Finite Group Databasebeta

← C73×#23889 #32933293

Subgroups — C73×#23889 #32933293

Order 18688.

1648 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C73C211yesmaximal, characteristic, complemented
2C2×#577×C73C211yesmaximal, characteristic, complemented
3C2×#454×C73C211yesmaximal, characteristic, complemented
4C2×#455×C73C211yesmaximal, characteristic, complemented
5C73×#3013C211yesmaximal, characteristic, complemented
6C73×#3012C211yesmaximal, characteristic, complemented
7C73×#2020C211yesmaximal, characteristic, complemented
8C73×#2019C211yesmaximal, characteristic, complemented
9C73×#2015C211yesmaximal, characteristic, complemented
10C73×#2007C211yesmaximal, characteristic, complemented
11C73×#1908C211yesmaximal, characteristic, complemented
12C73×#1907C211yesmaximal, characteristic, complemented
13C73×#1876C211yesmaximal, characteristic, complemented
14C73×#1876C211yesmaximal, characteristic, complemented
15C73×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C73C2211yescharacteristic
17C2×2−1+4×C73C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C73C2211yescharacteristic
19#578×C73—24no—
20#578×C73—24no—
21#577×C73—24no—
22#577×C73—24no—
23C2×#137×C73—21no—
24C2×#137×C73—21no—
25C2×#137×C73—21no—
26C2×#137×C73C2211yescharacteristic
27C2×#137×C73C2211yescharacteristic
28C2×#137×C73C2211yescharacteristic
29C2×#137×C73C2211yescharacteristic, complemented
30C2×AGL(1,ℤ/8)×C73—21no—
31C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
32C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
33C2×#135×C73—21no—
34C2×#135×C73—21no—
35C2×#135×C73C2211yescharacteristic
36C2×#135×C73C2211yescharacteristic
37C22×Q16×C73—21no—
38C22×Q16×C73C2211yescharacteristic, complemented
39C22×SD16×C73—21no—
40C22×SD16×C73C2211yescharacteristic
41C2×#131×C73C2211yescharacteristic
42C2×#131×C73C2211yescharacteristic, complemented
43#537×C73C2211yescharacteristic
44C2×#124×C73C2211yescharacteristic
45#455×C73—24no—
46#454×C73—24no—
47#452×C73—21no—
48#452×C73—21no—
49#451×C73—21no—
50#450×C73—21no—
51#449×C73—21no—
52#449×C73—21no—
53#448×C73—21no—
54#447×C73—21no—
55C2×#104×C73C2211yescharacteristic
56C2×#104×C73C2211yescharacteristic
57C2×#104×C73C2211yescharacteristic, complemented
58C2×#104×C73C2211yescharacteristic, complemented
59#417×C73C2211yescharacteristic
60#417×C73C2211yescharacteristic, complemented
61C2×#103×C73C2211yescharacteristic, complemented
62C2×#102×C73C2211yescharacteristic
63C2×#101×C73C2211yescharacteristic, complemented
64C2×#101×C73C2211yescharacteristic, complemented
65C2×#100×C73C2211yescharacteristic
66#408×C73C2211yescharacteristic
67#408×C73C2211yescharacteristic, complemented
68#391×C73C2211yescharacteristic, complemented
69#343×C73C2211yescharacteristic, complemented
70#341×C73C2211yescharacteristic, complemented
71#341×C73C2211yescharacteristic, complemented
72#336×C73C2211yescharacteristic, complemented
732−1+4×C73—22no—
742−1+4×C73—22no—
752−1+4×C73—22no—
762−1+4×C73—22no—
772−1+4×C73—22no—
782−1+4×C73—41no—
792−1+4×C73—41no—
802−1+4×C73D414yescomplemented
81H(5,𝔽2)×C73—22no—
82H(5,𝔽2)×C73—22no—
83H(5,𝔽2)×C73—22no—
84H(5,𝔽2)×C73—41no—
85C2×#41×C73—21no—
86C2×#41×C73—21no—
87C2×#41×C73—21no—
88C2×#41×C73—21no—
89C2×#41×C73—21no—
90C2×#41×C73—21no—
91C2×#41×C73—41no—
92C2×#41×C73—41no—
93C2×#41×C73C2311yescharacteristic
94C2×#41×C73C2311yescharacteristic
95C2×#41×C73C2311yescharacteristic
96C2×#41×C73C2311yescharacteristic
97C22×Q8×C73—21no—
98C22×Q8×C73—21no—
99C22×Q8×C73—21no—
100C22×Q8×C73—21no—
101C22×Q8×C73C2311yescharacteristic
102C22×Q8×C73C2311yescharacteristic
103C22×D4×C73—21no—
104C22×D4×C73—21no—
105C22×D4×C73—41no—
106C22×D4×C73C2311yescharacteristic
107#137×C73—28no—
108#137×C73—28no—
109#137×C73—28no—
110#137×C73—22no—
111#137×C73—22no—
112#137×C73—22no—
113#137×C73—22no—
114#137×C73—22no—
115#137×C73—22no—
116#137×C73—41no—
117#137×C73D414yescomplemented
118AGL(1,ℤ/8)×C73—28no—
119AGL(1,ℤ/8)×C73—22no—
120AGL(1,ℤ/8)×C73—22no—
121AGL(1,ℤ/8)×C73—41no—
122AGL(1,ℤ/8)×C73D414yescomplemented
123#135×C73—28no—
124#135×C73—28no—
125#135×C73—22no—
126#135×C73—22no—
127#135×C73—22no—
128#135×C73—22no—
129C2×Q16×C73—28no—
130C2×Q16×C73—21no—
131C2×Q16×C73—21no—
132C2×Q16×C73—22no—
133C2×Q16×C73—22no—
134C2×Q16×C73—21no—
135C2×Q16×C73—21no—
136C2×Q16×C73—21no—
137C2×Q16×C73—21no—
138C2×Q16×C73D411yescharacteristic
139C2×Q16×C73D411yescharacteristic
140C2×SD16×C73—28no—
141C2×SD16×C73—21no—
142C2×SD16×C73—22no—
143C2×SD16×C73—21no—
144C2×SD16×C73—22no—
145C2×SD16×C73—21no—
146C2×SD16×C73—21no—
147C2×SD16×C73—21no—
148C2×SD16×C73—21no—
149C2×SD16×C73—21no—
150C2×SD16×C73—21no—
151C2×SD16×C73D411yescharacteristic
152C2×SD16×C73D411yescharacteristic
153C2×SD16×C73D411yescharacteristic
154C2×SD16×C73D411yescharacteristic
155C2×D8×C73—21no—
156C2×D8×C73—21no—
157C2×D8×C73D411yescharacteristic
158C2×D8×C73D411yescharacteristic
159#131×C73—22no—
160#131×C73—22no—
161#131×C73—22no—
162#131×C73—22no—
163C2×M16×C73—21no—
164C2×M16×C73—21no—
165C2×M16×C73C2311yescharacteristic
166C2×M16×C73C2311yescharacteristic
167C2×M16×C73C2311yescharacteristic
168C2×M16×C73C2311yescharacteristic
169C22×C8×C73—21no—
170C22×C8×C73—21no—
171C22×C8×C73C2311yescharacteristic
172C22×C8×C73C2311yescharacteristic
173#124×C73—22no—
174#124×C73—22no—
175C22⋊Q8×C73—21no—
176C22⋊Q8×C73—21no—
177#121×C73—21no—
178#121×C73—21no—
179#121×C73—41no—
180C2×C4⋊C4×C73C2311yescharacteristic
181C2×C22⋊C4×C73—41no—
182C2×C42×C73C2311yescharacteristic
183#104×C73—22no—
184#104×C73—22no—
185#104×C73—22no—
186#104×C73—22no—
187#103×C73—21no—
188#103×C73—21no—
189#103×C73—21no—
190#103×C73—21no—
191#102×C73—21no—
192#102×C73—21no—
193#102×C73—21no—
194#102×C73—21no—
195#101×C73—22no—
196#101×C73—41no—
197#100×C73—22no—
198C22⋊C8×C73—21no—
199C22⋊C8×C73—21no—
200C22⋊C8×C73—21no—
201C22⋊C8×C73—21no—
202#95×C73—41no—
203C24×C73—21no—
204C24×C73—41no—
205#41×C73—21no—
206#41×C73—21no—
207#41×C73—21no—
208#41×C73—21no—
209#41×C73—24no—
210#41×C73—24no—
211#41×C73—24no—
212#41×C73—24no—
213#41×C73—21no—
214#41×C73—21no—
215#41×C73—21no—
216#41×C73—21no—
217#41×C73—21no—
218#41×C73—21no—
219#41×C73—21no—
220#41×C73—21no—
221#41×C73—44no—
222#41×C73—42no—
223#41×C73—42no—
224#41×C73—42no—
225#41×C73—44no—
226#41×C73—42no—
227#41×C73—44no—
228#41×C73—42no—
229#41×C73—42no—
230#41×C73—44no—
231#41×C73—42no—
232#41×C73—42no—
233#41×C73C2×D412yes—
234#41×C73C2×D412yes—
235#41×C73C2×D412yes—
236#41×C73C2×D412yes—
237C2×Q8×C73—21no—
238C2×Q8×C73—21no—
239C2×Q8×C73—24no—
240C2×Q8×C73—24no—
241C2×Q8×C73—24no—
242C2×Q8×C73—21no—
243C2×Q8×C73—21no—
244C2×Q8×C73—21no—
245C2×Q8×C73—21no—
246C2×Q8×C73—21no—
247C2×Q8×C73—21no—
248C2×Q8×C73—21no—
249C2×Q8×C73—21no—
250C2×Q8×C73—41no—
251C2×Q8×C73—41no—
252C2×Q8×C73—42no—
253C2×Q8×C73—42no—
254C2×Q8×C73—42no—
255C2×Q8×C73—42no—
256C2×Q8×C73—42no—
257C2×Q8×C73C2×D411yescharacteristic
258C2×Q8×C73C2×D411yescharacteristic
259C2×Q8×C73C2×D412yes—
260C2×Q8×C73C2×D412yes—
261C2×Q8×C73C2×D411yescharacteristic
262C2×Q8×C73C2×D411yescharacteristic
263C2×D4×C73—21no—
264C2×D4×C73—21no—
265C2×D4×C73—24no—
266C2×D4×C73—21no—
267C2×D4×C73—21no—
268C2×D4×C73—21no—
269C2×D4×C73—21no—
270C2×D4×C73—21no—
271C2×D4×C73—21no—
272C2×D4×C73—21no—
273C2×D4×C73—42no—
274C2×D4×C73—41no—
275C2×D4×C73—41no—
276C2×D4×C73—42no—
277C2×D4×C73—44no—
278C2×D4×C73—44no—
279C2×D4×C73—41no—
280C2×D4×C73—41no—
281C2×D4×C73—42no—
282C2×D4×C73—41no—
283C2×D4×C73C2×D411yescharacteristic
284C2×D4×C73C2×D411yescharacteristic
285C2×D4×C73C2×D412yes—
286C2×D4×C73C2×D411yescharacteristic
287C2×D4×C73C2×D411yescharacteristic
288C22×C4×C73—21no—
289C22×C4×C73—21no—
290C22×C4×C73—21no—
291C22×C4×C73—21no—
292C22×C4×C73—21no—
293C22×C4×C73—21no—
294C22×C4×C73—21no—
295C22×C4×C73—21no—
296C22×C4×C73—41no—
297C22×C4×C73—41no—
298C22×C4×C73—41no—
299C22×C4×C73—41no—
300C22×C4×C73—41no—
301C22×C4×C73C2411yescharacteristic
302Q16×C73—24no—
303Q16×C73—24no—
304Q16×C73—24no—
305Q16×C73—24no—
306Q16×C73—22no—
307Q16×C73—24no—
308Q16×C73—22no—
309Q16×C73—42no—
310SD16×C73—24no—
311SD16×C73—24no—
312SD16×C73—24no—
313SD16×C73—24no—
314SD16×C73—22no—
315SD16×C73—24no—
316SD16×C73—22no—
317SD16×C73—24no—
318SD16×C73—22no—
319SD16×C73—22no—
320SD16×C73—42no—
321SD16×C73—42no—
322D8×C73—24no—
323D8×C73—22no—
324D8×C73—22no—
325D8×C73—42no—
326M16×C73—24no—
327M16×C73—24no—
328M16×C73—21no—
329M16×C73—21no—
330M16×C73—21no—
331M16×C73—21no—
332M16×C73—21no—
333M16×C73—21no—
334M16×C73C2×D412yes—
335M16×C73C2×D412yes—
336C2×C8×C73—24no—
337C2×C8×C73—24no—
338C2×C8×C73—21no—
339C2×C8×C73—21no—
340C2×C8×C73—21no—
341C2×C8×C73—21no—
342C2×C8×C73—21no—
343C2×C8×C73—21no—
344C2×C8×C73—21no—
345C2×C8×C73—21no—
346C2×C8×C73C2×D411yescharacteristic
347C2×C8×C73C2×D411yescharacteristic
348C2×C8×C73C2×D411yescharacteristic
349C2×C8×C73C2×D411yescharacteristic
350C4⋊C4×C73—21no—
351C4⋊C4×C73—21no—
352C4⋊C4×C73—41no—
353C22⋊C4×C73—44no—
354C22⋊C4×C73—41no—
355C22⋊C4×C73—41no—
356C42×C73—21no—
357C42×C73—21no—
358C23×C73—21no—
359C23×C73—21no—
360C23×C73—21no—
361C23×C73—21no—
362C23×C73—22no—
363C23×C73—44no—
364C23×C73—41no—
365C23×C73—41no—
366C23×C73—81no—
367C23×C73—81no—
368C23×C73—161no—
369C23×C73—161no—
370C23×C73H(5,𝔽2)11yescharacteristic
371Q8×C73—21no—
372Q8×C73—21no—
373Q8×C73—22no—
374Q8×C73—22no—
375Q8×C73—22no—
376Q8×C73—21no—
377Q8×C73—21no—
378Q8×C73—21no—
379Q8×C73—22no—
380Q8×C73—21no—
381Q8×C73—44no—
382Q8×C73—44no—
383Q8×C73—41no—
384Q8×C73—41no—
385Q8×C73—41no—
386Q8×C73—41no—
387Q8×C73#12012yes—
388Q8×C73#12012yes—
389D4×C73—22no—
390D4×C73—22no—
391D4×C73—22no—
392D4×C73—22no—
393D4×C73—22no—
394D4×C73—21no—
395D4×C73—21no—
396D4×C73—21no—
397D4×C73—21no—
398D4×C73—21no—
399D4×C73—22no—
400D4×C73—21no—
401D4×C73—44no—
402D4×C73—44no—
403D4×C73—44no—
404D4×C73—44no—
405D4×C73—41no—
406D4×C73—41no—
407D4×C73—41no—
408D4×C73—41no—
409D4×C73—41no—
410D4×C73—41no—
411D4×C73—161no—
412D4×C73#12012yes—
413D4×C73#12012yes—
414C2×C4×C73—21no—
415C2×C4×C73—21no—
416C2×C4×C73—22no—
417C2×C4×C73—22no—
418C2×C4×C73—22no—
419C2×C4×C73—22no—
420C2×C4×C73—22no—
421C2×C4×C73—22no—
422C2×C4×C73—21no—
423C2×C4×C73—21no—
424C2×C4×C73—44no—
425C2×C4×C73—44no—
426C2×C4×C73—44no—
427C2×C4×C73—44no—
428C2×C4×C73—44no—
429C2×C4×C73—41no—
430C2×C4×C73—41no—
431C2×C4×C73—41no—
432C2×C4×C73—41no—
433C2×C4×C73—41no—
434C2×C4×C73—41no—
435C2×C4×C73—41no—
436C2×C4×C73—41no—
437C2×C4×C73—41no—
438C2×C4×C73—41no—
439C2×C4×C73—41no—
440C2×C4×C73—41no—
441C2×C4×C73—81no—
442C2×C4×C73C22×D411yescharacteristic
443C2×C4×C73C22×D411yescharacteristic
444C2×C4×C73C22×D411yescharacteristic
445C2×C4×C73C22×D411yescharacteristic
446C2×C4×C73C22×D411yescharacteristic
447C2×C4×C73H(5,𝔽2)11yescharacteristic
448C8×C73—21no—
449C8×C73—21no—
450C8×C73—22no—
451C8×C73—22no—
452C8×C73—21no—
453C8×C73—21no—
454C8×C73—41no—
455C8×C73—41no—
456C22×C73—21no—
457C22×C73—21no—
458C22×C73—22no—
459C22×C73—22no—
460C22×C73—41no—
461C22×C73—41no—
462C22×C73—41no—
463C22×C73—41no—
464C22×C73—41no—
465C22×C73—41no—
466C22×C73—42no—
467C22×C73—41no—
468C22×C73—41no—
469C22×C73—41no—
470C22×C73—41no—
471C22×C73—82no—
472C22×C73—81no—
473C22×C73—81no—
474C22×C73—161no—
475C22×C73—164no—
476C22×C73#53411yescharacteristic
477C22×C73D4211yescharacteristic
478C22×C73D4211yescharacteristic
479C4×C73—22no—
480C4×C73—22no—
481C4×C73—41no—
482C4×C73—42no—
483C4×C73—42no—
484C4×C73—41no—
485C4×C73—81no—
486C4×C73—81no—
487C4×C73C2×#12011yescharacteristic
488C4×C73C2×#12011yescharacteristic
489C4×C73D4211yescharacteristic
490C4×C73D4211yescharacteristic
491#23889C7311yesmaximal, characteristic, direct product factor, Sylow
492C2×C73—21no—
493C2×C73—21no—
494C2×C73—42no—
495C2×C73—42no—
496C2×C73—81no—
497C2×C73—81no—
498C2×C73—82no—
499C2×C73#240311yescharacteristic
500C2×C73#328911yescharacteristic
501C2×C73#329011yescharacteristic
502C2×#578C2×C7311yescharacteristic, complemented
503C2×#577C2×C7311yescharacteristic, complemented
504C2×#454C2×C7311yescharacteristic, complemented
505C2×#455C2×C7311yescharacteristic, complemented
506#3013C2×C7311yescharacteristic, complemented
507#3012C2×C7311yescharacteristic, complemented
508#2020C2×C7311yescharacteristic, complemented
509#2019C2×C7311yescharacteristic, complemented
510#2015C2×C7311yescharacteristic, complemented
511#2007C2×C7311yescharacteristic, complemented
512#1908C2×C7311yescharacteristic, complemented
513#1907C2×C7311yescharacteristic, complemented
514#1876C2×C7311yescharacteristic, complemented
515#1876C2×C7311yescharacteristic, complemented
516#1793C2×C7311yescharacteristic, complemented
517C73#2388911yescharacteristic, direct product factor, Sylow
518C2×2−1+4C22×C7311yescharacteristic
519C2×2−1+4C22×C7311yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C7311yescharacteristic
521#578—24no—
522#578—24no—
523#577—24no—
524#577—24no—
525C2×#137—21no—
526C2×#137—21no—
527C2×#137—21no—
528C2×#137C22×C7311yescharacteristic
529C2×#137C22×C7311yescharacteristic
530C2×#137C22×C7311yescharacteristic
531C2×#137C22×C7311yescharacteristic, complemented
532C2×AGL(1,ℤ/8)—21no—
533C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
534C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
535C2×#135—21no—
536C2×#135—21no—
537C2×#135C22×C7311yescharacteristic
538C2×#135C22×C7311yescharacteristic
539C22×Q16—21no—
540C22×Q16C22×C7311yescharacteristic, complemented
541C22×SD16—21no—
542C22×SD16C22×C7311yescharacteristic
543C2×#131C22×C7311yescharacteristic
544C2×#131C22×C7311yescharacteristic, complemented
545#537C22×C7311yescharacteristic
546C2×#124C22×C7311yescharacteristic
547#455—24no—
548#454—24no—
549#452—21no—
550#452—21no—
551#451—21no—
552#450—21no—
553#449—21no—
554#449—21no—
555#448—21no—
556#447—21no—
557C2×#104C22×C7311yescharacteristic
558C2×#104C22×C7311yescharacteristic
559C2×#104C22×C7311yescharacteristic, complemented
560C2×#104C22×C7311yescharacteristic, complemented
561#417C22×C7311yescharacteristic
562#417C22×C7311yescharacteristic, complemented
563C2×#103C22×C7311yescharacteristic, complemented
564C2×#102C22×C7311yescharacteristic
565C2×#101C22×C7311yescharacteristic, complemented
566C2×#101C22×C7311yescharacteristic, complemented
567C2×#100C22×C7311yescharacteristic
568#408C22×C7311yescharacteristic
569#408C22×C7311yescharacteristic, complemented
570#391C22×C7311yescharacteristic, complemented
571#343C22×C7311yescharacteristic, complemented
572#341C22×C7311yescharacteristic, complemented
573#341C22×C7311yescharacteristic, complemented
574#336C22×C7311yescharacteristic, complemented
5752−1+4—22no—
5762−1+4—22no—
5772−1+4—22no—
5782−1+4—22no—
5792−1+4—22no—
5802−1+4—41no—
5812−1+4—41no—
5822−1+4D4×C7314yescomplemented
583H(5,𝔽2)—22no—
584H(5,𝔽2)—22no—
585H(5,𝔽2)—22no—
586H(5,𝔽2)—41no—
587C2×#41—21no—
588C2×#41—21no—
589C2×#41—21no—
590C2×#41—21no—
591C2×#41—21no—
592C2×#41—21no—
593C2×#41—41no—
594C2×#41—41no—
595C2×#41C23×C7311yescharacteristic
596C2×#41C23×C7311yescharacteristic
597C2×#41C23×C7311yescharacteristic
598C2×#41C23×C7311yescharacteristic
599C22×Q8—21no—
600C22×Q8—21no—
601C22×Q8—21no—
602C22×Q8—21no—
603C22×Q8C23×C7311yescharacteristic
604C22×Q8C23×C7311yescharacteristic
605C22×D4—21no—
606C22×D4—21no—
607C22×D4—41no—
608C22×D4C23×C7311yescharacteristic
609#137—28no—
610#137—28no—
611#137—28no—
612#137—22no—
613#137—22no—
614#137—22no—
615#137—22no—
616#137—22no—
617#137—22no—
618#137—41no—
619#137D4×C7314yescomplemented
620AGL(1,ℤ/8)—28no—
621AGL(1,ℤ/8)—22no—
622AGL(1,ℤ/8)—22no—
623AGL(1,ℤ/8)—41no—
624AGL(1,ℤ/8)D4×C7314yescomplemented
625#135—28no—
626#135—28no—
627#135—22no—
628#135—22no—
629#135—22no—
630#135—22no—
631C2×Q16—28no—
632C2×Q16—21no—
633C2×Q16—21no—
634C2×Q16—22no—
635C2×Q16—22no—
636C2×Q16—21no—
637C2×Q16—21no—
638C2×Q16—21no—
639C2×Q16—21no—
640C2×Q16D4×C7311yescharacteristic
641C2×Q16D4×C7311yescharacteristic
642C2×SD16—28no—
643C2×SD16—21no—
644C2×SD16—22no—
645C2×SD16—21no—
646C2×SD16—22no—
647C2×SD16—21no—
648C2×SD16—21no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—21no—
653C2×SD16D4×C7311yescharacteristic
654C2×SD16D4×C7311yescharacteristic
655C2×SD16D4×C7311yescharacteristic
656C2×SD16D4×C7311yescharacteristic
657C2×D8—21no—
658C2×D8—21no—
659C2×D8D4×C7311yescharacteristic
660C2×D8D4×C7311yescharacteristic
661#131—22no—
662#131—22no—
663#131—22no—
664#131—22no—
665C2×M16—21no—
666C2×M16—21no—
667C2×M16C23×C7311yescharacteristic
668C2×M16C23×C7311yescharacteristic
669C2×M16C23×C7311yescharacteristic
670C2×M16C23×C7311yescharacteristic
671C22×C8—21no—
672C22×C8—21no—
673C22×C8C23×C7311yescharacteristic
674C22×C8C23×C7311yescharacteristic
675#124—22no—
676#124—22no—
677C22⋊Q8—21no—
678C22⋊Q8—21no—
679#121—21no—
680#121—21no—
681#121—41no—
682C2×C4⋊C4C23×C7311yescharacteristic
683C2×C22⋊C4—41no—
684C2×C42C23×C7311yescharacteristic
685#104—22no—
686#104—22no—
687#104—22no—
688#104—22no—
689#103—21no—
690#103—21no—
691#103—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#101—22no—
698#101—41no—
699#100—22no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8—21no—
704#95—41no—
705C24—21no—
706C24—41no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—24no—
712#41—24no—
713#41—24no—
714#41—24no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—21no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—44no—
724#41—42no—
725#41—42no—
726#41—42no—
727#41—44no—
728#41—42no—
729#41—44no—
730#41—42no—
731#41—42no—
732#41—44no—
733#41—42no—
734#41—42no—
735#41C2×D4×C7312yes—
736#41C2×D4×C7312yes—
737#41C2×D4×C7312yes—
738#41C2×D4×C7312yes—
739C2×Q8—21no—
740C2×Q8—21no—
741C2×Q8—24no—
742C2×Q8—24no—
743C2×Q8—24no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—41no—
753C2×Q8—41no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—42no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8C2×D4×C7311yescharacteristic
760C2×Q8C2×D4×C7311yescharacteristic
761C2×Q8C2×D4×C7312yes—
762C2×Q8C2×D4×C7312yes—
763C2×Q8C2×D4×C7311yescharacteristic
764C2×Q8C2×D4×C7311yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—42no—
776C2×D4—41no—
777C2×D4—41no—
778C2×D4—42no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—41no—
782C2×D4—41no—
783C2×D4—42no—
784C2×D4—41no—
785C2×D4C2×D4×C7311yescharacteristic
786C2×D4C2×D4×C7311yescharacteristic
787C2×D4C2×D4×C7312yes—
788C2×D4C2×D4×C7311yescharacteristic
789C2×D4C2×D4×C7311yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—41no—
799C22×C4—41no—
800C22×C4—41no—
801C22×C4—41no—
802C22×C4—41no—
803C22×C4C24×C7311yescharacteristic
804Q16—24no—
805Q16—24no—
806Q16—24no—
807Q16—24no—
808Q16—22no—
809Q16—24no—
810Q16—22no—
811Q16—42no—
812SD16—24no—
813SD16—24no—
814SD16—24no—
815SD16—24no—
816SD16—22no—
817SD16—24no—
818SD16—22no—
819SD16—24no—
820SD16—22no—
821SD16—22no—
822SD16—42no—
823SD16—42no—
824D8—24no—
825D8—22no—
826D8—22no—
827D8—42no—
828M16—24no—
829M16—24no—
830M16—21no—
831M16—21no—
832M16—21no—
833M16—21no—
834M16—21no—
835M16—21no—
836M16C2×D4×C7312yes—
837M16C2×D4×C7312yes—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8C2×D4×C7311yescharacteristic
849C2×C8C2×D4×C7311yescharacteristic
850C2×C8C2×D4×C7311yescharacteristic
851C2×C8C2×D4×C7311yescharacteristic
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—41no—
855C22⋊C4—44no—
856C22⋊C4—41no—
857C22⋊C4—41no—
858C42—21no—
859C42—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—22no—
865C23—44no—
866C23—41no—
867C23—41no—
868C23—81no—
869C23—81no—
870C23—161no—
871C23—161no—
872C23H(5,𝔽2)×C7311yescharacteristic
873Q8—21no—
874Q8—21no—
875Q8—22no—
876Q8—22no—
877Q8—22no—
878Q8—21no—
879Q8—21no—
880Q8—21no—
881Q8—22no—
882Q8—21no—
883Q8—44no—
884Q8—44no—
885Q8—41no—
886Q8—41no—
887Q8—41no—
888Q8—41no—
889Q8#120×C7312yes—
890Q8#120×C7312yes—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—21no—
897D4—21no—
898D4—21no—
899D4—21no—
900D4—21no—
901D4—22no—
902D4—21no—
903D4—44no—
904D4—44no—
905D4—44no—
906D4—44no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—41no—
912D4—41no—
913D4—161no—
914D4#120×C7312yes—
915D4#120×C7312yes—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—81no—
944C2×C4C22×D4×C7311yescharacteristic
945C2×C4C22×D4×C7311yescharacteristic
946C2×C4C22×D4×C7311yescharacteristic
947C2×C4C22×D4×C7311yescharacteristic
948C2×C4C22×D4×C7311yescharacteristic
949C2×C4H(5,𝔽2)×C7311yescharacteristic
950C8—21no—
951C8—21no—
952C8—22no—
953C8—22no—
954C8—21no—
955C8—21no—
956C8—41no—
957C8—41no—
958C22—21no—
959C22—21no—
960C22—22no—
961C22—22no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—42no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—161no—
977C22—164no—
978C22#534×C7311yescharacteristic
979C22D42×C7311yescharacteristic
980C22D42×C7311yescharacteristic
981C4—22no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—42no—
986C4—41no—
987C4—81no—
988C4—81no—
989C4C2×#120×C7311yescharacteristic
990C4C2×#120×C7311yescharacteristic
991C4D42×C7311yescharacteristic
992C4D42×C7311yescharacteristic
993C2—21no—
994C2—21no—
995C2—42no—
996C2—42no—
997C2—81no—
998C2—81no—
999C2—82no—
1000C2C73×#240311yescharacteristic
1001C2C73×#328911yescharacteristic
1002C2C73×#329011yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#578×C73C2semidirect
2. C2×#577×C73C2semidirect
3. C2×#454×C73C2semidirect
4. C2×#455×C73C2semidirect
5. C73×#3013C2semidirect
6. C73×#3012C2semidirect
7. C73×#2020C2semidirect
8. C73×#2019C2semidirect
9. C73×#2015C2semidirect
10. C73×#2007C2semidirect
11. C73×#1908C2semidirect
12. C73×#1907C2semidirect
13. C73×#1876C2semidirect
14. C73×#1876C2semidirect
15. C73×#1793C2semidirect
17. C2×2−1+4×C73C22semidirect
29. C2×#137×C73C22semidirect
38. C22×Q16×C73C22semidirect
42. C2×#131×C73C22semidirect
57. C2×#104×C73C22semidirect
58. C2×#104×C73C22semidirect
60. #417×C73C22semidirect
61. C2×#103×C73C22semidirect
63. C2×#101×C73C22semidirect
64. C2×#101×C73C22semidirect
67. #408×C73C22semidirect
68. #391×C73C22semidirect
69. #343×C73C22semidirect
70. #341×C73C22semidirect
71. #341×C73C22semidirect
72. #336×C73C22semidirect
80. 2−1+4×C73D4semidirect
117. #137×C73D4semidirect
122. AGL(1,ℤ/8)×C73D4semidirect
491. #23889C73direct (N × H)
502. C2×#578C2×C73semidirect
503. C2×#577C2×C73semidirect
504. C2×#454C2×C73semidirect
505. C2×#455C2×C73semidirect
506. #3013C2×C73semidirect
507. #3012C2×C73semidirect
508. #2020C2×C73semidirect
509. #2019C2×C73semidirect
510. #2015C2×C73semidirect
511. #2007C2×C73semidirect
512. #1908C2×C73semidirect
513. #1907C2×C73semidirect
514. #1876C2×C73semidirect
515. #1876C2×C73semidirect
516. #1793C2×C73semidirect
517. C73#23889direct (N × H)
519. C2×2−1+4C22×C73semidirect
531. C2×#137C22×C73semidirect
540. C22×Q16C22×C73semidirect
544. C2×#131C22×C73semidirect
559. C2×#104C22×C73semidirect
560. C2×#104C22×C73semidirect
562. #417C22×C73semidirect
563. C2×#103C22×C73semidirect
565. C2×#101C22×C73semidirect
566. C2×#101C22×C73semidirect
569. #408C22×C73semidirect
570. #391C22×C73semidirect
571. #343C22×C73semidirect
572. #341C22×C73semidirect
573. #341C22×C73semidirect
574. #336C22×C73semidirect
582. 2−1+4D4×C73semidirect
619. #137D4×C73semidirect
624. AGL(1,ℤ/8)D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C732
C2×#577×C732
C2×#454×C732
C2×#455×C732
C73×#30132
C73×#30122
C73×#20202
C73×#20192
C73×#20152
C73×#20072
C73×#19082
C73×#19072
C73×#18762
C73×#17932
#2388973