Finite Group Databasebeta

← C2×D3×#909 #11918706

Subgroups — C2×D3×#909 #11918706

Order 1152.

3057 conjugacy classes of subgroups.

The subgroup lattice has 949 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3C2×#64118C211yesmaximal, characteristic, complemented
4C2×C3×#909C211yesmaximal, characteristic, complemented
5C2×C3×D3×M16C211yesmaximal, characteristic, complemented
6C2×#63833C211yesmaximal, characteristic, complemented
7C2×#63831C211yesmaximal, characteristic, complemented
8D3×#909C2116yesmaximal, direct product factor
9C2×#63801C212yesmaximal, complemented
10C2×#63800C212yesmaximal, complemented
11C2×D3×Dic12C212yesmaximal, complemented
12C2×D3×#204C212yesmaximal, complemented
13C2×D3×#137—31nomaximal
14C22×#909—31nomaximal
15C2×#3828C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C2×C3×#235C2211yescharacteristic
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×D3×#67—21no—
21C22×#627—21no—
22C2×#3804—21no—
23C22×D3×Dic3—21no—
24D3×#235—24no—
25D3×#235C2218yes—
26C2×D3×D12C2211yescharacteristic
27C2×C4×D32—21no—
28C2×#3799C2211yescharacteristic
29C2×#3798—21no—
30C2×#3795C2211yescharacteristic
31C2×D3×Dic6—24no—
32C2×D3×Dic6—21no—
33C2×D3×Dic6—21no—
34C2×D3×Dic6C2212yes—
35C2×D3×Dic6C2211yescharacteristic
36C2×D3×Dic6C2218yescomplemented
37C2×D3×Dic6C2212yescomplemented
38C2×C32×M16C2211yescharacteristic, complemented
39#64118C2218yescomplemented
40C2×#3746C2212yescomplemented
41C2×#3744C2212yescomplemented
42C2×C3×#208C2211yescharacteristic, complemented
43C3×#909C2218yescomplemented
44C3×D3×M16C2218yescomplemented
45C2×C3×Dic12C2212yescomplemented
46C2×C3×#204C2212yescomplemented
47C2×C3×ΓL(1,𝔽25)C2212yescomplemented
48C2×C3×D3×C8C2212yes—
49C2×#3719C2212yescomplemented
50C2×#3719C2212yescomplemented
51#63833C2218yescomplemented
52C2×#3717C2212yescomplemented
53#63831C2218yescomplemented
54C2×#3716C2212yescomplemented
55#63801C22116yescomplemented
56#63800C22116yescomplemented
57D3×Dic12C22116yescomplemented
58D3×#204C22116yescomplemented
59C2×D3×#41—31no—
60C22×D3×Q8—31no—
61C22×#235—31no—
62C23×Dic6—31no—
63C2×C3×#137—31no—
64C22×C3×M16—31no—
65C2×#951—31no—
66C2×#942—31no—
67D3×#137—316no—
68C2×#918—32no—
69C2×D3×Q16—32no—
70C2×#915—32no—
71C2×D3×SD16—32no—
72C2×#909—31no—
73C2×#909—31no—
74C2×#909—31no—
75C2×#909—31no—
76C2×#909—316no—
77C2×#909—32no—
78C2×#909—32no—
79C2×#909—61no—
80C2×#909D311yescharacteristic, direct product factor
81C2×D3×M16D311yescharacteristic, complemented
82C22×Dic12—32no—
83C22×#204—32no—
84C23×C3×D3D411yescharacteristic
85C22×D32—21no—
86C22×C32×C4C2311yescharacteristic
87C2×#638—21no—
88C22×C3⋊Dic3—21no—
89#3828—22no—
90#3828C2314yes—
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4×C3⋊D3—21no—
93C2×#634—22no—
94C2×#634—21no—
95C2×#634C2312yes—
96C2×#634C2311yescharacteristic
97C2×#634C2314yescomplemented
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3D411yescharacteristic
101C3×#235—22no—
102C3×#235C2314yes—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3D414yes—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2314yes—
111C2×C3×Dic6—22no—
112C2×C3×Dic6—21no—
113C2×C3×Dic6C2312yes—
114C2×C3×Dic6C2311yescharacteristic
115C2×C3×Dic6C2314yescomplemented
116D3×#67—28no—
117C2×#627—22no—
118C2×#627—28no—
119C2×#627—22no—
120C2×#627—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#625—21no—
124C2×#624—21no—
125#3804—28no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—28no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—21no—
130C2×D3×Dic3—21no—
131D3×D12—22no—
132D3×D12C2314yes—
133C4×D32—28no—
134#3799—22no—
135#3799C2314yes—
136#3798—28no—
137#3795—22no—
138#3795C2314yes—
139D3×Dic6—24no—
140D3×Dic6—28no—
141D3×Dic6—28no—
142D3×Dic6—24no—
143D3×Dic6—22no—
144D3×Dic6C2318yes—
145D3×Dic6C2314yes—
146D3×Dic6C2318yescomplemented
147C32×M16C2314yescomplemented
148C2×C32×C8C2312yes—
149#3746C2318yescomplemented
150#3744C2318yescomplemented
151C3×#208C2314yescomplemented
152C2×C3×C3⋊C8C2312yes—
153C3×Dic12C2318yescomplemented
154C3×#204C2318yescomplemented
155C3×ΓL(1,𝔽25)C2318yescomplemented
156C3×D3×C8C2318yes—
157#3719C2318yescomplemented
158#3719C2318yescomplemented
159#3717C2318yescomplemented
160#3716C2318yescomplemented
161C22×#137—91noSylow
162C2×C3×#41—31no—
163C22×C3×Q8—31no—
164C23×C3×C4—31no—
165C22×#67—61no—
166C23×Dic3—61no—
167D3×#41—38no—
168D3×#41—64no—
169C2×#239—31no—
170C2×D3×Q8—32no—
171C2×D3×Q8—31no—
172C2×D3×Q8—32no—
173C2×D3×Q8—38no—
174C2×D3×Q8—61no—
175C2×D3×Q8—61no—
176C2×D3×Q8—64no—
177C2×#237—31no—
178C2×#237—61no—
179C2×D3×D4—31no—
180C2×D3×D4—61no—
181C2×#235—31no—
182C2×#235—31no—
183C2×#235—38no—
184C2×#235—31no—
185C2×#235—31no—
186C2×#235—61no—
187C2×#235—61no—
188C2×#235—64no—
189C2×#235—61no—
190C2×#235—61no—
191C2×#235C2×D311yescharacteristic
192C22×D12—31no—
193C22×C4×D3—61no—
194C22×C4×D3—61no—
195C22×C4×D3—61no—
196C22×C4×D3C2×D311yescharacteristic
197C22×Dic6—31no—
198C22×Dic6—31no—
199C22×Dic6—32no—
200C22×Dic6—31no—
201C22×Dic6—32no—
202C22×Dic6—38no—
203C22×Dic6—61no—
204C22×Dic6—61no—
205C22×Dic6—64no—
206C22×Dic6—61no—
207C22×Dic6—61no—
208C22×Dic6—61no—
209C22×Dic6C2×D311yescharacteristic, complemented
210C3×#137—38no—
211C2×C3×Q16—32no—
212C2×C3×SD16—32no—
213C2×C3×M16—21no—
214C2×C3×M16—31no—
215C2×C3×M16—38no—
216C2×C3×M16—32no—
217C2×C3×M16C2×D311yescharacteristic, complemented
218C2×C3×M16C2×D311yescharacteristic, complemented
219C22×C3×C8—32no—
220#951—38no—
221C2×#216—32no—
222C2×#216—32no—
223#942—38no—
224C2×#215—32no—
225C2×#214—32no—
226C2×#208C2×D311yescharacteristic, complemented
227#918—316no—
228D3×Q16—316no—
229#915—316no—
230D3×SD16—316no—
231#909—38no—
232#909—38no—
233#909—38no—
234#909—38no—
235#909—316no—
236#909—316no—
237#909—68no—
238#909C2×D318yesdirect product factor
239D3×M16C2×D318yescomplemented
240C2×Dic12—32no—
241C2×Dic12—32no—
242C2×Dic12—32no—
243C2×Dic12—32no—
244C2×Dic12—316no—
245C2×Dic12—62no—
246C2×Dic12C2×D312yescomplemented
247C2×#204—32no—
248C2×#204—32no—
249C2×#204—32no—
250C2×#204—32no—
251C2×#204—316no—
252C2×#204—62no—
253C2×#204C2×D312yescomplemented
254C2×ΓL(1,𝔽25)C2×D312yescomplemented
255C2×D3×C8C2×D312yes—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—24no—
259C22×C3×D3—21no—
260C22×C3×D3C2×D411yescharacteristic
261C22×C3×D3C2×D414yes—
262C22×C3×D3C2×D411yescharacteristic
263C2×D32—24no—
264C2×D32—44no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2×D412yes—
267C2×C32×C4C2411yescharacteristic
268C2×C32×C4C2412yes—
269#638—24no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—22no—
272C2×C3⋊Dic3—24no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2412yes—
275C4×C3⋊D3—24no—
276#634—22no—
277#634—24no—
278#634—21no—
279#634C2414yes—
280#634C2412yes—
281C3×#67—24no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—24no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D414yes—
287C2×C3×Dic3C2×D411yescharacteristic
288C3×D12—21no—
289C3×D12C2412yes—
290C3×C4×D3—24no—
291C3×C4×D3C2×D412yes—
292C3×C4×D3C2×D412yes—
293C3×C4×D3C2×D414yes—
294C3×C4×D3C2×D414yes—
295C3×C4×D3C2412yes—
296C3×C4×D3C2412yes—
297C3×Dic6—22no—
298C3×Dic6—24no—
299C3×Dic6—21no—
300C3×Dic6C2414yes—
301C3×Dic6C2412yes—
302#627—28no—
303#627—28no—
304#627—24no—
305#626—24no—
306#626—24no—
307#625—24no—
308#624—24no—
309D3×Dic3—28no—
310D3×Dic3—28no—
311D3×Dic3—24no—
312D3×Dic3—24no—
313C32×C8C2414yes—
314C3×C3⋊C8C2414yes—
315C22×#41—91no—
316C23×Q8—91no—
317C2×#137—31no—
318C2×#137—92no—
319C2×#137—92no—
320C2×#137—916no—
321C2×#137—91no—
322C2×#137—91no—
323C2×#137—91no—
324C22×Q16—92no—
325C22×SD16—92no—
326C22×M16—31no—
327C24×C3—31no—
328C23×D3—61no—
329C23×D3—61no—
330C23×D3D1211yescharacteristic
331C3×#41—34no—
332C3×#41—62no—
333C2×C3×Q8—32no—
334C2×C3×Q8—34no—
335C2×C3×Q8—31no—
336C2×C3×Q8—61no—
337C2×C3×Q8—62no—
338C2×C3×D4—31no—
339C2×C3×D4—61no—
340C22×C3×C4—21no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—34no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—34no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—21no—
353C2×#67—61no—
354C2×#67—68no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—121no—
361C22×Dic3—21no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3—68no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—121no—
370C22×Dic3D1211yescharacteristic
371#239—34no—
372#239—62no—
373D3×Q8—38no—
374D3×Q8—38no—
375D3×Q8—34no—
376D3×Q8—68no—
377D3×Q8—68no—
378D3×Q8—64no—
379D3×Q8—64no—
380D3×Q8—62no—
381#237—34no—
382#237—68no—
383#237—62no—
384D3×D4—34no—
385D3×D4—68no—
386D3×D4—62no—
387#235—22no—
388#235—34no—
389#235—34no—
390#235—34no—
391#235—34no—
392#235—64no—
393#235—62no—
394#235—68no—
395#235—62no—
396#235—68no—
397#235—62no—
398#235—62no—
399#235—68no—
400#235—122no—
401#235C22×D314yes—
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—34no—
405C2×D12—61no—
406C2×D12—62no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12C22×D311yescharacteristic
410C2×C4×D3—21no—
411C2×C4×D3—68no—
412C2×C4×D3—61no—
413C2×C4×D3—61no—
414C2×C4×D3—61no—
415C2×C4×D3—62no—
416C2×C4×D3—68no—
417C2×C4×D3—62no—
418C2×C4×D3—61no—
419C2×C4×D3—61no—
420C2×C4×D3—61no—
421C2×C4×D3—68no—
422C2×C4×D3—121no—
423C2×C4×D3D1211yescharacteristic
424C2×C4×D3D1211yescharacteristic
425C2×C4×D3D1214yes—
426C2×C4×D3C22×D311yescharacteristic
427C2×C4×D3C22×D311yescharacteristic
428C2×C4×D3C22×D314yes—
429C2×Dic6—22no—
430C2×Dic6—21no—
431C2×Dic6—32no—
432C2×Dic6—32no—
433C2×Dic6—31no—
434C2×Dic6—31no—
435C2×Dic6—34no—
436C2×Dic6—34no—
437C2×Dic6—38no—
438C2×Dic6—34no—
439C2×Dic6—38no—
440C2×Dic6—62no—
441C2×Dic6—61no—
442C2×Dic6—64no—
443C2×Dic6—64no—
444C2×Dic6—64no—
445C2×Dic6—68no—
446C2×Dic6—68no—
447C2×Dic6—62no—
448C2×Dic6—62no—
449C2×Dic6—62no—
450C2×Dic6—68no—
451C2×Dic6—61no—
452C2×Dic6—61no—
453C2×Dic6—62no—
454C2×Dic6—61no—
455C2×Dic6—62no—
456C2×Dic6—62no—
457C2×Dic6—62no—
458C2×Dic6—68no—
459C2×Dic6—61no—
460C2×Dic6—121no—
461C2×Dic6—122no—
462C2×Dic6C22×D312yes—
463C2×Dic6C22×D311yescharacteristic
464C2×Dic6C22×D314yescomplemented
465C3×Q16—38no—
466C3×SD16—38no—
467C3×M16—24no—
468C3×M16—34no—
469C3×M16—38no—
470C3×M16C22×D314yescomplemented
471C3×M16C22×D314yescomplemented
472C2×C3×C8—22no—
473C2×C3×C8—32no—
474C2×C3×C8—38no—
475C2×C3×C8C22×D312yes—
476C2×C3×C8C22×D312yes—
477#216—38no—
478#216—38no—
479#215—38no—
480#214—38no—
481#208C22×D314yescomplemented
482C2×C3⋊C8C22×D312yes—
483Dic12—38no—
484Dic12—38no—
485Dic12—38no—
486Dic12—38no—
487Dic12—68no—
488Dic12C22×D318yescomplemented
489#204—38no—
490#204—38no—
491#204—38no—
492#204—38no—
493#204—68no—
494#204C22×D318yescomplemented
495ΓL(1,𝔽25)C22×D318yescomplemented
496D3×C8C22×D318yes—
497C22×C32—22no—
498C22×C32C22×D412yes—
499C22×C32C22×D411yescharacteristic
500C2×C3⋊D3—22no—
501C2×C3⋊D3—42no—
502C2×C3×D3—22no—
503C2×C3×D3—28no—
504C2×C3×D3—22no—
505C2×C3×D3—42no—
506C2×C3×D3#13714yescomplemented
507C2×C3×D3C22×D412yes—
508C2×C3×D3C22×D412yes—
509D32—48no—
510C32×C4C22×D411yescharacteristic
511C32×C4C22×D412yes—
512C32×C4C2511yescharacteristic
513C3⋊Dic3—22no—
514C3⋊Dic3—24no—
515C3×Dic3—24no—
516C3×Dic3—22no—
517C3×Dic3C22×D412yes—
518C3×Dic3C22×D412yes—
519C2×#41—31no—
520C2×#41—91no—
521C2×#41—91no—
522C2×#41—98no—
523C2×#41—91no—
524C2×#41—181no—
525C2×#41—181no—
526C2×#41—184no—
527C22×Q8—31no—
528C22×Q8—92no—
529C22×Q8—91no—
530C22×Q8—92no—
531C22×Q8—98no—
532C22×Q8—91no—
533C22×Q8—181no—
534C22×Q8—181no—
535C22×Q8—184no—
536C22×Q8—181no—
537C22×D4—91no—
538C22×D4—181no—
539C23×C4—31no—
540C23×C4—181no—
541C23×C4—181no—
542#137—38no—
543#137—916no—
544#137—916no—
545#137—98no—
546#137—98no—
547#137—98no—
548C2×Q16—32no—
549C2×Q16—916no—
550C2×Q16—92no—
551C2×Q16—92no—
552C2×Q16—92no—
553C2×SD16—32no—
554C2×SD16—916no—
555C2×SD16—92no—
556C2×SD16—92no—
557C2×SD16—92no—
558C2×M16—31no—
559C2×M16—38no—
560C2×M16—32no—
561C2×M16D3211yescharacteristic, complemented
562C22×C8—32no—
563C23×C3—21no—
564C23×C3—31no—
565C23×C3—34no—
566C23×C3—31no—
567C23×C3—64no—
568C23×C3—61no—
569C23×C3C2×D1211yescharacteristic
570C23×C3D3×D411yescharacteristic
571C22×D3—24no—
572C22×D3—21no—
573C22×D3—64no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—64no—
577C22×D3—121no—
578C22×D3—124no—
579C22×D3—124no—
580C22×D3C2×D1211yescharacteristic
581C22×D3C2×D1214yes—
582C22×D3C2×D1211yescharacteristic
583C3×Q8—34no—
584C3×Q8—32no—
585C3×Q8—62no—
586C3×Q8—64no—
587C3×Q8—61no—
588C3×D4—32no—
589C3×D4—64no—
590C3×D4—61no—
591C2×C3×C4—21no—
592C2×C3×C4—22no—
593C2×C3×C4—21no—
594C2×C3×C4—22no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—34no—
598C2×C3×C4—32no—
599C2×C3×C4—34no—
600C2×C3×C4—34no—
601C2×C3×C4—32no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—64no—
605C2×C3×C4—62no—
606C2×C3×C4—61no—
607C2×C3×C4—64no—
608C2×C3×C4C2×D1211yescharacteristic
609C2×C3×C4C2×D1212yes—
610C2×C3×C4D3×D411yescharacteristic
611C2×C3×C4D3×D412yes—
612C2×C3×C4C23×D311yescharacteristic
613C2×C3×C4C23×D312yes—
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D312yes—
616#67—24no—
617#67—64no—
618#67—64no—
619#67—64no—
620#67—64no—
621#67—64no—
622#67—64no—
623#67—124no—
624C2×Dic3—22no—
625C2×Dic3—24no—
626C2×Dic3—21no—
627C2×Dic3—68no—
628C2×Dic3—68no—
629C2×Dic3—64no—
630C2×Dic3—64no—
631C2×Dic3—62no—
632C2×Dic3—61no—
633C2×Dic3—64no—
634C2×Dic3—62no—
635C2×Dic3—61no—
636C2×Dic3—64no—
637C2×Dic3—124no—
638C2×Dic3—122no—
639C2×Dic3—121no—
640C2×Dic3C2×D1211yescharacteristic
641C2×Dic3C2×D1211yescharacteristic
642C2×Dic3C2×D1214yes—
643D12—21no—
644D12—32no—
645D12—32no—
646D12—62no—
647D12—64no—
648D12—64no—
649D12—61no—
650D12—61no—
651D12—121no—
652D12C23×D312yes—
653C4×D3—24no—
654C4×D3—64no—
655C4×D3—64no—
656C4×D3—64no—
657C4×D3—68no—
658C4×D3—68no—
659C4×D3—64no—
660C4×D3—64no—
661C4×D3—64no—
662C4×D3—124no—
663C4×D3C2×D1214yes—
664C4×D3C2×D1214yes—
665C4×D3C2×D1212yes—
666C4×D3C2×D1212yes—
667C4×D3C23×D312yes—
668C4×D3C23×D312yes—
669Dic6—22no—
670Dic6—24no—
671Dic6—21no—
672Dic6—34no—
673Dic6—34no—
674Dic6—32no—
675Dic6—32no—
676Dic6—64no—
677Dic6—62no—
678Dic6—68no—
679Dic6—68no—
680Dic6—64no—
681Dic6—62no—
682Dic6—64no—
683Dic6—61no—
684Dic6—62no—
685Dic6—64no—
686Dic6—61no—
687Dic6—68no—
688Dic6—68no—
689Dic6—64no—
690Dic6—122no—
691Dic6—124no—
692Dic6—121no—
693Dic6C23×D314yes—
694Dic6C23×D312yes—
695C3×C8—24no—
696C3×C8—34no—
697C3×C8C23×D314yes—
698C3×C8C23×D314yes—
699C3⋊C8C23×D314yes—
700C2×C32—22no—
701C2×C32C2×#13712yescomplemented
702C2×C32C23×D411yescharacteristic
703C3⋊D3—42no—
704C3×D3—22no—
705C3×D3—42no—
706C3×D3C2×#13714yescomplemented
707C24—31no—
708C24—181no—
709#41—34no—
710#41—62no—
711#41—94no—
712#41—94no—
713#41—94no—
714#41—188no—
715#41—188no—
716#41—182no—
717#41—182no—
718#41—182no—
719C2×Q8—32no—
720C2×Q8—31no—
721C2×Q8—34no—
722C2×Q8—62no—
723C2×Q8—61no—
724C2×Q8—98no—
725C2×Q8—94no—
726C2×Q8—98no—
727C2×Q8—92no—
728C2×Q8—91no—
729C2×Q8—94no—
730C2×Q8—188no—
731C2×Q8—182no—
732C2×Q8—182no—
733C2×Q8—181no—
734C2×Q8—188no—
735C2×Q8—184no—
736C2×Q8—184no—
737C2×Q8—188no—
738C2×Q8—182no—
739C2×Q8—182no—
740C2×Q8—181no—
741C2×D4—31no—
742C2×D4—61no—
743C2×D4—94no—
744C2×D4—91no—
745C2×D4—182no—
746C2×D4—181no—
747C2×D4—181no—
748C2×D4—188no—
749C2×D4—181no—
750C2×D4—181no—
751C22×C4—31no—
752C22×C4—31no—
753C22×C4—34no—
754C22×C4—31no—
755C22×C4—31no—
756C22×C4—34no—
757C22×C4—31no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—181no—
761C22×C4—188no—
762C22×C4—181no—
763C22×C4—181no—
764C22×C4—188no—
765C22×C4—182no—
766C22×C4—182no—
767C22×C4—181no—
768C22×C4—181no—
769C22×C4C2×D3211yescharacteristic
770Q16—38no—
771Q16—98no—
772Q16—98no—
773Q16—98no—
774SD16—38no—
775SD16—98no—
776SD16—98no—
777SD16—98no—
778M16—34no—
779M16—38no—
780M16C2×D3214yescomplemented
781C2×C8—32no—
782C2×C8—38no—
783C2×C8C2×D3212yes—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—21no—
788C22×C3—32no—
789C22×C3—34no—
790C22×C3—32no—
791C22×C3—42no—
792C22×C3—68no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—122no—
796C22×C3C22×D1212yes—
797C22×C3C22×D1211yescharacteristic
798C22×C3C2×D3×D412yes—
799C22×C3C2×D3×D411yescharacteristic
800C2×D3—22no—
801C2×D3—28no—
802C2×D3—22no—
803C2×D3—42no—
804C2×D3—62no—
805C2×D3—62no—
806C2×D3—122no—
807C2×D3—128no—
808C2×D3—122no—
809C2×D3—122no—
810C2×D3—128no—
811C2×D3—242no—
812C2×D3#90914yesdirect product factor
813C2×D3C22×D1212yes—
814C2×D3C22×D1212yes—
815C3×C4—21no—
816C3×C4—22no—
817C3×C4—21no—
818C3×C4—32no—
819C3×C4—32no—
820C3×C4—64no—
821C3×C4—62no—
822C3×C4C22×D1211yescharacteristic
823C3×C4C22×D1212yes—
824C3×C4C2×D3×D411yescharacteristic
825C3×C4C2×D3×D412yes—
826C3×C4C24×D311yescharacteristic
827C3×C4C24×D311yescharacteristic
828Dic3—24no—
829Dic3—22no—
830Dic3—64no—
831Dic3—62no—
832Dic3—64no—
833Dic3—62no—
834Dic3—124no—
835Dic3—122no—
836Dic3C22×D1212yes—
837Dic3C22×D1212yes—
838C32C22×#13711yescharacteristic, complemented, Sylow
839C23—31no—
840C23—34no—
841C23—31no—
842C23—64no—
843C23—61no—
844C23—184no—
845C23—181no—
846C23—364no—
847C23D3×D1211yescharacteristic
848Q8—34no—
849Q8—32no—
850Q8—64no—
851Q8—62no—
852Q8—61no—
853Q8—94no—
854Q8—92no—
855Q8—188no—
856Q8—188no—
857Q8—184no—
858Q8—184no—
859Q8—182no—
860Q8—181no—
861D4—32no—
862D4—64no—
863D4—61no—
864D4—92no—
865D4—184no—
866D4—184no—
867D4—184no—
868D4—184no—
869D4—181no—
870C2×C4—34no—
871C2×C4—31no—
872C2×C4—31no—
873C2×C4—34no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—34no—
877C2×C4—32no—
878C2×C4—32no—
879C2×C4—64no—
880C2×C4—61no—
881C2×C4—62no—
882C2×C4—64no—
883C2×C4—184no—
884C2×C4—184no—
885C2×C4—184no—
886C2×C4—188no—
887C2×C4—188no—
888C2×C4—184no—
889C2×C4—181no—
890C2×C4—182no—
891C2×C4—184no—
892C2×C4D3×D1212yes—
893C2×C4D3×D1211yescharacteristic
894C2×C4C22×D3212yes—
895C2×C4C22×D3211yescharacteristic
896C8—34no—
897C8C22×D3214yes—
898C2×C3—22no—
899C2×C3—22no—
900C2×C3—21no—
901C2×C3—22no—
902C2×C3—34no—
903C2×C3—42no—
904C2×C3—62no—
905C2×C3—122no—
906C2×C3C2×#90912yescomplemented
907C2×C3D3×#13712yescomplemented
908C2×C3C23×D1211yescharacteristic
909C2×C3C22×D3×D411yescharacteristic
910D3—22no—
911D3—42no—
912D3—122no—
913D3—122no—
914D3—242no—
915D3C2×#90914yesdirect product factor
916C22—22no—
917C22—32no—
918C22—34no—
919C22—32no—
920C22—68no—
921C22—62no—
922C22—62no—
923C22—122no—
924C22—182no—
925C22—368no—
926C22—362no—
927C22C2×D3×D1212yes—
928C22C2×D3×D1211yescharacteristic
929C4—32no—
930C4—32no—
931C4—62no—
932C4—64no—
933C4—182no—
934C4—184no—
935C4C2×D3×D1212yes—
936C4C2×D3×D1211yescharacteristic
937C4C23×D3211yescharacteristic
938C3—21no—
939C3C22×#90911yescharacteristic, complemented
940C3C2×D3×#13711yescharacteristic, complemented
941C2—22no—
942C2—34no—
943C2—62no—
944C2—122no—
945C2—362no—
946C2D3×#90912yesdirect product factor
947C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC2×D3×#235C2
hypercenterC2×M16D32
hypocenterC32C22×#137
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C22×D3×Dic6C2semidirect
3. C2×#64118C2semidirect
4. C2×C3×#909C2semidirect
5. C2×C3×D3×M16C2semidirect
6. C2×#63833C2semidirect
7. C2×#63831C2semidirect
8. D3×#909C2direct (N × H)
9. C2×#63801C2semidirect
10. C2×#63800C2semidirect
11. C2×D3×Dic12C2semidirect
12. C2×D3×#204C2semidirect
16. C22×#634C22semidirect
19. C22×C3×Dic6C22semidirect
36. C2×D3×Dic6C22semidirect
37. C2×D3×Dic6C22semidirect
38. C2×C32×M16C22semidirect
39. #64118C22semidirect
40. C2×#3746C22semidirect
41. C2×#3744C22semidirect
42. C2×C3×#208C22semidirect
43. C3×#909C22semidirect
44. C3×D3×M16C22semidirect
45. C2×C3×Dic12C22semidirect
46. C2×C3×#204C22semidirect
47. C2×C3×ΓL(1,𝔽25)C22semidirect
49. C2×#3719C22semidirect
50. C2×#3719C22semidirect
51. #63833C22semidirect
52. C2×#3717C22semidirect
53. #63831C22semidirect
54. C2×#3716C22semidirect
55. #63801C22semidirect
56. #63800C22semidirect
57. D3×Dic12C22semidirect
58. D3×#204C22semidirect
80. C2×#909D3direct (N × H)
81. C2×D3×M16D3semidirect
97. C2×#634C23semidirect
115. C2×C3×Dic6C23semidirect
146. D3×Dic6C23semidirect
147. C32×M16C23semidirect
149. #3746C23semidirect
150. #3744C23semidirect
151. C3×#208C23semidirect
153. C3×Dic12C23semidirect
154. C3×#204C23semidirect
155. C3×ΓL(1,𝔽25)C23semidirect
157. #3719C23semidirect
158. #3719C23semidirect
159. #3717C23semidirect
160. #3716C23semidirect
209. C22×Dic6C2×D3semidirect
217. C2×C3×M16C2×D3semidirect
218. C2×C3×M16C2×D3semidirect
226. C2×#208C2×D3semidirect
238. #909C2×D3direct (N × H)
239. D3×M16C2×D3semidirect
246. C2×Dic12C2×D3semidirect
253. C2×#204C2×D3semidirect
254. C2×ΓL(1,𝔽25)C2×D3semidirect
464. C2×Dic6C22×D3semidirect
470. C3×M16C22×D3semidirect
471. C3×M16C22×D3semidirect
481. #208C22×D3semidirect
488. Dic12C22×D3semidirect
494. #204C22×D3semidirect
495. ΓL(1,𝔽25)C22×D3semidirect
506. C2×C3×D3#137semidirect
561. C2×M16D32semidirect
701. C2×C32C2×#137semidirect
706. C3×D3C2×#137semidirect
780. M16C2×D32semidirect
812. C2×D3#909direct (N × H)
838. C32C22×#137semidirect
906. C2×C3C2×#909semidirect
907. C2×C3D3×#137semidirect
915. D3C2×#909direct (N × H)
939. C3C22×#909semidirect
940. C3C2×D3×#137semidirect
946. C2D3×#909direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C22×D3×Dic62
C2×#641182
C2×C3×#9092
C2×C3×D3×M162
C2×#638332
C2×#638312
D3×#9092
C2×#638012
C2×#638002
C2×D3×Dic122
C2×D3×#2042
C2×D3×#1373
C22×#9093