Finite Group Databasebeta

← C3×#25737 #10644344

Subgroups — C3×#25737 #10644344

Order 768.

1508 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#536C211yesmaximal, characteristic, complemented
2C2×C3×#497C211yesmaximal, characteristic, complemented
3C2×C3×#495C211yesmaximal, characteristic, complemented
4C2×C3×#452C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic
6C2×C3×#451C211yesmaximal, characteristic, complemented
7C2×C3×#448C211yesmaximal, characteristic, complemented
8C3×#2620C211yesmaximal, characteristic, complemented
9C3×#2016C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#2013C211yesmaximal, characteristic, complemented
12C3×#2012C211yesmaximal, characteristic, complemented
13C3×#1959C211yesmaximal, characteristic, complemented
14C3×#1956C211yesmaximal, characteristic, complemented
15C3×#1750C211yesmaximal, characteristic, complemented
16#25737C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×Q16C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×SD16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×D8C2211yescharacteristic
27C3×#536—24no—
28C3×#536—24no—
29C2×C3×C4⋊Q8C2211yescharacteristic
30C2×C3×C4⋊Q8C2211yescharacteristic
31C2×C3×#124C2211yescharacteristic
32C2×C3×#124C2211yescharacteristic
33C2×C3×#124C2211yescharacteristic
34C2×C3×#123—22no—
35C2×C3×C22⋊Q8—22no—
36C2×C3×C22⋊Q8C2211yescharacteristic
37C2×C3×#121C2211yescharacteristic
38C2×C3×#117C2211yescharacteristic
39C3×#497—24no—
40C3×#495—24no—
41C3×#452—24no—
42C3×#451—24no—
43C3×#449—24no—
44C3×#448—24no—
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×C22⋊C8C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55C2×C3×#97C2211yescharacteristic
56C2×C3×C4×C8C2211yescharacteristic
57C3×#396—22no—
58C3×#394—22no—
59C3×#391C2211yescharacteristic
60C3×#390C2211yescharacteristic
61C3×#384C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#536C2×C311yescharacteristic, complemented
65C2×#497C2×C311yescharacteristic, complemented
66C2×#495C2×C311yescharacteristic, complemented
67C2×#452C2×C311yescharacteristic, complemented
68C2×#449C2×C311yescharacteristic
69C2×#451C2×C311yescharacteristic, complemented
70C2×#448C2×C311yescharacteristic, complemented
71#2620C2×C311yescharacteristic, complemented
72#2016C2×C311yescharacteristic, complemented
73#2015C2×C311yescharacteristic, complemented
74#2013C2×C311yescharacteristic, complemented
75#2012C2×C311yescharacteristic, complemented
76#1959C2×C311yescharacteristic, complemented
77#1956C2×C311yescharacteristic, complemented
78#1750C2×C311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8—22no—
86C22×C3×Q8—22no—
87C22×C3×Q8—21no—
88C22×C3×Q8—22no—
89C22×C3×Q8—22no—
90C22×C3×Q8—41no—
91C22×C3×Q8—41no—
92C22×C3×Q8C2311yescharacteristic
93C22×C3×Q8C2311yescharacteristic
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4C2311yescharacteristic
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—22no—
115C2×C3×SD16—22no—
116C2×C3×SD16—22no—
117C2×C3×SD16—22no—
118C2×C3×SD16—22no—
119C2×C3×SD16—22no—
120C2×C3×SD16—41no—
121C2×C3×SD16—41no—
122C2×C3×SD16—41no—
123C2×C3×SD16—41no—
124C2×C3×D8—22no—
125C2×C3×D8—22no—
126C2×C3×D8—41no—
127C22×C3×C8C2311yescharacteristic
128C22×C3×C8C2311yescharacteristic
129C22×C3×C8C2311yescharacteristic
130C22×C3×C8C2311yescharacteristic
131C3×C4⋊Q8—22no—
132C3×C4⋊Q8—22no—
133C3×C4⋊Q8—22no—
134C3×C4⋊Q8D414yescomplemented
135C3×#124—22no—
136C3×#124—22no—
137C3×#124—22no—
138C3×#124—22no—
139C3×#124—22no—
140C3×#124D414yescomplemented
141C3×#123—216no—
142C3×C22⋊Q8—216no—
143C3×C22⋊Q8—22no—
144C3×C22⋊Q8—22no—
145C3×#121—22no—
146C3×#121—22no—
147C3×#117—22no—
148C3×#117—22no—
149C2×C3×C4⋊C4—22no—
150C2×C3×C4⋊C4—22no—
151C2×C3×C4⋊C4—21no—
152C2×C3×C4⋊C4—22no—
153C2×C3×C4⋊C4D412yes—
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C4⋊C4C2311yescharacteristic
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—22no—
162C2×C3×C22⋊C4D412yes—
163C2×C3×C42C2311yescharacteristic
164C2×C3×C42C2311yescharacteristic
165C3×#103—22no—
166C3×#103—22no—
167C3×#103—22no—
168C3×#103—22no—
169C3×#103—22no—
170C3×#103—22no—
171C3×#102—22no—
172C3×#102—22no—
173C3×C22⋊C8D414yes—
174C3×C22⋊C8D414yes—
175C3×#97—22no—
176C3×C4×C8—22no—
177C3×#95—22no—
178C22×#41C22×C311yescharacteristic
179C23×Q8C22×C311yescharacteristic
180C22×Q16C22×C311yescharacteristic
181C22×Q16C22×C311yescharacteristic
182C22×Q16C22×C311yescharacteristic
183C22×SD16C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×D8C22×C311yescharacteristic
188#536—24no—
189#536—24no—
190C2×C4⋊Q8C22×C311yescharacteristic
191C2×C4⋊Q8C22×C311yescharacteristic
192C2×#124C22×C311yescharacteristic
193C2×#124C22×C311yescharacteristic
194C2×#124C22×C311yescharacteristic
195C2×#123—22no—
196C2×C22⋊Q8—22no—
197C2×C22⋊Q8C22×C311yescharacteristic
198C2×#121C22×C311yescharacteristic
199C2×#117C22×C311yescharacteristic
200#497—24no—
201#495—24no—
202#452—24no—
203#451—24no—
204#449—24no—
205#448—24no—
206C2×#103C22×C311yescharacteristic
207C2×#103C22×C311yescharacteristic
208C2×#103C22×C311yescharacteristic
209C2×#103C22×C311yescharacteristic
210C2×#103C22×C311yescharacteristic
211C2×#103C22×C311yescharacteristic
212C2×#102C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×C22⋊C8C22×C311yescharacteristic
215C2×C22⋊C8C22×C311yescharacteristic
216C2×#97C22×C311yescharacteristic
217C2×C4×C8C22×C311yescharacteristic
218#396—22no—
219#394—22no—
220#391C22×C311yescharacteristic
221#390C22×C311yescharacteristic
222#384C22×C311yescharacteristic
223#336C22×C311yescharacteristic
224#336C22×C311yescharacteristic
225C24×C3—21no—
226C24×C3—21no—
227C24×C3C2×D411yescharacteristic
228C3×#41—44no—
229C3×#41—44no—
230C3×#41—44no—
231C3×#41—44no—
232C2×C3×Q8—24no—
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×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—44no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C2×C3×Q8—44no—
258C2×C3×Q8—42no—
259C2×C3×Q8—42no—
260C2×C3×Q8C2×D412yes—
261C2×C3×Q8C2×D412yes—
262C2×C3×Q8C2×D412yes—
263C2×C3×D4—24no—
264C2×C3×D4—21no—
265C2×C3×D4—21no—
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—42no—
276C2×C3×D4—42no—
277C2×C3×D4—42no—
278C2×C3×D4—82no—
279C2×C3×D4C2×D412yes—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—24no—
285C22×C3×C4—24no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—42no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4—42no—
296C22×C3×C4C2×D412yes—
297C22×C3×C4C2×D412yes—
298C22×C3×C4C2×D411yescharacteristic
299C22×C3×C4C2×D412yes—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2411yescharacteristic
302C3×Q16—44no—
303C3×Q16—44no—
304C3×Q16—44no—
305C3×SD16—44no—
306C3×SD16—44no—
307C3×SD16—44no—
308C3×SD16—44no—
309C3×D8—44no—
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—
318C2×C3×C8C2×D412yes—
319C2×C3×C8C2×D412yes—
320C2×C3×C8C2×D412yes—
321C2×C3×C8C2×D412yes—
322C3×C4⋊C4—28no—
323C3×C4⋊C4—28no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—42no—
330C3×C4⋊C4—82no—
331C3×C22⋊C4—28no—
332C3×C22⋊C4—28no—
333C3×C22⋊C4—24no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—82no—
338C3×C42—21no—
339C3×C42—21no—
340C3×C42C2×D412yes—
341C3×C42C2×D412yes—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—41no—
347C2×#41—41no—
348C22×Q8—22no—
349C22×Q8—22no—
350C22×Q8—21no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—41no—
354C22×Q8—41no—
355C22×Q8C23×C311yescharacteristic
356C22×Q8C23×C311yescharacteristic
357C22×Q8C23×C311yescharacteristic
358C22×Q8C23×C311yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C22×D4C23×C311yescharacteristic
362C22×D4C23×C311yescharacteristic
363C23×C4—21no—
364C23×C4—21no—
365C23×C4C23×C311yescharacteristic
366C2×Q16—22no—
367C2×Q16—22no—
368C2×Q16—22no—
369C2×Q16—22no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—41no—
373C2×Q16—41no—
374C2×Q16—41no—
375C2×SD16—22no—
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—41no—
384C2×SD16—41no—
385C2×SD16—41no—
386C2×SD16—41no—
387C2×D8—22no—
388C2×D8—22no—
389C2×D8—41no—
390C22×C8C23×C311yescharacteristic
391C22×C8C23×C311yescharacteristic
392C22×C8C23×C311yescharacteristic
393C22×C8C23×C311yescharacteristic
394C4⋊Q8—22no—
395C4⋊Q8—22no—
396C4⋊Q8—22no—
397C4⋊Q8C3×D414yescomplemented
398#124—22no—
399#124—22no—
400#124—22no—
401#124—22no—
402#124—22no—
403#124C3×D414yescomplemented
404#123—216no—
405C22⋊Q8—216no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408#121—22no—
409#121—22no—
410#117—22no—
411#117—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4C3×D412yes—
417C2×C4⋊C4C23×C311yescharacteristic
418C2×C4⋊C4C23×C311yescharacteristic
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4C3×D412yes—
426C2×C42C23×C311yescharacteristic
427C2×C42C23×C311yescharacteristic
428#103—22no—
429#103—22no—
430#103—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#102—22no—
435#102—22no—
436C22⋊C8C3×D414yes—
437C22⋊C8C3×D414yes—
438#97—22no—
439C4×C8—22no—
440#95—22no—
441C23×C3—21no—
442C23×C3—21no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—42no—
454C23×C3—42no—
455C23×C3#12712yes—
456C23×C3C22×D411yescharacteristic
457C3×Q8—22no—
458C3×Q8—22no—
459C3×Q8—22no—
460C3×Q8—22no—
461C3×Q8—22no—
462C3×Q8—22no—
463C3×Q8—48no—
464C3×Q8—41no—
465C3×Q8—41no—
466C3×Q8—41no—
467C3×Q8—41no—
468C3×Q8—41no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×D4—22no—
475C3×D4—22no—
476C3×D4—48no—
477C3×D4—41no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—84no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—48no—
499C2×C3×C4—48no—
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—42no—
512C2×C3×C4—42no—
513C2×C3×C4#12014yes—
514C2×C3×C4#12712yes—
515C2×C3×C4C22×D411yescharacteristic
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4H(5,𝔽2)11yescharacteristic
520C2×C3×C4H(5,𝔽2)11yescharacteristic
521C3×C8—22no—
522C3×C8—22no—
523C3×C8—22no—
524C3×C8—22no—
525C24—21no—
526C24—21no—
527C24C2×C3×D411yescharacteristic
528#41—44no—
529#41—44no—
530#41—44no—
531#41—44no—
532C2×Q8—24no—
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×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8C2×C3×D412yes—
561C2×Q8C2×C3×D412yes—
562C2×Q8C2×C3×D412yes—
563C2×D4—24no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—82no—
579C2×D4C2×C3×D412yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4C2×C3×D412yes—
597C22×C4C2×C3×D412yes—
598C22×C4C2×C3×D411yescharacteristic
599C22×C4C2×C3×D412yes—
600C22×C4C2×C3×D412yes—
601C22×C4C24×C311yescharacteristic
602Q16—44no—
603Q16—44no—
604Q16—44no—
605SD16—44no—
606SD16—44no—
607SD16—44no—
608SD16—44no—
609D8—44no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×C3×D412yes—
619C2×C8C2×C3×D412yes—
620C2×C8C2×C3×D412yes—
621C2×C8C2×C3×D412yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—42no—
630C4⋊C4—82no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—24no—
634C22⋊C4—42no—
635C22⋊C4—44no—
636C22⋊C4—42no—
637C22⋊C4—82no—
638C42—21no—
639C42—21no—
640C42C2×C3×D412yes—
641C42C2×C3×D412yes—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—42no—
646C22×C3—42no—
647C22×C3—42no—
648C22×C3—44no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—82no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—82no—
656C22×C3—82no—
657C22×C3C2×#12011yescharacteristic
658C22×C3C2×#12711yescharacteristic
659C22×C3#53511yescharacteristic
660C22×C3#57712yes—
661C22×C3#57812yes—
662C3×C4—22no—
663C3×C4—24no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—42no—
667C3×C4—42no—
668C3×C4—81no—
669C3×C4—81no—
670C3×C4—81no—
671C3×C4D4211yescharacteristic
672C3×C4D4211yescharacteristic
673C3×C4D4211yescharacteristic
674C3×C4D4211yescharacteristic
675C23—22no—
676C23—22no—
677C23—21no—
678C23—21no—
679C23—22no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23C3×#12712yes—
690C23C22×C3×D411yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—22no—
695Q8—22no—
696Q8—22no—
697Q8—48no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—41no—
703Q8—41no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708D4—22no—
709D4—22no—
710D4—48no—
711D4—41no—
712D4—41no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—48no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4C3×#12014yes—
748C2×C4C3×#12712yes—
749C2×C4C22×C3×D411yescharacteristic
750C2×C4C22×C3×D411yescharacteristic
751C2×C4C22×C3×D411yescharacteristic
752C2×C4C22×C3×D411yescharacteristic
753C2×C4C3×H(5,𝔽2)11yescharacteristic
754C2×C4C3×H(5,𝔽2)11yescharacteristic
755C8—22no—
756C8—22no—
757C8—22no—
758C8—22no—
759C2×C3—42no—
760C2×C3—82no—
761C2×C3—161no—
762C2×C3#243311yescharacteristic
763C2×C3#301312yes—
764C2×C3#315411yescharacteristic
765C2×C3#315611yescharacteristic
766C2×C3#322512yes—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—44no—
774C22—81no—
775C22—81no—
776C22—82no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—82no—
781C22—82no—
782C22C2×C3×#12011yescharacteristic
783C22C2×C3×#12711yescharacteristic
784C22C3×#53511yescharacteristic
785C22C3×#57712yes—
786C22C3×#57812yes—
787C4—22no—
788C4—24no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C3×D4211yescharacteristic
797C4C3×D4211yescharacteristic
798C4C3×D4211yescharacteristic
799C4C3×D4211yescharacteristic
800C3#2573711yescharacteristic, direct product factor, Sylow
801C2—42no—
802C2—82no—
803C2—161no—
804C2C3×#243311yescharacteristic
805C2C3×#301312yes—
806C2C3×#315411yescharacteristic
807C2C3×#315611yescharacteristic
808C2C3×#322512yes—
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×#536C2semidirect
2. C2×C3×#497C2semidirect
3. C2×C3×#495C2semidirect
4. C2×C3×#452C2semidirect
6. C2×C3×#451C2semidirect
7. C2×C3×#448C2semidirect
8. C3×#2620C2semidirect
9. C3×#2016C2semidirect
10. C3×#2015C2semidirect
11. C3×#2013C2semidirect
12. C3×#2012C2semidirect
13. C3×#1959C2semidirect
14. C3×#1956C2semidirect
15. C3×#1750C2semidirect
16. #25737C3direct (N × H)
64. C2×#536C2×C3semidirect
65. C2×#497C2×C3semidirect
66. C2×#495C2×C3semidirect
67. C2×#452C2×C3semidirect
69. C2×#451C2×C3semidirect
70. C2×#448C2×C3semidirect
71. #2620C2×C3semidirect
72. #2016C2×C3semidirect
73. #2015C2×C3semidirect
74. #2013C2×C3semidirect
75. #2012C2×C3semidirect
76. #1959C2×C3semidirect
77. #1956C2×C3semidirect
78. #1750C2×C3semidirect
134. C3×C4⋊Q8D4semidirect
140. C3×#124D4semidirect
397. C4⋊Q8C3×D4semidirect
403. #124C3×D4semidirect
800. C3#25737direct (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×#4972
C2×C3×#4952
C2×C3×#4522
C2×C3×#4492
C2×C3×#4512
C2×C3×#4482
C3×#26202
C3×#20162
C3×#20152
C3×#20132
C3×#20122
C3×#19592
C3×#19562
C3×#17502
#257373