Finite Group Databasebeta

← SD16×#41×C73 #32970830

Subgroups — SD16×#41×C73 #32970830

Order 18688.

2116 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#41×C73C211yesmaximal, characteristic, complemented
2D4×#41×C73C211yesmaximal, characteristic
3C73×#3392C211yesmaximal, characteristic, complemented
4Q8×SD16×C73C211yesmaximal, characteristic, complemented
5C73×#3362C211yesmaximal, characteristic, complemented
6C73×#3359C211yesmaximal, characteristic, complemented
7C73×#3335C213yesmaximal, complemented
8C73×#3298C213yesmaximal, complemented
9C73×#3295C213yesmaximal, complemented
10D4×SD16×C73C213yesmaximal, complemented
11C73×#3167C213yesmaximal, complemented
12C73×#3103C213yesmaximal, complemented
13C73×#3101C213yesmaximal, complemented
14C8×#41×C73C211yesmaximal, characteristic, complemented
15C2×C4×SD16×C73C213yesmaximal, complemented
16C22×#41×C73—21no—
17C22×SD16×C73C2213yes—
18Q82×C73C2211yescharacteristic, complemented
19#557×C73—21no—
20#557×C73C2211yescharacteristic, complemented
21#554×C73—23no—
22#554×C73C2213yescomplemented
23#550×C73C2211yescharacteristic
24D4×Q8×C73C2211yescharacteristic
25D4×Q8×C73C2213yescomplemented
26#548×C73—21no—
27#547×C73C2213yes—
28#546×C73—23no—
29D42×C73C2213yes—
30#533×C73—23no—
31#533×C73C2213yescomplemented
32#532×C73C2213yes—
33#525×C73—23no—
34C4×#41×C73—21no—
35C4×#41×C73C2211yescharacteristic
36C2×C4×Q8×C73C2213yescomplemented
37C2×C4×D4×C73C2213yes—
38#498×C73C2213yescomplemented
39#492×C73C2213yescomplemented
40#487×C73C2213yescomplemented
41#486×C73C2213yescomplemented
42#483×C73C2216yescomplemented
43#481×C73C2216yescomplemented
44#476×C73C2213yes—
45#476×C73C2213yescomplemented
46#475×C73C2213yescomplemented
47#475×C73C2213yescomplemented
48#465×C73C2216yescomplemented
49#465×C73C2216yescomplemented
50#461×C73C2213yes—
51#461×C73C2213yescomplemented
52#460×C73C2213yescomplemented
53#460×C73C2213yescomplemented
54#450×C73C2216yes—
55#448×C73C2216yescomplemented
56C8×Q8×C73C2211yescharacteristic, complemented
57C8×Q8×C73C2211yescharacteristic, complemented
58C4×SD16×C73C2213yes—
59C4×SD16×C73C2213yes—
60C4×SD16×C73C2213yes—
61C4×SD16×C73C2211yescharacteristic
62C4×SD16×C73C2213yescomplemented
63C4×SD16×C73C2213yescomplemented
64C4×SD16×C73C2216yescomplemented
65C4×SD16×C73C2213yescomplemented
66C4×SD16×C73C2213yescomplemented
67C8×D4×C73C2213yescomplemented
68C8×D4×C73C2213yescomplemented
69#431×C73C2213yescomplemented
70C2×#106×C73C2213yescomplemented
71C2×#103×C73C2213yescomplemented
72C2×#102×C73C2213yes—
73C2×C4×C8×C73C2213yescomplemented
74C2×#41×C73—21no—
75C2×#41×C73—23no—
76C2×#41×C73—23no—
77C2×#41×C73—48no—
78C2×#41×C73D411yescharacteristic
79C22×Q8×C73—21no—
80C22×Q8×C73C2313yes—
81C22×D4×C73—23no—
82C22×D4×C73C2313yes—
83C23×C4×C73—23no—
84C2×SD16×C73—212no—
85C2×SD16×C73C2313yes—
86C2×SD16×C73C2313yes—
87C2×SD16×C73C2313yes—
88C2×SD16×C73C2316yes—
89C2×SD16×C73C2311yescharacteristic
90C22×C8×C73C2313yes—
91C22×C8×C73C2313yes—
92C4⋊Q8×C73—23no—
93C4⋊Q8×C73—23no—
94C4⋊Q8×C73C2313yes—
95C4⋊Q8×C73C2313yes—
96C4⋊Q8×C73C2313yes—
97#127×C73C2313yes—
98#125×C73—23no—
99#125×C73—23no—
100#125×C73—23no—
101#124×C73—23no—
102#123×C73—26no—
103C22⋊Q8×C73—23no—
104C22⋊Q8×C73—23no—
105C22⋊Q8×C73—23no—
106C22⋊Q8×C73—26no—
107C22⋊Q8×C73—26no—
108C22⋊Q8×C73C2316yes—
109#121×C73—23no—
110#121×C73—23no—
111#121×C73—23no—
112#121×C73C2316yes—
113#120×C73—26no—
114C4×Q8×C73—21no—
115C4×Q8×C73—21no—
116C4×Q8×C73—23no—
117C4×Q8×C73—23no—
118C4×Q8×C73—23no—
119C4×Q8×C73D411yescharacteristic
120C4×Q8×C73C2311yescharacteristic
121C4×Q8×C73C2313yes—
122C4×Q8×C73C2313yes—
123C4×Q8×C73C2313yes—
124C4×Q8×C73C2311yescharacteristic
125C4×D4×C73—23no—
126C4×D4×C73—23no—
127C4×D4×C73—23no—
128C4×D4×C73—23no—
129C4×D4×C73—23no—
130C4×D4×C73D413yes—
131C4×D4×C73C2311yescharacteristic
132C4×D4×C73C2313yes—
133C4×D4×C73C2313yes—
134C4×D4×C73C2313yes—
135C4×D4×C73C2313yes—
136#117×C73—23no—
137#117×C73D413yes—
138C2×C4⋊C4×C73—23no—
139C2×C4⋊C4×C73C2313yes—
140C2×C4⋊C4×C73C2313yes—
141C2×C22⋊C4×C73—23no—
142C2×C42×C73—23no—
143C2×C42×C73C2313yes—
144#106×C73C2311yescharacteristic
145#106×C73C2313yes—
146#106×C73C2313yes—
147#106×C73C2313yes—
148#106×C73C2316yes—
149C4⋊C8×C73C2313yes—
150C4⋊C8×C73C2313yes—
151#103×C73C2311yescharacteristic
152#103×C73C2313yes—
153#103×C73C2313yes—
154#103×C73C2313yes—
155#103×C73C2316yes—
156#102×C73C2311yescharacteristic
157#102×C73C2313yes—
158#102×C73C2313yes—
159#102×C73C2313yes—
160#102×C73C2316yes—
161C22⋊C8×C73C2316yes—
162C4×C8×C73C2311yescharacteristic
163C4×C8×C73C2313yes—
164C4×C8×C73C2313yes—
165C4×C8×C73C2313yes—
166C24×C73—23no—
167#41×C73—44no—
168#41×C73—412no—
169#41×C73—412no—
170#41×C73SD1618yesdirect product factor
171C2×Q8×C73—23no—
172C2×Q8×C73—23no—
173C2×Q8×C73—23no—
174C2×Q8×C73—26no—
175C2×Q8×C73—43no—
176C2×Q8×C73—44no—
177C2×Q8×C73C2×D411yescharacteristic
178C2×Q8×C73C2413yes—
179C2×Q8×C73C2411yescharacteristic
180C2×D4×C73—26no—
181C2×D4×C73—26no—
182C2×D4×C73—23no—
183C2×D4×C73—23no—
184C2×D4×C73—23no—
185C2×D4×C73—43no—
186C2×D4×C73—412no—
187C2×D4×C73C2×D413yes—
188C2×D4×C73C2413yes—
189C2×D4×C73C2411yescharacteristic
190C22×C4×C73—23no—
191C22×C4×C73—23no—
192C22×C4×C73—23no—
193C22×C4×C73—23no—
194C22×C4×C73—23no—
195C22×C4×C73—21no—
196C22×C4×C73—23no—
197C22×C4×C73—412no—
198C22×C4×C73C2×D413yes—
199C22×C4×C73C2×D413yes—
200C22×C4×C73C2413yes—
201SD16×C73—26no—
202SD16×C73—26no—
203SD16×C73—26no—
204SD16×C73—46no—
205SD16×C73#4114yesdirect product factor
206C2×C8×C73—26no—
207C2×C8×C73—43no—
208C2×C8×C73C2411yescharacteristic
209C2×C8×C73C2413yes—
210C2×C8×C73C2413yes—
211C2×C8×C73C2411yescharacteristic
212C4⋊C4×C73—21no—
213C4⋊C4×C73—23no—
214C4⋊C4×C73—23no—
215C4⋊C4×C73—23no—
216C4⋊C4×C73—23no—
217C4⋊C4×C73—23no—
218C4⋊C4×C73—23no—
219C4⋊C4×C73—23no—
220C4⋊C4×C73—23no—
221C4⋊C4×C73—23no—
222C4⋊C4×C73—26no—
223C4⋊C4×C73C2×D413yes—
224C4⋊C4×C73C2×D413yes—
225C4⋊C4×C73C2411yescharacteristic
226C4⋊C4×C73C2413yes—
227C4⋊C4×C73C2411yescharacteristic
228C4⋊C4×C73C2413yes—
229C22⋊C4×C73—26no—
230C22⋊C4×C73—21no—
231C22⋊C4×C73—23no—
232C22⋊C4×C73—23no—
233C22⋊C4×C73—23no—
234C22⋊C4×C73—26no—
235C22⋊C4×C73C2×D416yes—
236C42×C73—23no—
237C42×C73—23no—
238C42×C73—21no—
239C42×C73—23no—
240C42×C73C2×D413yes—
241C42×C73C2×D413yes—
242C42×C73C2413yes—
243C42×C73C2411yescharacteristic
244C23×C73—21no—
245C23×C73—23no—
246C23×C73—46no—
247C23×C73—46no—
248C23×C73—83no—
249C23×C73C22×D413yes—
250Q8×C73—21no—
251Q8×C73—23no—
252Q8×C73—23no—
253Q8×C73—46no—
254Q8×C73—46no—
255Q8×C73—83no—
256Q8×C73C2×SD1614yescomplemented
257Q8×C73C2×#4112yescomplemented
258D4×C73—23no—
259D4×C73—21no—
260D4×C73—23no—
261D4×C73—46no—
262D4×C73—412no—
263D4×C73—46no—
264D4×C73—83no—
265D4×C73C2×SD16112yescomplemented
266D4×C73C2×#4112yes—
267C2×C4×C73—21no—
268C2×C4×C73—23no—
269C2×C4×C73—23no—
270C2×C4×C73—21no—
271C2×C4×C73—23no—
272C2×C4×C73—23no—
273C2×C4×C73—21no—
274C2×C4×C73—23no—
275C2×C4×C73—43no—
276C2×C4×C73—46no—
277C2×C4×C73—46no—
278C2×C4×C73—42no—
279C2×C4×C73—46no—
280C2×C4×C73—46no—
281C2×C4×C73—46no—
282C2×C4×C73—83no—
283C2×C4×C73C2×SD16112yescomplemented
284C2×C4×C73C22×D411yescharacteristic
285C2×C4×C73C22×D413yes—
286C2×C4×C73C22×D413yes—
287C2×C4×C73C22×D413yes—
288C2×C4×C73C22×D411yescharacteristic
289C2×C4×C73C2511yescharacteristic
290C8×C73—23no—
291C8×C73—21no—
292C8×C73—23no—
293C8×C73C2×#4112yescomplemented
294C22×C73—23no—
295C22×C73—23no—
296C22×C73—22no—
297C22×C73—41no—
298C22×C73—41no—
299C22×C73—43no—
300C22×C73—43no—
301C22×C73—43no—
302C22×C73—812no—
303C22×C73C22×SD1616yes—
304C22×C73C23×D411yescharacteristic
305C4×C73—21no—
306C4×C73—23no—
307C4×C73—23no—
308C4×C73—22no—
309C4×C73—41no—
310C4×C73—43no—
311C4×C73—43no—
312C4×C73—41no—
313C4×C73—43no—
314C4×C73C22×SD1612yes—
315C4×C73C22×SD1616yes—
316C4×C73C22×#4111yescharacteristic
317C4×C73#58511yescharacteristic
318SD16×#41C7311yesmaximal, characteristic, direct product factor, Sylow
319C2×C73—26no—
320C2×C73—42no—
321C2×C73—83no—
322C2×C73D4×#4111yescharacteristic
323C2×C73C23×SD1611yescharacteristic
324C2×C73#358411yescharacteristic
325Q8×#41C2×C7311yescharacteristic, complemented
326D4×#41C2×C7311yescharacteristic
327#3392C2×C7311yescharacteristic, complemented
328Q8×SD16C2×C7311yescharacteristic, complemented
329#3362C2×C7311yescharacteristic, complemented
330#3359C2×C7311yescharacteristic, complemented
331#3335C2×C7313yescomplemented
332#3298C2×C7313yescomplemented
333#3295C2×C7313yescomplemented
334D4×SD16C2×C7313yescomplemented
335#3167C2×C7313yescomplemented
336#3103C2×C7313yescomplemented
337#3101C2×C7313yescomplemented
338C8×#41C2×C7311yescharacteristic, complemented
339C2×C4×SD16C2×C7313yescomplemented
340C73SD16×#4111yescharacteristic, direct product factor, Sylow
341C22×#41—21no—
342C22×SD16C22×C7313yes—
343Q82C22×C7311yescharacteristic, complemented
344#557—21no—
345#557C22×C7311yescharacteristic, complemented
346#554—23no—
347#554C22×C7313yescomplemented
348#550C22×C7311yescharacteristic
349D4×Q8C22×C7311yescharacteristic
350D4×Q8C22×C7313yescomplemented
351#548—21no—
352#547C22×C7313yes—
353#546—23no—
354D42C22×C7313yes—
355#533—23no—
356#533C22×C7313yescomplemented
357#532C22×C7313yes—
358#525—23no—
359C4×#41—21no—
360C4×#41C22×C7311yescharacteristic
361C2×C4×Q8C22×C7313yescomplemented
362C2×C4×D4C22×C7313yes—
363#498C22×C7313yescomplemented
364#492C22×C7313yescomplemented
365#487C22×C7313yescomplemented
366#486C22×C7313yescomplemented
367#483C22×C7316yescomplemented
368#481C22×C7316yescomplemented
369#476C22×C7313yes—
370#476C22×C7313yescomplemented
371#475C22×C7313yescomplemented
372#475C22×C7313yescomplemented
373#465C22×C7316yescomplemented
374#465C22×C7316yescomplemented
375#461C22×C7313yes—
376#461C22×C7313yescomplemented
377#460C22×C7313yescomplemented
378#460C22×C7313yescomplemented
379#450C22×C7316yes—
380#448C22×C7316yescomplemented
381C8×Q8C22×C7311yescharacteristic, complemented
382C8×Q8C22×C7311yescharacteristic, complemented
383C4×SD16C22×C7313yes—
384C4×SD16C22×C7313yes—
385C4×SD16C22×C7313yes—
386C4×SD16C22×C7311yescharacteristic
387C4×SD16C22×C7313yescomplemented
388C4×SD16C22×C7316yescomplemented
389C4×SD16C22×C7313yescomplemented
390C4×SD16C22×C7313yescomplemented
391C4×SD16C22×C7313yescomplemented
392C8×D4C22×C7313yescomplemented
393C8×D4C22×C7313yescomplemented
394#431C22×C7313yescomplemented
395C2×#106C22×C7313yescomplemented
396C2×#103C22×C7313yescomplemented
397C2×#102C22×C7313yes—
398C2×C4×C8C22×C7313yescomplemented
399C2×#41—21no—
400C2×#41—23no—
401C2×#41—23no—
402C2×#41—48no—
403C2×#41D4×C7311yescharacteristic
404C22×Q8—21no—
405C22×Q8C23×C7313yes—
406C22×D4—23no—
407C22×D4C23×C7313yes—
408C23×C4—23no—
409C2×SD16—212no—
410C2×SD16C23×C7313yes—
411C2×SD16C23×C7313yes—
412C2×SD16C23×C7313yes—
413C2×SD16C23×C7316yes—
414C2×SD16C23×C7311yescharacteristic
415C22×C8C23×C7313yes—
416C22×C8C23×C7313yes—
417C4⋊Q8—23no—
418C4⋊Q8—23no—
419C4⋊Q8C23×C7313yes—
420C4⋊Q8C23×C7313yes—
421C4⋊Q8C23×C7313yes—
422#127C23×C7313yes—
423#125—23no—
424#125—23no—
425#125—23no—
426#124—23no—
427#123—26no—
428C22⋊Q8—23no—
429C22⋊Q8—23no—
430C22⋊Q8—23no—
431C22⋊Q8—26no—
432C22⋊Q8—26no—
433C22⋊Q8C23×C7316yes—
434#121—23no—
435#121—23no—
436#121—23no—
437#121C23×C7316yes—
438#120—26no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—23no—
442C4×Q8—23no—
443C4×Q8—23no—
444C4×Q8D4×C7311yescharacteristic
445C4×Q8C23×C7311yescharacteristic
446C4×Q8C23×C7313yes—
447C4×Q8C23×C7313yes—
448C4×Q8C23×C7313yes—
449C4×Q8C23×C7311yescharacteristic
450C4×D4—23no—
451C4×D4—23no—
452C4×D4—23no—
453C4×D4—23no—
454C4×D4—23no—
455C4×D4D4×C7313yes—
456C4×D4C23×C7311yescharacteristic
457C4×D4C23×C7313yes—
458C4×D4C23×C7313yes—
459C4×D4C23×C7313yes—
460C4×D4C23×C7313yes—
461#117—23no—
462#117D4×C7313yes—
463C2×C4⋊C4—23no—
464C2×C4⋊C4C23×C7313yes—
465C2×C4⋊C4C23×C7313yes—
466C2×C22⋊C4—23no—
467C2×C42—23no—
468C2×C42C23×C7313yes—
469#106C23×C7311yescharacteristic
470#106C23×C7313yes—
471#106C23×C7313yes—
472#106C23×C7313yes—
473#106C23×C7316yes—
474C4⋊C8C23×C7313yes—
475C4⋊C8C23×C7313yes—
476#103C23×C7311yescharacteristic
477#103C23×C7313yes—
478#103C23×C7313yes—
479#103C23×C7313yes—
480#103C23×C7316yes—
481#102C23×C7311yescharacteristic
482#102C23×C7313yes—
483#102C23×C7313yes—
484#102C23×C7313yes—
485#102C23×C7316yes—
486C22⋊C8C23×C7316yes—
487C4×C8C23×C7311yescharacteristic
488C4×C8C23×C7313yes—
489C4×C8C23×C7313yes—
490C4×C8C23×C7313yes—
491C24—23no—
492#41—44no—
493#41—412no—
494#41—412no—
495#41SD16×C7318yesdirect product factor
496C2×Q8—23no—
497C2×Q8—23no—
498C2×Q8—23no—
499C2×Q8—26no—
500C2×Q8—43no—
501C2×Q8—44no—
502C2×Q8C2×D4×C7311yescharacteristic
503C2×Q8C24×C7313yes—
504C2×Q8C24×C7311yescharacteristic
505C2×D4—26no—
506C2×D4—26no—
507C2×D4—23no—
508C2×D4—23no—
509C2×D4—23no—
510C2×D4—43no—
511C2×D4—412no—
512C2×D4C2×D4×C7313yes—
513C2×D4C24×C7313yes—
514C2×D4C24×C7311yescharacteristic
515C22×C4—23no—
516C22×C4—23no—
517C22×C4—23no—
518C22×C4—21no—
519C22×C4—23no—
520C22×C4—23no—
521C22×C4—23no—
522C22×C4—412no—
523C22×C4C2×D4×C7313yes—
524C22×C4C2×D4×C7313yes—
525C22×C4C24×C7313yes—
526SD16—26no—
527SD16—26no—
528SD16—26no—
529SD16—46no—
530SD16#41×C7314yesdirect product factor
531C2×C8—26no—
532C2×C8—43no—
533C2×C8C24×C7311yescharacteristic
534C2×C8C24×C7313yes—
535C2×C8C24×C7313yes—
536C2×C8C24×C7311yescharacteristic
537C4⋊C4—21no—
538C4⋊C4—23no—
539C4⋊C4—23no—
540C4⋊C4—23no—
541C4⋊C4—23no—
542C4⋊C4—23no—
543C4⋊C4—23no—
544C4⋊C4—23no—
545C4⋊C4—23no—
546C4⋊C4—23no—
547C4⋊C4—26no—
548C4⋊C4C2×D4×C7313yes—
549C4⋊C4C2×D4×C7313yes—
550C4⋊C4C24×C7311yescharacteristic
551C4⋊C4C24×C7313yes—
552C4⋊C4C24×C7311yescharacteristic
553C4⋊C4C24×C7313yes—
554C22⋊C4—26no—
555C22⋊C4—21no—
556C22⋊C4—23no—
557C22⋊C4—23no—
558C22⋊C4—23no—
559C22⋊C4—26no—
560C22⋊C4C2×D4×C7316yes—
561C42—21no—
562C42—23no—
563C42—23no—
564C42—23no—
565C42C2×D4×C7313yes—
566C42C2×D4×C7313yes—
567C42C24×C7311yescharacteristic
568C42C24×C7313yes—
569C23—21no—
570C23—23no—
571C23—46no—
572C23—46no—
573C23—83no—
574C23C22×D4×C7313yes—
575Q8—21no—
576Q8—23no—
577Q8—23no—
578Q8—46no—
579Q8—46no—
580Q8—83no—
581Q8C2×SD16×C7314yescomplemented
582Q8C2×#41×C7312yescomplemented
583D4—23no—
584D4—21no—
585D4—23no—
586D4—46no—
587D4—412no—
588D4—46no—
589D4—83no—
590D4C2×SD16×C73112yescomplemented
591D4C2×#41×C7312yes—
592C2×C4—21no—
593C2×C4—23no—
594C2×C4—23no—
595C2×C4—21no—
596C2×C4—23no—
597C2×C4—23no—
598C2×C4—21no—
599C2×C4—23no—
600C2×C4—43no—
601C2×C4—46no—
602C2×C4—46no—
603C2×C4—42no—
604C2×C4—46no—
605C2×C4—46no—
606C2×C4—46no—
607C2×C4—83no—
608C2×C4C2×SD16×C73112yescomplemented
609C2×C4C22×D4×C7311yescharacteristic
610C2×C4C22×D4×C7313yes—
611C2×C4C22×D4×C7313yes—
612C2×C4C22×D4×C7311yescharacteristic
613C2×C4C22×D4×C7313yes—
614C2×C4C25×C7311yescharacteristic
615C8—23no—
616C8—21no—
617C8—23no—
618C8C2×#41×C7312yescomplemented
619C22—23no—
620C22—23no—
621C22—22no—
622C22—41no—
623C22—41no—
624C22—43no—
625C22—43no—
626C22—43no—
627C22—812no—
628C22C22×SD16×C7316yes—
629C22C23×D4×C7311yescharacteristic
630C4—23no—
631C4—22no—
632C4—21no—
633C4—23no—
634C4—43no—
635C4—41no—
636C4—43no—
637C4—41no—
638C4—43no—
639C4C22×SD16×C7312yes—
640C4C22×SD16×C7316yes—
641C4C22×#41×C7311yescharacteristic
642C4#585×C7311yescharacteristic
643C2—26no—
644C2—42no—
645C2—83no—
646C2D4×#41×C7311yescharacteristic
647C2C23×SD16×C7311yescharacteristic
648C2C73×#358411yescharacteristic
subgroupG/H
centerC2×C4×C73C22×D4
commutator, Frattini, cosocleC2×C4C25×C73
socleC22×C73C23×D4
prime radicalD4×#41×C73C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C73 ◁ C4×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. Q8×#41×C73C2semidirect
3. C73×#3392C2semidirect
4. Q8×SD16×C73C2semidirect
5. C73×#3362C2semidirect
6. C73×#3359C2semidirect
7. C73×#3335C2semidirect
8. C73×#3298C2semidirect
9. C73×#3295C2semidirect
10. D4×SD16×C73C2semidirect
11. C73×#3167C2semidirect
12. C73×#3103C2semidirect
13. C73×#3101C2semidirect
14. C8×#41×C73C2semidirect
15. C2×C4×SD16×C73C2semidirect
18. Q82×C73C22semidirect
20. #557×C73C22semidirect
22. #554×C73C22semidirect
25. D4×Q8×C73C22semidirect
31. #533×C73C22semidirect
36. C2×C4×Q8×C73C22semidirect
38. #498×C73C22semidirect
39. #492×C73C22semidirect
40. #487×C73C22semidirect
41. #486×C73C22semidirect
42. #483×C73C22semidirect
43. #481×C73C22semidirect
45. #476×C73C22semidirect
46. #475×C73C22semidirect
47. #475×C73C22semidirect
48. #465×C73C22semidirect
49. #465×C73C22semidirect
51. #461×C73C22semidirect
52. #460×C73C22semidirect
53. #460×C73C22semidirect
55. #448×C73C22semidirect
56. C8×Q8×C73C22semidirect
57. C8×Q8×C73C22semidirect
62. C4×SD16×C73C22semidirect
63. C4×SD16×C73C22semidirect
64. C4×SD16×C73C22semidirect
65. C4×SD16×C73C22semidirect
66. C4×SD16×C73C22semidirect
67. C8×D4×C73C22semidirect
68. C8×D4×C73C22semidirect
69. #431×C73C22semidirect
70. C2×#106×C73C22semidirect
71. C2×#103×C73C22semidirect
73. C2×C4×C8×C73C22semidirect
170. #41×C73SD16direct (N × H)
205. SD16×C73#41direct (N × H)
256. Q8×C73C2×SD16semidirect
257. Q8×C73C2×#41semidirect
265. D4×C73C2×SD16semidirect
283. C2×C4×C73C2×SD16semidirect
293. C8×C73C2×#41semidirect
318. SD16×#41C73direct (N × H)
325. Q8×#41C2×C73semidirect
327. #3392C2×C73semidirect
328. Q8×SD16C2×C73semidirect
329. #3362C2×C73semidirect
330. #3359C2×C73semidirect
331. #3335C2×C73semidirect
332. #3298C2×C73semidirect
333. #3295C2×C73semidirect
334. D4×SD16C2×C73semidirect
335. #3167C2×C73semidirect
336. #3103C2×C73semidirect
337. #3101C2×C73semidirect
338. C8×#41C2×C73semidirect
339. C2×C4×SD16C2×C73semidirect
340. C73SD16×#41direct (N × H)
343. Q82C22×C73semidirect
345. #557C22×C73semidirect
347. #554C22×C73semidirect
350. D4×Q8C22×C73semidirect
356. #533C22×C73semidirect
361. C2×C4×Q8C22×C73semidirect
363. #498C22×C73semidirect
364. #492C22×C73semidirect
365. #487C22×C73semidirect
366. #486C22×C73semidirect
367. #483C22×C73semidirect
368. #481C22×C73semidirect
370. #476C22×C73semidirect
371. #475C22×C73semidirect
372. #475C22×C73semidirect
373. #465C22×C73semidirect
374. #465C22×C73semidirect
376. #461C22×C73semidirect
377. #460C22×C73semidirect
378. #460C22×C73semidirect
380. #448C22×C73semidirect
381. C8×Q8C22×C73semidirect
382. C8×Q8C22×C73semidirect
387. C4×SD16C22×C73semidirect
388. C4×SD16C22×C73semidirect
389. C4×SD16C22×C73semidirect
390. C4×SD16C22×C73semidirect
391. C4×SD16C22×C73semidirect
392. C8×D4C22×C73semidirect
393. C8×D4C22×C73semidirect
394. #431C22×C73semidirect
395. C2×#106C22×C73semidirect
396. C2×#103C22×C73semidirect
398. C2×C4×C8C22×C73semidirect
495. #41SD16×C73direct (N × H)
530. SD16#41×C73direct (N × H)
581. Q8C2×SD16×C73semidirect
582. Q8C2×#41×C73semidirect
590. D4C2×SD16×C73semidirect
608. C2×C4C2×SD16×C73semidirect
618. C8C2×#41×C73semidirect

Maximal subgroups

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

subgroupindex
Q8×#41×C732
D4×#41×C732
C73×#33922
Q8×SD16×C732
C73×#33622
C73×#33592
C73×#33352
C73×#32982
C73×#32952
D4×SD16×C732
C73×#31672
C73×#31032
C73×#31012
C8×#41×C732
C2×C4×SD16×C732
SD16×#4173