Finite Group Databasebeta

← C73×#25748 #32935152

Subgroups — C73×#25748 #32935152

Order 18688.

1544 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3500C211yesmaximal, characteristic, complemented
2C73×#3153C211yesmaximal, characteristic, complemented
3C73×#3040C211yesmaximal, characteristic, complemented
4C2×#456×C73C211yesmaximal, characteristic, complemented
5C2×#454×C73C211yesmaximal, characteristic, complemented
6C2×#455×C73C211yesmaximal, characteristic, complemented
7C2×#453×C73C211yesmaximal, characteristic, complemented
8C73×#2858C211yesmaximal, characteristic, complemented
9C73×#2005C211yesmaximal, characteristic, complemented
10C73×#2004C211yesmaximal, characteristic, complemented
11C73×#2003C211yesmaximal, characteristic, complemented
12C73×#2002C211yesmaximal, characteristic, complemented
13C73×#1967C211yesmaximal, characteristic, complemented
14C73×#1962C211yesmaximal, characteristic, complemented
15C4×#104×C73C211yesmaximal, characteristic, complemented
16C2×2−1+4×C73C2211yescharacteristic
17C2×H(5,𝔽2)×C73C2211yescharacteristic
18C2×#137×C73C2211yescharacteristic
19C2×#137×C73C2211yescharacteristic
20C2×#137×C73C2211yescharacteristic, complemented
21C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
22C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
23C2×AGL(1,ℤ/8)×C73C2211yescharacteristic, complemented
24#548×C73—22no—
25#546×C73—22no—
26#546×C73—24no—
27#536×C73—21no—
28#536×C73C2211yescharacteristic
29#535×C73—21no—
30#535×C73C2211yescharacteristic
31#532×C73—21no—
32#532×C73C2211yescharacteristic
33C2×C4⋊Q8×C73C2211yescharacteristic, complemented
34C2×#127×C73C2211yescharacteristic
35C2×#124×C73—21no—
36C2×#124×C73C2211yescharacteristic
37C2×#124×C73C2211yescharacteristic
38C2×#124×C73C2211yescharacteristic, complemented
39C2×#124×C73C2211yescharacteristic, complemented
40C4×#41×C73C2211yescharacteristic
41#497×C73—21no—
42#496×C73—21no—
43#495×C73—21no—
44#495×C73—21no—
45#464×C73—22no—
46#463×C73—22no—
47#456×C73—24no—
48#455×C73—24no—
49#454×C73—24no—
50#453×C73—24no—
51#423×C73C2211yescharacteristic, complemented
52C2×#104×C73C2211yescharacteristic
53C2×#104×C73C2211yescharacteristic
54C2×#104×C73C2211yescharacteristic
55C2×#104×C73C2211yescharacteristic
56C2×#104×C73C2211yescharacteristic, complemented
57C2×#104×C73C2211yescharacteristic, complemented
58#419×C73C2211yescharacteristic, complemented
59#418×C73C2211yescharacteristic, complemented
60C2×#101×C73C2211yescharacteristic, complemented
61C2×#101×C73C2211yescharacteristic, complemented
62C2×#100×C73C2211yescharacteristic
63C2×#100×C73C2211yescharacteristic
64C4×M16×C73C2211yescharacteristic, complemented
65#390×C73—24no—
66C43×C73C2211yescharacteristic, complemented
67#339×C73C2211yescharacteristic, complemented
68#339×C73C2211yescharacteristic, complemented
692−1+4×C73—22no—
702−1+4×C73—22no—
712−1+4×C73—41no—
722−1+4×C73—41no—
73H(5,𝔽2)×C73—22no—
74H(5,𝔽2)×C73—22no—
75H(5,𝔽2)×C73—41no—
76H(5,𝔽2)×C73—41no—
77C2×#41×C73—21no—
78C2×#41×C73—21no—
79C2×#41×C73—21no—
80C2×#41×C73—21no—
81C2×#41×C73—22no—
82C2×#41×C73C2311yescharacteristic
83C2×#41×C73C2311yescharacteristic
84C2×#41×C73C2311yescharacteristic
85C22×Q8×C73—21no—
86C22×Q8×C73—21no—
87C22×Q8×C73C2311yescharacteristic
88C22×Q8×C73C2311yescharacteristic
89C22×D4×C73—22no—
90C22×D4×C73—21no—
91C22×D4×C73—21no—
92C22×D4×C73—22no—
93C22×D4×C73C2311yescharacteristic
94C22×D4×C73C2311yescharacteristic
95#137×C73—22no—
96#137×C73—22no—
97#137×C73—22no—
98#137×C73—22no—
99#137×C73—41no—
100#137×C73—41no—
101AGL(1,ℤ/8)×C73—22no—
102AGL(1,ℤ/8)×C73—22no—
103AGL(1,ℤ/8)×C73—22no—
104AGL(1,ℤ/8)×C73—22no—
105AGL(1,ℤ/8)×C73—41no—
106AGL(1,ℤ/8)×C73—41no—
107C2×Q16×C73—21no—
108C2×Q16×C73—21no—
109C2×Q16×C73—21no—
110C2×SD16×C73—21no—
111C2×SD16×C73—21no—
112C2×SD16×C73—21no—
113C2×SD16×C73—21no—
114C2×SD16×C73—21no—
115C2×SD16×C73—21no—
116C2×D8×C73—21no—
117C2×D8×C73—21no—
118C2×D8×C73—21no—
119C2×M16×C73C2311yescharacteristic
120C2×M16×C73C2311yescharacteristic
121C2×M16×C73C2311yescharacteristic
122C2×M16×C73C2311yescharacteristic
123C4⋊Q8×C73—21no—
124C4⋊Q8×C73—22no—
125C4⋊Q8×C73—41no—
126C4⋊Q8×C73D411yescharacteristic, complemented
127#127×C73—21no—
128#127×C73—22no—
129#127×C73—41no—
130#127×C73D411yescharacteristic, complemented
131#124×C73—24no—
132#124×C73—21no—
133#124×C73—21no—
134#124×C73—21no—
135#124×C73—21no—
136#124×C73—22no—
137#124×C73—22no—
138#124×C73—22no—
139#124×C73—22no—
140#124×C73—21no—
141#124×C73—21no—
142#124×C73—41no—
143#124×C73—41no—
144#124×C73D411yescharacteristic, complemented
145#124×C73D411yescharacteristic, complemented
146#123×C73—24no—
147#123×C73—22no—
148C22⋊Q8×C73—24no—
149C22⋊Q8×C73—22no—
150#121×C73—24no—
151#121×C73—24no—
152#121×C73—22no—
153#121×C73—22no—
154#120×C73—24no—
155#120×C73—22no—
156C4×Q8×C73D412yescomplemented
157C4×D4×C73—24no—
158C4×D4×C73—22no—
159C4×D4×C73—22no—
160C4×D4×C73D412yescomplemented
161#117×C73—21no—
162#117×C73C2311yescharacteristic
163C2×C4⋊C4×C73—22no—
164C2×C22⋊C4×C73—24no—
165C2×C22⋊C4×C73—22no—
166C2×C22⋊C4×C73—22no—
167C2×C22⋊C4×C73—22no—
168C2×C22⋊C4×C73D414yes—
169C2×C42×C73—21no—
170C2×C42×C73—22no—
171C2×C42×C73C2311yescharacteristic
172C2×C42×C73C2311yescharacteristic
173C2×C42×C73C2311yescharacteristic
174C4⋊C8×C73—22no—
175#104×C73—22no—
176#104×C73—22no—
177#104×C73—22no—
178#104×C73—22no—
179#104×C73D414yescomplemented
180#104×C73D414yescomplemented
181#103×C73—22no—
182#102×C73—22no—
183#101×C73—22no—
184#101×C73—22no—
185#100×C73—22no—
186#100×C73—22no—
187#97×C73—21no—
188C4×C8×C73—21no—
189C24×C73—22no—
190C24×C73—21no—
191C24×C73C2×D412yes—
192#41×C73—21no—
193#41×C73—21no—
194#41×C73—21no—
195#41×C73—21no—
196#41×C73—21no—
197#41×C73—21no—
198#41×C73—21no—
199#41×C73—21no—
200#41×C73—21no—
201#41×C73—21no—
202#41×C73—42no—
203#41×C73—42no—
204#41×C73—44no—
205#41×C73—44no—
206#41×C73—42no—
207#41×C73—42no—
208#41×C73—42no—
209#41×C73—42no—
210#41×C73—42no—
211#41×C73—42no—
212#41×C73C2×D412yes—
213#41×C73C2×D412yes—
214C2×Q8×C73—22no—
215C2×Q8×C73—21no—
216C2×Q8×C73—21no—
217C2×Q8×C73—21no—
218C2×Q8×C73—21no—
219C2×Q8×C73—21no—
220C2×Q8×C73—21no—
221C2×Q8×C73—21no—
222C2×Q8×C73—21no—
223C2×Q8×C73—21no—
224C2×Q8×C73—21no—
225C2×Q8×C73—21no—
226C2×Q8×C73—21no—
227C2×Q8×C73—42no—
228C2×Q8×C73—42no—
229C2×Q8×C73—42no—
230C2×Q8×C73—42no—
231C2×Q8×C73C2×D411yescharacteristic
232C2×Q8×C73C2×D411yescharacteristic
233C2×Q8×C73C2×D411yescharacteristic
234C2×D4×C73—21no—
235C2×D4×C73—22no—
236C2×D4×C73—22no—
237C2×D4×C73—22no—
238C2×D4×C73—21no—
239C2×D4×C73—21no—
240C2×D4×C73—24no—
241C2×D4×C73—22no—
242C2×D4×C73—21no—
243C2×D4×C73—21no—
244C2×D4×C73—21no—
245C2×D4×C73—21no—
246C2×D4×C73—21no—
247C2×D4×C73—21no—
248C2×D4×C73—21no—
249C2×D4×C73—21no—
250C2×D4×C73—21no—
251C2×D4×C73—21no—
252C2×D4×C73—21no—
253C2×D4×C73—21no—
254C2×D4×C73—42no—
255C2×D4×C73—42no—
256C2×D4×C73—44no—
257C2×D4×C73—48no—
258C2×D4×C73—44no—
259C2×D4×C73—44no—
260C2×D4×C73—42no—
261C2×D4×C73—42no—
262C2×D4×C73C2×D411yescharacteristic
263C2×D4×C73C2×D411yescharacteristic
264C2×D4×C73C2×D411yescharacteristic
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—22no—
268C22×C4×C73—22no—
269C22×C4×C73—22no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—22no—
274C22×C4×C73—21no—
275C22×C4×C73C2×D412yes—
276C22×C4×C73C2×D412yes—
277C22×C4×C73C2411yescharacteristic
278Q16×C73—42no—
279Q16×C73—42no—
280Q16×C73—42no—
281SD16×C73—42no—
282SD16×C73—42no—
283SD16×C73—42no—
284SD16×C73—42no—
285SD16×C73—42no—
286SD16×C73—42no—
287D8×C73—42no—
288D8×C73—42no—
289D8×C73—42no—
290M16×C73—21no—
291M16×C73—21no—
292M16×C73—21no—
293M16×C73—21no—
294M16×C73—21no—
295M16×C73—21no—
296M16×C73C2×D412yes—
297M16×C73C2×D412yes—
298C2×C8×C73—21no—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—21no—
302C4⋊C4×C73—24no—
303C4⋊C4×C73—22no—
304C4⋊C4×C73—22no—
305C4⋊C4×C73—44no—
306C4⋊C4×C73C2×D412yes—
307C22⋊C4×C73—24no—
308C22⋊C4×C73—24no—
309C22⋊C4×C73—21no—
310C22⋊C4×C73—22no—
311C22⋊C4×C73—24no—
312C22⋊C4×C73—24no—
313C22⋊C4×C73—22no—
314C22⋊C4×C73—22no—
315C22⋊C4×C73—44no—
316C22⋊C4×C73—44no—
317C22⋊C4×C73—42no—
318C22⋊C4×C73—42no—
319C42×C73—22no—
320C42×C73—21no—
321C42×C73—21no—
322C42×C73—21no—
323C42×C73—44no—
324C42×C73C2×D412yes—
325C42×C73C2×D412yes—
326C42×C73C2×D411yescharacteristic
327C42×C73C2×D411yescharacteristic
328C42×C73C2×D412yes—
329C23×C73—21no—
330C23×C73—22no—
331C23×C73—21no—
332C23×C73—21no—
333C23×C73—22no—
334C23×C73—22no—
335C23×C73—44no—
336C23×C73—44no—
337C23×C73—44no—
338C23×C73—41no—
339C23×C73—41no—
340C23×C73—41no—
341C23×C73—84no—
342C23×C73C22×D411yescharacteristic
343Q8×C73—21no—
344Q8×C73—21no—
345Q8×C73—21no—
346Q8×C73—21no—
347Q8×C73—21no—
348Q8×C73—44no—
349Q8×C73—41no—
350Q8×C73—41no—
351Q8×C73—41no—
352Q8×C73—41no—
353Q8×C73—41no—
354Q8×C73—41no—
355Q8×C73—41no—
356Q8×C73—41no—
357Q8×C73#12712yes—
358D4×C73—22no—
359D4×C73—22no—
360D4×C73—21no—
361D4×C73—21no—
362D4×C73—21no—
363D4×C73—21no—
364D4×C73—21no—
365D4×C73—44no—
366D4×C73—44no—
367D4×C73—44no—
368D4×C73—41no—
369D4×C73—41no—
370D4×C73—41no—
371D4×C73—41no—
372D4×C73—41no—
373D4×C73—41no—
374D4×C73—41no—
375D4×C73—41no—
376D4×C73—41no—
377D4×C73—41no—
378D4×C73—41no—
379D4×C73—41no—
380D4×C73—82no—
381D4×C73—88no—
382D4×C73—84no—
383D4×C73#12712yes—
384C2×C4×C73—24no—
385C2×C4×C73—21no—
386C2×C4×C73—22no—
387C2×C4×C73—22no—
388C2×C4×C73—22no—
389C2×C4×C73—22no—
390C2×C4×C73—21no—
391C2×C4×C73—22no—
392C2×C4×C73—21no—
393C2×C4×C73—22no—
394C2×C4×C73—22no—
395C2×C4×C73—22no—
396C2×C4×C73—42no—
397C2×C4×C73—44no—
398C2×C4×C73—44no—
399C2×C4×C73—42no—
400C2×C4×C73—44no—
401C2×C4×C73—41no—
402C2×C4×C73—41no—
403C2×C4×C73—41no—
404C2×C4×C73—41no—
405C2×C4×C73—41no—
406C2×C4×C73—41no—
407C2×C4×C73—41no—
408C2×C4×C73—82no—
409C2×C4×C73#12012yes—
410C2×C4×C73#12012yes—
411C2×C4×C73C22×D411yescharacteristic
412C2×C4×C73C22×D411yescharacteristic
413C2×C4×C73C22×D411yescharacteristic
414C2×C4×C73C22×D411yescharacteristic
415C2×C4×C73H(5,𝔽2)11yescharacteristic
416C2×C4×C73H(5,𝔽2)11yescharacteristic
417C8×C73—22no—
418C8×C73—22no—
419C8×C73—41no—
420C8×C73—41no—
421C22×C73—22no—
422C22×C73—22no—
423C22×C73—42no—
424C22×C73—41no—
425C22×C73—41no—
426C22×C73—42no—
427C22×C73—42no—
428C22×C73—44no—
429C22×C73—42no—
430C22×C73—82no—
431C22×C73—82no—
432C22×C73—82no—
433C22×C73—82no—
434C22×C73—81no—
435C22×C73—82no—
436C22×C73—164no—
437C22×C73C2×#12011yescharacteristic
438C22×C73D4211yescharacteristic
439C22×C73D4211yescharacteristic
440C4×C73—24no—
441C4×C73—22no—
442C4×C73—22no—
443C4×C73—22no—
444C4×C73—42no—
445C4×C73—42no—
446C4×C73—41no—
447C4×C73—41no—
448C4×C73—42no—
449C4×C73—81no—
450C4×C73C2×#12711yescharacteristic
451C4×C73#53511yescharacteristic
452C4×C73D4211yescharacteristic
453C4×C73D4211yescharacteristic
454#25748C7311yesmaximal, characteristic, direct product factor, Sylow
455C2×C73—21no—
456C2×C73—21no—
457C2×C73—42no—
458C2×C73—81no—
459C2×C73—82no—
460C2×C73—81no—
461C2×C73—161no—
462C2×C73#243311yescharacteristic
463C2×C73#301812yes—
464#3500C2×C7311yescharacteristic, complemented
465#3153C2×C7311yescharacteristic, complemented
466#3040C2×C7311yescharacteristic, complemented
467C2×#456C2×C7311yescharacteristic, complemented
468C2×#454C2×C7311yescharacteristic, complemented
469C2×#455C2×C7311yescharacteristic, complemented
470C2×#453C2×C7311yescharacteristic, complemented
471#2858C2×C7311yescharacteristic, complemented
472#2005C2×C7311yescharacteristic, complemented
473#2004C2×C7311yescharacteristic, complemented
474#2003C2×C7311yescharacteristic, complemented
475#2002C2×C7311yescharacteristic, complemented
476#1967C2×C7311yescharacteristic, complemented
477#1962C2×C7311yescharacteristic, complemented
478C4×#104C2×C7311yescharacteristic, complemented
479C73#2574811yescharacteristic, direct product factor, Sylow
480C2×2−1+4C22×C7311yescharacteristic
481C2×H(5,𝔽2)C22×C7311yescharacteristic
482C2×#137C22×C7311yescharacteristic
483C2×#137C22×C7311yescharacteristic
484C2×#137C22×C7311yescharacteristic, complemented
485C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
486C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
487C2×AGL(1,ℤ/8)C22×C7311yescharacteristic, complemented
488#548—22no—
489#546—22no—
490#546—24no—
491#536—21no—
492#536C22×C7311yescharacteristic
493#535—21no—
494#535C22×C7311yescharacteristic
495#532—21no—
496#532C22×C7311yescharacteristic
497C2×C4⋊Q8C22×C7311yescharacteristic, complemented
498C2×#127C22×C7311yescharacteristic
499C2×#124—21no—
500C2×#124C22×C7311yescharacteristic
501C2×#124C22×C7311yescharacteristic
502C2×#124C22×C7311yescharacteristic, complemented
503C2×#124C22×C7311yescharacteristic, complemented
504C4×#41C22×C7311yescharacteristic
505#497—21no—
506#496—21no—
507#495—21no—
508#495—21no—
509#464—22no—
510#463—22no—
511#456—24no—
512#455—24no—
513#454—24no—
514#453—24no—
515#423C22×C7311yescharacteristic, complemented
516C2×#104C22×C7311yescharacteristic
517C2×#104C22×C7311yescharacteristic
518C2×#104C22×C7311yescharacteristic
519C2×#104C22×C7311yescharacteristic
520C2×#104C22×C7311yescharacteristic, complemented
521C2×#104C22×C7311yescharacteristic, complemented
522#419C22×C7311yescharacteristic, complemented
523#418C22×C7311yescharacteristic, complemented
524C2×#101C22×C7311yescharacteristic, complemented
525C2×#101C22×C7311yescharacteristic, complemented
526C2×#100C22×C7311yescharacteristic
527C2×#100C22×C7311yescharacteristic
528C4×M16C22×C7311yescharacteristic, complemented
529#390—24no—
530C43C22×C7311yescharacteristic, complemented
531#339C22×C7311yescharacteristic, complemented
532#339C22×C7311yescharacteristic, complemented
5332−1+4—22no—
5342−1+4—22no—
5352−1+4—41no—
5362−1+4—41no—
537H(5,𝔽2)—22no—
538H(5,𝔽2)—22no—
539H(5,𝔽2)—41no—
540H(5,𝔽2)—41no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—21no—
545C2×#41—22no—
546C2×#41C23×C7311yescharacteristic
547C2×#41C23×C7311yescharacteristic
548C2×#41C23×C7311yescharacteristic
549C22×Q8—21no—
550C22×Q8—21no—
551C22×Q8C23×C7311yescharacteristic
552C22×Q8C23×C7311yescharacteristic
553C22×D4—22no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4C23×C7311yescharacteristic
558C22×D4C23×C7311yescharacteristic
559#137—22no—
560#137—22no—
561#137—22no—
562#137—22no—
563#137—41no—
564#137—41no—
565AGL(1,ℤ/8)—22no—
566AGL(1,ℤ/8)—22no—
567AGL(1,ℤ/8)—22no—
568AGL(1,ℤ/8)—22no—
569AGL(1,ℤ/8)—41no—
570AGL(1,ℤ/8)—41no—
571C2×Q16—21no—
572C2×Q16—21no—
573C2×Q16—21no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—21no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—21no—
580C2×D8—21no—
581C2×D8—21no—
582C2×D8—21no—
583C2×M16C23×C7311yescharacteristic
584C2×M16C23×C7311yescharacteristic
585C2×M16C23×C7311yescharacteristic
586C2×M16C23×C7311yescharacteristic
587C4⋊Q8—21no—
588C4⋊Q8—22no—
589C4⋊Q8—41no—
590C4⋊Q8D4×C7311yescharacteristic, complemented
591#127—21no—
592#127—22no—
593#127—41no—
594#127D4×C7311yescharacteristic, complemented
595#124—24no—
596#124—21no—
597#124—21no—
598#124—21no—
599#124—21no—
600#124—22no—
601#124—22no—
602#124—22no—
603#124—22no—
604#124—21no—
605#124—21no—
606#124—41no—
607#124—41no—
608#124D4×C7311yescharacteristic, complemented
609#124D4×C7311yescharacteristic, complemented
610#123—24no—
611#123—22no—
612C22⋊Q8—24no—
613C22⋊Q8—22no—
614#121—24no—
615#121—24no—
616#121—22no—
617#121—22no—
618#120—24no—
619#120—22no—
620C4×Q8D4×C7312yescomplemented
621C4×D4—24no—
622C4×D4—22no—
623C4×D4—22no—
624C4×D4D4×C7312yescomplemented
625#117—21no—
626#117C23×C7311yescharacteristic
627C2×C4⋊C4—22no—
628C2×C22⋊C4—24no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4D4×C7314yes—
633C2×C42—21no—
634C2×C42—22no—
635C2×C42C23×C7311yescharacteristic
636C2×C42C23×C7311yescharacteristic
637C2×C42C23×C7311yescharacteristic
638C4⋊C8—22no—
639#104—22no—
640#104—22no—
641#104—22no—
642#104—22no—
643#104D4×C7314yescomplemented
644#104D4×C7314yescomplemented
645#103—22no—
646#102—22no—
647#101—22no—
648#101—22no—
649#100—22no—
650#100—22no—
651#97—21no—
652C4×C8—21no—
653C24—22no—
654C24—21no—
655C24C2×D4×C7312yes—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—21no—
660#41—21no—
661#41—21no—
662#41—21no—
663#41—21no—
664#41—21no—
665#41—21no—
666#41—42no—
667#41—42no—
668#41—44no—
669#41—44no—
670#41—42no—
671#41—42no—
672#41—42no—
673#41—42no—
674#41—42no—
675#41—42no—
676#41C2×D4×C7312yes—
677#41C2×D4×C7312yes—
678C2×Q8—22no—
679C2×Q8—21no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—42no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8—42no—
695C2×Q8C2×D4×C7311yescharacteristic
696C2×Q8C2×D4×C7311yescharacteristic
697C2×Q8C2×D4×C7311yescharacteristic
698C2×D4—21no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—44no—
721C2×D4—48no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4C2×D4×C7311yescharacteristic
727C2×D4C2×D4×C7311yescharacteristic
728C2×D4C2×D4×C7311yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4C2×D4×C7312yes—
740C22×C4C2×D4×C7312yes—
741C22×C4C24×C7311yescharacteristic
742Q16—42no—
743Q16—42no—
744Q16—42no—
745SD16—42no—
746SD16—42no—
747SD16—42no—
748SD16—42no—
749SD16—42no—
750SD16—42no—
751D8—42no—
752D8—42no—
753D8—42no—
754M16—21no—
755M16—21no—
756M16—21no—
757M16—21no—
758M16—21no—
759M16—21no—
760M16C2×D4×C7312yes—
761M16C2×D4×C7312yes—
762C2×C8—21no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—21no—
766C4⋊C4—24no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—44no—
770C4⋊C4C2×D4×C7312yes—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—21no—
774C22⋊C4—22no—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4—22no—
778C22⋊C4—22no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C42—22no—
784C42—21no—
785C42—21no—
786C42—21no—
787C42—44no—
788C42C2×D4×C7312yes—
789C42C2×D4×C7312yes—
790C42C2×D4×C7311yescharacteristic
791C42C2×D4×C7311yescharacteristic
792C42C2×D4×C7312yes—
793C23—21no—
794C23—22no—
795C23—21no—
796C23—21no—
797C23—22no—
798C23—22no—
799C23—44no—
800C23—44no—
801C23—44no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—84no—
806C23C22×D4×C7311yescharacteristic
807Q8—21no—
808Q8—21no—
809Q8—21no—
810Q8—21no—
811Q8—21no—
812Q8—44no—
813Q8—41no—
814Q8—41no—
815Q8—41no—
816Q8—41no—
817Q8—41no—
818Q8—41no—
819Q8—41no—
820Q8—41no—
821Q8#127×C7312yes—
822D4—22no—
823D4—22no—
824D4—21no—
825D4—21no—
826D4—21no—
827D4—21no—
828D4—21no—
829D4—44no—
830D4—44no—
831D4—44no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—82no—
845D4—88no—
846D4—84no—
847D4#127×C7312yes—
848C2×C4—24no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—42no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—82no—
873C2×C4#120×C7312yes—
874C2×C4#120×C7312yes—
875C2×C4C22×D4×C7311yescharacteristic
876C2×C4C22×D4×C7311yescharacteristic
877C2×C4C22×D4×C7311yescharacteristic
878C2×C4C22×D4×C7311yescharacteristic
879C2×C4H(5,𝔽2)×C7311yescharacteristic
880C2×C4H(5,𝔽2)×C7311yescharacteristic
881C8—22no—
882C8—22no—
883C8—41no—
884C8—41no—
885C22—22no—
886C22—22no—
887C22—42no—
888C22—42no—
889C22—44no—
890C22—42no—
891C22—41no—
892C22—41no—
893C22—42no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22—81no—
900C22—164no—
901C22C2×#120×C7311yescharacteristic
902C22D42×C7311yescharacteristic
903C22D42×C7311yescharacteristic
904C4—24no—
905C4—22no—
906C4—22no—
907C4—22no—
908C4—42no—
909C4—42no—
910C4—42no—
911C4—41no—
912C4—41no—
913C4—81no—
914C4C2×#127×C7311yescharacteristic
915C4#535×C7311yescharacteristic
916C4D42×C7311yescharacteristic
917C4D42×C7311yescharacteristic
918C2—21no—
919C2—21no—
920C2—42no—
921C2—82no—
922C2—81no—
923C2—81no—
924C2—161no—
925C2C73×#243311yescharacteristic
926C2C73×#301812yes—
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3500C2semidirect
2. C73×#3153C2semidirect
3. C73×#3040C2semidirect
4. C2×#456×C73C2semidirect
5. C2×#454×C73C2semidirect
6. C2×#455×C73C2semidirect
7. C2×#453×C73C2semidirect
8. C73×#2858C2semidirect
9. C73×#2005C2semidirect
10. C73×#2004C2semidirect
11. C73×#2003C2semidirect
12. C73×#2002C2semidirect
13. C73×#1967C2semidirect
14. C73×#1962C2semidirect
15. C4×#104×C73C2semidirect
20. C2×#137×C73C22semidirect
23. C2×AGL(1,ℤ/8)×C73C22semidirect
33. C2×C4⋊Q8×C73C22semidirect
38. C2×#124×C73C22semidirect
39. C2×#124×C73C22semidirect
51. #423×C73C22semidirect
56. C2×#104×C73C22semidirect
57. C2×#104×C73C22semidirect
58. #419×C73C22semidirect
59. #418×C73C22semidirect
60. C2×#101×C73C22semidirect
61. C2×#101×C73C22semidirect
64. C4×M16×C73C22semidirect
66. C43×C73C22semidirect
67. #339×C73C22semidirect
68. #339×C73C22semidirect
126. C4⋊Q8×C73D4semidirect
130. #127×C73D4semidirect
144. #124×C73D4semidirect
145. #124×C73D4semidirect
156. C4×Q8×C73D4semidirect
160. C4×D4×C73D4semidirect
179. #104×C73D4semidirect
180. #104×C73D4semidirect
454. #25748C73direct (N × H)
464. #3500C2×C73semidirect
465. #3153C2×C73semidirect
466. #3040C2×C73semidirect
467. C2×#456C2×C73semidirect
468. C2×#454C2×C73semidirect
469. C2×#455C2×C73semidirect
470. C2×#453C2×C73semidirect
471. #2858C2×C73semidirect
472. #2005C2×C73semidirect
473. #2004C2×C73semidirect
474. #2003C2×C73semidirect
475. #2002C2×C73semidirect
476. #1967C2×C73semidirect
477. #1962C2×C73semidirect
478. C4×#104C2×C73semidirect
479. C73#25748direct (N × H)
484. C2×#137C22×C73semidirect
487. C2×AGL(1,ℤ/8)C22×C73semidirect
497. C2×C4⋊Q8C22×C73semidirect
502. C2×#124C22×C73semidirect
503. C2×#124C22×C73semidirect
515. #423C22×C73semidirect
520. C2×#104C22×C73semidirect
521. C2×#104C22×C73semidirect
522. #419C22×C73semidirect
523. #418C22×C73semidirect
524. C2×#101C22×C73semidirect
525. C2×#101C22×C73semidirect
528. C4×M16C22×C73semidirect
530. C43C22×C73semidirect
531. #339C22×C73semidirect
532. #339C22×C73semidirect
590. C4⋊Q8D4×C73semidirect
594. #127D4×C73semidirect
608. #124D4×C73semidirect
609. #124D4×C73semidirect
620. C4×Q8D4×C73semidirect
624. C4×D4D4×C73semidirect
643. #104D4×C73semidirect
644. #104D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35002
C73×#31532
C73×#30402
C2×#456×C732
C2×#454×C732
C2×#455×C732
C2×#453×C732
C73×#28582
C73×#20052
C73×#20042
C73×#20032
C73×#20022
C73×#19672
C73×#19622
C4×#104×C732
#2574873