Finite Group Databasebeta

← C3×#30446 #10649053

Subgroups — C3×#30446 #10649053

Order 768.

1182 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×#495C211yesmaximal, characteristic, complemented
2C2×C3×#459C211yesmaximal, characteristic, complemented
3C2×C3×#452C211yesmaximal, characteristic, complemented
4C2×C3×#449C211yesmaximal, characteristic, complemented
5C3×#2431C211yesmaximal, characteristic, complemented
6C3×#2427C211yesmaximal, characteristic, complemented
7C3×#2056C211yesmaximal, characteristic, complemented
8C3×#2042C211yesmaximal, characteristic, complemented
9C3×#2014C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic, complemented
13C3×#1934C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic, complemented
15C3×#1877C211yesmaximal, characteristic, complemented
16#30446C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#127C2211yescharacteristic
25C2×C3×#124C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×D4C2211yescharacteristic
31C3×#495—24no—
32C3×#459—24no—
33C3×#452—24no—
34C3×#449—24no—
35C2×C3×C4⋊C8C2211yescharacteristic
36C2×C3×#103C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
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×#397—21no—
48C3×#394—21no—
49C3×#392—21no—
50C3×#392—21no—
51C3×#391C2211yescharacteristic
52C3×#391C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#389C2211yescharacteristic
55C3×#386—21no—
56C3×#386—21no—
57C3×#386—21no—
58C3×#380—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#495C2×C311yescharacteristic, complemented
65C2×#459C2×C311yescharacteristic, complemented
66C2×#452C2×C311yescharacteristic, complemented
67C2×#449C2×C311yescharacteristic, complemented
68#2431C2×C311yescharacteristic, complemented
69#2427C2×C311yescharacteristic, complemented
70#2056C2×C311yescharacteristic, complemented
71#2042C2×C311yescharacteristic, complemented
72#2014C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1934C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic, complemented
78#1877C2×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×D4—21no—
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4C2311yescharacteristic
93C22×C3×D4C2311yescharacteristic
94C22×C3×D4C2311yescharacteristic
95C23×C3×C4—21no—
96C23×C3×C4—21no—
97C23×C3×C4C2311yescharacteristic
98C2×C3×Q16—22no—
99C2×C3×Q16—22no—
100C2×C3×Q16—41no—
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—41no—
104C2×C3×SD16—41no—
105C2×C3×SD16—41no—
106C2×C3×SD16—41no—
107C2×C3×SD16—41no—
108C2×C3×SD16—41no—
109C2×C3×SD16D414yescomplemented
110C2×C3×D8—22no—
111C2×C3×D8—22no—
112C2×C3×D8—22no—
113C2×C3×D8—22no—
114C2×C3×D8—41no—
115C2×C3×D8—41no—
116C22×C3×C8C2311yescharacteristic
117C22×C3×C8C2311yescharacteristic
118C22×C3×C8C2311yescharacteristic
119C22×C3×C8C2311yescharacteristic
120C3×#127—22no—
121C3×#127—41no—
122C3×#124—22no—
123C3×#124—22no—
124C3×#124—41no—
125C3×#124—41no—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—41no—
128C3×#121—22no—
129C3×#121—41no—
130C3×#121—41no—
131C3×#121—41no—
132C3×C4×D4—22no—
133C3×C4×D4—41no—
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⋊C4D411yescharacteristic
150C2×C3×C22⋊C4D411yescharacteristic
151C2×C3×C42C2311yescharacteristic
152C2×C3×C42C2311yescharacteristic
153C3×C4⋊C8—22no—
154C3×#103—22no—
155C3×#103—22no—
156C3×#103—41no—
157C3×#102—22no—
158C3×#102—22no—
159C3×#102—41no—
160C3×#102—41no—
161C3×#102D414yescomplemented
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×SD16C22×C311yescharacteristic
175C22×SD16C22×C311yescharacteristic
176C22×SD16C22×C311yescharacteristic
177C22×D8C22×C311yescharacteristic
178C22×D8C22×C311yescharacteristic
179C2×#127C22×C311yescharacteristic
180C2×#124C22×C311yescharacteristic
181C2×#124C22×C311yescharacteristic
182C2×C22⋊Q8C22×C311yescharacteristic
183C2×#121C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185C2×C4×D4C22×C311yescharacteristic
186#495—24no—
187#459—24no—
188#452—24no—
189#449—24no—
190C2×C4⋊C8C22×C311yescharacteristic
191C2×#103C22×C311yescharacteristic
192C2×#103C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#102C22×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#397—21no—
203#394—21no—
204#392—21no—
205#392—21no—
206#391C22×C311yescharacteristic
207#391C22×C311yescharacteristic
208#390C22×C311yescharacteristic
209#389C22×C311yescharacteristic
210#386—21no—
211#386—21no—
212#386—21no—
213#380—21no—
214C4×C22⋊C4C22×C311yescharacteristic
215#340C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217#336C22×C311yescharacteristic
218#336C22×C311yescharacteristic
219C24×C3—21no—
220C24×C3—21no—
221C24×C3—21no—
222C24×C3C2×D411yescharacteristic
223C3×#41—44no—
224C3×#41—44no—
225C3×#41—44no—
226C3×#41—44no—
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×Q8C2×D412yes—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
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—42no—
264C2×C3×D4—42no—
265C2×C3×D4—81no—
266C2×C3×D4—81no—
267C2×C3×D4—81no—
268C2×C3×D4—81no—
269C2×C3×D4—81no—
270C2×C3×D4C2×D412yes—
271C2×C3×D4C2×D412yes—
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—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—42no—
284C22×C3×C4—42no—
285C22×C3×C4—42no—
286C22×C3×C4—42no—
287C22×C3×C4—42no—
288C22×C3×C4—81no—
289C22×C3×C4C2×D411yescharacteristic
290C22×C3×C4C2×D411yescharacteristic
291C22×C3×C4C2×D411yescharacteristic
292C22×C3×C4C2×D411yescharacteristic
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4C2411yescharacteristic
295C3×Q16—44no—
296C3×SD16—44no—
297C3×SD16—44no—
298C3×SD16—44no—
299C3×D8—44no—
300C3×D8—44no—
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—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8C2×D412yes—
312C2×C3×C8C2×D412yes—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—42no—
319C3×C4⋊C4—81no—
320C3×C4⋊C4C2×D412yes—
321C3×C22⋊C4—22no—
322C3×C22⋊C4—41no—
323C3×C22⋊C4—42no—
324C3×C22⋊C4—42no—
325C3×C22⋊C4—42no—
326C3×C22⋊C4—42no—
327C3×C22⋊C4—42no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—42no—
330C3×C22⋊C4—42no—
331C3×C22⋊C4—81no—
332C3×C22⋊C4—81no—
333C3×C42—21no—
334C3×C42—21no—
335C3×C42—21no—
336C3×C42—21no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—41no—
340C2×#41—41no—
341C2×#41—41no—
342C2×#41—41no—
343C22×Q8C23×C311yescharacteristic
344C22×Q8C23×C311yescharacteristic
345C22×D4—21no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4—21no—
349C22×D4—21no—
350C22×D4C23×C311yescharacteristic
351C22×D4C23×C311yescharacteristic
352C22×D4C23×C311yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4C23×C311yescharacteristic
356C2×Q16—22no—
357C2×Q16—22no—
358C2×Q16—41no—
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
368C2×D8—22no—
369C2×D8—22no—
370C2×D8—22no—
371C2×D8—22no—
372C2×D8—41no—
373C2×D8—41no—
374C22×C8C23×C311yescharacteristic
375C22×C8C23×C311yescharacteristic
376C22×C8C23×C311yescharacteristic
377C22×C8C23×C311yescharacteristic
378#127—22no—
379#127—41no—
380#124—22no—
381#124—22no—
382#124—41no—
383#124—41no—
384C22⋊Q8—22no—
385C22⋊Q8—41no—
386#121—22no—
387#121—41no—
388#121—41no—
389#121—41no—
390C4×D4—22no—
391C4×D4—41no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4C23×C311yescharacteristic
395C2×C4⋊C4C23×C311yescharacteristic
396C2×C4⋊C4C23×C311yescharacteristic
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⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4C3×D411yescharacteristic
408C2×C22⋊C4C3×D411yescharacteristic
409C2×C42C23×C311yescharacteristic
410C2×C42C23×C311yescharacteristic
411C4⋊C8—22no—
412#103—22no—
413#103—22no—
414#103—41no—
415#102—22no—
416#102—22no—
417#102—41no—
418#102—41no—
419#102C3×D414yescomplemented
420C22⋊C8—22no—
421C22⋊C8—22no—
422C4×C8—22no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95C3×D411yescharacteristic
429#95C3×D411yescharacteristic
430C23×C3—21no—
431C23×C3—22no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—22no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
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—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3C22×D411yescharacteristic
459C3×Q8—22no—
460C3×Q8—22no—
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—
476C3×D4—41no—
477C3×D4—41no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—84no—
481C3×D4—84no—
482C3×D4—84no—
483C3×D4—84no—
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—22no—
491C2×C3×C4—21no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—48no—
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×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—84no—
519C2×C3×C4#13512yes—
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4H(5,𝔽2)11yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524C2×C3×C4H(5,𝔽2)11yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C3×C8—22no—
527C3×C8—22no—
528C3×C8—41no—
529C3×C8—41no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24C2×C3×D411yescharacteristic
534#41—44no—
535#41—44no—
536#41—44no—
537#41—44no—
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×Q8C2×C3×D412yes—
550C2×D4—21no—
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—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—81no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×C3×D412yes—
582C2×D4C2×C3×D412yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—81no—
600C22×C4C2×C3×D411yescharacteristic
601C22×C4C2×C3×D411yescharacteristic
602C22×C4C2×C3×D411yescharacteristic
603C22×C4C2×C3×D411yescharacteristic
604C22×C4C2×C3×D411yescharacteristic
605C22×C4C24×C311yescharacteristic
606Q16—44no—
607SD16—44no—
608SD16—44no—
609SD16—44no—
610D8—44no—
611D8—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×C8C2×C3×D412yes—
623C2×C8C2×C3×D412yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—42no—
630C4⋊C4—81no—
631C4⋊C4C2×C3×D412yes—
632C22⋊C4—22no—
633C22⋊C4—41no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C22×C3—42no—
649C22×C3—41no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—42no—
655C22×C3—42no—
656C22×C3—41no—
657C22×C3—42no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—42no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—81no—
667C22×C3—81no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—81no—
674C22×C3—81no—
675C22×C3—81no—
676C22×C3#53511yescharacteristic
677C22×C3D4211yescharacteristic
678C22×C3D4211yescharacteristic
679C22×C3C2×#13511yescharacteristic
680C22×C3#57511yescharacteristic
681C22×C3#57611yescharacteristic
682C22×C3#57711yescharacteristic
683C3×C4—22no—
684C3×C4—41no—
685C3×C4—42no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—42no—
689C3×C4—41no—
690C3×C4—81no—
691C3×C4—81no—
692C3×C4—81no—
693C3×C4#53411yescharacteristic
694C3×C4#53511yescharacteristic
695C3×C4D4211yescharacteristic
696C3×C4#56011yescharacteristic
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—22no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23C22×C3×D411yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—48no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4—84no—
749D4—84no—
750D4—84no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—48no—
768C2×C4—41no—
769C2×C4—41no—
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—84no—
786C2×C4C3×#13512yes—
787C2×C4C22×C3×D411yescharacteristic
788C2×C4C22×C3×D411yescharacteristic
789C2×C4C3×H(5,𝔽2)11yescharacteristic
790C2×C4C3×H(5,𝔽2)11yescharacteristic
791C2×C4C3×H(5,𝔽2)11yescharacteristic
792C2×C4C3×H(5,𝔽2)11yescharacteristic
793C8—22no—
794C8—22no—
795C8—41no—
796C8—41no—
797C2×C3—81no—
798C2×C3—82no—
799C2×C3—82no—
800C2×C3—161no—
801C2×C3#266911yescharacteristic
802C2×C3#321211yescharacteristic
803C2×C3#322411yescharacteristic
804C2×C3#326811yescharacteristic
805C2×C3#327511yescharacteristic
806C2×C3#328011yescharacteristic
807C2×C3#328411yescharacteristic
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22C3×#53511yescharacteristic
837C22C3×D4211yescharacteristic
838C22C3×D4211yescharacteristic
839C22C2×C3×#13511yescharacteristic
840C22C3×#57511yescharacteristic
841C22C3×#57611yescharacteristic
842C22C3×#57711yescharacteristic
843C4—22no—
844C4—41no—
845C4—42no—
846C4—41no—
847C4—41no—
848C4—42no—
849C4—41no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4C3×#53411yescharacteristic
854C4C3×#53511yescharacteristic
855C4C3×D4211yescharacteristic
856C4C3×#56011yescharacteristic
857C3#3044611yescharacteristic, direct product factor, Sylow
858C2—81no—
859C2—82no—
860C2—82no—
861C2—161no—
862C2C3×#266911yescharacteristic
863C2C3×#321211yescharacteristic
864C2C3×#322411yescharacteristic
865C2C3×#326811yescharacteristic
866C2C3×#327511yescharacteristic
867C2C3×#328011yescharacteristic
868C2C3×#328411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
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×#495C2semidirect
2. C2×C3×#459C2semidirect
3. C2×C3×#452C2semidirect
4. C2×C3×#449C2semidirect
5. C3×#2431C2semidirect
6. C3×#2427C2semidirect
7. C3×#2056C2semidirect
8. C3×#2042C2semidirect
9. C3×#2014C2semidirect
10. C3×#2012C2semidirect
11. C3×#2000C2semidirect
12. C3×#1999C2semidirect
13. C3×#1934C2semidirect
14. C3×#1923C2semidirect
15. C3×#1877C2semidirect
16. #30446C3direct (N × H)
64. C2×#495C2×C3semidirect
65. C2×#459C2×C3semidirect
66. C2×#452C2×C3semidirect
67. C2×#449C2×C3semidirect
68. #2431C2×C3semidirect
69. #2427C2×C3semidirect
70. #2056C2×C3semidirect
71. #2042C2×C3semidirect
72. #2014C2×C3semidirect
73. #2012C2×C3semidirect
74. #2000C2×C3semidirect
75. #1999C2×C3semidirect
76. #1934C2×C3semidirect
77. #1923C2×C3semidirect
78. #1877C2×C3semidirect
109. C2×C3×SD16D4semidirect
161. C3×#102D4semidirect
367. C2×SD16C3×D4semidirect
419. #102C3×D4semidirect
857. C3#30446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4952
C2×C3×#4592
C2×C3×#4522
C2×C3×#4492
C3×#24312
C3×#24272
C3×#20562
C3×#20422
C3×#20142
C3×#20122
C3×#20002
C3×#19992
C3×#19342
C3×#19232
C3×#18772
#304463