescharacteristic
93C23×C3×C4—21no—
94C23×C3×C4—21no—
95C23×C3×C4—21no—
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C2×C3×Q16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×D8—22no—
108C2×C3×D8—22no—
109C2×C3×D8—22no—
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C3×#124—22no—
115C3×#124—22no—
116C3×C22⋊Q8—22no—
117C3×C22⋊Q8—22no—
118C3×#121—22no—
119C3×#121—22no—
120C3×C4×Q8—22no—
121C3×C4×Q8—22no—
122C3×C4×Q8—22no—
123C3×C4×Q8D414yescomplemented
124C3×C4×D4—28no—
125C3×C4×D4—28no—
126C3×C4×D4—22no—
127C3×C4×D4—22no—
128C3×C4×D4—22no—
129C3×C4×D4D414yescomplemented
130C3×#117—28no—
131C3×#117—22no—
132C3×#117—22no—
133C2×C3×C4⋊C4—28no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—22no—
138C2×C3×C4⋊C4—22no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4D411yescharacteristic
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
161C2×C3×C42C2311yescharacteristic
162C3×C4⋊C8—22no—
163C3×C4⋊C8—22no—
164C3×#103—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×#102—22no—
171C3×#102—22no—
172C3×C22⋊C8—22no—
173C3×C22⋊C8—22no—
174C3×#95—21no—
175C3×#95—21no—
176C22×#41C22×C311yescharacteristic
177C22×Q16C22×C311yescharacteristic
178C22×SD16C22×C311yescharacteristic
179C22×SD16C22×C311yescharacteristic
180C22×D8C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×#121C22×C311yescharacteristic
184#520—24no—
185#520—24no—
186C2×C4×Q8C22×C311yescharacteristic
187C2×C4×Q8C22×C311yescharacteristic
188C2×C4×D4—21no—
189C2×C4×D4—21no—
190C2×C4×D4C22×C311yescharacteristic
191C2×C4×D4C22×C311yescharacteristic
192C2×#117—21no—
193C2×#117C22×C311yescharacteristic
194C22×C4⋊C4—21no—
195C22×C4⋊C4C22×C311yescharacteristic
196#464—24no—
197#463—24no—
198#452—24no—
199#449—24no—
200C2×C4⋊C8C22×C311yescharacteristic
201C2×C4⋊C8C22×C311yescharacteristic
202C2×#103C22×C311yescharacteristic
203C2×#103C22×C311yescharacteristic
204C2×#103C22×C311yescharacteristic
205C2×#103C22×C311yescharacteristic
206C2×#102C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic
210C2×C22⋊C8C22×C311yescharacteristic
211C2×C22⋊C8C22×C311yescharacteristic
212#396—21no—
213#396—21no—
214#394—21no—
215#394—21no—
216#391C22×C311yescharacteristic
217#390C22×C311yescharacteristic
218#384C22×C311yescharacteristic
219#340C22×C311yescharacteristic
220#340C22×C311yescharacteristic
221#340C22×C311yescharacteristic
222#340C22×C311yescharacteristic
223#336C22×C311yescharacteristic
224#336C22×C311yescharacteristic
225C24×C3—21no—
226C24×C3—21no—
227C24×C3C2×D411yescharacteristic
228C3×#41—28no—
229C3×#41—28no—
230C3×#41—28no—
231C3×#41—28no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8C2×D412yes—
242C2×C3×Q8C2×D412yes—
243C2×C3×Q8#4112yes—
244C2×C3×D4—24no—
245C2×C3×D4—24no—
246C2×C3×D4—24no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—42no—
257C2×C3×D4—81no—
258C2×C3×D4—81no—
259C2×C3×D4C2×D412yes—
260C2×C3×D4C2×D412yes—
261C2×C3×D4#4112yes—
262C22×C3×C4—24no—
263C22×C3×C4—24no—
264C22×C3×C4—21no—
265C22×C3×C4—24no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—24no—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—81no—
279C22×C3×C4—81no—
280C22×C3×C4—81no—
281C22×C3×C4—81no—
282C22×C3×C4—81no—
283C22×C3×C4—81no—
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4C2×D411yescharacteristic
288C22×C3×C4C2×D411yescharacteristic
289C22×C3×C4C2×D412yes—
290C22×C3×C4#4112yes—
291C22×C3×C4C2411yescharacteristic
292C3×Q16—44no—
293C3×SD16—44no—
294C3×SD16—44no—
295C3×D8—44no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8—21no—
301C2×C3×C8—21no—
302C2×C3×C8—21no—
303C2×C3×C8—21no—
304C2×C3×C8—21no—
305C2×C3×C8—21no—
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—24no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—24no—
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—42no—
320C3×C4⋊C4—81no—
321C3×C4⋊C4—81no—
322C3×C4⋊C4C2×D412yes—
323C3×C4⋊C4C2×D412yes—
324C3×C22⋊C4—24no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—22no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330C3×C22⋊C4—42no—
331C3×C22⋊C4—42no—
332C3×C22⋊C4—81no—
333C3×C22⋊C4—81no—
334C3×C42—24no—
335C3×C42—24no—
336C3×C42—21no—
337C3×C42—21no—
338C3×C42C2×D412yes—
339C3×C42C2×D412yes—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41C3×D414yes—
346C22×Q8C23×C311yescharacteristic
347C22×Q8C23×C311yescharacteristic
348C22×D4—21no—
349C22×D4—21no—
350C22×D4C23×C311yescharacteristic
351C22×D4C23×C311yescharacteristic
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4C23×C311yescharacteristic
357C2×Q16—22no—
358C2×Q16—22no—
359C2×Q16—22no—
360C2×SD16—22no—
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—22no—
364C2×SD16—22no—
365C2×SD16—22no—
366C2×D8—22no—
367C2×D8—22no—
368C2×D8—22no—
369C22×C8C23×C311yescharacteristic
370C22×C8C23×C311yescharacteristic
371C22×C8C23×C311yescharacteristic
372C22×C8C23×C311yescharacteristic
373#124—22no—
374#124—22no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377#121—22no—
378#121—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8C3×D414yescomplemented
383C4×D4—28no—
384C4×D4—28no—
385C4×D4—22no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4C3×D414yescomplemented
389#117—28no—
390#117—22no—
391#117—22no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4C3×D411yescharacteristic
402C2×C4⋊C4C3×D411yescharacteristic
403C2×C4⋊C4C23×C311yescharacteristic
404C2×C4⋊C4C23×C311yescharacteristic
405C2×C4⋊C4C23×C311yescharacteristic
406C2×C4⋊C4C23×C311yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4C3×D411yescharacteristic
416C2×C22⋊C4C3×D411yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42C23×C311yescharacteristic
420C2×C42C23×C311yescharacteristic
421C4⋊C8—22no—
422C4⋊C8—22no—
423#103—22no—
424#103—22no—
425#103—22no—
426#103—22no—
427#102—22no—
428#102—22no—
429#102—22no—
430#102—22no—
431C22⋊C8—22no—
432C22⋊C8—22no—
433#95—21no—
434#95—21no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—21no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3#12112yes—
456C23×C3C22×D411yescharacteristic
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8#12114yes—
465C3×D4—216no—
466C3×D4—22no—
467C3×D4—22no—
468C3×D4—22no—
469C3×D4—41no—
470C3×D4—41no—
471C3×D4—41no—
472C3×D4—41no—
473C3×D4—84no—
474C3×D4#12114yes—
475C2×C3×C4—216no—
476C2×C3×C4—22no—
477C2×C3×C4—21no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
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—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—84no—
511C2×C3×C4—84no—
512C2×C3×C4—84no—
513C2×C3×C4#12012yes—
514C2×C3×C4#12012yes—
515C2×C3×C4#12112yes—
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C2×#4111yescharacteristic
520C2×C3×C4C2×#4111yescharacteristic
521C2×C3×C4C2×#4111yescharacteristic
522C3×C8—41no—
523C3×C8—41no—
524C3×C8—41no—
525C3×C8—41no—
526C24—21no—
527C24—21no—
528C24C2×C3×D411yescharacteristic
529#41—28no—
530#41—28no—
531#41—28no—
532#41—28no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C2×C3×D412yes—
543C2×Q8C2×C3×D412yes—
544C2×Q8C3×#4112yes—
545C2×D4—24no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—81no—
559C2×D4—81no—
560C2×D4C2×C3×D412yes—
561C2×D4C2×C3×D412yes—
562C2×D4C3×#4112yes—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4C2×C3×D411yescharacteristic
586C22×C4C2×C3×D411yescharacteristic
587C22×C4C2×C3×D411yescharacteristic
588C22×C4C2×C3×D411yescharacteristic
589C22×C4C2×C3×D411yescharacteristic
590C22×C4C2×C3×D412yes—
591C22×C4C3×#4112yes—
592C22×C4C24×C311yescharacteristic
593Q16—44no—
594SD16—44no—
595SD16—44no—
596D8—44no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4—81no—
622C4⋊C4—81no—
623C4⋊C4C2×C3×D412yes—
624C4⋊C4C2×C3×D412yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42C2×C3×D412yes—
640C42C2×C3×D412yes—
641C22×C3—22no—
642C22×C3—24no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—41no—
646C22×C3—42no—
647C22×C3—41no—
648C22×C3—42no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3C2×#12011yescharacteristic
663C22×C3C2×#12111yescharacteristic
664C22×C3#52511yescharacteristic
665C22×C3#57611yescharacteristic
666C22×C3#57711yescharacteristic
667C22×C3#57711yescharacteristic
668C22×C3#57811yescharacteristic
669C3×C4—22no—
670C3×C4—24no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—41no—
674C3×C4—42no—
675C3×C4—42no—
676C3×C4—41no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—81no—
680C3×C4C2×#12111yescharacteristic
681C3×C4C2×#12111yescharacteristic
682C3×C4#52511yescharacteristic
683C3×C4#52511yescharacteristic
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—22no—
691C23—21no—
692C23—22no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23C3×#12112yes—
705C23C22×C3×D411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712Q8—41no—
713Q8C3×#12114yes—
714D4—216no—
715D4—22no—
716D4—22no—
717D4—22no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—84no—
723D4C3×#12114yes—
724C2×C4—216no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
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—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4C3×#12012yes—
763C2×C4C3×#12012yes—
764C2×C4C3×#12112yes—
765C2×C4C22×C3×D411yescharacteristic
766C2×C4C22×C3×D411yescharacteristic
767C2×C4C22×C3×D411yescharacteristic
768C2×C4C2×C3×#4111yescharacteristic
769C2×C4C2×C3×#4111yescharacteristic
770C2×C4C2×C3×#4111yescharacteristic
771C8—41no—
772C8—41no—
773C8—41no—
774C8—41no—
775C2×C3—42no—
776C2×C3—44no—
777C2×C3—161no—
778C2×C3#284711yescharacteristic
779C2×C3#301211yescharacteristic
780C2×C3#301311yescharacteristic
781C2×C3#304511yescharacteristic
782C2×C3#304611yescharacteristic
783C2×C3#312411yescharacteristic
784C2×C3#312511yescharacteristic
785C22—22no—
786C22—22no—
787C22—22no—
788C22—24no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—41no—
796C22—42no—
797C22—41no—
798C22—42no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22C2×C3×#12011yescharacteristic
807C22C2×C3×#12111yescharacteristic
808C22C3×#52511yescharacteristic
809C22C3×#57611yescharacteristic
810C22C3×#57711yescharacteristic
811C22C3×#57711yescharacteristic
812C22C3×#57811yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—24no—
817C4—41no—
818C4—42no—
819C4—42no—
820C4—41no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4C2×C3×#12111yescharacteristic
825C4C2×C3×#12111yescharacteristic
826C4C3×#52511yescharacteristic
827C4C3×#52511yescharacteristic
828C3#3291911yescharacteristic, direct product factor, Sylow
829C2—42no—
830C2—44no—
831C2—161no—
832C2C3×#284711yescharacteristic
833C2C3×#301211yescharacteristic
834C2C3×#301311yescharacteristic
835C2C3×#304511yescharacteristic
836C2C3×#304611yescharacteristic
837C2C3×#312411yescharacteristic
838C2C3×#312511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#449C2
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
1. C2×C3×#520C2semidirect
2. C2×C3×#464C2semidirect
3. C2×C3×#463C2semidirect
4. C2×C3×#452C2semidirect
6. C3×#2620C2semidirect
7. C3×#1880C2semidirect
8. C3×#1879C2semidirect
9. C3×#1878C2semidirect
10. C3×#1877C2semidirect
11. C3×#1874C2semidirect
12. C3×#1872C2semidirect
13. C3×#1803C2semidirect
14. C3×#1802C2semidirect
15. C3×#1798C2semidirect
16. #32919C3direct (N × H)
66. C2×#520C2×C3semidirect
67. C2×#464C2×C3semidirect
68. C2×#463C2×C3semidirect
69. C2×#452C2×C3semidirect
71. #2620C2×C3semidirect
72. #1880C2×C3semidirect
73. #1879C2×C3semidirect
74. #1878C2×C3semidirect
75. #1877C2×C3semidirect
76. #1874C2×C3semidirect
77. #1872C2×C3semidirect
78. #1803C2×C3semidirect
79. #1802C2×C3semidirect
80. #1798C2×C3semidirect
123. C3×C4×Q8D4semidirect
129. C3×C4×D4D4semidirect
382. C4×Q8C3×D4semidirect
388. C4×D4C3×D4semidirect
828. C3#32919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5202
C2×C3×#4642
C2×C3×#4632
C2×C3×#4522
C2×C3×#4492
C3×#26202
C3×#18802
C3×#18792
C3×#18782
C3×#18772
C3×#18742
C3×#18722
C3×#18032
C3×#18022
C3×#17982
#329193