Finite Group Databasebeta

← C3×#30464 #10649071

Subgroups — C3×#30464 #10649071

Order 768.

1196 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#497C211yesmaximal, characteristic, complemented
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#450C211yesmaximal, characteristic
4C2×C3×#450C211yesmaximal, characteristic
5C3×#2435C211yesmaximal, characteristic
6C3×#2429C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2013C211yesmaximal, characteristic, complemented
11C3×#2001C211yesmaximal, characteristic, complemented
12C3×#2001C211yesmaximal, characteristic, complemented
13C3×#1936C211yesmaximal, characteristic, complemented
14C3×#1924C211yesmaximal, characteristic, complemented
15C3×#1880C211yesmaximal, characteristic, complemented
16#30464C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×D4C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic, complemented
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic, complemented
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic, complemented
31C3×#497—24no—
32C3×#464—24no—
33C3×#450—24no—
34C3×#450—24no—
35C2×C3×C4⋊C8C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×#103C2211yescharacteristic, complemented
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×#97C2211yescharacteristic, complemented
47C3×#398—21no—
48C3×#396—21no—
49C3×#394—21no—
50C3×#394—21no—
51C3×#391C2211yescharacteristic, complemented
52C3×#390C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#389—21no—
55C3×#389C2211yescharacteristic, complemented
56C3×#388—21no—
57C3×#379—21no—
58C3×#379—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#336C2211yescharacteristic, complemented
63C3×#336C2211yescharacteristic, complemented
64C2×#497C2×C311yescharacteristic, complemented
65C2×#464C2×C311yescharacteristic, complemented
66C2×#450C2×C311yescharacteristic
67C2×#450C2×C311yescharacteristic
68#2435C2×C311yescharacteristic
69#2429C2×C311yescharacteristic, complemented
70#2055C2×C311yescharacteristic, complemented
71#2042C2×C311yescharacteristic, complemented
72#2015C2×C311yescharacteristic, complemented
73#2013C2×C311yescharacteristic, complemented
74#2001C2×C311yescharacteristic, complemented
75#2001C2×C311yescharacteristic, complemented
76#1936C2×C311yescharacteristic, complemented
77#1924C2×C311yescharacteristic, complemented
78#1880C2×C311yescharacteristic, complemented
79C25×C3—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×Q8C2311yescharacteristic
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4—22no—
84C22×C3×D4—22no—
85C22×C3×D4—21no—
86C22×C3×D4—41no—
87C22×C3×D4—41no—
88C22×C3×D4—41no—
89C22×C3×D4—41no—
90C22×C3×D4C2311yescharacteristic
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C2×C3×Q16—22no—
94C2×C3×Q16—22no—
95C2×C3×Q16—22no—
96C2×C3×Q16—41no—
97C2×C3×Q16—41no—
98C2×C3×Q16—41no—
99C2×C3×SD16—22no—
100C2×C3×SD16—22no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—41no—
105C2×C3×SD16—41no—
106C2×C3×SD16—41no—
107C2×C3×SD16—41no—
108C2×C3×SD16—41no—
109C2×C3×SD16—41no—
110C2×C3×SD16D414yes—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C3×C4⋊Q8—22no—
116C3×C4⋊Q8—41no—
117C3×#124—22no—
118C3×#124—22no—
119C3×#124—41no—
120C3×#124—41no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—22no—
123C3×C22⋊Q8—41no—
124C3×C22⋊Q8—41no—
125C3×C22⋊Q8—41no—
126C3×C22⋊Q8—41no—
127C3×C4×Q8—22no—
128C3×C4×Q8—41no—
129C2×C3×C4⋊C4—21no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4C2311yescharacteristic
137C2×C3×C4⋊C4C2311yescharacteristic
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C22⋊C4—21no—
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⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4D411yescharacteristic
151C2×C3×C22⋊C4D411yescharacteristic
152C2×C3×C42—21no—
153C2×C3×C42C2311yescharacteristic
154C2×C3×C42C2311yescharacteristic
155C3×C4⋊C8—22no—
156C3×#103—22no—
157C3×#103—41no—
158C3×#103—41no—
159C3×#103—41no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—22no—
163C3×#102D414yes—
164C3×C22⋊C8—22no—
165C3×C22⋊C8—22no—
166C3×#97—22no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C3×#95D411yescharacteristic
171C3×#95D411yescharacteristic
172C23×D4C22×C311yescharacteristic
173C22×Q16C22×C311yescharacteristic, complemented
174C22×Q16C22×C311yescharacteristic, complemented
175C22×SD16C22×C311yescharacteristic
176C22×SD16C22×C311yescharacteristic
177C22×SD16C22×C311yescharacteristic
178C22×SD16C22×C311yescharacteristic
179C2×C4⋊Q8C22×C311yescharacteristic, complemented
180C2×#124C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×C22⋊Q8C22×C311yescharacteristic
185C2×C4×Q8C22×C311yescharacteristic, complemented
186#497—24no—
187#464—24no—
188#450—24no—
189#450—24no—
190C2×C4⋊C8C22×C311yescharacteristic, complemented
191C2×#103C22×C311yescharacteristic, complemented
192C2×#103C22×C311yescharacteristic, complemented
193C2×#103C22×C311yescharacteristic, complemented
194C2×#103C22×C311yescharacteristic, complemented
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×C22⋊C8C22×C311yescharacteristic
200C2×C22⋊C8C22×C311yescharacteristic
201C2×#97C22×C311yescharacteristic, complemented
202#398—21no—
203#396—21no—
204#394—21no—
205#394—21no—
206#391C22×C311yescharacteristic, complemented
207#390C22×C311yescharacteristic
208#390C22×C311yescharacteristic
209#389—21no—
210#389C22×C311yescharacteristic, complemented
211#388—21no—
212#379—21no—
213#379—21no—
214C4×C22⋊C4C22×C311yescharacteristic
215#340C22×C311yescharacteristic, complemented
216#340C22×C311yescharacteristic, complemented
217#336C22×C311yescharacteristic, complemented
218#336C22×C311yescharacteristic, complemented
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—42no—
222C24×C3—42no—
223C24×C3—42no—
224C24×C3—42no—
225C24×C3—42no—
226C24×C3—81no—
227C24×C3—81no—
228C24×C3C2×D411yescharacteristic
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
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×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8C2×D412yes—
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—21no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4—42no—
260C2×C3×D4—44no—
261C2×C3×D4—44no—
262C2×C3×D4—44no—
263C2×C3×D4—44no—
264C2×C3×D4C2×D412yes—
265C2×C3×D4C2×D412yes—
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—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4C2×D411yescharacteristic
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C3×Q16—44no—
285C3×Q16—44no—
286C3×SD16—44no—
287C3×SD16—44no—
288C3×SD16—44no—
289C3×SD16—44no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8—21no—
297C2×C3×C8—21no—
298C2×C3×C8—21no—
299C2×C3×C8—21no—
300C2×C3×C8C2×D412yes—
301C2×C3×C8C2×D412yes—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—42no—
308C3×C4⋊C4—42no—
309C3×C4⋊C4—42no—
310C3×C4⋊C4—42no—
311C3×C4⋊C4—42no—
312C3×C4⋊C4—42no—
313C3×C4⋊C4—42no—
314C3×C4⋊C4C2×D412yes—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—41no—
317C3×C22⋊C4—42no—
318C3×C22⋊C4—42no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—42no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—81no—
325C3×C22⋊C4—81no—
326C3×C22⋊C4—81no—
327C3×C22⋊C4—81no—
328C3×C42—21no—
329C3×C42—21no—
330C3×C42—21no—
331C3×C42—21no—
332C3×C42—42no—
333C25—21no—
334C22×Q8C23×C311yescharacteristic
335C22×Q8C23×C311yescharacteristic
336C22×Q8C23×C311yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—41no—
341C22×D4—41no—
342C22×D4—41no—
343C22×D4—41no—
344C22×D4C23×C311yescharacteristic
345C22×D4C23×C311yescharacteristic
346C23×C4C23×C311yescharacteristic
347C2×Q16—22no—
348C2×Q16—22no—
349C2×Q16—22no—
350C2×Q16—41no—
351C2×Q16—41no—
352C2×Q16—41no—
353C2×SD16—22no—
354C2×SD16—22no—
355C2×SD16—22no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—41no—
359C2×SD16—41no—
360C2×SD16—41no—
361C2×SD16—41no—
362C2×SD16—41no—
363C2×SD16—41no—
364C2×SD16C3×D414yes—
365C22×C8C23×C311yescharacteristic
366C22×C8C23×C311yescharacteristic
367C22×C8C23×C311yescharacteristic
368C22×C8C23×C311yescharacteristic
369C4⋊Q8—22no—
370C4⋊Q8—41no—
371#124—22no—
372#124—22no—
373#124—41no—
374#124—41no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8—41no—
378C22⋊Q8—41no—
379C22⋊Q8—41no—
380C22⋊Q8—41no—
381C4×Q8—22no—
382C4×Q8—41no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C23×C311yescharacteristic
391C2×C4⋊C4C23×C311yescharacteristic
392C2×C4⋊C4C23×C311yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4C3×D411yescharacteristic
405C2×C22⋊C4C3×D411yescharacteristic
406C2×C42—21no—
407C2×C42C23×C311yescharacteristic
408C2×C42C23×C311yescharacteristic
409C4⋊C8—22no—
410#103—22no—
411#103—41no—
412#103—41no—
413#103—41no—
414#102—22no—
415#102—22no—
416#102—22no—
417#102C3×D414yes—
418C22⋊C8—22no—
419C22⋊C8—22no—
420#97—22no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95C3×D411yescharacteristic
425#95C3×D411yescharacteristic
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—48no—
435C23×C3—41no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—41no—
439C23×C3—41no—
440C23×C3—41no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—84no—
448C23×C3—84no—
449C23×C3—84no—
450C23×C3—84no—
451C23×C3—84no—
452C23×C3—84no—
453C23×C3#13712yes—
454C23×C3C22×D411yescharacteristic
455C3×Q8—22no—
456C3×Q8—22no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×Q8—41no—
461C3×Q8—41no—
462C3×Q8—41no—
463C3×Q8—41no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×D4—22no—
468C3×D4—22no—
469C3×D4—22no—
470C3×D4—22no—
471C3×D4—48no—
472C3×D4—41no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—41no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
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—21no—
492C2×C3×C4—21no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
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—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4C22×D411yescharacteristic
514C2×C3×C4C22×D411yescharacteristic
515C2×C3×C4H(5,𝔽2)11yescharacteristic
516C2×C3×C4H(5,𝔽2)11yescharacteristic
517C2×C3×C4H(5,𝔽2)11yescharacteristic
518C2×C3×C4H(5,𝔽2)11yescharacteristic
519C3×C8—22no—
520C3×C8—22no—
521C3×C8—41no—
522C3×C8—41no—
523C24—21no—
524C24—21no—
525C24—42no—
526C24—42no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—81no—
531C24—81no—
532C24C2×C3×D411yescharacteristic
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×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8C2×C3×D412yes—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—44no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4C2×C3×D412yes—
569C2×D4C2×C3×D412yes—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4C2×C3×D411yescharacteristic
583C22×C4C2×C3×D411yescharacteristic
584C22×C4C2×C3×D411yescharacteristic
585C22×C4C2×C3×D411yescharacteristic
586C22×C4C2×C3×D411yescharacteristic
587C22×C4C24×C311yescharacteristic
588Q16—44no—
589Q16—44no—
590SD16—44no—
591SD16—44no—
592SD16—44no—
593SD16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8C2×C3×D412yes—
605C2×C8C2×C3×D412yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4C2×C3×D412yes—
619C22⋊C4—22no—
620C22⋊C4—41no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C42—21no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—42no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—42no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—42no—
649C22×C3—42no—
650C22×C3—816no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3#53511yescharacteristic
660C22×C3D4211yescharacteristic
661C22×C3D4211yescharacteristic
662C22×C3C2×#13711yescharacteristic
663C22×C3#57511yescharacteristic
664C22×C3#57711yescharacteristic
665C22×C3#57711yescharacteristic
666C3×C4—41no—
667C3×C4—42no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—42no—
672C3×C4—41no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4#53411yescharacteristic
678C3×C4#53511yescharacteristic
679C3×C4D4211yescharacteristic
680C3×C4#56011yescharacteristic
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—22no—
688C23—22no—
689C23—48no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—84no—
703C23—84no—
704C23—84no—
705C23—84no—
706C23—84no—
707C23—84no—
708C23C3×#13712yes—
709C23C22×C3×D411yescharacteristic
710Q8—22no—
711Q8—22no—
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720Q8—41no—
721Q8—41no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
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—21no—
747C2×C4—21no—
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—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4C22×C3×D411yescharacteristic
769C2×C4C22×C3×D411yescharacteristic
770C2×C4C3×H(5,𝔽2)11yescharacteristic
771C2×C4C3×H(5,𝔽2)11yescharacteristic
772C2×C4C3×H(5,𝔽2)11yescharacteristic
773C2×C4C3×H(5,𝔽2)11yescharacteristic
774C8—22no—
775C8—22no—
776C8—41no—
777C8—41no—
778C2×C3—42no—
779C2×C3—82no—
780C2×C3—82no—
781C2×C3#266911yescharacteristic
782C2×C3#321511yescharacteristic
783C2×C3#322211yescharacteristic
784C2×C3#326611yescharacteristic
785C2×C3#326611yescharacteristic
786C2×C3#326711yescharacteristic
787C2×C3#327511yescharacteristic
788C22—22no—
789C22—22no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—816no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22C3×#53511yescharacteristic
811C22C3×D4211yescharacteristic
812C22C3×D4211yescharacteristic
813C22C2×C3×#13711yescharacteristic
814C22C3×#57511yescharacteristic
815C22C3×#57711yescharacteristic
816C22C3×#57711yescharacteristic
817C4—41no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4—81no—
828C4C3×#53411yescharacteristic
829C4C3×#53511yescharacteristic
830C4C3×D4211yescharacteristic
831C4C3×#56011yescharacteristic
832C3#3046411yescharacteristic, direct product factor, Sylow
833C2—42no—
834C2—82no—
835C2—82no—
836C2C3×#266911yescharacteristic
837C2C3×#321511yescharacteristic
838C2C3×#322211yescharacteristic
839C2C3×#326611yescharacteristic
840C2C3×#326611yescharacteristic
841C2C3×#326711yescharacteristic
842C2C3×#327511yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC23×C3×D4C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#497C2semidirect
2. C2×C3×#464C2semidirect
6. C3×#2429C2semidirect
7. C3×#2055C2semidirect
8. C3×#2042C2semidirect
9. C3×#2015C2semidirect
10. C3×#2013C2semidirect
11. C3×#2001C2semidirect
12. C3×#2001C2semidirect
13. C3×#1936C2semidirect
14. C3×#1924C2semidirect
15. C3×#1880C2semidirect
16. #30464C3direct (N × H)
18. C22×C3×Q16C22semidirect
19. C22×C3×Q16C22semidirect
24. C2×C3×C4⋊Q8C22semidirect
30. C2×C3×C4×Q8C22semidirect
35. C2×C3×C4⋊C8C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
38. C2×C3×#103C22semidirect
39. C2×C3×#103C22semidirect
46. C2×C3×#97C22semidirect
51. C3×#391C22semidirect
55. C3×#389C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#336C22semidirect
63. C3×#336C22semidirect
64. C2×#497C2×C3semidirect
65. C2×#464C2×C3semidirect
69. #2429C2×C3semidirect
70. #2055C2×C3semidirect
71. #2042C2×C3semidirect
72. #2015C2×C3semidirect
73. #2013C2×C3semidirect
74. #2001C2×C3semidirect
75. #2001C2×C3semidirect
76. #1936C2×C3semidirect
77. #1924C2×C3semidirect
78. #1880C2×C3semidirect
173. C22×Q16C22×C3semidirect
174. C22×Q16C22×C3semidirect
179. C2×C4⋊Q8C22×C3semidirect
185. C2×C4×Q8C22×C3semidirect
190. C2×C4⋊C8C22×C3semidirect
191. C2×#103C22×C3semidirect
192. C2×#103C22×C3semidirect
193. C2×#103C22×C3semidirect
194. C2×#103C22×C3semidirect
201. C2×#97C22×C3semidirect
206. #391C22×C3semidirect
210. #389C22×C3semidirect
215. #340C22×C3semidirect
216. #340C22×C3semidirect
217. #336C22×C3semidirect
218. #336C22×C3semidirect
832. C3#30464direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4972
C2×C3×#4642
C2×C3×#4502
C3×#24352
C3×#24292
C3×#20552
C3×#20422
C3×#20152
C3×#20132
C3×#20012
C3×#19362
C3×#19242
C3×#18802
#304643