Finite Group Databasebeta

← Dic3×#4064 #14416864

Subgroups — Dic3×#4064 #14416864

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4064C211yesmaximal, characteristic
2Dic3×#713C211yesmaximal, characteristic
3Q8×D5×Dic3C211yesmaximal, characteristic, complemented
4#11751285C211yesmaximal, characteristic, complemented
5C5×Dic3×Q16C211yesmaximal, characteristic, complemented
6#11749264C211yesmaximal, characteristic, complemented
7Dic3×#689C211yesmaximal, characteristic, complemented
8#11749241C211yesmaximal, characteristic, complemented
9Dic3×#688C211yesmaximal, characteristic, complemented
10#11749208C211yesmaximal, characteristic, complemented
11#11749198C211yesmaximal, characteristic
12#11747812C211yesmaximal, characteristic, complemented
13Dic3×#677C211yesmaximal, characteristic, complemented
14#11747619C211yesmaximal, characteristic, complemented
15Dic3×#676C211yesmaximal, characteristic, complemented
16C4×#4064—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×Q8×D5C2211yescharacteristic
19C2×C3×C5×Q16C2211yescharacteristic
20Q8×Dic15C2211yescharacteristic
21Q8×Dic15C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C5×Q8×Dic3C2211yescharacteristic
24C2×C3×#689C2211yescharacteristic
25C2×C3×#688C2211yescharacteristic
26C3×#4064C418yescomplemented
27C2×C3×#677C2211yescharacteristic
28C2×C3×#676C2211yescharacteristic
29#91434—21no—
30#91434C2211yescharacteristic
31Dic3×D20—21no—
32Dic3×D20C2211yescharacteristic
33D5×C4⋊Dic3—21no—
34D5×C4⋊Dic3C2211yescharacteristic
35C4×D5×Dic3—21no—
36C4×D5×Dic3—21no—
37C4×D5×Dic3C2211yescharacteristic
38#91358—21no—
39#91358C2211yescharacteristic
40#91331—21no—
41#91331C2211yescharacteristic
42Dic3×Dic10—21no—
43Dic3×Dic10C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45#91119C2211yescharacteristic
46#91119C2211yescharacteristic
47#91101C2211yescharacteristic
48#91099C2211yescharacteristic
49C5×#835C2211yescharacteristic
50C5×#835C2211yescharacteristic
51C5×#818C2211yescharacteristic
52C5×C8×Dic3C2211yescharacteristic
53#90988C2211yescharacteristic
54#90985C2211yescharacteristic
55#90971C2211yescharacteristic
56#90970C2211yescharacteristic
57#90965C2211yescharacteristic
58#90964C2211yescharacteristic
59#90954C2211yescharacteristic
60Dic3×#168C2211yescharacteristic
61Dic3×#137—51nomaximal, Hall
62C2×#4064D311yescharacteristic
63C4×#713—31no—
64C4×Q8×D5—31no—
65C4×C5×Q16—31no—
66#65473—31no—
67C4×#689—31no—
68C4×#688—31no—
69#65178—31no—
70#65170—31no—
71#65106—31no—
72#65092—31no—
73#65091—31no—
74#65078—31no—
75C4×#677—31no—
76C4×#676—31no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×Q8C2311yescharacteristic
79C3×#713—22no—
80C3×#713C2×C414yes—
81C3×Q8×D5—22no—
82C3×Q8×D5C2×C414yescomplemented
83C2×C3×D20—21no—
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5C2311yescharacteristic
88C2×C3×Dic10—21no—
89C2×C3×Dic10C2311yescharacteristic
90C2×D5×Dic3—21no—
91C2×D5×Dic3—21no—
92C2×D5×Dic3—21no—
93C2×D5×Dic3D411yescharacteristic
94C2×D5×Dic3D411yescharacteristic
95C3×C5×Q16C2×C414yescomplemented
96C2×C3×C5×C8C2311yescharacteristic
97C4⋊Dic15—21no—
98C4⋊Dic15—21no—
99C4⋊Dic15C2311yescharacteristic
100C4⋊Dic15C2311yescharacteristic
101C4×Dic15—21no—
102C4×Dic15—21no—
103C4×Dic15C2311yescharacteristic
104C2×C3⋊#168C2311yescharacteristic
105C5×C4⋊Dic3—21no—
106C5×C4⋊Dic3—21no—
107C5×C4⋊Dic3C2311yescharacteristic
108C5×C4⋊Dic3C2311yescharacteristic
109C4×C5×Dic3—21no—
110C4×C5×Dic3—21no—
111C4×C5×Dic3C2311yescharacteristic
112C2×C5×C3⋊C8C2311yescharacteristic
113C3×#689C2×C414yescomplemented
114C3×#688C2×C414yescomplemented
115C2×C3×#168C2311yescharacteristic
116C3×#677C2×C414yescomplemented
117C3×#676C2×C414yescomplemented
118#6668—21no—
119#6668—21no—
120#6668—21no—
121#6665—21no—
122#6665—21no—
123#6665—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127Dic3×Dic5D411yescharacteristic
128Dic3×Dic5D411yescharacteristic
129#6649—22no—
130C2×C3×#137—51no—
131Dic3×#41—51no—
132C2×Q8×Dic3—51no—
133#5232—51no—
134#5225—51no—
135#5184—51no—
136#5184—51no—
137Dic3×Q16—51no—
138Dic3×Q16D511yescharacteristic, complemented
139#5164—51no—
140#5164—51no—
141Dic3×SD16—51no—
142Dic3×SD16—51no—
143#5121—51no—
144Dic3×M16—51no—
145C2×#713C2×D311yescharacteristic
146C2×Q8×D5C2×D311yescharacteristic
147C2×C5×Q16C2×D311yescharacteristic
148C4×C5×Q8—31no—
149C4×C5×Q8—31no—
150Q8×Dic5—31no—
151Q8×Dic5—31no—
152C2×#689C2×D311yescharacteristic
153C2×#688C2×D311yescharacteristic
154#4064Dic318yesdirect product factor
155C2×#677C2×D311yescharacteristic
156C2×#676—31no—
157C2×#676C2×D311yescharacteristic
158#4039—31no—
159#4039—61no—
160#4038—31no—
161#4038—61no—
162D5×C4⋊C4—31no—
163D5×C4⋊C4—61no—
164#4033—31no—
165#4033—61no—
166C4×D20—31no—
167C4×D20—61no—
168C42×D5—31no—
169C42×D5—61no—
170C42×D5—61no—
171C4×Dic10—31no—
172C4×Dic10—61no—
173C5×#107—31no—
174C5×#103—31no—
175C5×#103—31no—
176C4×C5×C8—31no—
177#3967—31no—
178#3967—31no—
179#3953—31no—
180#3949—31no—
181#3948—31no—
182#3947—31no—
183#3947—31no—
184#3942—31no—
185#3941—31no—
186#3940—31no—
187#3939—31no—
188C4×#168—31no—
189C4×#137—151noSylow
190C22×C3×D5—21no—
191C22×C3×D5C2×D411yescharacteristic
192C3×C5×Q8—21no—
193C3×C5×Q8—21no—
194C3×C5×Q8C22×C412yes—
195C3×C5×Q8C22×C412yes—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C2411yescharacteristic
199C2×Dic15—21no—
200C2×Dic15—21no—
201C2×Dic15C2×D411yescharacteristic
202C2×Dic15C2×D411yescharacteristic
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3C2×D411yescharacteristic
206C2×C5×Dic3C2×D411yescharacteristic
207C2×C3×Dic5—21no—
208C2×C3×Dic5C2×D411yescharacteristic
209C3×D20—24no—
210C3×D20—21no—
211C3×D20C22×C412yes—
212C3×C4×D5—24no—
213C3×C4×D5—24no—
214C3×C4×D5C22×C412yes—
215C3×C4×D5#4112yes—
216C3×Dic10—21no—
217C3×Dic10—24no—
218C3×Dic10C22×C412yes—
219D5×Dic3—22no—
220D5×Dic3—41no—
221D5×Dic3—42no—
222D5×Dic3—42no—
223D5×Dic3—42no—
224C3×C5×C8C22×C412yes—
225C3⋊#168—21no—
226C3×#168C22×C412yes—
227C5×C3⋊C8—21no—
228C2×C3×#41—51no—
229C22×C3×Q8—51no—
230C3×#137—58no—
231C2×C3×Q16—51no—
232C2×C3×Q16C2×D511yescharacteristic
233C2×C3×SD16—51no—
234C2×C3×SD16—51no—
235C2×C3×M16—51no—
236Q8×Dic3—51no—
237Q8×Dic3—51no—
238Q8×Dic3—51no—
239Q8×Dic3—51no—
240Q8×Dic3—101no—
241Q8×Dic3—101no—
242Q8×Dic3C2×D511yescharacteristic
243Q8×Dic3C2×D511yescharacteristic
244D4×Dic3—51no—
245D4×Dic3—51no—
246D4×Dic3—101no—
247D4×Dic3—101no—
248#926—51no—
249#926—101no—
250C2×C4⋊Dic3—51no—
251C2×C4⋊Dic3—101no—
252C2×C4×Dic3—51no—
253C2×C4×Dic3—101no—
254C2×C4×Dic3—101no—
255C2×#208—51no—
256#835—51no—
257#835—51no—
258#835—51no—
259#835—51no—
260#835C2×D511yescharacteristic
261#835C2×D511yescharacteristic
262#832—51no—
263#832—51no—
264#818—51no—
265#818C2×D511yescharacteristic
266#817—51no—
267#817—51no—
268#815—51no—
269#815—51no—
270C8×Dic3—51no—
271C8×Dic3C2×D511yescharacteristic
272C2×C5×Q8C22×D311yescharacteristic
273C2×C5×Q8C22×D311yescharacteristic
274#713—22no—
275#713C2×Dic314yes—
276Q8×D5—22no—
277Q8×D5C2×Dic314yescomplemented
278C2×D20—21no—
279C2×D20C22×D311yescharacteristic
280C2×C4×D5—21no—
281C2×C4×D5—21no—
282C2×C4×D5—31no—
283C2×C4×D5—31no—
284C2×C4×D5—61no—
285C2×C4×D5—61no—
286C2×C4×D5—61no—
287C2×C4×D5C22×D311yescharacteristic
288C2×Dic10—21no—
289C2×Dic10C22×D311yescharacteristic
290C5×Q16C2×Dic314yescomplemented
291C2×C5×C8—31no—
292C2×C5×C8C22×D311yescharacteristic
293C5×C4⋊C4—31no—
294C5×C4⋊C4—31no—
295C5×C4⋊C4—61no—
296C5×C4⋊C4—61no—
297C42×C5—31no—
298C42×C5—61no—
299C42×C5—61no—
300#689C2×Dic314yescomplemented
301#688C2×Dic314yescomplemented
302#685—61no—
303#685—61no—
304#685—61no—
305C4⋊Dic5—31no—
306C4⋊Dic5—31no—
307C4⋊Dic5—61no—
308C4⋊Dic5—61no—
309#683—61no—
310#683—61no—
311#683—61no—
312C4×Dic5—31no—
313C4×Dic5—31no—
314C4×Dic5—31no—
315C4×Dic5—61no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C4×Dic5—61no—
319C4×Dic5—61no—
320C2×#168—31no—
321C2×#168C22×D311yescharacteristic
322#677C2×Dic314yescomplemented
323#676—62no—
324#676C2×Dic314yescomplemented
325C2×#137—51no—
326C4×#41—151no—
327C2×C4×Q8—151no—
328#441—151no—
329#441—151no—
330#440—151no—
331#440—151no—
332C4×Q16—31no—
333C4×Q16—151no—
334C4×SD16—151no—
335C4×SD16—151no—
336#428—151no—
337#419—151no—
338#417—151no—
339C4×M16—151no—
340C22×C3×C5C22×D411yescharacteristic
341C2×C3×D5—21no—
342C2×C3×D5—21no—
343C2×C3×D5—22no—
344C2×C3×D5—41no—
345C2×C3×D5—41no—
346C2×C3×D5C4×D412yes—
347C3×C4×C5—22no—
348C3×C4×C5—22no—
349C3×C4×C5C23×C411yescharacteristic
350C3×C4×C5C2×#4111yescharacteristic
351Dic15—21no—
352Dic15—21no—
353Dic15—41no—
354Dic15—41no—
355C3×Dic5—22no—
356C3×Dic5C4×D412yes—
357C5×Dic3—21no—
358C5×Dic3—41no—
359C5×Dic3—41no—
360C5×Dic3#13712yescomplemented
361C3×#41—54no—
362C3×#41—102no—
363C2×C3×Q8—54no—
364C2×C3×Q8—51no—
365C2×C3×Q8—101no—
366C2×C3×Q8—102no—
367C2×C3×Q8C22×D511yescharacteristic
368C2×C3×Q8C22×D511yescharacteristic
369C2×C3×D4—51no—
370C2×C3×D4—101no—
371C22×C3×C4—51no—
372C22×C3×C4—101no—
373C22×C3×C4—101no—
374C22×Dic3—51no—
375C22×Dic3—51no—
376C22×Dic3—101no—
377C22×Dic3—101no—
378C22×Dic3—101no—
379C3×Q16—54no—
380C3×Q16C4×D514yescomplemented
381C3×SD16—54no—
382C3×SD16—54no—
383C3×M16—54no—
384C2×C3×C8—51no—
385C2×C3×C8C22×D511yescharacteristic
386#217—101no—
387#217—101no—
388#217—101no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—51no—
392C4⋊Dic3—51no—
393C4⋊Dic3—101no—
394C4⋊Dic3—101no—
395C4⋊Dic3—101no—
396C4⋊Dic3—101no—
397C4⋊Dic3—101no—
398C4⋊Dic3C22×D511yescharacteristic
399C4⋊Dic3C22×D511yescharacteristic
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—51no—
403C4×Dic3—51no—
404C4×Dic3—51no—
405C4×Dic3—101no—
406C4×Dic3—101no—
407C4×Dic3—101no—
408C4×Dic3—101no—
409C4×Dic3—101no—
410C4×Dic3C22×D511yescharacteristic
411#208—102no—
412C2×C3⋊C8—51no—
413C2×C3⋊C8C22×D511yescharacteristic
414C22×D5—21no—
415C22×D5D3×D411yescharacteristic
416C5×Q8—21no—
417C5×Q8—21no—
418C5×Q8C22×Dic312yes—
419C5×Q8C22×Dic312yes—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—31no—
423C2×C4×C5—31no—
424C2×C4×C5—61no—
425C2×C4×C5—61no—
426C2×C4×C5C23×D311yescharacteristic
427C2×Dic5—21no—
428C2×Dic5—31no—
429C2×Dic5—31no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5D3×D411yescharacteristic
433D20—24no—
434D20—21no—
435D20C22×Dic312yes—
436C4×D5—24no—
437C4×D5—24no—
438C4×D5—62no—
439C4×D5—121no—
440C4×D5—122no—
441C4×D5—122no—
442C4×D5—122no—
443C4×D5#23712yes—
444C4×D5C22×Dic312yes—
445Dic10—21no—
446Dic10—24no—
447Dic10C22×Dic312yes—
448C5×C8—61no—
449C5×C8C22×Dic312yes—
450#168—61no—
451#168C22×Dic312yes—
452C2×#41—51no—
453C22×Q8—51no—
454#137—58no—
455C2×Q16—51no—
456C2×Q16D3×D511yescharacteristic
457C2×SD16—51no—
458C2×SD16—51no—
459C2×M16—51no—
460C2×M16—151no—
461C4×Q8—31no—
462C4×Q8—31no—
463C4×Q8—151no—
464C4×Q8—151no—
465C4×Q8—151no—
466C4×Q8—151no—
467C4×Q8—301no—
468C4×Q8—301no—
469C4×D4—151no—
470C4×D4—151no—
471C4×D4—301no—
472C4×D4—301no—
473#117—151no—
474#117—301no—
475C2×C4⋊C4—151no—
476C2×C4⋊C4—301no—
477C2×C42—151no—
478C2×C42—301no—
479C2×C42—301no—
480#107—31no—
481#107—151no—
482#106—151no—
483#106—151no—
484#103—31no—
485#103—31no—
486#103—151no—
487#103—151no—
488#103—151no—
489#103—151no—
490#102—151no—
491#102—151no—
492#97—151no—
493#97—151no—
494C4×C8—31no—
495C4×C8—151no—
496C2×C3×C5C2×C4×D411yescharacteristic
497C2×C3×C5C2×#13711yescharacteristic
498C2×C3×C5#57511yescharacteristic
499C3×D5—22no—
500C3×D5—42no—
501C23×C3—51no—
502C23×C3—101no—
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—52no—
506C3×Q8—104no—
507C3×Q8—101no—
508C3×Q8C2×C4×D512yes—
509C3×Q8C2×C4×D512yes—
510C3×D4—52no—
511C3×D4—104no—
512C3×D4—101no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—51no—
516C2×C3×C4—52no—
517C2×C3×C4—52no—
518C2×C3×C4—104no—
519C2×C3×C4—104no—
520C2×C3×C4—101no—
521C2×C3×C4C23×D511yescharacteristic
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—51no—
525C2×Dic3—51no—
526C2×Dic3—102no—
527C2×Dic3—101no—
528C2×Dic3—101no—
529C2×Dic3—201no—
530C2×Dic3—202no—
531C2×Dic3—202no—
532C2×Dic3—202no—
533C2×Dic3D4×D511yescharacteristic
534C2×Dic3D4×D511yescharacteristic
535C3×C8—52no—
536C3×C8C2×C4×D512yes—
537C3⋊C8—21no—
538C3⋊C8—101no—
539C22×C5C2×D3×D411yescharacteristic
540C2×D5—21no—
541C2×D5—21no—
542C2×D5—22no—
543C2×D5—41no—
544C2×D5—41no—
545C2×D5D4×Dic312yes—
546C4×C5—22no—
547C4×C5—22no—
548C4×C5—32no—
549C4×C5—61no—
550C4×C5—121no—
551C4×C5—121no—
552C4×C5C2×#23711yescharacteristic
553C4×C5C23×Dic311yescharacteristic
554Dic5—22no—
555Dic5—61no—
556Dic5—61no—
557Dic5—121no—
558Dic5—121no—
559Dic5D4×Dic312yes—
560#41—54no—
561#41—102no—
562C2×Q8—54no—
563C2×Q8—51no—
564C2×Q8—101no—
565C2×Q8—102no—
566C2×Q8C2×D3×D511yescharacteristic
567C2×Q8C2×D3×D511yescharacteristic
568C2×D4—51no—
569C2×D4—101no—
570C22×C4—51no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—151no—
574C22×C4—151no—
575C22×C4—301no—
576C22×C4—301no—
577C22×C4—301no—
578Q16—54no—
579Q16D5×Dic314yescomplemented
580SD16—54no—
581SD16—54no—
582M16—54no—
583M16—302no—
584C2×C8—31no—
585C2×C8—51no—
586C2×C8—151no—
587C2×C8C2×D3×D511yescharacteristic
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—151no—
593C4⋊C4—151no—
594C4⋊C4—301no—
595C4⋊C4—301no—
596C4⋊C4—301no—
597C4⋊C4—301no—
598C4⋊C4—301no—
599C22⋊C4—301no—
600C22⋊C4—301no—
601C22⋊C4—301no—
602C42—31no—
603C42—61no—
604C42—61no—
605C42—151no—
606C42—151no—
607C42—151no—
608C42—301no—
609C42—301no—
610C42—301no—
611C42—301no—
612C42—301no—
613C3×C5C4×#13711yescharacteristic, complemented, Hall
614C22×C3—52no—
615C22×C3—101no—
616C22×C3—101no—
617C22×C3—102no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3C2×D4×D511yescharacteristic
621C3×C4—22no—
622C3×C4—22no—
623C3×C4—52no—
624C3×C4—102no—
625C3×C4C22×C4×D511yescharacteristic
626C3×C4D5×#4111yescharacteristic
627Dic3—21no—
628Dic3—41no—
629Dic3—41no—
630Dic3—101no—
631Dic3—101no—
632Dic3—201no—
633Dic3—201no—
634Dic3#406412yesdirect product factor
635C2×C5D3×#13711yescharacteristic
636C2×C5#577711yescharacteristic
637C2×C5C2×D4×Dic311yescharacteristic
638D5—22no—
639D5—42no—
640C23—51no—
641C23—101no—
642Q8—21no—
643Q8—21no—
644Q8—52no—
645Q8—104no—
646Q8—101no—
647Q8C2×D5×Dic312yes—
648Q8C2×D5×Dic312yes—
649D4—52no—
650D4—104no—
651D4—101no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—31no—
655C2×C4—31no—
656C2×C4—51no—
657C2×C4—52no—
658C2×C4—52no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—104no—
662C2×C4—104no—
663C2×C4—101no—
664C2×C4—151no—
665C2×C4—151no—
666C2×C4—302no—
667C2×C4—301no—
668C2×C4—301no—
669C2×C4—602no—
670C2×C4—601no—
671C2×C4—602no—
672C2×C4—602no—
673C2×C4C22×D3×D511yescharacteristic
674C8—52no—
675C8—61no—
676C8—301no—
677C8C2×D5×Dic312yes—
678C2×C3—102no—
679C2×C3—202no—
680C2×C3C4×D4×D511yescharacteristic
681C2×C3C2×#406411yescharacteristic
682C2×C3#6610211yescharacteristic
683C5Dic3×#13711yescharacteristic, complemented, Sylow
684C22—52no—
685C22—101no—
686C22—101no—
687C22—102no—
688C22—201no—
689C22—201no—
690C22D3×D4×D511yescharacteristic
691C4—22no—
692C4—22no—
693C4—32no—
694C4—52no—
695C4—61no—
696C4—102no—
697C4—121no—
698C4—121no—
699C4—301no—
700C4—301no—
701C4—601no—
702C4—601no—
703C4D5×#23711yescharacteristic
704C4C22×D5×Dic311yescharacteristic
705C3C4×#406411yescharacteristic, complemented, Sylow
706C2—102no—
707C2—202no—
708C2D3×#406411yescharacteristic
709C2#1175410211yescharacteristic
710C2D4×D5×Dic311yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#713C22
cosocleC2×C3×C4×C5C24
hypercenterC2×Q16D3×D5
hypocenterC3×C5C4×#137
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. Q8×D5×Dic3C2semidirect
4. #11751285C2semidirect
5. C5×Dic3×Q16C2semidirect
6. #11749264C2semidirect
7. Dic3×#689C2semidirect
8. #11749241C2semidirect
9. Dic3×#688C2semidirect
10. #11749208C2semidirect
12. #11747812C2semidirect
13. Dic3×#677C2semidirect
14. #11747619C2semidirect
15. Dic3×#676C2semidirect
26. C3×#4064C4semidirect
82. C3×Q8×D5C2×C4semidirect
95. C3×C5×Q16C2×C4semidirect
113. C3×#689C2×C4semidirect
114. C3×#688C2×C4semidirect
116. C3×#677C2×C4semidirect
117. C3×#676C2×C4semidirect
138. Dic3×Q16D5semidirect
154. #4064Dic3direct (N × H)
277. Q8×D5C2×Dic3semidirect
290. C5×Q16C2×Dic3semidirect
300. #689C2×Dic3semidirect
301. #688C2×Dic3semidirect
322. #677C2×Dic3semidirect
324. #676C2×Dic3semidirect
360. C5×Dic3#137semidirect
380. C3×Q16C4×D5semidirect
579. Q16D5×Dic3semidirect
613. C3×C5C4×#137semidirect
634. Dic3#4064direct (N × H)
683. C5Dic3×#137semidirect
705. C3C4×#4064semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40642
Dic3×#7132
Q8×D5×Dic32
#117512852
C5×Dic3×Q162
#117492642
Dic3×#6892
#117492412
Dic3×#6882
#117492082
#117491982
#117478122
Dic3×#6772
#117476192
Dic3×#6762
C4×#40643
Dic3×#1375