Finite Group Databasebeta

← #10956218

Subgroups — #10956218

Order 768.

5050 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1010C211yesmaximal, characteristic
2C2×#5572C211yesmaximal, characteristic, complemented
3C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
4C3×#2341C211yesmaximal, characteristic, complemented
5#84089C211yesmaximal, characteristic, complemented
6Q8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7Q8×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#76301C213yesmaximal, complemented
9#76301C213yesmaximal, complemented
10#76294C213yesmaximal, complemented
11#76290C213yesmaximal, complemented
12#74003C213yesmaximal, complemented
13#73876C213yesmaximal, complemented
14#73563C213yesmaximal, complemented
15C22⋊C4×Dic6C213yesmaximal, complemented
16#34257—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×#1010—28no—
19C2×#1010—28no—
20C2×#1010C4116yescomplemented
21C22×D3×Q8C2211yescharacteristic
22C22×D3×Q8C2211yescharacteristic
23C22×#237C2213yes—
24C22×#237C2213yes—
25C22×#235C2213yes—
26C23×Dic6C2213yes—
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×Q8×Dic3C2211yescharacteristic
30C2×Q8×Dic3C2211yescharacteristic
31#5572—28no—
32C4×D3×Q8—28no—
33C2×#892C2213yes—
34C2×D3×C4⋊C4C2213yes—
35C2×#887C2213yes—
36C2×#887C2213yes—
37C2×#872C2213yes—
38C2×C42×D3C2213yes—
39C2×C4×Dic6C2213yes—
40C2×C4×Dic6C2213yes—
41C3×#390C2213yes—
42C3×#390C2213yes—
43C3×#380C2213yes—
44C3×C4×C22⋊C4C2213yes—
45#5221C2213yes—
46#5221C2213yes—
47#5212C2213yes—
48C4×#217C2213yes—
49#4987C2213yes—
50#4987C2213yes—
51#4973C2213yes—
52#4973C2213yes—
53#4957C2216yes—
54#4957C2213yes—
55#4957C2213yes—
56#4956C2213yes—
57#4956C2216yes—
58#4956C2213yes—
59#4942C2216yes—
60#4942C2216yes—
61Dic3×C22⋊C4C2216yes—
62Dic3×C22⋊C4C2216yes—
63C4×(C2×D3)⋊C4C2213yes—
64C4×(C2×D3)⋊C4C2213yes—
65#4929C2213yes—
66#4929C2213yes—
67#4665C2213yes—
68#4665C2211yescharacteristic
69#4646C2216yes—
70#4646C2213yes—
71#4646C2213yes—
72C22×2−1+4—31no—
73C2×#519—31no—
74C22×C4×Q8—31no—
75#2341—33no—
76#2341—33no—
77#2341—31no—
78#2341D311yescharacteristic, complemented
79Q8×C22⋊C4—33no—
80Q8×C22⋊C4—33no—
81Q8×C22⋊C4—31no—
82Q8×C22⋊C4—31no—
83#2311—33no—
84#2311—33no—
85#2297—33no—
86#2297—33no—
87C2×C3×#41—24no—
88C2×C3×#41—24no—
89C2×C3×#41C2×C418yescomplemented
90C22×C3×Q8C2311yescharacteristic
91C22×C3×D4C2313yes—
92C23×C3×C4C2313yes—
93C22×#67C2313yes—
94C22×#67C2313yes—
95C23×Dic3C2316yes—
96#1010—2128no—
97C2×D3×Q8—24no—
98C2×D3×Q8—24no—
99C2×D3×Q8C2×C418yes—
100C2×D3×Q8C2×C418yescomplemented
101C2×D3×Q8D418yes—
102C2×D3×Q8D418yes—
103C2×#237—212no—
104C2×#237—212no—
105C2×#237—212no—
106C2×#237—212no—
107C2×#237C2×C4124yes—
108C2×#237C2×C4124yescomplemented
109C2×#235—212no—
110C2×#235—212no—
111C2×#235C2×C4124yes—
112C22×D12C2311yescharacteristic
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2313yes—
115C22×C4×D3C2313yes—
116C22×C4×D3C2313yes—
117C22×Dic6—212no—
118C22×Dic6—212no—
119C22×Dic6C2×C4124yescomplemented
120C22×Dic6C2313yes—
121C22×Dic6C2313yes—
122C22×Dic6C2313yes—
123C3×C4×Q8—24no—
124C3×C4×Q8—24no—
125C2×C3×C4⋊C4C2313yes—
126C2×C3×C4⋊C4C2313yes—
127C2×C3×C22⋊C4C2313yes—
128C2×C3×C22⋊C4C2316yes—
129C2×C3×C22⋊C4C2313yes—
130C2×C3×C42C2313yes—
131C2×C3×C42C2313yes—
132C2×#217C2313yes—
133C2×#217C2316yes—
134C2×#217C2313yes—
135Q8×Dic3—24no—
136Q8×Dic3—24no—
137C2×(C2×D3)⋊C4C2311yescharacteristic
138C2×(C2×D3)⋊C4C2311yescharacteristic
139C2×(C2×D3)⋊C4C2311yescharacteristic
140C2×(C2×D3)⋊C4C2313yes—
141C2×(C2×D3)⋊C4C2313yes—
142C2×(C2×D3)⋊C4C2313yes—
143C2×C4⋊Dic3C2313yes—
144C2×C4⋊Dic3C2313yes—
145C2×Dic3⋊C4C2313yes—
146C2×Dic3⋊C4C2316yes—
147C2×Dic3⋊C4C2313yes—
148C2×C4×Dic3C2313yes—
149C2×C4×Dic3C2316yes—
150C2×C4×Dic3C2313yes—
151C2×C4×Dic3C2313yes—
152C2×C4×Dic3C2313yes—
153#892—212no—
154D3×C4⋊C4—212no—
155#887—212no—
156#887—212no—
157#872—212no—
158C42×D3—212no—
159C4×Dic6—212no—
160C4×Dic6—212no—
161C3×#95C2311yescharacteristic
162C3×#95C2313yes—
163C3⋊#95C2311yescharacteristic
164C3⋊#95C2313yes—
165C3⋊#95C2313yes—
166C3⋊#95C2313yes—
167C3⋊#95C2316yes—
168C3⋊#95C2316yes—
169C3⋊#95C2313yes—
170C3⋊#95C2313yes—
171C2×2−1+4—316no—
172C2×2−1+4—68no—
173C2×2−1+4—68no—
174C22×#41—33no—
175C22×#41—33no—
176C22×#41—33no—
177C22×#41C2×D311yescharacteristic
178C23×Q8—31no—
179C23×Q8—31no—
180C23×Q8—33no—
181#519—68no—
182C2×C4×Q8—31no—
183C2×C4×Q8—31no—
184C2×C4×Q8—33no—
185C2×C4×Q8—33no—
186C2×C4×Q8—33no—
187C2×C4×Q8—33no—
188C2×C4×Q8—68no—
189C2×C4×Q8C2×D311yescharacteristic
190C2×C4×Q8C2×D311yescharacteristic
191C2×#117—33no—
192C2×#117—33no—
193C22×C4⋊C4—33no—
194C22×C42—33no—
195#391—33no—
196#391—33no—
197#391—33no—
198#391—33no—
199#391—36no—
200#391—33no—
201#391—33no—
202#390—33no—
203#390—33no—
204#390—36no—
205#390—33no—
206#390—33no—
207#390C2×D313yes—
208#390C2×D313yes—
209#386—36no—
210#386—33no—
211#386—33no—
212#386—33no—
213#386—31no—
214#380—33no—
215#380—33no—
216#380—33no—
217#380—36no—
218#380—36no—
219#380C2×D313yes—
220C4×C22⋊C4—33no—
221C4×C22⋊C4—36no—
222C4×C22⋊C4—36no—
223C4×C22⋊C4—33no—
224C4×C22⋊C4—33no—
225C4×C22⋊C4C2×D313yes—
226C24×C3C2413yes—
227C23×D3C2411yescharacteristic
228C23×D3C2411yescharacteristic
229C3×#41—232no—
230C2×C3×Q8C22×C414yes—
231C2×C3×Q8C2×D414yes—
232C2×C3×Q8C2×D414yes—
233C2×C3×D4—26no—
234C2×C3×D4—26no—
235C2×C3×D4C22×C4112yes—
236C22×C3×C4—26no—
237C22×C3×C4—26no—
238C22×C3×C4C22×C4112yes—
239C22×C3×C4C2413yes—
240C22×C3×C4C2413yes—
241C22×C3×C4C2411yescharacteristic
242C22×C3×C4C2411yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C22×C3×C4C2413yes—
245C2×#67—26no—
246C2×#67—26no—
247C2×#67—26no—
248C2×#67—26no—
249C2×#67C22×C4112yes—
250C2×#67C22×C4112yes—
251C22×Dic3—212no—
252C22×Dic3—212no—
253C22×Dic3C22×C4124yes—
254C22×Dic3C2411yescharacteristic
255C22×Dic3C2413yes—
256C22×Dic3C2413yes—
257C22×Dic3C2413yes—
258C22×Dic3C2411yescharacteristic
259C22×Dic3C2413yes—
260D3×Q8—232no—
261D3×Q8C22⋊C4164yescomplemented
262#237—296no—
263#237—296no—
264#235—296no—
265C2×D12—22no—
266C2×D12—22no—
267C2×D12C22×C414yes—
268C2×C4×D3—22no—
269C2×C4×D3—26no—
270C2×C4×D3—26no—
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—26no—
274C2×C4×D3—43no—
275C2×C4×D3—43no—
276C2×C4×D3C22×C4112yes—
277C2×C4×D3C22×C4112yes—
278C2×C4×D3C2×D4112yes—
279C2×C4×D3C2×D4112yes—
280C2×Dic6—26no—
281C2×Dic6—26no—
282C2×Dic6—26no—
283C2×Dic6—26no—
284C2×Dic6—296no—
285C2×Dic6C22×C4112yes—
286C2×Dic6C22×C4112yes—
287C2×Dic6C22×C4112yes—
288C2×Dic6C2×D4112yes—
289C2×Dic6C2×D4112yes—
290C3×C4⋊C4—26no—
291C3×C4⋊C4—26no—
292C3×C22⋊C4—26no—
293C3×C22⋊C4—46no—
294C3×C22⋊C4—43no—
295C3×C42—26no—
296C3×C42—26no—
297#217—26no—
298#217—46no—
299#217—43no—
300(C2×D3)⋊C4—22no—
301(C2×D3)⋊C4—26no—
302(C2×D3)⋊C4—22no—
303(C2×D3)⋊C4—22no—
304(C2×D3)⋊C4—43no—
305(C2×D3)⋊C4—43no—
306C4⋊Dic3—26no—
307C4⋊Dic3—26no—
308Dic3⋊C4—26no—
309Dic3⋊C4—212no—
310Dic3⋊C4—26no—
311C4×Dic3—26no—
312C4×Dic3—26no—
313C4×Dic3—26no—
314C4×Dic3—212no—
315C4×Dic3—26no—
3162−1+4—6128no—
317C2×#41—24no—
318C2×#41—24no—
319C2×#41—324no—
320C2×#41—324no—
321C2×#41—324no—
322C2×#41—612no—
323C2×#41—612no—
324C2×#41—612no—
325C2×#41—612no—
326C2×#41—612no—
327C2×#41—612no—
328C2×#41C4×D318yescomplemented
329C22×Q8—38no—
330C22×Q8—38no—
331C22×Q8—38no—
332C22×Q8—38no—
333C22×Q8—324no—
334C22×Q8—33no—
335C22×Q8—33no—
336C22×Q8—33no—
337C22×Q8—612no—
338C22×Q8—612no—
339C22×Q8—64no—
340C22×Q8—64no—
341C22×Q8C22×D311yescharacteristic
342C22×D4—33no—
343C22×D4—33no—
344C22×D4—31no—
345C22×D4C22×D313yes—
346C23×C4—33no—
347C23×C4—36no—
348C23×C4—33no—
349C23×C4—31no—
350C23×C4—33no—
351C23×C4C22×D313yes—
352C4×Q8—24no—
353C4×Q8—24no—
354C4×Q8—612no—
355C4×Q8—612no—
356C4×Q8—612no—
357C4×Q8—612no—
358C4×Q8—64no—
359C4×Q8—64no—
360#117—612no—
361#117—612no—
362C2×C4⋊C4—36no—
363C2×C4⋊C4—33no—
364C2×C4⋊C4—33no—
365C2×C4⋊C4—33no—
366C2×C4⋊C4—33no—
367C2×C4⋊C4—612no—
368C2×C4⋊C4C22×D313yes—
369C2×C4⋊C4C22×D313yes—
370C2×C22⋊C4—33no—
371C2×C22⋊C4—33no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—31no—
375C2×C22⋊C4—33no—
376C2×C22⋊C4—36no—
377C2×C22⋊C4—33no—
378C2×C22⋊C4—33no—
379C2×C22⋊C4C22×D313yes—
380C2×C22⋊C4C22×D316yes—
381C2×C22⋊C4C22×D313yes—
382C2×C42—36no—
383C2×C42—33no—
384C2×C42—33no—
385C2×C42—33no—
386C2×C42—33no—
387C2×C42—612no—
388C2×C42C22×D313yes—
389C2×C42C22×D313yes—
390#95—33no—
391#95—33no—
392#95—31no—
393#95—36no—
394#95—33no—
395#95—36no—
396#95—33no—
397#95—33no—
398#95C22×D311yescharacteristic
399#95C22×D313yes—
400C23×C3—23no—
401C23×C3—23no—
402C23×C3—23no—
403C23×C3—23no—
404C23×C3—23no—
405C23×C3—23no—
406C23×C3C23×C416yes—
407C23×C3C2511yescharacteristic
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—21no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—21no—
416C22×D3—21no—
417C22×D3—21no—
418C22×D3C23×C412yes—
419C22×D3C23×C412yes—
420C22×D3C22×D412yes—
421C22×D3C22×D412yes—
422C3×Q8C2×C22⋊C4116yes—
423C3×D4—224no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—224no—
429C2×C3×C4—23no—
430C2×C3×C4—23no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—23no—
434C2×C3×C4—23no—
435C2×C3×C4—23no—
436C2×C3×C4—21no—
437C2×C3×C4—23no—
438C2×C3×C4C23×C412yes—
439C2×C3×C4C23×C416yes—
440C2×C3×C4C22×D416yes—
441C2×C3×C4C22×D416yes—
442C2×C3×C42−1+412yescomplemented
443#67—224no—
444#67—224no—
445C2×Dic3—21no—
446C2×Dic3—23no—
447C2×Dic3—23no—
448C2×Dic3—21no—
449C2×Dic3—248no—
450C2×Dic3—21no—
451C2×Dic3—23no—
452C2×Dic3—23no—
453C2×Dic3—21no—
454C2×Dic3—23no—
455C2×Dic3—23no—
456C2×Dic3—23no—
457C2×Dic3—21no—
458C2×Dic3—23no—
459C2×Dic3C23×C416yes—
460C2×Dic3C23×C416yes—
461C2×Dic3C22×D416yes—
462C2×Dic3C22×D416yes—
463C2×Dic32−1+412yescomplemented
464D12—28no—
465C4×D3—28no—
466C4×D3—224no—
467C4×D3—412no—
468C4×D3C2×C22⋊C4148yes—
469Dic6—224no—
470Dic6—224no—
471Dic6C2×C22⋊C4148yes—
472C24—31no—
473C24—31no—
474C24C23×D313yes—
475#41—232no—
476#41—696no—
477#41—696no—
478#41—696no—
479C2×Q8—364no—
480C2×Q8—312no—
481C2×Q8—312no—
482C2×Q8—312no—
483C2×Q8—312no—
484C2×Q8—312no—
485C2×Q8—66no—
486C2×Q8—66no—
487C2×Q8—696no—
488C2×Q8—632no—
489C2×Q8—66no—
490C2×Q8—66no—
491C2×Q8C2×C4×D314yes—
492C2×Q8D3×D414yes—
493C2×Q8D3×D414yes—
494C2×D4—26no—
495C2×D4—26no—
496C2×D4—312no—
497C2×D4—312no—
498C2×D4—34no—
499C2×D4—62no—
500C2×D4—62no—
501C2×D4—66no—
502C2×D4—66no—
503C2×D4—66no—
504C2×D4—66no—
505C2×D4C2×C4×D3112yes—
506C22×C4—26no—
507C22×C4—26no—
508C22×C4—33no—
509C22×C4—312no—
510C22×C4—312no—
511C22×C4—312no—
512C22×C4—324no—
513C22×C4—33no—
514C22×C4—31no—
515C22×C4—312no—
516C22×C4—31no—
517C22×C4—33no—
518C22×C4—33no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—66no—
522C22×C4—612no—
523C22×C4—612no—
524C22×C4—66no—
525C22×C4—66no—
526C22×C4—62no—
527C22×C4—123no—
528C22×C4—123no—
529C22×C4C2×C4×D3112yes—
530C22×C4C23×D313yes—
531C22×C4C23×D313yes—
532C22×C4C23×D311yescharacteristic
533C22×C4C23×D311yescharacteristic
534C22×C4C23×D311yescharacteristic
535C22×C4C23×D313yes—
536C4⋊C4—26no—
537C4⋊C4—26no—
538C4⋊C4—612no—
539C4⋊C4—66no—
540C4⋊C4—66no—
541C4⋊C4—66no—
542C4⋊C4—66no—
543C22⋊C4—26no—
544C22⋊C4—43no—
545C22⋊C4—46no—
546C22⋊C4—62no—
547C22⋊C4—62no—
548C22⋊C4—66no—
549C22⋊C4—66no—
550C22⋊C4—62no—
551C22⋊C4—123no—
552C22⋊C4—123no—
553C22⋊C4—126no—
554C22⋊C4—123no—
555C42—26no—
556C42—26no—
557C42—66no—
558C42—66no—
559C42—612no—
560C42—66no—
561C42—66no—
562C22×C3—26no—
563C22×C3—26no—
564C22×C3—26no—
565C22×C3—43no—
566C22×C3—43no—
567C22×C3—43no—
568C22×C3—43no—
569C22×C3C24×C411yescharacteristic
570C22×C3C23×D411yescharacteristic
571C22×C3C23×D411yescharacteristic
572C22×C3C2×2−1+411yescharacteristic
573C22×C3C2×2−1+411yescharacteristic
574C22×C3#58511yescharacteristic
575C22×C3#58511yescharacteristic
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—22no—
579C2×D3—22no—
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—22no—
583C2×D3—22no—
584C2×D3—22no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—41no—
588C2×D3—41no—
589C2×D3C22×C22⋊C414yes—
590C3×C4—22no—
591C3×C4—22no—
592C3×C4—43no—
593C3×C4—43no—
594C3×C4—41no—
595C3×C4C22×C22⋊C4112yes—
596Dic3—26no—
597Dic3—22no—
598Dic3—43no—
599Dic3—41no—
600Dic3—43no—
601Dic3C22×C22⋊C4112yes—
602C23—23no—
603C23—23no—
604C23—23no—
605C23—23no—
606C23—23no—
607C23—23no—
608C23—32no—
609C23—32no—
610C23—32no—
611C23—32no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23—61no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23C22×C4×D316yes—
623C23C24×D311yescharacteristic
624Q8—348no—
625Q8—624no—
626Q8—624no—
627Q8D3×C22⋊C4116yes—
628D4—224no—
629D4—68no—
630D4—624no—
631D4—624no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—224no—
637C2×C4—21no—
638C2×C4—23no—
639C2×C4—23no—
640C2×C4—23no—
641C2×C4—21no—
642C2×C4—23no—
643C2×C4—23no—
644C2×C4—23no—
645C2×C4—21no—
646C2×C4—36no—
647C2×C4—36no—
648C2×C4—36no—
649C2×C4—348no—
650C2×C4—36no—
651C2×C4—32no—
652C2×C4—68no—
653C2×C4—648no—
654C2×C4—61no—
655C2×C4—63no—
656C2×C4—63no—
657C2×C4—61no—
658C2×C4—624no—
659C2×C4—61no—
660C2×C4—63no—
661C2×C4—63no—
662C2×C4—61no—
663C2×C4—63no—
664C2×C4—63no—
665C2×C4—61no—
666C2×C4—63no—
667C2×C4—63no—
668C2×C4—1212no—
669C2×C4C22×C4×D312yes—
670C2×C4C22×C4×D316yes—
671C2×C4C2×D3×D416yes—
672C2×C4C2×D3×D416yes—
673C2×C4#101012yescomplemented
674C2×C3—46no—
675C2×C3C23×C22⋊C411yescharacteristic
676C2×C3C4×2−1+411yescharacteristic
677C2×C3C4×2−1+411yescharacteristic
678C2×C3#348611yescharacteristic
679C2×C3#348711yescharacteristic
680C2×C3#349711yescharacteristic
681C2×C3#349711yescharacteristic
682D3—24no—
683D3—42no—
684C22—26no—
685C22—26no—
686C22—26no—
687C22—34no—
688C22—43no—
689C22—43no—
690C22—43no—
691C22—43no—
692C22—62no—
693C22—62no—
694C22—62no—
695C22—62no—
696C22—62no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—62no—
701C22—121no—
702C22—121no—
703C22—121no—
704C22—121no—
705C22C23×C4×D311yescharacteristic
706C22C22×D3×D411yescharacteristic
707C22C22×D3×D411yescharacteristic
708C22C2×#101011yescharacteristic
709C22#596411yescharacteristic
710C22#596611yescharacteristic
711C22D3×2−1+411yescharacteristic
712C4—22no—
713C4—22no—
714C4—312no—
715C4—43no—
716C4—41no—
717C4—43no—
718C4—66no—
719C4—62no—
720C4—121no—
721C4—123no—
722C4—123no—
723C4C2×D3×C22⋊C4112yes—
724C3#3425711yescharacteristic, complemented, Sylow
725C2—46no—
726C2—64no—
727C2—122no—
728C2C22×D3×C22⋊C411yescharacteristic
729C2C4×#101011yescharacteristic
730C2#8588711yescharacteristic
731C2#8673511yescharacteristic
732C2#8673711yescharacteristic
733C2#8678311yescharacteristic
734C2#8678411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×#2341C2
socle, cosocleC23×C3C25
prime radicalC22×#1010C2
hypercenter#2341D3
hypocenterC3#34257
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. C2×#5572C2semidirect
3. C2×C4×D3×Q8C2semidirect
4. C3×#2341C2semidirect
5. #84089C2semidirect
6. Q8×(C2×D3)⋊C4C2semidirect
7. Q8×(C2×D3)⋊C4C2semidirect
8. #76301C2semidirect
9. #76301C2semidirect
10. #76294C2semidirect
11. #76290C2semidirect
12. #74003C2semidirect
13. #73876C2semidirect
14. #73563C2semidirect
15. C22⋊C4×Dic6C2semidirect
20. C2×#1010C4semidirect
78. #2341D3semidirect
89. C2×C3×#41C2×C4semidirect
100. C2×D3×Q8C2×C4semidirect
108. C2×#237C2×C4semidirect
119. C22×Dic6C2×C4semidirect
261. D3×Q8C22⋊C4semidirect
328. C2×#41C4×D3semidirect
442. C2×C3×C42−1+4semidirect
463. C2×Dic32−1+4semidirect
673. C2×C4#1010semidirect
724. C3#34257semidirect

Maximal subgroups

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

subgroupindex
C22×#10102
C2×#55722
C2×C4×D3×Q82
C3×#23412
#840892
Q8×(C2×D3)⋊C42
#763012
#762942
#762902
#740032
#738762
#735632
C22⋊C4×Dic62
#342573