Finite Group Databasebeta

← C3×#147573 #72248113

Subgroups — C3×#147573 #72248113

Order 1536.

3750 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#35512C211yesmaximal, characteristic
2C2×C3×#2120C212yesmaximal, complemented
3C2×C3×#1795C212yesmaximal, complemented
4C3×#12587C211yesmaximal, characteristic, complemented
5C3×#12583C211yesmaximal, characteristic, complemented
6#147573C311yesmaximal, characteristic, direct product factor, Sylow
7C22×C3×H(5,𝔽2)C2211yescharacteristic
8C2×C3×#525C411yescharacteristic, complemented
9C2×C3×#525C2211yescharacteristic
10C22×C3×#121C411yescharacteristic, complemented
11C2×C3×#421—22no—
12C2×C3×#418—22no—
13C2×C3×#413C2212yes—
14C2×C3×#410C2212yes—
15C3×#2408—22no—
16C3×#2408—22no—
17C3×#2407—22no—
18C3×#2407—22no—
19C3×#2405—22no—
20C3×#2403—22no—
21C3×#2311C411yescharacteristic, complemented
22C3×#2311C2211yescharacteristic
23C3×#2309C411yescharacteristic, complemented
24C3×#2120—24no—
25C3×#2120—24no—
26C2×C3×#352—22no—
27C2×C3×AΣL(1,𝔽16)—22no—
28C3×#1795—24no—
29C3×#1795—24no—
30C3×#1394—22no—
31C3×#1393—22no—
32#35512C2×C311yescharacteristic
33C2×#2120C2×C312yescomplemented
34C2×#1795C2×C312yescomplemented
35#12587C2×C311yescharacteristic, complemented
36#12583C2×C311yescharacteristic, complemented
37C2×C3×H(5,𝔽2)—22no—
38C2×C3×H(5,𝔽2)—22no—
39C2×C3×H(5,𝔽2)—22no—
40C2×C3×H(5,𝔽2)—22no—
41C2×C3×H(5,𝔽2)—44no—
42C2×C3×H(5,𝔽2)—42no—
43C2×C3×H(5,𝔽2)—42no—
44C22×C3×#41—21no—
45C22×C3×#41C2×C411yescharacteristic
46C22×C3×#41D412yes—
47C22×C3×#41C2311yescharacteristic
48C23×C3×D4—22no—
49C23×C3×D4—21no—
50C23×C3×D4—21no—
51C23×C3×D4C2×C411yescharacteristic
52C23×C3×D4D412yes—
53C24×C3×C4C2×C411yescharacteristic
54C22×C3×M16—22no—
55C3×#525—22no—
56C3×#525—22no—
57C3×#525—22no—
58C3×#525—22no—
59C3×#525—42no—
60C3×#525—42no—
61C2×C3×#123—21no—
62C2×C3×#123D412yes—
63C2×C3×C22⋊Q8—21no—
64C2×C3×C22⋊Q8—21no—
65C2×C3×#121—22no—
66C2×C3×#121—21no—
67C2×C3×#121—21no—
68C2×C3×#121—22no—
69C2×C3×#121—44no—
70C2×C3×#120—24no—
71C2×C3×#120—21no—
72C2×C3×#120D412yes—
73C2×C3×C4×D4—22no—
74C2×C3×C4×D4—22no—
75C2×C3×#117—22no—
76C2×C3×#117C2×C411yescharacteristic
77C2×C3×#117C2×C411yescharacteristic
78C22×C3×C4⋊C4C2×C411yescharacteristic
79C22×C3×C22⋊C4—21no—
80C3×#421—28no—
81C3×#421—44no—
82C2×C3×#104—44no—
83C3×#418—28no—
84C3×#418—44no—
85C2×C3×#102—44no—
86C3×#413—22no—
87C3×#413—22no—
88C3×#413—22no—
89C3×#413D414yescomplemented
90C2×C3×#101—22no—
91C2×C3×#100—22no—
92C3×#410—22no—
93C3×#410—22no—
94C3×#410—22no—
95C3×#410D414yescomplemented
96C2×C3×#99—22no—
97C2×C3×#99—22no—
98C3×#394—24no—
99C3×#394—24no—
100C3×#392—24no—
101C3×#392—24no—
102C3×#391—21no—
103C3×#391D412yes—
104C3×#390—22no—
105C3×#390—21no—
106C3×#390—22no—
107C3×#390D412yes—
108C3×#386—24no—
109C3×#386—22no—
110C3×#386—22no—
111C3×#385—24no—
112C3×#380—22no—
113C3×#380—22no—
114C3×#379—24no—
115C3×#379—22no—
116C3×#352—28no—
117C3×AΣL(1,𝔽16)—28no—
118C22×H(5,𝔽2)C22×C311yescharacteristic
119C2×#525C3×C411yescharacteristic, complemented
120C2×#525C22×C311yescharacteristic
121C22×#121C3×C411yescharacteristic, complemented
122C2×#421—22no—
123C2×#418—22no—
124C2×#413C22×C312yes—
125C2×#410C22×C312yes—
126#2408—22no—
127#2408—22no—
128#2407—22no—
129#2407—22no—
130#2405—22no—
131#2403—22no—
132#2311C3×C411yescharacteristic, complemented
133#2311C22×C311yescharacteristic
134#2309C3×C411yescharacteristic, complemented
135#2120—24no—
136#2120—24no—
137C2×#352—22no—
138C2×AΣL(1,𝔽16)—22no—
139#1795—24no—
140#1795—24no—
141#1394—22no—
142#1393—22no—
143C25×C3—21no—
144C25×C3—22no—
145C25×C3C22⋊C411yescharacteristic
146C3×H(5,𝔽2)—48no—
147C3×H(5,𝔽2)—48no—
148C3×H(5,𝔽2)—48no—
149C3×H(5,𝔽2)—48no—
150C3×H(5,𝔽2)—48no—
151C3×H(5,𝔽2)—48no—
152C3×H(5,𝔽2)—48no—
153C3×H(5,𝔽2)—48no—
154C2×C3×#41—22no—
155C2×C3×#41—22no—
156C2×C3×#41—24no—
157C2×C3×#41—24no—
158C2×C3×#41—22no—
159C2×C3×#41—22no—
160C2×C3×#41—22no—
161C2×C3×#41—22no—
162C2×C3×#41—22no—
163C2×C3×#41—22no—
164C2×C3×#41—42no—
165C2×C3×#41—41no—
166C2×C3×#41—41no—
167C2×C3×#41—42no—
168C2×C3×#41—42no—
169C2×C3×#41—42no—
170C2×C3×#41—44no—
171C2×C3×#41—44no—
172C2×C3×#41—42no—
173C2×C3×#41—41no—
174C2×C3×#41—41no—
175C2×C3×#41C2×D412yes—
176C2×C3×#41C2×D412yes—
177C2×C3×#41#4112yes—
178C2×C3×#41#4112yes—
179C22×C3×Q8C22⋊C411yescharacteristic
180C22×C3×Q8C2×D411yescharacteristic
181C22×C3×D4—24no—
182C22×C3×D4—24no—
183C22×C3×D4—21no—
184C22×C3×D4—24no—
185C22×C3×D4—22no—
186C22×C3×D4—24no—
187C22×C3×D4—22no—
188C22×C3×D4—22no—
189C22×C3×D4—21no—
190C22×C3×D4—22no—
191C22×C3×D4—22no—
192C22×C3×D4—22no—
193C22×C3×D4—22no—
194C22×C3×D4—22no—
195C22×C3×D4—22no—
196C22×C3×D4—22no—
197C22×C3×D4—41no—
198C22×C3×D4—41no—
199C22×C3×D4—42no—
200C22×C3×D4—42no—
201C22×C3×D4—44no—
202C22×C3×D4—48no—
203C22×C3×D4—44no—
204C22×C3×D4—48no—
205C22×C3×D4—42no—
206C22×C3×D4—42no—
207C22×C3×D4—42no—
208C22×C3×D4—42no—
209C22×C3×D4—42no—
210C22×C3×D4—41no—
211C22×C3×D4—41no—
212C22×C3×D4—44no—
213C22×C3×D4—84no—
214C22×C3×D4C22⋊C412yes—
215C22×C3×D4C22⋊C411yescharacteristic
216C22×C3×D4C2×D411yescharacteristic
217C22×C3×D4C2×D412yes—
218C23×C3×C4—21no—
219C23×C3×C4—21no—
220C23×C3×C4—21no—
221C23×C3×C4—21no—
222C23×C3×C4—22no—
223C23×C3×C4—22no—
224C23×C3×C4—22no—
225C23×C3×C4—42no—
226C23×C3×C4—41no—
227C23×C3×C4—41no—
228C23×C3×C4C22⋊C411yescharacteristic
229C23×C3×C4C22×C411yescharacteristic
230C23×C3×C4C2×D412yes—
231C2×C3×M16—24no—
232C2×C3×M16—42no—
233C2×C3×M16—42no—
234C2×C3×M16—42no—
235C2×C3×M16—42no—
236C2×C3×M16—42no—
237C22×C3×C8—42no—
238C3×#123—22no—
239C3×#123—22no—
240C3×#123—22no—
241C3×#123—22no—
242C3×#123—44no—
243C3×C22⋊Q8—42no—
244C3×C22⋊Q8—42no—
245C3×C22⋊Q8—42no—
246C3×C22⋊Q8—41no—
247C3×C22⋊Q8—41no—
248C3×#121—48no—
249C3×#121—44no—
250C3×#121—42no—
251C3×#121—44no—
252C3×#121—42no—
253C3×#121—42no—
254C3×#121—41no—
255C3×#121—41no—
256C3×#120—22no—
257C3×#120—22no—
258C3×#120—22no—
259C3×#120—22no—
260C3×#120—44no—
261C3×#120—88no—
262C3×C4×D4—48no—
263C3×C4×D4—42no—
264C3×C4×D4—42no—
265C3×C4×D4—42no—
266C3×C4×D4—42no—
267C3×#117—22no—
268C3×#117—22no—
269C3×#117—24no—
270C3×#117—41no—
271C3×#117—41no—
272C3×#117—42no—
273C3×#117—42no—
274C3×#117—42no—
275C2×C3×C4⋊C4—22no—
276C2×C3×C4⋊C4—21no—
277C2×C3×C4⋊C4—21no—
278C2×C3×C4⋊C4—21no—
279C2×C3×C4⋊C4—22no—
280C2×C3×C4⋊C4—42no—
281C2×C3×C4⋊C4—42no—
282C2×C3×C4⋊C4C22⋊C412yes—
283C2×C3×C22⋊C4—22no—
284C2×C3×C22⋊C4—24no—
285C2×C3×C22⋊C4—22no—
286C2×C3×C22⋊C4—21no—
287C2×C3×C22⋊C4—22no—
288C2×C3×C22⋊C4—22no—
289C2×C3×C22⋊C4—24no—
290C2×C3×C22⋊C4—24no—
291C2×C3×C22⋊C4—24no—
292C2×C3×C22⋊C4—24no—
293C2×C3×C22⋊C4—44no—
294C2×C3×C22⋊C4—42no—
295C2×C3×C22⋊C4C22⋊C412yes—
296C2×C3×C42—21no—
297C2×C3×C42—42no—
298C2×C3×C42C22⋊C412yes—
299C3×#104—416no—
300C3×#102—416no—
301C3×#101—24no—
302C3×#101—42no—
303C3×#100—24no—
304C3×#100—42no—
305C3×#99—24no—
306C3×#99—24no—
307C3×#99—42no—
308C3×#99—42no—
309C3×#95—24no—
310C3×#95—24no—
311C2×H(5,𝔽2)—22no—
312C2×H(5,𝔽2)—22no—
313C2×H(5,𝔽2)—22no—
314C2×H(5,𝔽2)—22no—
315C2×H(5,𝔽2)—44no—
316C2×H(5,𝔽2)—42no—
317C2×H(5,𝔽2)—42no—
318C22×#41—21no—
319C22×#41C2×C3×C411yescharacteristic
320C22×#41C3×D412yes—
321C22×#41C23×C311yescharacteristic
322C23×D4—21no—
323C23×D4—22no—
324C23×D4—21no—
325C23×D4C2×C3×C411yescharacteristic
326C23×D4C3×D412yes—
327C24×C4C2×C3×C411yescharacteristic
328C22×M16—22no—
329#525—22no—
330#525—22no—
331#525—22no—
332#525—22no—
333#525—42no—
334#525—42no—
335C2×#123—21no—
336C2×#123C3×D412yes—
337C2×C22⋊Q8—21no—
338C2×C22⋊Q8—21no—
339C2×#121—22no—
340C2×#121—21no—
341C2×#121—21no—
342C2×#121—22no—
343C2×#121—44no—
344C2×#120—21no—
345C2×#120—24no—
346C2×#120C3×D412yes—
347C2×C4×D4—22no—
348C2×C4×D4—22no—
349C2×#117—22no—
350C2×#117C2×C3×C411yescharacteristic
351C2×#117C2×C3×C411yescharacteristic
352C22×C4⋊C4C2×C3×C411yescharacteristic
353C22×C22⋊C4—21no—
354#421—28no—
355#421—44no—
356C2×#104—44no—
357#418—28no—
358#418—44no—
359C2×#102—44no—
360#413—22no—
361#413—22no—
362#413—22no—
363#413C3×D414yescomplemented
364C2×#101—22no—
365C2×#100—22no—
366#410—22no—
367#410—22no—
368#410—22no—
369#410C3×D414yescomplemented
370C2×#99—22no—
371C2×#99—22no—
372#394—24no—
373#394—24no—
374#392—24no—
375#392—24no—
376#391—21no—
377#391C3×D412yes—
378#390—22no—
379#390—21no—
380#390—22no—
381#390C3×D412yes—
382#386—24no—
383#386—22no—
384#386—22no—
385#385—24no—
386#380—22no—
387#380—22no—
388#379—24no—
389#379—22no—
390#352—28no—
391AΣL(1,𝔽16)—28no—
392C24×C3—24no—
393C24×C3—21no—
394C24×C3—22no—
395C24×C3—21no—
396C24×C3—22no—
397C24×C3—44no—
398C24×C3—44no—
399C24×C3—42no—
400C24×C3—41no—
401C24×C3—42no—
402C24×C3—41no—
403C24×C3—42no—
404C24×C3—42no—
405C24×C3—42no—
406C24×C3—81no—
407C24×C3—82no—
408C24×C3—82no—
409C24×C3—84no—
410C24×C3—84no—
411C24×C3C2×C22⋊C411yescharacteristic
412C24×C3#12012yes—
413C3×#41—28no—
414C3×#41—28no—
415C3×#41—42no—
416C3×#41—42no—
417C3×#41—42no—
418C3×#41—42no—
419C3×#41—42no—
420C3×#41—42no—
421C3×#41—42no—
422C3×#41—42no—
423C3×#41—44no—
424C3×#41—44no—
425C3×#41—44no—
426C3×#41—44no—
427C3×#41—44no—
428C3×#41—44no—
429C3×#41—44no—
430C3×#41—44no—
431C3×#41—44no—
432C3×#41—44no—
433C3×#41—416no—
434C3×#41—48no—
435C3×#41—48no—
436C2×C3×Q8—21no—
437C2×C3×Q8—22no—
438C2×C3×Q8—22no—
439C2×C3×Q8—41no—
440C2×C3×Q8—41no—
441C2×C3×Q8#9912yes—
442C2×C3×Q8#12112yes—
443C2×C3×Q8#12411yescharacteristic
444C2×C3×Q8#12711yescharacteristic
445C2×C3×D4—28no—
446C2×C3×D4—28no—
447C2×C3×D4—24no—
448C2×C3×D4—24no—
449C2×C3×D4—22no—
450C2×C3×D4—22no—
451C2×C3×D4—22no—
452C2×C3×D4—22no—
453C2×C3×D4—22no—
454C2×C3×D4—22no—
455C2×C3×D4—22no—
456C2×C3×D4—21no—
457C2×C3×D4—44no—
458C2×C3×D4—44no—
459C2×C3×D4—44no—
460C2×C3×D4—44no—
461C2×C3×D4—44no—
462C2×C3×D4—44no—
463C2×C3×D4—44no—
464C2×C3×D4—44no—
465C2×C3×D4—41no—
466C2×C3×D4—42no—
467C2×C3×D4—41no—
468C2×C3×D4—42no—
469C2×C3×D4—44no—
470C2×C3×D4—44no—
471C2×C3×D4—44no—
472C2×C3×D4—42no—
473C2×C3×D4—44no—
474C2×C3×D4—44no—
475C2×C3×D4—44no—
476C2×C3×D4—42no—
477C2×C3×D4—416no—
478C2×C3×D4—48no—
479C2×C3×D4—48no—
480C2×C3×D4—416no—
481C2×C3×D4—416no—
482C2×C3×D4—416no—
483C2×C3×D4—416no—
484C2×C3×D4—42no—
485C2×C3×D4—42no—
486C2×C3×D4—42no—
487C2×C3×D4—44no—
488C2×C3×D4—44no—
489C2×C3×D4—44no—
490C2×C3×D4—48no—
491C2×C3×D4—48no—
492C2×C3×D4—42no—
493C2×C3×D4—42no—
494C2×C3×D4—41no—
495C2×C3×D4—41no—
496C2×C3×D4—42no—
497C2×C3×D4—42no—
498C2×C3×D4—82no—
499C2×C3×D4—82no—
500C2×C3×D4—84no—
501C2×C3×D4—88no—
502C2×C3×D4—88no—
503C2×C3×D4#9912yes—
504C2×C3×D4#9914yes—
505C2×C3×D4#12012yes—
506C2×C3×D4#12112yes—
507C2×C3×D4#12112yes—
508C2×C3×D4#12112yes—
509C2×C3×D4#12312yes—
510C2×C3×D4#12411yescharacteristic
511C2×C3×D4#12711yescharacteristic
512C22×C3×C4—22no—
513C22×C3×C4—22no—
514C22×C3×C4—22no—
515C22×C3×C4—22no—
516C22×C3×C4—22no—
517C22×C3×C4—21no—
518C22×C3×C4—21no—
519C22×C3×C4—24no—
520C22×C3×C4—21no—
521C22×C3×C4—22no—
522C22×C3×C4—22no—
523C22×C3×C4—22no—
524C22×C3×C4—21no—
525C22×C3×C4—22no—
526C22×C3×C4—44no—
527C22×C3×C4—44no—
528C22×C3×C4—42no—
529C22×C3×C4—42no—
530C22×C3×C4—42no—
531C22×C3×C4—41no—
532C22×C3×C4—41no—
533C22×C3×C4—42no—
534C22×C3×C4—42no—
535C22×C3×C4—42no—
536C22×C3×C4—42no—
537C22×C3×C4—41no—
538C22×C3×C4—41no—
539C22×C3×C4—42no—
540C22×C3×C4—41no—
541C22×C3×C4—41no—
542C22×C3×C4—41no—
543C22×C3×C4—41no—
544C22×C3×C4—82no—
545C22×C3×C4—82no—
546C22×C3×C4—82no—
547C22×C3×C4—82no—
548C22×C3×C4—82no—
549C22×C3×C4—82no—
550C22×C3×C4C2×C22⋊C411yescharacteristic
551C22×C3×C4C2×C22⋊C411yescharacteristic
552C22×C3×C4C4×D412yes—
553C22×C3×C4C4×D412yes—
554C22×C3×C4#12012yes—
555C22×C3×C4#12012yes—
556C22×C3×C4#12112yes—
557C22×C3×C4#12112yes—
558C22×C3×C4#12312yes—
559C3×M16—44no—
560C3×M16—44no—
561C3×M16—82no—
562C3×M16—82no—
563C2×C3×C8—44no—
564C2×C3×C8—82no—
565C2×C3×C8—82no—
566C3×C4⋊C4—42no—
567C3×C4⋊C4—44no—
568C3×C4⋊C4—44no—
569C3×C4⋊C4—41no—
570C3×C4⋊C4—41no—
571C3×C4⋊C4—42no—
572C3×C4⋊C4—42no—
573C3×C4⋊C4—42no—
574C3×C4⋊C4—41no—
575C3×C4⋊C4—41no—
576C3×C4⋊C4—82no—
577C3×C22⋊C4—22no—
578C3×C22⋊C4—22no—
579C3×C22⋊C4—44no—
580C3×C22⋊C4—48no—
581C3×C22⋊C4—42no—
582C3×C22⋊C4—44no—
583C3×C22⋊C4—42no—
584C3×C22⋊C4—42no—
585C3×C22⋊C4—42no—
586C3×C22⋊C4—42no—
587C3×C22⋊C4—44no—
588C3×C22⋊C4—84no—
589C3×C22⋊C4—84no—
590C3×C22⋊C4—84no—
591C3×C22⋊C4—84no—
592C3×C22⋊C4—82no—
593C3×C42—42no—
594C3×C42—44no—
595C3×C42—42no—
596C3×C42—82no—
597C25—21no—
598C25—22no—
599C25C3×C22⋊C411yescharacteristic
600H(5,𝔽2)—48no—
601H(5,𝔽2)—48no—
602H(5,𝔽2)—48no—
603H(5,𝔽2)—48no—
604H(5,𝔽2)—48no—
605H(5,𝔽2)—48no—
606H(5,𝔽2)—48no—
607H(5,𝔽2)—48no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—24no—
611C2×#41—24no—
612C2×#41—22no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—22no—
618C2×#41—42no—
619C2×#41—41no—
620C2×#41—41no—
621C2×#41—42no—
622C2×#41—42no—
623C2×#41—42no—
624C2×#41—44no—
625C2×#41—44no—
626C2×#41—42no—
627C2×#41—41no—
628C2×#41—41no—
629C2×#41C2×C3×D412yes—
630C2×#41C2×C3×D412yes—
631C2×#41C3×#4112yes—
632C2×#41C3×#4112yes—
633C22×Q8C3×C22⋊C411yescharacteristic
634C22×Q8C2×C3×D411yescharacteristic
635C22×D4—24no—
636C22×D4—24no—
637C22×D4—21no—
638C22×D4—24no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—24no—
642C22×D4—22no—
643C22×D4—21no—
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—41no—
652C22×D4—41no—
653C22×D4—42no—
654C22×D4—42no—
655C22×D4—44no—
656C22×D4—48no—
657C22×D4—44no—
658C22×D4—48no—
659C22×D4—42no—
660C22×D4—42no—
661C22×D4—42no—
662C22×D4—42no—
663C22×D4—42no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4—44no—
667C22×D4—84no—
668C22×D4C3×C22⋊C412yes—
669C22×D4C3×C22⋊C411yescharacteristic
670C22×D4C2×C3×D411yescharacteristic
671C22×D4C2×C3×D412yes—
672C23×C4—21no—
673C23×C4—21no—
674C23×C4—21no—
675C23×C4—21no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—42no—
680C23×C4—41no—
681C23×C4—41no—
682C23×C4C3×C22⋊C411yescharacteristic
683C23×C4C22×C3×C411yescharacteristic
684C23×C4C2×C3×D412yes—
685C2×M16—24no—
686C2×M16—42no—
687C2×M16—42no—
688C2×M16—42no—
689C2×M16—42no—
690C2×M16—42no—
691C22×C8—42no—
692#123—22no—
693#123—22no—
694#123—22no—
695#123—22no—
696#123—44no—
697C22⋊Q8—42no—
698C22⋊Q8—42no—
699C22⋊Q8—42no—
700C22⋊Q8—41no—
701C22⋊Q8—41no—
702#121—48no—
703#121—44no—
704#121—42no—
705#121—44no—
706#121—42no—
707#121—42no—
708#121—41no—
709#121—41no—
710#120—22no—
711#120—22no—
712#120—22no—
713#120—22no—
714#120—44no—
715#120—88no—
716C4×D4—48no—
717C4×D4—42no—
718C4×D4—42no—
719C4×D4—42no—
720C4×D4—42no—
721#117—22no—
722#117—22no—
723#117—24no—
724#117—41no—
725#117—41no—
726#117—42no—
727#117—42no—
728#117—42no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—21no—
731C2×C4⋊C4—21no—
732C2×C4⋊C4—21no—
733C2×C4⋊C4—22no—
734C2×C4⋊C4—42no—
735C2×C4⋊C4—42no—
736C2×C4⋊C4C3×C22⋊C412yes—
737C2×C22⋊C4—24no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—24no—
744C2×C22⋊C4—24no—
745C2×C22⋊C4—24no—
746C2×C22⋊C4—24no—
747C2×C22⋊C4—44no—
748C2×C22⋊C4—42no—
749C2×C22⋊C4C3×C22⋊C412yes—
750C2×C42—21no—
751C2×C42—42no—
752C2×C42C3×C22⋊C412yes—
753#104—416no—
754#102—416no—
755#101—24no—
756#101—42no—
757#100—24no—
758#100—42no—
759#99—24no—
760#99—24no—
761#99—42no—
762#99—42no—
763#95—24no—
764#95—24no—
765C23×C3—21no—
766C23×C3—21no—
767C23×C3—22no—
768C23×C3—22no—
769C23×C3—22no—
770C23×C3—22no—
771C23×C3—24no—
772C23×C3—41no—
773C23×C3—41no—
774C23×C3—42no—
775C23×C3—42no—
776C23×C3—42no—
777C23×C3—44no—
778C23×C3—44no—
779C23×C3—41no—
780C23×C3—41no—
781C23×C3—41no—
782C23×C3—42no—
783C23×C3—48no—
784C23×C3—48no—
785C23×C3—48no—
786C23×C3—42no—
787C23×C3—42no—
788C23×C3—41no—
789C23×C3—41no—
790C23×C3—42no—
791C23×C3—41no—
792C23×C3—42no—
793C23×C3—41no—
794C23×C3—41no—
795C23×C3—82no—
796C23×C3—84no—
797C23×C3—84no—
798C23×C3—84no—
799C23×C3—84no—
800C23×C3—82no—
801C23×C3—164no—
802C23×C3—164no—
803C23×C3—164no—
804C23×C3—164no—
805C23×C3—164no—
806C23×C3—164no—
807C23×C3—168no—
808C23×C3#37911yescharacteristic
809C23×C3#38612yes—
810C23×C3#39212yes—
811C23×C3#39412yes—
812C3×Q8—24no—
813C3×Q8—42no—
814C3×Q8—41no—
815C3×Q8—41no—
816C3×Q8—42no—
817C3×D4—24no—
818C3×D4—24no—
819C3×D4—24no—
820C3×D4—42no—
821C3×D4—42no—
822C3×D4—42no—
823C3×D4—42no—
824C3×D4—42no—
825C3×D4—41no—
826C3×D4—41no—
827C3×D4—48no—
828C3×D4—44no—
829C3×D4—44no—
830C3×D4—48no—
831C3×D4—48no—
832C3×D4—48no—
833C3×D4—48no—
834C3×D4—42no—
835C3×D4—42no—
836C3×D4—42no—
837C3×D4—84no—
838C3×D4—84no—
839C3×D4—88no—
840C3×D4—816no—
841C2×C3×C4—21no—
842C2×C3×C4—22no—
843C2×C3×C4—21no—
844C2×C3×C4—22no—
845C2×C3×C4—22no—
846C2×C3×C4—22no—
847C2×C3×C4—22no—
848C2×C3×C4—22no—
849C2×C3×C4—22no—
850C2×C3×C4—22no—
851C2×C3×C4—22no—
852C2×C3×C4—22no—
853C2×C3×C4—22no—
854C2×C3×C4—22no—
855C2×C3×C4—22no—
856C2×C3×C4—22no—
857C2×C3×C4—22no—
858C2×C3×C4—44no—
859C2×C3×C4—44no—
860C2×C3×C4—48no—
861C2×C3×C4—48no—
862C2×C3×C4—41no—
863C2×C3×C4—41no—
864C2×C3×C4—42no—
865C2×C3×C4—42no—
866C2×C3×C4—44no—
867C2×C3×C4—42no—
868C2×C3×C4—42no—
869C2×C3×C4—42no—
870C2×C3×C4—41no—
871C2×C3×C4—42no—
872C2×C3×C4—41no—
873C2×C3×C4—41no—
874C2×C3×C4—42no—
875C2×C3×C4—82no—
876C2×C3×C4—82no—
877C2×C3×C4—84no—
878C2×C3×C4—82no—
879C2×C3×C4—82no—
880C2×C3×C4—82no—
881C2×C3×C4—84no—
882C2×C3×C4—162no—
883C2×C3×C4—162no—
884C2×C3×C4#38612yes—
885C2×C3×C4#39011yescharacteristic
886C2×C3×C4#39011yescharacteristic
887C2×C3×C4#39212yes—
888C2×C3×C4#39412yes—
889C2×C3×C4C2×#9911yescharacteristic
890C2×C3×C4C2×#9911yescharacteristic
891C2×C3×C4C2×#9912yes—
892C3×C8—84no—
893C24—24no—
894C24—21no—
895C24—22no—
896C24—21no—
897C24—22no—
898C24—44no—
899C24—44no—
900C24—42no—
901C24—41no—
902C24—42no—
903C24—41no—
904C24—42no—
905C24—42no—
906C24—42no—
907C24—81no—
908C24—82no—
909C24—82no—
910C24—84no—
911C24—84no—
912C24C2×C3×C22⋊C411yescharacteristic
913C24C3×#12012yes—
914#41—28no—
915#41—28no—
916#41—42no—
917#41—42no—
918#41—42no—
919#41—42no—
920#41—42no—
921#41—42no—
922#41—42no—
923#41—42no—
924#41—44no—
925#41—44no—
926#41—44no—
927#41—44no—
928#41—44no—
929#41—44no—
930#41—44no—
931#41—44no—
932#41—44no—
933#41—44no—
934#41—416no—
935#41—48no—
936#41—48no—
937C2×Q8—21no—
938C2×Q8—22no—
939C2×Q8—22no—
940C2×Q8—41no—
941C2×Q8—41no—
942C2×Q8C3×#9912yes—
943C2×Q8C3×#12112yes—
944C2×Q8C3×#12411yescharacteristic
945C2×Q8C3×#12711yescharacteristic
946C2×D4—28no—
947C2×D4—28no—
948C2×D4—24no—
949C2×D4—24no—
950C2×D4—22no—
951C2×D4—22no—
952C2×D4—22no—
953C2×D4—22no—
954C2×D4—22no—
955C2×D4—22no—
956C2×D4—22no—
957C2×D4—21no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—44no—
961C2×D4—44no—
962C2×D4—44no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—41no—
967C2×D4—41no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—42no—
974C2×D4—44no—
975C2×D4—44no—
976C2×D4—44no—
977C2×D4—42no—
978C2×D4—416no—
979C2×D4—48no—
980C2×D4—48no—
981C2×D4—416no—
982C2×D4—416no—
983C2×D4—416no—
984C2×D4—416no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—48no—
992C2×D4—48no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—41no—
996C2×D4—41no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—84no—
1000C2×D4—82no—
1001C2×D4—82no—
1002C2×D4—88no—
1003C2×D4—88no—
1004C2×D4C3×#9912yes—
1005C2×D4C3×#9914yes—
1006C2×D4C3×#12012yes—
1007C2×D4C3×#12112yes—
1008C2×D4C3×#12112yes—
1009C2×D4C3×#12112yes—
1010C2×D4C3×#12312yes—
1011C2×D4C3×#12411yescharacteristic
1012C2×D4C3×#12711yescharacteristic
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—24no—
1021C22×C4—21no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—21no—
1026C22×C4—22no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—41no—
1039C22×C4—41no—
1040C22×C4—42no—
1041C22×C4—41no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—82no—
1046C22×C4—82no—
1047C22×C4—82no—
1048C22×C4—82no—
1049C22×C4—82no—
1050C22×C4—82no—
1051C22×C4C2×C3×C22⋊C411yescharacteristic
1052C22×C4C2×C3×C22⋊C411yescharacteristic
1053C22×C4C3×C4×D412yes—
1054C22×C4C3×C4×D412yes—
1055C22×C4C3×#12012yes—
1056C22×C4C3×#12012yes—
1057C22×C4C3×#12112yes—
1058C22×C4C3×#12112yes—
1059C22×C4C3×#12312yes—
1060M16—44no—
1061M16—44no—
1062M16—82no—
1063M16—82no—
1064C2×C8—44no—
1065C2×C8—82no—
1066C2×C8—82no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—41no—
1076C4⋊C4—41no—
1077C4⋊C4—82no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—44no—
1081C22⋊C4—48no—
1082C22⋊C4—42no—
1083C22⋊C4—44no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—44no—
1089C22⋊C4—84no—
1090C22⋊C4—84no—
1091C22⋊C4—84no—
1092C22⋊C4—84no—
1093C22⋊C4—82no—
1094C42—42no—
1095C42—44no—
1096C42—42no—
1097C42—82no—
1098C22×C3—21no—
1099C22×C3—21no—
1100C22×C3—22no—
1101C22×C3—22no—
1102C22×C3—22no—
1103C22×C3—42no—
1104C22×C3—42no—
1105C22×C3—42no—
1106C22×C3—42no—
1107C22×C3—42no—
1108C22×C3—42no—
1109C22×C3—44no—
1110C22×C3—41no—
1111C22×C3—42no—
1112C22×C3—42no—
1113C22×C3—41no—
1114C22×C3—42no—
1115C22×C3—44no—
1116C22×C3—44no—
1117C22×C3—42no—
1118C22×C3—44no—
1119C22×C3—82no—
1120C22×C3—81no—
1121C22×C3—81no—
1122C22×C3—82no—
1123C22×C3—84no—
1124C22×C3—84no—
1125C22×C3—84no—
1126C22×C3—84no—
1127C22×C3—81no—
1128C22×C3—81no—
1129C22×C3—81no—
1130C22×C3—81no—
1131C22×C3—168no—
1132C22×C3—168no—
1133C22×C3—168no—
1134C22×C3#143811yescharacteristic
1135C22×C3#178111yescharacteristic
1136C22×C3#178111yescharacteristic
1137C3×C4—22no—
1138C3×C4—21no—
1139C3×C4—21no—
1140C3×C4—22no—
1141C3×C4—42no—
1142C3×C4—82no—
1143C3×C4—82no—
1144C3×C4—82no—
1145C3×C4—81no—
1146C3×C4—164no—
1147C3×C4#189812yes—
1148C3×C4#189812yes—
1149C23—21no—
1150C23—21no—
1151C23—22no—
1152C23—22no—
1153C23—22no—
1154C23—22no—
1155C23—24no—
1156C23—41no—
1157C23—41no—
1158C23—42no—
1159C23—42no—
1160C23—42no—
1161C23—44no—
1162C23—44no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—42no—
1167C23—48no—
1168C23—48no—
1169C23—48no—
1170C23—42no—
1171C23—42no—
1172C23—41no—
1173C23—41no—
1174C23—42no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—42no—
1179C23—82no—
1180C23—84no—
1181C23—84no—
1182C23—84no—
1183C23—84no—
1184C23—82no—
1185C23—164no—
1186C23—164no—
1187C23—164no—
1188C23—164no—
1189C23—164no—
1190C23—164no—
1191C23—168no—
1192C23C3×#37911yescharacteristic
1193C23C3×#38612yes—
1194C23C3×#39212yes—
1195C23C3×#39412yes—
1196Q8—24no—
1197Q8—42no—
1198Q8—41no—
1199Q8—41no—
1200Q8—42no—
1201D4—24no—
1202D4—24no—
1203D4—24no—
1204D4—42no—
1205D4—42no—
1206D4—42no—
1207D4—42no—
1208D4—42no—
1209D4—41no—
1210D4—41no—
1211D4—48no—
1212D4—44no—
1213D4—44no—
1214D4—48no—
1215D4—48no—
1216D4—48no—
1217D4—48no—
1218D4—42no—
1219D4—42no—
1220D4—42no—
1221D4—816no—
1222D4—84no—
1223D4—84no—
1224D4—88no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—44no—
1243C2×C4—44no—
1244C2×C4—48no—
1245C2×C4—48no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—44no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—41no—
1259C2×C4—82no—
1260C2×C4—82no—
1261C2×C4—84no—
1262C2×C4—82no—
1263C2×C4—82no—
1264C2×C4—82no—
1265C2×C4—84no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4C3×#38612yes—
1269C2×C4C3×#39011yescharacteristic
1270C2×C4C3×#39011yescharacteristic
1271C2×C4C3×#39212yes—
1272C2×C4C3×#39412yes—
1273C2×C4C2×C3×#9911yescharacteristic
1274C2×C4C2×C3×#9911yescharacteristic
1275C2×C4C2×C3×#9912yes—
1276C8—84no—
1277C2×C3—21no—
1278C2×C3—21no—
1279C2×C3—42no—
1280C2×C3—42no—
1281C2×C3—42no—
1282C2×C3—82no—
1283C2×C3—82no—
1284C2×C3—84no—
1285C2×C3#1096511yescharacteristic
1286C2×C3#1271111yescharacteristic
1287C2×C3#1271311yescharacteristic
1288C22—21no—
1289C22—21no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—44no—
1300C22—41no—
1301C22—42no—
1302C22—42no—
1303C22—41no—
1304C22—42no—
1305C22—44no—
1306C22—44no—
1307C22—42no—
1308C22—44no—
1309C22—82no—
1310C22—81no—
1311C22—81no—
1312C22—84no—
1313C22—82no—
1314C22—84no—
1315C22—84no—
1316C22—84no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22—168no—
1323C22—168no—
1324C22C3×#143811yescharacteristic
1325C22C3×#178111yescharacteristic
1326C22C3×#178111yescharacteristic
1327C4—22no—
1328C4—21no—
1329C4—21no—
1330C4—22no—
1331C4—42no—
1332C4—82no—
1333C4—82no—
1334C4—82no—
1335C4—81no—
1336C4—164no—
1337C4C3×#189812yes—
1338C4C3×#189812yes—
1339C3#14757311yescharacteristic, direct product factor, Sylow
1340C2—21no—
1341C2—21no—
1342C2—42no—
1343C2—42no—
1344C2—42no—
1345C2—82no—
1346C2—82no—
1347C2—84no—
1348C2C3×#1096511yescharacteristic
1349C2C3×#1271111yescharacteristic
1350C2C3×#1271311yescharacteristic
subgroupG/H
center, socleC22×C3#1781
commutatorC23×C4C22×C3×C4
Frattini, cosocleC22×#41C23×C3
prime radicalC3×#35512C2
LCSG ▷ C23×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C22×C3×H(5,𝔽2) ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#2120C2semidirect
3. C2×C3×#1795C2semidirect
4. C3×#12587C2semidirect
5. C3×#12583C2semidirect
6. #147573C3direct (N × H)
8. C2×C3×#525C4semidirect
10. C22×C3×#121C4semidirect
21. C3×#2311C4semidirect
23. C3×#2309C4semidirect
33. C2×#2120C2×C3semidirect
34. C2×#1795C2×C3semidirect
35. #12587C2×C3semidirect
36. #12583C2×C3semidirect
89. C3×#413D4semidirect
95. C3×#410D4semidirect
119. C2×#525C3×C4semidirect
121. C22×#121C3×C4semidirect
132. #2311C3×C4semidirect
134. #2309C3×C4semidirect
363. #413C3×D4semidirect
369. #410C3×D4semidirect
1339. C3#147573direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#355122
C2×C3×#21202
C2×C3×#17952
C3×#125872
C3×#125832
#1475733