Finite Group Databasebeta

← C3×#359507 #72271462

Subgroups — C3×#359507 #72271462

Order 1536.

9136 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#525C211yesmaximal, characteristic
2C3×#60064C211yesmaximal, characteristic, complemented
3C2×C3×#1891C214yesmaximal, complemented
4C3×#20591C211yesmaximal, characteristic, complemented
5C3×#20579C212yesmaximal, complemented
6C3×#10993C214yesmaximal, complemented
7C3×#10738C212yesmaximal, complemented
8#359507C311yesmaximal, characteristic, direct product factor, Sylow
9C23×C3×#41C2211yescharacteristic
10C25×C3×C4C2211yescharacteristic
11C2×C3×#568C2212yescomplemented
12C2×C3×#525—216no—
13C2×C3×#525—21no—
14C2×C3×#525—21no—
15C2×C3×#525—22no—
16C2×C3×#525C414yes—
17C2×C3×#525C2212yes—
18C2×C3×#525C2212yes—
19C22×C3×#123C412yes—
20C22×C3×C22⋊Q8—21no—
21C22×C3×#121—21no—
22C22×C3×#120C412yes—
23C22×C3×C4×D4—22no—
24C22×C3×#117C2211yescharacteristic
25C2×C3×#413C2212yescomplemented
26C2×C3×#413C2212yescomplemented
27C3×#2880—28no—
28C3×#2879—22no—
29C3×#2879C2212yescomplemented
30C2×C3×#407—22no—
31C2×C3×#407C2212yes—
32C2×C3×#407C2212yes—
33C2×C3×#407C2218yescomplemented
34C3×#1891—216no—
35C3×#1785—21no—
36C3×#1785—21no—
37C3×#1784—21no—
38C3×#1783—21no—
39C3×#1779—28no—
40C2×C3×#344C2218yescomplemented
41C22×#525C2×C311yescharacteristic
42#60064C2×C311yescharacteristic, complemented
43C2×#1891C2×C314yescomplemented
44#20591C2×C311yescharacteristic, complemented
45#20579C2×C312yescomplemented
46#10993C2×C314yescomplemented
47#10738C2×C312yescomplemented
48C26×C3C2×C411yescharacteristic
49C22×C3×#41—28no—
50C22×C3×#41—24no—
51C22×C3×#41—24no—
52C22×C3×#41—44no—
53C22×C3×#41C2×C412yes—
54C22×C3×#41D411yescharacteristic
55C22×C3×#41D411yescharacteristic
56C22×C3×#41D412yes—
57C22×C3×#41C2311yescharacteristic
58C22×C3×#41C2311yescharacteristic
59C23×C3×Q8D411yescharacteristic
60C23×C3×D4—22no—
61C23×C3×D4C2×C412yes—
62C23×C3×D4D411yescharacteristic
63C24×C3×C4—21no—
64C24×C3×C4—21no—
65C24×C3×C4—28no—
66C24×C3×C4—21no—
67C24×C3×C4—21no—
68C24×C3×C4—24no—
69C24×C3×C4—24no—
70C24×C3×C4—44no—
71C24×C3×C4C2×C411yescharacteristic
72C24×C3×C4C2×C412yes—
73C24×C3×C4D412yes—
74C24×C3×C4C2312yes—
75C24×C3×C4C2311yescharacteristic
76C3×#568—28no—
77C3×#568—44no—
78C2×C3×#131—28no—
79C22×C3×M16—24no—
80C22×C3×M16C2314yes—
81C22×C3×M16C2314yes—
82C3×#525—216no—
83C3×#525—216no—
84C3×#525—232no—
85C3×#525—28no—
86C3×#525—28no—
87C3×#525—216no—
88C3×#525—216no—
89C3×#525—28no—
90C3×#525D4116yes—
91C2×C3×#123—22no—
92C2×C3×#123—22no—
93C2×C3×#123—216no—
94C2×C3×#123C2×C414yes—
95C2×C3×#123C2×C414yes—
96C2×C3×C22⋊Q8—216no—
97C2×C3×C22⋊Q8—24no—
98C2×C3×C22⋊Q8—22no—
99C2×C3×C22⋊Q8—22no—
100C2×C3×#121—216no—
101C2×C3×#121—24no—
102C2×C3×#121—22no—
103C2×C3×#121—22no—
104C2×C3×#120—22no—
105C2×C3×#120—22no—
106C2×C3×#120—216no—
107C2×C3×#120C2×C414yes—
108C2×C3×#120C2×C414yes—
109C2×C3×C4×D4—232no—
110C2×C3×C4×D4—24no—
111C2×C3×C4×D4—24no—
112C2×C3×C4×D4—24no—
113C2×C3×C4×D4—24no—
114C2×C3×#117—21no—
115C2×C3×#117—21no—
116C2×C3×#117—28no—
117C2×C3×#117C2×C412yes—
118C2×C3×#117C2312yes—
119C22×C3×C4⋊C4—22no—
120C22×C3×C4⋊C4—21no—
121C22×C3×C22⋊C4—22no—
122C22×C3×C22⋊C4—22no—
123C22×C3×C22⋊C4C2×C412yes—
124C22×C3×C42—21no—
125C3×#413—28no—
126C3×#413—44no—
127C2×C3×#101—22no—
128C2×C3×#101—22no—
129C2×C3×#100—22no—
130C2×C3×#100—22no—
131C3×#408—216no—
132C3×#408—28no—
133C3×#407—28no—
134C3×#407—22no—
135C3×#407—24no—
136C3×#407—22no—
137C3×#407—24no—
138C3×#407—22no—
139C3×#407—22no—
140C3×#407—216no—
141C3×#407—24no—
142C3×#407—48no—
143C2×C3×C22⋊C8—28no—
144C2×C3×C22⋊C8—24no—
145C2×C3×C22⋊C8—216no—
146C2×C3×C22⋊C8D418yescomplemented
147C3×#344—216no—
148C23×#41C22×C311yescharacteristic
149C25×C4C22×C311yescharacteristic
150C2×#568C22×C312yescomplemented
151C2×#525—21no—
152C2×#525—21no—
153C2×#525—22no—
154C2×#525—216no—
155C2×#525C3×C414yes—
156C2×#525C22×C312yes—
157C2×#525C22×C312yes—
158C22×#123C3×C412yes—
159C22×C22⋊Q8—21no—
160C22×#121—21no—
161C22×#120C3×C412yes—
162C22×C4×D4—22no—
163C22×#117C22×C311yescharacteristic
164C2×#413C22×C312yescomplemented
165C2×#413C22×C312yescomplemented
166#2880—28no—
167#2879—22no—
168#2879C22×C312yescomplemented
169C2×#407—22no—
170C2×#407C22×C312yes—
171C2×#407C22×C312yes—
172C2×#407C22×C318yescomplemented
173#1891—216no—
174#1785—21no—
175#1785—21no—
176#1784—21no—
177#1783—21no—
178#1779—28no—
179C2×#344C22×C318yescomplemented
180C25×C3—21no—
181C25×C3—24no—
182C25×C3—21no—
183C25×C3—24no—
184C25×C3—42no—
185C25×C3—48no—
186C25×C3C22⋊C412yes—
187C25×C3C22×C412yes—
188C25×C3C22×C411yescharacteristic
189C2×C3×#41—24no—
190C2×C3×#41—28no—
191C2×C3×#41—24no—
192C2×C3×#41—28no—
193C2×C3×#41—24no—
194C2×C3×#41—28no—
195C2×C3×#41—24no—
196C2×C3×#41—24no—
197C2×C3×#41—24no—
198C2×C3×#41—22no—
199C2×C3×#41—22no—
200C2×C3×#41—24no—
201C2×C3×#41—22no—
202C2×C3×#41—22no—
203C2×C3×#41—24no—
204C2×C3×#41—24no—
205C2×C3×#41—44no—
206C2×C3×#41—44no—
207C2×C3×#41—42no—
208C2×C3×#41—42no—
209C2×C3×#41—432no—
210C2×C3×#41—432no—
211C2×C3×#41C2×D418yes—
212C22×C3×Q8—24no—
213C22×C3×Q8—24no—
214C22×C3×Q8—42no—
215C22×C3×Q8C22⋊C412yes—
216C22×C3×Q8C2×D411yescharacteristic
217C22×C3×Q8C2×D411yescharacteristic
218C22×C3×D4—216no—
219C22×C3×D4—24no—
220C22×C3×D4—24no—
221C22×C3×D4—28no—
222C22×C3×D4—28no—
223C22×C3×D4—24no—
224C22×C3×D4—24no—
225C22×C3×D4—42no—
226C22×C3×D4—44no—
227C22×C3×D4—416no—
228C22×C3×D4C22⋊C412yes—
229C22×C3×D4C22⋊C412yes—
230C22×C3×D4C22⋊C412yes—
231C22×C3×D4C22×C412yes—
232C22×C3×D4C22×C412yes—
233C22×C3×D4C2×D411yescharacteristic
234C22×C3×D4C2×D411yescharacteristic
235C23×C3×C4—24no—
236C23×C3×C4—24no—
237C23×C3×C4—28no—
238C23×C3×C4—28no—
239C23×C3×C4—28no—
240C23×C3×C4—28no—
241C23×C3×C4—21no—
242C23×C3×C4—21no—
243C23×C3×C4—24no—
244C23×C3×C4—22no—
245C23×C3×C4—22no—
246C23×C3×C4—22no—
247C23×C3×C4—24no—
248C23×C3×C4—24no—
249C23×C3×C4—24no—
250C23×C3×C4—28no—
251C23×C3×C4—24no—
252C23×C3×C4—24no—
253C23×C3×C4—22no—
254C23×C3×C4—22no—
255C23×C3×C4—24no—
256C23×C3×C4—24no—
257C23×C3×C4—28no—
258C23×C3×C4—24no—
259C23×C3×C4—28no—
260C23×C3×C4—44no—
261C23×C3×C4—44no—
262C23×C3×C4—42no—
263C23×C3×C4—432no—
264C23×C3×C4—432no—
265C23×C3×C4—44no—
266C23×C3×C4—44no—
267C23×C3×C4—44no—
268C23×C3×C4—44no—
269C23×C3×C4—42no—
270C23×C3×C4—42no—
271C23×C3×C4—44no—
272C23×C3×C4—44no—
273C23×C3×C4—42no—
274C23×C3×C4—42no—
275C23×C3×C4C22⋊C412yes—
276C23×C3×C4C22⋊C412yes—
277C23×C3×C4C22⋊C412yes—
278C23×C3×C4C22×C412yes—
279C23×C3×C4C22×C411yescharacteristic
280C23×C3×C4C2×D418yes—
281C23×C3×C4C2×D412yes—
282C23×C3×C4C2×D412yes—
283C23×C3×C4C2×D411yescharacteristic
284C23×C3×C4C2×D411yescharacteristic
285C23×C3×C4C2×D411yescharacteristic
286C23×C3×C4C2×D411yescharacteristic
287C23×C3×C4C2×D414yes—
288C23×C3×C4#4114yes—
289C23×C3×C4C2411yescharacteristic
290C3×#131—432no—
291C2×C3×M16—28no—
292C2×C3×M16—24no—
293C2×C3×M16—24no—
294C2×C3×M16—28no—
295C2×C3×M16—28no—
296C2×C3×M16—24no—
297C2×C3×M16—28no—
298C2×C3×M16—24no—
299C2×C3×M16—28no—
300C2×C3×M16—48no—
301C2×C3×M16—48no—
302C22×C3×C8—28no—
303C22×C3×C8—24no—
304C22×C3×C8C2×D418yescomplemented
305C3×#123—216no—
306C3×#123—216no—
307C3×#123—28no—
308C3×#123—28no—
309C3×#123—28no—
310C3×#123C22⋊C4116yes—
311C3×C22⋊Q8—216no—
312C3×C22⋊Q8—232no—
313C3×C22⋊Q8—216no—
314C3×#121—216no—
315C3×#121—232no—
316C3×#121—216no—
317C3×#120—216no—
318C3×#120—216no—
319C3×#120—28no—
320C3×#120—28no—
321C3×#120—28no—
322C3×#120C22⋊C4116yes—
323C3×C4×D4—232no—
324C3×C4×D4—232no—
325C3×C4×D4—232no—
326C3×C4×D4—232no—
327C3×#117—28no—
328C3×#117—28no—
329C3×#117—24no—
330C3×#117—28no—
331C3×#117C2×D418yes—
332C2×C3×C4⋊C4—28no—
333C2×C3×C4⋊C4—216no—
334C2×C3×C4⋊C4—22no—
335C2×C3×C4⋊C4—24no—
336C2×C3×C4⋊C4—24no—
337C2×C3×C4⋊C4—22no—
338C2×C3×C22⋊C4—216no—
339C2×C3×C22⋊C4—216no—
340C2×C3×C22⋊C4—24no—
341C2×C3×C22⋊C4—24no—
342C2×C3×C22⋊C4—22no—
343C2×C3×C22⋊C4—24no—
344C2×C3×C22⋊C4—24no—
345C2×C3×C22⋊C4—28no—
346C2×C3×C22⋊C4C22×C414yes—
347C2×C3×C42—28no—
348C2×C3×C42—22no—
349C2×C3×C42—22no—
350C3×#101—44no—
351C3×#101—44no—
352C3×#100—44no—
353C3×#100—44no—
354C3×C22⋊C8—216no—
355C3×C22⋊C8—28no—
356C3×C22⋊C8—28no—
357C3×C22⋊C8—432no—
358C3×C22⋊C8—44no—
359C3×C22⋊C8—44no—
360C26C2×C3×C411yescharacteristic
361C22×#41—28no—
362C22×#41—24no—
363C22×#41—24no—
364C22×#41—44no—
365C22×#41C2×C3×C412yes—
366C22×#41C3×D411yescharacteristic
367C22×#41C3×D411yescharacteristic
368C22×#41C3×D412yes—
369C22×#41C23×C311yescharacteristic
370C22×#41C23×C311yescharacteristic
371C23×Q8C3×D411yescharacteristic
372C23×D4—22no—
373C23×D4C2×C3×C412yes—
374C23×D4C3×D411yescharacteristic
375C24×C4—21no—
376C24×C4—21no—
377C24×C4—28no—
378C24×C4—21no—
379C24×C4—21no—
380C24×C4—24no—
381C24×C4—24no—
382C24×C4—44no—
383C24×C4C2×C3×C411yescharacteristic
384C24×C4C2×C3×C412yes—
385C24×C4C3×D412yes—
386C24×C4C23×C312yes—
387C24×C4C23×C311yescharacteristic
388#568—28no—
389#568—44no—
390C2×#131—28no—
391C22×M16—24no—
392C22×M16C23×C314yes—
393C22×M16C23×C314yes—
394#525—216no—
395#525—216no—
396#525—232no—
397#525—28no—
398#525—28no—
399#525—216no—
400#525—216no—
401#525—28no—
402#525C3×D4116yes—
403C2×#123—22no—
404C2×#123—22no—
405C2×#123—216no—
406C2×#123C2×C3×C414yes—
407C2×#123C2×C3×C414yes—
408C2×C22⋊Q8—216no—
409C2×C22⋊Q8—24no—
410C2×C22⋊Q8—22no—
411C2×C22⋊Q8—22no—
412C2×#121—216no—
413C2×#121—24no—
414C2×#121—22no—
415C2×#121—22no—
416C2×#120—22no—
417C2×#120—22no—
418C2×#120—216no—
419C2×#120C2×C3×C414yes—
420C2×#120C2×C3×C414yes—
421C2×C4×D4—232no—
422C2×C4×D4—24no—
423C2×C4×D4—24no—
424C2×C4×D4—24no—
425C2×C4×D4—24no—
426C2×#117—21no—
427C2×#117—21no—
428C2×#117—28no—
429C2×#117C2×C3×C412yes—
430C2×#117C23×C312yes—
431C22×C4⋊C4—22no—
432C22×C4⋊C4—21no—
433C22×C22⋊C4—22no—
434C22×C22⋊C4—22no—
435C22×C22⋊C4C2×C3×C412yes—
436C22×C42—21no—
437#413—28no—
438#413—44no—
439C2×#101—22no—
440C2×#101—22no—
441C2×#100—22no—
442C2×#100—22no—
443#408—216no—
444#408—28no—
445#407—28no—
446#407—22no—
447#407—24no—
448#407—22no—
449#407—24no—
450#407—22no—
451#407—22no—
452#407—216no—
453#407—24no—
454#407—48no—
455C2×C22⋊C8—28no—
456C2×C22⋊C8—24no—
457C2×C22⋊C8—216no—
458C2×C22⋊C8C3×D418yescomplemented
459#344—216no—
460C24×C3—24no—
461C24×C3—28no—
462C24×C3—22no—
463C24×C3—22no—
464C24×C3—24no—
465C24×C3—22no—
466C24×C3—24no—
467C24×C3—216no—
468C24×C3—22no—
469C24×C3—24no—
470C24×C3—24no—
471C24×C3—24no—
472C24×C3—44no—
473C24×C3—48no—
474C24×C3—42no—
475C24×C3—416no—
476C24×C3—44no—
477C24×C3—432no—
478C24×C3—48no—
479C24×C3—416no—
480C24×C3—48no—
481C24×C3—42no—
482C24×C3—42no—
483C24×C3—48no—
484C24×C3—432no—
485C24×C3—42no—
486C24×C3—42no—
487C24×C3C2×C22⋊C411yescharacteristic
488C24×C3C2×C22⋊C414yes—
489C24×C3C2×C22⋊C412yes—
490C24×C3C2×C22⋊C412yes—
491C24×C3C2×C22⋊C411yescharacteristic
492C24×C3C4×D414yes—
493C24×C3C23×C411yescharacteristic
494C3×#41—216no—
495C3×#41—216no—
496C3×#41—416no—
497C3×#41—416no—
498C3×#41—432no—
499C3×#41—416no—
500C3×#41—416no—
501C3×#41—48no—
502C3×#41—48no—
503C2×C3×Q8—22no—
504C2×C3×Q8—22no—
505C2×C3×Q8—22no—
506C2×C3×Q8—22no—
507C2×C3×Q8—22no—
508C2×C3×Q8—24no—
509C2×C3×Q8—24no—
510C2×C3×Q8—42no—
511C2×C3×Q8—416no—
512C2×C3×Q8#12014yes—
513C2×C3×D4—24no—
514C2×C3×D4—24no—
515C2×C3×D4—216no—
516C2×C3×D4—24no—
517C2×C3×D4—24no—
518C2×C3×D4—24no—
519C2×C3×D4—216no—
520C2×C3×D4—24no—
521C2×C3×D4—24no—
522C2×C3×D4—24no—
523C2×C3×D4—24no—
524C2×C3×D4—22no—
525C2×C3×D4—22no—
526C2×C3×D4—22no—
527C2×C3×D4—22no—
528C2×C3×D4—22no—
529C2×C3×D4—24no—
530C2×C3×D4—24no—
531C2×C3×D4—416no—
532C2×C3×D4—42no—
533C2×C3×D4—42no—
534C2×C3×D4—42no—
535C2×C3×D4—432no—
536C2×C3×D4—416no—
537C2×C3×D4—416no—
538C2×C3×D4—464no—
539C2×C3×D4C2×C22⋊C418yes—
540C2×C3×D4#12014yes—
541C22×C3×C4—22no—
542C22×C3×C4—22no—
543C22×C3×C4—22no—
544C22×C3×C4—22no—
545C22×C3×C4—22no—
546C22×C3×C4—22no—
547C22×C3×C4—22no—
548C22×C3×C4—22no—
549C22×C3×C4—24no—
550C22×C3×C4—22no—
551C22×C3×C4—22no—
552C22×C3×C4—22no—
553C22×C3×C4—22no—
554C22×C3×C4—216no—
555C22×C3×C4—216no—
556C22×C3×C4—28no—
557C22×C3×C4—24no—
558C22×C3×C4—28no—
559C22×C3×C4—28no—
560C22×C3×C4—24no—
561C22×C3×C4—24no—
562C22×C3×C4—22no—
563C22×C3×C4—22no—
564C22×C3×C4—24no—
565C22×C3×C4—24no—
566C22×C3×C4—24no—
567C22×C3×C4—24no—
568C22×C3×C4—28no—
569C22×C3×C4—24no—
570C22×C3×C4—28no—
571C22×C3×C4—22no—
572C22×C3×C4—22no—
573C22×C3×C4—24no—
574C22×C3×C4—216no—
575C22×C3×C4—216no—
576C22×C3×C4—24no—
577C22×C3×C4—24no—
578C22×C3×C4—24no—
579C22×C3×C4—24no—
580C22×C3×C4—42no—
581C22×C3×C4—42no—
582C22×C3×C4—42no—
583C22×C3×C4—416no—
584C22×C3×C4—416no—
585C22×C3×C4—416no—
586C22×C3×C4—416no—
587C22×C3×C4—416no—
588C22×C3×C4—44no—
589C22×C3×C4—44no—
590C22×C3×C4—416no—
591C22×C3×C4—416no—
592C22×C3×C4—416no—
593C22×C3×C4—416no—
594C22×C3×C4—432no—
595C22×C3×C4—432no—
596C22×C3×C4—42no—
597C22×C3×C4—42no—
598C22×C3×C4—48no—
599C22×C3×C4—42no—
600C22×C3×C4—42no—
601C22×C3×C4—42no—
602C22×C3×C4—44no—
603C22×C3×C4—42no—
604C22×C3×C4—44no—
605C22×C3×C4—44no—
606C22×C3×C4—48no—
607C22×C3×C4—48no—
608C22×C3×C4—44no—
609C22×C3×C4—44no—
610C22×C3×C4C2×C22⋊C412yes—
611C22×C3×C4C2×C22⋊C414yes—
612C22×C3×C4C2×C22⋊C412yes—
613C22×C3×C4C2×C22⋊C411yescharacteristic
614C22×C3×C4C2×C22⋊C411yescharacteristic
615C22×C3×C4C4×D414yes—
616C22×C3×C4#12018yes—
617C22×C3×C4#12012yes—
618C22×C3×C4#12012yes—
619C22×C3×C4#12114yes—
620C22×C3×C4#12114yes—
621C22×C3×C4#12312yes—
622C22×C3×C4#12312yes—
623C22×C3×C4C22×D411yescharacteristic
624C22×C3×C4C22×D411yescharacteristic
625C22×C3×C4C22×D414yes—
626C22×C3×C4C22×D412yes—
627C22×C3×C4C2×#4112yes—
628C22×C3×C4H(5,𝔽2)14yes—
629C3×M16—416no—
630C3×M16—44no—
631C3×M16—44no—
632C3×M16—48no—
633C3×M16—44no—
634C3×M16—44no—
635C3×M16—48no—
636C2×C3×C8—28no—
637C2×C3×C8—216no—
638C2×C3×C8—416no—
639C2×C3×C8—44no—
640C2×C3×C8—48no—
641C3×C4⋊C4—28no—
642C3×C4⋊C4—216no—
643C3×C4⋊C4—28no—
644C3×C4⋊C4—216no—
645C3×C22⋊C4—28no—
646C3×C22⋊C4—216no—
647C3×C22⋊C4—216no—
648C3×C22⋊C4—24no—
649C3×C22⋊C4—216no—
650C3×C22⋊C4—216no—
651C3×C22⋊C4C2×C22⋊C418yes—
652C3×C42—28no—
653C3×C42—28no—
654C25—21no—
655C25—24no—
656C25—21no—
657C25—24no—
658C25—42no—
659C25—48no—
660C25C3×C22⋊C412yes—
661C25C22×C3×C412yes—
662C25C22×C3×C411yescharacteristic
663C2×#41—24no—
664C2×#41—28no—
665C2×#41—24no—
666C2×#41—28no—
667C2×#41—28no—
668C2×#41—24no—
669C2×#41—24no—
670C2×#41—24no—
671C2×#41—24no—
672C2×#41—22no—
673C2×#41—24no—
674C2×#41—22no—
675C2×#41—22no—
676C2×#41—22no—
677C2×#41—24no—
678C2×#41—24no—
679C2×#41—44no—
680C2×#41—44no—
681C2×#41—42no—
682C2×#41—42no—
683C2×#41—432no—
684C2×#41—432no—
685C2×#41C2×C3×D418yes—
686C22×Q8—24no—
687C22×Q8—24no—
688C22×Q8—42no—
689C22×Q8C3×C22⋊C412yes—
690C22×Q8C2×C3×D411yescharacteristic
691C22×Q8C2×C3×D411yescharacteristic
692C22×D4—216no—
693C22×D4—24no—
694C22×D4—24no—
695C22×D4—28no—
696C22×D4—28no—
697C22×D4—24no—
698C22×D4—24no—
699C22×D4—42no—
700C22×D4—44no—
701C22×D4—416no—
702C22×D4C3×C22⋊C412yes—
703C22×D4C3×C22⋊C412yes—
704C22×D4C3×C22⋊C412yes—
705C22×D4C22×C3×C412yes—
706C22×D4C22×C3×C412yes—
707C22×D4C2×C3×D411yescharacteristic
708C22×D4C2×C3×D411yescharacteristic
709C23×C4—24no—
710C23×C4—24no—
711C23×C4—28no—
712C23×C4—28no—
713C23×C4—28no—
714C23×C4—28no—
715C23×C4—22no—
716C23×C4—21no—
717C23×C4—21no—
718C23×C4—24no—
719C23×C4—22no—
720C23×C4—22no—
721C23×C4—24no—
722C23×C4—24no—
723C23×C4—28no—
724C23×C4—24no—
725C23×C4—24no—
726C23×C4—22no—
727C23×C4—22no—
728C23×C4—24no—
729C23×C4—24no—
730C23×C4—24no—
731C23×C4—28no—
732C23×C4—24no—
733C23×C4—28no—
734C23×C4—44no—
735C23×C4—44no—
736C23×C4—42no—
737C23×C4—432no—
738C23×C4—432no—
739C23×C4—44no—
740C23×C4—44no—
741C23×C4—44no—
742C23×C4—44no—
743C23×C4—42no—
744C23×C4—42no—
745C23×C4—44no—
746C23×C4—44no—
747C23×C4—42no—
748C23×C4—42no—
749C23×C4C3×C22⋊C412yes—
750C23×C4C3×C22⋊C412yes—
751C23×C4C3×C22⋊C412yes—
752C23×C4C22×C3×C412yes—
753C23×C4C22×C3×C411yescharacteristic
754C23×C4C2×C3×D412yes—
755C23×C4C2×C3×D418yes—
756C23×C4C2×C3×D412yes—
757C23×C4C2×C3×D411yescharacteristic
758C23×C4C2×C3×D411yescharacteristic
759C23×C4C2×C3×D411yescharacteristic
760C23×C4C2×C3×D411yescharacteristic
761C23×C4C2×C3×D414yes—
762C23×C4C3×#4114yes—
763C23×C4C24×C311yescharacteristic
764#131—432no—
765C2×M16—28no—
766C2×M16—24no—
767C2×M16—24no—
768C2×M16—28no—
769C2×M16—28no—
770C2×M16—28no—
771C2×M16—24no—
772C2×M16—24no—
773C2×M16—28no—
774C2×M16—48no—
775C2×M16—48no—
776C22×C8—28no—
777C22×C8—24no—
778C22×C8C2×C3×D418yescomplemented
779#123—216no—
780#123—216no—
781#123—28no—
782#123—28no—
783#123—28no—
784#123C3×C22⋊C4116yes—
785C22⋊Q8—216no—
786C22⋊Q8—232no—
787C22⋊Q8—216no—
788#121—216no—
789#121—232no—
790#121—216no—
791#120—216no—
792#120—216no—
793#120—28no—
794#120—28no—
795#120—28no—
796#120C3×C22⋊C4116yes—
797C4×D4—232no—
798C4×D4—232no—
799C4×D4—232no—
800C4×D4—232no—
801#117—28no—
802#117—28no—
803#117—24no—
804#117—28no—
805#117C2×C3×D418yes—
806C2×C4⋊C4—28no—
807C2×C4⋊C4—216no—
808C2×C4⋊C4—22no—
809C2×C4⋊C4—24no—
810C2×C4⋊C4—24no—
811C2×C4⋊C4—22no—
812C2×C22⋊C4—216no—
813C2×C22⋊C4—216no—
814C2×C22⋊C4—24no—
815C2×C22⋊C4—24no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—24no—
818C2×C22⋊C4—24no—
819C2×C22⋊C4—28no—
820C2×C22⋊C4C22×C3×C414yes—
821C2×C42—28no—
822C2×C42—22no—
823C2×C42—22no—
824#101—44no—
825#101—44no—
826#100—44no—
827#100—44no—
828C22⋊C8—216no—
829C22⋊C8—28no—
830C22⋊C8—28no—
831C22⋊C8—432no—
832C22⋊C8—44no—
833C22⋊C8—44no—
834C23×C3—21no—
835C23×C3—24no—
836C23×C3—21no—
837C23×C3—216no—
838C23×C3—28no—
839C23×C3—216no—
840C23×C3—21no—
841C23×C3—28no—
842C23×C3—28no—
843C23×C3—28no—
844C23×C3—24no—
845C23×C3—21no—
846C23×C3—22no—
847C23×C3—22no—
848C23×C3—22no—
849C23×C3—22no—
850C23×C3—22no—
851C23×C3—42no—
852C23×C3—48no—
853C23×C3—44no—
854C23×C3—42no—
855C23×C3—48no—
856C23×C3—48no—
857C23×C3—48no—
858C23×C3—48no—
859C23×C3—48no—
860C23×C3—48no—
861C23×C3—416no—
862C23×C3—44no—
863C23×C3—48no—
864C23×C3—48no—
865C23×C3—48no—
866C23×C3—416no—
867C23×C3—416no—
868C23×C3—464no—
869C23×C3—416no—
870C23×C3—44no—
871C23×C3—44no—
872C23×C3—416no—
873C23×C3—464no—
874C23×C3—416no—
875C23×C3—42no—
876C23×C3—44no—
877C23×C3—48no—
878C23×C3—42no—
879C23×C3—48no—
880C23×C3—84no—
881C23×C3—88no—
882C23×C3#37914yes—
883C23×C3#38612yes—
884C23×C3#38612yes—
885C23×C3C22×C22⋊C411yescharacteristic
886C23×C3C22×C22⋊C412yes—
887C23×C3C2×C4×D412yes—
888C23×C3#51812yes—
889C3×Q8—28no—
890C3×Q8—48no—
891C3×Q8—44no—
892C3×D4—216no—
893C3×D4—28no—
894C3×D4—48no—
895C3×D4—48no—
896C3×D4—48no—
897C3×D4—432no—
898C3×D4—432no—
899C3×D4—48no—
900C3×D4—44no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—22no—
904C2×C3×C4—28no—
905C2×C3×C4—21no—
906C2×C3×C4—21no—
907C2×C3×C4—22no—
908C2×C3×C4—28no—
909C2×C3×C4—24no—
910C2×C3×C4—24no—
911C2×C3×C4—24no—
912C2×C3×C4—24no—
913C2×C3×C4—28no—
914C2×C3×C4—28no—
915C2×C3×C4—28no—
916C2×C3×C4—22no—
917C2×C3×C4—28no—
918C2×C3×C4—28no—
919C2×C3×C4—24no—
920C2×C3×C4—22no—
921C2×C3×C4—22no—
922C2×C3×C4—48no—
923C2×C3×C4—48no—
924C2×C3×C4—48no—
925C2×C3×C4—416no—
926C2×C3×C4—416no—
927C2×C3×C4—48no—
928C2×C3×C4—48no—
929C2×C3×C4—416no—
930C2×C3×C4—48no—
931C2×C3×C4—42no—
932C2×C3×C4—44no—
933C2×C3×C4—42no—
934C2×C3×C4—48no—
935C2×C3×C4—44no—
936C2×C3×C4—48no—
937C2×C3×C4—44no—
938C2×C3×C4—416no—
939C2×C3×C4#37914yes—
940C2×C3×C4#38612yes—
941C2×C3×C4#38612yes—
942C2×C3×C4C2×#12012yes—
943C2×C3×C4C2×#12012yes—
944C2×C3×C4C2×#12011yescharacteristic
945C2×C3×C4C2×#12112yes—
946C2×C3×C4C2×#12311yescharacteristic
947C2×C3×C4#53412yes—
948C2×C3×C4#53412yes—
949C2×C3×C4D4218yes—
950C2×C3×C4#54618yes—
951C3×C8—48no—
952C3×C8—84no—
953C24—24no—
954C24—28no—
955C24—22no—
956C24—22no—
957C24—24no—
958C24—22no—
959C24—24no—
960C24—216no—
961C24—24no—
962C24—22no—
963C24—24no—
964C24—24no—
965C24—44no—
966C24—48no—
967C24—42no—
968C24—416no—
969C24—42no—
970C24—42no—
971C24—44no—
972C24—432no—
973C24—48no—
974C24—416no—
975C24—48no—
976C24—48no—
977C24—432no—
978C24—42no—
979C24—42no—
980C24C2×C3×C22⋊C411yescharacteristic
981C24C2×C3×C22⋊C412yes—
982C24C2×C3×C22⋊C414yes—
983C24C2×C3×C22⋊C412yes—
984C24C2×C3×C22⋊C411yescharacteristic
985C24C3×C4×D414yes—
986C24C23×C3×C411yescharacteristic
987#41—216no—
988#41—216no—
989#41—416no—
990#41—416no—
991#41—432no—
992#41—416no—
993#41—416no—
994#41—48no—
995#41—48no—
996C2×Q8—24no—
997C2×Q8—24no—
998C2×Q8—22no—
999C2×Q8—22no—
1000C2×Q8—22no—
1001C2×Q8—22no—
1002C2×Q8—22no—
1003C2×Q8—42no—
1004C2×Q8—416no—
1005C2×Q8C3×#12014yes—
1006C2×D4—24no—
1007C2×D4—24no—
1008C2×D4—216no—
1009C2×D4—216no—
1010C2×D4—24no—
1011C2×D4—24no—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—22no—
1020C2×D4—22no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—22no—
1024C2×D4—416no—
1025C2×D4—42no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4—432no—
1029C2×D4—416no—
1030C2×D4—416no—
1031C2×D4—464no—
1032C2×D4C2×C3×C22⋊C418yes—
1033C2×D4C3×#12014yes—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—22no—
1042C22×C4—24no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—216no—
1048C22×C4—216no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—28no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—24no—
1065C22×C4—22no—
1066C22×C4—28no—
1067C22×C4—24no—
1068C22×C4—28no—
1069C22×C4—22no—
1070C22×C4—24no—
1071C22×C4—216no—
1072C22×C4—216no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—416no—
1077C22×C4—416no—
1078C22×C4—416no—
1079C22×C4—416no—
1080C22×C4—416no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—416no—
1084C22×C4—416no—
1085C22×C4—416no—
1086C22×C4—416no—
1087C22×C4—432no—
1088C22×C4—432no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—48no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—48no—
1102C22×C4—48no—
1103C22×C4C2×C3×C22⋊C412yes—
1104C22×C4C2×C3×C22⋊C414yes—
1105C22×C4C2×C3×C22⋊C412yes—
1106C22×C4C2×C3×C22⋊C411yescharacteristic
1107C22×C4C2×C3×C22⋊C411yescharacteristic
1108C22×C4C3×C4×D414yes—
1109C22×C4C3×#12018yes—
1110C22×C4C3×#12012yes—
1111C22×C4C3×#12012yes—
1112C22×C4C3×#12114yes—
1113C22×C4C3×#12114yes—
1114C22×C4C3×#12312yes—
1115C22×C4C3×#12312yes—
1116C22×C4C22×C3×D411yescharacteristic
1117C22×C4C22×C3×D411yescharacteristic
1118C22×C4C22×C3×D414yes—
1119C22×C4C22×C3×D412yes—
1120C22×C4C2×C3×#4112yes—
1121C22×C4C3×H(5,𝔽2)14yes—
1122M16—416no—
1123M16—44no—
1124M16—44no—
1125M16—48no—
1126M16—44no—
1127M16—44no—
1128M16—48no—
1129C2×C8—28no—
1130C2×C8—216no—
1131C2×C8—416no—
1132C2×C8—44no—
1133C2×C8—48no—
1134C4⋊C4—28no—
1135C4⋊C4—216no—
1136C4⋊C4—216no—
1137C4⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—216no—
1140C22⋊C4—216no—
1141C22⋊C4—216no—
1142C22⋊C4—24no—
1143C22⋊C4—216no—
1144C22⋊C4C2×C3×C22⋊C418yes—
1145C42—28no—
1146C42—28no—
1147C22×C3—24no—
1148C22×C3—24no—
1149C22×C3—22no—
1150C22×C3—22no—
1151C22×C3—24no—
1152C22×C3—22no—
1153C22×C3—28no—
1154C22×C3—216no—
1155C22×C3—22no—
1156C22×C3—24no—
1157C22×C3—24no—
1158C22×C3—42no—
1159C22×C3—42no—
1160C22×C3—416no—
1161C22×C3—44no—
1162C22×C3—44no—
1163C22×C3—42no—
1164C22×C3—48no—
1165C22×C3—42no—
1166C22×C3—432no—
1167C22×C3—416no—
1168C22×C3—48no—
1169C22×C3—44no—
1170C22×C3—432no—
1171C22×C3—44no—
1172C22×C3—48no—
1173C22×C3—44no—
1174C22×C3—42no—
1175C22×C3—44no—
1176C22×C3—82no—
1177C22×C3—816no—
1178C22×C3—82no—
1179C22×C3#189114yescomplemented
1180C22×C3C2×#37911yescharacteristic
1181C22×C3C2×#38611yescharacteristic
1182C22×C3#230811yescharacteristic
1183C22×C3D4×C22⋊C414yes—
1184C3×C4—22no—
1185C3×C4—22no—
1186C3×C4—24no—
1187C3×C4—48no—
1188C3×C4—44no—
1189C3×C4—42no—
1190C3×C4#240312yes—
1191C3×C4#240512yes—
1192C3×C4#241014yes—
1193C23—24no—
1194C23—21no—
1195C23—21no—
1196C23—216no—
1197C23—28no—
1198C23—216no—
1199C23—28no—
1200C23—24no—
1201C23—21no—
1202C23—22no—
1203C23—21no—
1204C23—28no—
1205C23—28no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—42no—
1211C23—48no—
1212C23—44no—
1213C23—42no—
1214C23—48no—
1215C23—48no—
1216C23—48no—
1217C23—48no—
1218C23—48no—
1219C23—48no—
1220C23—416no—
1221C23—44no—
1222C23—48no—
1223C23—48no—
1224C23—48no—
1225C23—416no—
1226C23—416no—
1227C23—464no—
1228C23—416no—
1229C23—44no—
1230C23—44no—
1231C23—416no—
1232C23—464no—
1233C23—416no—
1234C23—48no—
1235C23—42no—
1236C23—42no—
1237C23—44no—
1238C23—48no—
1239C23—84no—
1240C23—88no—
1241C23C3×#37914yes—
1242C23C3×#38612yes—
1243C23C3×#38612yes—
1244C23C22×C3×C22⋊C411yescharacteristic
1245C23C22×C3×C22⋊C412yes—
1246C23C2×C3×C4×D412yes—
1247C23C3×#51812yes—
1248Q8—28no—
1249Q8—48no—
1250Q8—44no—
1251D4—216no—
1252D4—28no—
1253D4—48no—
1254D4—48no—
1255D4—48no—
1256D4—432no—
1257D4—432no—
1258D4—48no—
1259D4—44no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—28no—
1267C2×C4—28no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—28no—
1273C2×C4—28no—
1274C2×C4—28no—
1275C2×C4—28no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—28no—
1281C2×C4—48no—
1282C2×C4—48no—
1283C2×C4—48no—
1284C2×C4—416no—
1285C2×C4—416no—
1286C2×C4—48no—
1287C2×C4—48no—
1288C2×C4—416no—
1289C2×C4—48no—
1290C2×C4—42no—
1291C2×C4—42no—
1292C2×C4—44no—
1293C2×C4—48no—
1294C2×C4—44no—
1295C2×C4—48no—
1296C2×C4—44no—
1297C2×C4—416no—
1298C2×C4C3×#37914yes—
1299C2×C4C3×#38612yes—
1300C2×C4C3×#38612yes—
1301C2×C4C2×C3×#12011yescharacteristic
1302C2×C4C2×C3×#12012yes—
1303C2×C4C2×C3×#12012yes—
1304C2×C4C2×C3×#12112yes—
1305C2×C4C2×C3×#12311yescharacteristic
1306C2×C4C3×#53412yes—
1307C2×C4C3×#53412yes—
1308C2×C4C3×D4218yes—
1309C2×C4C3×#54618yes—
1310C8—48no—
1311C8—84no—
1312C2×C3—21no—
1313C2×C3—21no—
1314C2×C3—24no—
1315C2×C3—24no—
1316C2×C3—48no—
1317C2×C3—42no—
1318C2×C3—44no—
1319C2×C3—82no—
1320C2×C3#1386711yescharacteristic
1321C2×C3C2×#189112yes—
1322C22—24no—
1323C22—24no—
1324C22—22no—
1325C22—22no—
1326C22—24no—
1327C22—22no—
1328C22—28no—
1329C22—216no—
1330C22—22no—
1331C22—24no—
1332C22—24no—
1333C22—42no—
1334C22—42no—
1335C22—416no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—432no—
1340C22—48no—
1341C22—42no—
1342C22—416no—
1343C22—48no—
1344C22—44no—
1345C22—432no—
1346C22—44no—
1347C22—48no—
1348C22—44no—
1349C22—42no—
1350C22—44no—
1351C22—82no—
1352C22—816no—
1353C22—82no—
1354C22C3×#189114yescomplemented
1355C22C2×C3×#37911yescharacteristic
1356C22C2×C3×#38611yescharacteristic
1357C22C3×#230811yescharacteristic
1358C22C3×D4×C22⋊C414yes—
1359C4—22no—
1360C4—22no—
1361C4—24no—
1362C4—48no—
1363C4—44no—
1364C4—42no—
1365C4C3×#240312yes—
1366C4C3×#240512yes—
1367C4C3×#241014yes—
1368C3#35950711yescharacteristic, direct product factor, Sylow
1369C2—21no—
1370C2—24no—
1371C2—21no—
1372C2—24no—
1373C2—48no—
1374C2—42no—
1375C2—44no—
1376C2—82no—
1377C2C3×#1386711yescharacteristic
1378C2C2×C3×#189112yes—
subgroupG/H
centerC2×C3×C4C2×#120
commutatorC24C23×C3×C4
Frattini, cosocleC23×C4C24×C3
socleC22×C3C2×#386
prime radicalC22×C3×#525C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C3×C4 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#60064C2semidirect
3. C2×C3×#1891C2semidirect
4. C3×#20591C2semidirect
5. C3×#20579C2semidirect
6. C3×#10993C2semidirect
7. C3×#10738C2semidirect
8. #359507C3direct (N × H)
11. C2×C3×#568C22semidirect
25. C2×C3×#413C22semidirect
26. C2×C3×#413C22semidirect
29. C3×#2879C22semidirect
33. C2×C3×#407C22semidirect
40. C2×C3×#344C22semidirect
42. #60064C2×C3semidirect
43. C2×#1891C2×C3semidirect
44. #20591C2×C3semidirect
45. #20579C2×C3semidirect
46. #10993C2×C3semidirect
47. #10738C2×C3semidirect
146. C2×C3×C22⋊C8D4semidirect
150. C2×#568C22×C3semidirect
164. C2×#413C22×C3semidirect
165. C2×#413C22×C3semidirect
168. #2879C22×C3semidirect
172. C2×#407C22×C3semidirect
179. C2×#344C22×C3semidirect
304. C22×C3×C8C2×D4semidirect
458. C2×C22⋊C8C3×D4semidirect
778. C22×C8C2×C3×D4semidirect
1179. C22×C3#1891semidirect
1354. C22C3×#1891semidirect
1368. C3#359507direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#5252
C3×#600642
C2×C3×#18912
C3×#205912
C3×#205792
C3×#109932
C3×#107382
#3595073