Finite Group Databasebeta

← C73×#25810 #32935214

Subgroups — C73×#25810 #32935214

Order 18688.

1498 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#576×C73C211yesmaximal, characteristic, complemented
2C73×#3154C211yesmaximal, characteristic, complemented
3C2×#496×C73C211yesmaximal, characteristic, complemented
4C2×#471×C73C211yesmaximal, characteristic, complemented
5C2×#455×C73C211yesmaximal, characteristic, complemented
6C2×#453×C73C211yesmaximal, characteristic, complemented
7C73×#3009C211yesmaximal, characteristic, complemented
8C73×#3008C211yesmaximal, characteristic, complemented
9C73×#2019C211yesmaximal, characteristic, complemented
10C73×#2018C211yesmaximal, characteristic, complemented
11C73×#2003C211yesmaximal, characteristic, complemented
12C73×#2002C211yesmaximal, characteristic, complemented
13C73×#1978C211yesmaximal, characteristic, complemented
14C73×#1975C211yesmaximal, characteristic, complemented
15C73×#1765C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C73C2211yescharacteristic
17C2×H(5,𝔽2)×C73C2211yescharacteristic
18#576×C73—24no—
19#576×C73—24no—
20C2×#137×C73C2211yescharacteristic
21C2×#137×C73C2211yescharacteristic, complemented
22C2×AGL(1,ℤ/8)×C73—21no—
23C2×AGL(1,ℤ/8)×C73—21no—
24C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
26C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C73C2211yescharacteristic, complemented
28C2×#135×C73—21no—
29C2×#135×C73C2211yescharacteristic
30C22×SD16×C73C2211yescharacteristic, complemented
31C22×SD16×C73C2211yescharacteristic, complemented
32C22×D8×C73—21no—
33C22×D8×C73C2211yescharacteristic
34C22×D8×C73C2211yescharacteristic, complemented
35C2×#131×C73C2211yescharacteristic
36#536×C73C2211yescharacteristic, complemented
37#535×C73C2211yescharacteristic, complemented
38C2×#127×C73C2211yescharacteristic, complemented
39C2×#124×C73C2211yescharacteristic, complemented
40#497×C73—21no—
41#496×C73—24no—
42#496×C73—21no—
43#495×C73—21no—
44#492×C73—21no—
45#471×C73—24no—
46#455×C73—24no—
47#453×C73—24no—
48#452×C73—22no—
49#450×C73—22no—
50#449×C73—22no—
51#447×C73—22no—
52C2×#108×C73C2211yescharacteristic, complemented
53C2×#104×C73C2211yescharacteristic
54C2×#104×C73C2211yescharacteristic, complemented
55C2×#104×C73C2211yescharacteristic, complemented
56#418×C73C2211yescharacteristic, complemented
57#418×C73C2211yescharacteristic, complemented
58#416×C73C2211yescharacteristic
59C2×#101×C73C2211yescharacteristic, complemented
60C2×#100×C73C2211yescharacteristic, complemented
61C2×#100×C73C2211yescharacteristic, complemented
62C2×#100×C73C2211yescharacteristic, complemented
63#408×C73C2211yescharacteristic, complemented
64#408×C73C2211yescharacteristic, complemented
65#405×C73C2211yescharacteristic, complemented
66C2×#97×C73C2211yescharacteristic, complemented
67#341×C73C2211yescharacteristic, complemented
68#339×C73C2211yescharacteristic, complemented
69H(5,𝔽2)×C73—22no—
70H(5,𝔽2)×C73—22no—
71H(5,𝔽2)×C73—22no—
72H(5,𝔽2)×C73—22no—
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×C73C2311yescharacteristic
82C2×#41×C73C2311yescharacteristic
83C2×#41×C73C2311yescharacteristic
84C22×Q8×C73C2311yescharacteristic
85C22×D4×C73—21no—
86C22×D4×C73—21no—
87C22×D4×C73—21no—
88C22×D4×C73—21no—
89C22×D4×C73—41no—
90C22×D4×C73—41no—
91C22×D4×C73—41no—
92C22×D4×C73C2311yescharacteristic
93C22×D4×C73C2311yescharacteristic
94C22×D4×C73C2311yescharacteristic
95#137×C73—22no—
96#137×C73—22no—
97#137×C73—22no—
98#137×C73—41no—
99AGL(1,ℤ/8)×C73—28no—
100AGL(1,ℤ/8)×C73—28no—
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—22no—
106AGL(1,ℤ/8)×C73—22no—
107AGL(1,ℤ/8)×C73—22no—
108AGL(1,ℤ/8)×C73—41no—
109#135×C73—28no—
110#135×C73—22no—
111#135×C73—22no—
112C2×Q16×C73—21no—
113C2×Q16×C73—21no—
114C2×Q16×C73D411yescharacteristic, complemented
115C2×SD16×C73—21no—
116C2×SD16×C73—21no—
117C2×SD16×C73—21no—
118C2×SD16×C73—21no—
119C2×SD16×C73—21no—
120C2×SD16×C73—21no—
121C2×SD16×C73—22no—
122C2×SD16×C73—22no—
123C2×SD16×C73—22no—
124C2×SD16×C73—21no—
125C2×SD16×C73—22no—
126C2×SD16×C73—21no—
127C2×SD16×C73—41no—
128C2×SD16×C73D411yescharacteristic, complemented
129C2×SD16×C73D411yescharacteristic, complemented
130C2×D8×C73—28no—
131C2×D8×C73—21no—
132C2×D8×C73—21no—
133C2×D8×C73—21no—
134C2×D8×C73—21no—
135C2×D8×C73—22no—
136C2×D8×C73—21no—
137C2×D8×C73—21no—
138C2×D8×C73—22no—
139C2×D8×C73—22no—
140C2×D8×C73—41no—
141C2×D8×C73D411yescharacteristic, complemented
142C2×D8×C73D414yescomplemented
143#131×C73—22no—
144#131×C73D414yescomplemented
145C2×M16×C73—21no—
146C2×M16×C73C2311yescharacteristic
147C2×M16×C73C2311yescharacteristic
148C2×M16×C73C2311yescharacteristic
149C2×M16×C73C2311yescharacteristic
150C22×C8×C73—21no—
151C22×C8×C73C2311yescharacteristic
152C22×C8×C73C2311yescharacteristic
153C4⋊Q8×C73—21no—
154#127×C73—21no—
155#127×C73—22no—
156#127×C73—22no—
157#124×C73—21no—
158#124×C73—21no—
159#124×C73—22no—
160#124×C73—22no—
161#123×C73—41no—
162C22⋊Q8×C73—22no—
163#121×C73—22no—
164#120×C73—41no—
165#117×C73C2311yescharacteristic
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×C73D412yescomplemented
173#102×C73—22no—
174#102×C73—22no—
175#102×C73D412yescomplemented
176#101×C73—22no—
177#100×C73—22no—
178#100×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—
186C24×C73—21no—
187C24×C73—21no—
188C24×C73—41no—
189C24×C73—41no—
190#41×C73—21no—
191#41×C73—21no—
192#41×C73—24no—
193#41×C73—24no—
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—42no—
205#41×C73—42no—
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—21no—
213C2×Q8×C73—21no—
214C2×Q8×C73—21no—
215C2×Q8×C73—21no—
216C2×Q8×C73C2×D411yescharacteristic
217C2×Q8×C73C2×D411yescharacteristic
218C2×Q8×C73C2×D411yescharacteristic
219C2×D4×C73—21no—
220C2×D4×C73—24no—
221C2×D4×C73—24no—
222C2×D4×C73—21no—
223C2×D4×C73—21no—
224C2×D4×C73—21no—
225C2×D4×C73—21no—
226C2×D4×C73—21no—
227C2×D4×C73—21no—
228C2×D4×C73—21no—
229C2×D4×C73—21no—
230C2×D4×C73—21no—
231C2×D4×C73—21no—
232C2×D4×C73—21no—
233C2×D4×C73—21no—
234C2×D4×C73—21no—
235C2×D4×C73—21no—
236C2×D4×C73—21no—
237C2×D4×C73—21no—
238C2×D4×C73—21no—
239C2×D4×C73—21no—
240C2×D4×C73—42no—
241C2×D4×C73—42no—
242C2×D4×C73—41no—
243C2×D4×C73—41no—
244C2×D4×C73—41no—
245C2×D4×C73—41no—
246C2×D4×C73—44no—
247C2×D4×C73—42no—
248C2×D4×C73—42no—
249C2×D4×C73—42no—
250C2×D4×C73—44no—
251C2×D4×C73—44no—
252C2×D4×C73—44no—
253C2×D4×C73—44no—
254C2×D4×C73—42no—
255C2×D4×C73—42no—
256C2×D4×C73—84no—
257C2×D4×C73C2×D411yescharacteristic
258C2×D4×C73C2×D412yes—
259C2×D4×C73C2×D411yescharacteristic
260C2×D4×C73C2×D412yes—
261C2×D4×C73C2×D411yescharacteristic
262C22×C4×C73—21no—
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—41no—
268C22×C4×C73—41no—
269C22×C4×C73C2411yescharacteristic
270Q16×C73—22no—
271Q16×C73—42no—
272Q16×C73—42no—
273SD16×C73—24no—
274SD16×C73—24no—
275SD16×C73—22no—
276SD16×C73—22no—
277SD16×C73—44no—
278SD16×C73—42no—
279SD16×C73—42no—
280SD16×C73—42no—
281SD16×C73—42no—
282SD16×C73—42no—
283SD16×C73—42no—
284D8×C73—24no—
285D8×C73—24no—
286D8×C73—22no—
287D8×C73—24no—
288D8×C73—24no—
289D8×C73—44no—
290D8×C73—42no—
291D8×C73—42no—
292M16×C73—21no—
293M16×C73—21no—
294M16×C73—24no—
295M16×C73—21no—
296M16×C73—21no—
297M16×C73—21no—
298M16×C73—21no—
299M16×C73C2×D412yes—
300M16×C73C2×D412yes—
301C2×C8×C73—21no—
302C2×C8×C73—21no—
303C2×C8×C73—21no—
304C2×C8×C73—21no—
305C2×C8×C73—24no—
306C2×C8×C73—21no—
307C2×C8×C73—21no—
308C2×C8×C73C2×D412yes—
309C2×C8×C73C2×D411yescharacteristic
310C2×C8×C73C2×D411yescharacteristic
311C2×C8×C73C2×D412yes—
312C2×C8×C73C2×D412yes—
313C4⋊C4×C73—42no—
314C4⋊C4×C73C2×D412yes—
315C22⋊C4×C73—21no—
316C22⋊C4×C73—42no—
317C22⋊C4×C73—44no—
318C22⋊C4×C73—42no—
319C42×C73—21no—
320C42×C73—21no—
321C42×C73C2×D412yes—
322C23×C73—21no—
323C23×C73—21no—
324C23×C73—21no—
325C23×C73—22no—
326C23×C73—22no—
327C23×C73—44no—
328C23×C73—44no—
329C23×C73—41no—
330C23×C73—41no—
331C23×C73—41no—
332C23×C73—41no—
333C23×C73—41no—
334C23×C73—41no—
335C23×C73—41no—
336C23×C73—82no—
337C23×C73—82no—
338C23×C73—82no—
339C23×C73—162no—
340C23×C73—162no—
341C23×C73H(5,𝔽2)11yescharacteristic
342Q8×C73—21no—
343Q8×C73—21no—
344Q8×C73—21no—
345Q8×C73—21no—
346Q8×C73—21no—
347Q8×C73—41no—
348Q8×C73—41no—
349Q8×C73—41no—
350Q8×C73—41no—
351Q8×C73#12712yes—
352D4×C73—22no—
353D4×C73—22no—
354D4×C73—21no—
355D4×C73—21no—
356D4×C73—22no—
357D4×C73—22no—
358D4×C73—21no—
359D4×C73—22no—
360D4×C73—21no—
361D4×C73—22no—
362D4×C73—21no—
363D4×C73—44no—
364D4×C73—44no—
365D4×C73—44no—
366D4×C73—44no—
367D4×C73—41no—
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—88no—
380D4×C73—162no—
381D4×C73#12712yes—
382C2×C4×C73—21no—
383C2×C4×C73—22no—
384C2×C4×C73—22no—
385C2×C4×C73—22no—
386C2×C4×C73—22no—
387C2×C4×C73—21no—
388C2×C4×C73—21no—
389C2×C4×C73—44no—
390C2×C4×C73—44no—
391C2×C4×C73—42no—
392C2×C4×C73—41no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—41no—
396C2×C4×C73—41no—
397C2×C4×C73—41no—
398C2×C4×C73—41no—
399C2×C4×C73C22×D411yescharacteristic
400C2×C4×C73C22×D411yescharacteristic
401C2×C4×C73C22×D411yescharacteristic
402C2×C4×C73C22×D411yescharacteristic
403C2×C4×C73C22×D411yescharacteristic
404C2×C4×C73H(5,𝔽2)11yescharacteristic
405C8×C73—22no—
406C8×C73—22no—
407C8×C73—22no—
408C8×C73—41no—
409C8×C73—41no—
410C8×C73#12012yes—
411C8×C73#12012yes—
412C22×C73—22no—
413C22×C73—22no—
414C22×C73—42no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—42no—
418C22×C73—42no—
419C22×C73—42no—
420C22×C73—42no—
421C22×C73—82no—
422C22×C73—82no—
423C22×C73—82no—
424C22×C73—82no—
425C22×C73—82no—
426C22×C73—81no—
427C22×C73—82no—
428C22×C73—161no—
429C22×C73—161no—
430C22×C73—161no—
431C22×C73—164no—
432C22×C73—164no—
433C22×C73#53511yescharacteristic
434C22×C73D4211yescharacteristic
435C22×C73D4211yescharacteristic
436C4×C73—22no—
437C4×C73—42no—
438C4×C73—41no—
439C4×C73—41no—
440C4×C73—42no—
441C4×C73—81no—
442C4×C73C2×#12011yescharacteristic
443C4×C73C2×#12711yescharacteristic
444C4×C73D4211yescharacteristic
445C4×C73D4211yescharacteristic
446#25810C7311yesmaximal, characteristic, direct product factor, Sylow
447C2×C73—21no—
448C2×C73—21no—
449C2×C73—42no—
450C2×C73—81no—
451C2×C73—81no—
452C2×C73—82no—
453C2×C73—82no—
454C2×C73—161no—
455C2×C73#243311yescharacteristic
456C2×C73#328812yes—
457C2×#576C2×C7311yescharacteristic, complemented
458#3154C2×C7311yescharacteristic, complemented
459C2×#496C2×C7311yescharacteristic, complemented
460C2×#471C2×C7311yescharacteristic, complemented
461C2×#455C2×C7311yescharacteristic, complemented
462C2×#453C2×C7311yescharacteristic, complemented
463#3009C2×C7311yescharacteristic, complemented
464#3008C2×C7311yescharacteristic, complemented
465#2019C2×C7311yescharacteristic, complemented
466#2018C2×C7311yescharacteristic, complemented
467#2003C2×C7311yescharacteristic, complemented
468#2002C2×C7311yescharacteristic, complemented
469#1978C2×C7311yescharacteristic, complemented
470#1975C2×C7311yescharacteristic, complemented
471#1765C2×C7311yescharacteristic, complemented
472C73#2581011yescharacteristic, direct product factor, Sylow
473C2×H(5,𝔽2)C22×C7311yescharacteristic
474C2×H(5,𝔽2)C22×C7311yescharacteristic
475#576—24no—
476#576—24no—
477C2×#137C22×C7311yescharacteristic
478C2×#137C22×C7311yescharacteristic, complemented
479C2×AGL(1,ℤ/8)—21no—
480C2×AGL(1,ℤ/8)—21no—
481C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
482C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
483C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
484C2×AGL(1,ℤ/8)C22×C7311yescharacteristic, complemented
485C2×#135—21no—
486C2×#135C22×C7311yescharacteristic
487C22×SD16C22×C7311yescharacteristic, complemented
488C22×SD16C22×C7311yescharacteristic, complemented
489C22×D8—21no—
490C22×D8C22×C7311yescharacteristic
491C22×D8C22×C7311yescharacteristic, complemented
492C2×#131C22×C7311yescharacteristic
493#536C22×C7311yescharacteristic, complemented
494#535C22×C7311yescharacteristic, complemented
495C2×#127C22×C7311yescharacteristic, complemented
496C2×#124C22×C7311yescharacteristic, complemented
497#497—21no—
498#496—24no—
499#496—21no—
500#495—21no—
501#492—21no—
502#471—24no—
503#455—24no—
504#453—24no—
505#452—22no—
506#450—22no—
507#449—22no—
508#447—22no—
509C2×#108C22×C7311yescharacteristic, complemented
510C2×#104C22×C7311yescharacteristic
511C2×#104C22×C7311yescharacteristic, complemented
512C2×#104C22×C7311yescharacteristic, complemented
513#418C22×C7311yescharacteristic, complemented
514#418C22×C7311yescharacteristic, complemented
515#416C22×C7311yescharacteristic
516C2×#101C22×C7311yescharacteristic, complemented
517C2×#100C22×C7311yescharacteristic, complemented
518C2×#100C22×C7311yescharacteristic, complemented
519C2×#100C22×C7311yescharacteristic, complemented
520#408C22×C7311yescharacteristic, complemented
521#408C22×C7311yescharacteristic, complemented
522#405C22×C7311yescharacteristic, complemented
523C2×#97C22×C7311yescharacteristic, complemented
524#341C22×C7311yescharacteristic, complemented
525#339C22×C7311yescharacteristic, complemented
526H(5,𝔽2)—22no—
527H(5,𝔽2)—22no—
528H(5,𝔽2)—22no—
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—22no—
532H(5,𝔽2)—41no—
533H(5,𝔽2)—41no—
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41C23×C7311yescharacteristic
539C2×#41C23×C7311yescharacteristic
540C2×#41C23×C7311yescharacteristic
541C22×Q8C23×C7311yescharacteristic
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—41no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C23×C7311yescharacteristic
550C22×D4C23×C7311yescharacteristic
551C22×D4C23×C7311yescharacteristic
552#137—22no—
553#137—22no—
554#137—22no—
555#137—41no—
556AGL(1,ℤ/8)—28no—
557AGL(1,ℤ/8)—28no—
558AGL(1,ℤ/8)—22no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)—22no—
561AGL(1,ℤ/8)—22no—
562AGL(1,ℤ/8)—22no—
563AGL(1,ℤ/8)—22no—
564AGL(1,ℤ/8)—22no—
565AGL(1,ℤ/8)—41no—
566#135—28no—
567#135—22no—
568#135—22no—
569C2×Q16—21no—
570C2×Q16—21no—
571C2×Q16D4×C7311yescharacteristic, complemented
572C2×SD16—21no—
573C2×SD16—21no—
574C2×SD16—21no—
575C2×SD16—21no—
576C2×SD16—22no—
577C2×SD16—21no—
578C2×SD16—21no—
579C2×SD16—22no—
580C2×SD16—22no—
581C2×SD16—21no—
582C2×SD16—22no—
583C2×SD16—21no—
584C2×SD16—41no—
585C2×SD16D4×C7311yescharacteristic, complemented
586C2×SD16D4×C7311yescharacteristic, complemented
587C2×D8—28no—
588C2×D8—21no—
589C2×D8—21no—
590C2×D8—22no—
591C2×D8—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×D8—22no—
596C2×D8—22no—
597C2×D8—41no—
598C2×D8D4×C7311yescharacteristic, complemented
599C2×D8D4×C7314yescomplemented
600#131—22no—
601#131D4×C7314yescomplemented
602C2×M16—21no—
603C2×M16C23×C7311yescharacteristic
604C2×M16C23×C7311yescharacteristic
605C2×M16C23×C7311yescharacteristic
606C2×M16C23×C7311yescharacteristic
607C22×C8—21no—
608C22×C8C23×C7311yescharacteristic
609C22×C8C23×C7311yescharacteristic
610C4⋊Q8—21no—
611#127—22no—
612#127—21no—
613#127—22no—
614#124—21no—
615#124—22no—
616#124—21no—
617#124—22no—
618#123—41no—
619C22⋊Q8—22no—
620#121—22no—
621#120—41no—
622#117C23×C7311yescharacteristic
623C2×C22⋊C4—41no—
624C2×C42C23×C7311yescharacteristic
625#108—22no—
626#104—22no—
627#104—22no—
628#104D4×C7314yescomplemented
629#103D4×C7312yescomplemented
630#102—22no—
631#102—22no—
632#102D4×C7312yescomplemented
633#101—22no—
634#100—22no—
635#100—22no—
636#100—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639#97—22no—
640#97—21no—
641C4×C8—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—41no—
646C24—41no—
647#41—21no—
648#41—21no—
649#41—24no—
650#41—24no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—21no—
657#41—21no—
658#41—21no—
659#41—42no—
660#41—42no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—42no—
665#41C2×D4×C7312yes—
666#41C2×D4×C7312yes—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8C2×D4×C7311yescharacteristic
674C2×Q8C2×D4×C7311yescharacteristic
675C2×Q8C2×D4×C7311yescharacteristic
676C2×D4—21no—
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
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—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—41no—
702C2×D4—41no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—42no—
707C2×D4—44no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—84no—
714C2×D4C2×D4×C7311yescharacteristic
715C2×D4C2×D4×C7312yes—
716C2×D4C2×D4×C7311yescharacteristic
717C2×D4C2×D4×C7312yes—
718C2×D4C2×D4×C7311yescharacteristic
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—41no—
725C22×C4—41no—
726C22×C4C24×C7311yescharacteristic
727Q16—22no—
728Q16—42no—
729Q16—42no—
730SD16—24no—
731SD16—24no—
732SD16—22no—
733SD16—22no—
734SD16—44no—
735SD16—42no—
736SD16—42no—
737SD16—42no—
738SD16—42no—
739SD16—42no—
740SD16—42no—
741D8—24no—
742D8—24no—
743D8—22no—
744D8—24no—
745D8—24no—
746D8—44no—
747D8—42no—
748D8—42no—
749M16—21no—
750M16—21no—
751M16—24no—
752M16—21no—
753M16—21no—
754M16—21no—
755M16—21no—
756M16C2×D4×C7312yes—
757M16C2×D4×C7312yes—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—24no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8C2×D4×C7312yes—
766C2×C8C2×D4×C7311yescharacteristic
767C2×C8C2×D4×C7311yescharacteristic
768C2×C8C2×D4×C7312yes—
769C2×C8C2×D4×C7312yes—
770C4⋊C4—42no—
771C4⋊C4C2×D4×C7312yes—
772C22⋊C4—21no—
773C22⋊C4—42no—
774C22⋊C4—44no—
775C22⋊C4—42no—
776C42—21no—
777C42—21no—
778C42C2×D4×C7312yes—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—22no—
783C23—22no—
784C23—44no—
785C23—44no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—82no—
794C23—82no—
795C23—82no—
796C23—162no—
797C23—162no—
798C23H(5,𝔽2)×C7311yescharacteristic
799Q8—21no—
800Q8—21no—
801Q8—21no—
802Q8—21no—
803Q8—21no—
804Q8—41no—
805Q8—41no—
806Q8—41no—
807Q8—41no—
808Q8#127×C7312yes—
809D4—22no—
810D4—22no—
811D4—21no—
812D4—21no—
813D4—22no—
814D4—22no—
815D4—21no—
816D4—22no—
817D4—21no—
818D4—22no—
819D4—21no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—88no—
837D4—162no—
838D4#127×C7312yes—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4C22×D4×C7311yescharacteristic
857C2×C4C22×D4×C7311yescharacteristic
858C2×C4C22×D4×C7311yescharacteristic
859C2×C4C22×D4×C7311yescharacteristic
860C2×C4C22×D4×C7311yescharacteristic
861C2×C4H(5,𝔽2)×C7311yescharacteristic
862C8—22no—
863C8—22no—
864C8—22no—
865C8—41no—
866C8—41no—
867C8#120×C7312yes—
868C8#120×C7312yes—
869C22—22no—
870C22—22no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—41no—
875C22—41no—
876C22—42no—
877C22—42no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—82no—
884C22—81no—
885C22—161no—
886C22—161no—
887C22—161no—
888C22—164no—
889C22—164no—
890C22#535×C7311yescharacteristic
891C22D42×C7311yescharacteristic
892C22D42×C7311yescharacteristic
893C4—22no—
894C4—42no—
895C4—42no—
896C4—41no—
897C4—41no—
898C4—81no—
899C4C2×#120×C7311yescharacteristic
900C4C2×#127×C7311yescharacteristic
901C4D42×C7311yescharacteristic
902C4D42×C7311yescharacteristic
903C2—21no—
904C2—21no—
905C2—42no—
906C2—81no—
907C2—81no—
908C2—82no—
909C2—82no—
910C2—161no—
911C2C73×#243311yescharacteristic
912C2C73×#328812yes—
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×#576×C73C2semidirect
2. C73×#3154C2semidirect
3. C2×#496×C73C2semidirect
4. C2×#471×C73C2semidirect
5. C2×#455×C73C2semidirect
6. C2×#453×C73C2semidirect
7. C73×#3009C2semidirect
8. C73×#3008C2semidirect
9. C73×#2019C2semidirect
10. C73×#2018C2semidirect
11. C73×#2003C2semidirect
12. C73×#2002C2semidirect
13. C73×#1978C2semidirect
14. C73×#1975C2semidirect
15. C73×#1765C2semidirect
21. C2×#137×C73C22semidirect
27. C2×AGL(1,ℤ/8)×C73C22semidirect
30. C22×SD16×C73C22semidirect
31. C22×SD16×C73C22semidirect
34. C22×D8×C73C22semidirect
36. #536×C73C22semidirect
37. #535×C73C22semidirect
38. C2×#127×C73C22semidirect
39. C2×#124×C73C22semidirect
52. C2×#108×C73C22semidirect
54. C2×#104×C73C22semidirect
55. C2×#104×C73C22semidirect
56. #418×C73C22semidirect
57. #418×C73C22semidirect
59. C2×#101×C73C22semidirect
60. C2×#100×C73C22semidirect
61. C2×#100×C73C22semidirect
62. C2×#100×C73C22semidirect
63. #408×C73C22semidirect
64. #408×C73C22semidirect
65. #405×C73C22semidirect
66. C2×#97×C73C22semidirect
67. #341×C73C22semidirect
68. #339×C73C22semidirect
114. C2×Q16×C73D4semidirect
128. C2×SD16×C73D4semidirect
129. C2×SD16×C73D4semidirect
141. C2×D8×C73D4semidirect
142. C2×D8×C73D4semidirect
144. #131×C73D4semidirect
171. #104×C73D4semidirect
172. #103×C73D4semidirect
175. #102×C73D4semidirect
446. #25810C73direct (N × H)
457. C2×#576C2×C73semidirect
458. #3154C2×C73semidirect
459. C2×#496C2×C73semidirect
460. C2×#471C2×C73semidirect
461. C2×#455C2×C73semidirect
462. C2×#453C2×C73semidirect
463. #3009C2×C73semidirect
464. #3008C2×C73semidirect
465. #2019C2×C73semidirect
466. #2018C2×C73semidirect
467. #2003C2×C73semidirect
468. #2002C2×C73semidirect
469. #1978C2×C73semidirect
470. #1975C2×C73semidirect
471. #1765C2×C73semidirect
472. C73#25810direct (N × H)
478. C2×#137C22×C73semidirect
484. C2×AGL(1,ℤ/8)C22×C73semidirect
487. C22×SD16C22×C73semidirect
488. C22×SD16C22×C73semidirect
491. C22×D8C22×C73semidirect
493. #536C22×C73semidirect
494. #535C22×C73semidirect
495. C2×#127C22×C73semidirect
496. C2×#124C22×C73semidirect
509. C2×#108C22×C73semidirect
511. C2×#104C22×C73semidirect
512. C2×#104C22×C73semidirect
513. #418C22×C73semidirect
514. #418C22×C73semidirect
516. C2×#101C22×C73semidirect
517. C2×#100C22×C73semidirect
518. C2×#100C22×C73semidirect
519. C2×#100C22×C73semidirect
520. #408C22×C73semidirect
521. #408C22×C73semidirect
522. #405C22×C73semidirect
523. C2×#97C22×C73semidirect
524. #341C22×C73semidirect
525. #339C22×C73semidirect
571. C2×Q16D4×C73semidirect
585. C2×SD16D4×C73semidirect
586. C2×SD16D4×C73semidirect
598. C2×D8D4×C73semidirect
599. C2×D8D4×C73semidirect
601. #131D4×C73semidirect
628. #104D4×C73semidirect
629. #103D4×C73semidirect
632. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#576×C732
C73×#31542
C2×#496×C732
C2×#471×C732
C2×#455×C732
C2×#453×C732
C73×#30092
C73×#30082
C73×#20192
C73×#20182
C73×#20032
C73×#20022
C73×#19782
C73×#19752
C73×#17652
#2581073