Finite Group Databasebeta

← C3×#25797 #10644404

Subgroups — C3×#25797 #10644404

Order 768.

1570 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic, complemented
2C2×C3×#496C211yesmaximal, characteristic, complemented
3C2×C3×#495C211yesmaximal, characteristic, complemented
4C2×C3×#469C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×C3×#448C211yesmaximal, characteristic, complemented
7C3×#2436C211yesmaximal, characteristic, complemented
8C3×#2431C211yesmaximal, characteristic, complemented
9C3×#2015C211yesmaximal, characteristic, complemented
10C3×#2015C211yesmaximal, characteristic, complemented
11C3×#2014C211yesmaximal, characteristic, complemented
12C3×#2012C211yesmaximal, characteristic, complemented
13C3×#1971C211yesmaximal, characteristic, complemented
14C3×#1968C211yesmaximal, characteristic, complemented
15C3×#1753C211yesmaximal, characteristic, complemented
16#25797C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C23×C3×Q8C2211yescharacteristic
19C2×C3×#137—24no—
20C2×C3×#137—24no—
21C2×C3×#137—24no—
22C22×C3×Q16C2211yescharacteristic
23C22×C3×Q16C2211yescharacteristic
24C22×C3×SD16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×SD16C2211yescharacteristic
29C22×C3×D8C2211yescharacteristic
30C22×C3×D8C2211yescharacteristic
31C22×C3×M16C2211yescharacteristic
32C2×C3×#127C2211yescharacteristic
33C2×C3×#124C2211yescharacteristic
34C2×C3×#124C2211yescharacteristic
35C2×C3×#124C2211yescharacteristic
36C2×C3×#121C2211yescharacteristic
37C2×C3×#121C2211yescharacteristic
38C3×#496—24no—
39C3×#495—24no—
40C3×#469—24no—
41C3×#449—24no—
42C3×#448—24no—
43C2×C3×#106C2211yescharacteristic
44C2×C3×#103C2211yescharacteristic
45C2×C3×#103C2211yescharacteristic
46C2×C3×#103C2211yescharacteristic
47C2×C3×#102C2211yescharacteristic
48C2×C3×#102C2211yescharacteristic
49C2×C3×#102C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×#97C2211yescharacteristic
52C2×C3×C4×C8C2211yescharacteristic
53C3×#393—22no—
54C3×#392—22no—
55C3×#391C2211yescharacteristic
56C3×#391C2211yescharacteristic
57C3×#391C2211yescharacteristic
58C3×#390C2211yescharacteristic
59C3×#386—22no—
60C3×#386—22no—
61C3×C4×C22⋊C4C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C22×#137C2×C311yescharacteristic, complemented
65C2×#496C2×C311yescharacteristic, complemented
66C2×#495C2×C311yescharacteristic, complemented
67C2×#469C2×C311yescharacteristic, complemented
68C2×#449C2×C311yescharacteristic, complemented
69C2×#448C2×C311yescharacteristic, complemented
70#2436C2×C311yescharacteristic, complemented
71#2431C2×C311yescharacteristic, complemented
72#2015C2×C311yescharacteristic, complemented
73#2015C2×C311yescharacteristic, complemented
74#2014C2×C311yescharacteristic, complemented
75#2012C2×C311yescharacteristic, complemented
76#1971C2×C311yescharacteristic, complemented
77#1968C2×C311yescharacteristic, complemented
78#1753C2×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—21no—
86C22×C3×Q8—22no—
87C22×C3×Q8—22no—
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×D4—21no—
96C22×C3×D4—21no—
97C22×C3×D4—21no—
98C22×C3×D4—22no—
99C22×C3×D4C2311yescharacteristic
100C22×C3×D4C2311yescharacteristic
101C22×C3×D4C2311yescharacteristic
102C23×C3×C4—21no—
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C3×#137—232no—
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—22no—
109C2×C3×Q16—22no—
110C2×C3×Q16—22no—
111C2×C3×Q16D414yescomplemented
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—22no—
121C2×C3×SD16—22no—
122C2×C3×SD16—22no—
123C2×C3×SD16—41no—
124C2×C3×SD16—41no—
125C2×C3×SD16—41no—
126C2×C3×SD16D414yescomplemented
127C2×C3×D8—22no—
128C2×C3×D8—22no—
129C2×C3×D8—22no—
130C2×C3×D8—22no—
131C2×C3×D8—22no—
132C2×C3×D8—41no—
133C2×C3×M16—22no—
134C2×C3×M16—22no—
135C2×C3×M16D414yescomplemented
136C22×C3×C8C2311yescharacteristic
137C22×C3×C8C2311yescharacteristic
138C22×C3×C8C2311yescharacteristic
139C22×C3×C8C2311yescharacteristic
140C3×#127—22no—
141C3×#127—41no—
142C3×#124—22no—
143C3×#124—22no—
144C3×#124—22no—
145C3×#124—41no—
146C3×#124—41no—
147C3×#124—41no—
148C3×#121—22no—
149C3×#121—22no—
150C3×#121—22no—
151C3×#121—22no—
152C2×C3×C4⋊C4C2311yescharacteristic
153C2×C3×C4⋊C4C2311yescharacteristic
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—22no—
156C2×C3×C22⋊C4—22no—
157C2×C3×C22⋊C4—22no—
158C2×C3×C22⋊C4—21no—
159C2×C3×C22⋊C4—22no—
160C2×C3×C22⋊C4D412yes—
161C2×C3×C42C2311yescharacteristic
162C2×C3×C42C2311yescharacteristic
163C3×#106—22no—
164C3×#103—22no—
165C3×#103—22no—
166C3×#103—22no—
167C3×#102—22no—
168C3×#102—22no—
169C3×#102—22no—
170C3×C22⋊C8D414yescomplemented
171C3×#97—22no—
172C3×C4×C8—22no—
173C3×#95—22no—
174C3×#95—22no—
175C3×#95—22no—
176C3×#95D412yes—
177C22×#41C22×C311yescharacteristic
178C23×Q8C22×C311yescharacteristic
179C2×#137—24no—
180C2×#137—24no—
181C2×#137—24no—
182C22×Q16C22×C311yescharacteristic
183C22×Q16C22×C311yescharacteristic
184C22×SD16C22×C311yescharacteristic
185C22×SD16C22×C311yescharacteristic
186C22×SD16C22×C311yescharacteristic
187C22×SD16C22×C311yescharacteristic
188C22×SD16C22×C311yescharacteristic
189C22×D8C22×C311yescharacteristic
190C22×D8C22×C311yescharacteristic
191C22×M16C22×C311yescharacteristic
192C2×#127C22×C311yescharacteristic
193C2×#124C22×C311yescharacteristic
194C2×#124C22×C311yescharacteristic
195C2×#124C22×C311yescharacteristic
196C2×#121C22×C311yescharacteristic
197C2×#121C22×C311yescharacteristic
198#496—24no—
199#495—24no—
200#469—24no—
201#449—24no—
202#448—24no—
203C2×#106C22×C311yescharacteristic
204C2×#103C22×C311yescharacteristic
205C2×#103C22×C311yescharacteristic
206C2×#103C22×C311yescharacteristic
207C2×#102C22×C311yescharacteristic
208C2×#102C22×C311yescharacteristic
209C2×#102C22×C311yescharacteristic
210C2×C22⋊C8C22×C311yescharacteristic
211C2×#97C22×C311yescharacteristic
212C2×C4×C8C22×C311yescharacteristic
213#393—22no—
214#392—22no—
215#391C22×C311yescharacteristic
216#391C22×C311yescharacteristic
217#391C22×C311yescharacteristic
218#390C22×C311yescharacteristic
219#386—22no—
220#386—22no—
221C4×C22⋊C4C22×C311yescharacteristic
222#336C22×C311yescharacteristic
223#336C22×C311yescharacteristic
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3C2×D411yescharacteristic
228C3×#41—28no—
229C3×#41—44no—
230C3×#41—44no—
231C3×#41—44no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—28no—
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—42no—
249C2×C3×Q8—42no—
250C2×C3×Q8—44no—
251C2×C3×Q8—44no—
252C2×C3×Q8—44no—
253C2×C3×Q8—42no—
254C2×C3×Q8C2×D412yes—
255C2×C3×Q8C2×D412yes—
256C2×C3×Q8C2×D412yes—
257C2×C3×D4—21no—
258C2×C3×D4—21no—
259C2×C3×D4—21no—
260C2×C3×D4—21no—
261C2×C3×D4—21no—
262C2×C3×D4—21no—
263C2×C3×D4—21no—
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—42no—
275C2×C3×D4—44no—
276C2×C3×D4—44no—
277C2×C3×D4—42no—
278C2×C3×D4—42no—
279C2×C3×D4—44no—
280C2×C3×D4—42no—
281C2×C3×D4—42no—
282C2×C3×D4—82no—
283C2×C3×D4—82no—
284C2×C3×D4C2×D412yes—
285C22×C3×C4—21no—
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—21no—
293C22×C3×C4—21no—
294C22×C3×C4—42no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—42no—
299C22×C3×C4—42no—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2411yescharacteristic
306C3×Q16—28no—
307C3×Q16—28no—
308C3×SD16—28no—
309C3×SD16—28no—
310C3×SD16—44no—
311C3×SD16—44no—
312C3×SD16—44no—
313C3×D8—44no—
314C3×D8—44no—
315C3×M16—28no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8C2×D412yes—
323C2×C3×C8C2×D412yes—
324C2×C3×C8C2×D412yes—
325C2×C3×C8C2×D412yes—
326C2×C3×C8C2×D412yes—
327C2×C3×C8C2×D412yes—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C22⋊C4—42no—
333C3×C22⋊C4—44no—
334C3×C22⋊C4—44no—
335C3×C22⋊C4—44no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—82no—
339C3×C42—21no—
340C3×C42—21no—
341C3×C42—21no—
342C3×C42—21no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—41no—
348C2×#41—41no—
349C22×Q8—21no—
350C22×Q8—22no—
351C22×Q8—22no—
352C22×Q8—22no—
353C22×Q8—22no—
354C22×Q8—41no—
355C22×Q8—41no—
356C22×Q8C23×C311yescharacteristic
357C22×Q8C23×C311yescharacteristic
358C22×Q8C23×C311yescharacteristic
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—22no—
363C22×D4C23×C311yescharacteristic
364C22×D4C23×C311yescharacteristic
365C22×D4C23×C311yescharacteristic
366C23×C4—21no—
367C23×C4—21no—
368C23×C4C23×C311yescharacteristic
369#137—232no—
370C2×Q16—22no—
371C2×Q16—22no—
372C2×Q16—22no—
373C2×Q16—22no—
374C2×Q16—22no—
375C2×Q16C3×D414yescomplemented
376C2×SD16—22no—
377C2×SD16—22no—
378C2×SD16—22no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—22no—
382C2×SD16—22no—
383C2×SD16—22no—
384C2×SD16—22no—
385C2×SD16—22no—
386C2×SD16—22no—
387C2×SD16—41no—
388C2×SD16—41no—
389C2×SD16—41no—
390C2×SD16C3×D414yescomplemented
391C2×D8—22no—
392C2×D8—22no—
393C2×D8—22no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—41no—
397C2×M16—22no—
398C2×M16—22no—
399C2×M16C3×D414yescomplemented
400C22×C8C23×C311yescharacteristic
401C22×C8C23×C311yescharacteristic
402C22×C8C23×C311yescharacteristic
403C22×C8C23×C311yescharacteristic
404#127—22no—
405#127—41no—
406#124—22no—
407#124—22no—
408#124—22no—
409#124—41no—
410#124—41no—
411#124—41no—
412#121—22no—
413#121—22no—
414#121—22no—
415#121—22no—
416C2×C4⋊C4C23×C311yescharacteristic
417C2×C4⋊C4C23×C311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4C3×D412yes—
425C2×C42C23×C311yescharacteristic
426C2×C42C23×C311yescharacteristic
427#106—22no—
428#103—22no—
429#103—22no—
430#103—22no—
431#102—22no—
432#102—22no—
433#102—22no—
434C22⋊C8C3×D414yescomplemented
435#97—22no—
436C4×C8—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95C3×D412yes—
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—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—42no—
457C23×C3—42no—
458C23×C3—42no—
459C23×C3—42no—
460C23×C3#12712yes—
461C23×C3C22×D411yescharacteristic
462C3×Q8—22no—
463C3×Q8—22no—
464C3×Q8—22no—
465C3×Q8—22no—
466C3×Q8—22no—
467C3×Q8—22no—
468C3×Q8—48no—
469C3×Q8—41no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—41no—
473C3×Q8—41no—
474C3×Q8—41no—
475C3×D4—22no—
476C3×D4—22no—
477C3×D4—48no—
478C3×D4—41no—
479C3×D4—41no—
480C3×D4—41no—
481C3×D4—41no—
482C3×D4—41no—
483C3×D4—41no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—88no—
489C3×D4—84no—
490C3×D4—84no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—22no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—48no—
507C2×C3×C4—48no—
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—42no—
517C2×C3×C4—42no—
518C2×C3×C4#12712yes—
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524C2×C3×C4H(5,𝔽2)11yescharacteristic
525C3×C8—22no—
526C3×C8—22no—
527C3×C8—22no—
528C3×C8#12014yes—
529C24—21no—
530C24—21no—
531C24—21no—
532C24C2×C3×D411yescharacteristic
533#41—28no—
534#41—44no—
535#41—44no—
536#41—44no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—28no—
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—42no—
554C2×Q8—42no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—42no—
559C2×Q8C2×C3×D412yes—
560C2×Q8C2×C3×D412yes—
561C2×Q8C2×C3×D412yes—
562C2×D4—21no—
563C2×D4—21no—
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—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—44no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—44no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—82no—
588C2×D4—82no—
589C2×D4C2×C3×D412yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4C2×C3×D412yes—
606C22×C4C2×C3×D412yes—
607C22×C4C2×C3×D411yescharacteristic
608C22×C4C2×C3×D412yes—
609C22×C4C2×C3×D412yes—
610C22×C4C24×C311yescharacteristic
611Q16—28no—
612Q16—28no—
613SD16—28no—
614SD16—28no—
615SD16—44no—
616SD16—44no—
617SD16—44no—
618D8—44no—
619D8—44no—
620M16—28no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×C3×D412yes—
628C2×C8C2×C3×D412yes—
629C2×C8C2×C3×D412yes—
630C2×C8C2×C3×D412yes—
631C2×C8C2×C3×D412yes—
632C2×C8C2×C3×D412yes—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C22⋊C4—42no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—44no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—82no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—21no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—44no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3—82no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—81no—
661C22×C3—81no—
662C22×C3—81no—
663C22×C3—81no—
664C22×C3—82no—
665C22×C3—82no—
666C22×C3—82no—
667C22×C3—82no—
668C22×C3C2×#12711yescharacteristic
669C22×C3D4211yescharacteristic
670C22×C3D4211yescharacteristic
671C22×C3#57512yes—
672C22×C3#57712yes—
673C3×C4—22no—
674C3×C4—42no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—81no—
680C3×C4—81no—
681C3×C4C2×#12011yescharacteristic
682C3×C4#53511yescharacteristic
683C3×C4D4211yescharacteristic
684C3×C4D4211yescharacteristic
685C23—22no—
686C23—22no—
687C23—21no—
688C23—21no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23C3×#12712yes—
705C23C22×C3×D411yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—22no—
712Q8—48no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719D4—22no—
720D4—22no—
721D4—48no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—88no—
733D4—84no—
734D4—84no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—48no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4C3×#12712yes—
763C2×C4C22×C3×D411yescharacteristic
764C2×C4C22×C3×D411yescharacteristic
765C2×C4C22×C3×D411yescharacteristic
766C2×C4C22×C3×D411yescharacteristic
767C2×C4C3×H(5,𝔽2)11yescharacteristic
768C2×C4C3×H(5,𝔽2)11yescharacteristic
769C8—22no—
770C8—22no—
771C8—22no—
772C8C3×#12014yes—
773C2×C3—42no—
774C2×C3—82no—
775C2×C3—161no—
776C2×C3—161no—
777C2×C3#243311yescharacteristic
778C2×C3#315311yescharacteristic
779C2×C3#315411yescharacteristic
780C2×C3#327112yes—
781C2×C3#327512yes—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—81no—
790C22—81no—
791C22—82no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—82no—
799C22—82no—
800C22—82no—
801C22—82no—
802C22C2×C3×#12711yescharacteristic
803C22C3×D4211yescharacteristic
804C22C3×D4211yescharacteristic
805C22C3×#57512yes—
806C22C3×#57712yes—
807C4—22no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—81no—
814C4—81no—
815C4C2×C3×#12011yescharacteristic
816C4C3×#53511yescharacteristic
817C4C3×D4211yescharacteristic
818C4C3×D4211yescharacteristic
819C3#2579711yescharacteristic, direct product factor, Sylow
820C2—42no—
821C2—82no—
822C2—161no—
823C2—161no—
824C2C3×#243311yescharacteristic
825C2C3×#315311yescharacteristic
826C2C3×#315411yescharacteristic
827C2C3×#327112yes—
828C2C3×#327512yes—
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. C22×C3×#137C2semidirect
2. C2×C3×#496C2semidirect
3. C2×C3×#495C2semidirect
4. C2×C3×#469C2semidirect
5. C2×C3×#449C2semidirect
6. C2×C3×#448C2semidirect
7. C3×#2436C2semidirect
8. C3×#2431C2semidirect
9. C3×#2015C2semidirect
10. C3×#2015C2semidirect
11. C3×#2014C2semidirect
12. C3×#2012C2semidirect
13. C3×#1971C2semidirect
14. C3×#1968C2semidirect
15. C3×#1753C2semidirect
16. #25797C3direct (N × H)
64. C22×#137C2×C3semidirect
65. C2×#496C2×C3semidirect
66. C2×#495C2×C3semidirect
67. C2×#469C2×C3semidirect
68. C2×#449C2×C3semidirect
69. C2×#448C2×C3semidirect
70. #2436C2×C3semidirect
71. #2431C2×C3semidirect
72. #2015C2×C3semidirect
73. #2015C2×C3semidirect
74. #2014C2×C3semidirect
75. #2012C2×C3semidirect
76. #1971C2×C3semidirect
77. #1968C2×C3semidirect
78. #1753C2×C3semidirect
111. C2×C3×Q16D4semidirect
126. C2×C3×SD16D4semidirect
135. C2×C3×M16D4semidirect
170. C3×C22⋊C8D4semidirect
375. C2×Q16C3×D4semidirect
390. C2×SD16C3×D4semidirect
399. C2×M16C3×D4semidirect
434. C22⋊C8C3×D4semidirect
819. C3#25797direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1372
C2×C3×#4962
C2×C3×#4952
C2×C3×#4692
C2×C3×#4492
C2×C3×#4482
C3×#24362
C3×#24312
C3×#20152
C3×#20142
C3×#20122
C3×#19712
C3×#19682
C3×#17532
#257973