Finite Group Databasebeta

← C3×#24235 #10642842

Subgroups — C3×#24235 #10642842

Order 768.

1376 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3500C211yesmaximal, characteristic
2C3×#3037C211yesmaximal, characteristic, complemented
3C2×C3×#456C211yesmaximal, characteristic, complemented
4C2×C3×#455C211yesmaximal, characteristic, complemented
5C3×C4×#137C211yesmaximal, characteristic, complemented
6C3×#2545C211yesmaximal, characteristic, complemented
7C3×#2038C211yesmaximal, characteristic, complemented
8C3×#2037C211yesmaximal, characteristic, complemented
9C3×#2005C211yesmaximal, characteristic, complemented
10C3×#2004C211yesmaximal, characteristic, complemented
11C3×#1980C211yesmaximal, characteristic, complemented
12C3×#1967C211yesmaximal, characteristic, complemented
13C3×#1806C211yesmaximal, characteristic, complemented
14C3×#1793C211yesmaximal, characteristic, complemented
15C3×#1792C211yesmaximal, characteristic, complemented
16#24235C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×2−1+4C2211yescharacteristic
18C2×C3×H(5,𝔽2)C2211yescharacteristic
19C2×C3×#137C2211yescharacteristic
20C2×C3×#137C2211yescharacteristic
21C2×C3×#137C2211yescharacteristic, complemented
22C3×#548—21no—
23C3×#548—21no—
24C3×#546—21no—
25C3×#546—21no—
26C3×#546—22no—
27C3×#546—22no—
28C3×#536—21no—
29C3×#536C2211yescharacteristic
30C3×#535—21no—
31C3×#535C2211yescharacteristic
32C3×#532—21no—
33C3×#532C2211yescharacteristic
34C2×C3×C4⋊Q8C2211yescharacteristic, complemented
35C2×C3×#124—21no—
36C2×C3×#124C2211yescharacteristic
37C2×C3×#124C2211yescharacteristic
38C3×C4×#41C2211yescharacteristic
39C2×C3×C4×Q8C2211yescharacteristic, complemented
40C3×#464—21no—
41C3×#464—21no—
42C3×#462—21no—
43C3×#460—21no—
44C3×#456—24no—
45C3×#455—24no—
46C3×#441—21no—
47C3×#440—21no—
48C3×C4×Q16—21no—
49C3×C4×SD16—21no—
50C3×#428C2211yescharacteristic, complemented
51C3×#423C2211yescharacteristic, complemented
52C2×C3×#104C2211yescharacteristic
53C2×C3×#104C2211yescharacteristic
54C2×C3×#104C2211yescharacteristic
55C2×C3×#104C2211yescharacteristic
56C2×C3×#104C2211yescharacteristic, complemented
57C2×C3×#104C2211yescharacteristic, complemented
58C3×#419C2211yescharacteristic, complemented
59C3×#417C2211yescharacteristic
60C3×#417C2211yescharacteristic
61C3×#417C2211yescharacteristic, complemented
62C2×C3×#101C2211yescharacteristic, complemented
63C2×C3×#101C2211yescharacteristic, complemented
64C2×C3×#100C2211yescharacteristic
65C2×C3×#100C2211yescharacteristic
66C3×C4×M16C2211yescharacteristic, complemented
67C3×#396—22no—
68C3×#391C2211yescharacteristic, complemented
69C3×#390C2211yescharacteristic
70C3×#388—22no—
71C3×C4×C4⋊C4C2211yescharacteristic, complemented
72C3×#339C2211yescharacteristic, complemented
73C3×#339C2211yescharacteristic, complemented
74#3500C2×C311yescharacteristic
75#3037C2×C311yescharacteristic, complemented
76C2×#456C2×C311yescharacteristic, complemented
77C2×#455C2×C311yescharacteristic, complemented
78C4×#137C2×C311yescharacteristic, complemented
79#2545C2×C311yescharacteristic, complemented
80#2038C2×C311yescharacteristic, complemented
81#2037C2×C311yescharacteristic, complemented
82#2005C2×C311yescharacteristic, complemented
83#2004C2×C311yescharacteristic, complemented
84#1980C2×C311yescharacteristic, complemented
85#1967C2×C311yescharacteristic, complemented
86#1806C2×C311yescharacteristic, complemented
87#1793C2×C311yescharacteristic, complemented
88#1792C2×C311yescharacteristic, complemented
89C3×2−1+4—22no—
90C3×2−1+4—22no—
91C3×2−1+4—41no—
92C3×2−1+4—41no—
93C3×H(5,𝔽2)—22no—
94C3×H(5,𝔽2)—22no—
95C3×H(5,𝔽2)—41no—
96C3×H(5,𝔽2)—41no—
97C2×C3×#41—21no—
98C2×C3×#41—21no—
99C2×C3×#41—21no—
100C2×C3×#41—21no—
101C2×C3×#41—22no—
102C2×C3×#41C2311yescharacteristic
103C2×C3×#41C2311yescharacteristic
104C2×C3×#41C2311yescharacteristic
105C22×C3×Q8—21no—
106C22×C3×Q8—21no—
107C22×C3×Q8C2311yescharacteristic
108C22×C3×Q8C2311yescharacteristic
109C22×C3×D4—22no—
110C22×C3×D4—21no—
111C22×C3×D4—21no—
112C22×C3×D4C2311yescharacteristic
113C3×#137—22no—
114C3×#137—22no—
115C3×#137—22no—
116C3×#137—41no—
117C3×#137—41no—
118C3×#137D414yescomplemented
119C2×C3×Q16—21no—
120C2×C3×Q16—21no—
121C2×C3×Q16—21no—
122C2×C3×SD16—21no—
123C2×C3×SD16—21no—
124C2×C3×SD16—21no—
125C2×C3×M16C2311yescharacteristic
126C2×C3×M16C2311yescharacteristic
127C2×C3×M16C2311yescharacteristic
128C2×C3×M16C2311yescharacteristic
129C3×C4⋊Q8—21no—
130C3×C4⋊Q8—22no—
131C3×C4⋊Q8—41no—
132C3×C4⋊Q8D411yescharacteristic
133C3×#127—21no—
134C3×#127D411yescharacteristic
135C3×#124—22no—
136C3×#124—22no—
137C3×#124—21no—
138C3×#124—21no—
139C3×#124—22no—
140C3×#124—21no—
141C3×#124—21no—
142C3×#124—21no—
143C3×#124—21no—
144C3×#124—41no—
145C3×#124D411yescharacteristic
146C3×#124D411yescharacteristic
147C3×#123—22no—
148C3×#123—22no—
149C3×#123—22no—
150C3×C22⋊Q8—22no—
151C3×C22⋊Q8—22no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—21no—
154C3×#121—22no—
155C3×#121—22no—
156C3×#121—22no—
157C3×#121—22no—
158C3×#121—21no—
159C3×#121—21no—
160C3×#121—21no—
161C3×#121—21no—
162C3×#120—22no—
163C3×#120—22no—
164C3×#120—22no—
165C3×C4×Q8—21no—
166C3×C4×Q8—21no—
167C3×C4×Q8—21no—
168C3×C4×Q8—21no—
169C3×C4×Q8D411yescharacteristic
170C3×C4×Q8D411yescharacteristic
171C3×C4×D4—22no—
172C3×C4×D4—22no—
173C3×C4×D4—21no—
174C3×C4×D4—21no—
175C3×C4×D4—21no—
176C3×C4×D4—21no—
177C3×C4×D4D411yescharacteristic
178C3×C4×D4D411yescharacteristic
179C3×#117—21no—
180C3×#117C2311yescharacteristic
181C2×C3×C4⋊C4—21no—
182C2×C3×C4⋊C4—22no—
183C2×C3×C4⋊C4—21no—
184C2×C3×C4⋊C4C2311yescharacteristic
185C2×C3×C22⋊C4—22no—
186C2×C3×C22⋊C4—22no—
187C2×C3×C22⋊C4—22no—
188C2×C3×C22⋊C4—22no—
189C2×C3×C22⋊C4D412yes—
190C2×C3×C22⋊C4D412yes—
191C2×C3×C42—21no—
192C2×C3×C42—21no—
193C2×C3×C42C2311yescharacteristic
194C2×C3×C42C2311yescharacteristic
195C2×C3×C42C2311yescharacteristic
196C3×#107—21no—
197C3×#106—21no—
198C3×C4⋊C8—21no—
199C3×C4⋊C8—21no—
200C3×#104—22no—
201C3×#104—22no—
202C3×#104—22no—
203C3×#104—22no—
204C3×#104—41no—
205C3×#104—41no—
206C3×#103—21no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—21no—
210C3×#103—21no—
211C3×#102—21no—
212C3×#102—21no—
213C3×#102—21no—
214C3×#101—22no—
215C3×#101—41no—
216C3×#100—22no—
217C3×#100—41no—
218C3×#97—21no—
219C3×C4×C8—21no—
220C3×#95—21no—
221C3×#95—22no—
222C2×2−1+4C22×C311yescharacteristic
223C2×H(5,𝔽2)C22×C311yescharacteristic
224C2×#137C22×C311yescharacteristic
225C2×#137C22×C311yescharacteristic
226C2×#137C22×C311yescharacteristic, complemented
227#548—21no—
228#548—21no—
229#546—21no—
230#546—21no—
231#546—22no—
232#546—22no—
233#536—21no—
234#536C22×C311yescharacteristic
235#535—21no—
236#535C22×C311yescharacteristic
237#532—21no—
238#532C22×C311yescharacteristic
239C2×C4⋊Q8C22×C311yescharacteristic, complemented
240C2×#124—21no—
241C2×#124C22×C311yescharacteristic
242C2×#124C22×C311yescharacteristic
243C4×#41C22×C311yescharacteristic
244C2×C4×Q8C22×C311yescharacteristic, complemented
245#464—21no—
246#464—21no—
247#462—21no—
248#460—21no—
249#456—24no—
250#455—24no—
251#441—21no—
252#440—21no—
253C4×Q16—21no—
254C4×SD16—21no—
255#428C22×C311yescharacteristic, complemented
256#423C22×C311yescharacteristic, complemented
257C2×#104C22×C311yescharacteristic
258C2×#104C22×C311yescharacteristic
259C2×#104C22×C311yescharacteristic
260C2×#104C22×C311yescharacteristic
261C2×#104C22×C311yescharacteristic, complemented
262C2×#104C22×C311yescharacteristic, complemented
263#419C22×C311yescharacteristic, complemented
264#417C22×C311yescharacteristic
265#417C22×C311yescharacteristic
266#417C22×C311yescharacteristic, complemented
267C2×#101C22×C311yescharacteristic, complemented
268C2×#101C22×C311yescharacteristic, complemented
269C2×#100C22×C311yescharacteristic
270C2×#100C22×C311yescharacteristic
271C4×M16C22×C311yescharacteristic, complemented
272#396—22no—
273#391C22×C311yescharacteristic, complemented
274#390C22×C311yescharacteristic
275#388—22no—
276C4×C4⋊C4C22×C311yescharacteristic, complemented
277#339C22×C311yescharacteristic, complemented
278#339C22×C311yescharacteristic, complemented
279C24×C3—22no—
280C24×C3C2×D412yes—
281C3×#41—21no—
282C3×#41—21no—
283C3×#41—21no—
284C3×#41—21no—
285C3×#41—21no—
286C3×#41—21no—
287C3×#41—21no—
288C3×#41—21no—
289C3×#41—21no—
290C3×#41—21no—
291C3×#41—42no—
292C3×#41—42no—
293C3×#41—44no—
294C3×#41—44no—
295C3×#41—42no—
296C3×#41—42no—
297C3×#41—42no—
298C3×#41—42no—
299C3×#41—42no—
300C3×#41—42no—
301C3×#41C2×D412yes—
302C3×#41#4112yes—
303C2×C3×Q8—22no—
304C2×C3×Q8—21no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—21no—
312C2×C3×Q8—21no—
313C2×C3×Q8—21no—
314C2×C3×Q8—21no—
315C2×C3×Q8—42no—
316C2×C3×Q8—42no—
317C2×C3×Q8—42no—
318C2×C3×Q8—42no—
319C2×C3×Q8C2×D411yescharacteristic
320C2×C3×Q8C2×D411yescharacteristic
321C2×C3×Q8C2×D412yes—
322C2×C3×Q8C2×D411yescharacteristic
323C2×C3×D4—21no—
324C2×C3×D4—22no—
325C2×C3×D4—22no—
326C2×C3×D4—22no—
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—22no—
330C2×C3×D4—22no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—21no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—42no—
340C2×C3×D4—42no—
341C2×C3×D4—44no—
342C2×C3×D4—44no—
343C2×C3×D4—42no—
344C2×C3×D4—42no—
345C2×C3×D4C2×D411yescharacteristic
346C2×C3×D4C2×D411yescharacteristic
347C2×C3×D4C2×D411yescharacteristic
348C22×C3×C4—21no—
349C22×C3×C4—22no—
350C22×C3×C4—22no—
351C22×C3×C4—22no—
352C22×C3×C4—21no—
353C22×C3×C4—21no—
354C22×C3×C4—21no—
355C22×C3×C4—21no—
356C22×C3×C4—21no—
357C22×C3×C4—21no—
358C22×C3×C4—21no—
359C22×C3×C4—21no—
360C22×C3×C4C2×D412yes—
361C22×C3×C4C2×D411yescharacteristic
362C22×C3×C4C2×D411yescharacteristic
363C22×C3×C4C2411yescharacteristic
364C3×Q16—24no—
365C3×Q16—42no—
366C3×Q16—42no—
367C3×SD16—24no—
368C3×SD16—42no—
369C3×SD16—42no—
370C3×M16—21no—
371C3×M16—21no—
372C3×M16—21no—
373C3×M16—21no—
374C3×M16—21no—
375C3×M16—21no—
376C3×M16—21no—
377C3×M16C2×D412yes—
378C2×C3×C8—21no—
379C2×C3×C8—21no—
380C2×C3×C8—21no—
381C2×C3×C8—21no—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—44no—
391C3×C4⋊C4—42no—
392C3×C4⋊C4—41no—
393C3×C4⋊C4—41no—
394C3×C4⋊C4C2×D411yescharacteristic
395C3×C4⋊C4C2×D411yescharacteristic
396C3×C22⋊C4—22no—
397C3×C22⋊C4—22no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4—21no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—22no—
404C3×C22⋊C4—22no—
405C3×C22⋊C4—22no—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—21no—
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—44no—
412C3×C22⋊C4—44no—
413C3×C42—21no—
414C3×C42—21no—
415C3×C42—21no—
416C3×C42—21no—
417C3×C42—21no—
418C3×C42—21no—
419C3×C42—21no—
420C3×C42—41no—
421C3×C42—41no—
422C3×C42C2×D411yescharacteristic
423C3×C42C2×D411yescharacteristic
424C3×C42C2×D411yescharacteristic
425C3×C42C2×D411yescharacteristic
4262−1+4—22no—
4272−1+4—22no—
4282−1+4—41no—
4292−1+4—41no—
430H(5,𝔽2)—22no—
431H(5,𝔽2)—22no—
432H(5,𝔽2)—41no—
433H(5,𝔽2)—41no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—22no—
439C2×#41C23×C311yescharacteristic
440C2×#41C23×C311yescharacteristic
441C2×#41C23×C311yescharacteristic
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8C23×C311yescharacteristic
445C22×Q8C23×C311yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4C23×C311yescharacteristic
450#137—22no—
451#137—22no—
452#137—22no—
453#137—41no—
454#137—41no—
455#137C3×D414yescomplemented
456C2×Q16—21no—
457C2×Q16—21no—
458C2×Q16—21no—
459C2×SD16—21no—
460C2×SD16—21no—
461C2×SD16—21no—
462C2×M16C23×C311yescharacteristic
463C2×M16C23×C311yescharacteristic
464C2×M16C23×C311yescharacteristic
465C2×M16C23×C311yescharacteristic
466C4⋊Q8—21no—
467C4⋊Q8—22no—
468C4⋊Q8—41no—
469C4⋊Q8C3×D411yescharacteristic
470#127—21no—
471#127C3×D411yescharacteristic
472#124—22no—
473#124—22no—
474#124—21no—
475#124—21no—
476#124—22no—
477#124—21no—
478#124—21no—
479#124—21no—
480#124—21no—
481#124—41no—
482#124C3×D411yescharacteristic
483#124C3×D411yescharacteristic
484#123—22no—
485#123—22no—
486#123—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491#121—22no—
492#121—22no—
493#121—22no—
494#121—22no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#120—22no—
500#120—22no—
501#120—22no—
502C4×Q8—21no—
503C4×Q8—21no—
504C4×Q8—21no—
505C4×Q8—21no—
506C4×Q8C3×D411yescharacteristic
507C4×Q8C3×D411yescharacteristic
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4C3×D411yescharacteristic
515C4×D4C3×D411yescharacteristic
516#117—21no—
517#117C23×C311yescharacteristic
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4C23×C311yescharacteristic
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4C3×D412yes—
527C2×C22⋊C4C3×D412yes—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42C23×C311yescharacteristic
531C2×C42C23×C311yescharacteristic
532C2×C42C23×C311yescharacteristic
533#107—21no—
534#106—21no—
535C4⋊C8—21no—
536C4⋊C8—21no—
537#104—22no—
538#104—22no—
539#104—22no—
540#104—22no—
541#104—41no—
542#104—41no—
543#103—21no—
544#103—21no—
545#103—21no—
546#103—21no—
547#103—21no—
548#102—21no—
549#102—21no—
550#102—21no—
551#101—22no—
552#101—41no—
553#100—22no—
554#100—41no—
555#97—21no—
556C4×C8—21no—
557#95—21no—
558#95—22no—
559C23×C3—21no—
560C23×C3—22no—
561C23×C3—21no—
562C23×C3—21no—
563C23×C3—22no—
564C23×C3—22no—
565C23×C3—44no—
566C23×C3—42no—
567C23×C3—42no—
568C23×C3—82no—
569C23×C3—82no—
570C23×C3C22×D411yescharacteristic
571C3×Q8—21no—
572C3×Q8—22no—
573C3×Q8—22no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—21no—
577C3×Q8—21no—
578C3×Q8—44no—
579C3×Q8—41no—
580C3×Q8—41no—
581C3×Q8—41no—
582C3×Q8—41no—
583C3×Q8—41no—
584C3×Q8—41no—
585C3×Q8#12112yes—
586C3×D4—22no—
587C3×D4—22no—
588C3×D4—21no—
589C3×D4—21no—
590C3×D4—21no—
591C3×D4—21no—
592C3×D4—21no—
593C3×D4—44no—
594C3×D4—44no—
595C3×D4—44no—
596C3×D4—41no—
597C3×D4—41no—
598C3×D4—41no—
599C3×D4—41no—
600C3×D4—41no—
601C3×D4—41no—
602C3×D4—41no—
603C3×D4—41no—
604C3×D4—81no—
605C3×D4—81no—
606C3×D4—82no—
607C3×D4—82no—
608C3×D4#12112yes—
609C2×C3×C4—21no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—22no—
617C2×C3×C4—21no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—44no—
624C2×C3×C4—44no—
625C2×C3×C4—41no—
626C2×C3×C4—44no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×C3×C4—41no—
634C2×C3×C4—42no—
635C2×C3×C4—41no—
636C2×C3×C4—41no—
637C2×C3×C4—41no—
638C2×C3×C4—41no—
639C2×C3×C4—81no—
640C2×C3×C4—81no—
641C2×C3×C4#12011yescharacteristic
642C2×C3×C4#12011yescharacteristic
643C2×C3×C4#12011yescharacteristic
644C2×C3×C4#12011yescharacteristic
645C2×C3×C4C22×D411yescharacteristic
646C2×C3×C4C22×D411yescharacteristic
647C2×C3×C4C22×D411yescharacteristic
648C2×C3×C4C2×#4111yescharacteristic
649C2×C3×C4H(5,𝔽2)11yescharacteristic
650C2×C3×C4H(5,𝔽2)11yescharacteristic
651C3×C8—22no—
652C3×C8—41no—
653C3×C8—41no—
654C3×C8—41no—
655C24—22no—
656C24C2×C3×D412yes—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—21no—
667#41—42no—
668#41—42no—
669#41—44no—
670#41—44no—
671#41—42no—
672#41—42no—
673#41—42no—
674#41—42no—
675#41—42no—
676#41—42no—
677#41C2×C3×D412yes—
678#41C3×#4112yes—
679C2×Q8—22no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8—42no—
695C2×Q8C2×C3×D411yescharacteristic
696C2×Q8C2×C3×D411yescharacteristic
697C2×Q8C2×C3×D412yes—
698C2×Q8C2×C3×D411yescharacteristic
699C2×D4—21no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4C2×C3×D411yescharacteristic
722C2×D4C2×C3×D411yescharacteristic
723C2×D4C2×C3×D411yescharacteristic
724C22×C4—21no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4C2×C3×D412yes—
737C22×C4C2×C3×D411yescharacteristic
738C22×C4C2×C3×D411yescharacteristic
739C22×C4C24×C311yescharacteristic
740Q16—24no—
741Q16—42no—
742Q16—42no—
743SD16—24no—
744SD16—42no—
745SD16—42no—
746M16—21no—
747M16—21no—
748M16—21no—
749M16—21no—
750M16—21no—
751M16—21no—
752M16—21no—
753M16C2×C3×D412yes—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C4⋊C4—22no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—44no—
767C4⋊C4—42no—
768C4⋊C4—41no—
769C4⋊C4—41no—
770C4⋊C4C2×C3×D411yescharacteristic
771C4⋊C4C2×C3×D411yescharacteristic
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—22no—
775C22⋊C4—22no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—22no—
782C22⋊C4—22no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—44no—
788C22⋊C4—44no—
789C42—21no—
790C42—21no—
791C42—21no—
792C42—21no—
793C42—21no—
794C42—21no—
795C42—21no—
796C42—41no—
797C42—41no—
798C42C2×C3×D411yescharacteristic
799C42C2×C3×D411yescharacteristic
800C42C2×C3×D411yescharacteristic
801C42C2×C3×D411yescharacteristic
802C22×C3—21no—
803C22×C3—21no—
804C22×C3—22no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—42no—
810C22×C3—41no—
811C22×C3—42no—
812C22×C3—41no—
813C22×C3—41no—
814C22×C3—42no—
815C22×C3—41no—
816C22×C3—82no—
817C22×C3—82no—
818C22×C3—164no—
819C22×C3C2×#12011yescharacteristic
820C22×C3D4211yescharacteristic
821C22×C3#54611yescharacteristic
822C3×C4—22no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—21no—
826C3×C4—21no—
827C3×C4—42no—
828C3×C4—42no—
829C3×C4—41no—
830C3×C4—41no—
831C3×C4—42no—
832C3×C4—41no—
833C3×C4—41no—
834C3×C4—81no—
835C3×C4—81no—
836C3×C4C2×#12111yescharacteristic
837C3×C4#53511yescharacteristic
838C3×C4D4211yescharacteristic
839C3×C4#54611yescharacteristic
840C23—21no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—22no—
845C23—22no—
846C23—44no—
847C23—42no—
848C23—42no—
849C23—82no—
850C23—82no—
851C23C22×C3×D411yescharacteristic
852Q8—21no—
853Q8—22no—
854Q8—22no—
855Q8—21no—
856Q8—21no—
857Q8—21no—
858Q8—21no—
859Q8—44no—
860Q8—41no—
861Q8—41no—
862Q8—41no—
863Q8—41no—
864Q8—41no—
865Q8—41no—
866Q8C3×#12112yes—
867D4—22no—
868D4—22no—
869D4—21no—
870D4—21no—
871D4—21no—
872D4—21no—
873D4—21no—
874D4—44no—
875D4—44no—
876D4—44no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—81no—
887D4—82no—
888D4—82no—
889D4C3×#12112yes—
890C2×C4—21no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—81no—
922C2×C4C3×#12011yescharacteristic
923C2×C4C3×#12011yescharacteristic
924C2×C4C3×#12011yescharacteristic
925C2×C4C3×#12011yescharacteristic
926C2×C4C22×C3×D411yescharacteristic
927C2×C4C22×C3×D411yescharacteristic
928C2×C4C22×C3×D411yescharacteristic
929C2×C4C2×C3×#4111yescharacteristic
930C2×C4C3×H(5,𝔽2)11yescharacteristic
931C2×C4C3×H(5,𝔽2)11yescharacteristic
932C8—22no—
933C8—41no—
934C8—41no—
935C8—41no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—42no—
939C2×C3—81no—
940C2×C3—82no—
941C2×C3—81no—
942C2×C3#240811yescharacteristic
943C2×C3#301811yescharacteristic
944C2×C3#302211yescharacteristic
945C22—21no—
946C22—21no—
947C22—22no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—42no—
953C22—41no—
954C22—42no—
955C22—41no—
956C22—41no—
957C22—42no—
958C22—41no—
959C22—82no—
960C22—82no—
961C22—164no—
962C22C2×C3×#12011yescharacteristic
963C22C3×D4211yescharacteristic
964C22C3×#54611yescharacteristic
965C4—22no—
966C4—21no—
967C4—21no—
968C4—21no—
969C4—21no—
970C4—42no—
971C4—42no—
972C4—41no—
973C4—41no—
974C4—42no—
975C4—41no—
976C4—41no—
977C4—81no—
978C4—81no—
979C4C2×C3×#12111yescharacteristic
980C4C3×#53511yescharacteristic
981C4C3×D4211yescharacteristic
982C4C3×#54611yescharacteristic
983C3#2423511yescharacteristic, direct product factor, Sylow
984C2—21no—
985C2—21no—
986C2—42no—
987C2—82no—
988C2—81no—
989C2—81no—
990C2C3×#240811yescharacteristic
991C2C3×#301811yescharacteristic
992C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3500C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3037C2semidirect
3. C2×C3×#456C2semidirect
4. C2×C3×#455C2semidirect
5. C3×C4×#137C2semidirect
6. C3×#2545C2semidirect
7. C3×#2038C2semidirect
8. C3×#2037C2semidirect
9. C3×#2005C2semidirect
10. C3×#2004C2semidirect
11. C3×#1980C2semidirect
12. C3×#1967C2semidirect
13. C3×#1806C2semidirect
14. C3×#1793C2semidirect
15. C3×#1792C2semidirect
16. #24235C3direct (N × H)
21. C2×C3×#137C22semidirect
34. C2×C3×C4⋊Q8C22semidirect
39. C2×C3×C4×Q8C22semidirect
50. C3×#428C22semidirect
51. C3×#423C22semidirect
56. C2×C3×#104C22semidirect
57. C2×C3×#104C22semidirect
58. C3×#419C22semidirect
61. C3×#417C22semidirect
62. C2×C3×#101C22semidirect
63. C2×C3×#101C22semidirect
66. C3×C4×M16C22semidirect
68. C3×#391C22semidirect
71. C3×C4×C4⋊C4C22semidirect
72. C3×#339C22semidirect
73. C3×#339C22semidirect
75. #3037C2×C3semidirect
76. C2×#456C2×C3semidirect
77. C2×#455C2×C3semidirect
78. C4×#137C2×C3semidirect
79. #2545C2×C3semidirect
80. #2038C2×C3semidirect
81. #2037C2×C3semidirect
82. #2005C2×C3semidirect
83. #2004C2×C3semidirect
84. #1980C2×C3semidirect
85. #1967C2×C3semidirect
86. #1806C2×C3semidirect
87. #1793C2×C3semidirect
88. #1792C2×C3semidirect
118. C3×#137D4semidirect
226. C2×#137C22×C3semidirect
239. C2×C4⋊Q8C22×C3semidirect
244. C2×C4×Q8C22×C3semidirect
255. #428C22×C3semidirect
256. #423C22×C3semidirect
261. C2×#104C22×C3semidirect
262. C2×#104C22×C3semidirect
263. #419C22×C3semidirect
266. #417C22×C3semidirect
267. C2×#101C22×C3semidirect
268. C2×#101C22×C3semidirect
271. C4×M16C22×C3semidirect
273. #391C22×C3semidirect
276. C4×C4⋊C4C22×C3semidirect
277. #339C22×C3semidirect
278. #339C22×C3semidirect
455. #137C3×D4semidirect
983. C3#24235direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#35002
C3×#30372
C2×C3×#4562
C2×C3×#4552
C3×C4×#1372
C3×#25452
C3×#20382
C3×#20372
C3×#20052
C3×#20042
C3×#19802
C3×#19672
C3×#18062
C3×#17932
C3×#17922
#242353