Finite Group Databasebeta

← C73×#25809 #32935213

Subgroups — C73×#25809 #32935213

Order 18688.

1414 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C73C211yesmaximal, characteristic, complemented
2C73×#3154C211yesmaximal, characteristic, complemented
3C2×#497×C73C211yesmaximal, characteristic, complemented
4C2×#471×C73C211yesmaximal, characteristic, complemented
5C2×#456×C73C211yesmaximal, characteristic, complemented
6C2×#454×C73C211yesmaximal, characteristic, complemented
7C73×#3011C211yesmaximal, characteristic, complemented
8C73×#3010C211yesmaximal, characteristic, complemented
9C73×#2020C211yesmaximal, characteristic, complemented
10C73×#2019C211yesmaximal, characteristic, complemented
11C73×#2005C211yesmaximal, characteristic, complemented
12C73×#2004C211yesmaximal, characteristic, complemented
13C73×#1979C211yesmaximal, characteristic, complemented
14C73×#1975C211yesmaximal, characteristic, complemented
15C73×#1765C211yesmaximal, characteristic, complemented
16C2×2−1+4×C73C2211yescharacteristic
17C2×2−1+4×C73C2211yescharacteristic
18#578×C73—24no—
19#578×C73—24no—
20C2×#137×C73—21no—
21C2×#137×C73—21no—
22C2×#137×C73C2211yescharacteristic
23C2×#137×C73C2211yescharacteristic
24C2×#137×C73C2211yescharacteristic
25C2×#137×C73C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
28C2×#135×C73—21no—
29C2×#135×C73C2211yescharacteristic
30C22×Q16×C73—21no—
31C22×Q16×C73C2211yescharacteristic
32C22×Q16×C73C2211yescharacteristic
33C22×SD16×C73C2211yescharacteristic
34C22×SD16×C73C2211yescharacteristic
35C2×#131×C73C2211yescharacteristic
36#536×C73C2211yescharacteristic
37#535×C73C2211yescharacteristic
38C2×C4⋊Q8×C73C2211yescharacteristic
39C2×#124×C73C2211yescharacteristic
40#497×C73—21no—
41#497×C73—24no—
42#496×C73—21no—
43#495×C73—21no—
44#492×C73—21no—
45#471×C73—24no—
46#456×C73—24no—
47#454×C73—24no—
48#452×C73—22no—
49#451×C73—22no—
50#449×C73—22no—
51#448×C73—22no—
52C2×#108×C73C2211yescharacteristic
53C2×#104×C73C2211yescharacteristic
54C2×#104×C73C2211yescharacteristic
55C2×#104×C73C2211yescharacteristic
56#419×C73C2211yescharacteristic
57#419×C73C2211yescharacteristic
58#416×C73C2211yescharacteristic
59C2×#101×C73C2211yescharacteristic
60C2×#101×C73C2211yescharacteristic
61C2×#101×C73C2211yescharacteristic
62C2×#100×C73C2211yescharacteristic
63#408×C73C2211yescharacteristic
64#408×C73C2211yescharacteristic
65#405×C73C2211yescharacteristic
66C2×#97×C73C2211yescharacteristic
67#341×C73C2211yescharacteristic
68#339×C73C2211yescharacteristic
692−1+4×C73—22no—
702−1+4×C73—22no—
712−1+4×C73—22no—
722−1+4×C73—22no—
732−1+4×C73—22no—
742−1+4×C73—22no—
752−1+4×C73—41no—
762−1+4×C73—41no—
77C2×#41×C73—21no—
78C2×#41×C73—21no—
79C2×#41×C73—21no—
80C2×#41×C73—21no—
81C2×#41×C73—41no—
82C2×#41×C73—41no—
83C2×#41×C73C2311yescharacteristic
84C2×#41×C73C2311yescharacteristic
85C2×#41×C73C2311yescharacteristic
86C22×Q8×C73—21no—
87C22×Q8×C73—21no—
88C22×Q8×C73—21no—
89C22×Q8×C73—21no—
90C22×Q8×C73C2311yescharacteristic
91C22×Q8×C73C2311yescharacteristic
92C22×Q8×C73C2311yescharacteristic
93C22×D4×C73C2311yescharacteristic
94#137×C73—28no—
95#137×C73—28no—
96#137×C73—22no—
97#137×C73—22no—
98#137×C73—22no—
99#137×C73—22no—
100#137×C73—22no—
101#137×C73—22no—
102#137×C73—22no—
103#137×C73—41no—
104AGL(1,ℤ/8)×C73—22no—
105AGL(1,ℤ/8)×C73—22no—
106AGL(1,ℤ/8)×C73—22no—
107AGL(1,ℤ/8)×C73—41no—
108#135×C73—28no—
109#135×C73—22no—
110#135×C73—22no—
111C2×Q16×C73—28no—
112C2×Q16×C73—21no—
113C2×Q16×C73—21no—
114C2×Q16×C73—21no—
115C2×Q16×C73—21no—
116C2×Q16×C73—22no—
117C2×Q16×C73—21no—
118C2×Q16×C73—21no—
119C2×Q16×C73—22no—
120C2×Q16×C73—22no—
121C2×Q16×C73—41no—
122C2×Q16×C73D411yescharacteristic
123C2×Q16×C73D414yescomplemented
124C2×SD16×C73—21no—
125C2×SD16×C73—21no—
126C2×SD16×C73—21no—
127C2×SD16×C73—21no—
128C2×SD16×C73—22no—
129C2×SD16×C73—21no—
130C2×SD16×C73—21no—
131C2×SD16×C73—22no—
132C2×SD16×C73—22no—
133C2×SD16×C73—21no—
134C2×SD16×C73—21no—
135C2×SD16×C73—22no—
136C2×SD16×C73—41no—
137C2×SD16×C73D411yescharacteristic
138C2×SD16×C73D411yescharacteristic
139C2×D8×C73—21no—
140C2×D8×C73—21no—
141C2×D8×C73D411yescharacteristic
142#131×C73—22no—
143#131×C73D414yescomplemented
144C2×M16×C73—21no—
145C2×M16×C73C2311yescharacteristic
146C2×M16×C73C2311yescharacteristic
147C2×M16×C73C2311yescharacteristic
148C2×M16×C73C2311yescharacteristic
149C22×C8×C73—21no—
150C22×C8×C73C2311yescharacteristic
151C22×C8×C73C2311yescharacteristic
152C4⋊Q8×C73—21no—
153C4⋊Q8×C73—22no—
154C4⋊Q8×C73—22no—
155#127×C73—21no—
156#124×C73—21no—
157#124×C73—22no—
158#124×C73—21no—
159#124×C73—22no—
160#123×C73—41no—
161C22⋊Q8×C73—22no—
162#121×C73—22no—
163#120×C73—41no—
164#117×C73C2311yescharacteristic
165C2×C4⋊C4×C73—41no—
166C2×C22⋊C4×C73—41no—
167C2×C42×C73C2311yescharacteristic
168#108×C73—22no—
169#104×C73—22no—
170#104×C73—22no—
171#104×C73D414yescomplemented
172#103×C73—22no—
173#103×C73—22no—
174#103×C73D412yes—
175#102×C73D412yes—
176#101×C73—22no—
177#101×C73—22no—
178#101×C73—22no—
179#100×C73—22no—
180C22⋊C8×C73—22no—
181C22⋊C8×C73—22no—
182#97×C73—22no—
183#97×C73—21no—
184C4×C8×C73—21no—
185C24×C73—21no—
186#41×C73—21no—
187#41×C73—21no—
188#41×C73—24no—
189#41×C73—24no—
190#41×C73—21no—
191#41×C73—21no—
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—42no—
199#41×C73—42no—
200#41×C73—44no—
201#41×C73—44no—
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×C73C2×D412yes—
209#41×C73C2×D412yes—
210C2×Q8×C73—21no—
211C2×Q8×C73—21no—
212C2×Q8×C73—24no—
213C2×Q8×C73—24no—
214C2×Q8×C73—21no—
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—21no—
228C2×Q8×C73—41no—
229C2×Q8×C73—41no—
230C2×Q8×C73—42no—
231C2×Q8×C73—42no—
232C2×Q8×C73—42no—
233C2×Q8×C73—42no—
234C2×Q8×C73—42no—
235C2×Q8×C73—42no—
236C2×Q8×C73C2×D411yescharacteristic
237C2×Q8×C73C2×D412yes—
238C2×Q8×C73C2×D411yescharacteristic
239C2×Q8×C73C2×D412yes—
240C2×Q8×C73C2×D411yescharacteristic
241C2×D4×C73—21no—
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—42no—
251C2×D4×C73—41no—
252C2×D4×C73—41no—
253C2×D4×C73C2×D411yescharacteristic
254C2×D4×C73C2×D411yescharacteristic
255C2×D4×C73C2×D411yescharacteristic
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—21no—
261C22×C4×C73—21no—
262C22×C4×C73—21no—
263C22×C4×C73—41no—
264C22×C4×C73—41no—
265C22×C4×C73—41no—
266C22×C4×C73—41no—
267C22×C4×C73C2411yescharacteristic
268Q16×C73—24no—
269Q16×C73—24no—
270Q16×C73—22no—
271Q16×C73—24no—
272Q16×C73—24no—
273Q16×C73—44no—
274Q16×C73—42no—
275Q16×C73—42no—
276SD16×C73—24no—
277SD16×C73—24no—
278SD16×C73—22no—
279SD16×C73—22no—
280SD16×C73—42no—
281SD16×C73—44no—
282SD16×C73—42no—
283SD16×C73—42no—
284SD16×C73—42no—
285SD16×C73—42no—
286SD16×C73—42no—
287D8×C73—22no—
288D8×C73—42no—
289D8×C73—42no—
290M16×C73—21no—
291M16×C73—21no—
292M16×C73—24no—
293M16×C73—21no—
294M16×C73—21no—
295M16×C73—21no—
296M16×C73—21no—
297M16×C73C2×D412yes—
298M16×C73C2×D412yes—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—21no—
302C2×C8×C73—21no—
303C2×C8×C73—24no—
304C2×C8×C73—21no—
305C2×C8×C73—21no—
306C2×C8×C73C2×D412yes—
307C2×C8×C73C2×D411yescharacteristic
308C2×C8×C73C2×D411yescharacteristic
309C2×C8×C73C2×D412yes—
310C2×C8×C73C2×D412yes—
311C4⋊C4×C73—44no—
312C4⋊C4×C73—42no—
313C4⋊C4×C73C2×D412yes—
314C22⋊C4×C73—21no—
315C22⋊C4×C73—44no—
316C22⋊C4×C73—42no—
317C22⋊C4×C73—42no—
318C42×C73—21no—
319C42×C73—21no—
320C42×C73C2×D412yes—
321C23×C73—21no—
322C23×C73—21no—
323C23×C73—21no—
324C23×C73—41no—
325C23×C73—41no—
326C23×C73—41no—
327C23×C73—82no—
328C23×C73H(5,𝔽2)11yescharacteristic
329Q8×C73—21no—
330Q8×C73—22no—
331Q8×C73—22no—
332Q8×C73—21no—
333Q8×C73—21no—
334Q8×C73—22no—
335Q8×C73—21no—
336Q8×C73—22no—
337Q8×C73—21no—
338Q8×C73—44no—
339Q8×C73—44no—
340Q8×C73—41no—
341Q8×C73—41no—
342Q8×C73—41no—
343Q8×C73—41no—
344Q8×C73—41no—
345Q8×C73—41no—
346Q8×C73—41no—
347Q8×C73—41no—
348Q8×C73#12712yes—
349D4×C73—22no—
350D4×C73—22no—
351D4×C73—21no—
352D4×C73—21no—
353D4×C73—21no—
354D4×C73—21no—
355D4×C73—21no—
356D4×C73—44no—
357D4×C73—44no—
358D4×C73—41no—
359D4×C73—41no—
360D4×C73—41no—
361D4×C73—41no—
362D4×C73—41no—
363D4×C73—41no—
364D4×C73—41no—
365D4×C73—41no—
366D4×C73—162no—
367D4×C73#12712yes—
368C2×C4×C73—21no—
369C2×C4×C73—22no—
370C2×C4×C73—22no—
371C2×C4×C73—22no—
372C2×C4×C73—22no—
373C2×C4×C73—22no—
374C2×C4×C73—22no—
375C2×C4×C73—21no—
376C2×C4×C73—21no—
377C2×C4×C73—44no—
378C2×C4×C73—44no—
379C2×C4×C73—42no—
380C2×C4×C73—44no—
381C2×C4×C73—44no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73C22×D411yescharacteristic
394C2×C4×C73C22×D411yescharacteristic
395C2×C4×C73C22×D411yescharacteristic
396C2×C4×C73C22×D411yescharacteristic
397C2×C4×C73C22×D411yescharacteristic
398C2×C4×C73H(5,𝔽2)11yescharacteristic
399C8×C73—22no—
400C8×C73—22no—
401C8×C73—22no—
402C8×C73—41no—
403C8×C73—41no—
404C8×C73#12012yes—
405C8×C73#12012yes—
406C22×C73—22no—
407C22×C73—22no—
408C22×C73—42no—
409C22×C73—41no—
410C22×C73—41no—
411C22×C73—42no—
412C22×C73—42no—
413C22×C73—82no—
414C22×C73—81no—
415C22×C73—82no—
416C22×C73—161no—
417C22×C73#53511yescharacteristic
418C22×C73D4211yescharacteristic
419C22×C73D4211yescharacteristic
420C4×C73—22no—
421C4×C73—42no—
422C4×C73—42no—
423C4×C73—42no—
424C4×C73—41no—
425C4×C73—41no—
426C4×C73—42no—
427C4×C73—81no—
428C4×C73C2×#12011yescharacteristic
429C4×C73C2×#12711yescharacteristic
430C4×C73D4211yescharacteristic
431C4×C73D4211yescharacteristic
432#25809C7311yesmaximal, characteristic, direct product factor, Sylow
433C2×C73—21no—
434C2×C73—21no—
435C2×C73—42no—
436C2×C73—81no—
437C2×C73—81no—
438C2×C73—161no—
439C2×C73#243311yescharacteristic
440C2×C73#328912yes—
441C2×#578C2×C7311yescharacteristic, complemented
442#3154C2×C7311yescharacteristic, complemented
443C2×#497C2×C7311yescharacteristic, complemented
444C2×#471C2×C7311yescharacteristic, complemented
445C2×#456C2×C7311yescharacteristic, complemented
446C2×#454C2×C7311yescharacteristic, complemented
447#3011C2×C7311yescharacteristic, complemented
448#3010C2×C7311yescharacteristic, complemented
449#2020C2×C7311yescharacteristic, complemented
450#2019C2×C7311yescharacteristic, complemented
451#2005C2×C7311yescharacteristic, complemented
452#2004C2×C7311yescharacteristic, complemented
453#1979C2×C7311yescharacteristic, complemented
454#1975C2×C7311yescharacteristic, complemented
455#1765C2×C7311yescharacteristic, complemented
456C73#2580911yescharacteristic, direct product factor, Sylow
457C2×2−1+4C22×C7311yescharacteristic
458C2×2−1+4C22×C7311yescharacteristic
459#578—24no—
460#578—24no—
461C2×#137—21no—
462C2×#137—21no—
463C2×#137C22×C7311yescharacteristic
464C2×#137C22×C7311yescharacteristic
465C2×#137C22×C7311yescharacteristic
466C2×#137C22×C7311yescharacteristic
467C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
468C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
469C2×#135—21no—
470C2×#135C22×C7311yescharacteristic
471C22×Q16—21no—
472C22×Q16C22×C7311yescharacteristic
473C22×Q16C22×C7311yescharacteristic
474C22×SD16C22×C7311yescharacteristic
475C22×SD16C22×C7311yescharacteristic
476C2×#131C22×C7311yescharacteristic
477#536C22×C7311yescharacteristic
478#535C22×C7311yescharacteristic
479C2×C4⋊Q8C22×C7311yescharacteristic
480C2×#124C22×C7311yescharacteristic
481#497—21no—
482#497—24no—
483#496—21no—
484#495—21no—
485#492—21no—
486#471—24no—
487#456—24no—
488#454—24no—
489#452—22no—
490#451—22no—
491#449—22no—
492#448—22no—
493C2×#108C22×C7311yescharacteristic
494C2×#104C22×C7311yescharacteristic
495C2×#104C22×C7311yescharacteristic
496C2×#104C22×C7311yescharacteristic
497#419C22×C7311yescharacteristic
498#419C22×C7311yescharacteristic
499#416C22×C7311yescharacteristic
500C2×#101C22×C7311yescharacteristic
501C2×#101C22×C7311yescharacteristic
502C2×#101C22×C7311yescharacteristic
503C2×#100C22×C7311yescharacteristic
504#408C22×C7311yescharacteristic
505#408C22×C7311yescharacteristic
506#405C22×C7311yescharacteristic
507C2×#97C22×C7311yescharacteristic
508#341C22×C7311yescharacteristic
509#339C22×C7311yescharacteristic
5102−1+4—22no—
5112−1+4—22no—
5122−1+4—22no—
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—22no—
5162−1+4—41no—
5172−1+4—41no—
518C2×#41—21no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—21no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41C23×C7311yescharacteristic
525C2×#41C23×C7311yescharacteristic
526C2×#41C23×C7311yescharacteristic
527C22×Q8—21no—
528C22×Q8—21no—
529C22×Q8—21no—
530C22×Q8—21no—
531C22×Q8C23×C7311yescharacteristic
532C22×Q8C23×C7311yescharacteristic
533C22×Q8C23×C7311yescharacteristic
534C22×D4C23×C7311yescharacteristic
535#137—28no—
536#137—28no—
537#137—22no—
538#137—22no—
539#137—22no—
540#137—22no—
541#137—22no—
542#137—22no—
543#137—22no—
544#137—41no—
545AGL(1,ℤ/8)—22no—
546AGL(1,ℤ/8)—22no—
547AGL(1,ℤ/8)—22no—
548AGL(1,ℤ/8)—41no—
549#135—28no—
550#135—22no—
551#135—22no—
552C2×Q16—28no—
553C2×Q16—21no—
554C2×Q16—21no—
555C2×Q16—22no—
556C2×Q16—21no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—21no—
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—41no—
563C2×Q16D4×C7311yescharacteristic
564C2×Q16D4×C7314yescomplemented
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—22no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×SD16D4×C7311yescharacteristic
579C2×SD16D4×C7311yescharacteristic
580C2×D8—21no—
581C2×D8—21no—
582C2×D8D4×C7311yescharacteristic
583#131—22no—
584#131D4×C7314yescomplemented
585C2×M16—21no—
586C2×M16C23×C7311yescharacteristic
587C2×M16C23×C7311yescharacteristic
588C2×M16C23×C7311yescharacteristic
589C2×M16C23×C7311yescharacteristic
590C22×C8—21no—
591C22×C8C23×C7311yescharacteristic
592C22×C8C23×C7311yescharacteristic
593C4⋊Q8—22no—
594C4⋊Q8—21no—
595C4⋊Q8—22no—
596#127—21no—
597#124—22no—
598#124—21no—
599#124—21no—
600#124—22no—
601#123—41no—
602C22⋊Q8—22no—
603#121—22no—
604#120—41no—
605#117C23×C7311yescharacteristic
606C2×C4⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C42C23×C7311yescharacteristic
609#108—22no—
610#104—22no—
611#104—22no—
612#104D4×C7314yescomplemented
613#103—22no—
614#103—22no—
615#103D4×C7312yes—
616#102D4×C7312yes—
617#101—22no—
618#101—22no—
619#101—22no—
620#100—22no—
621C22⋊C8—22no—
622C22⋊C8—22no—
623#97—22no—
624#97—21no—
625C4×C8—21no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—24no—
630#41—24no—
631#41—21no—
632#41—21no—
633#41—21no—
634#41—21no—
635#41—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—42no—
640#41—42no—
641#41—44no—
642#41—44no—
643#41—42no—
644#41—42no—
645#41—44no—
646#41—44no—
647#41—42no—
648#41—42no—
649#41C2×D4×C7312yes—
650#41C2×D4×C7312yes—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—24no—
654C2×Q8—24no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—41no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8C2×D4×C7311yescharacteristic
678C2×Q8C2×D4×C7312yes—
679C2×Q8C2×D4×C7311yescharacteristic
680C2×Q8C2×D4×C7312yes—
681C2×Q8C2×D4×C7311yescharacteristic
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—42no—
692C2×D4—41no—
693C2×D4—41no—
694C2×D4C2×D4×C7311yescharacteristic
695C2×D4C2×D4×C7311yescharacteristic
696C2×D4C2×D4×C7311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—41no—
705C22×C4—41no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4C24×C7311yescharacteristic
709Q16—24no—
710Q16—24no—
711Q16—22no—
712Q16—24no—
713Q16—24no—
714Q16—44no—
715Q16—42no—
716Q16—42no—
717SD16—24no—
718SD16—24no—
719SD16—22no—
720SD16—22no—
721SD16—42no—
722SD16—44no—
723SD16—42no—
724SD16—42no—
725SD16—42no—
726SD16—42no—
727SD16—42no—
728D8—22no—
729D8—42no—
730D8—42no—
731M16—21no—
732M16—21no—
733M16—24no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16C2×D4×C7312yes—
739M16C2×D4×C7312yes—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—24no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8C2×D4×C7312yes—
748C2×C8C2×D4×C7311yescharacteristic
749C2×C8C2×D4×C7311yescharacteristic
750C2×C8C2×D4×C7312yes—
751C2×C8C2×D4×C7312yes—
752C4⋊C4—44no—
753C4⋊C4—42no—
754C4⋊C4C2×D4×C7312yes—
755C22⋊C4—21no—
756C22⋊C4—44no—
757C22⋊C4—42no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42C2×D4×C7312yes—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—82no—
769C23H(5,𝔽2)×C7311yescharacteristic
770Q8—21no—
771Q8—22no—
772Q8—22no—
773Q8—21no—
774Q8—21no—
775Q8—22no—
776Q8—21no—
777Q8—22no—
778Q8—21no—
779Q8—44no—
780Q8—44no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#127×C7312yes—
790D4—22no—
791D4—22no—
792D4—21no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—44no—
798D4—44no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—162no—
808D4#127×C7312yes—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4C22×D4×C7311yescharacteristic
835C2×C4C22×D4×C7311yescharacteristic
836C2×C4C22×D4×C7311yescharacteristic
837C2×C4C22×D4×C7311yescharacteristic
838C2×C4C22×D4×C7311yescharacteristic
839C2×C4H(5,𝔽2)×C7311yescharacteristic
840C8—22no—
841C8—22no—
842C8—22no—
843C8—41no—
844C8—41no—
845C8#120×C7312yes—
846C8#120×C7312yes—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—41no—
853C22—41no—
854C22—82no—
855C22—82no—
856C22—81no—
857C22—161no—
858C22#535×C7311yescharacteristic
859C22D42×C7311yescharacteristic
860C22D42×C7311yescharacteristic
861C4—22no—
862C4—42no—
863C4—42no—
864C4—41no—
865C4—42no—
866C4—41no—
867C4—42no—
868C4—81no—
869C4C2×#120×C7311yescharacteristic
870C4C2×#127×C7311yescharacteristic
871C4D42×C7311yescharacteristic
872C4D42×C7311yescharacteristic
873C2—21no—
874C2—21no—
875C2—42no—
876C2—81no—
877C2—81no—
878C2—161no—
879C2C73×#243311yescharacteristic
880C2C73×#328912yes—
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. C73×#3154C2semidirect
3. C2×#497×C73C2semidirect
4. C2×#471×C73C2semidirect
5. C2×#456×C73C2semidirect
6. C2×#454×C73C2semidirect
7. C73×#3011C2semidirect
8. C73×#3010C2semidirect
9. C73×#2020C2semidirect
10. C73×#2019C2semidirect
11. C73×#2005C2semidirect
12. C73×#2004C2semidirect
13. C73×#1979C2semidirect
14. C73×#1975C2semidirect
15. C73×#1765C2semidirect
123. C2×Q16×C73D4semidirect
143. #131×C73D4semidirect
171. #104×C73D4semidirect
432. #25809C73direct (N × H)
441. C2×#578C2×C73semidirect
442. #3154C2×C73semidirect
443. C2×#497C2×C73semidirect
444. C2×#471C2×C73semidirect
445. C2×#456C2×C73semidirect
446. C2×#454C2×C73semidirect
447. #3011C2×C73semidirect
448. #3010C2×C73semidirect
449. #2020C2×C73semidirect
450. #2019C2×C73semidirect
451. #2005C2×C73semidirect
452. #2004C2×C73semidirect
453. #1979C2×C73semidirect
454. #1975C2×C73semidirect
455. #1765C2×C73semidirect
456. C73#25809direct (N × H)
564. C2×Q16D4×C73semidirect
584. #131D4×C73semidirect
612. #104D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C732
C73×#31542
C2×#497×C732
C2×#471×C732
C2×#456×C732
C2×#454×C732
C73×#30112
C73×#30102
C73×#20202
C73×#20192
C73×#20052
C73×#20042
C73×#19792
C73×#19752
C73×#17652
#2580973