Finite Group Databasebeta

← C3×#30459 #10649066

Subgroups — C3×#30459 #10649066

Order 768.

1134 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×#492C211yesmaximal, characteristic, complemented
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C2×C3×#452C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C3×#2431C211yesmaximal, characteristic
6C3×#2429C211yesmaximal, characteristic, complemented
7C3×#2055C211yesmaximal, characteristic, complemented
8C3×#2041C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic, complemented
13C3×#1933C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic, complemented
15C3×#1880C211yesmaximal, characteristic, complemented
16#30459C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C2×C3×C4⋊Q8C2211yescharacteristic
25C2×C3×#127C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C3×#492—24no—
32C3×#464—24no—
33C3×#452—24no—
34C3×#452—24no—
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#103C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C4×C8C2211yescharacteristic
47C3×#398—21no—
48C3×#396—21no—
49C3×#392—21no—
50C3×#392—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#389—21no—
55C3×#389C2211yescharacteristic
56C3×#388—21no—
57C3×#386—21no—
58C3×#386—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#492C2×C311yescharacteristic, complemented
65C2×#464C2×C311yescharacteristic, complemented
66C2×#452C2×C311yescharacteristic, complemented
67C2×#452C2×C311yescharacteristic, complemented
68#2431C2×C311yescharacteristic
69#2429C2×C311yescharacteristic, complemented
70#2055C2×C311yescharacteristic, complemented
71#2041C2×C311yescharacteristic, complemented
72#2016C2×C311yescharacteristic, complemented
73#2015C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1933C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic, complemented
78#1880C2×C311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4C2311yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C23×C3×C4—21no—
95C23×C3×C4C2311yescharacteristic
96C2×C3×Q16—22no—
97C2×C3×Q16—22no—
98C2×C3×Q16—22no—
99C2×C3×Q16—41no—
100C2×C3×Q16—41no—
101C2×C3×Q16—41no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—22no—
105C2×C3×SD16—22no—
106C2×C3×SD16—22no—
107C2×C3×SD16—41no—
108C2×C3×SD16—41no—
109C2×C3×SD16—41no—
110C2×C3×SD16—41no—
111C2×C3×SD16—41no—
112C2×C3×SD16—41no—
113C2×C3×SD16D414yescomplemented
114C22×C3×C8C2311yescharacteristic
115C22×C3×C8C2311yescharacteristic
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C3×C4⋊Q8—22no—
119C3×C4⋊Q8—41no—
120C3×#127—22no—
121C3×#127—41no—
122C3×#124—22no—
123C3×#124—41no—
124C3×C22⋊Q8—22no—
125C3×C22⋊Q8—22no—
126C3×C22⋊Q8—41no—
127C3×C22⋊Q8—41no—
128C3×#121—41no—
129C3×#121—41no—
130C3×C4×Q8—22no—
131C3×C4×Q8—41no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—21no—
134C2×C3×C4⋊C4—21no—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
149C2×C3×C22⋊C4D411yescharacteristic
150C2×C3×C42—21no—
151C2×C3×C42C2311yescharacteristic
152C2×C3×C42C2311yescharacteristic
153C3×C4⋊C8—22no—
154C3×#103—22no—
155C3×#103—41no—
156C3×#103—41no—
157C3×#103D414yescomplemented
158C3×#102—22no—
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—41no—
162C3×C22⋊C8—22no—
163C3×C22⋊C8—22no—
164C3×C4×C8—22no—
165C3×#95—21no—
166C3×#95—21no—
167C3×#95—21no—
168C3×#95—21no—
169C3×#95—21no—
170C3×#95D411yescharacteristic
171C3×#95D411yescharacteristic
172C22×#41C22×C311yescharacteristic
173C22×Q16C22×C311yescharacteristic
174C22×Q16C22×C311yescharacteristic
175C22×SD16C22×C311yescharacteristic
176C22×SD16C22×C311yescharacteristic
177C22×SD16C22×C311yescharacteristic
178C22×SD16C22×C311yescharacteristic
179C2×C4⋊Q8C22×C311yescharacteristic
180C2×#127C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×Q8C22×C311yescharacteristic
186#492—24no—
187#464—24no—
188#452—24no—
189#452—24no—
190C2×C4⋊C8C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×C22⋊C8C22×C311yescharacteristic
200C2×C22⋊C8C22×C311yescharacteristic
201C2×C4×C8C22×C311yescharacteristic
202#398—21no—
203#396—21no—
204#392—21no—
205#392—21no—
206#391C22×C311yescharacteristic
207#391C22×C311yescharacteristic
208#390C22×C311yescharacteristic
209#389—21no—
210#389C22×C311yescharacteristic
211#388—21no—
212#386—21no—
213#386—21no—
214C4×C22⋊C4C22×C311yescharacteristic
215#340C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217#336C22×C311yescharacteristic
218#336C22×C311yescharacteristic
219C24×C3—21no—
220C24×C3—21no—
221C24×C3C2×D411yescharacteristic
222C3×#41—44no—
223C3×#41—44no—
224C3×#41—44no—
225C3×#41—44no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
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×Q8C2×D412yes—
243C2×C3×Q8C2×D412yes—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
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—42no—
256C2×C3×D4—42no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—81no—
264C2×C3×D4—81no—
265C2×C3×D4—81no—
266C2×C3×D4—81no—
267C2×C3×D4C2×D412yes—
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×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—42no—
281C22×C3×C4—42no—
282C22×C3×C4—42no—
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4C2×D411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C3×Q16—44no—
290C3×Q16—44no—
291C3×SD16—44no—
292C3×SD16—44no—
293C3×SD16—44no—
294C3×SD16—44no—
295C2×C3×C8—21no—
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×C8C2×D412yes—
306C2×C3×C8C2×D412yes—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4—21no—
312C3×C4⋊C4—42no—
313C3×C4⋊C4—42no—
314C3×C4⋊C4—42no—
315C3×C4⋊C4—42no—
316C3×C4⋊C4—42no—
317C3×C4⋊C4—42no—
318C3×C4⋊C4C2×D412yes—
319C3×C22⋊C4—22no—
320C3×C22⋊C4—22no—
321C3×C22⋊C4—42no—
322C3×C22⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C22⋊C4—42no—
326C3×C22⋊C4—81no—
327C3×C22⋊C4—81no—
328C3×C42—21no—
329C3×C42—21no—
330C3×C42—21no—
331C3×C42—21no—
332C3×C42—42no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—41no—
336C2×#41—41no—
337C2×#41—41no—
338C2×#41—41no—
339C22×Q8C23×C311yescharacteristic
340C22×Q8C23×C311yescharacteristic
341C22×Q8C23×C311yescharacteristic
342C22×D4—21no—
343C22×D4—21no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4C23×C311yescharacteristic
347C22×D4C23×C311yescharacteristic
348C23×C4—21no—
349C23×C4C23×C311yescharacteristic
350C2×Q16—22no—
351C2×Q16—22no—
352C2×Q16—22no—
353C2×Q16—41no—
354C2×Q16—41no—
355C2×Q16—41no—
356C2×SD16—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16—41no—
362C2×SD16—41no—
363C2×SD16—41no—
364C2×SD16—41no—
365C2×SD16—41no—
366C2×SD16—41no—
367C2×SD16C3×D414yescomplemented
368C22×C8C23×C311yescharacteristic
369C22×C8C23×C311yescharacteristic
370C22×C8C23×C311yescharacteristic
371C22×C8C23×C311yescharacteristic
372C4⋊Q8—22no—
373C4⋊Q8—41no—
374#127—22no—
375#127—41no—
376#124—22no—
377#124—41no—
378C22⋊Q8—22no—
379C22⋊Q8—22no—
380C22⋊Q8—41no—
381C22⋊Q8—41no—
382#121—41no—
383#121—41no—
384C4×Q8—22no—
385C4×Q8—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4C23×C311yescharacteristic
393C2×C4⋊C4C23×C311yescharacteristic
394C2×C4⋊C4C23×C311yescharacteristic
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⋊C4C3×D411yescharacteristic
403C2×C22⋊C4C3×D411yescharacteristic
404C2×C42—21no—
405C2×C42C23×C311yescharacteristic
406C2×C42C23×C311yescharacteristic
407C4⋊C8—22no—
408#103—22no—
409#103—41no—
410#103—41no—
411#103C3×D414yescomplemented
412#102—22no—
413#102—22no—
414#102—22no—
415#102—41no—
416C22⋊C8—22no—
417C22⋊C8—22no—
418C4×C8—22no—
419#95—21no—
420#95—21no—
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—22no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—41no—
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×C3C22×D411yescharacteristic
448C3×Q8—22no—
449C3×Q8—22no—
450C3×Q8—22no—
451C3×Q8—22no—
452C3×Q8—41no—
453C3×Q8—41no—
454C3×Q8—41no—
455C3×Q8—41no—
456C3×Q8—41no—
457C3×Q8—41no—
458C3×Q8—41no—
459C3×Q8—41no—
460C3×D4—22no—
461C3×D4—22no—
462C3×D4—48no—
463C3×D4—41no—
464C3×D4—41no—
465C3×D4—41no—
466C3×D4—41no—
467C3×D4—41no—
468C3×D4—41no—
469C3×D4—84no—
470C3×D4—84no—
471C3×D4—84no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—48no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
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#13512yes—
509C2×C3×C4#13712yes—
510C2×C3×C4C22×D411yescharacteristic
511C2×C3×C4C22×D411yescharacteristic
512C2×C3×C4H(5,𝔽2)11yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514C2×C3×C4H(5,𝔽2)11yescharacteristic
515C2×C3×C4H(5,𝔽2)11yescharacteristic
516C3×C8—22no—
517C3×C8—22no—
518C3×C8—41no—
519C3×C8—41no—
520C24—21no—
521C24—21no—
522C24C2×C3×D411yescharacteristic
523#41—44no—
524#41—44no—
525#41—44no—
526#41—44no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
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×Q8C2×C3×D412yes—
544C2×Q8C2×C3×D412yes—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
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—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4C2×C3×D412yes—
569C22×C4—21no—
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—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4C2×C3×D411yescharacteristic
585C22×C4C2×C3×D411yescharacteristic
586C22×C4C2×C3×D411yescharacteristic
587C22×C4C2×C3×D411yescharacteristic
588C22×C4C2×C3×D411yescharacteristic
589C22×C4C24×C311yescharacteristic
590Q16—44no—
591Q16—44no—
592SD16—44no—
593SD16—44no—
594SD16—44no—
595SD16—44no—
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×C8—21no—
605C2×C8—21no—
606C2×C8C2×C3×D412yes—
607C2×C8C2×C3×D412yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—42no—
614C4⋊C4—42no—
615C4⋊C4—42no—
616C4⋊C4—42no—
617C4⋊C4—42no—
618C4⋊C4—42no—
619C4⋊C4C2×C3×D412yes—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—21no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—42no—
634C22×C3—42no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—42no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3#53511yescharacteristic
656C22×C3D4211yescharacteristic
657C22×C3D4211yescharacteristic
658C22×C3C2×#13511yescharacteristic
659C22×C3C2×#13711yescharacteristic
660C22×C3#57711yescharacteristic
661C22×C3#57711yescharacteristic
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—41no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—42no—
670C3×C4—81no—
671C3×C4—81no—
672C3×C4—81no—
673C3×C4#53411yescharacteristic
674C3×C4#53511yescharacteristic
675C3×C4D4211yescharacteristic
676C3×C4#56011yescharacteristic
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—22no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23C22×C3×D411yescharacteristic
699Q8—22no—
700Q8—22no—
701Q8—22no—
702Q8—22no—
703Q8—41no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—84no—
721D4—84no—
722D4—84no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—48no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
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×C4C3×#13512yes—
760C2×C4C3×#13712yes—
761C2×C4C22×C3×D411yescharacteristic
762C2×C4C22×C3×D411yescharacteristic
763C2×C4C3×H(5,𝔽2)11yescharacteristic
764C2×C4C3×H(5,𝔽2)11yescharacteristic
765C2×C4C3×H(5,𝔽2)11yescharacteristic
766C2×C4C3×H(5,𝔽2)11yescharacteristic
767C8—22no—
768C8—22no—
769C8—41no—
770C8—41no—
771C2×C3—81no—
772C2×C3—82no—
773C2×C3—161no—
774C2×C3#266911yescharacteristic
775C2×C3#321011yescharacteristic
776C2×C3#322211yescharacteristic
777C2×C3#326611yescharacteristic
778C2×C3#327811yescharacteristic
779C2×C3#328211yescharacteristic
780C2×C3#328411yescharacteristic
781C22—42no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—42no—
789C22—41no—
790C22—41no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22C3×#53511yescharacteristic
803C22C3×D4211yescharacteristic
804C22C3×D4211yescharacteristic
805C22C2×C3×#13511yescharacteristic
806C22C2×C3×#13711yescharacteristic
807C22C3×#57711yescharacteristic
808C22C3×#57711yescharacteristic
809C4—22no—
810C4—22no—
811C4—41no—
812C4—42no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C3×#53411yescharacteristic
821C4C3×#53511yescharacteristic
822C4C3×D4211yescharacteristic
823C4C3×#56011yescharacteristic
824C3#3045911yescharacteristic, direct product factor, Sylow
825C2—81no—
826C2—82no—
827C2—161no—
828C2C3×#266911yescharacteristic
829C2C3×#321011yescharacteristic
830C2C3×#322211yescharacteristic
831C2C3×#326611yescharacteristic
832C2C3×#327811yescharacteristic
833C2C3×#328211yescharacteristic
834C2C3×#328411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2431C2
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×#492C2semidirect
2. C2×C3×#464C2semidirect
3. C2×C3×#452C2semidirect
4. C2×C3×#452C2semidirect
6. C3×#2429C2semidirect
7. C3×#2055C2semidirect
8. C3×#2041C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
11. C3×#2000C2semidirect
12. C3×#2000C2semidirect
13. C3×#1933C2semidirect
14. C3×#1923C2semidirect
15. C3×#1880C2semidirect
16. #30459C3direct (N × H)
64. C2×#492C2×C3semidirect
65. C2×#464C2×C3semidirect
66. C2×#452C2×C3semidirect
67. C2×#452C2×C3semidirect
69. #2429C2×C3semidirect
70. #2055C2×C3semidirect
71. #2041C2×C3semidirect
72. #2016C2×C3semidirect
73. #2015C2×C3semidirect
74. #2000C2×C3semidirect
75. #2000C2×C3semidirect
76. #1933C2×C3semidirect
77. #1923C2×C3semidirect
78. #1880C2×C3semidirect
113. C2×C3×SD16D4semidirect
157. C3×#103D4semidirect
367. C2×SD16C3×D4semidirect
411. #103C3×D4semidirect
824. C3#30459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4922
C2×C3×#4642
C2×C3×#4522
C3×#24312
C3×#24292
C3×#20552
C3×#20412
C3×#20162
C3×#20152
C3×#20002
C3×#19332
C3×#19232
C3×#18802
#304593